Full text of Economic Review (Federal Reserve Bank of San Francisco) : Summer 1988, Number 3

View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Economic

Review

Federal Reserve Bank
-of San Francisco
SUlIlmer 1988

Number 3

Reuven Glick

Saving-Investment Determinants of
Japan's External Balance

Carolyn Sherwood-Call

Exploring the Relationships between
National and Regional Economic Fluctuations

Adrian W. Throop

An Evaluation of Alternative Measures

of Expected Inflation

Table of Contents
Saving-Investment Determinants of
Japan9§ External Balance „„.»«, . „ 0„. . . „«„. 0

Eeevemi Glide

Exploring the Relationships between National
and Regional Economic Fluctuations »„. 0»»«,,

1§

Carolye SIhierwo<Ddl=Call

An Evaluation of Alternative Measures of
Expected Inflation

Adriae W. Tfaroop

Federal Reserve Rank off San Francisco

Opinions expressed in the Economic Review do not neces
sarily reflect the views of the management of the Federal
Reserve Bank of San Francisco, or of the Board of Governors
of the Federal Reserve System.
The Federal Reserve Bank of San Francisco’s Economic Review is
published quarterly by the Bank’s Research Department under the
supervision of Jack H. Beebe, Senior Vice President and Director of
Research. The publication is edited by Barbara A. Bennett. Design,
production, and distribution are handled by the Public Information
Department, with the assistance of Karen Rusk and William Rosenthal.
For free copies of this and other Federal Reserve publications, write or
phone the Public Information Department, Federal Reserve Bank of San
Francisco, PO. Box 7702, San Francisco, California 94120. Phone
(415) 974-2163.

Economic Review / Summer 1988

Saving-Investment Determinants
of Japan's External Balance

Reuven Glick
Senior Economist, Federal Reserve Bank of San Francisco. Able research assistance by Mark Thomas, Kim
Luce, and Laura Shoe is gratefully acknowledged. Editorial Committee members were Ramon Moreno, Carolyn
Sherwood-Call, and Bharat Trehan.

This article examines the'role of domestic and foreign
saving-investment behavior in the determination of Japan's current account. Declining fiscal spending in Japan
and rising fiscal spending in the United States both are
found to be major factors in the emergence of Japan's
recent external surpluses. This implies that policy changes
in both countries may be necessary to reduce Japan's large
surpluses.

Federal Reserve Bank of San Francisco

In recent years, Japan's large external surpluses have
drawn much attention. Its current account balance in
nominal dollars rose from a small surplus of $5 billion in
1981 to $86 billion in 1986. Relative to GNP, the surplus
increased over this period from less than one-half of one
percent to more than four percent.
The rising surplus has stirred conflicts with many of
Japan's trading partners. A better understanding of the
causes of this increase is needed to determine what policy
responses may be appropriate.
The explanations for Japan's apparent propensity to
export more than it imports have varied. Some have
focused on "closed markets" and "unfair trade practices"
that Japan allegedly has erected as barriers to foreign
goods. Advocates of this view have urged Japan to reduce
its trade barriers and to "buy foreign." However, there is
little evidence that Japan's existing trade barriers have risen
in the last several years at the time that its surpluses have,
grown. In fact, on balance, such barriers probably have
fallen. l
Others have asserted that an "undervalued" yen prior to
1985 contributed heavily to Japan's external surpluses. 2
However, when the yen appreciated more than fifty percent
against the dollar between February 1985 and the end of
1986, these surpluses did not show signs ofleveling off and
falling until recently. 3 As a result, most doubt that exchange rate changes alone will suffice to eliminate Japan's
surpluses. 4
The relation between the current account, the exchange
rate, and other macroeconomic variables depends fundamentally on underlying saving and investment flows.
National income account relationships imply that a country's current account depends on domestic private saving
and investment behavior, as well as on domestic fiscal
saving. An excess of domestic private saving over domestic
private investment that is not "absorbed" by an excess of
government expenditures over tax receipts can result in
domestic net savings flowing abroad. The counterpart of
this outflow of savings is a current account surplus. From
this point of view, some have argued that the Japanese
"save too much," and they suggest that the high saving
rate by the private sector in Japan is the cause of Japan's
trade surpluses. Accordingly, Japanese authorities have

been entreated, explicitly or implicitly, to adopt policy
measures to discourage saving.
Still others have suggested that the recent rise in Japan's
surpluses can be attributed in large part to the policies of
the United States, Japan's largest trading partner. Since
one country's current account deficit is another's surplus,
macro developments in the rest of the world also are among
the determinants of a country's current account. The rise in
U.S. government deficits, according to this view, generated an excess demand for foreign goods by U.S. residents
and accordingly, a rise in Japan's net exports. 5
This paper provides an empirical analysis of Japan's
current account as the product of its domestic and foreign
saving-investment balances. The strategy of the paper is to
estimate a current account equation relating the actual
current account to variables generating short-run business
cycle fluctuations in the current account and to nonbusiness cycle, or "autonomous," movements in domestic
and foreign net savings. The estimated equation is used to
decompose current account movements into autonomous
and cyclical components, and in particular, to determine
the extent to which Japan's current surpluses can be
attributed to domestic and foreign saving-investment
behavior.
The major conclusion of this analysis is that most of
Japan's present current account surplus can be related to
autonomous factors affecting private and government net

saving flows. Moreover, a decline in autonomous net
saving in the United States associated with the emergence
of fiscal spending deficits in the early 1980s has been a
major contributor to this surplus. Autonomous net saving
behavior in Japan and in the United States each accounts
for 2Yz percentage points of the 4 percentage point increase
in the ratio of Japan's current surplus to GNP between 1981
and 1986. Cyclical factors actually worked to reduce the
surplus by roughly 1 percentage point.
These findings suggest that adjustment by both the
United States as well as Japan may be necessary to reduce
Japan's external surplus. In fact, there are signs that these
adjustments already are occurring. Following the recommendations of the 1986 Maekawa Report, Japan has moved
to stimulate domestic demand and reduce net saving by
increasing government expenditures, providing greater
incentives for housing investment, and raising taxes on
saving accounts. 6 At the same time, since 1986 the United
States has moved in the direction of reducing its fiscal
deficits.
The plan of this paper is as follows: Section I reviews
recent trends in Japan's current account and in the private
saving-investment and government saving balances of both
Japan and the U. S. Section II presents a simple twocountry model of the determinants of the current account
balance. Section III describes the empirical analysis, and
Section IV summarizes the results.

I. Recent 'frends
From national account identities, the excess of the sum
of domestic private (S) and government saving (TG) over
domestic investment (I) equals a country's current account
surplus (CA):
CA = S - I

Chart 1 plots, over the period 1966 to 1986, four-quarter
moving averages of Japan's current account, private
saving-investment (SI = S - I), and government saving
balances, ea,ch as a share of GNP.7
Over the past twenty years, Japan's current account
balance has shifted widely, with deficits as well as surpluses. Surpluses averaging roughly 2 percent of GNP
were recorded in 1971-1972 and in 1978. Deficits averaging 1 percent emerged at the time of the oil price crises of
1974 and 1979-1980.
The most recent surpluses, however, are significantly
greater than those previously attained. From 1966-1980,
Japan's current account averaged a surplus of only 0.6

percent of GNP, with a peak of 2.4 percent in 1971. In
1985, the surplus reached 3.7 percent of GNP and in 1986,
4.3 percent.
Chart 1also shows that in recent years Japan's net private
saving-investment balance (SI) has increased as a percent
of GNP. From 1966 to 1974 this balance averaged 1.4
percent; from 1975 to 1980,3.2 percent, and from 1980 to
1986, 3.7 percent. Between 1980 and 1986 it rose by
almost three percentage points.
Contrary to the common view, this rise in Japan's net
private saving balance is the result of a sharp decline in
investment rather than a rise in saving. Private saving
averaged 17.5 percent of GNP from 1966 to 1974, 16.6
percent from 1975 to 1980, and 14.1 percent over the 19811986 period. 8 The long-run trend, in fact, has been a small
decline in Japan's private saving rate.
Since 1975, the rate of private investment in Japan has
fallen sharply. Net investment averaged 18.9 percent of
GNP during the 1966-74 period, 13.4 percent during
1975-80, and 10.3 percent from 1981 to 1986. A decelera-

Economic Review / Summer 1988

tion in Japan's long-run growth rate and a resulting reduction in domestic prospects for net investment have been
associated with this declining investment. 9
Japan's private saving-investment surplus is only part of
the reason that the current account recorded such large
surpluses in recent years. As the identity above implies,
the behavior of government saving (i.e., government receipts minus expenditures) also has played a role.
Over the period from 1975 to 1979, the growth in surplus
net private saving was largely matched by a rise in government budget deficits that reached 4.1 percent of gross

national output in 1978, well above the average of 2.2
percent over the period from 1966 to 1974. Budget deficits
rose because of increased government spending associated
with the oil price shocks of the 1970s and the growth of
social welfare programs. Since 1979, the budget deficit has
declined steadily, with a small surplus attained in 1985.
This improvement in the budget deficit reduced the demand for domestic saving. Thus the dramatic rise in
Japan's external surpluses in the 1980s can be attributed
more to sharp drops in private investment and the government budget deficit, than to an increase in private saving.

Chart 1
Japanese Net Saving
and Current Account Balances
Percent

6
4

2
0

-2
-4

~
Government Saving

-6
66

Chart 2
U.S. Net Saving Balances

Percent

8
Private Saving

- 6 .........TTTTTTTTTTTTTTTT...,.,.,.,TTTT...,.,.,.,...,.,.,.,...,.,.,.,TTTTTTTT...,.,.,.,TTTTTTTTTTTT...,.,.,.,...,.,.,.,TTTT...,.,.,.,...,.,.,.,."
66

Federal Reserve Bank of San Francisco

In a global context, Japan's net exports (CA) are net
imports by the rest of the world. Following the national
account relation above, these net imports equal the excess
of investment over private and government saving in the
rest of the world.
Chart 2 plots four-quarter moving averages of the private
saving-investment (SI*) and government saving (TG*)
balances of the United States, Japan's largest trading
partner, over the period 1966-1986. Observe that in contrast to recent trends in Japan, fiscal saving in the U.S.
shifted from small surpluses (0.5 percent of GNP in 1979)
to large deficits, averaging 3.4 percent during 1982-1986.
Mirroring these increasing deficits has been a fall in the
private saving-investment balance in recent years. This

suggests that budget policies in the United States may be
an important factor behind the development of Japan's
current account surpluses.
In a general equilibrium context, savingand investment
behavior both domestically and abroad are jointly determined by business cycle changes as well as by exogenous
monetary and fiscal policy variables at home and abroad,
and other fundamentally exogenous forces, such as autonomous shifts in private consumption or investment behavior.
The following sections examine the extent to which the
movements in private and government saving-investment
balances and Japan's current account reflect autonomous or
business cycle factors in Japan and abroad.

II. Theory
This section develops a simple two-country model of the
determinants of the current account. The purpose of the
analysis is not to capture all aspects of saving and investment behavior, but rather to focus on the essential channels
of current account adjustment within a simplified framework.
The conditions for equilibrium in the goods market in the
two countries can be written as (with time subscripts
omitted):
CA = SI

+ TG

-CA = S1*

+ TG*

According to (3) and (4), net private saving depends on
autonomous factors, the gap between actual and potential
GNP, and the real interest rate. ll The latter two terms
reflect the effects of the business cycle and other short-run
factors. The parameter S2 is assumed positive: a rise in the
interest rate raises saving and reduces investment. The
sign of SI depends on the relative effect of an increase in the
GNP gap on private saving versus investment.
Government net saving is specified as

(1)

TG = TGO[Z2J

(2)

TG* =

where SI, TG, and CA denote net private saving (private
saving minus investment), net government saving (government receipts minus expenditures), and the current account
balance, respectively. The variables with an asterisk denote
the equilibrium for the foreign country-referred to as the
United States. Those without an asterisk represent the
domestic country-Japan, in this analysis. 10
Net private saving for the domestic and foreign country
takes the following form:

s; (y* - y*)

s; r*

(4)

where for Japan SIo denotes autonomous net private savings; y, real output; y, full employment or potential output; r, the real interest rate; and ZI' a set of exogenous
variables that affect autonomous savings. The same variables for the United States again are denoted by an
asterisk.

[Z;J

(5)

+ t* (y* - y*)

(6)

where TGo, TG~ represent autonomous government saving, and Z2' Z; denote exogenous variables that affect
autonomous government saving for Japan and the United
States, respectively. The parameters t and t* are expected to
be positive. TGo and TG~ may be interpreted as fullemployment budget surpluses attained when actual output
equals potential output.
To proceed, substitute (3) - (6) in (1) and (2), multiply
(1) by s; and (2) by S2' take the difference, and solve for
CA:

(3)

SI* = S1:; [Z;J

TG~

+ t(y - y)

CA =

S2*
(SIo
S2 + S2 *

+ TGo) - + (SIo* + TGo*)
S2 S2*

S2 S2*
~-~
S2 + S2*

Economic Review / Summer 1988

Equation (7) provides an equation describing the determinants of the current account of the domestic country in both
the long and short run.
In long run equilibrium, y = y and y* = y* and, assuming domestic and foreign assets are perfect substitutes,
r = r* = r. Thus the first two terms of equation (7)
may be interpreted as the autonomous components of the
current account that are unrelated to the movements in the
domestic and foreign saving balances associated with
cyclical changes in GNP gaps and interest rates. The
difference between these components may be interpreted
as the domestic country's long run current account balance,

CAo· lZ
The long-run current account tends to improve when
autonomous domestic saving increases relative to that of
the foreign country. Thus an increase in domestic private
saving or domestic government saving, or a fall in autonomous foreign private or government saving leads to a rise in
the current account balance.
Intuitively, an autonomous decrease in, say, foreign
saving tends to reduce the net flow of capital to the
domestic country. The counterpart to the fall in foreign
saving and capital inflows to the domestic country is a rise
in goods bought in the domestic country relative to goods
bought abroad, causing a rise in the domestic country's
current account balance. The mechanism through which
these changes occur involves a rise in interest rates to
crowd out investment and dampen the fall in saving, as
well as a depreciation (appreciation) of the domestic (foreign) country's currency to dampen the rise (fall) in its
currrent account. 13
Note that the impact of autonomous changes on the
current account depend on the interest elasticities of net
saving both domestically and abroad (sz and s;). Moreover, a testable implication is that the absolute values of the
coefficients of these two terms sum to one.
The last three terms of (7) represent the short-run,

cyclical determinants of the current account. In the short
run the current account may differ from its long-run
equilibrium level because the determinants of private and
public saving-income and the interest rate-deviate
from their long-run values.
Whether a positive domestic GNP gap (y > y) increases
or decreases the current account below its long-run level
depends on the propensity for net private saving out of
income (Sl)' If this propensity is sufficiently negative (i.e.,
Sl < 0 and Sl + t < 0), then a rise in output above potential
reduces the current account. Intuitively, an increase in
income above its full employment level causes domestic
investment to rise by more than private saving does,
thereby inducing a fall in net domestic saving and a fall in
the current account. On the other hand, if Sl + t > 0 (a
sufficient condition is Sl > 0), a rise in output induces an
increase in the current account.
At first glance, this latter case may seem contrary to the
typical Keynesian view that a rise in domestic income
worsens the trade balance. However, the result here presumes that other determinants of the current account,
particularly the autonomous components, are held constant. If, for example, the increase in domestic income is
generated by an expansionary autonomous fiscal policy
(fall in TGo), equation (7) may indeed imply that a worsening of the current account would be observed at the same
time. Foreign GNP gaps produce symmetrical results.
Unlike the effect of a GNP gap, the effect of an interest
rate differential between the domestic and foreign countries is unambiguous. A positive domestic interest rate
differential induces greater net saving domestically than
abroad and a corresponding rise in the current account.
In summary, the long run current account is determined
by the autonomous levels of net private saving and government saving domestically and abroad. In the short run,
business cycle movements in output and in interest rates
can affect the current account as well.

III. Estimation
Methodology
The strategy of the paper now is to estimate the autonomous and cyclical components of Japan's current account
following the approach suggested by Ueda (1987). First,
measures of the autonomous components of net private and
government saving domestically and abroad are derived
from estimates of equations following the specifications of
(3)-(6). Next, an equation is estimated which relates the
current account to the autonomous factors and to cyclical
variables, as suggested by (7). The resulting equation is

Federal Reserve Bank of San Francisco

then employed to determine the relative magnitudes of
autonomous and cyclical factors.
Although Japan trades with many countries, it is difficult and cumbersome to construct savings measures for
most countries, particularly on a quarterly basis. Consequently, the United States, Japan's largest trading partner,
will be treated as representing the rest of the world in this
analysis. In (fiscal year) 1986 Japan's bilateral trade surplus with the United States accounted for more than half
(57.9 percent) of its total trade surplus.l4 Treatment of the

United States as a proxy for the "rest of the world" should
provide a rough approximation of the role of foreign
factors in Japan's current account. 15
The data sample covers the first quarter of 1965 through
the fourth quarter of 1986. The source and construction of
the data are described in the appendix. A proxy for
potential GNP was derived from fitted values of regressions of the log of GNP on constant, trend, and trendsquared tenns .16 In the case of Japan, separate regressions
were run for the periods from 1966:1 to 1973:4 and from
1974:1 to 1986:4 to account for a shift in the pattern of real
economic growth. Proxies for ex ante real interest rates
were obtained from ex post real long-tenn government
bond rates, deflated by two-year ahead inflation rates in the
case of the U. S. and two-quarter ahead inflation rates in the
case of Japan. I?

The equations were log-linear approximations of (3)(7), with dependent variables scaled by potential GNP.
Since the saving-investment balances, GNP gap, and real
interest rate measures are themselves endogenous, instrumental variables were employed in the estimation. The
instruments used in each equation included potential output and lagged values of the dependent and all explanatory
variables, except for the real interest rate. In addition, the
TG equations included current and lagged money supply
growth; the SI equations included four lags of the quarterly
inflation rate, the lagged nominal interest rate, current and
three lags of money supply growth, and two lags of
government savings; the current account included four lags
of the quarterly inflation rate for both countries, and four
lags of money supply growth for both countries and the
lagged nominal interest differential. 18

Economic Review / Summer 1988

The government saving equations were not corrected for
serial correlation since they are structural rather than
behavioral equations, and the t-statistics associated with
the coefficient estimates did not matter. The private saving
equations, however, were corrected for serial correlation in
the following way: an estimate of the serial correlation
parameter was obtained from the residuals of the initial
application of the instrumental variables regression. The
final results were then obtained by performing an ordinary
least squares regression on the quasi-differences of exogenous variables and the instrumented values of endogenous variables. 19 The current account equation did not
require correction for serial correlation.

Results
The results of the equations used to estimate autonomous and cyclical private saving and government saving
are reported in lines 1-4 in Table 1. ,
Net private saving in Japan (SI) is positively related to
the real interest rate and negatively to the lagged GNP gap.
For the United States, both the GNP-gap and the real
interest rate enter positively. In both countries, the interest
rate signs are as expected. The effect of the GNP gap on net
private saving is theoretically ambiguous, as discussed
earlier. An increase in the GNP gap causes saving to rise by
more than investment in the U.S. (s~ > 0) and by less than
investment in Japan (S1 < 0). In the government saving (TG,
TG*) equations the GNP gap entered significantly with the
expected positive sign for both countries.

With these results, measures of the autonomous net
private saving balances (SIo, SI(;) were obtained by subtracting the GNP gap and real interest rate terms from the
actual balances. Likewise, measures of autonomous government saving balances (TGo, TG~) were obtained by
subtracting the terms representing the effect of the GNP
gap from actual balances. This construction implicitly
attributes the error terms in the estimated equations to
autonomous factors.
Charts 3 and 4 depict four-quarter moving averages of
autonomous and actual net private saving balances relative
to potential GNP for Japan and the United States, respectively. Charts 5 and 6 depict the autonomous and actual
government saving balances for the two countries.
Chart 3 indicates that autonomous factors (SIo) account
for most of Japan's net private saving (SI), particularly
during the shift from deficits to surpluses in 1975. This
suggests that the decrease in investment that occurred
in the mid-1970s was not just a short-run business cycle phenomenon, but rather was the result of structural
changes in Japan's economy. Since 1981, Japan's autonomous private saving has increased moderately.
Chart 5 shows that since the early 1970s movements in
Japan's government saving balance (TG) have been dominated by autonomous factors (TGo) to an even greater
extent than was the case for private savings. In recent
years, Japan's rising level of government saving (falling
budget deficits) also primarily is the result of changes in
autonomous, rather than business cycle, factors.

Chart 3
Japanese Net Private Saving

Chart 4
U.S. Net Private Saving

Percent

Percent
8

Private
Saving

-2

-4

Autonomous
Private Saving

- 6 +nT""lI'""T,.,.",...,..,rrrrr""""T""lI"""T,.,.",...,..,rrrrr".....,T""lI"""T"""'''''''

Federal Reserve Bank of San Francisco

Chart 4 indicates that the portion of U.S. net private
saving (SI*) that is driven by autonomous factors (SI~) declined sharply in 1983 but has since remained relatively
flat.
Chart 6 shows that actual and autonomous government
saving balances for the United States (TG* and TG~, respectively) do not track as closely as in Japan. Thus for the
U.S., cyclical factors playa much greater role in government saving. Still: much of the fall in government saving
(increase in the budget deficit) in the early 1980s has been
autonomous in nature.
Summing autonomous government saving together with
autonomous net private saving gives total autonomous
domestic saving in each country (Slo + TGo, S~ + TG~).
In Japan, autonomous domestic saving averaged surpluses
of2 to 3 percent of potential GNP in the mid-1970s, but fell
to deficits of neady 3 percent in 1976, as a result of the
sharp increase in the structural government budget deficits. Since then, the reversal of fiscal policy and the
moderate rise in private saving in Japan, have induced a
strong rise in the autonomous domestic saving balance. In
the United States, aggregate private and government saving both have declined sharply since 1982; the U.S.
autonomous domestic saving balance, converted into yenequivalent terms by the real yen price of the dollar (denoted
by q in Table 1) has risen (in absolute value) to about 6
percent of Japan's potential output.
The estimated effects of domestic and foreign net saving
behavior on Japan's current account are reported in line 5

of Table 1. All coefficients have the expected signs, and,
except for the interest rate differential, are statistically
significant at the .05 level.
Note, in particular, that the current account depends
positively on autonomous Japanese saving and negatively
on U.S. autonomous saving. As implied by theory, the
hypotheses that the absolute values of these two coefficients sum to 1 cannot be rejected.
Cyclical factors also are important. An increase in the
Japanese income gap worsens Japan's current account; an
increase in the U.S. gap also reduces the current account.
As discussed earlier, the finding that an increase in the
U.S. GNP gap worsens its own external balance and
improves that of Japan's presumes that all other factors are
being held constant. If, for example, the increase in U.S.
income is generated by an expansionary autonomous fiscal
policy (fall in TG~), this analysis may imply that Japan's
current account would improve.
To see more clearly the effects of autonomous factors
(TGo + Slo and TG~ + SI~) on Japan's current account,
the actual (moving-average) current account balance (CA)
and the estimated autonomous balance (CAo) are plotted
separately in Chart 7. For the years in which Japan experienced large surpluses in its current account (1972-1973,
1978, and 1982-1985) autonomous saving-investment behavior appears to have played a large role. The influence of
cyclical factors assooiated with income and interest rate
movements is apparent, particularly in 1981 and 1982
when the autonomous current account appears to have been

Chart 5
Japanese Government Saving

Chart 6
U.S. Government Saving

Percent

Autonomous
Government Saving

4
2

o+-------\-----------.~

-2

-4

Government
Saving

Autonomous
Government Saving

-6
68

Economic Review I Summer 1988

Chart 7
Japanese Current
Account Balance
Percent

8
6
Current
Account

Autonomous
Current Account

-2
-4
68

in deficit and actual surpluses were occurring. However,
beginning in 1983, it is apparent that Japan's autonomous
current account moved strongly into surplus, and now
accounts for almost all of the recent actual balance.
Chart 7 also suggests that U. S. .fiscal policies have
played a major role in the recent emergence of Japan's
external surpluses. By comparing Japan's autonomous
current account (CAo) with the estimated autonomous
balance modified to remove the effects of autonomous U.S.
budget policy, it is clear that, in the absence of any effects
of U.S. fiscal policies, the autonomous current account in
Japan decreases in almost all periods, particularly in the

1980s. In 1986, for example, this analysis implies that
Japan's current account surplus would have been roughly
one-half its actual level.
In other words, of the cumulative 4 percentage point
increase in the ratio of its surplus to potential GNP
between 1981 and 1986, autonomous net saving behavior in
Japan explains 2.5 percentage points and net saving behavior in the U. S. accounts for 2.3 percentage points.
Cyclical factors worked to reduce the surplus by roughly 1
percentage point. Thus U.S. policies as well as developments in Japan have played a role in Japan's emergence as a
surplus country in international trade transactions.

IV. Conclusions
The framework used in this paper has focused on the role
of domestic and foreign saving-investment balances in the
determination of Japan's current account. This analysis
indicates that autonomous changes, particularly those related to government budget policies, have been important
determinants of Japan's current account. Most importantly, it suggests that Japanese saving-investment behavior alone does not explain recent increases in the
external surpluses. The large U.S. budget deficits since
1982 also have played a major role.
These results imply that changes in autonomous government or private saving in both countries may be necessary
to bring down Japan's large surpluses. Specifically, the
United States needs to reduce its fiscal deficits, and Japan
simultaneously ought to increase its deficit spending.

Federal Reserve Bank of San Francisco

In fact, there are signs that such adjustments already are
occurring. Following the recommendations of the 1986
Maekawa Report, Japan has moved to stimulate domestic
demand and reduce net saving. Government expenditures
have increased, stronger incentives for housing investment
have been provided, and taxes on previously exempt savings accounts have been introduced., The desire to stimulate a lagging economy was the motive, but such measures
also should contribute to a decline in Japan's current
account surpluses.
In the U. S., the federal budget deficit has been reduced
significantly, from $221 billion in 1986 to $156 billion in
1987. While it is unclear how quickly the deficit will be
reduced in the future, the trend is in the proper direction.

ENDNOTES
1. Bergstrand (1986) cites evidence that Japanese tariffs
are no higher on average than U.S. tariffs and that U.S.
non-tariff barriers are as widespread as those in Japan.
2. Frankel (1984) discusses how prevalent this view was
among U.S. Treasury officials when negotiating with Japan to reduce its barriers to international capital flows.
Neither Frankel, nor Haynes, Hutchison, and Mikesell
(1986), find any evidence that Japan's financial policies
were directed towards depressing the value of the yen.
3. Haynes, Hutchison, and Mikesell (1986) surveyed recent evidence and found that in the 1980s Japanese trade
flows have been relatively insensitive to exchange rate
changes.
4. See Sakamoto (1988).
5. See Hutchison and Pigott (1984) and Bergsten and
Cline (1985).
6. The Maekawa Report is formally known as "The Report
of the Advisory Group on Economic Structural Adjustment
for International Harmony," and was released by the Japanese government on April 17, 1986.
7. The GNP scaling variable used is "potential" output.
The method used to construct this measure is described
in Sec~ion III. The private saving measure used for Japan
is defined to include statistical discrepancy.
8. Japan's traditionally high level of saving may reflect the
need for retirement funds to supplement the low level of
social security benefits, the high cost of housing, and
heavy educational expenses. See Bergsten and Cline
(1985) and Islam (1986).
9. Kasman (1987) estimates that Japan's potential real
growth rate fell from 9 percent over the period 1967-1973
to 4.5 percent over 1976-1986. He attributes the deceleration of Japan's potential growth rate to declines in
the rate of capital accumulation and in the rate of technical
progress as the economy has matured. Other factors
besides the slowdown in growth that also may have
contributed to the sharp drop in the propensity to invest
include (i) declining budget deficits beginning in 1979,
which curbed public investment, and (ii) high real interest
rates and the price of urban land, which caused residential construction to fall.
Some have argued that the timing of the shift in Japan's
growth rate suggests that the oil price increases of the
1970s played a major role. While these shocks may explain cyclical movements in Japan's GNP, other countries
more dependent on oil experienced less deceleration in
trend growth in the 1970s.
10. Note that since goods market equilibrium in this
model depends on the government budget balance,
Ricardian equivalence does not hold.
11. Terms of trade and exchange rate effects on saving
and investment are neglected. This specification also
abstracts from the dynamics associated with the response of saving and investment to wealth accumulation.

Turner (1986) specifies a model in which investment and
saving depend directly on the exchange rate.
12. Since this specification abstractsfrom the dynamics
associated with the response of saving and investment to
wealth accumulation, in the long-run equilibrium of this
model the current account may not equal zero. It also
does not take into account complications arising from
debt financing of the deficit in the short-run and the
ultimate need to rais.e taxes to service the larger debt
implied by the government budget constraint.
13. The implicit adjustment of the exchange rate and
interest rate may be seen by specifying the determinants
of the current account generally as follows:

where q is the real exchange rate, defined as the real yen
price of the dollar, and Z3 is a vector of exogenous
variables that affect the current account. A Keynesian
theorywouldimplyc1>0,c2<0,c2> O. We abstract from
the interest payments on net foreign assets.
In the short run, the two equilibrium conditions (1) and (2)
determine the two output levels y and y', with the interest
rates determined elsewhere in asset markets in an unspecified manner. In the long run, y = 'I, y' = 'I', r = r*
= and q = q. Hence (1) - (6) imply

Si o + TG o + si' = CA a + c1Q
Si o + TG o + s; r = - (CAa + c1Q).
Solving these two equations for the two unknowns rand

q yields:

(1/c 1) {(S;/(S2+ S;))OSo

(1/(S2 + s;))(OSo + OS~)

- (S2/(S2 + s;))OS~ - CAa },

where OSo = Si o + TG o, OS; = SI6 + TG Thus, in the
long run, the real interest rate and the exchange rate
depend only on autonomous private and government
saving. Substituting in (A.1) gives the long-run current
account, CAo:

Economic Review / Summer 1988

The long-run current account depends on the exogenous
current account CAa and the long-run exchange rate q. An
increase in either domestic private or government saving
depreciates the country's currency and improves its current account.
14. Sakamoto (1988).
15. Ueda (1987) considers the saving behavior of both
the United States and OPEC. Knight and Masson (1988)
construct a simulation model of the interaction of saving
and investment behavior in Japan, the United States, and
Germany.
16. The trend-squared term allows trend growth to be
flexible. An alternative approach used by Ueda (1987)
and Kasman (1987) is to estimate full-employment GNP
for Japan from a production function.

17. These inflation horizons worked best in the empirical
analysis. Federal Reserve Bank of San Francisco staff
forecasts were used for U.S. inflation during 1988 where
appropriate.
18. Money growth, inflation, and nominal interest rates
were included in the list of instruments to properly instrument out the real interest rate.
19. The instruments are quasi-differenced by taking the
difference between the current value of the instrument
and the lagged actual value of the instrumental variable
(the latter, of course, multiplied by the serial correlation
estimate). See Fair (1972), who points out that in generating instruments, the exogenous variables should include
lagged values of all endogenous variables (including the
dependent variable), and current and lagged values of
predetermined variables.

DATA APPENDIX
Sources
Bank of Japan Statistical Monthly (BOJSM);
Bank of Japan Statistical Annual, National Income Statistics (BOJSANI);
Citibase (CB);
Data Resources, Japan Database (DRI);
International Financial Statistics (IFS)

Japan
Real GNP: billions of 1980 yen, BOJSM
Potential GNP: Calculated from antilog of fitted values of
an OLS regression of the log of real GNP on constant,
trend, and trend-squared terms estimated over periods 1965:2-1973:4 and 1974:1-1986:4
Price level: implicit GNP deflator, 1980 = 100, BOJSM
Long-term interest rate: central government bond rate,
percent per year, end of period, DRI
Exchange rate: yen per dollar, period average, IFS line
158rf
Money supply: M1 + Quasi-money + CDs, billions of yen,
end of period, IFS lines 34 + 35 + 36aa
The following series are in billions of yen and were seasonallyadjusted using the SAS X-11 procedure:
Current account balance = net lending to rest of world capital transfers from rest of world
Net lending to rest of world: BOJSANI, Table6, line 3.3
Capital transfers from rest of world: BOJSANI, Table 6,
line 3.6
Government savings = government receipts - government expenditures
Government receipts: BOJSANI, general government
section
Government expenditures = government receipts
- government savings + general government
gross fixed capital formation - general government capital consumption

Federal Reserve Bank of San Francisco

Government savings: BOJSANI, general government section; also DRI series SAVEGNS
General government gross fixed capital formation: BOJSANI, gross national expenditure
section-Table 1, line 3.1.b.c; also DRI series
GIFIXONS
General government capital consumption = total
gross fixed capital consumption - private
capital consumption
Total gross fixed capital consumption:
BOJSANI (also DRI series CCANS)
Private capital consumption available annually from DRI series CCAP. Quarterly series computed assuming percentage of
total to private capital consumption is
constant over the year.
Net private savings = private savings - private investment
Private savings = total savings - general government savings + statistical discrepancy
Total savings: BOJSANI, Table 6
General government savings: see above
Statistical discrepancy: BOJSANI, Table 6
Private investment = change in inventories + private
gross fixed capital formation - private capital
consumption
Change in inventories: BOJSANI, Table 6, line 3.2
Private gross fixed capital formation: BOJSANI,
Table 1, line 3.1.a
Private capital consumption: see above

United States
Real GNP: billions of 1982 dollars, CB
Potential GNP: Calculated from antilog of fitted values
of an OLS regression of the log of real GNP on
constant, trend, and trend-squared terms over period
1965:2-1986:4.

Long-term interest rate: 20 year Treasury bond rates,
monthly average, percent per annum, CB series
FYGT20
Money supply: M2, monthly average, billions of dollars,
CB
Price level: GNP implicit deflator, CB. (Figures for 1988
used in calculating ex post real interest rate from
FRBSF staff forecasts.)
The following series are in billions of dollars, at seasonally
adjusted annual rates:

Net private savings = gross private savings - gross
private domestic investment
Gross private savings: CB series GPS
Gross private domestic investment: CB series GPI
Government savings = government receipts - government expenditures
Total government receipts: CB series GGFR -I- GGSR
Total government expenditures: CB series GGFEX -IGGSEX

REFERENCES
Bergsten, C. Fred and William Cline. The United StatesJapan Economic Problem, Washington, D.C., Institute
for International Economics, No. 13, October 1985.
Bergstrand, Jeffrey. "United States-Japanese Trade: Predictions Using Selected Economic Models," New
England Economic Review, Federal Reserve Bank of
Boston, May/June 1986.
Fair, Ray. "The Estimation of Simultaneous Models with
Lagged Endogenous Variables and First Order Serially Correlated Errors," Econometrica, Vol. 38, May
1970, pp. 507-516.
Frankel, Jeffrey. The Yen-Dollar Agreement: Liberalizing
Japanese Capital Markets, Washington, D.C.: Institute for International Economics, 1984.
Haynes, Stephen, Michael Hutchison, and Raymond
Mikesell. "Japanese Financial Policies and the U.S.
Trade Deficit," Essays in International Finance, No.
162, Princeton University, International Finance Section, 1986.
Hutchison, Michael and Charles Pigott. "Budget Deficits,
Exchange Rates, and the Current Account: Theory
and U.S. Evidence," Economic Review, Federal Reserve Bank of San Francisco, Fall 1984.

Islam, Shafiqul. "Does Japan Save Too Much?" Washington, D.C.: Institute for International Economics, June
1986.
Kasman, Bruce. "Japan's Growth Performance over the
Last Decade," Quarterly Review, Federal Reserve
Bank of New York, Summer 1987.
Knight, Malcolm and Paul Masson. "Fiscal Policies, Net
Saving and Real Exchange Rates: The United States,
the Federal Republic of Germany, and Japan," in J.
Frankel (ed.), International Aspects of Fiscal Policies,
Chicago: University of Chicago Press, 1988.
Sakamoto, Tomohiko. "Japan-U.S. Bilateral Trade," Economic Review, Federal Reserve Bank of San Francisco, Spring 1988.
Turner, P. "Savings, Investment, and the Current Account: An Empirical Study of Seven Major Countries,
1965-84," Bank of Japan Monetary and Economic
Studies, October 1986.
Ueda, Kazuo. "Investment Savings Balance and the Japanese Current Account Surplus," Japan Center for
International Finance, Policy Study Series, No.7, May
1987.

Economic Review / Summer 1988

Exploring the Relationships between
National and Regional Economic Fluctuations

Carolyn Sherwood-Call
Economist, Federal Reserve Bank of San Francisco. The
author wishes to thank Bharat Trehan for his help with
VARs, and the editorial committee for many helpful
suggestions. Scott Gilbert provided invaluable research
assistance. Editorial committee members were Barbara
Bennett, Michael Keeley, and Ronald Schmidt.

Local economies are related to the national economy in
different ways. Although most economists agree that such
differences among states exist, the nature. of these differences is not well understood. This· paper· develops a
measure ofthe "strength oflinkage' between regional and
national economies that captures the degree of comovement between state and national economic growth rates.
This measure is used to determine which characteristics of
statei economies are associated with stronger or weaker
linkages to the national economy. The analysis reveals that
states that are linked more closely to the national economy
tend to be large and diverse, with smaller than average
farm and oil sectors and larger than average manufacturing sectors.

Federal Reserve Bank of San Francisco

Local economies are related to the national economy in
different ways. Casual observation suggests, for example,
that economic fluctuations in California are linked more
closely to national economic fortunes than are economic
fluctuations in Alaska. Economists who forecast states'
economies take these differences into account, relying
more on national economic forecasts for some states than
they do for others.
Although most economists agree that such differences
among· states exist, the. nature of these differences is not
well understood. Previous work has explored· related issues.Several authors, including Brewer (1985) and Kort
(1981), found that more diversified regions tend to have
more stable economies. Browne (1982) found that the
states that suffered the largest employment losses during
the 1981-1982 recession tended to have relatively high
wages and slow trend growth, and to depend more heavily
on agriculture than other states. Belongia and Gilbert
(1987) developed a simple measure of the relationship
between national and regional economies, and found that
farm and non~farm regions were not significantly different
from one .another according to that measure.
Like Belongia and Gilbert, this paper focusses on the
long-term relationship between the national and regional
economies. It develops a measure of the "strength of
linkage" (LINK) between regional and national economies. LINK captures .the degree of"comovement" between state and national economies. This measure is used
to determine which characteristics of states' economies are
associated with stronger or weaker linkages to the national
economy. The analysis reveals that states that are linked
more closely to the national economy tend to be large and
diverse, with smaller than average farm and oil sectors and
larger than average manufacturing sectors.
These findings make intuitive sense, and most of these
findings also are consistent with those of other authors
regarding related questions. However, they do contrast
with the results of Tweeten (1985) and Rausser(1985), who
found that agricultural economies are particularly susceptible to changes in macroeconomic variables such as
interest rates.
The· findings are interesting for several reasons. They
suggest that forecasts of national economic activity are

much more important in formulating some states' economic forecasts than they are for other states. Moreover,
the economic characteristics associated with these differences among states provide a basis for speculating on
the structural relationships between national and regional
economies, a topic that is beyond the scope of this paper.
The paper is organized as follows. Section I examines

alternative definitions of linkages between national and
state economies. Section II describes the LINK measure
used in this paper. Section III then examines characteristics of states' economies to determine which are associated
with high and low values of LINK. Section IV summarizes
the findings and draws conclusions.

I. Defining State-National Linkages
Several studies have examined the relationships between
state and national economies, but these relationships have
been defined in various ways. Browne (1982), for example,
explored differences among peak-to-trough declines in
employment for various states. This approach is useful for
examining a particular business cycle, but observations
drawn from such a short time frame have limited applicability for the whole cycle, let alone for longer periods.
Belongia and Gilbert, in contrast, focussed on changes
in state and national economic activity over a 26-year
period~ In particular, they were interested in the magni. tudes of the GNP coefficients in regressions of the following form:
(1)

piit

= ui

[3i

GNPt +

E it

where pii is the quarter-to-quarter growth rate of personal
income (PI) in region i, and GNP is the growth rate of
gross national product (GNP). They ran separate regressions for two groups of states, ten "farm states" and forty
"nonfarm states." They found that the coefficients on
national GNP, [3i' were not significantly different between
the two regions. Thus, they concluded that cyclical responses to the national economy were similar in farm and
nonfarm regions.
Belongia and Gilbert's measure of the responsiveness of
regions' economic fluctuations to those of the national
economy, 13, can answer only a limited range of questions.
For one thing, their division of the nation into "farm" and
"nonfarm" regions precludes analysis of other characteristics that might be associated with differences among
states. In addition, 13 captures only the magnitude of the
change in a region's economy that is associated with a
given change in the national economy. Belongia and Gilbert do not consider the extent of the comovement between
the national and regional economies.
These two concepts are quite distinct. Some regions
experience only small fluctuations associated with national
fluctuations, even though their economies exhibit substantial comovement with national cycles. These states would

have small J3s and high R2S in regressions like equation
(1) run on state data. Conversely, other regions respond
sharply to shocks associated with national business cycles,
but they also respond sharply to so many other economic
shocks that their economic fluctuations may bear little
resemblance to national fluctuations. These states would
have large J3s and low R2S in regressions like equation (1).1
This paper focusses on comovement between national
and regional economies, which also will be referred to as
the "strength of linkage" between national and regional
economies. In equations such as (1), this would be measured by the R2. LINK, defined in the following section,
provides an alternative measure of the strength of linkage.
Comovement between the pace of economic activity at
the state and national levels could occur for many reasons.
Comovement can result from common factors that drive all
states' economies. For example, lower interest rates tend to
stimulate economic activity in all states. Moreover, since
the nation is the sum of the states, an appropriately
weighted average of state growth rates would have to equal
the national growth rate. Consequently, large states may
exhibit comovement between their own growth rates and
the nation's simply because their economies represent a
large share of national economic activity.
It also is possible for changes in the national economy
literally to cause changes in states' economies. For example, if the national economy is healthy, consumers in all
states are more likely to purchase vacations (stimulating
growth in Florida) or construction materials (stimulating
growth in Oregon).
A state's economy also could exhibit comovement with
the nation's because of an indirect rather than a direct chain
of causation between the two economies. For example,
Nevada's economy depends heavily on California's, which
in turn is closely linked to the national economy (Cargill
and Morus 1987). This indirect linkage between Nevada
and the U.S. may be indistinguishable statistically from a
direct linkage between the two economies.

Economic Review· / Summer 1988

II. Measuring Strength of Linkage
This paper focusses on differences among states' comovements with the national economy, without attempting
to model the sources of those comovements. LINK, like
the R2 from equation (1), measures the extent to which the
national economy "predicts" the pace of state economic
activity. However, equation (1) assumes that any linkage
between the two economies is contemporaneous and that
causation always moves from the nation to the state. In
contrast, the vector autoregression (VAR) approach used
in this paper to derive LINK captures comovements that
are not contemporaneous, and also (in principle, at least)
allows causality to run in both directions.
VARs are atheoretical in their approach, and consequently have no structural content. In a VAR system,
explanatory variables for each equation include lags of the
dependent variable as well as lags of all other variables that
the modeler chooses to include in the system.
Hence, one conceptually simple way to model the relationships between state and national economies would be
to construct a 51-equation2 VAR model in which each
state's growth rate is a function of its own lags and lags of
all other states' growth rates. Such a system would be
huge, since using only one lag for each variable would
result in 51 explanatory variables for each of the 51
equations, and VARstypically use several lags for each of
the explanatory variables.
Although such a large VAR is impractical, a similar
system of only two equations could provide a simple and
more manageable way to model a given state's relationship
to the national economy. Consider a model of the form:
.

(2) PIUSt = 'Y
.

(3) Plit = Ai

1~18t-1 PIUS,t-1
4

+ Et
4

•

+ l~l'Y]i,t-1 PIUS,t-1 + l~l""i,t-l Pli,t-l +

£it

where pius equals the real quarter-to-quarter personal
income growth rate (seasonally adjusted) in the U.S., pii
equals the real quarter-to-quarter growth rate in state i's
personal income, the t subscripts refer to time, and 1
denotes lag length in quarters. Fifty-one separate twoequation systems represent the relationship between each
state's economy and the nation's.
Note that although an unrestricted VAR would include
states' economies as causes of national economic activity,
these variables are omitted in this system. Keach twoequation system included lags of one state's growth in its
U.S. equation, 51 different representations of the U.S.
economy would result. To determine how to resolve this

Federal Reserve Bank of San Francisco

problem, 51 variants of equation (2) were run, in which
four lags of a given state's growth rate were included. F
tests on the state variables in these equations reveal that
only two states provide significant explanatory power for
the national economy at the 5 percent level. 3 With 51 states,
two or three states are likely to appear statistically significant at the 5 percent level due solely to random chance.
Consequently, to make the U.S. equation consistent in all
two-equation systems, state lags are omitted as explanatory variables in the U.S. equation.
Personal income (PI) data are used rather than gross
product data because the latter are not readily available at
the state level. In order to avoid empirical problems caused
by differences between PI and GNP at the national level, PI
is used to measure national economic growth as well.
The system represented in equations (2) and (3) is
estimated for the period 1970 to 19864 , using seasonally
adjusted quarterly data. Estimates using data for earlier
years reveal that the relationships change over time. Starting the estimation period in 1970 omits observations from
the years before the oil shocks and other structural changes
that took place during the 1970s, but still provides a
reasonably long estimation period. Four quarters of lags
allow sufficient time for fluctuations to work through the
system, while avoiding problems with overlapping cycles.
Because the system is estimated using growth rates
rather than levels, individual states' equations are poor
predictors of their economic activity. 5 However, the approach that is widely applied in the VAR literature follows
the "atheoretic" logic of the VAR process and does not
place any particular significance on individual coefficients
or conventional econometric statistics. Instead, the approach uses the estimated relationship and the error structure from the estimation to attribute deviations in estimated
values from actual values to shocks or "surprises" in one of
the equations in the system. This "variance decomposition" procedure is based on the assumption that such
surprises reflect some exogenous force not explicitly modelled in the system. Equations (2) and (3) are linked
through lagged national values in the state equation, and
surprises occur to both equations in nearly every period.
Thus, the modeler can decompose the total observed
deviation estimated from actual values in each state equation into that attributable to national shocks and that
attributable to state shocks. (See Box.)
LINK represents the national component of this variance decomposition for each state. This statistic provides
an intuitively appealing measure of the strength of linkage
between state and national economies. A high value for

Economic Review / Summer 1988

Federal Reserve Bank of San Francisco

LINK means that most state fluctuations are associated
with national shocks, and cycles in the state economy tend
to be associated closely with national cycles. Conversely,
if a state's fluctuations generally result from shocks to the
state's economy, rather than from shocks to the nation's
economy, the state would have a low LINK value and a
relatively weak linkage to national cycles.
Table 1lists the values ofLINK for the fifty states and the
District of Columbia. On average, national surprises account for 44 percent of states' observed deviations. The
states exhibit a wide range of LINK measures, from 75
percent for Florida to 8 percent for West Virginia. Moreover, states that one would expect from casual observation
to be closely linked to the national economy, such as
California, have high LINK values, whereas states that do
not appear to be closely linked to the national economy,
like Alaska, have low LINK values.

III. Examining the LINK Measure
To examine the characteristics of states with higher or
lower LINK measures, some variables describing each
state's economic characteristics are constructed. These
characteristics, shown in Table 2, 6 were chosen to allow
comparisons with the results of previous studies on related
topics. The last three lines of Table 2 list the average value
for each variable for the entire group of 51 states, and for
the ten states with the highest LINK measures and the ten
states with the lowest LINK measures.
Several authors have found that states with larger (Smith
and Willis 1986) or more diverse (Brewer 1985, Kort 1981)
economies tend to be more stable or to experience smaller
job losses during cyclical downturns. These studies, however, focussed on the magnitude of the change in the state's
economy that was associated with a national economic
change, rather than the extent of comovement, which is
measured here.
In the analysis presented here, state personal income
(PI), in millions of constant 1982 dollars, measures the size
of the state's economy. DIV captures the extent to which the
industry structure in a given state's economy differs from

the nation's, and proxies for economic diversity? Using
data disaggregated to the two-digit Standard Industrial
Classification (SIC) level for all industries, the following
formula was calculated for each state:

where Ej denotes the share of total employment in industry
j, i subscripts denote states, and US subscripts denote
national figures. If state i's industrial composition is identical to the nation's, DIVi = 0, and DIVi is negative if the
state's economy deviates from U.S. industrial composition. The value of DIVi rises (although its absolute value
falls) as the state's industrial structure resembles U.S.
industrial structure more closely and, presumably, the
state's economy becomes more diversified.
It seems plausible that economic fluctuations in states
that depend heavily on resource industries such as agriculture and oil would be more closely associated with changes

Economic Review / Summer 1988

Federal Reserve Bank of San Francisco

in commodity prices and other factors peculiar to these
industries than with changes in macroeconomic factors.
However, several authors (Tweeten 1985, Rausser 1985)
have emphasized the sensitivity of agriculture to interest
rates and inflation, concluding that macroeconomic variables playa key role in explaining the farm problems of the
early 1980s. Belongia and Gilbert (1987), in contrast,
found no difference in the responsiveness to national
fluctuations between farm and nonfarm regions. It is
possible, however, that a state could respond sharply to
macroeconomic variables, without exhibiting strong co-

movement, if its economy also responds sharply to economic variables that are uncorrelated with macroeconomic
cycles. FARM, which measures each state's dependence
on agriculture, was calculated by taking the ratio of net
farm income to total state personal income. Similarly, a
state's dependence on energy extraction may be related to
the strength of its linkage to the national economy. OIL
captures the importance of the oil industry by calculating the proportion of total employment in oil extraction
(SIC 13).

Economic Review / Summer 1988

Some early studies also found a correlation between
dependence on (durable) manufacturing industries and the
extent to which state economies declined during national
recessions (Borts 1960, Engerman 1965). Thus, one might
expect states in which manufacturing is more important to
have higher LINK measures. The variables MFG and
DMFG capture the importance of the manufacturing and
durable manufacturing industries by calculating the proportions of total employment in manufacturing and durable manufacturing, respectively.
Table 3 presents the results of regressions in which the
variables listed in Table 2 are used to explain differences
among states' LINK measures. Various combinations of
variables are used to ensure that possible correlation
among explanatory variables does not contaminate the
results. 8 These regressions suggest that stronger linkages
between state and national economies are associated with
larger, more diversified state economies, and less dependence on oil and agriculture. The signs of the coefficients
suggest that states with higher LINK measures also depend more heavily than average on manufacturing activity,
and this relationship. is statistically significant in regressions in which FARM and OIL are omitted.
As expected, results for the size variable, PI, show that
states with larger economies tend to have stronger linkages
with the national economy. This relationship is statistically
significant at least at the 10 percent level in all eight
equations in which it is included, and at the 5 percent level
in seven of the eight. These results are consistent both with
a priori expectations and with the result~ of previous
studies.
Smaller deviations from national industry structure,
measured by DIV, are associated with higher LINK measures in all six regressions that include the measure. However, DIV is statistically significant only when PI is

omitted from the regressions. DIV and PI are positively
correlated with each other, and DIV appears to have little
or no explanatory power beyond that associated with state
size.
The coefficients on FARM and OIL suggest that states
that depend heavily on farming and oil extraction tend to be
linked less closely to the national economy. These results
are statistically significant at least at the 10 percent level in
all regressions that include FARM and OIL. 9 The FARM
results contrast with those of Tweeten (1985) and Rausser
(1985), who concluded that macroeconomic variables were
key causes of farmers' economic problems during the
mid-1980s. These results also differ from Belongia and
Gilbert's finding that farm and nonfarm states respond
similarly to macroeconomic shocks.
In all equations, the signs of coefficients on the manufacturing variables (MFG and DMFG) are consistent
with the previous literature, suggesting that greater dependence on manufacturing is associated with stronger
linkages between state and national economies. The coefficients are statistically significant only when FARM and
OIL are omitted, reflecting the negative correlations between these two sets of variables.
The regression results leave open the possibility that the
relationships between LINK and FARM, OIL, MFG, and
DMFG exist only for states that depend heavily on these
sectors,and that these relationships may not hold throughout the range of possible values. However, the mean values
of each variable for the ten states with the highest LINK
measures and the ten states with the lowest LINK measures, listed in Table 2, lead to the same conclusions as the
regression results do. This suggests that the regression
results describe the relationships among variables accurately throughout the range of LINK values, and not
simply at one extreme or the other.

IV. Summary and Conclusions
The empirical results presented in Section III suggest
that states differ in terms of their strength of linkage with
the national economy, and that these differences are associated with the economic structure of the states.
According to the LINK measure, states. tend to have
stronger linkages to the national economy if they are larger,
have industrial structures that resemble the nation's more
closely, depend relatively heavily on manufacturing industries, and depend relatively little on farming and oil
extraction. Most of these results are consistent with the
results of previous studies on similar topics.
However, results for the agricultural sector are different

Federal Reserve Bank of San Francisco

from what previous studies might lead one to expect. The
results for the FARM variable lead to a strong conclusion
that the linkages between national and state economies are
weaker in states that depend more heavily on agriculture.
This conclusion contrasts with the results of several recent
studies, including those by Rausser and TweeteIl, which
found that the agricultural economy is particularly sensitive to macroeconomic variables such as interest rates and
inflation during the past decade. While this study does not
test hypotheses regarding specific macroeconomic variables, the LINK results suggest that macro variables as a
group are less important determinants of economic activity

in states that depend heavily on agriculture than they are in
other states.
The results of this study also contrast with Belongia and
Gilbert's finding that fann and nonfann regions respond
similarly to macroeconomic shocks. Nevertheless, it is
possible that agriculture is more sensitive than other sectors are to macroeconomic variables, but that fann states
also are particularly sensitive to economic shocks that are
not associated with national cycles.
ENDNOTES
1. These regressions must be interpreted carefully. A
simple equation such as (1) can be used to summarize the
relationship,s between two variables, but causal or structural interpretations are likely to be inappropriate, since
the equation omits important variables at least for some of
the states.
2. The 51 equations represent the 50 states and the
District of Columbia. Throughout this paper, the District of
Columbia will be referred to as a "state." Note that, with
this structure, U.S. variables are not included explicitly,
necessitating further calculations to assess the relationship between a given state's economy and the nation's.
3. The two states with statistically significant F statistics
are Michigan, which makes intuitive sense, and the District of Columbia, which does not.
4. With four quarters of lags, data for 1969 were required
to estimate the system beginning in 1970.
5. Low predictive power is not unusual for VARs that use
growth rates, but it does cast doubt on the ability of LINK
to measure comovements accurately. Nevertheless, the
author has found no clearly superior way to measure
comovements, and the results presented in Section III are
strong enough to suggest that LINK is a viable measure of
comovements.
6. With the exception of DIV, each variable was calculated using 1973 data and 1983 data, and the value listed
is an average of the two. Due to data constraints, DIV was
calculated for 1973 only.

7. Interpreting this as a "diversity" measure involves
making the rather aribitrary assumption that the industry
structure of the national economy represents "absolute"
diversity. Nevertheless, it is a reasonably sensible measure, and its data requirements are not prohibitive. Other
diversity measures include the much more arbitrary
"ogive" measure, which measures the deviations from an
equal distribution of employment across different industry
categories, and the "portfolio variance" measure, which
has prohibitive data requirements. Conroy (1975) describes each measure.
8. Note that the shares of agriculture, oil, and manufacturing do not add up to one, mitigating a potential multicollinearity problem in these equations. The oil and
manufacturing measures are based on nonagricultural
employment data, which also include other industries,
such as trade, services, government, and finance. Because the employment data exclude agricultural jobs, the
farm measure is based on income data rather than employment data. Moreover, correlations between DIV and
other industry mix variables are low, at 0.10 or less. The
correlation between PI and DIV is only slightly higher at
0.13.
9. Interestingly, in all equations that include the MFG
variable, OIL is significant at the 10 percent level, and the
significance level improves to the 5 percent level in all
equations that include the DMFG variable. This suggests
that OIL may be correlated with the nondurable manufacturing component of MFG, which is not included in DMFG.
In fact, the correlation between OIL and MFG is 0.26,
compared with aO.14 correlation between OIL and DMFG.

Economic Review / Summer 1988

REFERENCES
Belongia, Michael 1. and R. Alton Gilbert. "The Farm
Economies of the Plains," Review of Regional Studies,
Fall 1987.
Borts, George H. "Regional Cycles of Manufacturing Employment in the United States, 1914-1953," National
Bureau of Economic Research Occasional Paper 73,
1960.
Brewer, H.L. "Measures of Diversification: Predictors of
Regional Economic Instability," Journal of Regional
Science (25:3), 1985, pp. 463-470.
Browne, Lynn E. "Two Years of Stagnation: A Regional
Perspective," New England Economic Review, September/October 1982, pp. 35-44.
Cargill, Thomas F. and Steven A. Morus. "A Vector Autoregression Model of the Nevada Economy," Economic
Review, Federal Reserve Bank of San Francisco, Winter 1988, pp. 21-32.
Conroy, .Michael E. "The Concept and Measurement of
Regional Industrial Diversification," Southern Economic Journal (41:3),1975, pp. 492-505.
Engerman, Stanley. "Regional Aspects of Stabilization
Policy," in Richard A. Musgrave, ed., Essays in Fiscal
Federalism. Washington, DC: The Brookings Institution,1965.
Fritz, Richard G. and W. Warren McHone. "Forecasting
Local Business Activity from Aggregate Indicators,"
The Annals of Regional Science (22:1),1988, pp.
63-74.
Howland, Marie. "The Business Cycle and Long-Run Regional Growth," in William C. Wheaton, ed., Interregional Movements and Regional Growth. Washington,
DC: The Urban Institute, 1979.
Kort, John R. "Regional Economic Instability and Industrial Diversification in the U.S.," Land Economics
(57:4),1981, pp. 596-608.

Federal Reserve Bank of San Francisco

Long, John B., Jr. and Charles I. Plosser. "Sectoral vs.
Aggregate Shocks in the Business Cycle," American
Economic Review (77:2),1987, pp. 333-336.
Lucier, Gary, Agnes Chesley, and Mary Ahearn. Farm
Income Data: A Historical Perspective, U.S. Department of Agriculture, Economic Research Service, Statistical Bulletin NO.740, May 1981.
Rausser, Gordon C. "Macroeconomics and U.S. Agricultural Policy," in Bruce L. Gardner (ed.), U.S. Agricultural Policy: the 1985 Farm Legislation. Washington
DC: American Enterprise Institute for Public Policy
Research, 1985.
Siegel, Richard A. "Do Regional Business Cycles Exist?,"
Western Economic Journal (5:1),1966, pp. 44-57.
Smith, Gary W. and David B. Willis. "An Analysis of the
Performance of Washington and Oregon Counties:
Three Years of Decline and Stagnation 1980~82,"
paper presented at the Pacific Northwest Regional
Economic Conference, Missoula, Montana, May 1-3,
1986.
Tweeten, Luther. "Farm Financial Stress, Structure of Agriculture, and Public Policy," in Bruce L. Gardner (ed.),
U.S. Agricultural Policy: the 1985 Farm Legislation.
Washington DC: American Enterprise Institute for
Public Policy Research, 1985.
U.S. Department of Commerce, Bureau of Economic
Analysis, State Personal Income: Estimates for
1929-1982 and a Statement of Sources and Methods.
Washington, DC, February 1984.
U.S. Department of Commerce, Bureau of Economic
Analysis, United States Department of Commerce
News. Washington DC, September 1986.
U.S. Department of Commerce, Bureau of Economic
Analysis, "State Quarterly Personal Income, 1984:11986:1," Survey of Current Business (66:7), July 1986,
p.93.

Economic Review / Summer 1988

An Evaluation of
Alternative Measures of Expected Inflation

Adrian W. Throop
Research Officer, Federal Reserve Bank of San Francisco. Research assistance by Mirjam Fried, Eric McClusky, and Jerry Metaxas is gratefully acknowledged.
Editorial committee members were Barbara Bennett,
Vivek Moorthy, Ramon Moreno, and Brian Motley.

This study evaluates the performance of three alternative measures ofinflationary expectations in the context of·
the investment sector ofa structural econometric model of
the u.s. economy. Overall, the evidence suggests that
actual expectations of inflation are close to being purely
autoregressive, depending only on current and past inflation itself. Survey measures of expectations, which potentially might contain more forward-looking and "rational"
elements, generally do not have any more explanatory
power than other measures. Also, purely autoregressive
measures remained a good representation ofactual expectations ofinflation even when monetary policy was changing sharply in the post-October1979 period ofdisinflation.

Federal Reserve Bank of San Francisco

Accurate forecasting of the response of the economy to
changes in monetary policy requires an accurate modeling
of the public's expectations of inflation. Conventional
macro-econometric models typically incorporate relatively backward looking and slowly adjusting expectations
of inflation. Critics stress that these models usually omit
information about past values of other variables, such as
the money supply, and also information about how monetary policy is likely to respond to the state of the economy
in the future. Moreover, backward looking models of
inflationary expectations tend to produce systematic forecasting errors, which economic agents might be expected
to correct. In view of these criticisms, Robert Lucas (1976)
has stated:
"The long run implications of current forecasting
models are without content, and the short-term forecasting ability of these models provides no evidence
of the accuracy to be expected from our simulations of
hypothetical policy rules."
In contrast, Lucas holds to the view that the inflationary
expectations of economic agents in all markets tend to be
fully "rational" in the sense that they are unbiased forecasts of future inflation. If this is the case, monetary policy
is not able systematically to affect either real interest rates
or output and employment.
On the other hand, many economists believe that the
condition of full rationality assumes too much about the
knowledge of economic agents. The assumption of full
rationality requires that economic agents know the "true"
model of the economy and make unbiased estimates of its
parameters. Furthermore, full rationality assumes that
economic agents know how policy affects the economy and
even what policy rules will be followed by the government
in the future. Given the inherent uncertainties about such
things, a model that gradually adjusts inflationary expectations according to recent experience may be an adequate
representation of the best that economic agents are able to
do. Reflecting this view, Otto Eckstein (1981) said:
"The data tell us that it takes workers, investors, and
businessmen several years to accept conditions of
inflation or output growth as permanent. . . The rational expectations school needs to specify the leaming process by which information enters decisions

explicitly, particularly how individuals form permanent expectations from temporary data and how they
modify their behavior to changes in the economic
structure."
To shed some light on the appropriate way of modeling
inflationary expectations, this article evaluates the performance of three alternative measures of inflationary
expectations in the context of the investment sector of a
structural econometric model of the U.S. economy. This
model is used for forecasting and policy simulations at the
Federal Reserve Bank of San Francisco. 1 The three alternative measures of expected inflation are: 1) a purely autoregressive measure that depends only on current and past
values of inflation; 2) an "augmented" autoregressive
measure that depends as well on current and past values of
other variables that determine the inflation rate in the San
Francisco model; and 3) a survey-based measure that
potentially might contain more forward-loooking information than either of the other two measures. While the tests
necessarily are joint tests of both the model's specifications
and the measurement of expected inflation, taken together,
the results provide useful evidence on the nature of actual
inflationary expectations.
Agents in different markets may have access to different
sets of information and incur varying costs of collecting
such information. Also, arbitrage may force rapid adjustments to new information in some markets but not in
others. As a result, different measures of inflationary
expectations may be appropriate in different markets. We
therefore examine the explanatory power of the three
different measures of expected inflation in three different
areas of the investment sector of the structural econometric

model: consumer durables, the Aaa corporate bond rate,
and nonresidential fixed investment.
Overall, the evidence suggests that inflationary expectations in the investment sector of the economy tend to
be relatively backward-looking and adjust only gradually
to new information. Survey measures of expectations,
which potentially might contain more forward-looking and
"rational" elements, generally do not have greater explanatory power than the other measures. Except in the bond
market, where past values of variables other than inflation
do have some significance, the actual formation of expectations of inflation generally appears to be purely autoregressive. Finally, the purely autoregressive measures remained
good representations of actual inflationary expectations
even when monetary policy was changing sharply in the
post-October 1979 period of disinflation.
In section I, we develop the three alternative measures of
short-term inflationary expectations and compare their
relative forecasting accuracies. Since the concern in this
paper is not with forecasting accuracy, but with accurate
representations of the way expectations are formed, Section II uses these measures to estimate corresponding real
short-term interest rates and then compares their explanatory powers in the equation for consumer spending on
durable goods. Section III develops three alternative measures of long-term expectations of inflation and tests their
explanatory power in an equation for the corporate bond
rate. Section IV tests similar measures of long-term expectations of inflation in equations for business investment in
structures and equipment. A summary and conclusions are
provided in Section V.

I.Alternative Measures of Short-Term Expectations of Inflation
In this section, we develop the three alternative measures of expected inflation over a short-term forecasting
horizon of two quarters ahead, and then compare their
relative forecasting accuracies. These measures of expected inflation are then used in the next section to estimate
thereal6-month commercial paper rate.

Purely Autoregressive Measure
In his pioneering studies of the effect of expected
inflation on nominal interest rates, Irving Fisher (1930)
used simple autoregressive measures of expected inflation
that depended on only current and past inflation. Phillip
Cagan (1956) subsequently developed a theoretical rationale for imposing geometrically declining weights on
the past values of inflation in his hypothesis of adaptive

expectations. Although rationales for more flexible lag
patterns and techniques for their estimation have been
developed since then, Cagan's adaptive expectations hypothesis has been widely used as an autoregressive representation of expectations. 2
According to this hypothesis, economic agents revise
expectations of inflation (pe) from one period to the next in
proportion to the difference between the actual inflation
rate (p) in the most recent period and the rate of inflation
the had been expected.
.e.e
(.
.e)
p - p -1 = ex P - P -1

(1)

Collecting terms, the adaptive expectations hypothesis
says that the current expectation of inflation is equal to a

Economic Review / Summer 1988

weighted average of current inflation and the most recent
expectation of inflation.
(2)

The coefficient of adjustment, <x, determines the weight
economic agents put on new information about inflation.
Solving this equation recursively, we obtain:

pe =

i~O<x(l - <x)ip_1

(3)

In the current context, pe is interpreted as the expectation
of inflation for two quarters ahead, and p is the quarterly
rate of inflation in the GNP fixed weighted price index. The
speed of adjustment, <x, is estimated at 0.2 from the
equations in the San Francisco model containing the real
6-month commercial paper rate. 3 The lag was truncated at
31 quarters, at which point the lag weight became trivially
small. Because 1><X>0, the sum ofthese weights on past
inflation equals one; and pe ultimately converges to any
steady actual rate of inflation. When inflation is rising,
however, the adaptive expectations model systematically
underestimates inflation; and when inflation is falling, it
systematically overestimates. A criticism of the adaptive
expectations hypothesis is that such errors potentially are
correctable.

Augmented Autoregressive Measure
A more sophisticated measure of expected inflation can
be derived from the inflation equation in the San Francisco
econometric model. This equation collapses wage and
price determination into one. The equation is an expectations-augmented Phillips curve, with inflation being determined as a function of the unemployment rate, past
inflation, and variables that capture the direct effects of
shocks to the price level from changes in the real price of
oil and the real value of the dollar. Past inflation enters in
the form of a polynomial distributed lag. In this augmented
specification, past inflation captures not only inflationary
expectations in the labor market, but also the effects of lags
introduced by the contracting process.
Given past inflation, the current rate of change in wages,
and hence prices in this equation, is assumed proportional
to the excess demand for labor. 4 The presence of excess
demand for, or excess supply of, labor implies that the
adjustment to equilibrium does not occur instantaneously.
The slow convergence to equilibrium in this-model is
appropriate because the labor market is not organized as an
auction market. 5 Furthermore, because of an inverse relationship between vacancies and unemployment, the unem-

Federal Reserve Bank of San Francisco

ployment rate can be used to measure excess demand for
labor. 6 Since the sum of the estimated coefficients on past
inflation is not significantly different from one, we constrain them to that value. This implies a vertical long-run
Phillips curve in which the rate of inflation at full employment is equal to the rate of inflation inherited from the past.
It also reflects the view that excess demand, corresponding
to an unemployment rate below the full employment level,
leads to a continuous acceleration in the inflation rate.
The GNP fixed weighted price index that we use for the
measure of prices does not include prices of imports.
However, changes in import prices that are brought about
by changes in the real value of the dollar indirectly influence prices of domestically produced goods. In purely
competitive product markets for homogeneous goods such
as agriculture, the "law of one price" suggests that changes
in the price of imports due to real exchange rate changes
will be fully passed through to domestic producers. In
markets for non-homogeneous products, the degree of
pass-through will be less though still greater than zero.
Changes in the real value of the dollar therefore have an
impact on the overall mark-up of domestic prices over
domestic unit labor costs. These relationships are captured
by a distributed lag on current and past percent changes in
the real trade-weighted value of the dollar.
A second type of "supply shock" to the price level
comes from changes in the real price of oil. Changes in the
real price of oil alter the mark-up of prices over unit labor
costs by changing the price of an important non-labor
input. A distributed lag on the percentage change in the
real price of oil is therefore the final component of the
inflation equation. 7
To obtain the augmented autoregressive measure of
expected short-term inflation, the inflation equation in
the San Francisco model was estimated with two-quarter
ahead inflation in the GNP fixed weighted price index as
the dependent variable. The sample period is 1958 to 1986.
The fitted values of this equation are:

pe =

.168 - .455U
3

+ i~O~-1

+ i I= 0 b·POIL· + i I= 0 c·EXCH·
1

i=O

where

a·1

= 1.0
.e

p
U

-1

I b· = 0.0289

i=O

(4)

-1

i=O

c·1 = -0.114

two quarter ahead inflation rate
civilian unemployment rate, adjusted
for demographic changes

= quarterly inflatiol). rate
POlL = rate ofchange in real price of oil
EXCH = rate of change in real value of the

Chart 1
Alternative Measures of
Expected Inflation*

dollar
Percent

Unlike the purely autoregressive measure, this augmented autoregressive forecasting equation allows economic agents to take into account other information in
forming expectations of inflation. This measure is based on
relevant theory describing the dynamics of the inflationary
process. It therefore contains information that is missing
from the simple adaptive expectations hypothesis.
It also corrects a possible deficiency of the adaptive
expectations hypothesis. Forecasts from the adaptive expectations model systematically underpredict inflation
when it is rising and overpredict it when it is falling. In
contrast, the augmented measure does not lead to systematic over- or underprediction. Therefore, it meets the condition of unbiased forecasts that is basic to the idea of
rational expectations.
The augmented autoregressive forecasting equation produces unbiased forecasts because it is based on an expectations-augmented Phillips curve. When the unemployment
rate is at its full employment level, it contributes nothing to
current inflation. Current inflation is then the same as past
inflation, except as it is disturbed by shocks to the price
level from oil or the dollar. But when the unemployment
rate is below full employment and current inflation exceeds
past inflation, the deviation ofthe unemployment rate from
its full employment level explains the extent to which
current inflation exceeds past inflation.
The augmented autoregressive forecasting equation
omits growth in the money supply-a variable that most
proponents of rational expectations think is important in
the formation of expectations of inflation. Since inflation
generally is believed by economists to be a monetary
phenomenon, particularly in the long run, Rutledge (1974)
and others have argued that past movements in the stock of
money should be the primary determinant of inflationary
expectations. But the augmented autoregressive equation
already describes the dynamic process by which monetary
impulses are transmitted to prices, and nothing is added by
including money growth. 8

Survey Measure
A survey measure of expected inflation might provide
even better forecasts of inflation, .as it could incorporate
projected values of any and all determinants of inflation
that market participants might think are important. In
particular, it could include information on current and past

10
9

8
7
6
5
4
3

Root Mean Square Error:
1958.2 to 1986.4
1958.2 to 1975.4
1976.1 to 1986.4

1.52
1.43
1.66

2
1
0-t-T...,..-r...,..-r...,..-r-rT-rT-rT-rT""'''''''''''''''rT"1rT"1rT"11'""T''"1
58
74
62
66
70
78
82
86

Percent

10
9

8
7
6
5
4
3

Root Mean Square Error:
1958.2 to 1986.4
1958.2 to 1975.4
1976.1 to 1986.4

1.00
1.09
0.84

2
1

o -t-T"""""""""''''''''''''''''T"T'T"TT""T'"T""T'"T""T'"r-r-r-r-r-r-n
58

Percent

Actual

10
9
8
7
6
5
4
3
2
1

Root Mean Square Error:
1958.2 to 1986.4
1958.2 to 1975.4
1976.1 to 1986.4

1.82
2.04
1.37

Survey

- 1 -t-r-'-'r-T""r-T""T""T""'I'"T'"T""T-'-'I"'"T""ir-T""rT'"TT"T""T-n-,-,1'""T""1
58

* Expected

two quarters ahead

Economic Review / Summer 1988

values of economic variables that are omitted from the
augmented autoregressive measure and judgments about
the likely stance of monetary policy and other government
actions in the future.
For a survey measure of two quarter ahead expectations,
we use the NBER-ASA survey for the period from the
fourth quarter of 1968 to the fourth quarter of 1986 and the
Livingston survey for the years not covered by the NBERASA survey. Both these surveys cover forecasts of professional business economists that were available to the
public. 9 The NBER-ASA survey is preferred for our purposes since it gauges inflation by a GNP index, while the
Livingston survey refers to consumer prices. Movements
in consumer prices and GNP prices have tended to diverge
the. most when there have been supply shocks from oil,
food, or the dollar. Consequently, little is lost by using the
Livingston survey for the relatively tranquil period through
the end of the 1960s. Moreover, we have adjusted the
Livingston survey to remove systematic differences between the trend rate of inflation in the consumer price index
and prices in the GNP index.l°
Ironically, extensive analysis of the NBER-ASA survey
by Zarnowitz (1985) and the Livingston survey by Carlson
(1977), Pearce (1979), and Figlewski and Wachter (1981)
shows that the inflation forecasts of professionals are not
fully rational and instead, display systematic bias in their
forecast errors, the more so the longer the term of the
forecast. As shown by Zarnowitz (1985), however, their
forecasts of most other variables have come considerably

closer to satisfying the criterion of rationality. 11
Also, the inflation forecasts of these surveys generally
have been no more accurate than the forecasts of either the
purely autoregressive or augmented autoregressive measures of expectations. Chart 1 shows the forecasts of these
three measures of expected inflation compared with the
actual inflation rate realized for two quarters ahead from
1958 to 1986. The root-mean-squared forecasting errors of
the survey, purely autoregressive, and augmented autoregressive measures of inflationary expectations for the
period 1958.2 to 1986.4 are 1.82, 1.52, and 1.00 percentage points, respectively. The purely autoregressive measure systematically lags behind actual inflation due to the
way it is constructed. But its forecast errors in the period
since 1958 actually are smaller than those of the survey
measure, and the errors of the augmented autoregressive
measure of inflationary expectations are smaller still.
Although the survey measure chronically underestimated inflation through the mid-1970s, the professional
forecasters covered by the surveys became more sophisticated over time. Despite continued shocks from oil and
the dollar, the root-mean-squared error of their forecasts
dropped from 2.04 percentage points in the period 1958.21975.4 to 1.37 percentage points in 1976.1-1986.4. As a
result, their forecasting error dropped below the 1.66
percentage point error of the purely autoregressive forecast
inthe second period, but still was considerably larger than
the 0.84 percentage error of the augmented autoregressive
forecast.

II. Short-Term InHationary Expectations and Consumer Durables
In this section, the San Francisco econometric model's
equation for expenditures on consumer durables is used to
determine which of the three alternative measures of
expected inflation best represents the short-term inflationary expectations of households. In this equation, expendituies on consumer durables follow a stock adjustment
process. The desired stock of durables is determined, in
part, by a real short-term interest rate. To obtain this rate,
the measures of short-term inflationary expectations derived in the preceding section are used. The best measure
of household inflationary expectations ought to generate a
measure of the real interest rate that gives the best fit to the
durables equation.
In the San Francisco model, the desired stock of durables depends upon the level of permanent income. 12 The
adaptive expectations hypothesis is used to measure permanent income, so that permanent income is a geometrically declining distributed lag on disposable income.

Federal Reserve Bank of San Francisco

Transitory income, which is the difference between current
income and permanent income, is allocated to either real or
financial assets, including consumer durables. A freely
fitted distributed lag on disposable income captures both of
these effects. If the speed of adjustment ofthe actual to the
desired stock of durables is slow compared with the rate of
replacement, then the stock of consumer durables in the
previous period enters the equation with a positive sign.
Finally, an important determinant ofthe relative price of
durables is the real short-term rate of interest. We use the
real 6-month commercial paper rate to measure this. The
effect of the real interest rate on the desired stock of
durables is captured by a distributed lag on the product of
the real interest rate and permanent disposable income,
which allows the absolute effect of a change in the real
interest rate on real expenditures to increase with the level
of real income. Thus, the form of the equation that is
estimated is: 13

CD = a

+ i~ObiYD_l
2

- i~lCi(i - petiYDP_i

diK_ 1

(5)

where CD = real expenditures on consumer durables
YD = real disposable personal income
1
= nominal6-month commercial paper rate
pe = measure of two quarter-ahead expected
inflation
YDP = permanent real disposable personal
income
K
= real stock of consumer durables

The estimated standard errors ofthis equation, using the
three alternative measures of two quarter-ahead expectations of inflation, are shown in Table 1. Since the survey
forecast became considerably more accurate after the
mid-1970s, the sample period was split into two subperiods of 1958.2-1975.4 and 1976.1-1986.4. In the first
sub-period, the standard errors associated with the three
alternative measures of expected inflation are quite close to
one another. Household expectations of inflation in this
period are not measured well by any of the three alternative
measures, given the maintained hypothesis that consumer
expenditures on durables are affected by expected inflation. Otherwise, one of the three measures would have fit
the data distinctly better than the others, given the strong
differences between them in this period.
In the second sub-period, household short-term expectations of inflation are most closely represented by the
purely autoregressive measure. The purely autoregressive
measure of expected inflation produces the lowest standard
error for the consumer durables equation of the three
alternative measures of expected inflation. There is a

relatively small difference from the survey measure and a
much larger difference from the augmented autoregressive measure. The relatively small difference between the
closeness of fit of the purely autoregressive and survey
measures in this period is due to the high correlation
between their movements, as shown in Chart 1. The
forecast errors of these two measures also are similar in the
second sub-period. Apparently, the survey measure does
not contain much extra information that households could
have used. Thus, households' expectations of in,flation in
recent years appear to have been basically adaptive.
In an important work, Lucas (1976) has criticized the
use of autoregressive expectations in econometric modeling. Lucas argued that agents form expectations rationally,
and not adaptively, and as a result, the relationship beween
past inflation and expected inflation would change if
economic agents recognize that a significant shift in monetary policy is taking place. Therefore, an additional test of
whether household expectations are adaptive is whether
the consumer durables equation that uses autoregressive
expectations of inflation is stable in a period of significant
change in monetary policy.
One such period is the post-October 1979 disinflation in
the U.S. economy. At the beginning of this period, a
technical change in the Fed's operating procedures both
signaled the Federal Reserve's commitment to lower inflation and facilitated the achievement of the desired reduction in monetary growth. The policy achieved its objective.
Inflation in the GNP price index dropped from a 9.8
percent rate in 1980 to 2.3 percent in 1986. If any recent
change in monetary policy could have altered expectations
of inflation independently of the past history of inflation,
this would appear to be it. Not only were there indications
of a new resolve on the part of the Federal Reserve, but the
Reagan Administration was highly supportive of a disinflationary policy. In addition, as Huizinga and Mishkin
(1986) recently have shown, the p'ost-October 1979 period

Economic Review / Summer 1988

meets the technIcal criteria for a "regime shift" in monetary policy.
According to the Lucas critique, this shift in the monetary policy regime should have helped to bring down
expectations of inflation faster than usual. As a result, an
autoregressive measure of expected inflation would tend to
overestimate true expectations and therefore underestimate true real interest rates. A consumer durables equation
using this estimate of real interest rates would therefore
tend to overpredict spending.
As shown in Chart 2, however, there is no systematic

tendency for the consumer durables equation to overpredict spending in the period after October 1979 even
when the autoregressive measure of inflationary expectations is used. Moreover, as shown in Table 2, an F test
rejects the hypothesis of instability in the coefficients of
the consumer durables equation, suggesting that no shift in
the formation of expectations occurred. 14 This is contrary
to the prediction of the Lucas critique. Not only do household expectations of inflation appear to be basically adaptive, but their estimated structure continued to hold up in a
period of significant policy change.

Chart 2
Out-of-Sample Forecasting Errors·
Expenditures on Consumer Durables
Billions of 1982
Dollars

Percent

35
30

0.8
0.6

25
20

0.4

0.2

-0.0

O-t---+t--i;:+-'"""""t-+t+-++---"--tf-++--t

-5

-0.2

-10

-0.4

-15
-20

.........,..,..,_,_r-r"'l_r_r_rT....-r-'1

+-r-.,....,...,..,..,_,_r-r"'l~_r_r_rT

Billions of 1982
Dollars

-0.6
80

Investment in Structures

Investment in Equipment

Billions of 1982
Dollars

O-t--_;_-It-------I-\-------

-5

-10

-15

O+--~(-----+-I------:::::..:.;-

-20

-5

-25

-10

- 3 0 +-r-.........,..,..,_,_r-r"'l.....,...,~_rT_._._.,....,...,..,..r-r"'l~_r_r'"T'"T'"l
79

Corporate Bond Rate

- 1 5 +-r-.........,..,..,_,_r-r"'l~_r_r..,.,. ...........,...,..,_,_....,....,~_r_r....;..r,
79

Actual less predicted

Federal Reserve Bank of San Francisco

III. Short-Term and Long-Term Inflationary Expectations and the Bond Rate
In this section, three alternative measures of expected
long-term inflation are developed within the context of the
equation in the San Francisco model that explains the Aaa
corporate bond rate. This equation is based on the "preferred habitat" theory of the term structure of interest rates
developed by Modigliani and his· colleagues. This approach synthesizes the market segmentation and expectational theories of the term structure of interest rates. In this
approach, the long-term rate is equal to the average of
current and expected short-term rates, modified by a risk
premium reflecting the relative preferences ofthe two sides
of the market for long versus short securities. In the
original statement by Modigliani and Sutch (1966), expectations are formed autoregressively, with thepast history of
nominal short-term rates being used to forecast expected
future short rates. In an improved version by Modigliani
and Shiller (1973), expectations continue to be formed
autoregressively, but the possibility that the process of
expectation formation may differ for the real and inflationary components of future short-term rates is allowed.
The Modigliani and Shiller model for the long-term
bond rate is:
(6)

where it
is
p
K

= Aaa corporate bond rate

= 6-month commmercial paper rate
= quarterly inflation rate
= constant risk premium

In this model, expectations of future real short-term
rates are formed autoregressively on the basis of a weighted average of current and past real short-term rates, with
weights Wi' Moreover, short-term inflationary expectations in current and past real rates are modeled in the
simplest possible autoregressive way. They are equal to the
inflation rate at issuance ofthe short-term security,·implying no expected change in inflation over the short-term
horizon. Expected inflation premiums in future short rates
-or equivalently, the long-term expectation of future
inflation -also are measured autoregressively, but with
weights Vi on current and past rates of inflation. Collecting
the inflation terms, the equation that Modigliani and Shiller estimate for the bond rate then becomes:

(7)
We use this Modigliani and Shiller equation (7) for the
purely autoregressive representation of inflationary expectations in the bond market. 15 Not only are expectations of
inflation in current and past short rates formed autoregressively, but so also are expectations ofthe two components of future short rates.

Economic Review / Summer 1988

More information would be incorporated if the augmented autoregressive measure of short-term expectations
of inflation developed in the first section of this paper were
used to calculate the current and past short-term real rates
in equation (6). Thus, for the augmented autoregressive
representation ofexpectations in the bond market, we
substitute the augmented autoregressive measure of current and past short-term real rates for is - P in equation
(6). Since current and past inflation represents current and
past short-term expectations of inflation in the Modigliani
and Shiller approach, the long-term expectation of inflation actually is formed on the basis of current and past
short-term expectations of inflation. Therefore, in the
augmented autoregressive representation of expectations,
we can substitute the augmented autoregressivemeasure of
short-term expectations for p in the rest of equation (6).
The augmented autoregressive measures of short-term
expectations of inflation can then be collected to form an
equivalent of equation (7).
For the model of the bond rate with survey-based measures of expectations, the Livingston and NBER-ASA data
were used for expected inflation in current and past shortterm real rates and a survey of 10 year-ahead expectations
of inflation collected by Richard Hoey of Drexel, Burnham, and Lambert was used for long-term expectations of
future inflation. These 2~quarter-ahead and 1O-year-ahead
survey measures of expected inflation are plotted in Chart
3. Since the Hoey survey of lO-year-ahead expectations
does not go back before 1978.4, we estimated the lO-yearahead expectations for the prior years, based on a geometric lag on the 2-quarter-ahead expectations. Analysis of the
two survey measures revealed that short-term and longterm expectations of inflation have a rather well behaved
term structure, similar to that assumed in the two autoregressi;ve.measures. Thus, it was reasonable to approximate the 1O-year-ahead expectations for the period prior to

Federal Reserve Bank of San Francisco

Chart 3
Survey Measures of Expected Inflation
Percent

10 years
ahead
(survey)

10
9
8

2 quarters
ahead

7
6
5
4
3
2

10 years ahead
(estimated)

o
- 1 +-rTT"TT"T"T""rnl'"T"T"""'"T"'T"TT"TT"T"T""rnl'"T"T""'"
57

the Hoey survey by means of a geometric lag on 2-quarterahead expectations. This geometric lag assumes that longterm expectations of inflation are revised in proportion to
the difference between the current short-term expectation
of inflation and the previous long-term expectation. 16
For the survey-based measure of expectations, the bond
rate equation was estimated in the form of equation (6),
with the survey measure of short-term expectations of
inflation incorporated into is ~ Pand the survey measure
of long-term expectations being used for the final term. In
contrast, the bond rate equation estimated for the other two
measures of expectations takes the form of equation (7),
where the measures of short-term expectations of inflation
are collected.
The sample period again was split in the mid-1970s.
Recall that the forecast errors of the survey measure of
short-term expectations of inflation dropped considerably
in the second of the sub-periods. Also, remember that the
survey measure of long-term expectations of inflation is

mostly actual data in this period, rather than being estimated through a term structure relation with short-term expectations. Nevertheless, as shown in Table 3, the bond
rate equation using the survey measure has distinctly the
largest standard errors of any of the three measures of
expectations in both sub-periods. A partial explanation of
the relatively poor fit of the survey measure in the bond rate
equation may be that the survey evidence measures average rather than marginal beliefs. The presence of arbitragers in this market suggests that actions of marginal
investors are likely to be much more critical than in other
markets.
The augmented autoregressive measure of expected
inflation has the lowest standard errorin the 1961.4-1975.4
subperiod, and about the same standard error as the purely
autoregressive measure in the 1976.1-1986.4 subperiod.
Thus, the forecasts of marginal investors appear usually to
have incorporated at least some of the extra information
contained in the augmented autoregressive measure of
expectations. This is true even in the second sub-period
when the standard errors of the bond rate equation are
about the same for these two measures of expectations.
Since the augmented autoregressive'measure of expectations contains more information and has a lower forecasting error, the equal standard errors generated by the bond
rate equation suggest that market participants used some,
but not all, of this extra information in this period.
Once again, we examine the Lucas critique of the
adaptive expectations approach by testing for stability of
the term-structure equation in the period following the
post-October 1979 shift in monetary policy. The Federal
Reserve's shift to a disinflationary monetary policy could
have produced two opposite effects on the term structure of
interest rates. On the one hand, a credible disinflationary
policy could produce expectations of a sustained period of
tight money in which the real short-term interest rates
expected in the relatively near future would rise by more
than ordinarily would be explained by the behavior of
current and past short-term rates. On the other hand, such
a policy also could dampen expectations of inflation,

which would reduce the nominal short-term rates expected
in the more far distant future due to lower inflationary
premiums in interest rates. If the first effect dominates, the
term-structure equation would tend to underpredict nominal long-term rates of interest. But if the second effect
dominated, overprediction would result. For a bond with a
long maturity, the second effect would be more likely to
dominate if inflationary expectations were significantly
affected.
Chart 2 shows out-of-sample forecast errors of the
equation for the Aaa corporate bond rate for the postOctober 1979 period. The augmented autoregressive measure of inflationary expectations was used since it best fits
the data for the entire sample period. From 1979.4 through
1982.1, the forecast errors (actual minus predicted) are
positive for eight out of the ten quarters, suggesting that
there was an upward shift in expectations of future real
short-term interest rates due to the shift to a disinflationary
policy. This shift is strong enough that an F test for the
whole period from October 1979 through the end of 1986
rejects stability at the 5 percent level, as shown in Table 2.
But the effect was only temporary. After the first quarter of
1981, forecast errors are neither predominantly positive nor
negative.
Thus, in the period immediately after October 1979,
there is evidence of an upward shift in expectations of
future real short-term interest rates. Any response of an
expected decline in inflationary premiums was not strong
enough to offset this, even though the Aaa corporate bond
has a long maturity. Moreover, after 1982 when real interest
rates had dropped, there is no predominance of negative
forecast errors, as would have been the case if the augmented autoregressive forecasts were overpredicting the
market's expectation of future inflation. Therefore, although there is evidence to suggest that bond market
participants believed tight monetary policy would affect
real interest rates in a manner that could not have been
predicted by extrapolation from past history, this belief
does not appear to have extended to their expectations of
disinflation in wages and prices. 17

IV. Long-Term Inflationary Expectations and Business Fixed Investment
Alternative measures of longer term expectations of
inflation are evaluated next within the context of the real
after-tax bond rate in the San Francisco econometric
model's equations for business investment in equipment
and structures. These equations follow the neoclassical
theory of investment developed by Jorgenson (1963) and
Hall and Jorgenson (1967). In this approach, capital is a

substitute for other factors of production, and firms combine capital with these other factors so as to minimize costs
and maximize profits.
These investment equations follow a stock-adjustment
process in which the desired stock of capital is determined
by final sales and the real rental cost of capital. Lag
weights are imposed according to the lags between capital

Economic Review / Summer 1988

appropriations and expenditures, as estimated by Almon
(1965). A 2-quarter time lag between investment decisions
and capital appropriations is assumed. In addition, we
allow investment plans to be cancelled or expanded after
the initial appropriations process when sales turn out to be
greater or less than originally anticipated. This is captured
by adding a variable equal to the difference between sales
lagged one quarter and expected sales, as measured by a
distributed lag (with weights the same as between appropriations and capital expenditures) on past sales, adjusted
for normal growth. Thus, the form of these equations is: 18
9

I = bo + bli~/w'FSt + b2i~/w'RC'FSt
10

- b3i~/w'Kt
+ b 4 [FS_ 1
where I

10
i~3W_i·FSj1+T)i-l].

(8)

= real investment in equipment or

structures
FS
RC
K
w

= real final sales
= real rental cost of capital
= real stock of capital at end of quarter
= lag weights

The real rental cost of capital can be shown to be
equal to: 19
RC = T(i where i

P
d
T

P + d)

(9)

= nominal long-term interest rate

long-term expectation of inflation
physical rate of depreciation of capital
= term that depends on corporate income
tax, any investment tax credits, and
allowable depreciation
=
=

The real rental cost of capital is a function of the real rate
of interest, i as well as the physical rate of depreciation and taxes. For long lived capital investment, such as
plant and equipment, the relevant real rate of interest is a
long-term one. We calculate this as a weighted average of
the real cost of debt and equity capital, with weights of Y3
and 7'3, respectively, equal to their average values over the
past two decades. The real cost of equity capital is measured by a distributed lag on earnings per dollllf of share
price. The real cost of debt is calculated on an after-tax
basis. Since interest cost is deductible from earnings,
every dollar of interest cost reduces corporate taxes by the

Federal Reserve Bank of San Francisco

amount of the corporate tax rate.
Equations for business investment in equipment and
structures were estimated with three alternative measures
ofthe long-term expectations of inflation that enterinto the
real after-tax Aaa bond rate in the rental cost of capital. The
autoregressive measure of long-term inflation expectations
is a purely adaptive one calculated as a geometrically
declining weighted average of past inflation, where the
estimated rate of decline is slower than in the adaptive
measure of two quarter-ahead expectations. 20 This adaptive measure is subtracted from the nominal after-tax Aaa
bond rate to obtain the purely autoregressive measure of
the real after-tax bond rate.
The augmented autoregressive measure of the real aftertax bond rate is obtained from a weighted average of
expected real after-tax short rates, plus a risk premium,
calculated from the first two terms of equation (6). Specifically, this measure of the real after-tax bond rate is calculated by weighting the augmented autoregressive measure
of current and past real after-tax short-term rates with
estimated weights, Wi' To this we add the tax-adjusted
value of the estimated risk premium, K, to obtain the
augmented autoregressive measure of the real after-tax
bond rate.
Finally, the survey measure of long-term expectations of
inflation that we use is simply the lO-year-ahead Hoey
survey, which was extrapolated backward on the basis of
the estimated relationship between the short- and longterm surveys, as discussed in Section III. This survey
measure is subtracted from the nominal after-tax Aaa bond
rate to obtain the survey measure of the real after-tax bond
rate.
The standard errors of the model's equations for investment in equipment and structures using the three alternative measures of long-term expectations of inflation are
presented in Table 4. The standard errors for the survey and
adaptive measures are about equally low, suggesting that
economic agents who make long-term capital investments
form their long-term expectations of inflation adaptively.
The augmented autoregressive measure of long-term expectations of inflation gives distinctly larger standard
errors in both equipment and structures than do the other
two measures. Even though this measure incorporates
information that is used to some extent by arbitragers in the
bond market, there is no indication that this information
also is utilized by economic agents undertaking business
investment in equipment and structures.
Turning to the question ofthe stability of the structure of
these adaptive expectations, out-of-sample forecast errors
for these investment equations in the period after October
1979 are shown in Chart 2. In the case of investment in

equipment, there is a general tendency for the equation to
overpredict, as would occur if the real bond rate were being
understated due to overpredictions of inflation associated
with adaptively formed expectations. However, the largest
of these errors occur during the 1981-82 recession when
the equation appears to be prone to missing a turning point.
Any errors from an adaptive mismeasurement of long-term
inflationary expectations likely would have died out more
gradually than these do. Also, an F test cannot reject
stability of the equipment equation, as indicated in Table
2. Thus, the forecast errors of the equipment equation are
not atypically large, and they appear to be more closely
related to business cycle factors than to the mismeasure-

ment of expected inflation.
The equation for investment in structures tends to underpredict in the post-October 1979 period, which is the
opposite of what would be expected from an adaptive
mismeasurement of expected inflation. Also, the F test
indicates stability. Taken together, the results for investment in equipment and structures do not suggest that the
Federal Reserve's shift to a disinflationary monetary policy
had any significant direct effect on the formation of longterm expectations of inflation over and above the adaptive response of market participants to current and past
inflation.

v. Summary and Conclusions
In this article, we have evaluated the explanatory power
of alternative measures of expected inflation in the investment sector of a structural econometric model of the U. S.
economy. Previous research has indicated that purely autoregressive models of expected inflation fit labor market
data about as well as survey measures that might capture
any additional information used by market participants in
the formation of expectations. 21 These studies also have
found that an autoregressive representation of inflationary
expectations in the labor market generally is robust to
sharp changes, such as the acceleration of inflation in the
1970s and the post-1981 disinflation in the United States. 22
Likewise, in this study, we have found that the inflationary
expectations of participants in the investment sector of the
economy generally have these same characteristics.
The short-term expectations of inflation reflected in
households' purchases of consumer durables are as well
represented by a purely autoregressive measure based on

past inflation alone as by a survey measure, suggesting that
actual expectations are basically adaptive.
We also examined alternative measures of long-term
expectations of inflation in the context of business decisions with respect to long-lived capital investment. These
long-term expectations of inflation are about equally well
represented by a purely autoregressive measure and a
survey measure, suggesting that here too, actual expectations of inflation are basically adaptive.
In contrast, investors who arbitrage between short-term
and long-term securities appear to take into account additional information that is not captured by either a purely
autoregressive or a survey measure of expected inflation.
This additional information is at least partly captured by an
augmented autoregressive measure containing not only
past inflation, but also current unemployment and current
and past changes in the real price of oil and the real value of
the dollar.

Economic Review / Summer 1988

Since neither the purely autoregressive nor the augmented autoregressive measure of expected inflation contains any forecast of future monetary policy, both might be
poor estimates of inflationary expectations when changes
occur in monetary policy that potentially might change
relationships between future inflation and the current and
past values of inflation or other variables-the Lucas
critique. An important example of such a change is the
disinflation that was produced by a change in U.S. monetary policy in October 1979. But stability tests on the
equations for spending on consumer durables, the longterm bond rate, and business fixed investment do not
indicate that the Federal Reserve's October 1979 shift in
monetary policy significantly affected the formation of
inflationary expectations, either short- or long-term, in any
direct way. Although there is evidence that this policy
temporarily affected expectations of future real interest

rates, its influence does not appear to have extended in any
significant way to the formation of expectations of inflation
premiums in future nominal interest rates.
In conclusion, inflationary expectations in the U.S.
economy appear close to being purely adaptive, formed
simply by extrapo,lating from past inflation. Moreover,
autoregressive representations of inflationary expectations
appear quite stable, even in the face of major changes in
monetary policy. Contrary to the Lucas critique, conventional macro-econometric models that contain relatively
backward looking and slowly adjusting autoregressive
expectations of inflation can be expected to generate
reasonably accurate forecasts of the economy's response to
changes in monetary policy.23 This response includes a
significant short-run effect on real interest rates, output,
and employment, but one that diminishes over several
years so that in the long run only inflation is affected.

ENDNOTES
1. An earlier version of this structural macro-econometric
model, described in Throop (1984b), contained only the
aggregate demand side of the economy. The current
version of the model includes additional equations for the
inflation rate, the unemployment rate, the share of disposable income in GNP, and the demand for money. A
complete description of the current version is forthcoming
in the Working Papers in Applied Economic Theory and
Econometrics series of this Bank, and an article summarizing its dynamic properties will be published shortly
in the Economic Review.
2. See, for example, Friedman (1957) and Nerlove (1958).
3. The parameter a was estimated from equations in the
model, rather than from the actual two quarter-ahead
inflation rate, because we want the best representation of
the public's expectation of inflation. This is not necessarily
the same thing as the best forecast of inflation.
4. This relationship between the speed of adjustment and
the degree of excess demand has been advanced by
Samuelson (1974), Baumol (1959), Reder (1947), and
Lipsey (1960), among others.
5. According to an alternative view, markets always are in
equilibrium, and movements in employment and output
are due solely to misperceptions of future inflation. The
equilibrium view, which was proposed in an early form by
Irving Fisher (1926), underpins the "new" classical macroeconomics of Lucas (1972, 1975) and Sargent (1976). In
the equilibrium view, price and wage changes cause
output and employment changes, and so would normally
tend to precede them; whereas in the more conventional
view, causation runs in the reverse direction and with
the opposite lags. The available evidence suggests that
changes in employment and output generally tend to
precede the price and wage changes associated with

Federal Reserve Bank of San Francisco

them, supporting the conventional view. See Gordon
(1980), Laidler (1978), Nelson (1981), Okun (1980), and
also the recent survey article by Kniesner and Goldsmith
(1987) on this subject.
6. The civilian unemployment rate is adjusted for the
effects of changes in the full employment rate of unemployment due to changes in the demographic composition of the labor force. This is done by subtracting from the
civilian unemployment rate a measure of variation in the
unemployment rate due to demographics that has been
calculated by the Congressional Budget Office (1987).
Partly as a result of these demographic changes, Medoff
and Abraham (1982) find that in the United States the
vacancy rate is a more accurate measure of excess
demand than the unemployment rate, but the Bureau of
Labor Statistics has collected vacancy data experimentally for only a relatively brief period. Better data on
vacancies is available in the U.K., where a stable inverse
relationship between vacancies and unemployment has
been observed. See Dicks-Mireaux and Dow (1958,
1959).
7. Our treatment of the role of the value of the dollar and
the price of oil in the inflation process draws on the earlier
work of McElhattan (1985). A useful survey of previous
studies on the impact of the value of the dollar on prices is
Hooper and Lowry (1979). For more recent evidence, see
Woo (1984).
8. The relationship between inflation and M1 growth deteriorated badly after 1982. Compare Karnosky (1976) with
Judd and Trehan (1987). But even before 1982, inflation
could be predicted as well by an augmented Phillips
curve that describes the dynamics of the process by
which monetary impulses are transmitted to prices as by
money itself, as shown by Throop (1984). Moreover, as

Wachter (1976) has demonstrated, past money growth
does not contribute any more to an explanation of inflation
than past inflation does when either one is included in an
augmented Phillips curve.
Some recent research has emphasized the distinction
between the effects of anticipated and unanticipated
money growth on prices. For example, Barro (1987)
argues that anticipated money growth has a one-to-one
contemporaneous effect on prices, while deviations in
output growth from trend are due only to unanticipated
money growth. However, the notion of an i~mediate
response in prices to anticipated changes In money
makes sense only in the case of auction markets where
there is no inertia in price adjustment. It would be difficult
to characterize U.S. labor markets .and many product
markets in such terms. Studies which dispute the importance of the distinction between anticipated and unanticipated money growth include Mishkin (1982) and Gordon
(1982).
9. The NBER-ASA survey is published periodically by the
Survey Research Center of the University of Michigan. in
Economic Outlook USA. Complete data tapes are maIntained by the National Bureau of Economic Research. We
used the Livingston survey as adjusted by Carlson's
(1977) method and maintained by the Federal Reserve
Bank of Philadelphia.
10. Actually, the NBER-ASA survey uses the GNP implicit
price deflator, rather than the GNP fixed-weighted price
index used in our structural econometric model. But each
of the survey measures of expectations was adjusted to
remove any systematic difference between their trend
rates of inflation and the trend rate of change in the GNP
fixed-weighted price index. This was done by subtracting
from each the average difference between two quarterahead inflation in its concept and two quarter-ahead
inflation in the GNP fixed-weighted price index in neighboring quarters.
11. Zarnowitz (1985) shows that the NBER-ASA survey is
not free of systematic bias, the more so the longer the term
of the forecast. A lack of randomness in the errors from
the Livingston forecast is confirmed by Carlson (1977).
Pearce (1979) has found that univariate time series models yield better inflation predictions than the Livingston
survey. In addition, Figlewski and Wach~el (19~1). have
examined the individual forecasts contained within the
Livingston sample. They conclude that the condition of
unbiasedness can easily be rejected and that current
forecast errors can be explained by past forecast errors.
Webb (1987) points out a number of pitfalls in using ex
post tests of statistical bias to infer the ex ante rationality of
forecasts. Even so, the difference between the accuracy
of survey forecasts of inflation and the accuracy of their
other forecasts is striking.
12. The permanent income hypothesis of Friedman
(1957) was used in early versions of the San Francisco
econometric model. Studies applying this approach to
consumer durables include Juster and Wachtel (1972)
and Darby (1975). In the forthcoming version, however,

the consumption function is based on the life-cycle model
of Ando and Modigliani (1963).
13. Permanent disposable income was calculated as a 16
quarter geometric lag on current disposable income,
adjusted for the trend in income:
15

YD P = .~ u(1-u)i(1 + T)iYD_ i"
1=0

The parameter a was estimated at 0.5. Also, dummy
variables were included to capture the effects of the
Carter administration's credit controls in the period 1980.2
through 1980.4.
Until the 1986 reform of the tax law, interest paid on the
purchases of consumer durables was deductible from
taxable income for households who itemized. Thus, the
real after-tax rate of interest is the theoretically correct
measure of the cost of capital for these individuals, as well
as households whose alternative is investment in financial
assets. The consumer durables equation was first estimated with the real after-tax commercial paper rate, using
the Barro and Shahasakul (1983) estimates of the average
marginal tax rate of households. However, when alternative weights between zero and one were placed on the tax
rate, the best fitting equation was the one with a zero
weight. Therefore, the real pre-tax commercial paper rate
was chosen for the equation.
14. In Table 2, the variables were all transformed according to the estimated serial correlation coefficient for the full
period. F tests were then performed on the residuals fro~
the estimated equations that use these transformed vanabies. This procedure avoids a rejection of stability simply
because of instability in the error pattern, as opposed to a
shift in the structural equation itself.
15. An additional component of the term structure equation that we estimated, which for simplicity is not discussed in the text, allows for the fact that the average
effective maturity, or "duration," of a coupon bond depends upon the level of interest rates. When interest rates
are high, the duration of newly issued bonds is shorter
because a larger portion of the total payment of interest
and principal occurs relatively early. Conversely, when
interest rates are low, the duration of a bond becomes
longer. Thus, the lags on past interest rates in an autoregressive model of expectations should be shorter the
shorter is the average effective maturity of the bond. The
term structure equation captures this duration effect by
adding a term formed by multiplying a distributed lag on
the commercial paper rate by the recent average level of
the commercial paper rate, with the sum of the weights on
the lagged values of the commercial paper being constrained to zero. The estimated coefficients on these
lagged values of the commercial paper rate are first
positive and then negative. Thus, the mean length of the
overall lag distribution on the commercial paper rate
shortens when the level of interest rates rises, confirming
the existence of a duration effect. For further discussion of
the duration effect, see Van Horne (1984).

Economic Review / Summer 1988

We also experimented with the assumption of a greater
degree of rationality in expectations by including the
change in the ratio of the federal high employment budget
to high employment GNP from the last four quarters to four
quarters ahead as an additional variable. Information is
generally available about what the budget will look like in
the coming year, and a rational market should incorporate
this information into its view of where short-term interest
rates in the future will be, and therefore what bond yields
should be today. However, even when the test for such an
effect was restricted to the period of large and growing
budget deficits under the Reagan administration, no statistically significant impact of expected changes in the
bUdget deficit could be detected.
16. The best fitting geometric lag has a speed of adjustment, equal to the coefficient u in equation (3), of 0.17.
17. Blanchard (1984) reaches a similar conclusion.
18. The equation for structures also contains a distributed
lag on the real price of oil. An important component of
investment in structures is oil drilling, which responds
positively to its price.
19. For a derivation, see Hall and Jorgenson (1967) or
Throop (1984b).
20. The best fitting geometric lag in equipment and structures has a speed of adjustment, equal to the coefficient u
in equation (3), of 0.05.
21. McNess (1979) compared an expectations-augmented Phillips curve using an autoregressive measure of
expected inflation with an alternative version using the
survey measure collected by Joseph Livingston, a columnist with the Philadelphia Inquirer. Kaufman and Woglom
(1984) perform a similar test on union wages using micro-

economic data and conclude that their data "do not
provide strong support to allow us to reject the hypothesis
that inflationary expectations are backward looking."
22. Blanchard (1984), Englander and Los (1983), and
Perry (1983) found that expectations-augmented Phillips
curves with autoregressive expectations were stable in
face of the sharp disinflation after 1981. An earlier study
demonstrating similar stability in the 1970s is Smaistrla
and Throop (1980).
23. This conclusion holds only for the time periods and
policies in this and other studies cited-basically postWorld War II U.S. experience. Although there has been a
significant amount of variation in inflation in the U.S.
economy during this period, extreme variability could
cause an autoregressive model of the formation of inflationary expectations to break down. Thus, for example,
when comparing countries with vastly different variability
in inflation rates, Lucas (1973) finds that the short-run
trade-off between inflation and unemployment tends to
steepen in those countries where the variability in inflation
is greater. A stable autoregressive structure of inflationary
expectations, therefore, would not hold up across this
range of experience. Similarly, Sargent (1982) finds that in
cases where hyperinflations caused by the monetization
of government debt have been ended by the creation of
an independent central bank and a simultaneous alteration in the fiscal policy regime, inflations were ended
quickly and with little adverse effect on output and
employment. In these instances, extreme changes in
policy and institutions caused an abrupt shift in inflationary expectations that would be inconsistent with a stable
autoregressive structure of expectations.

REFERENCES
Anderson, Paul A. "Rational Expectations Forecasts from
Nonrational Models," Journal of Monetary Economics, No.5, 1979.
Ando, Albert and Franco Modigliani. "The 'Life-Cycle'
Hypothesis of Saving: Aggregate Implications and
Tests," American Economic Review, March 1963.
Almon, Shirley. "The Distributed Lag Between Capital
Appropriations and Expenditures," Econometrica,
January 1965.
Barro, Robert J. "Unanticipated Money, Output, and the
Price Level in the United States," Journal of Political
Economy, August 1978.
_ _ _ _and Chaipot Shahasakul. "Measuring the Average Marginal Tax Rate from the Individual Income
Tax," Journal of Business, October 1983.
Baumol, William J. Economic Dynamics. New York: Macmillan Co., 1959.
Blanchard, Oliver J. "The Lucas Critique and the Volcker
Deflation," American Economic Review, May 1984.

Federal Reserve Bank of San Francisco

Cagan, Phillip. "The Monetary Dynamics of Hyperinflation," in Milton Friedman (ed.), Studies in the Quantity
Theory of Money. Chicago: University of Chicago
Press, 1956.
Carlson, John A. "A Study of Price Forecasts," Annals of
Economic and Social Measurement, Winter 1977.
Congressional Budget Office, The Economic and Budget
Outlook, An Update 1987, Appendix B.
Darby, Michael. "Postwar U.S. Consumption, Consumer
Expenditures, and Saving," American Economic Review, May 1975.
Dicks-Mireaux, L.A. and J.C.R. Dow. "The Excess Demand for Labor: A Study of Conditions in Great Britain,
1946-56, Oxford Economic Papers, February 1958.
--'-"The Determinants of Wage Inflation: United
Kingdom, 1946-56," Journal of the Royal Statistical
Society, Part II, 1959.
Eckstein, Otto. The DRI Model of the U.S. Economy. New
York: McGraw-Hili Book Co., 1983.

Englander, A. Steven and Cornelis A. Los. "The Stability of
the Phillips Curve and Its Implications for the 1980s,"
Working Paper, Federal Reserve Bank of New York,
January 1983.
Figlewski, S. and P. Wachtel. "The Formation of Inflationary Expectations," Review of Economics and Statistics, February 1981.
Fisher, Irving. The Theory of Interest. New York: Macmillan, 1930.
_ _ _ _"A Statistical Relation Between Unemployment
and Price Changes," International Labor Review,
1926. (Reprinted as: "I Discovered the Phillips Curve,"
Journal of Political Economy, March/April 1973.)
Friedman, Milton. A Theory of the Consumption Function.
Princeton: Princeton Unviersity Press, 1957.
Gordon, Robert J. "A Consistent Characterization of a
Near-Century of Price Behavior," American Economic
Review, May 1980.
_ _ _ _ "Price Inertia and Policy Effectiveness in the
United States, 1890-1980," Journal of Political Economy, December 1982.
Hall, Robert E. and Dale W. Jorgenson. "Tax Policy and
Investment Behavior," American Economic Review,
June 1967.
Hooper, Peter and Barbara Lowrey. "Impact of the Dollar
Depreciation on the U.S. Price Level: An Analytical
Survey of Empirical Estimates," International Finance
Discussion Paper 128, Board of Governors of the
Federal Reserve System, January 1979.
Huizinga, John and Frederic Mishkin. "Monetary Policy
Regime Shifts and the Unusual Behavior of Real Interest Rates" in Karl Brunner and Allan Meltzer (eds.),
The National Bureau Method, International Capital
Mobility and Other Essays, Carnegie Rochester Conference on Public Policy, Vol. 24 (1986).
Jorgenson, Dale W. "Capital Theory and Investment
Behavior," American Economic Review, May 1963.
Judd, John L. and Bharat Trehan. "Portfolio Substitution
and the Reliability of M1, M2, and M3 as Monetary
Policy Indicators," Economic Review, Federal Reserve Bank of San Francisco, Summer 1987.
Juster, F. Thomas and Paul Wachtel. "Anticipatory and
Objective Models of Durable Goods Demand," American Economic Review, September 1972.
Karnosky, Denis. "The Link Between Money and Prices,"
Review, Federal Reserve Bank of St. Louis, June 1976.
Kaufman, Roger 1. and Geoffrey Woglom. "The Effects of
Expectations on Union Wages," American Economic
Review, June 1984.
Kniesner, Thomas J. and Arthur Goldsmith. "A Survey of
Alternative Models of the Aggregate U.S. Labor
Market," Journal of Economic Literature, September
1987.

Laidler, David. "Money and Money Income: An Essay on
the Transmission Mechanism," Journal of Monetary
Economics, April 1978.
Lipsey, Richard G. "The Relation Between Unemployment
and the Rate of Change of Money Wage Rates in the
United Kingdom, 1862-1957: A Further Analysis,"
Economica, February 1960.
Lucas, Robert. "Expectations and the Neutrality of
Money," Journal of Economic Theory, November/
December 1972.
_ _ _~ "Some International Evidence on Output-Inflation Trade-Offs," American Economic Review, June
1983.
_ _ _ _ "An Equilibrium Model of the Business Cycle,"
Journal of Political Economy, December 1975.
_ _ _ _ "Econometric Policy Evaluation; A Critique," in
Karl Brunner and Allan H. Meltzer (eds.), The Phillips
Curve and Labor Markets, Carnegie-Rochester Conference on Public Policy, Vol. 1 (1976).
McElhattan, Rose. "Inflation, Supply Shocks and the Stable-Inflation Rate of Capacity Utilization," Economic
Review, Federal Reserve Bank of San Francisco, Winter 1985.
McNess, Stephen K. "The Phillips Curve: Forward- or
Backward-Looking," New England Economic Review.
Federal Reserve Bank of Boston, July/August 1979.
Medoff, James L. and Katharine G. Abraham. "Unemployment, Unsatisfied Demand for Labor, and Compensation Growth," in Martin N. Bailey (ed.), Workers, Jobs,
and Inflation. Washington, D.C.: The Brookings Institution, 1982.
Mishkin, Frederic S. "Does Anticipated Monetary Policy
MaUer? An Econometric Investigation," Journal of
Political Economy, February 1982.
Modigliani, Franco and Richard Sutch. "Innovations in
Interest Rate Policy," American Economic Review,
May 1966.
Modigliani, Franco and Robert L. Shiller. "Inflation, Rational Expectations, and the Term Structure of Interest
Rates," Economica, February 1973.
Muth, John F. "Rational Expectations and a Theory of
Price Movements," Econometria, July 1961.
Nelson, Charles R. "Adjustment Lags Versus Information
Lags: A Test of Alternative Explanations of the Phillips
Curve Phenomenon," Journal of Money, Credit and
Banking, February 1961.
Nerlove, Marc. "Adaptive Expectations and Cobweb Phenomena," Quarterly Journal of Economics, May 1958.
Okun, Arthur M. "Rational-Expectations-with-Misperceptions as the Theory of the Business Cycle, Journal of
Money, Credit and Banking, November 1980, Part 2.
Pearce, Douglas K. "Comparing Survey and Rational
Measures of Expected Inflation." Journal of Money,
Credit, and Banking, November 1979.

Economic Review / Summer 1988

Perry, George L. "What Have We Learned About Disinflation?" Brookings Papers on Economic Activity, No.2,
1983.
Reder, Melvin W. Studies in the Theory of Welfare Economies. New York: Columbia University Press, 1947.
Rutledge, John. A Monetarist Model of Inflationary Expectations. Lexington, Mass.: D.C. Heath & Co., 1974.
Samuelson, Paul A. Foundations of Economic Analysis.
Cambridge: Harvard University Press, 1947.
Sargent, Thomas. "A Classical Macroeconomic Model of
the United States," Journal of Political Economy, April
1976.
_ _ _ _ "The Ends of Four Big Inflations," in Robert E.
Hall (ed.), Inflation: Causes and Effects. Chicago: The
University of Chicago Press, 1972.
____ Macroeconomic Theory. Orlando: Academic
Press, 1987.
Smaistrla, Charles, and Adrian W. Throop. "A New Inflation in the 1970s7" Financial Analysts Journal, March/
April 1980.
Throop, Adrian W. "Comparing Inflation Forecasts,"
Weekly Letter, Federal Reserve Bank of San Francisco, March 16, 1984a.
_ _ _ _ "A Structural Model of Real Aggregate Demand," Working Paper in Applied Economic Theory
and Econometrics, No. 84-03, Federal Reserve Bank
of San Francisco, July 1984b.
Van Horne, James C. Financial Market Rates and Flows.
Englewood Cliffs, N.J.: Prentice Hall, 1984.
Wachter, Michael L. "The Changing Cyclical Responsiveness of Wage Inflation," Brookings Papers on Economic Activity, No.1, 1976.
Webb, Roy H. "The Irrelevance of Tests for Bias in Series of
Macroeconomic Forecasts," Economic Review,
Federal Reserve Bank of Richmond, November/December 1987.

Federal Reserve Bank of San Francisco

Full text of Economic Review (Federal Reserve Bank of San Francisco) : Summer 1988, Number 3

FRASER