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Federal Reserve Bank of Chicago

Welfare Implications of the Transition
to High Household Debt
Jeffrey R. Campbell and Zvi Hercowitz

WP 2006-27

Welfare Implications of the Transition to
High Household Debt∗
Jeffrey R. Campbell† Zvi Hercowitz‡
November, 2006

Abstract
Aggressive deregulation of the mortgage market in the early 1980s triggered innovations that greatly reduced the required home equity of U.S. households. This allowed
households to cash-out a large part of accumulated equity, which equaled 71 percent
of GDP in 1982. A borrowing surge followed: Household debt increased from 43 to 62
percent of GDP in the 1982-2000 period. What are the welfare implications of such a reform for borrowers and savers? This paper uses a calibrated general equilibrium model
of lending from the wealthy to the middle class to evaluate these effects quantitatively.

∗

We are grateful to Erik Hurst and Richard Rogerson for their discussions of an earlier version of this
paper.
†
Federal Reserve Bank of Chicago and NBER. e-mail: jcampbell@frbchi.org
‡
Tel Aviv University. e-mail: zvih@post.tau.ac.il
JEL Codes E44, E65
Keywords: Financial Reform, Mortgage Debt, Interest Rates

1

Introduction

Who benefits the most from a reform which relaxes a binding borrowing constraint? Borrowers or savers? At the microeconomic level, only borrowers benefit because they are constrained. In other words, only for them the Lagrange multiplier on the constraint is positive.
The macroeconomic interaction involves an additional consideration: Allowing larger borrowing raises the interest rate for while, i.e., the borrowers’ terms of trade worsen for some
time, and this redistributes the benefits. Hence, who gains the most is a quantitative issue.
The U.S. economy underwent a drastic reform of this type in the early 1980s. Most
household debt in the United States requires an initial equity share in the home or vehicle
that serves as collateral—a down payment—and a minimum rate of debt amortization—
which determines the rate of equity accumulation. The Monetary Control and the Garn-St.
Germain Acts of 1980 and 1982 allowed market innovations that dramatically reduced these
equity requirements: Greater access to sub-prime mortgages, mortgage refinancing, and home
equity loans, reduced effective down payments and increased effective repayment periods.
More important for the short run, it enabled households to cash-out previously accumulated
home equity, which in 1982 amounted to 71 percent of GDP. This was followed by a huge
wave of household borrowing.
In this paper we focus on the welfare effects of such a reform using a calibrated model
economy. The model is a general equilibrium framework for household borrowing from Campbell and Hercowitz (2006), which combines trade between a patient saver and an impatient
borrower with equity requirements on housing and consumer durables typical of collateralized
loan contracts. The model has a simple structure, but it captures the main features of the
distribution of debt and financial assets across households in the US economy. Households in
the first-to-ninth deciles of the wealth distribution owed 73.0 percent of total household debt
in 1962, and 73.4 percent in 2001. Households in the tenth decile held 54.2 percent of total
financial assets in 1962 and 72.8 percent in 2001. Hence, a large fraction of households owe
debt to a small fraction of households. The model’s equilibrium resembles this in an extreme
way. The borrower owes all the debt to the saver.
With the model calibrated to the period prior to 1983, and the financial reform calibrated
to the actual reduction of equity requirements on households, we compute the transition
across the two corresponding steady states. Because the reform allows the borrower to cashout a large amount of accumulated equity, the equity constraint may not bind for some time.
We use a modified version of the Fair-Taylor (1983) algorithm to solve the model, which
determines when along the transition path the equity constraint binds. Across steady states,
1

savers’ welfare increases and borrowers’ declines due to the higher debt. The borrowers’ gains
can accrue only during the transition.
The model’s transition starts off with previously constrained households cashing out some
of the home equity in excess of the new lower requirement. This borrowing surge increases the
interest rate. Over time, the debt stabilizes at a higher level while the interest rate returns
gradually to it’s steady state. This resembles the evidence on the comovement of household
debt and interest rates since 1983.
The welfare analysis of the calibrated economy indicates that both households gain in
terms of discounted utility at the time of the reform, although the saver’s gain is much larger
than the borrower’s. The borrowers’ gain is due to high consumption and durable goods
purchases during the period following the reform. Of course, accumulated debt implies that
at the new steady state a borrower’s utility flow is lower than at the starting steady state.
The savers gains initially while the terms of trade changed in their favor, i.e., the interest
rate is high, and moving to the new steady state with higher assets.
The paper proceeds as follows. The next section provides the institutional background for
the analysis and Section 3 presents the model. The steady-state to steady-state comparison
following the reform is addressed in Section 4. In Section 5 we report first the calibration of
the model and then the computed transition process. It concludes with the evaluation of the
reform’s welfare effects. In Section 6 we discuss the actual evolution of household debt and
interest rates. Section 7 presents an extension of the model with an irreversibility constraint
on durable goods investment. We conclude in Section 8.

2

Institutional Background

Our analysis takes the institutions structuring the household debt market as determined by
regulation, so we begin with a review of how these have changed since 1982. It is helpful
to emphasize first one feature of this market that remains the same: Homes and vehicles
collateralize most household debt. According to the 1962 Survey of Financial Characteristics
of Consumers, homes and vehicles collateralized 85 percent of total U.S. household debt. The
analogous percentage from the 2001 Survey of Consumer Finances was 90 percent.1
From the middle 1930s until the early 1980s, 15 and 30 year amortized mortgages accounted for most of collateralized household debt. These required the home owner to take
an initial equity share at the time of purchase and to accumulate further equity as the debt
1

Details of these observations are provided in Campbell and Hercowitz (2006), Appendix A.

2

amortizes. The implied forced savings reflected the desire of the Roosevelt administration
to reduce the likelihood of a mass default of highly-leveraged mortgagees, as occurred at
the beginning of the Great Depression. A host of financial regulations supported this policy. The most prominent gave tax incentives for Savings and Loan associations to finance
home mortgage lending with demand deposits and protected this trade from other financial
intermediaries. The volatile financial markets of the 1970’s made these and other New Deal
financial regulations untenable. Congress and Presidents Carter and Reagan responded with
the Monetary Control Act of 1980 and the Garn-St. Germain Act of 1982. These led to an
aggressive reorganization of the housing finance system.2
Instruments for avoiding forced saving existed before financial deregulation. One could
cash-out previously accumulated home equity either by taking a second mortgage or homeequity loan or by refinancing the debt with a loan exceeding the current mortgage balance,
but lack of competition in lending made these rare. Deregulation lowered the cost of these
instruments for all financial intermediaries and households. Accordingly, household debt
began to grow. The ratio of mortgage debt to the value of owner-occupied homes was 0.31 in
1982, 0.37 in 1990, and 0.42 in 1995. Since then, it has fluctuated around this higher level.
A more detailed appreciation of how deregulation affected home equity accumulation
can be gained by examining how households structured their mortgage debts. Time-series
observations on typical terms of first mortgages are available from the Federal Home Finance
Board’s Monthly Interest Rate Survey, but these provide an incomplete picture because they
ignore subordinated debt used to lower the effective down payments. Hence, we proceed
by examining households debts in the Survey of Consumer Finances. Understanding that
deregulation had the potential to vastly change households’ financial decisions, the Federal
Reserve Board resurrected its Survey of Consumer Finances program in the early 1980s,
which collected the first “modern” SCF data set in 1983.3 The Federal Reserve carried
out subsequent SCFs every three years. These surveys gathered detailed information on
households’ balance sheets and use of different financial instruments and institutions, so they
2

Green and Wachter (2005) provide a history of New Deal mortgage institutions and of the process of
dismantling them in the early 1980’s. See also Florida (1986) and the articles contained therein.
3
The code book to the 1983 SCF (written initially in 1985) begins “There have been many changes in
financial markets during the last decade. Inflation and interest rates increased sharply in the late 1970s and
then fell after recessions in 1980 and 1981-82. Major financial innovations occurred, such as the introduction
of money market funds, and the regulation of financial markets altered dramatically after enactment of the
Depository Institutions Deregulation and Monetary Control Act of 1980. To assess the effects of these changes
on the financial position of households, the Board of Governors of the Federal Reserve System (and other
agencies) joined together to sponsor the 1983 Survey of Consumer Finances (SCF).”

3

Year
1983
1989
1992
1995
1998
2001

Percent of Mortgagees
Refinanced
9.9
21.2
33.0
40.9
42.3
44.4

Average Equity/Value
at Purchase
22.6
23.4
20.9
16.9
16.4
16.4

Table 1: Mortgage Terms and Instruments from the Survey of Consumer Finances

provide the data required for tracking the effects of deregulation on households’ mortgage
borrowing decisions.
For six SCFs, Table 1 reports two key summary statistics characterizing households’
mortgage borrowing, the percentage of mortgagees who have refinanced the mortgage on
their current residence, and the average home equity to value ratio for new home purchases.
The first survey considered is that of 1983, which was collected only shortly after the GarnSt. Germain Act became law in October 1982. We consider these observations as indicative
of mortgage borrowing just before deregulation’s completion. We do not report results from
the 1986 SCF, because of its problematic sampling procedure.4 The other surveys we do use
are from 1989, 1992, 1995, 1998, and 2001.
Consider first the percentage of mortgagees who have ever refinanced.5 In 1983, approximately 10 percent of mortgagees had refinanced. By 1989, this had more than doubled, and
it increased again to 33 percent in 1992. In 1995, it reached almost 41 percent, and it was
slightly higher than that in 1998 and 2001. Hence, mortgage refinancing went from atypical
to commonplace in about 12 years.
The final column reports the ratio of home equity to home value for newly purchased
homes.6 These homes’ owners have had very little time to accumulate equity through debt
4

To create a panel data set, the 1986 survey sampled households living in the same housing units as the
respondents to the 1983 survey. This non-standard sampling makes the resulting observations not representative of the U.S. population in that year
5
We identify these households by comparing the year of home purchase with the year their oldest mortgage
debt was issued.
6
For the 1983 SCF, we defined a newly-purchased home as any home purchased in 1982 or 1983. For
the other surveys, all such homes were purchased by their current occupant in the survey year. The values
reported equal the averages of this ratio across all such homes with mortgage debt exceeding 50 percent of

4

amortization, so these ratios are very close to the homeowners’ effective down payments. We
expect deregulation to lower down payments, because it allowed lenders to more easily issue
second or third mortgages when closing the home purchase. Because of these widespread options, down payments on individual mortgages after deregulation do not provide information
about the effective initial equity shares. In 1983, this ratio equalled 22.6 percent. Although
it changed little through 1992, it dropped four percentage points between 1992 and 1995 (to
16.9 percent). In the 1998 and 2001 surveys it equaled 16.4 percent.
These figures reflect the substantial changes in homeowners’ financing options after deregulation. Refinancing became cheaper and thus also more widespread, and typical down payments on new homes fell considerably although with a delay of about ten years. We have
also examined mortgagees use of home-equity lines of credit. Total debt incurred with this
instrument never exceeded 1.5 percent of mortgagees’ home value. Explaining the timing
and relative magnitudes of these institutional changes lies beyond the scope of this paper.
Our analysis takes the reduced equity requirements for household debt as given and uses a
quantitative general-equilibrium model to determine their implications for macroeconomic
dynamics and market participants’ welfare.

3

The Model

The model builds on the general equilibrium framework with household debt in Campbell
and Hercowitz (2006). It combines financial trade between a patient saver and an impatient
borrower with an equity requirement typical of collateralized loan contracts in the United
States. The different rates of time preference generate intertemporal trade in the form of
household debt owed by the borrower to the saver. Becker (1980) showed that there exists
no steady-state with positive consumption by all households in a similar economy without
constraints on debt. In our model, the equity requirement limits the borrower’s debt, so
both households have positive consumption in the steady state. The interest rate equals
the saver’s rate of time preference, and the equity requirement prevents the borrower from
expanding debt without further purchases of durable goods.
We study the transition path from one steady state to another with a lower equity requirement. The borrower begins this transition with a large amount of equity no longer required
for borrowing, so the equity requirement might not always bind.
This section presents preferences, production technology, and the constraints on trade
the home’s value.

5

between the two households. It concludes with a discussion of both households’ utility maximization problems and the definition of a competitive equilibrium.

3.1

Preferences

The saver’s and the borrower’s preferences differ in two respects: The saver is more patient
and does not work. The first assumption generates a concentration of assets in a relatively
small number of households. This follows Krusell and Smith’s (1998) use of heterogeneity
in thrift to generate an empirically realistic wealth distribution. The second assumption
simplifies the model along and unimportant dimension. Because there are few savers and
because they should each enjoy some of their wealth in the form of leisure, we expect them
to contribute little to aggregate labor supply. Accordingly, abstracting from the saver’s labor
supply choice does not substantially alter the results.7
The borrower’s and the saver’s utility functions are:
∞
h

i
X
β̂ θ ln Ŝt + (1 − θ) ln Ĉt + ω ln 1 − N̂t ,

0 < θ < 1, ω > 0,

(1)

t=0
∞


X
β̃ θ ln S̃t + (1 − θ) ln C̃t ,

(2)

t=0

where β̂ < β̃. In (1), Ŝt , Ĉt , and N̂t are the borrower’s stock of durable goods—assumed to
be proportional to the service flow—its consumption of non-durable goods and labor supply.
In (2), S̃t , and C̃t are the saver’s consumption of the two goods. We use  and à to represent
borrower and saver specific versions of A for the remainder of the paper.

3.2

Technology

The aggregate production function is Yt = K α Nt1−α , where 0 < α < 1, Yt is output, K is
a constant capital stock, and Nt is labor input. We discuss the implications of allowing for
productive capital accumulation below in Section 8.
The households can use output for either non-durable consumption or durable goods
purchases. That is, Yt = Ct + Xt , where Ct represents aggregate non-durable consumption
and Xt = St+1 − (1 − δ) St is aggregate investment in the durable good, which depreciates at
the rate δ.
7

When we endow savers with the borrowers’ intratemporal preferences and calculate the steady state of
the model calibrated as described below, savers choose to not work at all.

6

3.3

Trade

All trade takes place in competitive markets. The households sell capital services at the rental
rate Ht and labor at the wage Wt to the representative firm. They also trade in collateralized
debt, which is the only available security. The households’ outstanding debts at the end of
period t are B̂t+1 and B̃t+1 . We denote the corresponding gross interest rate with Rt , which
adjusts every period.
3.3.1

The Equity Requirement

An exogenous equity requirement on collateral constrains debt. This mimics a typical feature
of loan contracts in the United States: An equity share that starts from a positive level
(the down payment) and increases over time (if debt amortizes more rapidly than the good
depreciates). In the model, the parameters capturing this feature are 0 ≤ π < 1, the initial
equity share, and φ, which governs the speed of subsequent equity accumulation. When
a loan is collateralized by a durable good j periods old, the required equity share at the
beginning of the following period is
j

1−φ
(1 − π) .
(3)
ej = 1 −
1−δ
For newly purchased goods (j = 0) , the equity share is π. As the good ages (j increases), the
equity share converges to one when φ > δ, and stays constant when φ = δ. We call the case
of φ > δ accelerated amortization, because the equity share increases over time. When φ = δ
the equity share remains at its initial level because debt and durable goods depreciate at the
same rate. The institutional background presented above suggests modelling deregulation by
lowering the initial equity share with a drop in π and lowering the rate of equity accumulation
by bringing φ closer to δ.
For a household with positive debt, the total amount of equity at the beginning of period
t + 1 is (1 − δ)St+1 − Rt Bt+1 , where the durable stock is adjusted for depreciation and the
debt for accumulated interest. This household’s required equity in durable goods sums the
equity requirements on the (depreciated) goods of all ages from equation (3):
(1 − δ)St+1 − Rt Bt+1 ≥ (1 − δ)

∞
X

(1 − δ)j Xt−j ej .

(4)

j=0

Using the definition of ej , (4) can be expressed as a repayment constraint.
Rt Bt+1 ≤ (1 − δ)(1 − π)

∞
X

(1 − φ)j Xt−j

j=0

7

(5)

Here, a debtor’s total liability cannot exceed a linear function of the value of the goods that
collateralize it with coefficients which decrease with π and φ. If φ = δ, the right-hand side
of (5) reduces to (1 − δ)(1 − π)St+1 . In this case, the constraint is formally identical to that
which Kiyotaki (1998) derives from an environment with costly repossession. We do not
stress this interpretation of the constraint, because we assume that public policy decisions
determined π and φ rather than considerations of private contracting.

3.4

Utility Maximization

We now examine both households’ utility maximization problems. For this, we conjecture
that in equilibrium the saver owns all physical capital and the borrower’s debt. With the
proposed equilibrium in hand, verifying this is straightforward.
3.4.1

The Borrower’s Problem

To formulate the borrower’s utility maximization problem, it is helpful to first represent the
equity requirement recursively. Define
V̂t+1 = (1 − δ)(1 − π)

∞
X

(1 − φ)j X̂t−j /Rt .

(6)

j=0

This is the maximum debt principle this household can carry out of period t. Multiplying V̂t
by (1 − φ)Rt−1 /Rt and subtracting the result from V̂t+1 yields
V̂t+1 = (1 − φ)

(1 − δ)(1 − π)
Rt−1
V̂t +
X̂t
Rt
Rt

(7)

That is, the limit to the borrower’s debts evolves recursively. With this definition of Vt , the
equity requirement becomes
B̂t+1 ≤ V̂t+1 .,

(8)

Together, (7) and (8) represent the borrower’s required equity in its durable goods stock.
Given V̂0 , R−1 B̂0 and Ŝ0 , the borrower chooses sequences of Ĉt , X̂t , N̂t , and B̂t+1 and V̂t
to maximize the utility function in (1), subject to the sequence of budget constraints
Ĉt + X̂t + Rt−1 Bt = Wt Nt + Bt+1

(9)

and the sequences of constraints in (7) and (8). Denote the current-value Lagrange multiplier
on (9) with Ψt . Expressing the Lagrange multipliers on (7) and (8) with Ψt Ξt and Ψt Γt , then
8

Ξt and Γt measure the value in units of either consumption good of marginally relaxing their
associated constraints.
In addition to the three constraints and the transversality conditions,
lim β̂ t Ψt = lim β̂ t Ψt Γt = lim β̂ t Ψt Ξt = 0,

t→∞

t→∞

t→∞

(10)

the optimality conditions for this maximization problem are
Ψt =

1−θ
Ĉt

,

(11)

Rt−1
Ψt+1
Ξt+1 (1 − φ)
,
(12)
Ψt
Rt
Ψt+1
Γt = 1 − β̂
Rt ,
(13)
Ψt
"
#


(1 − π) (1 − δ)
Ψt+1
θ Ĉt+1
Ξt+1 (1 − π) (1 − δ)
1 − Ξt
= β̂
,
+ (1 − δ) 1 −
Rt
Ψt 1 − θ Ŝt+1
Rt+1
Ξt = Γt + β̂

(14)

Wt =

ϕ
1−θ



Ĉt
1 − N̂t

.

(15)

The equity requirement alters the interpretation of the multiplier on the budget constraint.
For an unconstrained household such as the saver, it equals the marginal value of permanent
income. In (11), Ψt represents the marginal value of additional current resources, because
the borrower cannot freely substitute intertemporally.
In (13), Γt equals the deviation from the standard Euler equation, the shadow value of
borrowing at time t. It is positive if the equity constraint binds at t and zero otherwise.
Iterating (12) forward yields Ξt as the present value expression of the current and future
values of Γt . Hence, even if the equity constraint does not bind currently, i.e., Γt = 0, Ξt
is positive if the constraint is expected to bind sometime in the future. This is because Ξt
equals the price of an asset that allows its holder to borrow today and in the future.
Equation (14) characterizes optimal durable good purchases. If the borrower’s equity
requirement never binds, then Ξt = Ξt+1 = 0 and (14) equates the purchase price of the
durable good to its immediate payoff (the marginal rate of substitution between durable and
non-durable goods) plus its discounted expected resale value. In the more relevant case where
Ξt and Ξt+1 are both positive, it has the same interpretation where the borrower’s “purchase
price” is 1 − Ξt (1 − π) (1 − δ)/Rt . Because the durable good provides the household with
(1 − π) (1 − δ)/Rt units—the allowed loan-to-value ratio of the “asset” mentioned above —
the borrower’s effective price lies below the real resource cost of 1.
9

Equation (15) is the consumption-leisure condition. It has the usual form because it involves only intratemporal substitution, which financial market imperfections leave unchanged.
3.4.2

The Saver’s Problem

The saver’s utility maximization problem presents no novelties, but we present it here for the
sake of completeness. Given the constant capital stock, K̃, the initial durable goods S̃0 ,and
the financial assets −R−1 B̃0 ; the saver chooses sequences of C̃t , X̃t , and B̃t+1 to maximize
utility subject to
C̃t + X̃t − B̃t+1 = Ht K̃ − Rt B̃t .

(16)

The right-hand side of (16) sums the sources of funds: Capital rental revenue, and the
market value of household debt. The left-hand side includes the three uses of these funds:
Non-durable consumption, purchases of durable goods, and saving.
Denoting the current-value Lagrange multiplier on (16) with Υt , the problem’s first-order
conditions are
1−θ
,
C̃t
"
Υt+1
1 = β̃
Υt

(17)

Υt =

1 = β̃

!#

θ C̃t+1
+ (1 − δ)
1 − θ S̃t+1

,

Υt+1
Rt ,
Υt

(18)
(19)

Equation (18) is a typical condition for optimal durable goods purchases, and (19) is the
standard Euler equation.

3.5

Production and Equilibrium

The standard conditions for profit maximization of the representative firm are
 α
K
,
Wt = (1 − α)
Nt
 α−1
K
Ht = α
.
Nt

(20)
(21)

Given the two households’ initial stocks of durable goods, Ŝ0 and S̃0 , the stock of outstanding debt issued by the borrower and held by the saver, B0 = B̂0 = −B̃0 , the predetermined
10

interest rate, R−1 , and V̂0 , a competitive equilibrium is a set of sequences for all prices and the
borrower’s, saver’s, and representative firm’s choices such that both households maximize utility subject to the constraints, the representative firm maximizes its profit, the two households’
durable goods stocks evolve according to Ŝt+1 = (1 − δ) Ŝt + X̂t and S̃t+1 = (1 − δ) S̃t + X̃t ,
and the input, product and debt markets clear.
Before proceeding to apply the model, we wish to comment on the model’s demographics.
The model is written with one saver and one borrower, but we intend the saver to stand-in
for the wealthiest ten percent of households while the borrower represents all others. Because
both households’ preferences are homothetic and the saver earns no labor income, we can
show that increasing the number of borrowers while holding the aggregate time endowment
constant has no impact on any equilibrium object except consumption per borrower. With
this in mind, we maintain the simplifying convention of referring to “the” borrower and “the”
saver.

4

Steady State Analysis

Comparison of the model’s steady state with different values of π and φ provides an insight
into the long-run implications of changing the equity requirement and also guides the quantitative examination of the complete equilibrium path. Begin with the steady-state interest
rate, which equals R = β̃ −1 from the saver’s Euler equation. With this in hand, it follows
that Γ = 1 − β̂/β̃ and
Ξ=

Γ
1 − β̂(1 − φ)

> 0.

That is, the saver’s rate of time preference determines the interest rate at a level below the
borrower’s discount rate; and the equity requirement limits the borrower’s steady-state debt.
The interest rate , Ξ, and (14) together determine the steady-state value of Ŝ/Ĉ.
Ŝ
Ĉ

=

θ
β̂


1 − θ (1 − Ξ (1 − π) (1 − δ) /R) 1 − β̂ (1 − δ)

Lowering π and φ impacts Ŝ/Ĉ through this shadow price. Consider first lowering φ.
This increases Ξ and so shifts the borrower’s consumption towards durable goods. Lowering
π leaves Ξ unchanged but also has a positive impact on Ŝ/Ĉ.8
8

One question of possible interest that is tangential to this comparative steady-state analysis is “Which

11

Because the equity requirement limits the borrower’s debt, we can determine B̂/Ŝ by
solving for V̂ /Ŝ using (7) and equating B with V . The resulting debt to value ratio is
B̂

=

(1 − π)(1 − δ) δ
,
R
φ

Ŝ
which clearly decreases with both π and φ.
With these ratios in hand, we can determine the share of labor income spent on the
borrower’s consumption.
Ĉ
W N̂

=

1
1 + (R − 1) B̂Ŝ ĈŜ + δ ĈŜ

.

(22)

In turn this determines the borrower’s hours worked, because the steady-state version of (15)
can be rewritten as
Ĉ

=

1−θ1−N
.
ϕ
N

W N̂
The results above imply that the right hand side decreases with π and φ. Hence, N increases
with these parameters. Altogether, lowering equity requirements shifts the borrower’s steadystate allocation away from leisure and nondurable consumption and towards durable goods.
We now proceed to consider the saver’s steady-state consumption and wealth. Combining
the borrower’s steady-state labor supply with the firm’s optimality conditions immediately
yields W and H. Because lowering π and φ raises N , such a credit-market liberalization endogenously shifts factor prices in favor of the saver. The saver’s steady-state income equals
RB̂ + HK, which obviously increases as π and φ fall. Therefore, lowering the equity requirement increases steady-state income inequality. This redistribution has direct implications for
welfare: The saver is better off and the borrower is worse off in the new steady state. Of
course, a steady-state welfare comparison abstracts from the principle reason borrowers find
it attractive to expand debt after deregulation: They can increase current consumption and
pay later. The next section lays the foundation for a complete welfare analysis by calculating
the equilibrium transition path following a reduction of π and φ in a calibrated version of
the model.
household spends a greater fraction of income on durable goods?” They differ in two respects: The borrower
discounts the future with a lower discount factor, and the borrower faces a lower “shadow price” of durable
goods. The first difference lowers Ŝ/Ĉ relative to S̃/C̃, while the second difference works oppositely. It is
not hard to show that the first difference dominates the second, so that Ŝ/Ĉ < S̃/C̃. That is, although the
ability to buy durable goods with credit induces the borrower to raise Ŝ/Ĉ, the borrower spends a greater
fraction of income on nondurable consumption because she is impatient to receive the future utility from
durable goods.

12

5

Quantitative Results

We first describe the calibration of the model and the solution procedure, and then present
the results.

5.1

Calibration

The calibration of the model is similar to Campbell and Hercowitz (2006). The production
function elasticity α equals 0.3. The depreciation rate δ is 0.01, which is the appropriately
weighted average of 0.003 for owner-occupied residences and 0.031 for automobiles.9 For the
saver we chose β̃ = 1/1.01, so that the quarterly interest rate is 1.0 percent; for the borrower,
we assign a relative impatience of 0.5 percent per quarter, i.e., β̂ = 1/1.015. This degree of
impatience is similar in magnitude to that used by Krusell and Smith (1998). They use three
levels of time preference, with 0.72 percent between the two extremes.
The main aspect of the calibration is setting the values of π and φ for the high- and lowrequirement regimes. This calibration is based on the following correspondence between the
model and the data. The model’s loan-to-value ratio at the steady-state (1 − δ) (1 − π) /R is
matched to an average actual ratio; given the values of R and δ, this equality can be used to
solve for π. The steady-state amortization rate φ is matched to an average repayment rate.
Given the interpretation of the model’s durable goods stock St as homes and vehicles, the
values of these parameters are computed as weighted averages of estimates for mortgages and
car loans.
The calibration of π and φ involves the basic issues of choosing the sample period for
each of the model’s regimes and the type of data required. The discussion of the institutional
background in Section 2 provides guidance for these choices.
The sample period are determined as follows. For the high-requirement regime we use
observations through 1982, given that the timing of the Garn-St.Germain Act in October
of that year. We presume that immediately following deregulation the equity constraint is
not binding because of the large size of home equity that is cashable at that time. Because
it is much easier to read equity constraint parameters from data generated under a binding
constraint, we do not use observations immediately following 1982 to calibrate the postreform regime. According to Table 1, the effective down payment on mortgages and the
9

The source is “Fixed Assets and Consumer Durable Goods in the United States, 1925-1997.” The service
life of 1-4 units residences is 80 years. Automobiles’ service life of 8 years is inferred from the reported nonlinear depreciation profile. We used the weights 0.75 and 0.25, which are the shares of the owner occupied
residential stock and consumer durable goods stock in the 1954-2004 sample.

13

percentage of mortgages refinanced stabilize around 1995. This and the stabilization of the
debt/asset ratio around the same time—See Figure 3 below—both suggest that by then the
equity constraint binds again. Hence, we use observations from 1995 onwards to calibrate
the low-requirement regime.
As discussed in Section 2, data on individual mortgages have little relevance after deregulation: Loan-to-value ratios may not reflect initial equity shares because of the possibility
of more than one mortgage, and maturities are likely to be extended later by refinancing.
Hence, we proceed as follows. For car loans, we use observations on down payments and
loan maturities in car loan contracts, which we assume reflect actual equity requirements in
the two sample periods. For mortgages, we use data from the Survey of Consumer Finances,
as reported in Section 2. The initial equity share for homes is computed as the average
equity share of households that purchased their homes within 12 months of the interview
date. Because maturities reported at the interviews do not take into account the likelihood
of future refinancing, calibrating φ for the low-requirement regime necessitates an alternative
procedure. We set φ for this regime so that the model’s increase in the debt-to-asset ratio
across regimes equals the actual change from the pre-1983 sample to the post-1995 sample.
Additional details about calibration of π and φ are presented in Appendix A. The resulting
values are 0.16 and 0.0315 for the high-requirement regime, and 0.11 and 0.0161 for the lowrequirement regime.
The remaining parameters are θ and ω. We chose these simultaneously to match an average
share of hours worked of 0.3 and the average share of durable goods expenditure, 0.21, in
total households’ expenditures in the 1954:I-1982:IV sample.10 Given the other parameters,
including the π and φ values for the pre-reform regime, the unique values of θ and ω that
replicate these observations are 0.37 and 1.95. Table 2 summarizes the calibrated parameter
values.
In addition to lowering down payments on new loans and extending repayment of old
loans, the reduction of equity requirements enables immediate additional borrowing based
on accumulated equity. This is the “borrowing shock”, which is the difference between the
old and the new equity share on the stock Ŝ, held by the borrower in the initial steady state.
This difference equals
10

To calculate this ratio, we adjusted the NIPA’s nondurable personal consumption expenditures by subtracting the imputed service flow of housing. We then added residential investment to personal consumption
expenditures on durable goods.

14

Equity Requirement
High
Low

π
0.16
0.11

φ
0.0315
0.0186

α

δ

β̃

β̂

0.3

0.01

1
1.01

1
1.015

θ

ω

0.37 1.95

Table 2: Calibrated Parameter Values

δ Ŝ(1 − δ)
R



1 − π0 1 − π
−
φ0
φ


,

where π, φ and π 0 , φ0 are the pre- and post-reform pairs of values. Given the model’s
calibration, this amounts to 70 percent of initial output. We assume that only half of this
amount can be borrowed.11

5.2

Transition Dynamics

Given the calibrated parameter values, the reduction of π and φ substantially impacts the
economy’s steady state. The change directly raises B̂/Ŝ from 0.26 to 0.48. The greater debt
burden increases N̂ by 4 percent and lowers Ĉ by 3 percent. The greater borrowing capacity
of durable goods more than offsets the income effect from the additional debt, so Ŝ rises 2
percent. The saver’s additional wealth leads to a 12 percent expansion of both C̃ and S̃.
To calculate the equilibrium path between the initial and the new steady state, we use
a modified version of Fair and Taylor’s (1983) procedure. We conjecture that the equity
constraint does not bind for the borrower until some date t∗ ≥ 0 and then binds forever,
and we calculate the path of prices, quantities, and Lagrange multipliers that satisfies all of
the optimality and market clearing conditions. If the resulting multipliers on the constraints
are all nonnegative and the households’ choices violate none of the constraints, then the
resulting path is the desired equilibrium. Otherwise, we search other values of t∗ until such
an equilibrium path is found.
We find that t? = 30 given the parameters’ calibrated values. Figure 1 presents plots of
the equilibrium path for the model’s key quantities and the interest rate. The reform begins
at date 0 with a one-time unexpected reduction in π and φ and increase in V̂0 —the borrowing
Note that this assumption does not alter the new steady state, which is based only on π 0 and φ0 —along
with the constant parameters of the model.
11

15

Ŝt

Ĉt

S̃t /(S̃t + Ŝt )

107.3

108.5

0.37
0.36
100
98.6

100.0
97.6
1

30

100

1

30

S̃t

100

0.30

C̃t

1

30

100

Saver’s Share of Wealth

104.2

0.86
107.8

100

100.0
0.81
83.6

92.5
1

30

100

0.79
1

400 × (Rt − 1)

30

100

1

30

B̂t /(Ŝt + S̃t )

100

N̂t

5.04

103.4

29.6

100.0

4.30

16.8
1

30

100

1

30

100

90.5

1

30

100

Figure 1: The Model’s Equilibrium Path
All variables, except the interest rate and the shares, are expressed in percentage points relative to their
initial steady-state values. Dashed lines give the initial steady-state levels.

16

capacity of the durable goods’ stock given the equity requirements. The sudden excess of
equity over the required amount acts like a shock to the demand for loanable funds. Both the
debt and the interest rate immediately jump. Later, as debt growth slows down, the interest
rate gradually declines towards its steady-state value.
The interest rate jumps to a level between the two rates of time preference.12 The saver
defers consumption given the temporarily high rate of interest, and, before t? , the borrower
increases consumption of both goods and expands debt as would an unconstrained household
facing a temporarily low rate of interest. The behavior of hours worked traces the borrower’s
nondurable consumption. Its substantial fall implies a drop in output.
The borrower’s consumption pattern changes at t? because then the equity constraint
starts to bind again. The decline of nondurable consumption slows down, while Ŝt begins to
slope up. The intuition for this upward trend can be seen using the multiplier of the equity
constraint in (8),
Γt = 1 − β̂

Ĉt
Ĉt+1

Rt ,

which reflects the value of additional funds for the borrower. After t? , the gradual decline
of Rt increases Γt . Because durable goods provide borrowing possibilities, their value for the
borrower correspondingly increases over time. This lies behind the positive slope of Ŝt after
t? .
The evolution of inequality in wealth and durable goods over time follows directly from
the mechanism just described. Over the 25 year period shown in Figure 1, B̂t rises by 80
percent. This implies a redistribution of wealth from the borrower to the saver. This is the
main force raising the saver’s share of total wealth from 81 percent in the initial steady state
to 86 percent after 25 years.13
The saver’s sale of durable goods to the borrower drastically diminishes inequality in
durable goods following the reform: The saver’s share of durable goods drops initially from
0.37 to 0.30. However, this does not last. Over time, the inequality of durable goods holdings
increases monotonically as the debt mounts.
12

It is easy to show that in an endowment economy without borrowing constraints and only nondurable
consumption, the households’ rates of time preference bound the interest rate. Before t∗ , the present economy
differs from such economy in having also a fixed endowment of labor, a leisure choice, and durable consumption. However, the interest rate from this economy stays within the bounds from the simpler endowment
economy.
13
The saver’s wealth is: stock market value + S̃t + Bt ; the borrower’s wealth is Ŝt − Bt .

17

The initial small decline in the saver’s share of wealth appearing in Figure 1 is caused by
a stock market drop as the interest rate jumps up. The stock market value, computed as the
present value of capital income, falls initially by 10.8 percent, and then slowly recuperates
to approach its initial level in 25 years.

5.3

Welfare Analysis

With the equilibrium transition path in hand, we can calculate both households’ welfare
levels and compare them to their values in the initial steady state. Converting these utility
differences into permanent percentage changes in both goods required to achieve the new
utility level allows an interpersonal comparison of these gains. In principle a given household
could lose from the reform because the terms of trade move adversely, but in fact both households benefit from the reform. The Saver’s utility gain equals 2.02 percent of consumption,
while the borrower’s is an order of magnitude lower, 0.26 percent.
This result naturally leads one to ask why the saver’s gains are so much larger than the
borrower’s? For this, it is helpful to decompose the borrower’s utility gain into two different
components. The first is the component from changing π, φ, and V̂0 but leaving the wage
and interest rate at their initial steady-state values. The borrower’s gain in this experiment
equals 1.35 percent of initial steady-state consumption. The equilibrium welfare gain is much
less than this because of two adverse movements in the terms of trade, the persistent increase
in Rt and the long-run decrease in Wt . The short-run increase in Wt does not offset these.
All of the saver’s welfare gains arise from changes in the terms of trade, so the reason that
the borrower’s welfare gain is so much smaller than the saver’s is that the reform shifts the
terms of trade against the borrower.
To better understand which price changes influence these calculations more, we calculated
the transition path of an alternative model in which the saver receives an endowment of H
per period and the borrower operates a technology linear in labor with slope W . The only
endogenous price in this economy is the interest rate. In this case, the reform increases the
borrower’s welfare by 0.45 percent of initial consumption and the saver’s welfare by 1.36
percent. Apparently, the interest rate accounts for most of the welfare effects of changes in
the terms of trade.

18

Wealth
69.7

Owner-Occupied Housing
37.2

Vehicles
20.7

34.6

66.7
1983

19.5
1989 1992 1995 1998 2001

31.5
1983

1989 1992 1995 1998 2001

1983

1989 1992 1995 1998 2001

Figure 2: Ownership Shares of the Wealthiest Ten Percent of Households
All ratios expressed in percentage points.

6

Interpretation of Macroeconomic Evidence

In this section, we examine observations from the U.S. economy since 1983 in light of the
theoretical results. The model has two novel predictions about this period: One is that the
distribution of household capital becomes substantially more equal before converging to the
less-equal steady state. The other is that debt growth is accompanied by high interest rates.
These two predictions are two interconnected aspects of the story: As borrowers increase
debt to finance consumption and household capital, the interest rate increases and their
share of household capital increases, both temporarily. We first use SCF data to address
the evolution of the wealth distribution, and we then compare the joint evolution of interest
rates and household debt in the model and in the data.

6.1

The Distribution of Wealth and Durable Goods

In the U.S. economy, few rich households hold most wealth. The model economy’s saver
stands-in for these, while the borrower represents the remaining households. Accordingly, we
examine the evolution of inequality of wealth and its components by dividing households into
two groups: Those in the 1st through the 9th wealth deciles, and those in the 10th decile. The
first group owes most of the debt, whereas the second owns most of the assets. In the model,
this distinction is extreme. The SCF provides the household balance sheet observations
required to implement this division empirically. With it, we calculate three measures of
inequality: the share of total wealth owned by the wealthiest ten percent of households,
those households’ share of owner-occupied real estate, and their share of vehicles.
Figure 2 plots these three inequality measures.14 It is well known that the distribution
14

As mentioned in Section 2 we do not report results from the 1986 SCF due to the problematic sampling

19

of wealth has become more unequal since the early 1980’s. The observations from the SCF
indicate that increase in wealth concentration occurred mostly in the 1990’s. Hence, if the
reform of the early 1980s affected wealth inequality, this happened with a delay. To some
extent, the model reproduces such a delay, since wealth inequality initially drops after the
reform (due to stock-market decline caused by high interest rates) and only thereafter rises.
Regarding the other two assets, the wealthiest ten percent of households owned 35 percent
of owner-occupied housing and 20.7 percent of vehicles in 1983. These shares changed little in
the 1989 survey, then declined to 32 and 19.5 percent in 1995, and grew thereafter. In the 2001
SCF the owner-occupied housing share was 37 percent, while the vehicle share approached
its value in 1983. The model interprets this ”V” inequality shape as the allocative response
to borrowers’ increased demand for funds following the reform. Inequality in housing and
vehicles declines first as borrowers use the new funds, while later, as the debt accumulates,
the process is reversed. In the model, the drop in the saver’s share of durable goods occurs
immediately after the reform, so it reproduces the sequence of changes to this measure of
inequality in the data but not the timing.

6.2

Household Debt and the Interest Rate

This paper departs from the observation that household debt rose substantially following the
deregulation of the early 1980s. Figure 3 quantifies this expansion, which starts in 1983:III.
Using data from the Flow of Funds Accounts, it plots the ratio of nominal household debt
to the value of household capital (primarily homes and vehicles).15 The ratio grows from
0.32 in 1982 to 0.42 in 1995. The Figure’s dashed line gives the ratio of mortgage debt to
owner-occupied real estate, which displays virtually the same behavior. Both ratios level off
during the second half of the 1990s.
In the model, a large increase in the interest rate directly follows from the borrower’s
additional demand for funds, and it is well-known that interest rates rose dramatically in
1983. Figure 4 quantifies this with a plot of the real three-year treasury rate. For this, we
used realized inflation over the leading twelve months as expected inflation. Using the last 12
months inflation produces a very similar picture. The average real rate for the “pre-Volcker”
procedure in this survey.
15
In 1961, this ratio equalled 0.32 and it grew to 0.40 by 1966. This is the end of a long expansion of
household debt following the Korean War. The imposition of Regulation Q ceilings on Saving and Loans
institutions in 1966 combined with increasing nominal interest rates resulted in financial disintermediation
which shows in Figure 3 as the decline in the ratio of debt to assets until 1982. See Campbell and Hercowitz
(2006) for more discussion of this history.

20

0.45

Household Debt / Tangible Household Assets
Mortgage Debt / Owner Occupied Real Estate

0.40

0.35

0.30
1961:I

1966:III

1983:I

1995:IV

2002:IV

Figure 3: Ratios of Household Debt to Tangible Household Assets
period in this sample, 1961:I-1979:III, was 1.6 percent. During the Volcker monetary policy
experiment, taken here to be from 1979:IV to 1982:IV, the real rate jumped to an average
of 6 percent. After the peak of 10.3 percent in 1981:3, the easing of monetary policy was
followed by a sharp decline in the real interest to the 5 percent level in 1983. In 1983:IV, with
a lag of only one quarter after the beginning of the debt/asset ratio increase in Figure 3, the
real rate starts to soar again. On average over the 1983:1995 period, which corresponding to
the rapid expansion of household debt, the real rate is 4.40, which is much higher than in
the pre-Volcker era and the post-1995 period.
The model’s comovement of the debt/asset ratio and the interest rate in Figure 1 provides
a straightforward interpretation to the behavior of actual variables in Figures 3 and 4. The
expansion of household credit demand triggered by lowering equity requirements induces an
increase in interest rates in order for savers to be willing to supply those funds.
Contemporaneous macroeconomic observers attributed the high real interest rates from
1983 through 1986 to expansionary fiscal policy. The fourth of Friedman’s (1992) lessons
from the Reagan deficits is
Greater deficits did result in, or at least coincide with, higher real interest rates.
(pp. 301)
Similarly, Blanchard (1987) wrote
21

10.30

5.99
4.40

1.62

−2.72
1961:1

1966:8

1983:1

1995:12

2002:12

Figure 4: Three-Year Real Treasury Constant Maturity Rate
The Three-Year Treasury Constant Maturity Rate from Federal Reserve Release H.15 minus realized annual
inflation using the chain-type deflator for Personal Consumption Expenditures other than Food and Energy.

By the end of 1982, budget deficits had become the dominant macroeconomic
force. Large deficits were strongly increasing aggregate demand and putting pressure on interest rates. (pp. 27)
The growth of household debt after 1982 and our theoretical analysis suggest that increased demand for private credit substantially contributed to this period’s high interest
rates. If this was not the case (i.e., the only cause of the high interest rates was the government deficit) this should have led to a crowding out of household debt rather than the
dramatic increase which actually took place.
On the calculated transition path, the interest rate immediately rises about 0.9 percent.
It is of course hard to say how much of the actual interest rate increase in 1983 was caused
by additional borrowing demand (private or public), but it certainly exceeds the calibrated
model’s prediction. However, from the discussion in Section 5, the equilibrium interest rate
movements were confined between the two households’ rates of time preference. With this
in mind, we experimented with the borrower’s rate of time preference. Raising it from the
6 percent annual rate in the calibrated model to 12 percent raises the initial interest rate
jump from 4.9 to 6.5 percent. Increasing the borrower’s rate of time preference further to
18 percent increases the initial interest rate to 7.5 percent. These results indicate that the
22

interest rate change in the model can be quite large if the two households’ rates of time
preference differ enough.

7

An Extension with Irreversible Investment

In Section 5, one of the counterfactual results was the large overnight transfer of durable
goods from the saver to the borrower. Here, we constrain each of the households to disinvest
household capital no faster than it depreciates. That is
X̂t ≥ 0, X̃t ≥ 0.

(23)

We intend the constraints in (23) to reflect the difficulty of converting durable goods demanded by wealthy households (mansions) into durables more useful for the middle class
(2-bedroom houses). We next spell out how this constraint changes the model, and we then
describe the transition of the modified economy.

7.1

Utility Maximization

We solve the model using the following conjectures about the equity and irreversibility constraints. We verify that these hold good for the calculated equilibrium path.
• As in the basic model, the equity constraint binds for the borrower on and after some
date t? ≥ 0.
• The irreversibility constraint binds for the saver until some date t?? > 0. We conjecture
so because high interest rates generated by the additional borrowing demand should
induce the saver to substitute away from durable goods. This effects weakens as the
interest rate falls, so the constraint should eventually become slack.
• The irreversibility constraint never binds for the borrower. Immediately following the
reform, the borrower wishes to increase its durable stock, and we expect the later
decline in the desired stock to occur gradually enough to not violate (23).
Given these conjectures, only the saver’s problem changes. Denoting the Lagrange multiplier on the irreversibility constraint with Ωt Υt (where Υt is, as previously, the multiplier of

23

the saver’s resource constraint). With this, the first-order condition for the Saver’s optimal
choice of S̃t+1 is now
"
!#
θ C̃t+1
Υt+1
1 − Ωt = β̃
+ (1 − δ) (1 − Ωt+1 )
.
Υt
1 − θ S̃t+1
When the irreversibility constraint binds (Ωt > 0,), the shadow price of durable goods for
the saver declines to induce the saver to slow down disinvestment.
Before considering the equilibrium path with this constraint, it is worth emphasizing
that the constraints in (23) do not rule out all trade in durable goods. We think of the
representative saver and borrower as stand-in’s for a large number of similar households. In
a slightly extended version of the model, two savers can trade installed household capital at
the price of 1 − Ωt . What the constraints do eliminate is any large and sudden reallocation
of household capital from savers to borrowers.

7.2

Transition Dynamics with Irreversible Investment

Figure 5 presents plots of the equilibrium path analogous to those in Figure 1 in Section 5.
Overall, the same mechanism also operates here: The borrower issues debt to the saver to
expand consumption and this raises the interest rate. Adding the irreversibility constraint
changes two specific aspects of the story. The first follows directly from the friction introduced: The initial reduction of S̃t and initial increase of Ŝt are gradual now rather than
immediate. The calculated value of t?? is 17, so for four years after the reform, X̃t = 0. When
the irreversibility constraint ceases to bind, both durable goods stocks switch directions. The
limit to the saver’s disinvestment also slows down the borrower’s deaccumulation of equity.
Accordingly, the equity requirement does not limit the borrower’s debt until t? = 33 quarters
after the reform.
The second aspect follows from the typical amplification of price movements when quantities are slow to adjust. The limit on the saver’s ability to generate loanable funds by selling
household capital amplifies and sharpens the interest rate increase: Immediately after the
reform the interest rate jumps directly to it’s peak, 5.6 percent—rather than peaking later
and at a lower rate, 5.0 percent, as in Figure 1. The sluggish quantity behavior shows also
in the debt’s initial surge, which lasts t?? periods now, rather than one in the basic model.
A direct implication of the gradual initial changes in S̃t and Ŝt is the slow decline in the
saver’s share of durable goods during t?? quarters. Hence, inequality in durable goods declines
gradually for about 4 years, and only then it starts to increase due to wealth redistribution.
24

Ŝt

Ĉt

S̃t /(S̃t + Ŝt )

106.3

102.1

0.37
0.36
100
100.0
0.32
97.5

98.3
17

33

100

17

33

S̃t

100

C̃t

17

33

100

Saver’s Share of Wealth

104.1

0.86
107.8

100

100.0
0.81

84.6

0.79

90.4
17

33

100

17

400 × (Rt − 1)

33

100

17

33

B̂t = −B̃t

N̂t

179.6

5.59

100

103.4
100.0

4.30

17

33

100

100.0

91.6
17

33

100

17

33

100

Figure 5: The Equilibrium Path with Irreversible Investment(i)
(i) All consumption variables expressed in percentage points relative to their initial steady-state values.
Dashed lines give the initial steady-state values.

25

The stock market and the saver’s wealth share in Figure 5 behave very similarly as in
Figure 1. The only noticeable difference is that the initial drop in the stock market value is
more pronounced here, 12.5 percent instead of 10.8, due to the sharper interest rate hike.

8

Concluding Remarks

We contrast in this paper the transition of a calibrated model economy after a realistic
reduction of equity requirements on households with the evidence since the early 1980s.
A key feature of the model’s transition is the prolonged increase in household debt accompanied by high interest rates. This positive comovement reflects the effects of the borrowing
shock triggered by allowing previously equity constrained households to cash out part of their
equity. The distributional counterparts of this process are the long-run increase in the saver’s
share of wealth (reflecting the borrower’s rising debt), and the non-monotonic behavior of
the saver’s share of durable goods. This share declines first, and only later it increases to
a higher level than the initial one. More debt allows the relatively impatient households to
increase their share of durable goods during the first stage of the transition. Due to the
mounting debt, however, the borrower’s share of durable goods should eventually decline.
These results are quantitatively similar to the actual evolution of the wealth distribution
in the United States since 1983 as well as the actual comovement of household debt and
interest. Hence, the model provides a simple interpretation of these facts, connecting them
into one phenomenon.
The model’s large overnight decline of hours worked following the reform is obviously
counterfactual. The model’s result is driven by the fact that the newly additional funds
make it possible for borrowers to immediately increase consumption and leisure. Modelling
the access to new borrowing as gradual process extends the decline in hours worked over a
period. The resulting downward trend in hours is also counterfactual for the period starting in
1983. Modelling the initial state as a recession was another possibility we tested. Given that
the U.S. economy was at the through of a deep recession at the reform, the recovery dynamics
could in principle offset the decline in hours generated by this model. Quantitatively, however,
this effect did not reduce dramatically the decline in hours.
The behavior of hours in the model, in which labor supply is standard, suggests the relevance of indivisibilities and frictions in employment. For example, suppose that households
pay quadratic costs of adjusting hours worked. Such convex costs are relatively unimportant
for the small hours adjustments in business cycles, but they can be much more significant for

26

large changes such as that beginning the transition to high household debt. We examined
the impact of adjustment costs on our results in an extreme way by fixing the borrower’s
hours worked. The simulation results in this setup were very similar to those presented here,
so we expect the results to survive other more empirically relevant modifications to the labor
market primitives.
The present model can be extended in different directions to address additional aspects
of the link between financial reform and macroeconomic behavior observed in the U.S. since
the 1980s.
Endogenous capital accumulation is a basic extension of the model. In such an extension,
we expect the initial surge in borrowing to depress productive investment. This, due to high
interest rates as well as low marginal productivity of capital when hours worked decline.
Over time, as hours worked trend up, the marginal productivity of capital should increase,
so the productive capital stock should rise above the initial level.
Endogenizing the capital stock will also have implications for the behavior of factor prices
and thus welfare results. For example, in the present setup, the wage declines when approaching the new steady state—because the capital/labor ratio declines. With a variable capital
stock, the wage rate in the two steady states will be the same, and hence one of the saver’s
benefits and borrower’s costs from the reform will disappear.
The link between credit policy and housing prices is another route to explore. For example,
a fixed factor like land would generate curvature in the transformation of output into housing.
During the early stages of the transition, two opposite forces would affect housing prices: The
borrower’s demand for housing is higher due to his newly available credit, while the saver’s
demand is lower given high interest rates. Hence, the relative price movement is not clear a
priori. In the long-run, however, reducing equity requirements should raise the relative price
of housing because of the effective reduction in the cost of credit.

27

Appendix
A

Calibration of the Equity-Requirement Parameters

The calibration of the pre-reform values of π and φ proceeds as follows. For automobile loans,
we use the Federal Reserve Statistical release G.19, which reports average loan-to-value ratios
and repayment periods for automobile loans from 1971 onwards. Over the 1971-1982 sample,
the average loan-to-value ratio is 0.87 and the average term is 13.4 quarters. For mortgage
loans, the calibration is based on the Survey of Consumer Finances. The SCF includes the
year of home purchase, the equity stake in the home and the original maturity of the first
two mortgages. Our basic measure of the initial equity share for homes is the average equity
share of households that purchased their homes within 12 months of the interview date, and
borrowed at least half of the home’s value. In the 1983 SCF, there are 104 such homeowners.
Their average equity share is 0.2275 with a standard error of 0.0137. For the same sample,
average mortgage maturity and its standard error are 85.5 and 3.8 quarters.
Because the 1983 SCF immediately followed the Garn-St. Germain Act, we think of these
terms as representative of mortgage terms at the time of the reform. To check whether they
are typical for the period prior to the reform as well, we examined trends in average mortgage
terms before 1983, as reported in the Federal Home Loan Bank Board’s Monthly Interest Rate
Survey. This survey covers single-family homes only; hence, it is more restrictive than the
SCF. This survey reports stable loan-to-value ratios from 1963, the first available observation,
until 1982. Thus, the average initial equity share from the 1983 SCF of 0.2275 appears to be
a good estimate for the pre-reform period. In contrast to the stability of the loan-to-value
ratio, the average repayment period increased from 85.2 quarters in 1963 to 102.4 in 1982.
This increase indicates that average mortgage duration in 1983 was higher than the typical
duration for the period of interest. Hence, we adjust the 85.5 quarters measure from the
1983 SCF downwards by subtracting half of that increase. The resulting loan period is 76.9
quarters.
We measure mortgage and automobile debt repayment rates with the inverse of their
period-average terms to maturity, and then calculate φ as the weighted average of these
rates. The weights are the average shares of mortgage debt and consumer credit in total
household debt over the 1954-1982 period, that is 0.7 and 0.3. The resulting value of φ is
0.0315.

28

Similarly, π is a weighted average of the initial equity shares from automobile and mortgage debt. Ideally, the weights should reflect the flow of loans used to purchase new automobiles and homes. As such observations are not available, we construct the weights indirectly.
In a steady-state version of the model with two durable goods, loans extended in each category should equal the principle repayment rate multiplied by the category’s steady-state
debt. Given the repayment rates and debt shares used to calibrate φ for the period before
1983:I, the implied shares of home and automobile loans in total loans extended are 0.29 and
0.71.16 The resulting value of π for the high-equity requirement regime is 0.16 (the weighted
average of 0.2275 for homes and 0.13 for automobiles).
For the post-reform values of π and φ use observations from 1995 onwards, when debt/assets
ratios stabilize.
The value of π is calculated similarly as for the pre-reform period. The average loan-tovalue ratio for automobiles in the 1995:I–2004:II sample is 0.92. The average equity share
of new home owners in the 1995 SCF and the 2001 SCF are 0.1756 and 0.1749—with the
standard errors 0.0090 and 0.0094. There are 334 and 251 new homeowners in these two
surveys. We use the average of the two years’ observations as our measure of the mortgage
down-payment rate. The average initial equity shares for both automobiles and homes decline
by 0.05 from the pre- to the post-reform period. Hence, we set the value of π for the latter
period equal to 0.11.
The post-reform value of φ is much more problematic to estimate. Because the financial
reform substantially widened the options for refinancing and home equity loans, the terms of
the initial mortgages ceased to represent the actual equity requirements. One possibility for
evaluating φ is to assume that the terms of automobiles loans still represent actual equity
constraints, and for homes, refinancing and equity loans make it possible to extend the
loans’ terms to the entire life of the home. The latter assumption implies that the mortgage
repayment rate equals the home’s depreciation rate. Computing φ in this way causes the
debt/assets ratio to increase too much relative to the data. Hence, we set φ based on the
actual change in the debt/asset ratio from the 1954–1982 sample average of 0.34 to the 1995–
2005 sample average of 0.45. Given the other parameter values, for the model to reproduce
this 11 percentage point increase in the debt/asset ratio across steady states, the value of φ
has to decline from 0.0315 indicated above for the pre-reform period to 0.0186.

16

The weight for home loans is computed as (0.70/76.9)/ ((0.70/76.9) + (0.30/13.4)) = 0.29, where 0.7/76.9
is the mortgage/total debt ratio times the repayment rate of mortgages and, similarly, 0.30/13.4 is the car
loans/total debt ratio times the repayment rate of cars loans.

29

References
Becker, R. A. (1980, September). On the long-run steady state in a simple dynamic model
of equilibrium with heterogeneous households. Quarterly Journal of Economics 95 (2),
375–382.
Blanchard, O. J. (1987, October). Reaganomics. Economic Policy 2 (5), 15–48.
Campbell, J. R. and Z. Hercowitz (2006). The role of collateralized household debt in macroeconomic stabilization. Federal Reserve Bank of Chicago Working Paper.
Fair, R. C. and J. B. Taylor (1983, July). Solution and maximum likelihood estimation of
dynamic nonlinear rational expectations models. Econometrica 51 (4), 1169–1186.
Florida, R. L. (Ed.) (1986). Housing and the New Financial Markets. Rutgers, The State
University of New Jersey.
Friedman, B. M. (1992, May). Learning from the Reagan deficits. American Economic
Review 82 (2), 299–304.
Green, R. K. and S. M. Wachter (2005, Fall). The American mortgage in historical and
international context. Journal of Economic Perspectives 19 (4), 93–114.
Kiyotaki, N. (1998). Credit and business cycles. Japanese Economic Review , 18–35.
Krusell, P. and A. A. Smith (1998, October). Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy 106 (5), 867–896.

30

Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
A Proposal for Efficiently Resolving Out-of-the-Money Swap Positions
at Large Insolvent Banks
George G. Kaufman

WP-03-01

Depositor Liquidity and Loss-Sharing in Bank Failure Resolutions
George G. Kaufman

WP-03-02

Subordinated Debt and Prompt Corrective Regulatory Action
Douglas D. Evanoff and Larry D. Wall

WP-03-03

When is Inter-Transaction Time Informative?
Craig Furfine

WP-03-04

Tenure Choice with Location Selection: The Case of Hispanic Neighborhoods
in Chicago
Maude Toussaint-Comeau and Sherrie L.W. Rhine

WP-03-05

Distinguishing Limited Commitment from Moral Hazard in Models of
Growth with Inequality*
Anna L. Paulson and Robert Townsend

WP-03-06

Resolving Large Complex Financial Organizations
Robert R. Bliss

WP-03-07

The Case of the Missing Productivity Growth:
Or, Does information technology explain why productivity accelerated in the United States
but not the United Kingdom?
Susanto Basu, John G. Fernald, Nicholas Oulton and Sylaja Srinivasan

WP-03-08

Inside-Outside Money Competition
Ramon Marimon, Juan Pablo Nicolini and Pedro Teles

WP-03-09

The Importance of Check-Cashing Businesses to the Unbanked: Racial/Ethnic Differences
William H. Greene, Sherrie L.W. Rhine and Maude Toussaint-Comeau

WP-03-10

A Firm’s First Year
Jaap H. Abbring and Jeffrey R. Campbell

WP-03-11

Market Size Matters
Jeffrey R. Campbell and Hugo A. Hopenhayn

WP-03-12

The Cost of Business Cycles under Endogenous Growth
Gadi Barlevy

WP-03-13

The Past, Present, and Probable Future for Community Banks
Robert DeYoung, William C. Hunter and Gregory F. Udell

WP-03-14

1

Working Paper Series (continued)
Measuring Productivity Growth in Asia: Do Market Imperfections Matter?
John Fernald and Brent Neiman

WP-03-15

Revised Estimates of Intergenerational Income Mobility in the United States
Bhashkar Mazumder

WP-03-16

Product Market Evidence on the Employment Effects of the Minimum Wage
Daniel Aaronson and Eric French

WP-03-17

Estimating Models of On-the-Job Search using Record Statistics
Gadi Barlevy

WP-03-18

Banking Market Conditions and Deposit Interest Rates
Richard J. Rosen

WP-03-19

Creating a National State Rainy Day Fund: A Modest Proposal to Improve Future
State Fiscal Performance
Richard Mattoon

WP-03-20

Managerial Incentive and Financial Contagion
Sujit Chakravorti and Subir Lall

WP-03-21

Women and the Phillips Curve: Do Women’s and Men’s Labor Market Outcomes
Differentially Affect Real Wage Growth and Inflation?
Katharine Anderson, Lisa Barrow and Kristin F. Butcher

WP-03-22

Evaluating the Calvo Model of Sticky Prices
Martin Eichenbaum and Jonas D.M. Fisher

WP-03-23

The Growing Importance of Family and Community: An Analysis of Changes in the
Sibling Correlation in Earnings
Bhashkar Mazumder and David I. Levine

WP-03-24

Should We Teach Old Dogs New Tricks? The Impact of Community College Retraining
on Older Displaced Workers
Louis Jacobson, Robert J. LaLonde and Daniel Sullivan

WP-03-25

Trade Deflection and Trade Depression
Chad P. Brown and Meredith A. Crowley

WP-03-26

China and Emerging Asia: Comrades or Competitors?
Alan G. Ahearne, John G. Fernald, Prakash Loungani and John W. Schindler

WP-03-27

International Business Cycles Under Fixed and Flexible Exchange Rate Regimes
Michael A. Kouparitsas

WP-03-28

Firing Costs and Business Cycle Fluctuations
Marcelo Veracierto

WP-03-29

Spatial Organization of Firms
Yukako Ono

WP-03-30

Government Equity and Money: John Law’s System in 1720 France
François R. Velde

WP-03-31

2

Working Paper Series (continued)
Deregulation and the Relationship Between Bank CEO
Compensation and Risk-Taking
Elijah Brewer III, William Curt Hunter and William E. Jackson III

WP-03-32

Compatibility and Pricing with Indirect Network Effects: Evidence from ATMs
Christopher R. Knittel and Victor Stango

WP-03-33

Self-Employment as an Alternative to Unemployment
Ellen R. Rissman

WP-03-34

Where the Headquarters are – Evidence from Large Public Companies 1990-2000
Tyler Diacon and Thomas H. Klier

WP-03-35

Standing Facilities and Interbank Borrowing: Evidence from the Federal Reserve’s
New Discount Window
Craig Furfine

WP-04-01

Netting, Financial Contracts, and Banks: The Economic Implications
William J. Bergman, Robert R. Bliss, Christian A. Johnson and George G. Kaufman

WP-04-02

Real Effects of Bank Competition
Nicola Cetorelli

WP-04-03

Finance as a Barrier To Entry: Bank Competition and Industry Structure in
Local U.S. Markets?
Nicola Cetorelli and Philip E. Strahan

WP-04-04

The Dynamics of Work and Debt
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-05

Fiscal Policy in the Aftermath of 9/11
Jonas Fisher and Martin Eichenbaum

WP-04-06

Merger Momentum and Investor Sentiment: The Stock Market Reaction
To Merger Announcements
Richard J. Rosen

WP-04-07

Earnings Inequality and the Business Cycle
Gadi Barlevy and Daniel Tsiddon

WP-04-08

Platform Competition in Two-Sided Markets: The Case of Payment Networks
Sujit Chakravorti and Roberto Roson

WP-04-09

Nominal Debt as a Burden on Monetary Policy
Javier Díaz-Giménez, Giorgia Giovannetti, Ramon Marimon, and Pedro Teles

WP-04-10

On the Timing of Innovation in Stochastic Schumpeterian Growth Models
Gadi Barlevy

WP-04-11

Policy Externalities: How US Antidumping Affects Japanese Exports to the EU
Chad P. Bown and Meredith A. Crowley

WP-04-12

Sibling Similarities, Differences and Economic Inequality
Bhashkar Mazumder

WP-04-13

3

Working Paper Series (continued)
Determinants of Business Cycle Comovement: A Robust Analysis
Marianne Baxter and Michael A. Kouparitsas

WP-04-14

The Occupational Assimilation of Hispanics in the U.S.: Evidence from Panel Data
Maude Toussaint-Comeau

WP-04-15

Reading, Writing, and Raisinets1: Are School Finances Contributing to Children’s Obesity?
Patricia M. Anderson and Kristin F. Butcher

WP-04-16

Learning by Observing: Information Spillovers in the Execution and Valuation
of Commercial Bank M&As
Gayle DeLong and Robert DeYoung

WP-04-17

Prospects for Immigrant-Native Wealth Assimilation:
Evidence from Financial Market Participation
Una Okonkwo Osili and Anna Paulson

WP-04-18

Individuals and Institutions: Evidence from International Migrants in the U.S.
Una Okonkwo Osili and Anna Paulson

WP-04-19

Are Technology Improvements Contractionary?
Susanto Basu, John Fernald and Miles Kimball

WP-04-20

The Minimum Wage, Restaurant Prices and Labor Market Structure
Daniel Aaronson, Eric French and James MacDonald

WP-04-21

Betcha can’t acquire just one: merger programs and compensation
Richard J. Rosen

WP-04-22

Not Working: Demographic Changes, Policy Changes,
and the Distribution of Weeks (Not) Worked
Lisa Barrow and Kristin F. Butcher

WP-04-23

The Role of Collateralized Household Debt in Macroeconomic Stabilization
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-24

Advertising and Pricing at Multiple-Output Firms: Evidence from U.S. Thrift Institutions
Robert DeYoung and Evren Örs

WP-04-25

Monetary Policy with State Contingent Interest Rates
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-26

Comparing location decisions of domestic and foreign auto supplier plants
Thomas Klier, Paul Ma and Daniel P. McMillen

WP-04-27

China’s export growth and US trade policy
Chad P. Bown and Meredith A. Crowley

WP-04-28

Where do manufacturing firms locate their Headquarters?
J. Vernon Henderson and Yukako Ono

WP-04-29

Monetary Policy with Single Instrument Feedback Rules
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-30

4

Working Paper Series (continued)
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde

WP-05-01

Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse

WP-05-02

Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman

WP-05-03

Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton

WP-05-04

Characterizations in a random record model with a non-identically distributed initial record
Gadi Barlevy and H. N. Nagaraja

WP-05-05

Price discovery in a market under stress: the U.S. Treasury market in fall 1998
Craig H. Furfine and Eli M. Remolona

WP-05-06

Politics and Efficiency of Separating Capital and Ordinary Government Budgets
Marco Bassetto with Thomas J. Sargent

WP-05-07

Rigid Prices: Evidence from U.S. Scanner Data
Jeffrey R. Campbell and Benjamin Eden

WP-05-08

Entrepreneurship, Frictions, and Wealth
Marco Cagetti and Mariacristina De Nardi

WP-05-09

Wealth inequality: data and models
Marco Cagetti and Mariacristina De Nardi

WP-05-10

What Determines Bilateral Trade Flows?
Marianne Baxter and Michael A. Kouparitsas

WP-05-11

Intergenerational Economic Mobility in the U.S., 1940 to 2000
Daniel Aaronson and Bhashkar Mazumder

WP-05-12

Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-05-13

Fixed Term Employment Contracts in an Equilibrium Search Model
Fernando Alvarez and Marcelo Veracierto

WP-05-14

Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics
Lisa Barrow and Cecilia Elena Rouse

WP-05-15

5

Working Paper Series (continued)
Competition in Large Markets
Jeffrey R. Campbell

WP-05-16

Why Do Firms Go Public? Evidence from the Banking Industry
Richard J. Rosen, Scott B. Smart and Chad J. Zutter

WP-05-17

Clustering of Auto Supplier Plants in the U.S.: GMM Spatial Logit for Large Samples
Thomas Klier and Daniel P. McMillen

WP-05-18

Why are Immigrants’ Incarceration Rates So Low?
Evidence on Selective Immigration, Deterrence, and Deportation
Kristin F. Butcher and Anne Morrison Piehl

WP-05-19

Constructing the Chicago Fed Income Based Economic Index – Consumer Price Index:
Inflation Experiences by Demographic Group: 1983-2005
Leslie McGranahan and Anna Paulson

WP-05-20

Universal Access, Cost Recovery, and Payment Services
Sujit Chakravorti, Jeffery W. Gunther, and Robert R. Moore

WP-05-21

Supplier Switching and Outsourcing
Yukako Ono and Victor Stango

WP-05-22

Do Enclaves Matter in Immigrants’ Self-Employment Decision?
Maude Toussaint-Comeau

WP-05-23

The Changing Pattern of Wage Growth for Low Skilled Workers
Eric French, Bhashkar Mazumder and Christopher Taber

WP-05-24

U.S. Corporate and Bank Insolvency Regimes: An Economic Comparison and Evaluation
Robert R. Bliss and George G. Kaufman

WP-06-01

Redistribution, Taxes, and the Median Voter
Marco Bassetto and Jess Benhabib

WP-06-02

Identification of Search Models with Initial Condition Problems
Gadi Barlevy and H. N. Nagaraja

WP-06-03

Tax Riots
Marco Bassetto and Christopher Phelan

WP-06-04

The Tradeoff between Mortgage Prepayments and Tax-Deferred Retirement Savings
Gene Amromin, Jennifer Huang,and Clemens Sialm

WP-06-05

Why are safeguards needed in a trade agreement?
Meredith A. Crowley

WP-06-06

6

Working Paper Series (continued)
Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi

WP-06-07

A New Social Compact: How University Engagement Can Fuel Innovation
Laura Melle, Larry Isaak, and Richard Mattoon

WP-06-08

Mergers and Risk
Craig H. Furfine and Richard J. Rosen

WP-06-09

Two Flaws in Business Cycle Accounting
Lawrence J. Christiano and Joshua M. Davis

WP-06-10

Do Consumers Choose the Right Credit Contracts?
Sumit Agarwal, Souphala Chomsisengphet, Chunlin Liu, and Nicholas S. Souleles

WP-06-11

Chronicles of a Deflation Unforetold
François R. Velde

WP-06-12

Female Offenders Use of Social Welfare Programs Before and After Jail and Prison:
Does Prison Cause Welfare Dependency?
Kristin F. Butcher and Robert J. LaLonde
Eat or Be Eaten: A Theory of Mergers and Firm Size
Gary Gorton, Matthias Kahl, and Richard Rosen
Do Bonds Span Volatility Risk in the U.S. Treasury Market?
A Specification Test for Affine Term Structure Models
Torben G. Andersen and Luca Benzoni

WP-06-13

WP-06-14

WP-06-15

Transforming Payment Choices by Doubling Fees on the Illinois Tollway
Gene Amromin, Carrie Jankowski, and Richard D. Porter

WP-06-16

How Did the 2003 Dividend Tax Cut Affect Stock Prices?
Gene Amromin, Paul Harrison, and Steven Sharpe

WP-06-17

Will Writing and Bequest Motives: Early 20th Century Irish Evidence
Leslie McGranahan

WP-06-18

How Professional Forecasters View Shocks to GDP
Spencer D. Krane

WP-06-19

Evolving Agglomeration in the U.S. auto supplier industry
Thomas Klier and Daniel P. McMillen

WP-06-20

Mortality, Mass-Layoffs, and Career Outcomes: An Analysis using Administrative Data
Daniel Sullivan and Till von Wachter

WP-06-21

7

Working Paper Series (continued)
The Agreement on Subsidies and Countervailing Measures:
Tying One’s Hand through the WTO.
Meredith A. Crowley

WP-06-22

How Did Schooling Laws Improve Long-Term Health and Lower Mortality?
Bhashkar Mazumder

WP-06-23

Manufacturing Plants’ Use of Temporary Workers: An Analysis Using Census Micro Data
Yukako Ono and Daniel Sullivan

WP-06-24

What Can We Learn about Financial Access from U.S. Immigrants?
Una Okonkwo Osili and Anna Paulson

WP-06-25

Bank Imputed Interest Rates: Unbiased Estimates of Offered Rates?
Evren Ors and Tara Rice

WP-06-26

Welfare Implications of the Transition to High Household Debt
Jeffrey R. Campbell and Zvi Hercowitz

WP-06-27

8