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Direct Investments in
Securities: A Primer
RAMON P. D E GENNARO
The author is the SunTrust Professor of Finance at the University of Tennessee
and a visiting scholar at the Atlanta Fed. He gratefully acknowledges the support of a
University of Tennessee Finance Department Summer Faculty Research Award, a CBA
Scholarly Research Grant, and a University of Tennessee Professional Development Award.
T. Shawn Strother and Samuel L. Tibbs supplied excellent research support and, along with
Gerald Dwyer, Mark Fisher, Paula Tkac, and Larry Wall, provided helpful discussions.
He also thanks the research librarians at the Federal Reserve Bank of Atlanta.
quity investors today face the same problems that previous generations of investors
have faced: transactions costs, diversification, and the relatively large dollar amounts
necessary to purchase certain assets.
Investors want to minimize transactions
costs, but doing so usually means buying round lots
(100 shares), which implies large initial investments.
Investors also want diversification, but that, too,
requires large investments. For investors of constrained means, direct stock ownership has brought
high fees and inadequate diversification or has simply
been impossible.
Recently, dividend reinvestment plans and their
more general cousins, direct investment plans, have
virtually eliminated the problems of direct stock
ownership by permitting investors to bypass traditional investment channels, such as securities brokers.1 For the purposes of this article, a dividend
reinvestment plan is defined as a mechanism that
permits shareholders to reinvest the dividends paid
on their shares in additional shares automatically,
without the use of a broker. These plans may or may
not restrict investors to being current shareholders.
If the firm does not restrict its plan to current shareholders, instead permitting them to purchase their
first share directly from the company without resorting to a broker, then the plan is also what is called a
direct investment plan or an open-enrollment plan.
For brevity, in this article both types of plans are
E
labeled DRIPs and are differentiated only when the
distinction is relevant. Also, following common usage,
the redundant term “DRIP plan” is occasionally used.
DRIPs are not a different class of security, such
as swaps or futures contracts. Rather, they are a new
way of selling the traditional equity security. The
privileges and obligations of equity ownership are
unchanged. For example, DRIP investors retain all
voting rights and receive all mailings, including
annual reports and proxy statements. For taxable
investors, dividends are still taxable income, and sales
still generate capital gains or losses. DRIP investors
are still subject to the rules of the stock transfer agent
and to state and estate taxes. Many companies allow
their DRIP to be used as a vehicle for an individual
retirement account.
The key date in the proliferation of DRIPs was
December 1, 1994. On that date, the Securities and
Exchange Commission (SEC) granted an exemption
from Rule 10b-6, essentially approving two model
plans. This exemption eased restrictions on implementing and marketing these low-cost plans, cutting
the time to set up a plan from as much as two years
to under five weeks. Along with rapidly advancing
technology, DRIPs have driven transaction costs to
a bare minimum and brought diversified stock ownership to investors whose portfolios are well below
modest. Companies may sell shares directly to
investors without the services of brokers or investment bankers, in many cases absorbing all costs so
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that the investor’s transaction cost is measured in
pennies. As of this writing, at least fifty companies
impose absolutely no transactions costs at all, often
with tiny minimum investments. Trust Company Bank
of New York permits investors to purchase shares
directly from the company with an initial investment
of as little as $25. This is less than the cost of a single
share, and there are no transactions costs. In all, well
over 1,100 corporations—over 5 percent of the firms
listed in the 1999 Compustat database—offer some
type of direct investment plan.
This article serves as a primer on direct investment
plans. The discussion describes how the financial services industry has evolved to address the problems
DRIPs are not a different class of security,
such as swaps or futures contracts. Rather,
they are a new way of selling the traditional
equity security. The privileges and obligations
of equity ownership are unchanged.
facing the small investor, identifies the remaining limitations, and presents reasons why companies might
offer such plans. The article then describes the data
and identifies empirical differences between the types
of companies that offer DRIPs and those that do not.
Finally, the discussion speculates about the future of
direct investments and provides conclusions.
History and Overview
ntil the later portion of the twentieth century,
equity investors of minor means may well have
bemoaned the problems they faced. The financial
services industry, however, recognizes that identifying and resolving consumers’ financial problems is a
profit opportunity. The industry attacks these problems from two directions. One approach involves
pooling assets of many small investors, using professional managers to operate the fund. Mutual funds
and closed-end investment companies are common
examples. The other approach relies on different
delivery systems to reduce transactions costs and
the size of initial investments, thereby preserving
the individual investor as the direct owner. Direct
investment plans result from this approach. This
section traces the development of mutual funds and
DRIPs, clarifies similarities and differences between
them, and describes the limitations of both of these
investment options.
U
2
Some history. Mutual funds and closed-end
investment companies were among the first innovations to use emerging technology to address small
investors’ needs. The Investment Company Institute
credits the Scudder funds with opening the first noload mutual fund in the 1920s (Carlson 1997). Such
funds failed to generate much interest initially, and
growth, at least in terms of dollars, was slow. By 1945,
mutual funds’ assets were about $1 billion, and by
1955 the figure was only $8 billion (Bogle 1982). By
1999, though, total equity investments under fund
management had risen an average of over 15 percent
annually, to $4.041 trillion.
The concept behind a mutual fund is simple:
Fund managers pool money from small investors to
permit large purchases of many stocks. Through
this indirect ownership mechanism, each investor
receives or bears a pro rata share of the fund’s earnings or losses and pays a similar share of any costs
the fund bears. This financial innovation solves, or
nearly solves, many of the problems small investors
encounter. First, large purchases have proportionally lower transactions costs. Thus, mutual fund
investors pay lower transactions costs. Second, diversification becomes easy. Because fund managers
invest a large pool of individuals’ assets, managers
are able to invest in many different companies in
many different industries. In addition, investors may
choose between index funds and actively managed
funds. Index funds seek to match the returns on a
popular index, such as the Standard and Poor’s 500.
By extension, managers of these funds do not
attempt to uncover underpriced securities. Actively
managed funds, by contrast, seek to purchase securities that fund managers believe are likely to outperform the market in general. Direct investments
in individual securities remain extremely costly for
small investors, though.
Another approach to solving the problems small
investors face was the New York Stock Exchange’s
(NYSE) Monthly Investment Plan, which began in
1954 and ended in 1976.2 This plan, which was
operated by the NYSE itself, permitted individuals
to invest in about 1,200 stocks, starting with as little
as $40. Total fees were small for that time, about
6 percent for investments under $100. Moreover,
there were no fees to open an account, no annual
dues, and no obligation to invest. Participants could
reinvest dividends for a small fee and could sell
shares through the program. They could even purchase fractional shares if their investment did not
purchase an integer number of shares. Participation
in the NYSE’s Monthly Investment Plan peaked in
1970, but despite its apparent appeal for small
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
investors, participation began to decline. The NYSE
terminated the plan in 1976.
By 1976, and perhaps contributing to the demise
of the Monthly Investment Plan, direct investment
plans had emerged. DRIPs have obvious similarities
to the NYSE’s Monthly Investment Plan. Among
these are low or even no commissions and often no
explicit transactions costs at all. As with mutual
funds, DRIP investors enjoy full investment of their
funds because plans offer fractional shares. Initial
investments are very low, and additional investments
are convenient, even with tiny amounts. Coca-Cola,
for example, accepts contributions of as little as $10
from plan participants. Yet wealthier investors can
invest large amounts optionally. Unilever permits
optional investments of up to $100,000 per year
while for Southern Company the figure is $150,000
per year.
By the end of the Monthly Investment Plan, companies also had begun to incorporate various new
features into their plans. In 1972, almost eighteen
years after the NYSE introduced its Monthly
Investment Plan, Long Island Lighting Company
offered the first new-issue direct stock-purchase
plan (Finnerty 1989). This plan offered two fundamental differences from the Monthly Investment
Plan. First, investors no longer dealt with the NYSE.
Instead, they dealt with Long Island Lighting.
Second, unlike transactions through the Monthly
Investment Plan, purchases through Long Island
Lighting’s direct purchase plan increased the number
of outstanding shares and raised capital for the firm.
Other innovations followed. In 1972, AT&T was
the first company to offer shareholders the opportunity to buy more shares at a discount from the
market price. For example, a $95 investment might
buy $100 worth of stock. Other companies offered
safekeeping of shares, began accepting sales orders
by telephone, or permitted dividends on one security
to be reinvested in a different kind of the company’s
securities. For example, dividends on common shares
could be used to buy preferred stock. At one time,
ABT Building Products even offered a no-load directpurchase plan despite not paying a dividend. Rather
than reinvest dividends to increase their holdings of
ABT, investors simply mailed a check to the plan
administrator to purchase stock. Several foreign
stocks also allow direct purchases despite not paying dividends.
Beginning in the early 1980s, some corporations
no longer restricted plan participation to shareholders of record. Among the leaders were Citicorp,
Control Data, and W.R. Grace. Even investors who
were not currently shareholders could buy their
initial and subsequent shares through the plan without a broker.
Dollar-cost averaging. In addition to the benefits of these innovations, both mutual funds and
DRIPs are well suited for investors who believe that
dollar-cost averaging makes sense. In brief, dollarcost averaging involves investing (approximately) the
same amount in the same security at periodic intervals. The result is that the investor purchases more
shares when prices are lower so that his average
purchase price is less than the arithmetic average
of the shares’ prices on the purchase dates. The
apparent appeal of this procedure has led to widespread acceptance of its economic value despite
evidence that it has no wealth implications.3
Regardless of its value as an investing tool, though,
many writers tout it as a wise strategy, and many
investors use it. These investors see a benefit from
participating in DRIPs because reinvesting regular
dividend payments automatically results in dollarcost averaging.
Mutual fund limitations. The success of mutual
funds as an investment vehicle and the growing
number of DRIPs available stand as strong evidence
that these mechanisms serve investors’ needs. Both
approaches, though, have limitations. For example,
the concept of purchasing a pro rata share of a portfolio has inherent drawbacks. In particular, three
likely unavoidable features remain. First, no one
expects the mutual fund’s managers to work without pay. More generally, any mutual fund incurs
expenses that must be recouped. Such costs fall
into several categories. Management fees can range
from under 0.5 percent to 7 percent or more.
Updegrave (2001) reports that the typical U.S. stock
mutual fund has operating expenses of 1.43 percent
of assets annually. Load funds sold through brokers
charge 12b-1 fees to cover marketing expenses.
Administrative expenses, including mailing costs,
tend to be smaller. Yet even relatively small fees can
lead to large reductions in accumulated value over
time. For example, an investor who invests $1,000
per year for forty years at 6 percent accumulates
$154,762. If the total annual fund charges are only
1. Despite the similarity in names, direct investment plans discussed in this article have no relation to direct foreign investment.
2. Much of this section draws on Carlson (1997).
3. The apparent appeal probably traces to confusing the share-weighted average with the equal-weighted average of purchases.
See also Constantinides (1979).
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1 percent (about two-thirds of the average), so that
the realized return is 5 percent, then the figure falls
to $120,800—a net reduction of $33,962. The precise magnitude, of course, depends on management
and its investment strategy. Investors seeking to
minimize total fund charges can select an index
fund, but even that involves some trading costs.
The Vanguard Index Trust, perhaps the best-known
index fund, reports a total expense ratio of only 18
basis points. For accounts under $10,000, though,
Vanguard imposes a $10 annual maintenance fee.
Thus, investors can select a fund based on its
investment strategy and fees but still incur costs
and surrender direct control of expense charges.
An investor in a mutual fund loses a portion of
the value of tax-timing options. This loss occurs
because a mutual fund essentially combines the
options on each stock into just one option—the
option pertaining to the entire portfolio.
A second disadvantage of investing in a mutual
fund rather than holding stocks directly is that
doing so makes it difficult for investors to diversify
optimally. All investors in a single fund hold the
same portfolio for the portions of their investment
in the fund. A bank employee, though, might not
want to hold the same portfolio as his identical twin,
who is an auto worker. The bank employee probably
wants to hold fewer bank stocks because his earnings at work are positively correlated with bank
stocks. In other words, he could lose his job about
the same time that the bank stocks in his investment portfolio decline. By the same logic, the auto
worker might wish to own fewer automotive stocks.
Such portfolio adjustments are difficult with mutual
funds. Similarly, investors who wish to overweight
individual securities that they believe are underpriced cannot do so with mutual funds alone.
Third, and perhaps most important, a mutual
fund investor loses direct control of tax-timing
options. U.S. tax law generally recognizes only realized capital gains. Thus, an investor who owns stock
directly, unlike a mutual fund investor, can recognize losses for tax purposes by selling shares that
have declined in price while deferring capital gains
on shares that have increased in price.
How much are these tax-timing options worth?
Constantinides (1984) shows that their value
4
depends on several factors, including the investor’s
trading strategy, transactions costs, the tax rate on
capital gains, and the stock’s volatility. Clearly,
though, their value can be substantial. For example,
for a stock of average volatility and 4 percent roundtrip transactions costs, the tax-timing option is
worth about 3 percent of the stock’s value. If transactions costs are negligible, then the option’s value
increases to 6 percent. For high-volatility stocks, the
corresponding figures are 10 percent and over 14 percent, and other scenarios imply option values of
more than 25 percent of the original investment.
An investor in a mutual fund loses a portion of
the value of these tax-timing options. This loss
occurs because a mutual fund essentially combines
the options on each stock into just one option—the
option pertaining to the entire portfolio. This option
is worth less than the combined value of the individual options. This reduced value has been shown
formally by Merton (1973), but the intuition is simple. Consider a portfolio of stocks with some winners
and some losers. An investor holding an option on
the entire portfolio cannot take tax losses without
also taking gains. In contrast, an investor holding a
portfolio of options (one on each security in the
portfolio) can selectively realize losses for tax purposes while continuing to defer gains.
A second type of tax penalty on mutual funds can
be enormous. By law, funds must distribute nearly
all of their realized capital gains. CNNMoney (2001)
reports that in 2000, while the average U.S. stock
fund lost 10.1 percent, it still paid 9.19 percent in
taxable distributions. The SEC reports that more
than 2.5 percentage points of the average stock fund’s
total return is consumed by taxes each year.
In principle, a mutual fund manager can behave in
exactly the same manner as an individual investor,
recognizing losses on the underlying securities and
deferring the gains. Indeed, the Vanguard Group
began offering tax-managed funds in 1994 (Jacob
1996). However, fund investors cannot force the
manager to distribute gains and losses in this way. A
mutual fund investor can choose to invest in funds
that are sensitive to the tax-timing issue, but even
if she does, she has no explicit control of the timing
of sales and must bear the consequences of the
manager’s decisions. Even the most tax-conscious
mutual fund imaginable cannot consider other factors that affect an individual investor’s tax position,
such as changes in marginal tax brackets due to,
say, changes in marital status or a spouse’s decision
to enter or leave the work force.
Investors in mutual funds can also find themselves with a tax liability if their fund closes. Mutual
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funds can and do cease operations more often than
people realize. The Vanguard Group reports that of
the 356 general equity funds that existed in August
1976, fully 45 percent had ceased operations by the
summer of 2001 (Vanguard 2001). If the fund liquidates, then investors bear a pro rata share of any
capital gain—and of the resulting tax liability.
Sometimes, a mutual fund merges with another
fund. In this case there are no taxes due immediately, but the new shareholders inherit liability for
capital gains earned before they acquired shares of
the ongoing fund. Perhaps worst of all, investors
have no control over either liquidation or merger.
Finally, mutual fund investors face the problem
of accumulating the funds to meet minimum investment requirements. Though this problem is not
inherent in the concept of an intermediary holding
a diversified portfolio of stocks, most funds impose
an investment minimum that exceeds those of direct
investment plans. Of course, this analogy is not an
apples-to-apples comparison. An investment in a
single mutual fund might provide sufficient diversification for most people; this claim cannot be made
for an investment in a single DRIP. Still, investors
face the problem of accumulating the initial investment that funds require. The Vanguard Index Trust,
for example, requires a minimum investment of
$3,000 in most cases.
DRIP limitations. Investors who hold stocks
directly through DRIPs face a different set of problems than those of mutual fund investors. Scholes
and Wolfson (1989) say that DRIP investors bear a
variety of implicit costs. For example, DRIP investors
must become informed about the plans’ details and
must monitor the plans for changes in terms. Of
course, mutual fund investors must also do this but
for a much smaller number of investments. Though
DRIP purchases often have no explicit cost, nearly
all DRIPs provide for transactions costs when selling shares. Some even require plan participants to
request stock certificates and to deliver them to a
broker for sale in the traditional manner. Nor are
transactions costs the only costs plan participants
face: they also bear the costs of any tax implications
of their direct equity holdings. Foremost among
these are the usual taxes on dividends and capital
gains. In addition, in some plans, the company pays
commissions for the investor when the shares are
purchased. If so, then the IRS treats such commissions as taxable income. Discounts on purchases
are also taxable income.4
Tax rules also probably limit the value of the
individual tax options that DRIP investors hold.
Though the tax options in a DRIP are clearly more
valuable than those in a mutual fund, they are
unlikely to reach the levels that Constantinides
(1984) calculates. Under the current U.S. tax code,
gains and losses are calculated relative to the basis,
which is usually the purchase price plus any transactions costs. DRIPs usually generate four purchases
each year, so calculations of gains or losses tend to
be tedious compared to an investment strategy built
around larger purchases. One way around this problem is to receive dividends in cash. Nothing prevents
an investor from doing so, and she can still make
Investors who hold stocks directly through
DRIPs face a different set of problems than
those of mutual fund investors.
purchases through the plan if she wishes. In terms of
the timing of purchases, this strategy is essentially
the same one that an investor using a traditional broker would follow. Another solution is to sell all of the
shares in a company as a block. This strategy lets the
taxpayer use the average basis of the shares in the
block as the basis for all shares in the block. A third
strategy is to use one of the popular personal financial management software packages available today.
Most record the basis and compute the gain or loss
automatically when the shares are sold.
In defense of brokers. DRIPs and mutual funds
do, of course, carry disadvantages for investors.
Focusing solely on transactions costs ignores other
advantages that traditional brokers can provide. For
example, these investments offer less liquidity than
investments through traditional brokers. DRIP and
mutual funds investors cannot place limit orders or
buy on margin, and execution of transactions is usually slower. In contrast, brokers are almost always
faster in delivering the proceeds of sales. In addition,
brokers offer a much wider variety of investment
choices, such as bonds, options, money funds, collateralized mortgage obligations, unit trusts, and so on.
Competent brokers offer useful advice regarding
4. These costs, however, can be reflected in the tax basis so that subsequent gains taxes are reduced and tax losses are
increased. Thus, the tax liability is not only deferred but is also converted to a gain and usually taxed at a lower rate.
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tailoring portfolios, such as matching investment
opportunities with an individual investor’s risk preferences, and can help monitor an investor’s asset
mix. For example, after a prolonged increase in
stock prices, a busy investor might not realize that
his portfolio contains a far greater proportion of
risky assets than he prefers. A good broker can
monitor and notify the investor of this situation—as
well as the unhappy opposite case, when prices
have declined and the risk profile is too conservative. Finally, some investors prefer having all of
their transactions on one statement rather than
receiving separate statements for each company or
fund they own.
DRIP plans tend to attract a specific clientele.
These plans are likely to provide a broad,
relatively stable base of shareholders who,
because they hold relatively small positions,
are likely to be passive investors.
Many brokers provide some or all of these services at no explicit cost to their customers probably
because brokerage firms usually keep their customers’ securities in street name (that is, in the name
of the brokerage on behalf of the customers), giving
them the right to lend the securities for short sales
and to collect any fees for doing so. In a competitive
market for brokerage services, brokerage firms
must provide some compensation for this right or
else customers would move their accounts to firms
that do. By contrast, DRIP and mutual fund investors
must keep their securities in their own names. As
a result, lending the securities is impractical, and
the investors forfeit the fees they might gain. Two
forces could tend to offset this disadvantage. First,
the plan administrator may be able to lend the securities. If so, competition would tend to force him to
compensate investors, just as it does for brokers.
Second, if the plan administrator cannot arrange to
lend for short sales, then company management
may well view the resulting reduction in the number
of shares available for shorting as a benefit. This
situation would be especially true for DRIPs, and
perhaps this circumstance explains why some plans
offer such attractive terms to investors.
The best way of conceptualizing the role of brokers
in relation to direct investment plans is to realize
that brokers are no different from other middlemen.
6
They can stay in business only if they add sufficient
value to earn at least a normal profit. In general,
these services are of relatively little value to investors
with limited portfolios (that is, mostly stocks) using
a buy-and-hold strategy. Thus, DRIP plans, in particular, tend to attract a specific clientele. These plans
are likely to provide a broad, relatively stable base of
shareholders who, because they hold relatively small
positions, are likely to be passive investors.
Why Do Corporations Participate?
hat type of company might prefer a clientele of
buy-and-hold investors? More generally, why do
firms offer direct investment plans? Street lore offers
several possible explanations. Quite possibly, funds
can be raised more cheaply through DRIPs. DRIPs do
incur expenses such as telephone charges, added
personnel, extra printing, mailings, and so forth. One
estimate is that such costs are between $12 and $16
per account, and this figure is virtually independent
of the number of shares held (Carlson 2000). DRIPs,
however, substitute these direct costs for the investment banker and the related administrative, legal,
and accounting fees when issuing new shares.
These cost savings can be large. Carlson (1996, 16)
reports new-issue costs of between 5 percent and
15 percent of the equity issue. Eckbo and Masulis
(1992) report that total issue costs as a percentage
of gross proceeds average 6.09 percent for industrial
firms and 5.53 percent for utilities. Underwriter costs
alone account for about 90 percent of that amount.
In addition, existing stockholders can be worse off as
a result of an issue of additional shares. Asquith and
Mullins (1986) use event-study methods to conclude
that the two-day abnormal return for industrial
firms that announce equity issues is –3.14 percent.
For utilities, the figure is –0.75 percent. Eckbo and
Masulis report returns of –3.34 percent and –0.8 percent for announcements of firm-underwritten offers
for industrial and utility firms, respectively. Again,
these costs affect the entire equity base, not just the
new issue. Scholes and Wolfson (1989) report that the
equity base largely avoids these costs with DRIPs.
In addition to avoiding some of these costs, newissue DRIPs permit large sums to be raised. For
example, the prospectus for OneOk, Inc., dated
February 7, 2001, reports that, “This prospectus
covers 4,424,502 shares. . . .” Given a share price on
that date of about $22.25, almost $100 million could
conceivably be raised—and raised quickly—under
the terms of this single offering. South Jersey
Industries raised $8 million with its DRIP in June
1990 alone. Scholes and Wolfson (1989) report such
benefits in terms of the amount of dividends paid.
W
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They report that firms with no discounts on reinvestments raise an average of 12 percent of the total
common and preferred dividends they pay. If firms
offer a 5 percent discount, then this amount rises
to about 98 percent of the common and preferred dividends they pay. Clearly, many investors are reinvesting dividends or are making large optional payments.
Why firms simultaneously pay dividends and encourage reinvestment in newly issued shares is a separate
question, likely related to the question of why firms
simultaneously pay dividends and raise funds through
equity or debt issues.5
A second reason often given for the existence of
DRIPs is that companies simply wish to provide a
service to their owners. Goodwill is valuable, and
owners who desire to increase their stake in their
company want to do so in the lowest-cost manner.
Certainly, high levels of telecommunications and
computer technology are essential to administering
such plans efficiently, and this has become easy and
inexpensive in recent years. To the extent that a
firm enjoys scale economies in transactions in its
own stock, DRIPs are a logical option.
Third, having more shareholders could boost sales
of a company’s products. For example, an investor,
even one who is not a current shareholder, can enroll
in Bob Evans’ DRIP with a minimum investment of
only $50 and with no transactions costs. Once he is
an owner, an investor may be more likely to eat at
Bob Evans rather than at a competing restaurant.
Owners are also more likely to refer new customers
to the restaurant.
A fourth reason for the existence of DRIPs could
be what economists call economies of scope. A company that provides several goods or services may
have an advantage in satisfying consumers’ needs if
the consumers are shareholders. Because a shareholder is already on the company’s mailing list and
is familiar with the company, normal shareholder
correspondence provides an easy, inexpensive way
to approach these investors as customers for other
services. For example, Regions Financial often
includes pamphlets regarding refinancing home
mortgages or second mortgages with its mailings to
shareholders. ExxonMobil recently sent information promoting SmartPass, a transponder system
designed to save customers time at gasoline stations
and convenience stores. ExxonMobil also announced
its participation in Upromise, a plan to assist families saving for college expenses.
A fifth reason is rarely mentioned. Most plan
administrators usually retain the option to execute
the plan’s trades on more than one exchange or
market. Thus, a company or its agent might collect
fees for routing order flow.
A firm also might want to attract its own employees as shareholders. Employees who are not owners
have greater incentives to shirk because a larger portion of the costs are borne by the company’s owners.
To the extent that employees own the firm, shirking
becomes less attractive to them. This motivation
explains in part the popularity of employee stock
option plans (ESOPs) and 401(k) matching programs. Consistent with this idea, some companies
permit their employees to purchase their first share
of stock directly from the company while requiring
others to use a broker. Such preferential treatment is
impossible with a regular stock issue. The SEC would
probably prohibit a public offering that was available
only to employees of a specific company.
One commonly cited reason for offering DRIPs is
that they generate price pressure by providing a
steady stream of buyers, keeping share prices high.
This argument is implausible. For this scenario to be
true, DRIP investors must consistently be net buyers. Although this situation may occur around the
time of dividend payments, there is no reason to
expect it to occur during other periods. Even if DRIP
investors were net buyers, that motivation would
still be insufficient for a price-pressure argument to
carry force. This argument must further assume that
other investors make no adjustment in their purchases because of the higher prices around dividend
dates. In fact, though, other traders would probably
time their purchases to take advantage of such predictable price behavior. They would sell around dividend payment dates and buy at other times. In fact,
considerable academic work has shown that price
pressure tends to have little impact on share prices
(for example, see Smith 1986).6
Clienteles. Clearly, offering a DRIP appeals to
some companies, and buy-and-hold investors are
more likely to use DRIPs. What type of firm might
prefer a clientele of buy-and-hold investors? One
obvious candidate is a company that offers many
products and services so that it can benefit from
cross-selling. Customers who purchase one product
from a company are more likely to choose another
from that same company rather than incur the costs
of learning about competing products.
5. Both questions are fascinating and well beyond the scope of this paper.
6. Both Harris and Gurel (1986) and Ederington and Goh (2001) provide some evidence that price pressure is indeed large
enough to measure. Both report that any price effects vanish within a few weeks.
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A second candidate could be firms that are subject to regulation and are therefore more heavily
exposed to the political process. Voters, unlike
shareholders, are equally weighted. Other things
being equal, having ten shareholders with fifty
shares each is a better political base than having one
owner with 500 shares. Having many shareholders
(and thus many investors who are also voters)
makes it less likely that government will impose
onerous regulations on the company. The company
can even claim that voters are small investors and
set them against the allegedly helpless groups typically cited as the people protected by regulation.
Especially in the case of utilities, owners are less
A reason for the existence of DRIPs could be
what economists call economies of scope. A
company that provides several goods or services
may have an advantage in satisfying consumers’
needs if the consumers are shareholders.
likely to complain to regulators about rate increases
or to demand tight environmental restrictions.
This advantage for regulated firms is magnified
because management has routine access to its shareholders and can tell its side of any political story to
more people at lower cost. For example, CH Energy
Group, Inc., included copies of its chairman’s remarks
at its annual stockholders’ meeting with its routine
DRIP statements. About one-fifth of the remarks
were dedicated to explaining the company’s position
regarding power shortages in California (Ganci 2001).
Similarly, Duke Energy Corporation used two full
pages of a letter to shareholders to explain and
defend its position on the California crisis. This
explanation included reports of investigations by the
Federal Energy Regulatory Commission, the compliance unit of the California Power Exchange, and the
Northwest Power Planning Council—none of which
found any basis for the charges by government officials in California that electricity producers were artificially driving up power prices. The letter called for
“the cooperation and support of the highest levels of
State government” and added that “the regulatory
process must be streamlined to encourage investments in new power plants and the market must be
restructured to allow all participants the ability to
manage and hedge their exposure to power and gas
prices” (Priory 2001).
8
This line of reasoning can be carried still further:
Not all voters are equally valuable to a company. In
the case of utility firms, management would particularly want to have its customers and state residents
also be owners. These companies should be expected
to offer plans with features designed to entice these
individuals to buy shares. In fact, some DRIPs do
exactly that. For example, Carolina Power and Light
requires investors to purchase their first share from a
broker unless the prospective plan participant is a
customer. In that case, the company will sell the first
share directly to the customer. Until Central Fidelity
Banks, Inc., was acquired by Wachovia Corporation,
its plan required participants to be existing shareholders unless the prospective plan participant was a
resident of the state in which it operated. State residents, of course, carry more weight with local politicians than residents of other jurisdictions.
Regulated industries such as public utilities and
financial institutions are not the only ones that can
benefit from improved public relations and political
influence. Companies at risk of being regulated, or
at risk of increased regulation, may concentrate
their efforts on U.S. investors to provide a channel
for disseminating the company’s position on major
issues. For example, Pfizer, Inc., is a major force in
pharmaceutical products, another industry often
targeted for government intervention. Prior to the
presidential election of 2000, Pfizer’s letter to shareholders stated: “In the heat of campaigning, rhetoric
thrives. It would, however, be a sad day for American
health care if anti-industry rhetoric were translated
into policy. It would stifle pharmaceutical research,
deprive millions of people of new treatments and
herd every American senior into a vast drug-access
scheme administered by government bureaucrats”
(Clemente 2000).
One of the clearest attempts to rally shareholders
to support a company appeared in a SCANA
Corporation mailing. This letter explicitly asked
stockholders to join the Association of SCANA
Corporation Investors. This association was begun in
1978 “to help insure the Company received a fair
rate of return on its shareholders’ investment from
the state utility regulatory body.” The letter added
that, “More recently, the Association represented
the interests of its members and other shareholders
in the debate over restructuring the electric utility
industry in South Carolina. Association leaders testified before the South Carolina Public Service
Commission and legislative committees while
Association members from South Carolina explained
our organization’s position on this issue to their individual legislators” (Quattlebaum and Strock 2001).
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
Public relations is clearly an important component of shareholder mailings. To the extent that
DRIPs increase the number of stockholders, such
plans can play a part in maintaining a positive corporate image and lowering the costs of reaching them.
A company might also institute a direct investment
plan to insulate and protect management. To the
extent that DRIP investors hold small positions, they
are less likely to be active in monitoring management.
While it can make sense for an institutional investor
holding millions of shares to take action against weak
management, becoming informed about management
practices and acting on this information is very
unlikely to be worth the effort if one owns only a few
hundred shares. Such investors are likely to vote with
management, usually by proxy, or not to vote at all.
Thus, an active investor faces an uphill battle to convince a majority of voting shares to support his position. Management benefits by becoming entrenched,
and most research concludes that such entrenchment
is detrimental to shareholders.
In summary, there are several reasons that corporations offer DRIPs. Not all of these reasons have
equal appeal to all companies or industries. This
reasoning suggests that there may be systematic
differences between companies that offer DRIPs
and those that do not. The next section explores
this possibility empirically.
Comparisons between DRIP Companies and
Their No-DRIP Counterparts
o explore direct investment plans empirically,
this study examines the firms listed in the
Guide to Dividend Reinvestment Plans (1999).
According to the publisher, Temper of the Times
Communications, Inc., this guide encompasses all
firms that offered DRIPs on the publication date. Of
these approximately 1,135 companies, 906 provided
plan terms and are included in the 1999 Compustat
annual database for 1999.
It might seem tempting to compare these 906
companies with the universe of Compustat firms
without plans. The problem with this comparison is
that DRIP firms are, on average, much larger than
firms without DRIPs. For example, using total assets
as the measure of size, the mean DRIP firm in 1999
has total assets of $13.87 billion compared to only
$2.33 billion for firms without DRIPs. The mean
DRIP firm in 1999 is more than five times larger. The
likelihood of DRIP firms being a random sample of all
companies in Compustat is less than 0.01 percent.
Clearly, large firms are more likely to offer DRIPs
than small firms. This likelihood suggests that large
firms have an advantage in sponsoring direct invest-
T
ment plans. This advantage is not too surprising since
some administrative expenses are likely about the
same for 50,000 shareholders as they are for 25,000
shareholders. Thus, the cost of providing DRIPs
is lower per participant for larger companies. For
some purposes, such as investing, this preponderance of large companies may not be a problem.
Small companies would be underweighted in a portfolio comprising only DRIP companies, but many
mutual funds also underweight small firms. For gaining an understanding of the economic forces driving
the decision to offer a direct investment plan, though,
this large size differential complicates the analysis
because large firms differ from smaller ones in many
A company might also institute a direct investment plan to insulate and protect management.
To the extent that DRIP investors hold small
positions, they are less likely to be active in
monitoring management.
ways. Not the least of these differences is access
to capital markets; large firms have many more
options to obtain financing. To circumvent this difference, this analysis constructs a size-matched sample based on total assets in 1999. Each of the 906
companies offering DRIPs and having data in 1999
is matched to a company without a plan, for a total
of 1,812 companies. Paired differences are also computed for the variables. Some observations for certain
variables are missing from some firms, however, so
the number of matched pairs for many variables is
less than 906.
To obtain some evidence on how well the matching procedure worked, the mean total assets for the
two groups of 906 companies are computed. Those
without DRIPs have average total assets of $14.41
billion in 1999 while firms that offer DRIPs average
$13.87 billion. The difference is less than 4 percent,
and a t-test (0.25) is insignificant by any usual standard. Overall, the two groups are very similar in
size. But the size-matching procedure can go only
so far: For some ranges of total assets, there simply
are not enough companies to provide a good match
to each individual company. Thus, the difference in
total assets of the 906 paired differences does differ
statistically from zero.
The discussion in the previous section suggests
that some industries might benefit more from
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
9
instituting DRIP plans than others. If that is true,
then DRIPs would not be distributed randomly
across industries. To test this assumption, a chisquare test using two-digit Dun & Bradstreet
Standard Industrial Classification (SIC) codes is conducted.7 This test rejects the hypothesis that DRIP
firms are randomly distributed across industries.
Some caution is in order here, as some industries
have too few observations to merit too much faith in
the results. Still, the results are illuminating. The
likelihood that the departures from a random distribution are due to chance is less than 0.01 percent.
Table 1 shows the ten industries with the largest
absolute deviations from expected outcomes if the
Clearly, large firms are more likely to offer
DRIPs than small firms. This likelihood suggests that large firms have an advantage in
sponsoring direct investment plans.
distribution were random. The biggest departures
from the expected distribution are, in descending
order, the electric, gas, and sanitary services industries (DRIPs are over-represented), communications
(under-represented), holding and other investment
offices (over-represented), and business services
(under-represented).
The higher concentration of electric and gas
companies as DRIP providers makes sense because
these industries tend to be regulated. Holding and
other investment offices are over-represented
because the category includes real estate investment trusts (REITs). REITs must distribute at least
95 percent of their earnings to shareholders to retain
their preferred tax status. This limitation makes it
nearly impossible for a REIT to grow using internal
funds. Rather than continually going to the capital
markets to raise funds, many REITs offer DRIPs to
encourage reinvestment and essentially reduce the
dividend yield.
Why might communications and business services be under-represented? The easiest answer is
that, because some industries are over-represented,
some must be under-represented, and communications and business industries happen to be among
them. More insight can be gained, though, by realizing that the size-matching procedure, designed to
eliminate the large difference in scale economies
10
between the universe of DRIP companies and noDRIP companies, has limitations in practice. First,
because DRIP companies tend to be large, smaller
companies tend to be eliminated, and the sizematched sample comprises larger companies than
the universe of Compustat firms. Second, industries
dominated by smaller companies tend to be underrepresented in the size-matched sample. Just as
there are not enough companies to permit a good
match to each individual company, there simply are
not enough companies to permit accurate matching
within industries; size-matching the entire sample is
the best available option.
The business services industry illustrates these
effects. Business services companies, which include
advertising agencies, pest control services, employment agencies, computer-related services, security
systems, and so on, tend to have fewer total assets
than most other companies do. In the universe of
Compustat companies, the average total assets of
business services companies is about $352 million
compared to over $2 billion for other industries. The
size-matching procedure reduces the discrepancy
substantially: the average total assets of business
services companies is about $5.08 billion compared to
about $14.49 billion for other industries. The size differential declines from about seven-to-one to less than
three-to-one, but business services companies still
tend to be on the smaller side. This tendency might
explain why the business services industry is underrepresented among companies that offer DRIPs.
This explanation fails for the communications
industry, however, because communications companies tend to be a little larger than average after
size matching. A better explanation might be that
this industry includes telephone communications
and cable services, which grew rapidly during the
late 1990s. Many of these companies paid low or no
dividends at all.
These deviations from random distribution suggest that the concentration of DRIPs might be due
to a dividend effect. That is, perhaps DRIPs appear
more often in certain industries because those industries tend to pay dividends more often. The easiest
way to check this supposition is to drop all companies that reported no dividends in 1999 and repeat
the chi-square tests. The result shows that companies offering DRIPs are still concentrated in certain
industries, but the specific industries differ. In terms
of absolute deviations from the expected distribution, the biggest departure is again electric, gas, and
sanitary services, which are over-represented. The
insurance carriers industry is second, and it is underrepresented relative to the expected distribution.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
TABLE 1
The Ten Highest Absolute Deviations from the Expected Frequency of DRIP Plans, by Industry
Actual DRIP
frequency
Electric, gas, and sanitary services
Communications
Holding and other investment offices
Business services
Insurance carriers
Chemicals and allied products
Depository institutions
Nondepository credit institutions
Amusement and recreation services
Transportation by air
118
26
79
11
35
63
152
8
1
1
Expected DRIP
frequency
75.5
52.5
54
32.5
54.5
45.5
134.5
23
7.5
7
Difference
42.5
–26.5
25
–21.5
–19.5
17.5
17.5
–15
–6.5
–6
Source: Author’s calculations using data from Compustat and the Guide to Dividend Reinvestment Plans
Third are depository institutions, which are underrepresented. Holding and other investment offices
slip to fourth and remain over-represented. One
problem with this analysis, however, is that the
sample sizes are much too small for the results to be
reliable. Another is that almost all of the excluded
companies (ones that paid no dividends) do not
offer DRIPs. This fact points to a third problem: The
decision to pay a dividend and the decision to offer
a DRIP are not independent. Disentangling the
effects of DRIPs from those of dividends themselves
remains a difficult problem for future work.
Table 2 reports the 1999 sample means for
Compustat data for the size-matched sample of 906
companies with DRIPs and 906 companies without
DRIPs. It shows the means for companies with and
without plans and reports t-statistics for a test of
equality. It also contains similar results for the subset of paired differences.
These paired differences permit an analysis of
variance—specifically, whether or not the paired
differences between companies with DRIPs and
companies without them are jointly nonzero. This
distinction is important because the right-most
column in Table 2 reports almost forty t-tests. Some
of those tests are likely to appear statistically significant even if they are not. Economists call this
a type I error, and the chance of committing it
increases as the number of tests increases. An analysis of variance takes this possibility into account.
The trade-off is that, if differences are found, the
test provides no information about which variable
or variables are the source of the difference. In such
cases, further tests are necessary.
Here, the analysis of variance produces an Fstatistic of 5.14. A value this large is very unlikely to
be caused by chance, and the implication is that the
magnitude of the paired differences between DRIP
companies and no-DRIP companies is reliably different. The next task is to explore which of the variables are likely to be driving this result.
Previous discussion suggests that DRIPs are likely
to provide a broad, relatively stable base of shareholders who, because they hold relatively small positions, are likely to be passive investors. The data
support this. For example, in the size-matched sample of companies, firms with DRIP plans averaged
49,650 common shareholders in 1999 compared to
only 23,460 for companies without such plans. The
probability that this pattern is due to chance is less
than 1 percent. In addition, companies with DRIPs
had only 143.6 million common shares compared to
191.9 million traded by the shareholders of companies without plans. Put differently, the average number of shares traded per shareholder in a company
offering a DRIP is about 2,890 shares annually compared to almost 8,200 for a company without a DRIP.
Thus, the differences are economically and statistically significant. Using only the 521 paired companies with data on both firms, the results are similar.
DRIP firms have almost twice the number of shareholders, but each of them trades only about onethird as much on average. DRIP companies generally
have more stable shareholder bases.
7. SIC codes classify companies according to industry. For example, codes from 6000 through 6099 apply to the general category of depository institutions. Subcategories within this range represent specific different types of depository institutions.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
11
TABLE 2
Means and t-tests, 906 Companies with DRIP Plans Compared to 906 Companies without,
Size-Matched Sample, 1999
Unmatched sample
Variable
No DRIP plan
DRIP plan
Observations Mean Observations Mean
Total assets (MM$)
PPE, gross (MM$)
PPE, net (MM$)
PPE, capital expenditures (MM$)
Capital expenditures (MM$)
Research and development (MM$)
Common equity (MM$)
Stockholders equity (MM$)
Net sales (MM$)
Interest expense (MM$)
Dividends to common (MM$)
Dividends per share ($)
Payout ratio (%)
Dividend yield (%)
Number of common shares
outstanding (MM)
Number of common shares
traded (MM)
Treasury stock, number of
shares (MM)
Number of common
shareholders (M)
Number of employees (M)
Interest income (MM$)
Sales, common & preferred (MM$)
Purchases, common &
preferred (MM$)
Pretax income (MM$)
Net income (MM$)
Interest expense per share ($)
Net profit margin (%)
Return on stockholders’ equity (%)
Pretax interest coverage (X)1
Pretax profit margin (%)
Pretax return on assets (%)
Operating income before
depreciation to total assets (%)
Aftertax interest coverage (X)1
Aftertax ROE (common, %)
Aftertax return on total assets (%)
Debt ratio
Market-to-book (ratio)
P/E at fiscal year-end (ratio)
Market value of common stock
at calendar year-end (MM$)
Earnings per share
Matched
No. of
No DRIP
paired
plan
t-statistic differences Mean
sample
DRIP
t-statistic,
plan
paired
Mean differences
906
711
851
751
753
317
897
904
904
758
876
876
875
777
14,412
4,710
2,428
535.05
534.82
265.96
2,394
2,510
4,737
266.72
111.17
0.36
19.34
1.46
906
657
831
712
726
381
905
906
905
741
881
905
880
905
13,870
5,779
2,644
484.81
480.22
260.40
2,645
2,682
5,842
268.99
161.37
0.85
52.77
3.96
0.25
–1.55
–0.70
0.54
0.60
0.09
–0.72
–0.49
–1.79*
–0.03
–2.45**
–8.37**
–4.23**
–5.07**
906
509
780
587
599
131
896
904
903
617
851
875
849
776
14,412
4,313
2,504
501.89
499.98
263.30
2,397
2,510
4,742
250.98
113.70
0.36
19.54
1.46
13,870
5,742
2,546
475.36
470.74
105.00
2,655
2,685
5,855
205.21
161.39
0.85
49.41
4.07
2.41*
–2.82**
–0.18
0.35
0.39
2.34*
–0.91
–0.61
–2.54*
1.17
–2.98**
–8.20**
–3.85**
–4.91**
862
181.43
903
207.73
–1.20
859
181.04
205.07
–1.29
774
191.90
906
143.56
1.92*
774
191.90
128.20
884
5.16
891
14.39
–4.12**
870
5.12
13.96
–4.09
675
800
500
757
23.46
18.49
31.11
155.93
713
820
448
712
49.65
24.10
34.31
51.07
–3.17**
–2.08**
–0.35
4.32**
521
722
261
594
25.25
18.66
31.09
144.18
48.85
24.67
44.40
53.86
–2.34*
–2.22*
–0.99
4.21**
706
905
906
678
902
903
735
902
905
75.49
473.80
313.83
8.40
1.30
13.35
30.04
5.45
3.30
711
905
906
739
905
906
735
905
905
170.21
621.55
403.33
1.38
8.20
13.25
14.91
12.28
6.31
–4.16**
–2.09**
–1.88*
1.32
–3.06**
0.01
0.61
–2.57**
–5.66**
551
904
906
550
901
903
595
901
904
72.90
474.33
313.83
10.01
1.30
13.35
11.58
5.47
3.31
157.38
622.24
403.33
1.26
8.14
13.24
16.47
12.22
6.31
–3.81**
–2.80**
–2.45*
1.28
–3.09**
0.01
–0.26
–2.62**
–5.82**
857
735
896
906
905
766
777
9.16
22.87
14.79
1.53
0.69
3.07
20.80
825
735
905
906
905
903
905
11.38
9.84
4.85
4.04
0.69
2.87
16.31
–4.56**
0.53
0.78
–5.53**
0.44
0.46
0.91
780
595
895
906
904
763
776
9.18
3.09
14.80
1.53
0.69
3.06
20.80
11.38
10.79
4.78
4.04
0.69
2.72
15.73
–4.45**
–0.43
0.78
–5.67**
0.46
0.76
0.94
775
822
10,112
1.64
903
905
10,468
1.73
–0.21
–0.21
772
821
9,995
1.64
9,409
1.69
0.36
–0.11
2.50*
Note: The table is constructed so that positive t-statistics imply that the value for the companies without DRIPs is larger than for the companies
with them. ** indicates significance at the 1 percent level; * indicates significance at the 5 percent level.
1
Interest coverage is the ratio of income to interest expense. For example, $30 of income times $1 of interest expense yields an interest coverage of 30.
Source: Author’s calculations using data from Compustat and the Guide to Dividend Reinvestment Plans
12
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
To the extent that employee ownership is advantageous, companies in labor-intensive industries
would also be expected to offer more DRIPs for at
least two reasons. First, if they have more employees, the advantage to be gained is presumably larger.
Second, many employees are likely to be at most small
investors, and DRIPs tend to attract such investors.
In fact, DRIP firms are more labor-intensive than
their no-DRIP counterparts. Computed from data on
all 906 pairs, the mean number of employees for
DRIP firms is 24,100 while corresponding no-DRIP
firms average only 18,490. Statistically, this difference is much too large to be the result of chance.8
Previous discussion also suggests that companies
in industries subject to relatively high levels of regulation are more likely to offer preferential access
to their plans for customers, state residents, and
employees. The data confirm that these effects are
important. Of the twenty-three companies that offered
customers, state residents, or employees preferential
access to their plans in 1999, all but one are utilities.
Moreover, the other is a financial services company.
Given that only 16.7 percent of the DRIP companies
in the sample are utilities, this difference is very
unlikely to be due to chance, and tests confirm this.
One can make a case from Table 2 that DRIP
companies tend to be more mature than those without DRIPs. Mature firms have more assets in place
and fewer growth opportunities than younger firms.
Older firms also tend to pay higher dividends and
carry higher debt levels. Because such firms have
fewer growth options, they tend to have higher current earnings but (relatively) lower expected future
earnings; consequently, they usually have lower priceearnings ratios and market-to-book ratios.
All of these predictions for mature companies
hold for DRIP firms except for the debt ratio, for
which there is no significant difference. DRIP firms
do, however, pay higher dividends per share and
have higher payout ratios. They also tend to have
more property, plant, and equipment (assets in place)
but make smaller current capital expenditures, a
pattern consistent with fewer growth opportunities.
DRIP firms have higher net sales and higher profit
margins. The evidence regarding price-earnings ratios
and market-to-book ratios is mixed but generally
supportive of the conjecture that DRIP firms tend to
be more mature. In 1999 the mean ratios are higher
for companies without DRIPs, but the difference is
small enough that it may be due to chance. On balance, the evidence supports the conjecture that DRIP
firms tend to be more mature.
The Future
ontinuing technological advances, especially if
unimpeded by regulatory constraints, are sure
to foster the evolution of most financial services,
including DRIPs. More DRIP plans are introduced
every month, making it easier for investors to diversify as time passes. Another obvious tool for DRIP
investors is the Internet. Ford, McDonald’s, and
Fannie Mae, among others, already let investors use
the Internet to service their accounts. The Home
Depot, Inc., takes this convenience a step further,
permitting investors to buy their first share directly
from the company via the Internet.
The Internet has fostered competition for many
industries, and brokerage is no different. On-line brokers are now common; in a statement dated January 27, 1999, then-SEC Chairman Arthur Levitt
reported that on-line brokers handle about 25 percent
of all retail stock trades. Because on-line brokers offer
fewer services than traditional brokers, on-line services tend to be cheaper. It seems unlikely, though,
that on-line brokers can match the low costs of DRIPs.
On-line brokerage accounts typically require a deposit
balance, and these can be large. Brown & Company,
for example, requires a $15,000 minimum. Such a
large minimum balance is unlikely to appeal to new
investors, who tend to have smaller accounts.
Broker-run DRIPs provide another evolutionary
direction. Competitive pressures have led most
major brokerage firms to offer in-house DRIPs. These
plans are similar to true DRIPs only in that dividends
can be reinvested automatically and only sometimes
without brokerage fees. However, the brokerage
house usually holds the securities in street name,
usually does not credit fractional shares, and charges
commissions on optional purchases. This is not to say
that these accounts are necessarily inferior to true
DRIPs. Rather, brokerage DRIPs provide a different
menu of services and costs that may or may not
appeal to a given investor.
C
Conclusion
o one expects direct investment plans to be the
answer to all of the modern investor’s needs.
Mutual funds continue to offer convenience and
unmatched diversification for small accounts.
Investors seeking to hold individual stocks, whether
to compensate for nondiversifiable human capital, to
place bets on mispriced securities, or for some other
reason, can choose from a rich menu of financial service providers. Traditional brokerage accounts cost
more than transactions using DRIPs but offer a wide
N
8. The numbers are almost identical for the 722 pairs for which data are available on both firms.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
13
range of services that many investors find valuable.
On-line brokers offer lower costs but fewer services;
such brokers target investors who place less value on
the services that a traditional brokerage firm can provide. Direct investment plans, which are concentrated
by industry, make diversification more difficult. To
offset this disadvantage, they offer a transactions cost
advantage; they appeal to the buy-and-hold clientele
who seek the lowest possible transactions costs.
Viewed in the broadest sense, all of these methods
of distributing securities compete in the same arena
for customers’ favor. When examined more closely,
though, differences become clear. Each offers a different combination of services and costs that appeals
to different investors. The key is no different than
for any other menu of costs and services: Customers
choose the product that offers services that they
value and that charges less than the value of those
services to them.
What sets direct investment plans apart from the
other offerings of financial service providers is a clientele that is well suited for certain companies. A broad,
stable ownership base provides benefits to companies
that face political or regulatory scrutiny because the
company has easy access to many voters. Such shareholders also tend to vote with management; hence,
direct investment plans offer potential as a takeover
defense. Finally, a broad ownership base provides
opportunities for cross-selling, which is more valuable
to companies with large-scope economies.
REFERENCES
Asquith, Paul, and David Mullins Jr. 1986. Equity issues and
offering dilution. Journal of Financial Economics 15: 61–89.
Guide to Dividend Reinvestment Plans. 1999. Mamaroneck, N.Y.: Temper of the Times Communications, Inc.
Bogle, John C. 1982. Mutual funds. In The complete guide
to investment opportunities, edited by Marshall E. Blume
and Jack P. Friedman, 509–34. New York: The Free Press.
Harris, Lawrence, and Eitan Gurel. 1986. Price and volume
effects associated with changes in the S&P 500 list: New
evidence for the existence of price pressure. Journal of
Finance 41 (September): 815–29.
Carlson, Charles B. 1996. Buying stocks without a broker.
2d ed. New York: McGraw-Hill.
———. 1997. No-load stocks. Rev. ed. New York: McGraw-Hill.
———. 2000. Let’s talk DRIPs. Hammond, Ind.: Horizon
Publishing Company.
Clemente, C.L. 2000. Pfizer, Inc., letter to shareholders.
September 7.
Constantinides, George M. 1979. A note on the suboptimality
of dollar-cost averaging as an investment policy. Journal of
Financial and Quantitative Analysis 14 (June): 443–50.
———. 1984. Optimal stock trading with personal taxes:
Implications for prices and the abnormal January returns.
Journal of Financial Economics 13 (March): 65–89.
CNNMoney. 2001. Fund taxes do matter. February 21.
<cnnfn.cnn.com/2001/02/21/mutualfunds/q_funds_taxes_
wg/> (February 21, 2001).
Eckbo, B. Espen, and Ronald W. Masulis. 1992. Adverse selection and the rights offer paradox. Journal of Financial
Economics 32 (December): 293–332.
Ederington, Louis H., and Jeremy C. Goh. 2001. Is a convertible bond call really bad news? Journal of Business 74
(July): 459–76.
Finnerty, John D. 1989. New issue dividend reinvestment
plans and the cost of equity capital. Journal of Business
Research 18 (March): 127–39.
Ganci, Paul J. 2001. Remarks presented at the annual meeting of CH Energy Group, Inc., April 24.
14
Jacob, Nancy. 1996. Tax-efficient investing: Reduce tax drag,
improve asset growth. Dow Jones Publications Library,
Trusts & Estates, June.
Levitt, Arthur. 1999. Securities and Exchange Commission
statement concerning on-line trading. January 27.
<www.sec.gov/news/press/pressarchive/1999/99-9.txt>
(January 27, 1999).
Merton, Robert C. 1973. Theory of rational option pricing.
Bell Journal of Economics 4, no. 1:141–83.
Priory, Richard B. 2001. Duke Energy Corporation letter to
shareholders. February 12.
Quattlebaum, Paul, and Otto Strock. 2001. Association of
SCANA Corporation Investors letter to shareholders.
January.
Scholes, Myron S., and Mark A. Wolfson. 1989. Decentralized investment banking: The case of discount dividendreinvestment and stock-purchase plans. Journal of Financial Economics 24 (September): 7–35.
Smith, Clifford W., Jr. 1986. Investment banking and the
capital acquisition process. Journal of Financial Economics 15 (January/February): 3–29.
Updegrave, Walter. 2001. What’s the best way to invest on a
low income? August 14. <www.money.com/money/depts/
planning/expert/archive/010814.html> (August 14, 2001).
The Vanguard Group. 2001. A quarter-century of success
proves the power of indexing. In the Vanguard (Summer):1.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
Pension Systems and
Aggregate Shocks
KARSTEN JESKE
The author is an economist in the macropolicy section
of the Atlanta Fed’s research department. He thanks
Thomas Cunningham, Juan Rubio-Ramírez, and
Ellis Tallman for helpful comments.
o some analysts the prospective imbalances between pay-as-you-go pension
system benefits and the tax base present a great economic challenge in the
decades to come.1 It is currently estimated that the U.S. Social Security
Trust Funds will run out of money in 2041, after
which either benefit cuts or major tax hikes would
have to occur.2 Other countries face similar or even
tougher and shorter-term problems. For example, in
Germany wages reported to the defined benefit system are already taxed at a rate of about 20 percent
of gross income, compared to 12.4 percent in the
United States, and are expected to rise to a staggering 28 percent by 2035. Sinn (1999) calculates
that the current value of all implicitly promised future
benefits amounts to a number roughly 250 percent
of current German annual gross domestic product
(GDP), an overwhelming figure compared to the
current government-debt-to-GDP ratio of 60 percent.
In the United States and in most Western democracies, proposals to cut benefits to the extent necessary to save social security are politically infeasible.
Raising contributions is—from an economic point
of view—undesirable because proportional payroll
taxes have distortionary effects on both labor supply and savings decisions. In light of these impending funding problems, politicians and academics
alike are calling for a reform of social security. In the
United States there is a near consensus that such
T
reform is necessary, but there is also controversy
about what the reform should look like. One suggestion, put forward by the President’s Commission to
Strengthen Social Security, is a partial privatization
of social security (President 2001). In this proposal
current social security surpluses could be used to
fund private, individual retirement account (IRA)style accounts, and the private savings could make
up for future benefit cuts.
In the privatization debate, two opposing perceptions seem to hinder productive discussion. First,
social security is considered a low-risk vehicle for
the provision of old-age income. Second, the exact
size of the social security funding problem is
extremely difficult to forecast. Minute changes in
the growth assumptions of the forecasting models
lead to large changes in the long-term forecasts for
social security feasibility. In fact, a few economists
argue that with only slightly larger annual growth
rates than the conservatively chosen rates used by
the Social Security Administration, social security
will not face any funding problem whatsoever.3 For
example, Robert Reich, a former trustee of the Social
Security Trust Fund, argues that “The actuary’s
projections are based on the pessimistic assumption
that the economy will grow only 1.8 percent annually over the next three decades. Crank the economy
up just a bit, to a more realistic 2.2 percent a year,
and the fund is nearly flush for the next seventyfive years” (Reich 1998).
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
15
Unfortunately, the argument also works in the
opposite direction; just slightly smaller growth rates
than the ones predicted lead to even more catastrophic scenarios than the ones already discussed.
To see how sensitive the trust fund finances are with
respect to aggregate variables, one need look only at
the calculations of the Social Security Administration.
Under the benchmark assumption, the value of the
trust fund (in current dollars) will be $6.7 trillion in
2030, and the value decreases until 2041, when the
fund is depleted. Increasing the wage growth rate
from 1.1 percent to 1.6 percent and the labor force
growth rate from 0.2 percent to 0.6 percent would not
only almost double the trust fund value in 2030 to
The results of the model simulations show
that, in the long run, privatization makes
every generation better off, even if a large
aggregate shock occurs.
more than $12 trillion— almost $7 trillion in today’s
dollars—but would also ensure that the fund is never
depleted over the horizon of eighty years. On the
other hand, slightly lower growth rates of 0.6 percent
for wages and –0.3 percent for the labor force would
cause the trust fund to be depleted by 2029. The
implicit confidence interval for the estimated trust
fund value in 2030 then covers everything between
a slight trust fund liability up to a staggering $7 trillion
surplus in today’s dollars, more than four times the
federal budget for fiscal year 2002.
From an economist’s perspective, the two perceptions of low-risk social security and the extreme
sensitivity of social security finances with respect
to unpredictable economic fundamentals contradict
each other. Social security cannot be completely riskless, as the uncertainty about the predicted funding
problem demonstrates. The viability of social security crucially depends on what such volatile variables
as productivity growth, fertility, and immigration turn
out to be over the next decades. From a macroeconomic perspective, a pay-as-you-go (PAYGO) system
therefore implies a substantial amount of risk, contrary to the amount that proponents of social security would admit.
Moreover, the factors that tend to drive the performance of a PAYGO system are the same that drive
returns on financial market assets, and they push in
16
the same direction. For example, lower productivity
growth indeed has a negative effect on the returns to
physical capital and therefore reduces financial
market returns. At the same time, however, lower
productivity growth also jeopardizes a PAYGO system because the system’s promised benefits become
more difficult to finance if wage growth rates are
lower than expected.
PAYGO returns also tend to be lower than financial market returns. If, in addition to this low return,
PAYGO also has potentially high risk and a high correlation with financial market returns, then—from
the perspective of a Sharpe (1964) and Lintner (1965)
capital asset pricing model (CAPM)—a PAYGO system
may be viewed as a very undesirable asset. To determine whether and to what degree a PAYGO system is
undesirable, one must design a model economy in
which aggregate shocks affect not only financial market returns but also a PAYGO system. For policy analysis, this model can help to evaluate proposals. For
example, privatization may look unattractive because
it exposes the retirement income of a representative
generation to a substantial amount of risk. If, at the
same time, however, social security faces a symmetric
risk profile, then privatization appears more attractive.
This article provides such a model in order to
address the sensitivity of different retirement schemes
to large aggregate shocks, such as a major drop in productivity growth or demographic shocks like a babyboomer generation. The workhorse model used in the
analysis is a so-called life-cycle economy in which
agents work when they are young and their old-age
consumption is financed by a combination of a PAYGO
pension system and private savings. The model is then
used to determine how different retirement schemes
perform under different kinds of shocks.
The results of the model simulations show that,
in the long run, privatization makes every generation better off, even if a large aggregate shock occurs.
The intuition for this result is that, under a privatized
pension system, savings are higher, and this higher
savings level increases the aggregate capital stock
because private savings are more desirable and affordable if both benefits and contributions are lower. This
higher capital stock increases welfare by an amount
high enough to insulate all future generations even
from large aggregate shocks. Aggregate risk is mainly
a concern for the period immediately after a social
security reform.
A Simple Life-Cycle Model
his section introduces a simple model that allows
one to assess how sensitive different retirement
systems are with regard to a variety of aggregate
T
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
shocks. The model is extremely stylized and
abstracts from many real-world matters in order to
be analytically and computationally tractable. Many
simplifications, however, are performed in such a
way as to give a PAYGO system the best possible
chance to perform well relative to private retirement
accounts. Consequently, the model consistently
underestimates gains from privatizing social security;
therefore the potential welfare improvements presented here serve as a lower bound.
The model is an overlapping generations (OLG)
model; people live for a maximum number of periods,
and, to lend the model a greater degree of realism,
in each period they have a given probability of dying.
That is, in every period there is a distribution of agents
of different ages. At the beginning of each period a
new generation of young agents enters the economy,
and in each of the existing generations a specified
fraction of agents dies and leaves the economy.
Just as in the real world, agents have a humpshaped labor productivity profile; that is, people start
with a relatively low labor productivity associated
with lower wages and then accumulate human capital until their labor productivity peaks at about the
age of fifty, after which productivity slowly decreases
until age sixty-five. The model assumes that retirement is mandatory at age sixty-six; that is, productivity (and therefore labor income) falls to zero, and
people must live on their private savings and a
government-sponsored pension plan thereafter.
In the model simulations in the next section, it is
assumed that one period is six years. People enter
the labor force at the age of eighteen and may live
for up to fifteen periods, that is, to an age of 108; the
survival probabilities are matched to the probabilities computed from data from the National Center
for Health Statistics. For the computations and the
quantitative results presented later in the article,
this more sophisticated and realistic multigenerational model is used, but most of the intuition works
just fine with a simpler version of the model with
only two generations alive at any given time.
In this simpler model, even though the economy
has infinitely many periods, individuals live for only
exactly two periods; that is, there is no probability
that a person will die before reaching the second
period. (This assumption will be relaxed in the more
sophisticated model used in the numerical examples.) The precise timing is illustrated in Figure 1. In
period 1 there is an initial old generation (generation
0) that lives only for exactly one more period and
then dies and a young generation (generation 1) that
lives for two periods. In period 2, generation 2 is born
and serves as the young generation whereas generation 1, the previously young generation, is now the old
generation. More generally, in period t there are two
generations alive: Generation t – 1 is the old generation and generation t is the young. For example, in
period 3 generation 2 is old and generation 3 is young.
Introducing social security or even
expanding an existing social security
system is beneficial only for the initial
old and middle-aged generations.
While they are young, people work, receive
labor income, and pay a payroll tax to finance the
government-sponsored retirement scheme for the old
generation. When they are old, people cannot work
but must finance their consumption with the government pension and private savings. In the notation
used throughout the article, subscripts denote time
and superscripts denote the generation’s birth period.
t
is consumption of a generation
For example, c tt, c t+1
t agent in time periods t and t + 1.4 The budget constraint of this agent in period t takes the form
(1) ctt + k tt+1 = (1 – τt )wt.
The terms on the left-hand side are the expenses
of an agent. He can dedicate his income to either cont
, that pay off prinsumption, ctt, or private savings, kt+1
cipal and interest next period. The right-hand side is
net labor income, wt, after paying the proportional
1. It is important to note that the U.S. social security system does not fit the definition of a pay-as-you-go plan in the narrow
sense. The current surpluses due to the baby-boomer generation are saved in the Social Security Trust Fund rather than being
used to lower contribution rates.
2. The Social Security Trust Fund is actually two funds—the Old Age and Survivors Insurance Trust Fund and the Disability
Trust Fund. This article will refer to these two funds as a single fund.
3. Biggs (2000) has the opposite view. He addresses uncertainties about the estimates of a wide range of economic fundamentals underlying the Social Security Administration’s computations, such as fertility, longevity, and productivity, and concludes
that the estimates tend to be at most reasonable and sometimes on the optimistic side from a historical point of view.
4. This model assumes that agents in each cohort are identical, so there is no within-generation heterogeneity of wealth.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
17
FIGURE 1
Timing in the Overlapping Generations (OLG) Model
Generations
Young
Old
Generation 3
Young
Old
Generation 2
Young
Old
Generation 1
Old
Generation 0
1
2
3
4
Time
payroll tax, τt. After working for one period, the agent
retires in period t + 1 and has two sources of income:
t
t
= δwt + (1 + rt+1)k t+1
.
(2) c t+1
The first term on the right-hand side is the
government-sponsored retirement scheme, promising to pay a fraction δ of an individual’s wage as a
social security benefit. This social security system
is a defined-benefits system because it promises
a fixed replacement ratio of δ of the previously
earned wage. The second term is private savings
plus the earned interest. Agents take wages and
interest rates as given and maximize the objective
t
) subject
lifetime utility function U = u(c tt) + βu(c t+1
to the two budget constraints (1) and (2).
On the aggregate level there is both population
and productivity growth. It is easy to see that both
growth rates play a vital role for the feasibility of
social security. The higher the population growth
rate, the lower the retiree-to-worker ratio, and the
higher the productivity growth rate, the higher the
wage growth rate and thus the easier it is to finance
promised benefits out of the payroll tax base. Let
gλ denote the population growth rate, which is
assumed to be fixed for now, and λt, the size of the
generation born in period t. Then, by definition,
λt+1 = (1+gλ)λt. Output (Yt) is produced by combining labor (Lt) and capital (Kt) according to a pro18
duction function Yt = At Kαt L1–α
, where At is total fact
tor productivity. Market clearing dictates that the
amount of labor used in production is equal to the
amount of labor from the young generation, and the
amount of capital is equal to the amount of savings
the old generation accumulated during its working
)αλ1–α
,
years. That is, output is equal to Yt = At(λt–1k t–1
t
t
where productivity, At, grows at rate gA; that is,
At+1 = (1 + gA)At.
In the model it is assumed that the government
balances its budget period by period, and in order to
do so it sets the payroll tax so that the tax revenue
is exactly equal to the payments to retirees. (Later in
the article, when aggregate shocks are considered,
this assumption implies that the tax rate adjusts in
order to finance the predetermined benefits to the
retirees.5) The government budget constraint then
implies that the payroll tax revenue, λtτtwt, is equal
to the promised benefits to the old generation,
λt–1δwt–1;6 that is, the equilibrium payroll tax is
equal to τt = δ(λt–1/λt)(wt–1/wt). The intuition that
supports this result is that with no population or
wage growth, benefits are equal to contributions. If
there is wage or population growth, then a fixed
benefit level can be achieved with lower contributions because the tax base is increasing.
Alternatively, one could assume that contributions into the pension system are constant and that
the government distributes the proceeds to the
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
current retirees. In this case, if there are fluctuations
in wages, payroll taxes as a percentage of wages
would remain constant and benefits would adjust—
the classic example of a defined-contributions pension system. However, benefit cuts as a reaction
to aggregate fluctuations are considered politically
difficult to implement. Hence, it is more realistic
to use the defined-benefits scheme to model social
security in the United States because it is a closer
approximation to reality.
There are two main simplifying assumptions in
this model. First, labor supply is exogenous, that is,
agents’ provision of labor does not depend on the
wage or the payroll tax. In a more sophisticated
model where agents decide how much labor to supply, social security financed by payroll taxes has a
distortionary effect because people would work
less. Ruling out this effect makes a PAYGO system
more attractive than in reality, and the gains from
privatizing social security would be underestimated
in the model relative to the real world.
The second assumption is that the private savings have to be invested in the domestic economy;
that is, no international portfolio diversification is
possible. Therefore, the effect on financial asset
returns is likely to be overstated in the model,
again making social security more attractive than
in a more realistic, yet currently computationally
intractable, model. This article, therefore, makes
the best possible case in favor of social security,
and the gains from privatization it depicts are likely
a lower bound on the actual gains in a more realistic framework.
particular what the path back to the long-run equilibrium looks like. Without population and productivity growth, this long-run equilibrium, called
steady state, is an equilibrium in which all model
variables stay constant over time. Since there is
growth in both population and productivity, however, there is evidently no such steady state in this
economy. Instead, there is a long-run equilibrium in
which the growth rates rather than the levels stay
constant for all variables (but may differ across variables). This long-run equilibrium is also called a balanced growth path. Here, this balanced growth path
can be computed easily by noting that the tax, τ, must
remain constant and the variables in equation (1)—
Balanced Growth Paths
and therefore growth rates of wages and per capita
savings are given by
hen numerical simulations are performed, initial conditions in the model matter. In particular, the economy starts with an old generation that
owns capital, and the researcher therefore has a
choice about what the capital endowment of this
initial old generation should be. The preferred
choice in economics is to begin in a long-run equilibrium and see how a shock affects the economy, in
W
Social security reform has beneficial effects
in the long run, but in the short run a large
portion of the population will be worse off.
namely, consumption when young, savings, and
wages—all must grow exponentially at the same
rate. This result, together with the fact that the
wage is simply the marginal product of labor,
implies that
(3) 1+ gk = 1+ gw = (1+ gA)[(1+gλ)(1+ gk)]α(1+ gλ)–α,
(4) 1+ gk = 1 + gw = (1 + gA)1/(1–α).
Equation (4) means that independent of the population growth rate, both wages and savings grow at
identical rates equal to approximately 1/(1 – α)
times the productivity growth rate.
5. There are three reasons why this article abstracts from the possibility of a trust fund and instead considers a PAYGO system
in which the government adjusts payroll contributions period by period. First, a trust fund is only an option if temporary surpluses are saved to finance future deficits. In two of the three aggregate negative shocks considered here, there are no temporary surpluses and hence no room for a trust fund. Second, in the one case that does display temporary surpluses, namely,
the baby-boomer shock, it turns out that the negative welfare effects become even more pronounced with a trust fund; thus,
in order to give social security the best possible chance to do well compared to privatized social security, this article assumes
there is no trust fund. Third, the bulk of the actual trust fund savings in the United States was accumulated after 1987, well
after the first baby boomers entered the labor force, so that the trust fund can all but partially smooth out the future deficits.
In other words, because the trust fund build-up occurred so late, the actual U.S. social security system is not far from being
a pure PAYGO system.
6. Notice that the promised benefits depend on the lagged wage the current retirees earned when they were young.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
19
FIGURE 2
Increasing Benefits: Average Lifetime Consumption Relative to No Policy Change
1
0
Pe r c e n t
–1
–2
–3
–4
–5
–15
–10
–5
0
5
10
15
20
25
Coho rt b o rn in p e rio d
The Facts about Social Security
quipped with the tools from the OLG model, the
discussion now turns to some of the facts about
pension systems that are well known in the academic
literature but possibly less well understood in the
popular media.
The internal rate of return. Without aggregate
fluctuations, the internal rate of return of defined
benefit systems for a representative generation is
equal to the rate of population growth plus the
growth rate of real wages. This result, from Samuelson (1958), can be easily derived with the twoperiod OLG model. According to the calculations
from above, an agent’s flow of payments into the
social security system is δwt /[(1 + gλ)(1 + gw)] when
young and –δwt when old. Consequently, independent of the value for the replacement ratio, δ, the
internal rate of return on this flow is (1 + gλ)(1 +
g w) – 1, which is approximately equal to the sum
of the growth rates of population and wages. The
intuition for this result is that the higher the growth
rates for wages and population, and thus the higher
the growth rate of the payroll tax base, the easier
it is to finance social security. For every dollar of
old-age benefits, only 1/[(1 + gλ)(1 + gw)] dollars
of contributions have to be paid.
This result holds even if there is a positive probability of death before reaching old age. Suppose a
fraction π of agents die after their first period of life so
E
20
they naturally do not receive old-age benefits. In this
case the expected benefits of a representative generation are reduced by π, and at the same time the contributions are cut by the same fraction because fewer
old people receive old-age benefits, leaving the internal rate of return unchanged. The results from this
stylized economy with only a two-period horizon for
every generation carry over to more realistic settings
in which agents live longer than two periods.
Financial market returns. In the real world,
the potential average yield for social security is
equal to population plus wage growth, an amount
that is smaller than the average return on private
savings. This observation spurred the entire privatization debate because an individual worker could
invest her social security contributions in the financial market and, in expected terms, achieve a higher
level of benefits. For example, for the period 1960
to 2001, real wage plus population growth averaged
less than 3 percent per year, and it is expected to
average less than 2 percent per year for the next
three decades, according to the Social Security
Administration’s estimates. Individuals born in 2000
can even expect less than 1 percent return on their
social security contributions. On the other hand,
the long-term real return on financial assets is significantly higher—in the neighborhood of 5.5 percent
annually, according to Feldstein and Ranguelova
(2001), or 4.6 percent return from a diversified port-
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 3
Increasing Benefits in Period 0: Changes Relative to No Reform
0
30
Payroll tax (right axis)
–1
25
–2
20
–3
15
Capital (left axis)
–4
Percent
Percent
Wage (left axis)
10
–5
5
–6
–7
0
–1
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Period
folio considered by the President’s Commission to
Strengthen Social Security.
Introducing or enhancing a social security
system. Introducing social security or even expanding an existing social security system is very beneficial for the initial old and middle-aged generations,
but the young generation at the time of the program’s introduction and all generations born in the
future are worse off.7 In particular, social security
crowds out private savings and therefore leads to a
reduction in the level of capital. To demonstrate this
result, a more realistic version of the model above is
used in which generations live for up to fifteen periods. In the simulation it is assumed that in period 0
pensions increase by 25 percent; that is, the benefit
formula is adjusted unexpectedly to increase the
ratio of pension benefits to lifetime earnings by one
quarter.8 Notice that this policy affects not only generations born in period 0 and thereafter but also all
other current workers, namely, generations –7 to –1,
as well as current retirees in generations –14 to –8.
The results of the simulation are demonstrated in
Figure 2, which plots the average lifetime consumption of all cohorts affected by the policy change.9 The
ten cohorts that entered the labor force between
periods –14 and –5 post a gain in average lifetime
consumption. These are the seven cohorts currently
retired who get higher benefits without ever paying
higher contributions and the three cohorts of workers prior to retirement who profit from higher retirement benefits but must pay higher contributions only
for a very limited amount of time. All other cohorts,
whether currently alive or born in the future, suffer
substantial losses of lifetime consumption on the
order of about 4.5 percent.
The reason for this result lies in the response
of macroeconomic variables to the policy change.
Figure 3 plots aggregate capital, wages, and the
7. The scope of this article is social security reform, exactly the opposite of introducing or enhancing social security, but for
completeness this well-known result is included.
8. In this version of the model, since people work for a maximum of eight periods, the calculation of benefits is more complicated than in the two-period OLG model, where the benefit formula consisted of only one replacement ratio, δ. Specifically,
the more complex model must define how retirement benefits depend on a total of eight past wages and how they develop
during the maximum of seven periods in retirement. It is assumed that retirement benefits stay constant (in real terms) during
retirement and benefits are a share of the average lifetime earnings.
9. Average consumption in this context is defined as follows. Suppose an individual born in period t consumes a sequence (c tt,…,cTt );
then average consumption c taverage is defined as the constant consumption profile that makes the individual indifferent between
t
t
t
the actual and the constant profile. In the two-period example, u(caverage
) + βu(c average
) = (1 + β)u(caverage
) = u(c tt) + βu(c tt+1).
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
21
payroll tax relative to an economy without policy
change over time. A higher level of social security
triggers a drop in aggregate capital relative to an
economy with unchanged social security benefits.
The reason for this drop is that the aggregate capital stock is equal to the sum of all savings, and with
higher retirement benefits, private savings become
both less desirable as people rely more on social
security and less affordable as young and middleaged workers receive smaller net wages because of
higher payroll taxes. With the drop in capital comes
a drop in wages (making private savings even less
affordable), which in turn causes the payroll tax to
initially overshoot to more than 25 percent above
The longer ago privatization took place, the
more likely it is that all cohorts alive will be
better off under privatized social security.
There may be arguments against privatization,
but aggregate risk is not one of them.
the initial level, because now the promised benefits
to older cohorts must be financed out of a smaller
payroll tax base. It is interesting to note that, in
the long run, lifetime consumption drops by about
4.5 percent—much more than the 2 percent wage
drop. More than half the drop in lifetime consumption is due to the low internal rate of return on the
increased payroll tax contributions.
Theoretically, there is one positive effect for all
generations coming from the introduction or expansion of social security. If there are no markets for
annuities, private savings have a disadvantage that,
with a random lifespan, there is the risk of outliving
one’s savings. This risk can be eliminated by social
security. Since the expansion of social security in this
economy substantially reduces welfare in the long
run, the risk-sharing effect from social security must
be small, however. This effect is in line with the
results from Storesletten, Telmer, and Yaron (1999),
who show that the negative effect from crowding
out private savings is indeed larger than the positive
effect from risk sharing.
The effects of social security reform. Social
security reform has beneficial effects in the long
run, but in the short run a large portion of the population will be worse off. Naturally, a reform can
take many forms, but ultimately all reforms involve
lower benefits. This article assumes that a reform
22
takes the form of an immediate one-time reduction of
benefits. Alternatively, one could assume a delayed
or a stepwise reduction, in which case the initial
burden of the transition would be spread over more
generations. The long-term effects, however, would
be unchanged. The result of initial burden and longterm gains is the precise flip side of the previous
result as shown in Figure 4. Cutting benefits hurts
the currently retired cohorts (–15 through –9) and
even some of the older cohorts currently working
but close to retirement. In the long run, though,
agents are far better off—by about 4.5 percent of
average consumption—because lower retirement
benefits in conjunction with a lower tax burden
encourage more private savings and therefore more
capital accumulation. With more productive capital
in the economy, wages are higher, and the increase
in lifetime income, coupled with the higher returns
on private savings compared to the pension system,
makes future generations substantially better off.10
If retirement benefits are cut, however, all retirees
and even workers who are near retirement have to
suffer substantial losses. Even a delayed reform in
which benefits will be lower in the future penalizes
those generations that have to pay contributions
into the social security system but receive only
reduced benefits when they retire.
The fact that private accounts yield higher returns
than social security is therefore often misunderstood
as a miraculous way of saving the system by offering
higher returns from private accounts. It is often
ignored that, if such privatization took place, current
retirees’ benefits—being a burden on current and
future tax payers—would have to be cut or would
have to be financed through the general tax base or
government debt. In other words, the problem of privatization is the unfunded liability to pay for current
retirees if current workers start investing in their
private accounts.
Related Literature
he model presented here is neither new nor the
only one that tries to address the issue of aggregate fluctuations and social security. Auerbach and
Kotlikoff (1987) set up a similar large-scale OLG
model to address a wide array of interesting policy
questions, including tax reform and social security
reform. The model used here can be thought of as a
simplified version of the Auerbach and Kotlikoff model
that looks at a new set of experiments, namely, the
performance of different pension systems if a large
aggregate shock occurs.
De Nardi, Imrohoroglu, and Sargent (1999) do a
numerical exercise to study the effects of the demo-
T
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 4
Partial Privatization through Decreasing Benefits:
Average Lifetime Consumption Relative to No Reform
5
4
Pe r c e n t
3
2
1
0
–1
–15
–10
–5
0
5
10
15
20
25
Coho rt b o rn in p e rio d
graphic shock on social security that will be caused
by retirements among the baby-boomer generation
during the coming decades. As one of the main
points of the paper, the authors show that, without
reform of the public pension system, contributions
would have to increase substantially. Higher taxes,
however, magnify the distortions in the economy to
such a degree that the growth forecasts used by the
Social Security Administration seem too optimistic
from the perspective of a general equilibrium model
because social security taxes discourage agents
from both working and saving. In other words, De
Nardi, Imrohoroglu, and Sargent quantify a potential feedback effect from higher payroll taxes into
the growth forecasts that has been ignored by the
Social Security Administration and show that this
effect can be substantial.
As mentioned above and demonstrated by
Samuelson (1958), introducing a social security
system makes a few initial cohorts better off at the
cost of making all other future generations worse off.
Krueger and Kubler (2002) use an OLG model to test
whether this result still holds if aggregate macroeconomic shocks occur—for example, shocks to productivity. Krueger and Kubler point out that it is
theoretically possible that all generations may be
better off with the introduction of social security, contradicting conventional wisdom. The main ingredients in their model are the assumptions that returns
to labor and physical capital are imperfectly correlated
and that the social security system is designed as a
defined-contribution system. The latter assumption
means that the contributions are fixed and benefits
vary over time because they are a fixed proportion of
the payroll tax base. This setup is quite different from
the assumption used in this paper, in which taxes
adjust to finance promised benefits, and from the current U.S. social security setup. The welfare-improving
10. It is important to note that, theoretically, it is possible for OLG models to display so-called dynamically inefficient equilibria,
as first pointed out by Diamond (1965). The inefficiency involves overaccumulation of savings. In such a case, reducing
social security may actually reduce welfare even in the long run because it involves even more overaccumulation of capital.
For this reason, Imrohoroglu, Imrohoroglu, and Joines (1995) find in their economy, which displays this inefficiency, social
security replacement ratios should optimally be above zero. In the real world this inefficiency, however, appears to be nonexistent because it would involve observing real interest rates on capital that lie below real GDP growth rates, which do not
occur in the United States.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
23
FIGURE 5
Baby Boomers in Periods 3–5: Deviation in Average Consumption Relative to No Shock
8
Lower social security
6
Pe r c e n t
4
2
Benchmark
0
–2
–4
–15
–10
–5
0
5
10
15
20
25
Coho rt b o rn in p e rio d
property of social security in Krueger and Kubler’s
environment stems from the fact that retirees put a
value on the asset called labor because the returns of
labor and capital are not perfectly correlated and,
therefore, diversification gains are possible. Retirees,
however, have no labor endowment left, so giving
them a claim to labor income through the social security system improves their welfare.11 Still, there is the
well-known negative effect of social security crowding out private savings both through removing incentives on private savings and the tax distortion, but the
former effect theoretically could be larger than the
latter. Krueger and Kubler do, however, point out that
in an economy modeled to match the U.S. economy
the negative effect of crowding out savings dominates
the risk diversification.
Computations
sing the more complex version of the model,
with fifteen generations alive at any given period
and having realistic survival probabilities, this section
determines the impact of three different aggregate
shocks to the welfare of all current and future generations. Since now one period is only six years, the
groups entering the labor market each period will be
labeled cohorts rather than generations.
Two sets of experiments are conducted, each of
which examines the following three aggregate shocks:
U
24
1. A baby-boomer generation—three cohorts that
are larger relative to both their parents and children. In the computations using the fifteen-period
OLG model, it is assumed that in period 0 it
becomes apparent that the cohorts entering the
labor force in periods 3–5 are 40 percent larger
than in the benchmark economy. The three-period
gap (equal to eighteen years) accounts for the
years between the birth of a cohort and the time
the cohort actually enters the labor market.
2. A permanent drop in the productivity growth rate
by one-half starting in period 0, causing the longrun wage growth rate to drop from 1.1 percent—
the benchmark growth rate used by the Social
Security Administration—to only 0.55 percent.
3. A permanent drop in the labor force growth rate
from 0.2 percent per year—the benchmark labor
force growth rate used by the Social Security
Administration—to –0.3 percent per year, which is
the pessimistic demographic scenario used in the
calculations of the Social Security Administration.
Again, it is assumed, for the same reason as before,
that the change takes effect in period 3.
The first set of experiments looks at the three
alternative shocks’ impact on cohorts’ welfare under
different payroll tax levels when the economies
start down their respective balanced growth paths.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 6
Effect of Baby Boomers on Factor Prices and Payroll Taxes
.04
Wage (percentage deviation)
.03
Payroll tax (absolute deviation)
.02
D e via t io n
Annualized interest rates
(absolute deviation from benchmark)
.01
0
–.01
–.02
–.03
–5
0
5
10
15
20
25
Cohort b o rn in p e rio d
In particular, this analysis looks at one benchmark
economy with a benefits structure generating a
payroll tax of 12.5 percent, about the same as the
payroll tax in effect in the United States, and another
economy with both benefits and contributions
reduced to three-quarters of the benchmark economy. This second economy is on its long-run balanced growth path and consequently has a higher
capital stock than the benchmark economy. One
could think of this economy as one that partially
privatized social security many periods before and
is now on its balanced growth path with lower social
security benefits and higher private savings.
The results are plotted in Figures 5–9. In both
economies the shocks have an impact on welfare,
mostly negative, but people in the economy with
the lower payroll tax are uniformly better off; that
is, if asked in which economy it would rather live,
every cohort would prefer the one with lower payroll taxes.
Specifically, Figure 5 plots the average consumption for both the benchmark economy and the lowersocial-security economy relative to the benchmark
economy without a shock. In the economy with lower
social security coverage, every cohort is better off
than its respective cohort in the benchmark economy. Cohort-by-cohort lifetime consumption could
lie between 4 percent and 5 percent higher than in
the benchmark economy.
Quite interestingly, in the benchmark economy
not all cohorts are worse off because of the arrival
of the baby boomers. One could say that the parents
of the baby boomers gain about 0.5 percent of average lifetime consumption; the baby boomers themselves lose 1 percent, the children of the boomers
gain substantially, more than 2 percent, and the
biggest losers are the grandchildren of the baby
boomers, who lose more than 2 percent of average
lifetime consumption. The intuition for this result
comes from the general equilibrium structure of the
model, in which factor prices (namely, wages and
interest rates) and payroll taxes must adjust to macroeconomic shocks.
Figure 6 plots the response of factor prices and
payroll taxes to the arrival of the baby-boomer generation. The baby boomers increase the amount of
labor input available in the economy starting in
period 3. Therefore, the parents of the boomers
benefit because their savings yield higher interest
as the amount of labor increases. According to the
11. This outcome, of course, raises the question of why a government has to get into the business of providing risk diversification.
If there really is a diversification gain, a private market could do the same job without causing the distortions of private savings.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
25
FIGURE 7
Lower Productivity Growth: Deviation in Average Consumption Relative to No Shock
0.1
0
–0.1
Benchmark
Pe r c e n t
–0.2
Lower social security
–0.3
–0.4
–0.5
–0.6
–0.7
–15
–10
–5
0
5
10
15
20
25
Coho rt b o rn in p e rio d
simulations, interest rates are higher in this economy
relative to the no-shock economy until period 9,
during which the parents of the baby boomers accumulate the bulk of their savings, and the first couple
of periods of their retirement. The baby boomers
themselves suffer because the larger supply of labor
drives down wages until period 9—for almost as
long as cohorts 3–5 work. At the same time, interest
rates are lower from period 10 on, the start of the
baby boomers’ withdrawal phase.
The children of the baby boomers gain substantially because they benefit from two developments.
First, when they enter the labor force in periods
8–10, the boomers themselves are still working, driving down the payroll tax until period 11 and thus
helping to alleviate the future payroll tax hikes. The
baby boomers also drive up the aggregate capital
stock through their savings, so when they retire
they substantially drive up the wages of their children
during periods 10–15, covering most of the working
years of generations 8–10 and therefore causing
large gains for these cohorts. This result is consistent with Bohn’s (1999) for the same reason. The
relatively small generation of the baby boomers’
children posts a net gain because the factor price
effect is larger than the fiscal effect coming from
higher payroll taxes. By the time the grandchildren
enter the labor force, this positive wage effect has
26
reversed, and payroll taxes are still high, driving down
their average consumption.
This result is intriguing because conventional
wisdom suggests that the post-baby-boomer generations are worse off because they have to pay high
payroll taxes to finance the boomers’ retirement.
The children of the baby boomers, however, post
a net gain because their higher wages make up for
the payroll tax hike. The large losers are the baby
boomers and their grandchildren if general equilibrium effects are taken into account. Notice also that
these results are true in a pure PAYGO system, in
which contribution rates adjust period by period. If
the government were to start a trust fund at the
arrival of the baby-boomer generation, the path of
the payroll tax would be smoothed out. This fund
would even magnify the welfare effects, in particular
for the baby boomers and their children. With a
PAYGO system the lower payroll tax during the
working years of the baby boomers alleviated the
factor price effect. A trust fund would eliminate this
alleviating effect, causing the baby boomers to be hit
even harder. The children of the baby boomers, on
the other hand, who already benefit from the movement in factor prices, would get an additional advantage from the trust fund because part of the burden
of financing the baby boomers’ retirement would
now be financed by the baby boomers themselves.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 8
Lower Population Growth: Deviation in Average Consumption Relative to No Shock
5
4
Lower social security
Pe r c e n t
3
2
1
Benchmark
0
–1
–2
–15
–10
–5
0
5
10
15
20
25
Coho rt b o rn in p e rio d
Figure 7 plots the effect of lower productivity
growth on cohorts’ welfare. All cohorts are uniformly
better off in the economy with lower social security.
All cohorts are negatively affected by the productivity
slowdown, but agents in the economy with lower payroll taxes and higher private savings are shielded
better from the adverse effects of the shock.
Finally, in the economy with lower population
growth plotted in Figure 8, again every cohort is
better off living in an economy with less social security. In addition, the long-run effect in the benchmark economy is more pronounced than in the
economy with less social security; cohorts 15–25
lose about 1.6 percent of average consumption in
the benchmark economy and only 0.8 percent in the
lower-social-security economy. This result comes as
no surprise because the long-run rate of return of
social security is reduced by exactly the drop in the
population growth rate (as demonstrated earlier)
while the rate of return on private savings is not
affected as much in the long run.12 Hence, people
living in an economy with higher social security levels get penalized more by the adverse demographic
shock because their old-age income depends more
on social security, an asset whose return is more
negatively affected by the demographic shock than
private savings are.
Another interesting dimension is the internal rate
of return on both private savings and social security
in the event of a shock. Figure 9 plots those internal
rates of return in the benchmark economy when
productivity growth drops in period 0. As expected,
the drop in internal rates of returns for the first couple of cohorts is higher for private savings than it is
for the social security system. It seems that indeed
the social security system provides a better safety
net from aggregate shocks than private savings do.
However, this result is deceiving because in the long
run the drop in the social security yield is higher,
about 50 basis points, whereas the yield for private
savings recovers for later cohorts and is only about
30 basis points below its original level. In other
words, the relative safety of social security for the
first couple of cohorts comes at the price of future
generations losing a much larger share of their social
security yield.
Policy Issues
hat is the policy relevance of these results?
Evidently, the U.S. economy could not jump
W
12. The reason is that lower population growth indeed lowers the capital returns because fewer workers are alive, but a large
part of the decline is offset by the equilibrium effect of less capital accumulation coming from smaller cohort sizes.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
27
immediately from the regime with high payroll taxes
to the one with low payroll taxes and high private
savings because a large investment would be necessary to build up the higher capital stock of the
latter economy. The analysis shows that, after a partial privatization, in the long run people are better
shielded against aggregate shocks. Less social security indeed makes old-age income more sensitive to
an aggregate shock, but, since the aggregate capital
level is so much higher in the low-payroll-tax economy, this effect is sufficiently cushioned that people
are better off with more private savings. Put differently, a concern about a large aggregate shock many
years from today would be a reason in favor of privatization, not an objection against it.
Consequently, aggregate risk can be an issue in
the privatization debate only over the short horizon
right after privatization occurred, that is, before the
economy reached its new balanced growth path
with higher capital levels. This is the only point at
which social security has any chance to beat private
accounts on welfare grounds—right after the privatization, when the aggregate capital stock is still
low relative to its long-term path and retirees are
exposed to the aggregate shock to a higher degree
if their benefits are lower.
In the second set of experiments the economy is
shocked early on during the privatization, before
the new balanced growth path is reached. The three
shocks outlined earlier are introduced in each of
three new economies, in which the social security
reform in the form of a 25 percent reduction of benefits is introduced in periods 0, –5, and –10, respectively. The aggregate shock thus occurs at various
stages of the reform, namely, at the same time as
the reform, five periods after the reform, and ten
periods after the reform, respectively. The welfare
effects of the reform combined with the shock are
presented in Figures 10–12. The format of these figures is different from that in Figures 5, 7, and 8,
which plot the percentage deviation from a noshock, no-reform economy for the benchmark economy and an economy with lower social security,
each of which experienced a shock. Figures 10–12
plot the percentage deviation in the three reform
economies with a shock relative to a benchmark
economy that also experienced a shock. One could
view Figures 10–12 as Figure 4, where an aggregate
shock occurred at various stages of the privatization
process; that is, a negative number indicates that a
cohort is worse off compared to no reform given
that a shock occurred, and, vice versa, a positive
FIGURE 9
Internal Rates of Return after a Drop in Productivity Growth in Period 0
6
5
Private savings
Pe r ce n t
4
3
2
Social security
1
0
–15
–10
–5
0
5
Coho rt b o rn in p e rio d
28
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
10
15
20
25
FIGURE 10
Baby Boomers in Periods 3–5: Gain of Partial Privatization
6
5
Pe r c e n t
4
3
Reform in period 0
2
Reform in period –5
1
Reform in period –10
0
–1
–15
–10
–5
0
5
10
15
20
25
Cohort b o rn in p e rio d
FIGURE 11
Lower Productivity Growth Starting in Period 0: Gain of Partial Privatization
6
5
4
Reform in period 0
Pe r c en t
3
Reform in period –5
2
Reform in period –10
1
0
–1
–2
–15
–10
–5
0
5
10
15
20
25
Co h o rt
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
29
FIGURE 12
Lower Population Growth Starting in Period 3: Gain of Partial Privatization
6
5
4
Pe r c e n t
Reform in period 0
3
Reform in period –5
2
Reform in period –10
1
0
–1
–15
–10
–5
0
5
10
15
20
25
Co h o rt
number indicates a cohort is better off with privatization relative to no reform.
The welfare effects in this set of experiments
differ from those in the previous sets. Before, every
single cohort was better off with lower social security independent of the shock. Now, there are in fact
cohorts that are worse off—precisely the older
cohorts in the scenarios in which privatization took
place in the current period and five periods ago.
The interesting question is whether the older
cohorts are worse off because of the reform or the
shock. The effects on consumption in Figures 10–12
look strikingly similar to those in Figure 4; if the
reform takes place in period 0, in each case the welfare effects on cohorts –14 to 0 are very similar to the
ones in Figure 4. If the reform occured five or ten
periods ago, then the curves in Figures 10–12 are
close to being shifted by five and ten periods, respectively. Consequently, the welfare effects seem to be
due to the reform, not the shock. In other words, once
privatization is agreed upon, with its consequences on
welfare to the initial old cohorts, adding a shock to the
economy will reduce their welfare even further, but,
quantitatively, this effect is not much larger than it
would have been without the privatization. The benefit of the reform is that future generations, who are
normally hardest hit by the aggregate shock, benefit a
great deal from the privatization.
30
Conclusion
mplementing a social security system seems like
increasing social welfare out of nothing: One generation of initial old agents never has to pay contributions, but they receive benefits. What looks like
the modern version of an alchemist’s dream of turning lead into gold is in fact a rather costly endeavor
for all future generations because the internal rate
of return on their contributions and benefits is
almost certainly lower than that of financial assets.
There is no free lunch after all! Nevertheless, low
returns do not necessarily imply that an asset is
unattractive. In a standard Sharpe (1964) and Lintner
(1965) CAPM model, the attractiveness of an asset
is determined by both the expected return and the
variance-covariance structure. People perceive a
defined-benefits plan such as social security as a
relatively riskless asset.
This article establishes a more cautious view on
this matter. Social security is risky as well, and, even
worse, it is risky for exactly the same reasons that
financial assets are. The determinants of implicit
social security internal returns are productivity and
labor force growth, precisely the same as those for
long-term capital market returns. It is certainly true
that in the event of a negative shock, say, to productivity growth, the internal rates of return on the private savings of living cohorts drop by more than the
I
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
return on social security contributions. In the long
term, however, social security returns take a greater
hit than returns on physical capital. In other words,
the security in pension system returns is deceiving
because it pertains only to current retirees, not to
future ones. This seems to be a general feature of
PAYGO systems: They look attractive to current
cohorts, but future cohorts may suffer substantially.
If an economy with a low payroll tax reaches its
balanced growth path, then all people in that economy are better off than the people in an economy
with higher payroll taxes if an adverse shock hits
the economy. Low payroll taxes encourage more
private savings in the form of a larger aggregate
capital stock, and this cushion of savings ensures
that people are better off than they would otherwise be with a higher payroll tax. This result is true
for all three scenarios computed here. If an aggregate shock occurs during the transition to lower
benefits, certain generations of current retirees and
people about to retire suffer a stronger loss than
they otherwise would under an unchanged PAYGO
system. However, the effect is rather small compared to the welfare loss coming from the reform.
All future generations, on the other hand, in particular those that normally get hit the hardest by
aggregate shocks, benefit greatly from the reform.
Their average consumption can be far higher than it
would be in an economy without privatization if an
adverse shock occurs. Moreover, the longer ago privatization took place, the more likely it is that all
cohorts alive will be better off under privatized
social security. There may be arguments against privatization, but aggregate risk is not one of them.
REFERENCES
Auerbach, Alan, and Lawrence Kotlikoff. 1987. Dynamic
fiscal policy. Cambridge, New York, and Melbourne:
Cambridge University Press.
Biggs, Andrew. 2000. Social security. Is it a crisis that
doesn’t exist? The Cato Project on Social Security
Privatization. SSP No. 21, October.
Bohn, Henning. 1999. Social security and demographic
uncertainty: The risk-sharing properties of alternative
policies. National Bureau of Economic Research Working
Paper 7030, March.
De Nardi, Mariacristina, Selahattin Imrohoroglu, and
Thomas J. Sargent. 1999. Projected U.S. demographics
and social security. Review of Economic Dynamics 2
(July): 575–615.
Diamond, P.A. 1965. National debt in a neoclassical
growth model. American Economic Review 55 (December): 1126–50.
Feldstein, Martin, and Elena Ranguelova. 2001. Individual
risk in an investment-based social security system.
National Bureau of Economic Research Working Paper
8074, January.
Imrohoroglu, Ayse, Selahattin Imrohoroglu, and Douglas
H. Joines. 1995. A life-cycle analysis of social security.
Economic Theory 6 (June): 83–114.
Krueger, Dirk, and Felix Kubler. 2002. Intergenerational
risk sharing via social security when financial markets are
incomplete. Stanford University manuscript, December.
Lintner, John. 1965. The valuation of risky assets and the
selection of risky investments in stock portfolios and
capital budgets. Review of Economics and Statistics 47
(February): 13–37.
President’s Commission to Strengthen Social Security.
2001. Strengthening social security and creating personal
wealth for all Americans. Final report, December.
<www.commtostrengthensocsec.gov/reports/final_report.
pdf> (December 2002).
Reich, Robert B. 1998. The sham of saving social security.
The American Prospect Online. <www.prospect.org/
columns/reich/rr980600.html> (December 2002).
Samuelson, Paul A. 1958. An exact consumption-loan
model of interest with or without the social contrivance of
money. Journal of Political Economy 66 (December):
467–82.
Sharpe, William. 1964. Capital asset prices: A theory of
market equilibrium under conditions of risk. Journal of
Finance 19 (September): 425–42.
Sinn, Hans-Werner. 1999. The crisis in Germany’s pension insurance system and how it can be resolved.
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7304, August.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron.
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Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
31
How Much Do We Really Know
about Growth and Finance?
PAUL WACHTEL
The author is a professor of economics and the Jules Backman Faculty Fellow at
the Stern School of Business at New York University. This paper was presented at a
Federal Reserve Bank of Atlanta conference on finance and growth, November 15,
2002, and at the XI Tor Vergata Conference, University of Rome, December 5, 2002.
An earlier version of some of the ideas in this article appears in Wachtel (2001).
The author thanks Peter Rousseau for invaluable comments and advice.
evelopment economics has changed
profoundly in the course of one generation. Twenty-five years ago the emphasis
among development economists was on
planning and allocation mechanisms,
which separated the development community from the core of mainstream market-oriented
economics. Academicians who followed development
issues were often peripheral to the cutting edge in
the economics literature. However, that situation has
changed in recent years, and development issues are
now at the forefront. As part of this transformation,
the term “development” (which connotes a directed
process) has been largely replaced by the term
“emerging markets.” The very term emphasizes the
private sector and the market-oriented paradigm of
contemporary economics. In no other area is the
change in thinking more striking than in the analysis
of the role of the financial sector—banks and capital
markets—in the development process.
The modern literature on economic growth starts
with Robert Solow’s work in the mid-1950s, for
which he was awarded the Nobel Memorial Prize in
Economics. The early theoretical and empirical
literature focused on the role of capital and labor
resources and the use of technology as the sources
of growth. For the most part, any possible role of
the financial sector in the growth process was
ignored. In fact, development economists up until
the 1970s often advocated explicit manipulation of
D
the financial sector in order to achieve development
goals. Credit subsidies to favored activities were the
rule rather than the exception. Inflation was attractive since a tax on financial assets gave governments
with an otherwise weak tax base resources that could
be devoted to development projects.
Nevertheless, a few influential economists began
to draw attention to the contribution of the financial
structure to growth and the benefits of liberalization
(in particular, Goldsmith 1969 and McKinnon 1973).
Economists slowly acknowledged that credit allocation, interest rates ceilings, and high reserve
requirements were undesirable. Generally, high
inflation, negative real rates, and inflation taxes
create distortions that lead to extensive resource
misallocations and discourage saving and the use
of intermediaries. The pejorative term “financial
repression” was introduced to refer to restrictive
policies that inhibited the operation of the financial
sector. In 1993 McKinnon could write with confidence that “Now, however, there is widespread
agreement that flows of saving and investment
should be voluntary and significantly decentralized
in an open capital market at close to equilibrium
interest rates” (12). However, he characterizes the
path toward liberalization as a minefield where one
misstep might be the last.
There has been a major shift toward a marketoriented approach to the financial sector over the
past twenty-five years. Although capital controls
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
33
prevailed around the world in both developed and
less developed economies, there have been significant liberalizations in recent years.1 Today,
countries that maintain capital controls are almost
self-conscious pariahs in the international community. Liberalization of domestic financial markets
has occurred at a somewhat slower pace. Nevertheless, support for directed credit, interest rate
ceilings, and government ownership of financial
institutions has also disappeared. The prevailing
paradigm is that competitive private sector capital
markets should be able to gather savings at market
rates of interest and allocate capital to the most efficient private sector projects.
There are severe limitations to what we know.
The empirical literature has not yet adequately
explained what happens when the financial
sector deepens and how that deepening
affects behavior and economic growth.
The contemporary paradigm hardly needs restatement. Economists now take it for granted that a
well-developed, market-oriented financial sector
contributes to economic growth. However, it is curious how little solid evidence there is that relates the
financial sector to economic growth and stability.
The paradigm of financial liberalization was widely
accepted before there was evidence to relate it to
economic growth.
Only recently, since the early 1990s, has a large
body of empirical knowledge accumulated that
relates financial sector development—the depth
and activity of financial intermediaries—to growth.
An impressive array of econometric techniques has
been used to show the robustness of the financegrowth relationship. However, it is now time to pause
and take stock and ask what this literature has
taught us.
This article will briefly describe the approach to
assessing the finance-growth relationship that has
become virtually standard. The literature provides
some important results that relate different dimensions of financial sector development to economic
growth. The observed relationships appear convincingly to be causal, from finance to growth, and not
an artifact of simultaneity or reverse causality.
However, with all that said, there are severe limitations to what we know. The empirical literature
34
has not yet adequately explained what happens
when the financial sector deepens and how that
deepening affects behavior and economic growth.
There is convincing evidence that countries with
money-to-GDP (gross domestic product) ratios of
over 100 percent grow more rapidly than those with
ratios of 20 percent. However, no good explanation
exists of what happens when financial deepening
occurs that causes growth. Thus, it is not easy to
provide advice to a country with a weakly developed financial sector. The specific mechanisms that
relate financial sector deepening to changes in the
behavior of economic agents are still a mystery.
Although the finance-growth link is part of the
liberal consensus in modern economics, there are
still some detractors. Not everyone shares the same
degree of confidence in the consensus conclusions.
Economists as disparate as Joan Robinson and
Robert Lucas have expressed doubts about the
link.2 More importantly, a number of authors have
been less enthusiastic about the strength of the
empirical consensus. There seem to be differences
in temperament on either side of the Atlantic. The
Americans (Levine, Barro, myself, and others)
exhibit unbounded enthusiasm about the strength
of the relationship. The Europeans (Temple and
Arestis, among others) are much more cautious and
give more emphasis to the variability of the effects
and the lack of robustness in some studies. It might
well be time to temper some of the enthusiasm with
an examination of the skeptics.
There is an interesting analogy to this problem in
the short-run macroeconomics literature. Monetarist
empirical research in the 1960s and 1970s provided
an impressive and convincing body of evidence for
the influence of money on inflation and output. The
econometric evidence about the direction of causality was convincing, and the description of lags in the
effects is widely accepted. However, by the 1990s it
was clear that our understanding was limited. We
knew that money affected inflation but not how
money did so; there was a mysterious and unknown
“black box” that related money and inflation.
Research began to investigate the “transmission
mechanism” or the channels of influence that relate
money to the economy. Empirical investigations of
money and price aggregates are no longer in vogue
and have been replaced by efforts to use micro data
to illustrate particular channels of transmission.
The finance-growth literature is at the same
crossroads. Aggregate investigations will soon be
going out of style. In fact, empirical efforts to
describe specific channels of interest have already
begun to appear.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
The discussion will first consider the consensus
paradigm and selectively summarize the evidence
on the aggregate relationships. The focus then turns
to concerns about the strength of the econometric
evidence. Finally, the newer developments in the
literature—efforts to investigate the finance-growth
transmission mechanism with disaggregated data—
will be discussed.
Why Are Finance and Growth Related?
he financial sector is important because the
financial intermediaries are responsible for
resource allocation. Well-working financial intermediaries improve the efficiency of capital allocation,
encourage savings, and lead to more capital formation. King and Levine (1993b) were among the first
to emphasize that the efficiency-enhancing aspect of
financial sector development is more important than
the impact on the amount of investment. The financial sector’s impact on the allocation of resources
cannot be overemphasized. Think of countries with
high rates of investment and savings and poor
growth experience. The Soviet Union always had
high savings rates; there was always an abundance
of machinery and equipment, which simply was not
allocated to effective uses. Generally speaking,
countries with higher investment-to-GDP ratios
experience higher growth rates, but the evidence is
not overwhelming. The simple correlation of investment ratios and subsequent growth rates was 0.43 in
the 1980s and 0.24 in the 1990s.3 There is substantial variation in growth rates among countries with
similar investment ratios. Countries with similar
levels of capital investment can have widely diverse
growth experiences. The ability to allocate investments efficiently—the role of the financial services
industry—might be responsible for the differences.
In the process of providing payments and intermediary services, the financial industry promotes
the efficient allocation of resources. There are at
least four ways in which the financial sector contributes to growth. They are described in the surveys
T
by Pagano (1993) and Levine (1997) and presented
as a rationale for the endogenous growth model in
King and Levine (1993b). First, the financial sector
improves the screening of fund seekers and the
monitoring of the recipients of funds, and these activities improve the allocation of resources. Second,
the industry encourages the mobilization of savings
by providing attractive instruments and savings
vehicles. Such encouragement may also increase
the savings rate. Third, economies of scale in financial institutions lower costs of project evaluation
and origination and facilitate the monitoring of projects through corporate governance. Finally, financial intermediaries provide opportunities for risk
management and liquidity. They promote the development of markets and instruments with attractive
characteristics that enable risk sharing.
Broadly speaking, the role of the financial sector
in all economies is to channel resources from savers
to investment projects. In planned economies, the
process is conducted by administrative arrangements with few, if any, market-oriented elements of
the financial sector. Emerging market economies
will often rely on a single institution—the banking
sector—to provide intermediary functions. In contrast, modern economies have a wide range of marketoriented institutions for facilitating intermediation.
A successful financial sector will have a broad
continuum of financing techniques that channel
resources to investment opportunities. The effect of
entrepreneurial finance—self financing, informal
funding, etc.—on growth is not well explored
because there is little data. Nevertheless, the role of
venture capital financing is an area of considerable
research interest in the United States. More is
known about bank financing, and many countries
have bank-dominated financial sectors. Capital markets are rudimentary in many countries, including
some highly developed ones. There continues to be
considerable debate concerning the relative merits
of bank-dominated financial sectors and those that
give equal weight to capital markets.4
1. The International Monetary Fund (IMF) reports large numbers of countries taking measures to liberalize capital flows while
the number of tightening measures has declined (IMF 1999, chap. 3).
2. Lucas (1988) suggests that the role of finance is overemphasized, and Robinson (1962, 80) argues that “enterprise leads,
finance follows.”
3. Average investment-to-GDP ratios for 1979–83 and 1988–92 are compared to growth in 1980–88 and 1989–98, respectively.
GDP growth is real per capita; GDP is converted to dollars using purchasing power parity exchange rates and corrected for
U.S. inflation. Investment is gross domestic investment. There are eighty-seven countries with available data and a population of at least 2 million. Data are from the World Bank (2000).
4. The differences between Anglo-Saxon bank–dominated and European capital–dominated systems have been diminishing in
recent years as a result of globalization and technological and regulatory changes. One of the consequences of European unification is the increased importance of capital markets on the continent. In the United States, regulatory changes virtually
allow continental-style universal banking in which banks are involved in the entire spectrum of financing.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
35
The Evidence on Financial Sector
Development and Growth
mpirical investigations of the relationship
between financial sector development and economic growth began to appear in the 1990s with King
and Levine’s (1993a, b) cross-country studies for the
postwar period and Wachtel and Rousseau’s (1995)
evidence from long-time series for several countries.
These studies showed that the depth of financial
sector development and greater provision of financial intermediary services are associated with economic growth. In the decade since those studies
appeared, there has been a veritable explosion of
empirical interest in the finance-growth relationship.
E
Broadly speaking, the role of the financial
sector in all economies is to channel resources
from savers to investment projects.
tiles by real GDP per capita. The four measures of
financial sector development are the ratios of
• liquid liabilities of the financial system to GDP,
• bank credit to bank and central bank credit,
• claims on the nonfinancial private sector to total
domestic credit, and
• gross claims on the private sector to GDP.
The relationships are clear: Richer countries
have more developed intermediaries, and marketbased private sector institutions are more important than in poorer countries. Financial intermediary
liabilities are over two-thirds of GDP in very rich
countries and about half as much in below-medianincome countries. Central banks allocate as much
credit as commercial banks in countries with belowmedian income while they are only about one-tenth
as large in the very rich countries. Almost threequarters of credit is extended to the private sector
in the richest countries, almost twice the percentage
in the poorest countries.
The Standard Empirical Framework
his section presents the regression framework
for panel data that has become the standard
form.5 Results from Rousseau and Wachtel (2000,
2001, 2002) are used to illustrate the empirical consensus concerning the relationship between growth
and financial depth and to illustrate some of the
drawbacks. Econometric investigations with panel
data use a regression specification given by
T
Furthermore, the research has been extensively
surveyed elsewhere starting with Levine (1997) and
more recently in Theil (2001).
The first cross-county study of growth and financial development was Goldsmith (1969), which
introduced the idea of using a broad measure of
the size of financial intermediaries (his specific
choice was the value of intermediary assets to
GDP) as an indicator of the provision of intermediary services. Looking at decade averages for
thirty-five countries for about one hundred years,
he found broad indications of a relationship
between finance and growth. Goldsmith’s work
was econometrically unsophisticated and did not
seem to spur much research interest at that time.
More extensive econometric work was needed to
(1) hold constant other determinants of growth
and (2) identify the direction of causality.
Barro (1991) and King and Levine (1993a, b)
introduced growth studies with cross-country data
sets for the postwar period that have become the
benchmark for other studies. Their empirical specifications are widely used. King and Levine included
measures of intermediary activity developed from
IMF and World Bank data sources that are available
for a large number of countries. Table 1, reproduced
from Levine (1997, 705), shows values for the indicators in 1985 for 116 countries divided into quar36
Xit = αFit + βZit + uit .
Xit is the growth of per capita real GDP or of the real
capital stock or a measure of total factor productivity
growth in the ith country for some time period, t.
Zit is a standard set of conditioning variables that
usually includes the log of initial real GDP per capita
(a convergence effect) and the log of the initial secondary school enrollment rate (human capital investment). Additional conditioning variables may include
the ratio of government consumption to GDP (measure of private sector activity), the inflation rate,
a black market exchange rate premium, or the ratio
of exports plus imports to GDP (a measure of openness of the economy), among others. Finally, Fit is
one of the measures of financial sector development.
There are two econometric problems with
regressions of this type. First, there may be simultaneity or reverse causality between the finance
variable, F, and economic growth, X. Simply speaking, growing countries might have well-developed
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
TABLE 1
Aggregate Measures of Financial Development for 116 Countries, 1985
Depth
Bank
Private
Privy
Real GDP per capita (1987 $)
Very rich
Rich
Poor
Very poor
0.67
0.91
0.71
0.53
13,053
0.51
0.73
0.58
0.31
2,376
0.39
0.57
0.47
0.20
754
0.26
0.52
0.37
0.13
241
Correlation with
real per capita GDP
.51
.58
.51
.70
Note: “Depth” is the ratio of liquid liabilities of the financial system (currency plus demand and interest-bearing accounts of banks and nonbank intermediaries) to GDP. “Bank” is the ratio of bank credit (domestic deposit money banks) to bank credit plus central bank credit.
“Private” is claims on the nonfinancial private sector to total domestic credit. “Privy” is gross claims on private sector to GDP.
Source: Derived from Levine (1997)
financial sectors because the income elasticity of
the demand for financial services is large. That is,
wealthy people demand banking services. Second,
the regression specification assumes that any unobserved country-specific effects are part of the error
term. Thus, correlation between the error term and
included variables in F or X is likely, which leads to
biased estimation of the regression coefficients.
Modern econometrics offers a number of approaches
to solving these problems.
To deal with simultaneity, researchers have used
predetermined (initial) values for the independent
variables or instrumental variable estimation. Since
the underlying relationship is a long-run one, the time
period for observations is often set as a five- or tenyear period. To avoid simultaneity, the independent
variables are then measured as the initial (first-year)
values of the observation period. For example, if X
is the average growth rate for 1960–65, then F and
Z are the 1960 values for the respective variables.
More recent studies by Levine, Loayza, and Beck
(2000) and Rousseau and Wachtel (2000) have
introduced the use of instrumental variables to ameliorate the effects of simultaneity between F and X.
Typically, the instruments are initial values of the
regressors and perhaps some contemporaneous
indicators not included as regressors such as the
inflation rate and relative size of the government
sector and the degree of openness.
Rousseau and Wachtel (2000) argue that neither
of these approaches does an adequate job of solving
the simultaneity problem. In that study, the pre-
determined components of the F measures remain
correlated with the contemporaneous measures. In
addition, the X measures tend to be serially correlated. Thus, the techniques described do not remove
all doubt of causality from X to F.
Techniques for examining dynamic interactions
among variables have long been available for time
series where extensive data series are available.
Vector autoregression (VAR) is a widely used technique for looking at causality from lagged F to current X and vice versa. Wachtel and Rousseau (1995)
and Rousseau and Wachtel (1998), among others,
have applied VAR to the handful of countries with
adequate data for very long periods of time. The
results are consistent with the cross-country data
analyses for the postwar period.6
Panel VARs with a large number of cross-country
observations and relatively few time series observations can be estimated with recently developed
econometric techniques (see Holtz-Eakin, Newey,
and Rosen 1988; Arellano and Bond 1991). Rousseau
and Wachtel (2000) implement the technique to
estimate panel VARs with annual data and develop
Granger causality tests. Beck, Levine, and Loayza
(2000) and Levine, Loayza, and Beck (2000) also
find that measures of financial sector development
have a significant causal effect on growth in panel
VAR estimates.
The second econometric problem noted above
was the estimation bias introduced in any panel
estimation from unobserved country-specific influences. One way of dealing with this is to include
5. There is some literature that utilizes somewhat different frameworks to address some of the same issues, such as the work
done for the Organisation for Economic Co-operation and Development (OECD) growth project (see Leahy et al. 2001) and
Graff and Karmann (2001).
6. Both Arestis and Demetriades (1997) and Rousseau (2002) compare time series and cross-section approaches. Arestis is
skeptical of cross-country results because of the differences among countries in time series results. Rousseau finds the different approaches to be consistent.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
37
country-fixed effects (dummy variables) in all estimated equations. However, the colinearity between
the fixed effects and the phenomenon under investigation leads to very imprecise and unstable coefficient estimates. A measure of the financial structure
such as the ratio of credit to GDP varies considerably among countries but changes slowly over time
in any given country. Thus, the country-fixed effects
explain much of the panel variation in the financial
structure variable. The sensitivity of the standard
specification to the inclusion of country-fixed effects
will be demonstrated below. Although many econometricians would argue in favor of such countryfixed effects, most analysts reject this approach or
Countries with better creditor rights, rigorous
enforcement, and better accounting information tend to have more highly developed
financial intermediaries.
the simple solution of differencing the data on practical grounds. However, the Arellano-Bond estimator
ameliorates the country-specific effects by differencing a VAR specification in levels of the data and
leads to better estimates.
A Summary of the Evidence on Financial
Depth and Growth
espite the formidable econometric problems, a
wide body of literature has firmly established a
consensus in support of a relationship between financial sector development and economic growth. Several
studies by Rousseau and Wachtel will illustrate both
the approaches taken and the results established.
Rousseau and Wachtel (2000) examine the ratio of
the broad money supply to GDP with panel data that
include two eight-year average observations for fortyseven countries. Similarly, Rousseau and Wachtel
(2001) use seven five-year averages (1960–95) for
eighty-four countries. These studies present results
with panel data sets using instrumental variables.
The first paper also presents panel VAR models with
forty-seven countries and sixteen annual observations, estimated with an application of the Arellano
and Bond procedures.
The ratio of broad money to GDP averages about
40 percent; it is larger in countries where the depository institutions are more actively intermediating
D
38
between savers and investors, and it is smaller where
the banks do little more than provide transactions
services. The Rousseau and Wachtel results indicate
that an exogenous increase in the ratio of 10 percentage points (increasing the activity and depth
of the depository institutions) will, particularly in
countries without high inflation, increase the rate
of growth by between 0.6 and 1 percentage point a
year. Over a five-year period, real output would be
between 3 and 5 percent higher.
To address the issue of causality more directly,
we estimate VAR systems with the same data using
the Arellano and Bond approach. We find evidence
of significant causality from financial measures to
real GDP and no evidence of feedback from GDP to
the financial variables. These estimates indicate
that an increase in M3 that raises its average share
in output by 10 percentage points would raise output per capita over five years by 4.1 percent, or 0.8
percent per year. Interestingly, the results from the
two approaches—panel regressions and panel VAR—
are remarkably alike.
A change in the ratio of M3/GDP of 10 percentage points is quite large. For any given country, the
ratio is serially correlated and trends occur slowly.
However, there is a great deal of variation among
countries at different stages of financial development, and at any given time the distribution of the
ratio across countries is quite diffuse. In 1987, the
ratio is less than 40 percent in 38 percent of the
countries, between 40 and 60 percent in 34 percent
of the countries, and over 60 percent in 38 percent.7
Thus, an increase of 10 percentage points is not
unreasonable for a country experiencing financial
sector deepening. Both the VAR and panel results
indicate that such a change would have profound
effects on growth.
The results in Beck, Levine, and Loayza (2000),
which extend Levine’s earlier work and also introduce panel estimation, are very similar to those in
Rousseau and Wachtel (2000). This paper introduces
an improved measure of financial sector development—the ratio to GDP of credits from financial
intermediaries to the private sector from a World
Bank data set. This measure excludes credits from
the central bank and government and credits
among financial intermediaries. The researchers
estimate a variant of the now-standard specification
with data for seventy-seven countries for 1960–95
in two ways. First, they estimate a cross-section
regression with instrumental variables (using thirtyfive-year average data). Second, they estimate a
panel of five-year averages using the Blundell and
Bond (1998) modification of the Arellano and Bond
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
TABLE 2
Equity Markets, Financial Depth, and Growth: Summary of Panel Regression and VAR Estimates
Country mean
Effect on growth rate of a
10 percentage point increase
(five-year horizon)
Ratio to GDP of
1987
1995
Panel regression
VAR model
Liquid liabilities (M3)
Market capitalization
Total value traded
58.73
29.12
10.75
65.11
24.22
0.15
0.08
0.52
0.8
0.4
1.0
Source: Calculated from Rousseau and Wachtel (2000)
technique called the systems estimator, which
allows information in the levels of the variables to
be retained in the procedure rather than be swept
away through differencing.
When initial income and average years of schooling are the only conditioning variables, both estimation procedures give very similar results. An increase
of the private credit-to-GDP ratio of 10 percentage
points from its mean of 27.5 percent results in an
increase in the annual growth rate of 0.69 percent
with the cross-section and 0.74 percent with the
panel. When a broader set of conditioning variables is
used, the estimates vary between 0.5 and 1 percent.
The Role of Equity Markets
quity markets are always of interest because
data on equity market activity around the world
are available and because the stock market—Wall
Street—always attracts attention as the paramount
symbol of capitalism. Studies of the finance-growth
relationship with aggregate credit measures were
quickly followed by studies of the influence of the
equity market on growth.
Banks dominate financing in many places and
even in the most advanced industrialized countries;
equity markets are only a small part of the overall
financial markets. Most new investment is funded
either internally by firms, through banks and other
intermediaries, or directly through bond markets.
New issuance of stock is never a large fraction of
total sources of funds. Nevertheless, the existence
of a stock market is important even when equity
issuance is a relatively minor source of funds.
Why is the existence of a stock market so important? First, an equity market provides investors and
entrepreneurs with a potential exit mechanism.
Second, capital inflows—both foreign direct investment and portfolio investments—are potentially
important sources of investment funds for emerging
E
market and transition economies. Third, the provision of liquidity through organized exchanges
encourages both international and domestic
investors to transfer their surpluses from shortterm assets to the long-term capital market, where
the funds can provide access to permanent capital
for firms to finance large, indivisible projects that
enjoy substantive scale economies. Fourth, the
existence of a stock market provides important
information that improves the efficiency of financial
intermediation generally. Finally, the valuation of
company assets by the stock market provides
benchmarks for the value of business assets, which
can be helpful to other businesses and investors,
thereby improving the depth and efficiency of company assets generally.
Atje and Jovanovic (1993) construct a crosscountry panel for the 1980s and show that trading
volume has a strong influence on growth after controlling for lagged investment while bank credit
does not. Demirguc-Kunt and Levine (1996) provide
a descriptive investigation. Levine and Zervos (1996,
1998) introduce equity market measures to the standard growth-finance cross-section specifications
discussed earlier. Finally, a more comprehensive
effort to examine the dynamic relationships is found
in Rousseau and Wachtel (2000).
The Rousseau and Wachtel paper uses two measures of stock market development as financial sector indicators in the panel regressions: the ratio of
market capitalization to GDP and the ratio of total
value traded to GDP. Both have a positive coefficient,
but only the latter is significant at the 1 percent
level. The study also uses a VAR model to examine
causality and dynamic interactions among growth, a
measure of financial intermediation, and a stock
market indicator. Table 2 summarizes the results of
panel equations with alternative measures of financial sector development.
7. This result is based on the sample of forty-six countries with active equity markets.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
39
The results indicate that the development of a liquid and highly capitalized equity market increases
growth. The mean ratio of value traded to GDP was
just 10 percent in 1987; the panel regression results
indicate that an increase in the ratio of 10 percentage
points would add 0.5 percent to the growth rate.
Similarly, a 10 percentage point increase in the ratio
of M3 to GDP (with a 1987 mean of 59 percent) would
increase the growth rate by 0.15 percent. The equity
market effects are similar in magnitude to the effect
of more developed financial intermediaries.
mediaries. Thus, growth prospects are enhanced
because a sound legal environment encourages the
development of financial intermediation.
The analysis has already shown that “more banking”—a larger ratio of bank liabilities to GDP—is an
important correlate of economic growth. Further
investigation examines the type of banking activity,
the environment in which it is conducted, and by
whom it is conducted. Results indicate that the
following banking industry characteristics may be
related to growth and stability:
Other Financial Sector Characteristics
• more competitive and less concentrated banking
industry,
• more private as opposed to government ownership or control, and
• more foreign participation in banking.
R
esearch efforts so far have not examined the
impact of other financial markets or instruments
There are systematic differences in the
finance-growth relationship among countries
with different characteristics. For example,
the evidence of finance effects is not as
strong among developed countries as it is
among less developed countries.
on economic growth in a similar cross-country framework. A major reason for this dearth of research is
that data on other types of financial intermediaries
(for example, private placements, venture capital,
bond issuance, commercial paper, etc.) are not part
of any standardized data collection efforts and are
often simply not available. Furthermore, the number
of countries with these other instruments and markets
is not large. Although banks and related intermediaries
are found everywhere and equity markets are found
in most places, bond markets, commercial paper, organized venture capital industry, and so on are quite rare.
There is a body of work that focuses on the relationship between economic growth and the quality of
the financial sector environment. For example,
important elements of this environment that might
effect growth include clear and universally applied
accounting standards and auditing practices and a
legal framework for debtor-creditor relationships. The
effect of accounting, bankruptcy, and governance
standards and procedures on growth and on financial
sector development has been recently examined with
the standard cross-country framework by Levine,
Loayza, and Beck (2000). Among other things, they
find that countries with better creditor rights, rigorous enforcement, and better accounting information
tend to have more highly developed financial inter40
For example, La Porta, Lopez-de-Silanes, and
Shleifer (2002) examine the effect of bank ownership
on economic growth with the standard panel framework introduced earlier. They consistently find that
higher initial government bank ownership has a
negative impact on real per capita growth rates. A
10 percentage point increase in the proportions of
assets of the largest banks owned by the government
is associated with a decline in the annual growth rate
of about 0.2 percent. These preliminary regressions
do not address all of the econometric problems, but
the overall thrust of these results will probably
withstand a more careful empirical investigation.
Several recent papers relate the legal environment for the financial sector to economic growth.
Part of the motivation for these inquiries is econometric. The origins of the legal system (for example,
English common law or French civil law) are a completely exogenous variable determined by accidents
of history (and colonialism). However, the legal systems have different approaches to creditor-debtor
relationships that could be relevant to the performance of the financial system and, thus, economic
growth (La Porta et al. 1998; Levine 1999). The
exogenous characteristics (legal origins) can be used
as instruments to improve econometric estimates of
the basic finance-growth relationships.
A related issue addressed by Levine (2002) is
whether bank-dominated (the German model) or
market-dominated (the Anglo-Saxon model) financial systems generate better growth performances.
He finds that the quantity of financial services is
more important than the structure of the industry
that provides them. Convergence of financial systems around the world will probably make this specific question moot over time.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 1
Finance and Growth: Hypothetical Data
Growth rate
Country 2
Country 1
Financial depth
Drawbacks of the Standard Approach
he standard results seem to be very robust. The
papers by Rousseau and Wachtel are consistent
across techniques and data sets and are also consistent with the large body of work by Levine and
various coauthors. Moreover, the results that relate
growth to equity markets, banking sector structure, and the characteristics of the financial system
strengthen the conclusions. Nevertheless, not everyone is convinced by these results. Although I think
that the research results are convincing, there are
still issues to look at and concerns to note. We
should hesitate to declare victory.
Specifically, there are two questions I would like to
pose. The first is whether the standard approach does
an adequate job in controlling for country-specific
effects. The second is whether the estimates of
finance effects are robust or vary with other observed
phenomena. These questions have come up before in
regard to the growth literature in general (Temple
1999; Durlauf 2001; Kenny and Williams 2001). These
authors argue that since the relationship between
growth theory and empirical specifications is often
tenuous, it is not surprising that many empirical
results are sensitive to changes in specification.
My concern about the adequacy of efforts to hold
country-specific effects constant is illustrated in
Figure 1. If observations for growth and financial sector development are clustered by country, as shown
in the figure, panel regressions could indicate a spurious aggregate relationship. The observed finance-
T
growth relationship is due to between-country differences rather than within-country differences over
time. In this case, regression results would not provide any reason to make inferences about the effects
of financial deepening on growth.
This issue is further investigated with the regressions shown in Table 3. A standard panel specification is shown (with the panel data set from
Rousseau and Wachtel 2001). The first equation is
estimated by ordinary least squares (OLS), and the
independent variables are all initial values (value for
the first year of each five-year period). Estimates
are indistinguishable from the second equation that
uses contemporaneous values for the government
and liquid liabilities variables and estimates the
equation with instrumental variables. The choice of
technique to correct for simultaneity is immaterial.
Simultaneity bias does not seem to be an issue.
However, both of these equations include fixed
effects for time periods but not for countries. The
equation in the last column adds country-fixed
effects to the equation. The introduction of countryfixed effects has a profound effect on the results.
The fixed effects dominate the equation; the proportion of variance explained almost doubles, and
some of the coefficients have the wrong sign. The
finance effect is still positive, but the coefficient is
very small and barely one-tenth of a standard error
from zero. Figure 2 shows the strong relationship
between the fixed effect coefficients and the average
ratio of liquid liabilities to GDP. The between-country
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
41
TABLE 3
Panel Estimates for Five-Year Average Real per Capita GDP Growth
Constant
Log of initial real GDP
Log initial secondary school enrollment
Government expenditure to GDP
Liquid liabilities to GDP
Fixed effects
Corrected R2
OLS with
initial values
Instrumental
variables
–0.726 (1.0)
–0.203 (1.5)
0.841 (3.7)
–0.060 (2.6)
0.027 (4.7)
Time periods
–0.743 (1.0)
–0.199 (1.5)
0.819 (3.7)
–0.063 (2.5)
0.028 (5.0)
Time periods
.233
.247
OLS with initial values
and country-fixed effects
–3.447 (5.4)
–1.715 (3.7)
–0.081 (2.3)
0.001 (0.1)
Time periods
and countries
.440
Note: Absolute values of t-statistics are shown in parentheses.
Source: Panel with 426 observations from Rousseau and Wachtel (2001) for 80 countries, 1960–95.
differences in the finance ratios are more important
than the differences over time, and thus the fixed
country effects and the finance ratios convey largely
the same information. Although financial depth measures exhibit much short-run or cyclical volatility,
development of financial systems evolves slowly.
Data that span less than forty years may not reflect
much long-run change in the financial system.
The devastating impact of fixed (country) effects
on the estimates of a growth equation has been
shown with a different panel specification by
Benhabib and Spiegel (2000). They also show that
adding fixed effects leads to coefficient instability
and a loss of significance on the financial depth
measures. Although they recognize this result, they
seem reluctant to question the popular consensus
that finance matters.
Proponents of the standard growth rate equation
would argue that the specification does not call for
country-fixed effects. The equation is derived from
a production function relationship, so the countryspecific unobserved effects disappear with the differencing. But the fact that they enter the equation
significantly suggests that the country effects persist. It appears that the standard set of regressors
does not provide an adequate framework for making inferences about the change in financial depth
on growth from cross-country comparisons.
As noted earlier, there are some skeptics in the
growth literature, mostly Europeans who are worried
about a possible lack of robustness among empirical
results. Kenny and Williams (2001) provide a scathing
critique of the empirical growth literature (without
any reference to the role of finance). In their view
there is little consensus or robustness and most models are overly simple. A formal econometric investigation of robustness issues is found in Florax, de
Groot, and Heijungs (2002).
42
However, this issue highlights the importance of
the recent papers with panel VAR estimates that
remove the country-fixed effects by differencing
and exploit the time series variation more fully.
Nevertheless, there are several papers that are concerned with the robustness of VAR results. For
example, Luintel and Khan (1999) find some evidence of bidirectional causality between financial
sector development and growth in a VAR analysis of
developing countries. Similar problems are noted by
Shan, Morris, and Sun (2001) in VAR analyses of the
OECD countries.
There are systematic differences in the financegrowth relationship among countries with different
characteristics. For example, the evidence of finance
effects is not as strong among developed countries
as it is among less developed countries. In addition,
the finance effect varies systematically with a country’s inflation experiences (Rousseau and Wachtel
2001, 2002). These two studies find that the impact
of financial deepening on growth disappears when
inflation is high. This result would not be surprising
with hyperinflation that erodes the value of financial intermediation. However, the results indicate
that above a threshold inflation rate between 13 and
25 percent, financial deepening ceases to increase
economic growth.
Estimation issues aside, there are at least two reasons why the consensus model is only the first stage of
an important research agenda. First, even the refined
measure of financial depth introduced by Levine,
Loayza, and Beck provides a highly aggregated picture. There is wide variation in these financial sector
ratios that is hard to understand. For example, the
1987 ratio of M3 to GDP is 73 percent in Spain and
51 percent in Sweden. Does this difference reflect
more advanced financial sector development in Spain
or greater reliance on bank-based financing? Second,
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 2
Fixed Effects and Average Ratio of M3 to GDP for Eighty Countries
60
55
50
F ix e d e ffe c t s
45
40
35
30
25
20
0
25
50
75
100
125
150
175
A ver ag e M3/GDP (p e rc e n t)
Source: Calculated from the regression in the last column of Table 3.
a thrust of the earlier discussion was the variety
of financial sector institutions and activities that
contribute to efficient intermediation. The aggregate
measures mask a rich and diverse set of activities and
reveal little about how intermediation affects growth.
The Next Stage
eturn for a moment to the analogy with the
macro literature on monetary policy effects. The
St. Louis model developed in the late 1960s was a
standard reduced form that related money growth to
output growth and inflation. Later research debated
the stability and robustness of the relationship. Today
hardly anyone pays attention to the St. Louis model
specification. However, it played an important role
in the development of monetary economics. Its reliability and usefulness aside, it established the consensus view of the impact of monetary shocks on
the economy and set the scene for the next generation of research, which looks inside the black box
and tries to explain the transmission mechanism for
monetary policy.
The finance-growth empirical literature is in
the midst of a similar development. The standard
reduced-form equations might not be as robust as
originally thought, and their predictive value for
explaining the effects of financial deepening is lim-
R
ited. However, the research agenda of the 1990s firmly
established the consensus view that finance matters
and set the scene for the nest stage of research. Now
it is time to look into the black box and develop
empirical studies that shed light on the way in which
financial sector development improves intermediation and generates economic growth.
The next stage has already begun with a few
studies that exploit industry data to better understand how financial sector development works. Rajan
and Zingales (1998) were among the first to exploit
industry data to gain an understanding about the
finance-growth relationship. A well-developed financial system removes or reduces the barriers to external financing for firms. Moreover, some industries
tend to depend on external financing more than
others because of differences in cash flow patterns,
capital intensity, profit margins, and so forth. As a
consequence, industries that are more dependent
on external financing should do better in countries
with better financial systems. Industry data for a
number of countries gives Rajan and Zingales the
opportunity to test this hypothesis. They examine
data for forty-one countries during the 1980s. Their
results support the hypothesis.
The innovative use of industry data opens the
door toward more specific analysis of finance effects
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
43
on growth. The Rajan and Zingales paper is important for this reason although it makes a number of
rigid assumptions. In particular, it uses U.S. experience to determine which industries are heavy users
of external finance and assumes that these patterns
hold elsewhere. Fisman and Love (2002) take issue
with this assumption and provide a different interpretation. They are concerned that the Rajan and
Zingales results imply that countries with poorly
developed financial markets should concentrate on
industries that rely on internal financing. Instead
Fisman and Love provide support for the hypothesis that finance allows firms to respond to growth
opportunities. Industry growth rates across coun-
Although deeper financial intermediation may
be a significant causal factor in economic
growth, one cannot infer that every expansion
of intermediary activity will be beneficial.
tries are more highly correlated when the countries
both have well-developed financial sectors. Thus,
financial sector development enables industries to
take advantage of global growth opportunities.
Cetorelli and Gambera (2001) extend this analysis by examining the effect of bank concentration on
industries that rely on external finance. They find,
paradoxically, that higher concentration in the banking industry is associated with more growth in industries that require more external finance. However,
they also find an across-the-board depressing effect
of concentration on growth. All in all, these studies
provide specific illustrations of how financial sector
development improves allocative efficiency by channeling financial resources.
Wurgler (2000) makes another important step in
this literature with an effort to measure the relationship between allocative efficiency and financial
sector development. He estimates the efficiency
of capital allocation by the elasticity of industry
investment to value added across industries in a
given country. A higher elasticity indicates the extent
to which a country is increasing investment in its
growing industries. Using panel data for as many as
twenty-eight industries (and up to thirty-two years
of data), he obtains elasticity estimates for sixty-five
countries. The highest elasticities are in Germany,
Hong Kong, and New Zealand, and the lowest in
44
Bolivia and Swaziland; the United States is thirteenth.
Wurgler shows that the elasticities are related to
characteristics of financial sector development. A
specific mechanism of the finance growth relationship is that deeper financial sectors (measured by
the ratio of either stock market capitalization or
credit to GDP) help countries add to capital in growing industries. State ownership of industry inhibits
this mechanism, and minority investor protections
strengthen it.
Wurgler’s paper takes some important steps
toward identifying the channels of financial sector
effects on allocative efficiency and growth. For
example, he examines stock market synchronicity,
a measure introduced by Morck, Yeung, and Yu
(2000). We observed that equity market capitalization affects growth even though new equity
issuance is always small. The markets are important
because they assist the flow of information, which
improves the efficiency of allocation. There will be
more firm-specific information in markets where
prices are not synchronized and seem to respond to
firm-specific information.
Thus, the next stage of research has begun.
Whether or not we are satisfied with the empirical
literature of the 1990s, the finance growth nexus has
become an established part of the economists’
canon. The next generation of research is starting to
delve into the black box and will show how financial
deepening effects are transmitted to the real sector.
Conclusions
here is ample empirical evidence to make a convincing case that financial sector development
promotes economic growth. However, this study has
outlined some methodological reservations about
the evidence used to establish this consensus. Nevertheless, the first decade of research on finance and
growth identified relationships between growth and
aggregate measures of financial sector development.
The next stage, already under way, will identify
specific institutional characteristics and financial
sector channels that contribute to growth.
Research so far provides little in the way of rigorous guidance about how best to develop the financial sector. Although deeper financial intermediation
may be a significant causal factor in economic
growth, one cannot infer that every expansion of
intermediary activity will be beneficial. Financial
sector expansion that results from inflationary liquidity creation or deterioration in lending standards
will not enhance long-run growth prospects. The
observed association between financial sector deepening and growth does not, therefore, translate into
T
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
a simple prescription to encourage the unrestricted
growth of financial intermediaries.
Similarly, the research on growth and finance
provides policymakers with little guidance about
the sequencing of financial sector developments. For
example, we know that the expansion of bank credit
is growth enhancing, but we do not how to promote
credit expansion without compromising credit standards. Private sector credit evaluation capabilities,
public sector regulatory oversight, and a sound legal
and accounting infrastructure must all be in place as
credit deepening occurs. The sequencing of financial
sector developments is enormously important from a
policy perspective. The recipe is not simple because
the developments are likely to take place concurrently
and mistakes are easy to make. Developing institutional capabilities and a legal tradition with enforcement standards is likely to be a slow process. It is easy
to see how rapid credit expansion in a booming economy could wreak economic and political havoc even
when a government is following a generally prudent
prescription for financial sector development.
Recent history is full of examples of poor sequencing or a failure to have a robust institutional framework in place as financial deepening occurs. Bonin
and Wachtel (2003) describe the problems that
emerged in transition economies that opened equity
markets before effective securities regulation was
in place. Although securities laws were on the books,
regulators were inexperienced and unable to apply
them effectively. Thus, abuses were common, and
the ensuing problems set back the development of
equity markets.
The IMF has only recently introduced a program for financial sector stability assessments
intended to evaluate financial sector developments in member countries and develop financial
soundness indicators.8 Previously, the IMF monitored macroeconomic developments and paid little
attention to the financial sector. Perhaps as a result
of some of the empirical research cited here, the
IMF now understands that regulatory capabilities
and the quality of institutions are as important as
the growth of the money and credit aggregates.
This change would be welcome since recent empirical work suggests that the quality of institutions is
as important as their size.
Fundamental research on the finance-growth
relationship has mushroomed in just the last few
years. The strong evidence that financial development causes growth has contributed to the increased
interest of the economics profession in financial
institutions. However, much more needs to be done.
Policymakers need to learn how to encourage the
expansion of intermediation without creating
inflation or excessive leverage. Researchers need to
continue to develop the next stage of work on the
channels of financial sector effects.
8. The program is described and reports can be found at www.imf.org/external/np/fsap/fsap.asp.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
45
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Bonin, John P., and Paul Wachtel. 2003. Financial sector
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Demirguc-Kunt, Asli, and Ross Levine. 1996. Stock market development and financial intermediaries: Stylized
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Durlauf, Steven. 2001. Manifesto for a growth econometrics. Journal of Econometrics 100 (January ): 65–69.
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Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
47
Pricing Firms on the
Basis of Fundamentals
MARK KAMSTRA
The author is a financial economist in the Atlanta Fed’s research
department. He is grateful for useful conversations with Lisa Kramer,
Cesare Robotti, Tom Cunningham, and Paula Tkac and for extensive
comments from Jerry Dwyer, Mark Fisher, and Larry Wall.
eople often speculate that a particular
stock is overpriced, or underpriced, and
analysts sometimes issue stock price
targets followed abruptly by price “corrections.” A natural question is, What
is the right price for a stock? Mergers
and acquisitions of firms rely heavily on determining the right or fair price of a stock. One set of strategies to find the right price is to forecast cash flows
from a stock market investment and calculate what
that income is worth. Roughly speaking, this strategy
is what fundamental valuation is all about, and it
is the focus of this article.
Beyond an overview and illustration of commonly
used fundamental valuation techniques, the article
will discuss a new valuation approach developed in
Kamstra (2001). The discussion will also explore
severe market turndowns, such as the tech “bubble”
of the late 1990s, to see if market prices reflected
gross overvaluation of various stocks compared to
the estimated fundamental values. Application of
Kamstra (2001) to both blue chip and dot-com firms
improves the ability to track market price movements, as will be demonstrated below with applications to BellSouth, Starbucks, Sun Microsystems,
Microsoft, Yahoo, and the S&P 500 index.
The article first describes fundamental valuation
approaches and establishes links between these
methods. This review of techniques will draw on
practitioner and academic financial literatures as
well as the academic accounting literature.
P
The Literature
large literature deals with the issue of stock
valuation as a function of future cash flows and
discount rates. Valuation methods based on fundamental analysis—forecasting future cash flows and
discounting them to estimate the value of this
income stream—all face the common criticism that
these forecasts can be unreliable. Together with
assumptions about the firm’s ability to borrow funds
and about market efficiency, such forecasts depend
on a company’s maintaining its investment and business strategies. Pricing by discounting future cash
flows is intuitive, however.
The literature on fundamental valuation includes
studies from accounting that explore restatements
of the discounted dividend model in terms of
accounting information (see Feltham and Ohlson
1995; Penman 1996; Burgstahler and Dichev 1997)
and finance papers that often start with or derive
the discounted dividend model (see Gordon 1962;
Rubinstein 1976; Barksy and DeLong 1993;
Campbell and Kyle 1993; Donaldson and Kamstra
1996; Chiang, Davidson, and Okuney 1997; Bakshi
and Chen 1998). Finally, a literature written largely
by practitioners for practitioners typically starts
with the discounted dividend model of Gordon
(1962) and augments it to allow for more flexibility.
A related literature has focused on the question
of market efficiency, documenting abnormal return
predictability based on earnings, size, and financial
statement ratios.1 There is considerable ongoing
A
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
49
controversy over the issue of market efficiency. The
focus of the present work is not on market efficiency
questions but rather on fundamental valuation in
the context of efficient markets, though this study
will comment on the efficient markets implications
of the deviations observed between market and fundamental prices.
Contributions from the practitioner literature. The practitioner literature spans decades and
provides a number of equity valuation approaches.
There are somewhat indirect methods that are
intended to rank stocks using price-earnings ratios
(sometimes termed price relatives) or return-onequity ratios combined with book-to-price ratios (see
Valuation methods based on fundamental
analysis—forecasting future cash flows and
discounting them to estimate the value of this
income stream—all face the common criticism
that these forecasts can be unreliable.
Beaver and Morse 1978; Wilcox 1984; Estep 1985;
Peters 1991; Bauman and Miller 1997; Leibowitz
1999). There are equity valuation methods that use
sales to calculate present value of future cash flows
(see Leibowitz 1997). There are also methods based
on the dividend growth model of Gordon (1962), or
classic fundamental analysis.
The papers based on Gordon’s method start with
a model equating market price to the sum of discounted future dividends. To produce a tractable
formula, a structure is imposed, such as constant
growth rates of dividends and constant discount
rates. Many articles extend the simplest Gordon
growth model to allow dividend growth rates to
have several stages—for instance, permitting
growth firms to start with high dividend growth
rates and then decelerate to a stable long-run rate.
Some studies also propose random but independent
dividend growth rates.2 The variations of the discounted dividend growth model used in this literature are rarely more than ad hoc attempts to capture
real-world phenomena such as time-varying dividend
growth rates. Pricing firms that do not pay out dividends is not considered explicitly, or else dividends
are proxied as a constant fraction of observed earnings or sales. A good example of valuation based on
sales in the absence of dividends is Damodaran
(1994, 244–48), and standard investments texts
50
outline how dividends may be replaced by earnings
and payout ratios (see, for instance, Sharpe and
Alexander 1990, 474–76).
An often-mentioned financial measure of fundamental value in this literature is the price-toearnings (P/E) ratio. A high P/E ratio is often taken
to imply that investors expect a high dividend growth
rate, a low risk in holding the stock, or a high payout of earnings together with an average growth
rate. The valuation of stocks using P/E ratios, most
often termed relative value pricing, is studied by
both academics and practitioners. P/E ratios are
typically compared across similar firms to formulate
buy/sell recommendations and to forecast price by
multiplying a forecast of earnings by the current
P/E ratio. Shares of firms that are not actively traded
are often priced by finding an actively traded firm
with similar risk, profitability, and investment opportunity characteristics and multiplying the actively
traded firm’s P/E ratio by the inactively traded
firm’s earnings.3
Contributions from the accounting literature. Studies in the accounting literature begin with
the assumption of the discounted dividend model,
imposing constant discount rates. The focus is on
relating accounting information, such as earnings and
book value, to stock valuation. The most popular
techniques are the residual income valuation method
and the free cash flow valuation method (see, for
instance, Feltham and Ohlson 1995; Penman and
Sougiannis 1998; Lee, Meyers, and Swaminathan
1999). Residual income is typically defined as earnings generated by a firm in excess of a normal rate
of return on the company’s book value (also termed
abnormal earnings in the literature on residual
income models).4 Free cash flows are cash flows that
could be withdrawn from a firm without lowering the
current rate of growth.5 The residual income method
requires positive earnings and book value, and the
free cash flow method requires positive free cash
flows. Many firms have negative free cash flows, negative book value, and negative earnings. Among firms
that have been included in the S&P 500 index at some
point over the last twenty years, 6 percent have
recorded at least one year with nonpositive book
value; 12 percent have recorded at least one year with
nonpositive earnings before interest, taxes, depreciation, and amortization (EBITDA); 89 percent have
recorded at least one year with nonpositive free cash
flow; and 32 percent have never had positive free cash
flow. Of the more than 19,000 firms tracked by
Compustat over the last twenty years, over 20 percent have recorded simultaneous nonpositive book
value, nonpositive free cash flows, and nonpositive
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
EBITDA for at least one year on record; 6 percent
have never had a positive book value; 52 percent have
never had a positive free cash flow; and 22 percent
have never had a positive EBITDA.
Contributions from the finance literature.
In the finance literature, one approach taken to the
fundamental valuation problem has been to implement some variant of the Gordon (1962) model of
discounted dividends, which uses essentially the
same starting point as the accounting literature.
Although more formal, this literature also has much
in common with the practitioner literature on fundamental valuation. The models that have been proposed vary from the simplest Gordon model with
constant dividend growth rates and constant discount rates to multistage models with the growth
rates varying in a step-wise manner—constant for a
period of time (a step) and then shifting to a new
level for a period of time (see, for instance, Brooks
and Helms 1990, Barsky and DeLong 1993). The literature following directly out of Gordon (1962)
motivates restrictions on dividend growth and discount rates either in an ad hoc fashion or by arguments based on analytic tractability. Another
approach makes use of option-pricing methods but
also imposes ad hoc assumptions to make the methods more straightforward to apply.6
Both streams of this literature—that following
the Gordon (1962) growth model and that exploit-
ing option-pricing tools—are closely related to each
other. Both seek to impose sufficient structure on
the dividend growth and discount rate processes to
permit an explicit computable expression for the
present value of future dividends.7
Donaldson and Kamstra (1996) generalize the
Gordon (1962) model to allow arbitrary dividend
growth and discount rate processes. The point of
Donaldson and Kamstra’s procedure is to avoid
imposing structure on the dividend growth and
discount rate processes and to let the data speak
for themselves.8
Most investment professionals view any algorithmic valuation model as only a starting point to pricing
An often-mentioned financial measure of
fundamental value in this literature is the
price-to-earnings ratio.
equity, whether the model is based on price relatives
like the P/E ratio or on classic fundamental analysis.
For instance, in the context of zero-income stocks,
1. An efficient market is one in which the price of assets reflects their fair value; that is, prices are unbiased. For work that presents evidence consistent with market inefficiency, see, for instance, Basu (1977), Jaffe, Keim, and Westerfeld (1989), Ball
(1992), and Fama and French (1995). In contrast, Kirby (1997) demonstrates that the statistical significance of the evidence
of market inefficiency from long-horizon returns is overstated.
2. A few examples include Hawkins (1977), Farrell (1985), Sorensen and Williamson (1985), Rappaport (1986), Hurley and
Johnson (1994, 1998), and Yao (1997).
3. References to these sorts of rules can be found in textbooks like Brealey et al. (1992) and journal articles such as Peters
(1991). See also Wilcox (1984), Estep (1985), Bauman and Miller (1997), and Campbell and Shiller (1998).
4. Preinreich (1938) derived that the stock price of a firm should equal the book value of the firm plus discounted abnormal
earnings. Ohlson (1995) extends Preinreich and goes on to show the time period t stock price is a linear sum of time period
t book value and abnormal earnings. This result assumes the discounted dividend model, constant discount rates, the cleansurplus relation, and linear autoregressive stochastic abnormal earnings. Ohlson also generalizes this relationship to admit
information other than abnormal earnings. Feltham and Ohlson (1995) and Penman (1996), among others, extend Ohlson
(1995). Feltham and Ohlson do so by focusing on the implications of conservative versus unbiased accounting for the Ohlson
model while Penman focuses on the differential information contained in price-to-book versus price-to-earnings ratios in the
context of the Ohlson model.
5. For a discussion of free cash flows and equity valuation, see Hackel and Livnat (1996) or Penman and Sougiannis (1998). Free
cash flows are substantially different from accounting earnings and even accounting measures of the cash flow of a firm.
6. See Campbell and Kyle (1993), Chiang, Davidson, and Okuney (1997), Bakshi and Chen (1998), and Schwartz and Moon
(2000, 2001) for examples of this approach. This literature starts with the representative consumer-complete market economic paradigm. Models are derived from primitive assumptions on markets and preferences, and the solution to the fundamental valuation problem is derived with the same tools used to price financial derivatives.
7. Even the solutions are often similar—the Gordon (1962) model is explicitly considered as a special case in the Bakshi and
Chen (1998) option-pricing model.
8. The Donaldson-Kamstra methodology is similar to pricing path-dependent options because it involves a Monte Carlo simulation and numerical integration of the possible paths followed by the joint processes of dividend growth and discount rates,
explicitly allowing path-dependence of the evolutions. See Donaldson and Kamstra (1996) for details.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
51
Wilson (2000) argues that a practitioner should use
discounted cash flow analysis together with scenario analysis, considering the fair value of a company under various possible scenarios and then
judging which scenario is most likely to occur. If the
market price is below the most likely fair value, he
observes that it is appropriate to consider buying
the stock. Wilson also points out the many difficulties involved in the simple application of discounted
cash flow analysis, including the difficulty of determining the appropriate discount rate.
Fundamental Valuation
T
he fundamental value of a dividend-paying
stock is merely the present value of the flow of
Practitioners use a variety of relative value
models exploiting the notion that similar
companies should have similar multiples of
price to fundamental measures of value.
dividends that are expected into the future.9 That
is, fundamental valuation involves solving equations
A1 and A2 (in the appendix) to yield the market
price equal to the expected discounted value of
future dividends. This result holds if the stock market price contains no bubble—no “irrational exuberance.”10 Although this approach suggests that
one must look into the distant future in order to price
firms, there are a number of ingenious solutions that
do not require complex forecasting methods. Among
these are methods that simplify the basic formula
to solve for future dividends and discount rates
directly, such as Gordon growth models, and methods
that make use of known market prices of other firms,
such as the relative valuation model.
The relative value model. Practitioners use a
variety of relative value models exploiting the
notion that similar companies (in the same industry, at the same point in their growth cycle, of similar size, and so on) should have similar multiples of
price to fundamental measures of value. That is, if
company A is similar to company B, and company
A has a price that is ten times its earnings (reflecting a 10 percent return on investment, roughly
speaking), then company B’s price is expected to
be roughly ten times its earnings as well. The price
for company A reflects a risk-return trade-off for
52
that company, with market participants satisfied
with a 10 percent return for a company with the
characteristics of either company A or B. If market
participants suddenly reassessed these companies
as less risky, then a 10 percent return would be
considered rich, and the price of both companies
would be bid up, lowering the return until market
participants would no longer consider the return to
be unusually good.
Relative value models do not require that firms
pay out dividends. In the past, price-earnings multiples were most closely watched, but the advent of
the technology boom in the 1990s led many to rely
more on sales to price multiples because many
companies did not have positive earnings (see, for
instance, Leibowitz 1997). Other price relatives that
are closely watched include the price-to-cash flow,
the price-to-EBITDA ratio and the book-to-price
(B/P) ratio. A B/P ratio of 1 is expected for relatively
mature firms while growth firms are expected to
produce lower ratios.
To illustrate relative value pricing, Figure 1 shows
the price of BellSouth shares (NYSE:BLS), plotted
quarterly, over the past sixteen years, using dividends, book value of equity, earnings, and sales of
BellSouth and a similar firm, SBC Communications,
another Baby Bell. In each panel the price scale is
logarithmic, and the price is the closing price on the
last day of trading in the first month of the quarter.11 The respective relative value price is also
plotted. The relative value price based on dividends
for, say, the first quarter of 1985 is calculated by
multiplying BellSouth’s 1984 dividend by SBC
Communications’ 1985 price-dividend ratio.12 The
relative value prices based on earnings and on sales
were calculated similarly. For the relative value
price based on book value of equity, the book value
for BellSouth reported for the fiscal year preceding
a given quarter is multiplied by the price-to-book
value reported for the same quarter for SBC; this
calculation uses the closing price of SBC on the last
trading day of the first month of the quarter and the
book value reported for the fiscal year preceding
the quarter.
A relative value model based on sales performs
very well over most of the last sixteen years in this
example; the relative sales price tracks the actual
price very closely on average and in particular
tracks actual market price remarkably well through
the turmoil of the last three years. Relative valuation based on dividends also performs very well
while relative valuation based on book value of equity
or on earnings is much less reliable for the last sixteen years for BellSouth. More generally, relative
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 1
Relative Value Estimates of BellSouth Share Price
A: Using dividends
B: Using book value of equity
100
Pr ic e ( lo g s c a le )
Pr ic e ( lo g s c a le )
100
Fitted
Actual
10
1
Fitted
Actual
10
1
1986
1989
1992
1995
1998
2001
1986
1989
C: Using earnings
1992
1995
1998
2001
D: Using sales
100
100
P ric e (lo g sc a le )
P ric e (lo g sc a le )
Fitted
Actual
10
1
Actual
Fitted
10
1
1986
1989
1992
1995
1998
2001
1986
1989
1992
1995
1998
2001
Note: Panels A through D present logarithms of the quarterly BellSouth share price level and the forecast price level from the relative value
model. Panel A is based on dividends issued by BellSouth and the dividend yield of SBC Communications (SBC); panel B is based on the
BellSouth book value of equity and the SBC book-to-market ratio; panel C is based on BellSouth earnings and the SBC earnings yield; panel
D is based on BellSouth sales and the SBC sales yield.
valuation based on sales is attractive because most
companies report sales while a great many companies issue dividends only rarely or have negative
earnings or negative book value.
A word of caution—exploiting price relatives to
value firms requires great care. Truly comparable
firms must be found or the exercise is of little merit.
Firms with advantages like a monopoly will be able
to generate much higher profit margins and yields
and will be grossly undervalued if benchmarked
against otherwise similar firms. The best application
of relative valuation is in valuing individual firms,
provided a comparable firm can be found to the firm
being valued. Pricing an index like the S&P 500 can
be accomplished with relative valuation but only by
using past values of the index. The classic dividend
discounting valuation methods are easily applied to
indices, however, as shown below.
The Gordon growth model. Perhaps the most
widely used fundamental valuation method after
relative valuation is the Gordon growth model. The
Gordon fundamental price estimate does not, unlike
relative valuation, require a comparable firm to the
firm being valued and is derived with two simple
assumptions: a constant discount rate and a constant
growth rate of dividends. With these two assumptions, the valuation formula simplifies to a ratio
involving the average dividend growth rate and the
9. The appendix provides technical descriptions of the valuation methods and models discussed in this article.
10. See Garber (1990), Kindleberger (1978), Shiller (1989), and White (1990) for a discussion of bubbles. Bubbles in asset
prices are commonly defined as deviations of market prices from fundamental values.
11. The logarithm of price is presented to compress the scale of prices, making it possible to see detail throughout the period.
12. The SBC closing price used is that recorded on the last day of trading in January 1985, and the dividend used is the 1984 dividend.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
53
FIGURE 2
The Gordon Growth Model for the S&P 500 Index
A: Prices (1900–2000)
B: Dividend yields
0.21
0.17
1,000
S&P 500
0.13
Yie ld
Pr ic e ( lo g s c a le )
10,000
100
Gordon
10
1
1900
S&P 500
0.09
Gordon
0.05
1920
1940
1960
1980
0.01
1900
2000
1920
C: Prices (1900–1950)
1940
1960
1980
2000
D: Prices (1950–2000)
30
1,500
1,200
S&P 500
900
P ric e
P ric e
20
Gordon
S&P 500
600
10
300
Gordon
0
1900
1910
1920
1930
1940
1950
average discount rate multiplied by the most recent
dividend (see equations A3 and A4 in the appendix).
To illustrate this pricing method, one can apply the
Gordon growth model to the S&P 500 index over the
past 130 years. During this time the S&P 500 index
has enjoyed an average annual dividend growth rate
of approximately 4 percent, and most measures of r,
the average annual discount rate, would be close to
11 percent. The Gordon model price for, say, 1980
was calculated by estimating g as the average annual
growth rate in dividends and r as the average annual
return to holding the S&P 500 index for the
1871–1979 period and using dividends paid during
1979. This calculated Gordon price is then compared
to the January 1980 price. Hence, the Gordon prices
are all out-of-sample forecasts.
Figure 2 compares S&P 500 data with Gordon
model estimates. Panel A shows prices and the
Gordon model price for the period 1900 to 2000; a
logarithmic scale makes it possible to see detail
throughout the 100-year period. Panel B presents
the market dividend yield (the S&P 500 index dividend divided by the market price) and the dividend
yield using the Gordon price in place of the market
54
0
1950
1960
1970
1980
1990
2000
price. Panels C and D present the actual market
Gordon model prices (instead of the logarithmic
values shown in Panel A) for the 1900–1950 and
1950–2000 periods, respectively. This display of fiftyyear periods makes it easier to interpret deviations
of the forecast and actual S&P 500 prices. The dividend yield shown in panel B highlights deviations of
market and forecast prices. Evidence of large and
persistent deviations between the market and forecast yields reveals whether the market is making
systematic valuation errors or the forecasting model
is performing very poorly.
Applying the Gordon model to the S&P 500
index annual data produces evidence of excessive
market volatility (the forecast dividend yield is
much less variable than the realized market yield)
and of periods of inflated market prices—bubbles—
in particular, during the 1920s, the 1960s, and the
last half of the 1980s and 1990s. If the Gordon
model is too simple, however—ignoring as it does
changes in discount and dividend growth rates over
time—this evidence may be misleading.
The additive and geometric Markov Gordon
growth models. Hurley and Johnson (1994, 1998)
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 3
The Additive Markov Gordon Growth Model for the S&P 500 Index
A: Prices (1900–2000)
B: Dividend yields
0.21
0.17
1,000
S&P 500
Yie ld
Pr ic e ( lo g s c a le )
10,000
100
Additive Gordon
0.09
Additive
Gordon
10
1
1900
0.13
0.05
1920
1940
1960
1980
0.01
1900
2000
S&P 500
1920
C: Prices (1900–1950)
1940
1960
1980
2000
D: Prices (1950–2000)
30
1,500
1,200
S&P 500
P ric e
P ric e
20
900
S&P 500
600
10
Additive Gordon
300
Additive Gordon
0
1900
1910
1920
1930
1940
1950
and Yao (1997) develop Markov models—models that
presume a fixed probability of, say, maintaining the
dividend payment at current levels and a probability
of raising it—to estimate dividends more realistically.
These extensions of the Gordon growth model go
back to the fundamental valuation equation, imposing
less stringent assumptions. The simple Gordon
growth model imposes a constant growth rate on dividends—dividends are expected to grow at the same
rate every period—while these Markov models allow
the probability of zero dividend growth. Two examples of these models found in Yao (1997) are the additive Markov Gordon model (equation 1 in Yao) and
the geometric Markov Gordon model (equation 2 in
Yao) (see equations A5 and A6 in the appendix).
For the S&P 500, over the last 130 years annual
dividends have decreased 28.9 percent of the time
and increased 71.1 percent of the time, the average
absolute value of the change in annual dividends
has been 0.161, and the average absolute value of
the annual percentage change in dividends has been
9.2 percent.
0
1950
1960
1970
1980
1990
2000
Figures 3 and 4 show prices and dividend yields
from the additive and geometric Markov Gordon
models versus the market price and dividend yield
for the period 1900 to 2000. These models were
implemented to produce out-of-sample price estimates just as the Gordon growth model was. The
price for a given year was estimated using data up
to but not including that year. Applying these two
extensions of the Gordon model to the S&P 500
index annual data also produces evidence of excessive volatility and periods of inflated market
prices—the 1920s, the 1960s, the 1980s, and the
1990s. Overall, the simplest Gordon model performs
as well as the Markov model extensions, but none
perform well.
Again, this poor performance could be the result
of overly simple models that are not able to capture
changes in value of the index or of a mispriced (irrationally priced) market.13 The fact that the market
price typically exceeds the forecast price from
these models has led many to believe that the market has been overvalued at times, especially during
13. “Irrational pricing” can be defined as pricing based on expected price appreciation in the absence of expected cash flows.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
55
FIGURE 4
The Geometric Markov Gordon Growth Model for the S&P 500 Index
A: Prices (1900–2000)
B: Dividend yields
0.21
0.17
1,000
S&P 500
Yie ld
Pr ic e ( lo g s c a le )
10,000
100
S&P 500
Geometric Gordon
0.09
Geometric
Gordon
10
1
1900
0.13
0.05
1920
1940
1960
1980
0.01
1900
2000
1920
C: Prices (1900–1950)
1940
1960
1980
2000
D: Prices (1950–2000)
30
1,500
S&P 500
1,200
S&P 500
P ric e
P ric e
20
900
600
10
Geometric Gordon
300
Geometric Gordon
0
1900
1910
1920
1930
1940
boom times like the 1920s, the 1960s, the 1980s,
and the 1990s.
The Donaldson-Kamstra Gordon growth
model. Donaldson and Kamstra (1996) further
extend the Gordon model, imposing even fewer
assumptions on the fundamental valuation equation
than the Markov Gordon growth models and using
statistical models of discounted dividend growth
rates. The Donaldson-Kamstra model permits more
flexible modeling of autocorrelation in growth rates
than do simple Markov models. In the language of
practitioners, this autocorrelation affects the fade
rate: the speed at which company growth converges
to its long-run stable growth rate (see, for instance,
Wilson 2000). The greater the autocorrelation, the
slower the fade to the long-run growth rate and the
higher the value of a company enjoying temporarily
high growth.
Why should one worry about autocorrelation?
Take a simple example, a firm facing two equally
likely scenarios for future discount rates. In one scenario, the discount rate decreases from its past average of 8 percent to a new average of 6 percent; in the
other, the average rate increases to 10 percent.
56
0
1950
1950
1960
1970
1980
1990
2000
Once changed, the average rate remains fixed forever.
The expectation before the rate change is for an average rate of 8 percent, just as in the past. Suppose dividend growth is expected to be 4 percent and the most
recent dividend was $1. The Gordon growth model,
applied blindly, would yield a price of $1/(0.08 –
0.04), or $25 per share. However, if interest rate
changes are recognized as permanent (an extreme
form of autocorrelation), then Gordon prices could
be calculated separately for each scenario, and the
two prices could be averaged to get a price that
accounts for autocorrelation. The low discount rate
case yields a price of $1/(0.06 – 0.04), or $50 per
share, and the high discount rate case yields a price
of $1/(0.10 – 0.04) or $16.67 per share, for an average price of roughly $33.33. Accounting for the autocorrelation dramatically changes the price estimate,
increasing it by 30 percent. Although it is easy to
adjust the Gordon model for a simple scenario like
this one, the Donaldson and Kamstra technique
makes it possible to perform extremely complex
scenario analysis that is not feasible with simpler
methods, such as scenarios in which the discount
rate never settles to a constant, the dividend growth
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 5
The Donaldson-Kamstra Model for the S&P 500 Index
A: Prices (1900–2000)
B: Dividend yields
0.21
0.17
1,000
Yie ld
Pr ic e ( lo g s c a le )
10,000
100
DK
S&P 500
0.09
S&P 500
10
1
1900
0.13
0.05
1920
1940
1960
1980
0.01
1900
2000
DK
1920
C: Prices (1900–1950)
1940
1980
2000
D: Prices (1950–2000)
50
1,500
1,200
40
S&P 500
DK
30
P ric e
P ric e
1960
S&P 500
20
900
600
DK
300
10
0
1900
1910
1920
1930
1940
1950
rate also moves around, and the two rates influence
each other probabilistically.
Over the last 130 years the average annual value
of discounted dividend growth rates has been 0.965
based on an equity premium of 3 percent, a premium
recent research supports.14
Figure 5 presents the price and dividend yield for
the Donaldson-Kamstra (DK) model versus the market price and dividend yield for the period 1900 to
2000. The DK model was implemented to produce
out-of-sample price estimates as the Gordon models
were. The forecasts of discounted dividend growth
rates are based on the last year of rates.15 Applying the
DK model to the S&P 500 index annual data produces
much less evidence of surprisingly high market prices
0
1950
1960
1970
1980
1990
2000
although the late 1990s still exhibit higher prices than
the DK model’s price forecasts. The dividend yields in
panel B also provide evidence of excessively volatile
market price movements in the last fifty years.
The ability of the DK model to capture much more
market volatility, including the booms of the 1920s,
the 1960s, and the 1980s, highlights the importance
of accounting for the slow fade rate of dividend
growth rates and discount rates. The continued failure to capture the height of the 1990s boom still
leaves evidence of surprisingly high prices during
the late 1990s. There is, however, still the question
of a modeling failure; a large spike in prices could
still be rationalized by a decrease in the fade rate
during the 1990s.
14. The discounted dividend growth rate equals one plus the dividend growth rate divided by one plus the discount rate. This
value should be close to, but less than, one. The equity premium is the extra return generated by stock market equity over
relatively risk-free Treasury bills. The 3 percent premium is supported by, for instance, Fama and French (2002), Jorion and
Goetzmann (1999), Jagannathan, McGrattan, and Scherbina (2001), and Donaldson, Kamstra, and Kramer (2003).
15. This forecasting model is an autoregressive model of order 1. The logarithm of discounted dividend growth rates was modeled for this exercise. The average value of the coefficient on the AR(1) term in the model was approximately 0.26, implying a fairly rapid fade rate. In as little as four years the impact from a change in the discounted dividend growth rate is
expected to have virtually no remaining impact. An unexpected 10 percent increase in this growth would fade to less than
0.1 percent by year five. For implementation details, see Kamstra (2001) and Donaldson and Kamstra (forthcoming).
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
57
FIGURE 6
Forecasts of BellSouth Share Prices Based on Dividend-Forecasting Models
A: Gordon growth forecast
B: Additive Gordon growth forecast
100
Actual
Pr ic e ( lo g s c a le )
Pr ic e ( lo g s c a le )
100
10
Fitted
1
1986
1989
1992
1995
1998
Actual
10
Fitted
1
1986
2001
C: Geometric Gordon growth forecast
1989
1992
1995
1998
2001
D: Donaldson-Kamstra forecast
100
100
P ric e (lo g sc a le )
P ric e (lo g sc a le )
Slow fade
Actual
10
Fitted
1
1986
1989
1992
1995
1998
10
Rapid fade
Actual
1
1986
2001
1989
1992
1995
1998
2000
Note: Forecasts from the Donaldson-Kamstra model in panel D include models based on a rapid and a slow fade rate of growth in cash
flows calibrated to the S&P 500 index over the last 100 years.
Application of Gordon growth models to
BellSouth. It is interesting to apply the Gordon
models based on dividends to the earlier example of
BellSouth and explore how these models perform
compared to relative valuation. A shortfall of the
relative valuation approach is that a truly comparable firm may be difficult to find; great errors in valuation may follow an unwise choice of comparable
firm. A model that does not look at prices, such as
the Gordon growth models described earlier, should
be immune to this problem.
The Gordon growth, additive and geometric
Markov Gordon growth, and DK model price forecasts displayed in Figure 6 are formed using the
same calibration used for the S&P 500 (BellSouth
is, after all, a S&P 500 firm)—an average annual discount rate of 11 percent and an equity premium of
3 percent—and the same timing conventions used
to form the relative value forecasts (so that all forecasts are out-of-sample).16 For the DK model, price
forecasts can be formed with the model described
for the S&P 500 index, using the average annual
58
estimated fade rate of dividend growth experienced
by the S&P 500. This average fade rate is only an
estimate, and plausible fade rates include slower
and faster rates. These slower and faster rates allow
bracketing high and low estimates of the share
price. The low fade rate indicates a very slow reversion of growth to the long-term mean growth,
implying high prices for fast-growing firms and low
prices for firms that have experienced belowaverage or negative growth. A high fade rate indicates a very rapid reversion of growth to historic
levels, so that price is not moved much by unexpected high or low growth.17
The simple Gordon growth model and the additive and geometric Gordon growth models all perform poorly, capturing neither the overall level of
the share price nor the dramatic rise in share value
in the late 1990s. Again, this performance is dramatic evidence of either irrational price setting or
model failures. Allowing the Gordon models to
incorporate larger dividend growth rates or smaller
discount rates does not fix this problem—the
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
Gordon prices are not variable enough regardless of
these settings. The DK model captures the average
price level, reinforcing the notion that accounting
for the fade rate matters, but the magnitude of the
rise and fall of prices is not captured. The market
prices start from below the lower bracket DK price
and rise above the upper bracket DK price.
Forecast prices are also much less volatile than
actual market prices even when the fade rate is
slow, the case for which we expect to see the most
dramatic price swings. Clearly, relative valuation is
capturing something these fundamental valuation
methods fail to include. Hackel and Livnat (1996, 9)
and others argue that dividends may be unreliable
for assessing firm value because of institutional constraints on firm managers to smooth dividends over
time. So a third possibility is that the models and
the market prices are fine and that the problem is
simply one of overly smoothed dividends. The next
section presents discussions of formal extensions of
classic dividend valuation models that allow the use
of earnings, or sales, or other nondividend accounting numbers to value companies.
uidations because his portfolio will be 3 percent
smaller next period.
A reasonable question is, How might share liquidation help one value a firm? It is well known that
dividends are typically set low enough that the dividend payments can be maintained through economic downturns, leading them to be lowered only
rarely and to inaccurately reflect future prospects
for the firm, as argued by Hackel and Livnat (1996)
and others. Augmenting dividends with the proceeds of share liquidation—say, to produce a yield
equal to 3 percent of the sales yield—should produce valuation rules that more accurately reflect
future prospects. Accounting for the share liquida-
The Kamstra method extends dividend discount
models like the Gordon growth model to firms
that do not pay out dividends and incorporates
nondividend information like earnings or sales
figures into fundamental valuation of firms that
do pay out dividends.
Augmenting Dividend Discounting Models
amstra (2001) extends dividend discount models like the Gordon growth model to firms that
do not pay out dividends and incorporates nondividend information like earnings or sales figures into
fundamental valuation of firms that do pay out dividends. The basic premise of this work is to incorporate the proceeds from share liquidation into the
cash flows that are used to value the firm, accounting for the reduction in future growth of cash flows
from this liquidation of shares. Share liquidation
refers to selling a fraction of the stock holdings in a
portfolio of stock. This sale generates immediate
cash flow but reduces potential cash flows into the
future. For instance, if a shareholder sells 3 percent
of his shares this year, he will reduce his dividend
flow next period from his remaining shares by 3 percent as well as reduce the cash from further liq-
K
tion produces valuation formulas that are still tied
to fundamentals of cash flow paid to investors even
if the liquidation rule is itself calibrated to firm
sales, not firm dividends.
A wealth of other work has, of course, been done
on valuing zero-dividend firms. Among these studies
are approaches that extend formal dividend discounting to zero-dividend firms relying on techniques similar to those used in option-pricing (see
Bakshi and Chen 1998; Schwartz and Moon 2000,
2001), approaches that replace dividends with earnings and payout ratios or sales and profit margins,
and, of course, relative valuation methods.18
As the share liquidation rule of Kamstra (2001)
uses past prices (to form the yield ratio), depending
on how this rule is implemented it can have much in
16. The data range is shorter in Figure 6 than that displayed for relative valuation in Figure 1 because of the need to use greater
lags of the data to form forecasts.
17. The high-fade-rate model was implemented by taking the average fade rate AR(1) parameter estimate of 0.26 and the standard deviation estimate of this parameter of 0.09 and subtracting two standard deviations from the parameter estimate, leaving a fade rate parameter of approximately 0.08. An unexpected 10 percent increase in growth would fade to less than
0.1 percent by year three for this parameter setting. The low-fade-rate model was implemented by taking the average fade
rate AR(1) parameter of 0.26 and adding two standard deviations to it, producing a fade rate parameter of approximately
0.44. An unexpected 10 percent increase in growth would now take over seven years to fade to less than 0.1 percent.
Bracketing price estimates can also be formed for the other Gordon growth models, but these price estimates are fairly
small shifts up and down from the forecasts presented.
18. See Damodaran (1994, 244–48) for an example using sales and Sharpe and Alexander (1990, 474–76) for an example
using earnings.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
59
FIGURE 7
The Gordon Growth Model with Augmented Dividends
A: Prices (1900–2000)
B: Dividend yields
0.29
10,000
S&P 500
1,000
0.21
S&P 500
Yie ld
Pr ic e ( lo g s c a le )
0.25
100
Gordon
0.17
0.13
0.09
10
Gordon
0.05
1
1900
1920
1940
1960
1980
0.01
1900
2000
1920
C: Prices (1900–1950)
1940
1980
2000
D: Prices (1950–2000)
30
1,500
S&P 500
1,200
S&P 500
P ric e
20
P ric e
1960
Gordon
900
600
10
Gordon
300
0
1900
1910
1920
1930
1940
common with relative valuation. For instance, if one
were valuing private equity one would not have past
earnings yields to provide an expected earnings yield.
In this context, one would pick an expected yield ratio
by looking at the earnings-to-price ratio of similar but
publicly traded firms, an approach borrowed from
relative valuation.
An advantage of a share liquidation rule for valuation over relative valuation is that the fade rate
in cash flows and discount rates can be incorporated with share liquidation as outlined in Kamstra
(2001) while the relative value model ignores fade
rates. The relative value model, taken at face value,
assumes that the sales yield (or whatever yield is
being considered, say, the earnings yield) will
remain constant forever while Kamstra provides a
method that makes this yield trend to some longrun stable level.
A disadvantage of the Kamstra method compared to the relative valuation method is that the
long-run stable level of the yield ratio must be specified, and if this level is chosen incorrectly it can
bias price forecasts. Also, the dependence (the fade
60
0
1950
1950
1960
1970
1980
1990
2000
rate) of the yield ratio and cash flow growth as well
as the discount rate must be modeled, and typically
the companies this method would be applied to
would not have sufficient history to properly estimate fade rates based on own-company data. To
implement the Kamstra method on such firms, a
calibration to the S&P 500 index will be performed
here, similar to that described above.
Compared to the techniques using option-pricing
tools, the Kamstra method is simpler to apply though
very similar in spirit. The approaches that replace
dividends with earnings or sales have in common
with relative valuation the disadvantage of not
accounting for the fade rate of growth and discount
rates and the advantage of simplicity over the
Kamstra method.
Another valuation approach for zero-dividend
firms is scenario analysis, the strategy of forecasting
possible cash flows that a company might generate
and computing the fair value of that company under
the various scenarios. For instance, if there is a 50
percent chance that a company will be worth $5 per
share and a 50 percent chance that it will be worth
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 8
The Donaldson-Kamstra Model with Augmented Dividends
A: Prices (1900–2000)
B: Dividend yields
0.29
10,000
S&P 500
1,000
0.21
Yie ld
Pr ic e ( lo g s c a le )
0.25
100
DK
S&P 500
0.17
0.13
0.09
10
DK
0.05
1
1900
1920
1940
1960
1980
0.01
1900
2000
1920
C: Prices (1900–1950)
1940
1980
2000
D: Prices (1950–2000)
50
1,500
1,200
40
S&P 500
S&P 500
30
P ric e
P ric e
1960
DK
900
20
600
10
300
DK
0
1900
1910
1920
1930
1940
1950
$15 per share, then a price of $10 per share would
be expected. This approach often combines elements
of relative valuation and discounted cash flow analysis. Great skill and a great deal of detailed institutional knowledge of the firm and its industry are
required to implement this valuation technique.19
I will restrict myself in this review to techniques
I have already used, techniques that allow a narrow
set of information for implementation and are therefore reasonably straightforward to apply.
Application to the S&P 500 index. In the
case of the S&P 500 index with share liquidation set
to equal accounting earnings, the total cash flow to
the investor will equal the dividends paid plus earnings. The growth rate of this cash flow over the last
130 years equals 4.9 percent, and the annual yield
ratio (see the appendix for the definition of this
term) averages 8 percent. This information, together
0
1950
1960
1970
1980
1990
2000
with the average annual discount rate (11 percent,
as described above), allows us to produce Gordon
prices, which are displayed in Figure 7.
One can also produce DK prices based on the
discounted cash flow growth rates. Based on earnings
plus dividends and an equity premium of 3 percent,
the average S&P 500 discounted growth rate over
the last 130 years has been 0.974.20 Figure 8 presents price and cash flow (dividends plus earnings)
yields for the DK model versus the actual market
price and yield for the period 1900 to 2000.21
Both the simplest Gordon growth model (Figure 7)
and the DK model perform remarkably better when
conditioned on the extra information provided by
earnings. With the added consideration of earnings,
the Gordon model captures most of the price rise
and decline of the 1920s and tracks prices up to 1990
very well. In addition, the DK model now captures
19. See Wilson (2000) and Copeland, Koller, and Murrin (2000) for extended discussions that outline implementation details.
20. The discounted cash flow growth rate equals one plus the cash flow growth rate divided by one plus the discount rate. This
value should be, on average, close to but less than one.
21. Results are presented for the slow-fade-rate DK model, calibrated as described above.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
61
FIGURE 9
Forecasts of BellSouth Share Prices with Dividends Augmented by
Share Liquidation Based on Earnings
A: Gordon growth forecast
B: Additive Gordon growth forecast
100
100
Pr ic e ( lo g s c a le )
Pr ic e ( lo g s c a le )
Actual
Fitted
10
1
1986
1989
1992
1995
1998
Actual
10
Fitted
1
1986
2001
C: Geometric Gordon growth forecast
Actual
P ric e (lo g sc a le )
P ric e (lo g sc a le )
1995
1998
2001
100
10
Fitted
1989
1992
1995
1998
Slow fade
Rapid
fade
10
Actual
1
1986
2001
the timing of the turning point around the peak of
the market in 1929 whereas both models peaked
several years late when only dividends were used
for pricing. Results from the additive and geometric
Markov Gordon models are very similar to the basic
Gordon model and are thus not presented here. The
DK model forecasts prices and yields better than
the Gordon growth model does, but the market
yield ratio remains much more variable than can be
explained by this model of fundamentals, and the
market price at the end of the 1990s is approximately double what is forecast. Also worth noting is
that some of the largest and most persistent deviations of market prices from forecast prices have
occurred during periods of war, World War I and
World War II in particular. This pattern highlights
the fact that any algorithmic forecast based on a
very restricted set of information can produce forecast prices that are less than reliable.
Application to BellSouth. It is also possible
to apply these models to Bell South, augmenting
its dividend payments with share liquidation based
62
1992
D: Donaldson-Kamstra forecast
100
1
1986
1989
1989
1992
1995
1998
2001
on either earnings, sales, or book value of equity.
Figures 9, 10, and 11 show the logarithm of the price
of BellSouth shares and of the forecast share price
from the Gordon growth, additive and geometric
Markov Gordon growth, and DK models.22 Dividends
are augmented with a stream of cash from liquidating
shares equal to approximately 3 percent of the share
price, calibrated to either earnings, sales, or book
value of equity, and adjusting downward the growth
of this cash stream to take account of this liquidation
of shares.23 Again, all the models borrow from the
calibrations for the S&P 500 index, including setting
the average discount rate to 11 percent and the
equity premium to 3 percent and using the same timing conventions so that the forecasts are out-ofsample. The DK model results include forecasts from
the slow- and rapid-fade-rate models, providing
bracketing forecasts that one would expect to contain
the actual market price.
The additive and geometric Gordon growth models never perform particularly well, regardless of
the liquidation rule, but the classic Gordon growth
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 10
Forecasts of BellSouth Share Prices with Dividends Augmented by
Share Liquidation Based on Book Value of Equity
A: Gordon growth forecast
B: Additive Gordon growth forecast
100
100
Pr ic e ( lo g s c a le )
Pr ic e ( lo g s c a le )
Actual
Fitted
10
1
1986
1989
1992
1995
1998
Actual
10
Fitted
1
1986
2001
C: Geometric Gordon growth forecast
1995
1998
2001
100
Actual
P ric e (lo g sc a le )
P ric e (lo g sc a le )
1992
D: Donaldson-Kamstra forecast
100
10
Fitted
1
1986
1989
1989
1992
1995
1998
2001
model and the DK model perform reasonably well
with a liquidation rule based on sales or book value
of equity. The classic Gordon model picks up much
of the price rise and some of the decline over the
period considered. The price bracket formed by the
rapid- and slow-fade-rate DK models augmenting
dividends with liquidation based on sales or book
value indicates that the market price of BellSouth
was often within a reasonable range of values,
although a case for prices being somewhat high in
1999 and 2000 can still be made. Valuation based on
augmenting dividends with an earnings-calibrated
liquidation rule tends to have more false move-
Slow fade
Rapid
fade
10
Actual
1
1986
1989
1992
1995
1998
2001
ments and random volatility, but this is a subjective
judgment. The better performance when using
book value or sales mirrors the relative valuation
pattern found when using book value or sales for
BellSouth and suggests at least two things. First,
sales are more informative than earnings, at least
for BellSouth over the last twenty years or so.
Second, it is more difficult to argue that the price
bubble observed in BellSouth stock valuation over
the last three years was irrational—much of the up
and down movement can be explained by changes
in cash flows associated with high growth in sales,
book value, and earnings.24
22. The data range is shorter here than those displayed in earlier figures because more lags of the data were needed to form
forecasts.
23. The exact rule used when calibrating to sales was to liquidate a fraction of holdings equal to 3 percent multiplied by the most
recently observed sales multiplied by the average price-to-sales ratio over the preceding year, not including the most
recent quarter. The calibrations based on earnings and on book value of equity were performed similarly.
24. As the share liquidation scheme outlined here does make use of last year’s sales, earnings, or book yield to calibrate liquidation, however, an argument can be made that a bubble was built into the “fundamental” price estimates generated. A share
liquidation scheme based on the average yield over a longer period, as long as twenty years, does dampen the price rise in
the late 1990s. Qualitatively, however, the evidence still supports the no-bubble view.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
63
FIGURE 11
Forecasts of BellSouth Share Prices with Dividends Augmented by
Share Liquidation Based on Sales
A: Gordon growth forecast
B: Additive Gordon growth forecast
100
Actual
Fitted
Pr ic e ( lo g s c a le )
Pr ic e ( lo g s c a le )
100
10
1
1986
1989
1992
1995
1998
Actual
10
Fitted
1
1986
2001
C: Geometric Gordon growth forecast
Actual
P ric e (lo g sc a le )
P ric e (lo g sc a le )
1995
1998
2001
100
10
Fitted
1989
1992
1995
1998
Slow fade
Rapid
fade
10
Actual
1
1986
2001
Application to high-growth firms. High-growth
firms are particularly interesting for valuation exercises because such firms rarely pay out cash to shareholders, except perhaps to make share repurchases.
The analysis will next consider Microsoft, Sun
Microsystems, Starbucks, and Yahoo because all these
firms are prominent members of the new economy, all
have experienced very rapid growth, and all have had
extreme share price fluctuations over the last several
years. If the share liquidation scheme of Kamstra
(2001) is used, these firms can be valued by traditional dividend-discounting models. Because all the
Gordon growth models produce similar results, the
discussion will focus on only the additive Gordon
model and the DK model.
Figures 12 and 13 present forecasts from the
additive Markov Gordon growth model and the DK
model, respectively, based on a stream of cash from
liquidating shares equal to approximately 3 percent
of the share price, calibrated to sales. The calibrations used were identical to those used for
BellSouth.25 The DK model results include forecasts
64
1992
D: Donaldson-Kamstra forecast
100
1
1986
1989
1989
1992
1995
1998
2001
from the slow- and rapid-fade-rate models, providing bracketing forecasts that one would expect to
contain the actual market price. In Figure 13 the
prices are presented in logarithms to compress the
scale for easier viewing.
The additive Gordon growth model (and indeed
any Gordon model that ignores the fade rate) provides forecasts that are wildly at odds with the market prices for these four stocks. Even at the end of
the sample, the last quarter of 2001, all but Yahoo
still appear overvalued by the market. Given that
the discount rate was calibrated to the S&P 500
index, even these prices are likely generous
because these four stocks are arguably riskier than
the average S&P 500 firm.26 These plots of market
prices versus fundamentals appear to strongly support the notion of a bubble in tech stock prices.
In contrast, the evidence from Figure 13 and the
DK model prices—prices that take into account the
fade rate of growth—does not support the notion of
a bubble in the prices of these four stocks. By this
method, Starbucks and Yahoo even appear to have
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
FIGURE 12
Additive Gordon Growth Forecasts of Share Prices of Microsoft, Sun Microsystems, Starbucks,
and Yahoo Using Share Liquidation Based on Sales
A: Microsoft
B: Sun Microsystems
60
100
80
50
Actual
Actual
60
Pr ic e
Pr ic e
40
30
40
20
Fitted
20
0
1994
10
1997
0
1994
2000
C: Starbucks
Fitted
1997
2000
D: Yahoo
30
200
Actual
160
Actual
P ric e
P ric e
20
120
80
10
40
Fitted
0
1994
1997
0
1994
2000
been somewhat undervalued given the high growth
rate of sales that each experienced over the last five
years or so while Microsoft and Sun Microsystems
display market prices that generally lie within the
brackets formed by the slow- and rapid-fade-rate
models. It should be noted that the bracketing forecasts generate a wide range of “reasonable” prices.
Also, it should be noted that share value is estimated
with models calibrated to the average S&P 500 firm,
but an investor arguably faces more risk holding
these four stocks than holding the average S&P 500
firm. Scenario analysis would factor in several different possible outcomes for all these stocks, including outright bankruptcy, that would lower the price
estimates, possibly a great deal for Yahoo.
Fitted
1997
2000
Conclusions
he pricing of stock market equity is one of
the oldest problems in finance, but it is only
in the last few decades that formal models have
been developed to answer some of the most pressing questions. Many algorithms used to price equity
are based on discounting cash flows accruing to
the investor, though some methods base valuation
on relative standing (that is, similar companies
with similar balance sheets should be priced similarly, have similar price-to-sales ratios, similar
price-to-earnings ratios, and so on) or a mix of
discounting and relative valuation through scenario analysis. Valuation techniques based on the
Gordon growth model, relative valuation, and the
T
25. The single exception is to the liquidation rule used in the DK and additive Markov Gordon growth models. Instead of using
the average yield ratio from the past year, the average yield ratio is formed from the entire history of the stock. This rule is
used because the high-growth stocks have much more volatile yield ratios than BellSouth has. Using only the past year produces similar results, with more exaggerated price movements forecast.
26. These four firms are all high-beta firms—that is, their stock returns are correlated with the overall market return but exhibit
higher volatility than the overall market return.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
65
FIGURE 13
Donaldson-Kamstra Bracketing Forecasts of Share Prices of Microsoft, Sun Microsystems,
Starbucks, and Yahoo Using Share Liquidation Based on Sales
A: Microsoft
B: Sun Microsystems
100
1,000
100
Rapid fade
10
Average fade
0
1994
1997
Actual
Pr ic e ( lo g s c a le )
Pr ic e ( lo g s c a le )
Actual
Slow fade
Slow fade
10
Rapid fade
1
Average fade
0.1
1994
2000
1997
C: Starbucks
2000
D: Yahoo
100
1,000
Average fade
10
Rapid fade
Actual
1
1994
1997
P ric e (lo g sc a le )
P ric e (lo g sc a le )
Slow fade
Slow fade
100
Average fade
10
Rapid fade
Actual
1
1994
2000
1997
2000
Note: Various parameterizations of the Donaldson-Kamstra model include a model calibrated to the average annual fade rate of the S&P 500
index over the last 100 years and models based on a rapid and a slow fade rate of growth in cash flows.
valuation method of Kamstra (2001) have been
focused on here.
To demonstrate these methods in practice, they
have been applied to pricing BellSouth shares, the
S&P 500 index, and a few new-economy stocks.
Pricing BellSouth using sales and sales growth is
consistent with its dramatic rise and recent decline
in price; this method is also appropriate for a small
group of high-growth stocks, including Microsoft,
Sun Microsystems, Starbucks, and Yahoo.
66
Fundamental models, however, have more trouble
explaining the price movements of the overall market. Whether this failure to explain the overall market
in the late 1990s is a shortcoming of these models or
the kind of information used to price the index (earnings rather than, say, sales) or of an assumption of
market rationality is not resolved here. Perhaps the
most important point to take from this review is that
algorithmic valuation techniques provide, at best, a
rough starting point for firm valuation.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
APPENDIX
Technical Details
Fundamental Valuation
The fundamental valuation equation is
P + Dt +1
(A1) Pt = ε t t +1
,
1+ rt
where Pt is the price of the stock at the beginning
of time period t, Dt+1 is the per share dividend
paid on the stock, rt is the rate at which payments
are discounted, and εt denotes the expectation of
the future price and dividends conditional on
what is known at the end of period t.
Solving equation A1 forward (substituting out
for the future prices with future dividends) yields
the textbook result that the market price equals
the expected discounted value of future dividends.
D
Dt +2
(A2) Pt = ε t t +1 + ε t
+
+
r
r
r
1
(
1
)(
1
)
+
+
t
t +1
t
dividend decreases, and ∆ = Σ Tt=2|Dt – Dt–1|/(T–1)
is the average absolute value of the level change
in the dividend payment.
The geometric Markov Gordon growth model is
1+( qu − qd )∆%
(A6) PtGEO = Dt
,
u
d
%
r −( q − q )∆
where ∆% = Σ Tt=2|Dt – Dt–1|/ Dt–1|/(T–1)is the average
absolute value of the percentage rate of change in
the dividend payment.
The Donaldson-Kamstra Gordon Growth Model
Define the discounted dividend growth rate from
the beginning of period t to the beginning of period
t + 1 as yt ≡ (1 + gt)/(1 + rt) where again gt equals
(Dt+1 – Dt)/Dt (the dividend growth rate) and rt is
the discount rate. Rewrite equation A3 as follows:
(A7) Pt = Dt[εt{yt} + εt{yt yt+1} + εt{yt yt+1yt+2} + …].
Dt +3
+…
(1+ rt )(1+ rt +1 )(1+ rt +2 )
εt
where “...” means “and so on.”
The Gordon Growth Model
Define the growth rate of dividends from the
beginning of period t to the beginning of period
t + 1 as gt ≡ (Dt+1 – Dt)/Dt , so that Dt+1 = Dt(1 + gt ),
Dt+2 = Dt(1 + gt )(1 + gt+1), and so on, and rewrite
equation A2 as follows:
1+ gt
(1+ gt )(1+ gt +1 )
(A3) Pt = Dt ε t
+ Dt ε t
+
+
r
1
t
(1+ rt )(1+ rt +1 )
(1+ gt )(1+ gt +1 )(1+ gt +2 )
Dt ε t
+ ...
(1+ rt )(1+ rt +1 )(1+ rt +2 )
Assume constant discount rates rt+i = r and constant growth rates of dividends gt+i = g for all values
of i and with g < r. Substituting r and g into equation A3 and applying results from infinite series
yields the classic Gordon price defined as P Gt:
The Donaldson and Kamstra (1996) method
estimates the price by generating thousands of
possible values of yt , yt+1, yt+2, ..., yt+I (values of y
out into the distant future, I periods from the present) and calculating
PV= Dt[yt + yt yt+1 + yt yt+1yt+2 + … + yt yt+1yt+2 … yt+I]
for each, averaging these values of PV. Although
this sum indexed by the parameter I should, technically, include all future values of y to infinity,
if I is large enough there is only a very small truncation error. Donaldson and Kamstra (forthcoming)
have found values of I = 400 to 500 for annual data
to suffice. What distinguishes this method from
other Gordon growth models is the way yt is generated. Donaldson and Kamstra suggest time series
models for yt that have autoregressive patterns of
dependence, a forecastable process.
The Augmented Dividend Case
1 + g
Dt +1
G
(A4) P Gt = Dt
or P t = r − g.
r
−
g
The Additive and Geometric
Markov Gordon Growth Models
The additive Markov Gordon growth model is
(A5) P ADD
= Dt /r + [1/r + (1/r)2](q u – q d)∆,
t
where q u is the proportion of the time the dividend increases, q d is the proportion of the time the
Define At as the total cash an investor receives
from her stock holdings in a particular company,
including the payments the company makes to the
investor (dividends paid by the company) and any
proceeds the investor receives as a result of selling shares in the company (to other investors).
Define Vt as the accounting variable (earnings,
total asset value, sales, etc.) that will be used to
calibrate investor share liquidations and notice
that At = Dt + Vt, where again Dt is dividends.
Define A’s growth rate as g at ≡ (At+1 – At)/At.
Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2003
67
A P P E N D I X (continued)
Define ft = αVt /Pt where α is set to determine the
yield. (For instance, if the firm pays no dividends,
Vt is earnings, and one wants to extract from one’s
portfolio a yield equal to the earnings yield, one
would set α equal to 1; if Vt was annual sales, one
would set α to 7 percent to extract a yield of
roughly 7 percent, as annual sales per share equals
price per share for many firms, based on Compustat annual data for S&P 500 firms over the last
twenty years.) Define the average yield ratio ft as
f, the average cash payment growth rate g at as
g a, and the average discount rate rt as r. Then
Kamstra (2001) derives the Gordon price with
augmented dividends to be
For the zero-dividend case, it can be shown that
r must equal g a so that equation A8 reduces to
= Vt /f.1 This formula is the relative value
P G,v
t
model. Knowing what yield ( f ) to expect, say,
from knowing what yields similar firms generate
and knowing what V is for the firm one is valuing
reveals what the price of the firm should be. For
example, if the firm is generating earnings of $1
per share and similar firms have an earnings yield
of 5 percent, then the firm should have a value of
$1/0.05 = $20.
The Donaldson and Kamstra (1996) model was
also extended in Kamstra (2001). Define yat= (1– ft)
(1 + g at)/(1 + rt ) and rewrite equation A7 as
1 + ga
.
(A8) P Gt ,v = At
a
a
1
−
+
(
+
)
r
g
f
g
(A9) Pt = Atεt{yαt + yαt yαt+1 + yαt yαt+1 yαt+2 + …}.
1. See, for instance, Ohlson (1991) for a discussion in the context of the growth of earnings when firms pay out less than
100 percent of earnings.
68
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