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FEDERAL RESERVE BANK OF SAN FRANCISCO
WORKING PAPER SERIES

Do Credit Constraints Amplify Macroeconomic
Fluctuations?
Zheng Liu
Federal Reserve Bank of San Francisco
Pengfei Wang
Hong Kong University of Science and
Technology
Tao Zha
Federal Reserve Bank of Atlanta
and Emory University
December 2009

Working Paper 2009-28
http://www.frbsf.org/publications/economics/papers/2009/wp09-28bk.pdf

The views in this paper are solely the responsibility of the authors and should not be
interpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the
Board of Governors of the Federal Reserve System.

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC
FLUCTUATIONS?
ZHENG LIU, PENGFEI WANG, AND TAO ZHA
Abstract. Previous studies on financial frictions have been unable to establish the
empirical significance of credit constraints in macroeconomic fluctuations. This paper argues that the muted impact of credit constraints stems from the absence of a
mechanism to explain the observed persistent comovements between housing prices
and business investment. We develop such a mechanism by incorporating two key
features into a DSGE model: we identify shocks that shift the demand for collateral
assets and we allow productive agents to be credit-constrained. A combination of
these two features enables our model to successfully generate an empirically important mechanism that amplifies and propagates macroeconomic fluctuations through
credit constraints.

[T]he degree of ampliﬁcation provided by credit constraints seems to
depend crucially on the parameters of the economy. This sets up a
clear challenge for future work: to demonstrate, in a carefully calibrated
model environment, that the ampliﬁcation and propagation possible by
credit constraints are quantitatively signiﬁcant (Kocherlakota, 2000).

Date: December 4, 2009.
Key words and phrases. Credit constraints, collateral asset, housing prices, investment, financial
multiplier, business cycle, structural estimation.
JEL classification: E21, E27, E32.
For help discussions and comments, we are grateful to Susanto Basu, Larry Christiano, Marty
Eichenbaum, John Fernald, Kris Gerardi, Mark Gertler, Mike Golosov, Pat Higgins, Matteo Iacoviello,
Nobu Kiyotaki, Dirk Krueger, Junior Maih, Jim Nason, Lee Ohanian, Alberto Oritz-Bolanos, Richard
Rogerson, Julio Rotemberg, Tom Sargent, Frank Schorfheide, Mark Spiegel, Harald Uhlig, Dan Waggoner, Carl Walsh, John Williams, and seminar participates at Federal Reserve Banks of Atlanta and
San Francisco, the 2009 NBER Summer Workshop on Impulse and Propagation Mechanisms, University of Pennsylvania, University of Wisconsin, Georgetown University, UCLA, UCSD, UC Riverside,
UC Santa Cruz, UC Davis, and USC. We thank David Lang, Jacob Smith, and Diego Vilan for research assistance and Anita Todd for editorial assistance. The views expressed herein are those of
the authors and do not necessarily reflect the views of the Federal Reserve Banks of Atlanta and San
Francisco or the Federal Reserve System.
1

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

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I. Introduction
In an environment with limited contract enforcement, economic agents have limited ability to borrow and loans need to be secured by collateral assets. Such credit
constraints build a connection between asset prices and business investment, which
provides a mechanism to amplify and propagate economic shocks and transform small
shocks into large and persistent business cycle ﬂuctuations (Kiyotaki and Moore, 1997).
Although economic discussions frequently proceed as though this mechanism were
quantitatively important, empirical evidence has actually been scant.
Do credit constraints amplify macroeconomic ﬂuctuations? Existing studies ﬁnd that
the impact of credit constraints is muted (Kocherlakota, 2000; Cordoba and Ripoll,
2004). This ﬁnding is disappointing and indeed puzzling in light of the recent turmoil
in the housing market and the concurrent deep recession. A positive answer to the
question would change our way of macroeconomic modeling and our understanding of
macroeconomic policy, as emphasized by Kocherlakota (2000). We show that, in the
context of an estimated dynamic stochastic general equilibrium (DSGE) model, credit
constraints can substantially amplify and propagate macroeconomic ﬂuctuations.
Our model features two agents: the representative household and the representative
entrepreneur. The household consumes a homogeneous good, housing services (land),
and leisure and supplies labor and loanable funds in competitive markets. The entrepreneur consumes and produces the homogeneous good. Production of the good
requires labor, capital, and land as inputs. To ﬁnance consumption, production, and
investment, the entrepreneur borrows loanable funds subject to a credit constraint. In
particular, the borrowing capacity is constrained by a fraction of the present value of
land and the accumulated capital stock. Thus, land and capital serve as both inputs
for production and collateral for borrowing. We use this model to demonstrate that
the credit transmission mechanism elaborated by Kiyotaki and Moore (1997) is not
simply theoretically elegant but empirically relevant.
We build this key empirical result in two steps. First, we observe persistent comovements between the housing price and business investment in the U.S. data. The ﬁrst
column of Figure 1 displays the impulse responses of the land price and business investment following a shock to the land price series. These impulse responses are estimated
from a recursive bivariate Bayesian vector autoregression (BVAR) model with the Sims
and Zha (1998) prior. The persistent comovements between the land price and business
investment are evident. The comovements are robust to diﬀerent orderings of variables
and to diﬀerent land (housing) price series. We focus on the land price to be consistent

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

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with the assumption in our theoretical model that the total supply of land is ﬁxed.1
For credit constraints to play an important role in macroeconomic ﬂuctuations, the
model needs to be capable of explaining the observed comovements between housing
prices and business investment.
Second, we identify two key determinants of these comovements: an economic shock
that has direct impact on the price of collateral assets and a mechanism that propagates
this shock. In the context of our theoretical model, land is an important collateral asset.
Since the aggregate supply of land is ﬁxed, shifts in housing demand inﬂuence the land
price directly. But an initial impact on the land price would be insuﬃcient to generate
persistent comovements between the housing price and business investment unless there
is a mechanism that propagates the initial impact.
Figure 2 illustrates this point. Suppose the economy starts from the steady state
(point A) and consider the eﬀect of a positive shock to housing demand. In the standard
real business cycle (RBC) model with housing, this shock shifts the household’s land
demand curve upward. The land price rises and land gets redistributed from the
entrepreneur to the household (from point A to point B) and there are no further
actions. As land shifts away from the entrepreneur sector, business investment falls, as
does the future marginal product of capital. Thus, the unconstrained model predicts
negative comovements between the land price and business investment.
Consider an economy in which the entrepreneur is credit-constrained. In this case,
the initial rise in the land price through the shift in the household’s land demand
curve raises the entrepreneur’s net worth and expands the borrowing capacity. The
expansion of net worth and credit shifts up the entrepreneur’s land demand curve,
which reinforces the household’s response and results in a further rise in the land
price and a further expansion of credit, generating a static ﬁnancial multiplier (point
C). More importantly, the rise in the entrepreneur’s net worth and the expansion of
credit produce a dynamic ﬁnancial multiplier: more credit allows for more business
investment in the current period, which means more capital stock in the future; since
capital and land are complementary factors of production, more future capital stock
raises future marginal product of land, which increases the current land price further,
1

The land in our model can be viewed as a metaphor for assets that grow slowly or are in relatively

fixed supply. Another example of such an asset is intangible capital emphasized by Bond and Cummins
(2000) and Hall (2001). Davis and Heathcote (2007) show that land grows at a very slow rate and land
prices are the driving force behind the rise and fall of housing prices observed in the U.S. economy.
We therefore interchange the terms “land” and “housing” in the paper, as does Kocherlakota (2008).

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

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creating a ripple eﬀect (from point C to point E). Thus, a shift in housing demand in
the credit-constrained economy has a much bigger eﬀect on the land price and on its
comovements with investment than in the unconstrained economy.
Previous literature ﬁnds muted impacts of credit constraints because it focuses on
total factor productivity (TFP) shocks (Kocherlakota, 2000; Cordoba and Ripoll, 2004).
A TFP shock does not have a large impact on asset prices because it moves future
dividends and the risk-free interest rate in the same direction. Thus, the ampliﬁcation
mechanism cannot be activated by TFP shocks. TFP shocks contribute to the dynamics
of aggregate output and investment through the usual channels that are familiar to a
student of the RBC literature, but credit constraints do not amplify this type of shock.
In general, credit constraints do not amplify nonﬁnancial shocks (such as the TFP
shock) or ﬁnancial shocks that shift the supply of an asset.2 In contrast, a shock
that shifts the demand for a collateral asset generates a two-way feedback between the
asset price and business investment through the channel of credit constraints. In our
model, we ﬁnd that housing demand shocks alone account for over 90% of the observed
ﬂuctuations in the housing price.
Previous studies fail to obtain positive comovements between housing prices and business investment because they assume a subset of households, instead of entrepreneurs
(productive agents), are credit-constrained (Iacoviello and Neri, 2009). The distinction
is subtle but important. Allowing entrepreneurs to be credit-constrained is an essential feature in our model for generating persistent comovements between the housing
price and business investment. As the housing demand shock raises the land price,
it also raises the entrepreneur’s net worth and borrowing capacity, which provides an
incentive for and enhances the ability of the entrepreneur to increase business investment. Through the dynamic interactions between the land price and investment made
possible by credit constraints, a shock to housing demand is ampliﬁed and propagated
to generate important macroeconomic ﬂuctuations. Our estimation indicates that the
housing demand shock alone accounts for 36 − 46% of the ﬂuctuations in investment
and 22 − 38% of the ﬂuctuations in output.
The rest of the paper is organized as follows. In Section II we discuss the contribution
of our paper in relation to the literature. In Section III we present the DSGE model
2

A similar point is made by Christiano, Motto, and Rostagno (2008). Examples of asset supply

shocks include technology shocks in the housing sector (Iacoviello and Neri, 2009) and shocks affecting the marginal efficiency of transforming investment goods into capital goods (Justiniano and
Tambalotti, 2009).

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

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with credit constraints. In Section IV we analyze the model’s ampliﬁcation mechanism.
In Section V we describe our estimation methodology and report the estimated results.
Based on the estimated parameters and shock processes, we then discuss economic
implications of the model in Section VI. Section VII concludes.

II. Related Literature
The original idea that borrowing constraints play a critical role in amplifying business cycles can be traced back at least to Fisher (1933). Our work is related to a
recent strand of literature that builds on the work by Townsend (1979) and Gale and
Hellwig (1985) and focuses on the costly state veriﬁcation problem caused by asymmetric information between creditors and debtors. Examples includes Carlstrom and
Fuerst (1997), Bernanke, Gertler, and Gilchrist (1999), Cooley, Marimon, and Quadrini
(2004), De Fiore and Uhlig (2005), Gertler, Gilchrist, and Natalucci (2007), Christiano,
Trabandt, and Walentin (2007), Christiano, Motto, and Rostagno (2008), and Gilchrist,
Ortiz, and Zakrajsek (2009). In this class of models, as loans are priced to take into
account debtors’ default risks, there is an equilibrium spread between the loan rate
and the deposit rate. The credit spread interacts with entrepreneurs’ net worth to
generate a ﬁnancial accelerator: an increase in the credit spread reduces entrepreneurs’
net worth and increases the default probability and the external ﬁnance premium; as
the borrowing cost rises, entrepreneurs choose to reduce borrowing and cut investment
and these actions increase the credit spread further.
Similar to the ﬁnancial multiplier in Kiyotaki and Moore (1997), the ﬁnancial accelerator in Bernanke, Gertler, and Gilchrist (1999) can potentially amplify macroeconomic
ﬂuctuations. In recent papers, Christiano, Trabandt, and Walentin (2007) and Christiano, Motto, and Rostagno (2008) examine the empirical importance of the ﬁnancial
accelerator using time series data from the United States and the Euro Area; they
identify certain ﬁnancial shocks as demand shifters that drive the ﬂuctuations in both
the external ﬁnance premium and investment. This approach, however, is not designed
to address credit or liquidity constraints (i.e, limited participation in the capital market) or questions related to dynamic interactions between collateral prices and business
investment.

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To address these questions, our model builds on the recent literature that focuses
on the costly contract enforcement problem (i.e., the problem of controlling over assets) instead of the costly state veriﬁcation problem.3 A partial list of works in this
literature includes Kiyotaki and Moore (1997), Kiyotaki (1998), Kocherlakota (2000),
Krishnamurthy (2003), Cordoba and Ripoll (2004), Iacoviello (2005), Lorenzoni (2008),
Pintus and Wen (2008), and Iacoviello and Neri (2009).4 In this class of models, as
in our model, the debtor’s borrowing capacity is constrained by the value of his or
her collateral assets. If productive agents are constrained by credit, the price of a collateral asset directly interacts with the debt level and therefore with investment and
output. Such an interaction can, in theory, generate a ﬁnancial multiplier that ampliﬁes business cycle shocks. What is new in this paper is that we establish the empirical
signiﬁcance of credit constraints and make the theory of credit constraints relevant to
practical economic problems. To get a strong ampliﬁcation eﬀect, moreover, we match
the observed comovements between the housing price and business investment by identifying an economic shock that directly shifts the demand for housing and an economic
mechanism that sustains and propagates this shock.
The ampliﬁcation mechanism developed in this paper builds on an externality made
possible by credit constraints. When deciding on how much to borrow and how much
to invest, each individual entrepreneur takes as given asset prices, and in particular, the
land price. The entrepreneurs respond to changes in the land price by raising their optimal levels of debt and investment and they do not take into account the consequences of
their collective investment decisions on the land price. Thus, following a positive shift
in housing demand, the land price rises; as entrepreneurs are constrained by credit, the
rise in the land price generates a wealth eﬀect for each individual entrepreneur so that
she chooses to expand the levels of debt and investment. In a competitive equilibrium,
as all entrepreneurs make identical decisions, aggregate investment rises, driving up
the demand for land and the land price, leading to a further expansion of debt and
investment. Following a negative shock, the cycle reverses directions, and the credit
constraint generates a downward spiral in the land price and investment. This type of
externality or strategic complementarity leads to ineﬃcient credit booms and busts, a
3The

two approaches are complementary, however. For certain economic questions, it would be

desirable to combine them in one single model (Aoki, Proudman, and Vlieghe, 2004; Gertler and
Kiyotaki, 2009).
4Open-economy extensions of this class of models include Aoki, Benigno, and Kiyotaki (2007) and
Mendoza (2008) among others.

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

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feature similar to that studied by Lorenzoni (2008) in a three-period model with credit
constraints. We show that this feature with credit booms and busts can be generalized to a fully articulated DSGE model and the ampliﬁcation eﬀect is quantitatively
important.
III. The Model
The economy consists of two agents—the representative household and the representative entrepreneur. There are four types of commodities: labor, goods, land, and
loanable bonds. Goods production requires labor, capital, and land as inputs. The output can be used for consumption (by both types of agents) and for capital investment
(by the entrepreneurs). The representative household’s utility depends on consumption
goods, land services (housing), and leisure; the representative entrepreneur’s utility depends on consumption goods only. We assume that the household is more patient than
the entrepreneur so that the collateral constraint is binding in and near the steady-state
equilibrium.5
III.1. The representative household. Similar to Iacoviello (2005), the household
has the utility function
E

∞
X

β t At {log(Cht − γh Ch,t−1 ) + ϕt log Lht − ψt Nht } ,

(1)

t=0

where Cht denotes consumption, Lht denotes land holdings, and Nht denotes labor
hours. The parameter β ∈ (0, 1) is a subjective discount factor, the parameter γh
measures the degree of habit persistence, and the term E is a mathematical expectation
operator. The term At represent a shock to the household’s patience factor, ϕt a shock
to housing demand, and ψt a shock to labor supply. We assume that the intertemporal
preference shock At follows the stochastic process
At = At−1 (1 + λat ),

ln λat = (1 − ρa ) ln λ̄a + ρa ln λa,t−1 + εat ,

(2)

where λ̄a > 0 is a constant, ρa ∈ (−1, 1) is the persistence parameter, and εat is an
identically and independently distributed (i.i.d.) white noise process with mean zero
5In

Liu, Wang, and Zha (2009a), we provide a micro-foundation for the representative house-

hold’s patience factor. In particular, we consider an economy with heterogeneous households and
entrepreneurs, where the households face uninsurable idiosyncratic income risks and thus have a
precautionary motive for saving. We show that the desire for precautionary saving will make the
households appear more patient than the entrepreneurs at the aggregate level, provided that the
households face more persistent idiosyncratic shocks than do the entrepreneurs.

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

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and variance σa2 . The housing preference shock ϕt follows the stationary process
ln ϕt = (1 − ρϕ ) ln ϕ̄ + ρϕ ln ϕt−1 + εϕt ,

(3)

where ϕ̄ > 0 is a constant, ρϕ ∈ (−1, 1) measures the persistence of the shock, and εϕt
is a white noise process with mean zero and variance σϕ2 . The labor supply shock ψt
follows the stationary process
ln ψt = (1 − ρψ ) ln ψ̄ + ρψ ln ψt−1 + εψt ,

(4)

where ϕ̄ > 0 is a constant, ρψ ∈ (−1, 1) measures the persistence, and εψt ) is a white
noise process with mean zero and variance σψ2 .
Denote by qlt the relative price of housing (in consumption units), Rt the gross real
loan rate, and wt the real wage; denote by St the household’s purchase in period t of
the loanable bond that pays oﬀ one unit of consumption good in all states of nature
in period t + 1. In period 0, the household begins with Lh,−1 > 0 units of housing and
S−1 > 0 units of the loanable bond. The ﬂow of funds constraint for the household is
given by
St
≤ wt Nht + St−1 .
(5)
Rt
The household chooses Cht , Lh,t , Nht , and St to maximize (1) subject to (2)-(5) and
Cht + qlt (Lht − Lh,t−1 ) +

the borrowing constraint St ≥ −S̄ for some large number S̄.
III.2. The representative entrepreneur. The entrepreneur has the utility function
E

∞
X

β t [log(Cet − γe Ce,t−1 )] ,

(6)

t=0

where Cet denotes the entrepreneur’s consumption and γe is the habit persistence parameter.
The entrepreneur produces goods using capital, labor, and land as inputs. The
production function is given by
1−φ α 1−α
] Net ,
Yt = Zt [Lφe,t−1 Kt−1

(7)

where Yt denotes output, Kt−1 , Net , and Le,t−1 denote the inputs capital, labor, and
land, respectively, and the parameters α ∈ (0, 1) and φ ∈ (0, 1) measure the output
elasticities of these production factors. We assume that the total factor productivity
Zt is composed of a permanent component Ztp and a transitory component νt such that
Zt = Ztp νzt , where the permanent component Ztp follows the stochastic process
p
Ztp = Zt−1
λzt ,

ln λzt = (1 − ρz ) ln λ̄z + ρz ln λz,t−1 + εzt ,

(8)

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

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and the transitory component follows the stochastic process
(9)

ln νzt = ρνz ln νz,t−1 + ενz t .

The parameter λ̄z is the steady-state growth rate of Ztp ; the parameters ρz and ρνz
measure the degree of persistence. The innovations εzt and ενz t are i.i.d. white noise
processes that are mutually independent with mean zero and variances given by σz2 and
σν2z , respectively.
The entrepreneur is endowed with K−1 units of initial capital stock and Le,−1 units
of initial land. Capital accumulation follows the law of motion
"

2 #
Ω
It
Kt = (1 − δ)Kt−1 + 1 −
− λ̄I
It ,
2 It−1

(10)

where It denotes investment, λ̄I denotes the steady-state growth rate of investment,
and Ω > 0 is the adjustment cost parameter.
The entrepreneur faces the ﬂow of funds constraint
1−φ α 1−α
Cet + qlt (Let − Le,t−1 ) + Bt−1 = Zt [Lφe,t−1 Kt−1
] Net −

It
Bt
− wt Net + ,
Qt
Rt

(11)

where Bt−1 is the amount of matured debt and Bt /Rt is the value of new debt. Following
Greenwood, Hercowitz, and Krusell (1997), we interpret Qt as the investment-speciﬁc
technological change. Speciﬁcally, we assume that Qt = Qpt νqt , where the permanent
component Qpt follows the stochastic process
Qpt = Qpt−1 λqt ,

ln λqt = (1 − ρq ) ln λ̄q + ρq ln λq,t−1 + εqt ,

(12)

and the transitory component µt follows the stochastic process
ln νqt = ρνq ln νq,t−1 + ενq t .

(13)

The parameter λ̄q is the steady-state growth rate of Qpt ; the parameters ρq and ρνq
measure the degree of persistence. The innovations εqt and ενq t are i.i.d. white noise
processes that are mutually independent with mean zero and variances given by σq2 and
σν2q , respectively.
The entrepreneur faces the credit constraint
Bt ≤ θt Et [ql,t+1 Let + qk,t+1 Kt ],

(14)

where qk,t+1 is the shadow price of capital in consumption units.6 Under this credit
constraint, the amount that the entrepreneur can borrow is limited by a fraction of the
6Since

the price of new capital is 1/Qt , Tobin’s q in this model is given by qkt Qt , which is the ratio

of the value of installed capital to the price of new capital.

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

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value of the collateral assets—land and capital. Following Kiyotaki and Moore (1997),
we interpret this type of credit constraint as reﬂecting the problem of costly contract
enforcement: if the entrepreneur fails to pay the debt, the creditor can seize the land
and the accumulated capital; since it is costly to liquidate the seized land and capital
stock, the creditor can recoup up to a fraction θt of the total value of collateral assets.7
We interpret θt as a “collateral shock” that reﬂects the uncertainty in the tightness of
the credit market. We assume that θt follows the stochastic process
ln θt = (1 − ρθ ) ln θ̄ + ρθ ln θt−1 + εθt ,

(15)

where θ̄ is the steady-state value of θt , ρθ ∈ (0, 1) is the persistence parameter, and εθt
is an i.i.d. white noise process with mean zero and variance σθ2 .
The entrepreneur chooses Cet , Net , It , Le,t , Kt , and Bt to maximize (6) subject to
(7) through (15).
III.3. Market clearing conditions and equilibrium. In a competitive equilibrium,
the markets for goods, labor, land, and loanable bonds all clear. The goods market
clearing condition implies that
It
= Yt ,
(16)
Qt
denotes aggregate consumption. The labor market clearing
Ct +

where Ct = Cht + Cet

condition implies that labor demand equals labor supply:
Net = Nht ≡ Nt .

(17)

The land market clearing condition implies that
Lht + Let = L̄,

(18)

where L̄ is the ﬁxed aggregate land endowment. Finally, the bond market clearing
condition implies that
St = Bt .

(19)

A competitive equilibrium consists of sequences of prices {wt , qlt , Rt }∞
t=0 and allocations {Cht , Cet , It , Nht , Net , Lht , Let , St , Bt , Kt , Yt }∞
t=0 such that (i) taking the prices
as given, the allocations solve the optimizing problems for the household and the entrepreneur and (ii) all markets clear.
7Under

some conditions, this type of credit constraints can be consistent with an optimal contract

(Lorenzoni and Walentin, 2007).

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IV. Understanding the Model
Before we present the quantitative results, it is useful to explain the model’s transmission mechanism. As we have alluded to in the introduction, credit constraints do
not amplify non-ﬁnancial shocks such as TFP shocks or ﬁnancial shocks that shift the
supply of assets. TFP shocks cannot be ampliﬁed by credit constraints because these
shocks do not have large impacts on the prices of collateral assets. Shocks that shift
asset supply cannot be propagated through credit constraints because these shocks generate negative comovements between asset prices and investment. In contrast, shocks
that shift asset demand can generate positive comovements between asset prices and
real aggregate variables and thus can be ampliﬁed and propagated through credit constraints.
In our model, there are two types of ﬁnancial shocks that shift the demand for
collateral assets: the collateral shock and the housing demand shock. We now illustrate
the transmission mechanism of each of these two types of shocks.
Consider the intertemporal Euler equations for land holdings by the household and
the entrepreneur:
Cht
At ϕt Cht
ql,t+1 +
,
Ch,t+1
Lht


Yt+1
µbt
Cet
αφ
+ ql,t+1 +
θt Et ql,t+1 ,
= βEt
Ce,t+1
Let
µet

qlt = βEt

(20)

qlt

(21)

where, for simplicity, we abstract from habit formation by setting γh = γe = 0 and the
term

µbt
µet

in (21) is the shadow value of the entrepreneur’s existing loans (in consumption

units), which is strictly positive if and only if the credit constraint is binding.
Equation (20) describes the optimal land-holding decision by the household. The
cost of acquiring a marginal unit of land is qlt units of consumption goods; the beneﬁt
of having the marginal unit of land, which is summarized on the right-hand-side of
(20), consists of the marginal utility of housing services (in consumption units) and
the discounted resale value of land. At the margin, the marginal cost equals the
marginal beneﬁt. Equation (21) describes a similar optimal land-holding decision by
the entrepreneur. Here, however, since the entrepreneur is credit-constrained, acquiring
a marginal unit of land not only yields beneﬁts from the future marginal product of
land and the resale value, but also from the shadow value of land as a collateral asset.
These Euler equations can be intuitively thought of as the land demand equations
by the two types of agents. Figure 2 plots the land demand curves of the two agents;
that is, the static relation between the current land price qlt and the current quantity of

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

12

land held by the household (Lht ) and the relation between qlt and the quantity of land
held by the entrepreneur (Let ). In plotting these land demand curves, we treat other
variables such as the future land price, consumption growth, the marginal product of
land, and exogenous shocks as shift factors. Land is of ﬁxed supply and allocated
between the household and the entrepreneur. We assume that the initial equilibrium
is the steady state (Point A).
IV.1. Effects of a collateral shock. Consider ﬁrst the eﬀects of a persistent positive
collateral shock that expands the entrepreneur’s borrowing capacity for any given value
of the collateral (i.e., a persistent increase in θt in (21)). The collateral shock raises the
marginal value of land as collateral and, according to (21), shifts the entrepreneur’s
land demand curve upward. In consequence, the land price rises and land gets reallocated from the household to the entrepreneur. The increase in land holdings by the
entrepreneur raises future marginal products of capital and thus current investment.
The increase in investment leads to a rise in future capital stocks and future marginal products of land, which increase the entrepreneur’s current land demand further.
Thus, through the credit constraint, the collateral shock generates a multiplier that
can potentially amplify and propagate the initial shock.
The ampliﬁcation eﬀects of the collateral shock, however, are partly oﬀset by the
entrepreneur’s increased leverage when the borrowing capacity expands. The rise in
debt liability reduces the entrepreneur’s future net worth and thus dampens the initial
rise in land demand and the land price. Furthermore, since the collateral shock does
not shift the household’s land demand curve, it does not trigger competing demand for
land between the two sectors. In consequence, it is diﬃcult for the collateral shock to
generate a strong reaction in the land price and a strong ﬁnancial multiplier.
IV.2. Effects of a housing demand shock. Shocks to housing demand are much
more promising in generating a strong ﬁnancial multiplier. Like collateral shocks,
housing demand shocks are an asset-demand shifter and are thus capable of generating
positive comovements between the land price and business investment. Unlike the
collateral shock, however, a housing demand shock that raises the household’s marginal
utility of housing and land demand also raises the entrepreneur’s net worth and land
demand, triggering competing demand for land between the two sectors that drives up
the land price.
More speciﬁcally, consider the eﬀects of a persistent positive shock to the housing
demand (i.e., a persistent increase in ϕt in (20)). The shock raises the marginal utility

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13

of housing and shifts the household’s land demand curve upward. In consequence, the
land price rises and land gets redistributed from the entrepreneur to the household.
In an RBC model with housing but without credit constraints, the new equilibrium
would be established at point B and there would be no further actions. Thus, a housing
demand shock would lead to a rise in the land price. But the redistribution of land
from production to consumption reduces business investment, leading to a negative
comovement between the land price and investment. This result from the RBC model
would be inconsistent with the data.
Now consider the economy with the entrepreneur constrained by credit. The initial rise in the land price raises the entrepreneur’s net worth, which shifts up the
entrepreneur’s land demand curve. As the entrepreneur competes with the household
for land, the land price increases further and so does the entrepreneur’s net worth.
The rise in the entrepreneur’s net worth shifts the entrepreneur’s land demand further,
generating a static ﬁnancial multiplier (point C). The persistent rise in the land price
produces also a dynamic multiplier: the higher collateral value implies an expanded
credit limit, which allows for more business investment in the current period and help
accumulate more capital stock in the future; since capital and land are complementary factors of production, more capital stock raises future marginal products of land,
which increase the current land price further (from point C to point E). Thus, unlike
the collateral shock, the initial shift in housing demand can lead to a large rise in both
the land price and business investment.
IV.3. What is the housing demand shock? Given the central role the housing
demand shock plays in our model, it is useful to discuss what this type of ﬁnancial
shock might represent. One interpretation is that the housing demand shock simply
represents an exogenous shift in the household’s taste for housing services. Iacoviello
and Neri (2009) present evidence that supports this view.
Another interpretation is that the shock in our stylized aggregate model, like any
shocks in the model including diﬀerent technology shocks, is a reduced form representation of frictions or some “deeper” shocks that are outside of the model. In Liu, Wang,
and Zha (2009b), we present a theory of the housing demand shock. In particular, we
consider an economy with heterogeneous households who experience idiosyncratic and
uninsurable liquidity shocks and who face collateral constraints in borrowing. In the
aggregated version of that model, there is a term in the housing Euler equation that
corresponds to the housing demand shock in our current model. We show that this
term is a decreasing function of the tightness of the collateral constraints (i.e., the

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14

loan-to-value ratios) at the micro-level. Thus, ﬁnancial innovations or de-regulations
that relax the households’ collateral constraints and expand the households’ borrowing
capacity in the disaggregated model would translate into a positive housing demand
shock at the aggregate level.
V. Bayesian Estimation
We use the Bayesian method to ﬁt our model to quarterly U.S. time series data.
In this section, we describe the data, our strategies for estimating the model, and our
estimation results.
V.1. The data. The time series that we use include the relative price of land, the
inverse of the quality-adjusted relative price of investment, real per capita consumption, real per capita investment (in consumption units), real per capita nonfarm and
nonﬁnancial business debt, and per capita hours worked (as a fraction of total time
endowment).8 The sample covers the period from 1975:Q1 to 2009:Q3.
V.2. Priors for parameters. We partition the model parameters into three subsets. The ﬁrst subset of parameters includes the structural parameters on which
we have agnostic priors. This set of parameters, summarized in the vector Ψ1 =
{γh , γe , Ω, , gγ , λ̄q }, consists of the habit persistence parameters γh and γe , investmentadjustment cost parameter Ω, the growth rate of per capita output gγ , and the growth
rate of per capita investment λ̄q . These parameters are listed in the top panel of
Table 1.
We assume that the priors for γh and γe follow the beta distribution with the shape
parameters given by a = 1 and b = 2. Thus, we assign positive density to γh = γe = 0
and let the probability density decline linearly as the value of γh (or γe ) increases from
0 to 1. These hyper-parameter values imply that a lower probability (5%) bound for γh
and γe is 0.0256 and an upper probability (95%) bound is 0.7761. This 90% probability
interval covers most calibrated values for the habit persistence parameter used in the
literature (e.g., Boldrin, Christiano, and Fisher (2001) and Christiano, Eichenbaum,
and Evans (2005)). The prior for the investment adjustment cost parameter Ω follows
the gamma distribution with the shape parameter a = 1 and the rate parameter b = 0.5.
8Appendix

A describes the details of our data. The data on investment-specific technology are

needed to get the sizes of standard deviations of investment technology shocks in line with those in
Krusell, Ohanian, Ríos-Rull, and Violante (2000) and Fisher (2006). By using an explicit measure
of investment-specific technology shocks (i.e., biased technology shocks) in our estimation, we will be
able to assess the importance of biased technology shocks relative to neutral technology shocks.

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15

These hyper-parameters imply that the probability density at Ω = 0 is positive and
that the 90% prior probability interval for Ω ranges from 0.1 to 6, which covers most
values used in the DSGE literature (e.g., Christiano, Eichenbaum, and Evans (2005),
Smets and Wouters (2007), and Liu, Waggoner, and Zha (2009)). The priors for the
steady-state growth rates of output and of capital follow the gamma distribution with
the 90% probability interval covering the range between 0.1 and 1.5, corresponding to
annual growth rates between 0.4% and 6%.
The second subset of parameters includes the structural parameters for which we use
the steady-state relations for constructing informative priors. This set of parameters,
summarized in the vector Ψ2 = {β, λ̄a , ϕ̄, ψ̄, φ, α, θ, δ}, consists of the subjective discount factor β, the patience factor λ̄a , the housing preference parameter ϕ̄, the leisure
preference parameter ψ̄, the elasticity parameters in the production function φ and α,
the average loan-to-asset ratio θ, and the capital depreciation rate δ.
To construct the prior distributions for the parameters in Ψ2 , we ﬁrst simulate the
parameters in Ψ1 from their prior distributions and then, for each simulation, we
impose the steady-state restrictions on both Ψ1 and Ψ2 such that the model matches
the following moment conditions: (1) the average labor income share is 70% (α =
0.3); (2) the average real prime loan rate is 4% per annum (Huggett, Ventura, and
Yaron, 2009); (3) the capital-output ratio is on average 1.15 at the annual frequency;
(4) the investment-capital ratio is on average 0.209 at the annual frequency; (5) the
average land-output ratio is 0.65 at the annual frequency; (6) the average nonfarm and
nonﬁnancial businesses’ loan-asset ratio is 0.75 at the annual frequency (θ = 0.75);
(7) the average housing-output ratio is 1.45 at the annual frequency; and (8) the
average market hours is 25% of time endowment.9 Since the prior distributions for
the parameters in Ψ2 are of unknown form, the 90% probability bounds, reported in
Table 1 (the lower panel), are generated through simulations. As shown in the table,
the steady-state restrictions lead to informative probability intervals for the marginal
9Since

we have a closed-economy model with no government spending, we measure private domestic

output by the sum of personal consumption expenditures and private domestic investment, where
consumption is the expenditures on nondurable goods and non-housing services, and investment is
the expenditures on consumer durable goods and fixed investment in equipment and software. These
time series are provided by the Bureau of Economic Analysis (BEA) through Haver Analytics. Capital
and housing stock are in annual rates. Capital stock includes the annual stocks of equipment, software,
and consumer durable goods. The land-output ratio is the ratio of the nominal value of land input
and the nominal value of output in the private nonfarm and nonfinancial business sector for the period
1987-2007 taken from the Bureau of Labor Statistics (BLS).

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prior distributions of the parameters and thus help identify the structural parameters
in Ψ2 .10 Our method for constructing the prior distributions for Ψ2 is similar to the
approach studied by Del Negro and Schorfheide (2008), which combines the Baynesian
approach and the standard calibration approach for eliciting priors.
The third subset of parameters consists of those describing the shock processes
displayed in Table 2. These parameters are summarized by Ψ3 = {ρi , σi } for i ∈
{a, z, νz , q, νq , ϕ, ψ, θ}, where ρi and σi denote the persistence parameters and the standard deviations of the eight structural shocks. As for the parameters in Ψ1 , we adopt
agnostic priors for these parameters in Ψ3 .11
V.3. Posterior estimates. Table 1 reports the estimates of structural parameters
at the posterior mode, along with the 90% probability intervals for each estimated
parameter based on the posterior distributions (the last 3 columns).
The upper panel reports the estimated values of the parameters in Ψ1 . Both types
of agents have only modest degrees of habit persistence, with the entrepreneur’s habit
parameter somewhat larger than the household’s (0.61 vs. 0.47). The probability interval for the entrepreneur’s habit parameter is much wider than that for the household’s
habit parameter. Both parameters are statistically signiﬁcant.
In our model with credit constraints, explicit costs of investment adjustment turned
out to be unimportant, with the estimated adjustment cost parameter (Ω = 0.19) much
smaller than the values obtained in the literature.12 The probability interval around
this low estimate is tight. We obtain this sharp result because, unlike Smets and
Wouters (2007) and Justiniano and Primiceri (2008) who treat the investment-speciﬁc
shock as a latent time series, we ﬁt our model to the time series of the relative price
10Even

with a subset of deep parameters well identified, the posterior density function is still very

non-Gaussian and has many local peaks. For example, one would get estimates at a much lower
peak when using Dynare mechanically. We randomly simulate 100000 starting points and select the
converged result that gives the highest posterior density. Among these starting points, many converge
to the point that has the highest peak. The computing time is about 4-5 days on a cluster of 24
2.5GHz computers.
11Specifically, the priors for the persistent parameters follow the beta distribution with the 90%
probability interval given by [0.0256, 0.7761]; the priors for the standard deviations follow the inverse
gamma distribution with the 90% probability interval given by [0.0001, 1.0]. We have examined the
sensitivity of our estimates by extending both the lower and the upper bounds of this interval and
found that the results are not sensitive.
12The literature reports the estimates of the investment-adjustment cost parameter between 2.5
and 6 (Christiano, Eichenbaum, and Evans, 2005; Smets and Wouters, 2007).

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17

of investment. Consequently, we obtain smaller standard deviations of the investmentspeciﬁc shock (see Table 2).
Per capita output is estimated to grow at an annual rate of about 1.5%, consistent
with the average growth rate of real per capita GDP in the United States for the
postwar period. The investment-speciﬁc technology (IST) grows at a much faster
annual rate of about 5%, consistent with the calibration by Greenwood, Hercowitz,
and Krusell (1997). Indeed, our estimated growth rate of the IST is higher than that
calibrated by Greenwood, Hercowitz, and Krusell (1997), who use a shorter sample that
ends in 1990. For the sub-sample after the early 1990s, however, the United States
economy experienced even more rapid declines in the quality-adjusted relative price of
equipment, software, and consumer durable goods. The 90% probability intervals for
all the parameters in Ψ1 indicate that these parameters are tightly estimated.
The lower panel of Table 1 reports the estimated values of the parameters in Ψ2 ,
along with the 90% probability intervals.13 For this set of parameters, we impose
the steady-state relations to help identiﬁcation. The 90% probability intervals for the
posterior estimates are much tighter than those for the priors. The estimated patience
factor (0.0068) implies that the ﬁrst-order excess return (i.e., the steady-state return
from investment less the steady-state loan rate) is about 2.75% per annum. Thus, the
entrepreneur assigns a substantial premium to existing loans.
Table 2 displays the estimates of the parameters in the shock processes at the posterior mode and the 90% posterior probability intervals. Both permanent and transitory
technology shocks have smaller standard deviations than non-technology shocks. This
diﬀerence remains when the probability intervals are taken into account.
VI. Economic Implications
We now examine economic implications of the model’s transmission mechanism based
on the estimated parameters. We ﬁrst demonstrate the ampliﬁcation mechanism of
credit constraints through impulse responses of several key macroeconomic variables
following various shocks. In particular, we show that credit constraints amplify ﬁnancial
shocks that shift the demand for collateral assets, but they do not amplify non-ﬁnancial
shocks such as the TFP shock (Section VI.1). We then examine the relative importance
of each shock in driving ﬂuctuations in asset prices and macroeconomic aggregates
through variance decompositions (Section VI.2). Finally, we examine the quantitative
13The

last two rows of the table reports the calibrated values of α and θ̄ to match the average labor

income share 0.7 and the average loan-to-value ratio 0.75.

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importance of the model’s propagation mechanism. In particular, we demonstrate that
the model driven solely by ﬁnancial shocks is able to explain most of the observed
comovements between the land price and investment (Section VI.3).

VI.1. Amplification made possible by credit constraints. In our model, the entrepreneur’s credit limit is endogenous, depending on the collateral value and hence on
the price of the collateral asset. A shock can be ampliﬁed through credit constraints
if it can move this asset price, triggering a ﬁnancial multiplier. We now examine the
importance of this endogenous credit limit and thus the ability of credit constraints
to amplify economic shocks. We do this by plotting impulse responses of several key
macroeconomic variables in our estimated model and comparing these responses to
those obtained in a counterfactual economy in which the credit limit is ﬁxed exogenously at the steady-state level.
Our analysis indicates that the strength of ampliﬁcation depends both on how responsive the price of a collateral asset is to the shock and on the internal transmission
mechanism, not necessarily on the persistence of a shock alone. A shock to neutral
technology growth is a permanent shock to the level of technology and is thus very persistent. But such a permanent shock generates little eﬀect on the ﬁnancial multiplier.
Figure 3 indicates that the impulse responses of macroeconomic variables to a shock
to neutral technology growth in the economy with endogenous credit constraints (solid
lines) are not much diﬀerent from those in the economy with ﬁxed credit limits (dashed
lines). Indeed, the impulse responses in the counterfactual economy with ﬁxed credit
limits lie well within the standard error bands of the impulse responses estimated in
our benchmark model with endogenous credit limits. This result conﬁrms the similar ﬁnding by Kocherlakota (2000) and Cordoba and Ripoll (2004) that a TFP shock
generates weak eﬀect on the ﬁnancial multiplier. Since technology shocks move the
dividends (i.e., the rental values of land) and the discount rate (i.e., the loan rate) in
the same direction, they do not generate large ﬂuctuations in the price of the collateral
asset and therefore do not have signiﬁcant eﬀects on the borrowing capacity.
The borrowing capacity is inﬂuenced mainly by two sources of ﬁnancial shocks: the
collateral shock that directly aﬀects the borrowing capacity and the housing demand
shock that indirectly aﬀects the borrowing capacity by moving the land price. To
assess the quantitative importance of the transmission mechanism provided by the
credit constraint, we plot the impulse responses of several key variables following each
of these two ﬁnancial shocks.

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19

Figure 4 displays the impulse responses of four macroeconomic variables to a positive
collateral shock. The ampliﬁcation eﬀect is evident: compared to the economy with
the ﬁxed credit limit, the estimated peak response of output in our model with the
endogenous credit constraint is more than three times as large. The responses of
the land price, consumption, and investment are all ampliﬁed under the endogenous
credit constraint. The diﬀerences in impulse responses between the economy with
the endogenous credit constraint and the economy with the ﬁxed credit constraint
are considerable, as the responses for the economy with the ﬁxed credit constraint
lie mostly outside of the standard error bands of estimated impulse responses. This
ﬁnding is consistent with the common belief that a ﬁnancial shock to the borrowing
constraint matters to macroeconomic variables (Chaney, Sraer, and Thesmar, 2008;
Jermann and Quadrini, 2009).
Figures 5 displays the impulse responses to a positive housing demand shock. Similar
to the collateral shock, the housing demand shock generates hump-shaped responses
of the macroeconomic variables and the shock is ampliﬁed substantially through the
endogenous credit constraint. Compared to the economy where the credit limit is exogenously ﬁxed (thick dashed lines), the estimated responses of investment and output
to the housing demand shock are at least three times as large (solid lines). Again,
judged by the standard error bands of impulse responses, the diﬀerences in impulse responses between the economy with the endogenous credit constraint and the economy
with the ﬁxed credit constraint are statistically signiﬁcant.

VI.2. Relative importance of different shocks. What lacks in the literature is a
general-equilibrium analysis of the relative importance of each shock in driving the
dynamics of several key macroeconomic variables, especially the relative importance
of each of the two types of ﬁnancial shocks. As we have argued, a large and persistent exogenous shock does not necessarily have a large and persistent impact on asset
prices and real variables. Whether an economic shock has a signiﬁcant impact on the
equilibrium dynamics depends not only on the size and persistence of the shock itself
but also on the model’s internal transmission mechanism.
To take into account the model’s internal transmission mechanism and gauge the
relative importance of each shock, we use the variance decomposition method. Table 3
reports the variance decompositions for the land price and aggregate quantities across
the eight types of structural shocks at forecasting horizons between the impact period
(1Q) and six years after the shock (24Q).

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We begin with the patience shock, which is persistent and has the largest standard
deviation (almost four times the size of the second largest shock). Despite its persistence and large size, the patience shock has a very small impact on the dynamics
of the land price. It has some impacts on investment (about 20%) and on output
(about 10%). Similarly, we have two neutral technology shocks or TFP shocks, one
is permanent (and thus most persistent) and the other one is transitory. Both shocks
account for little of the ﬂuctuations in the land price but both, especially the shock
to the growth rate, account for a substantial fraction of ﬂuctuations in consumption
(about 55%) and in output (10 −36%) at business cycle frequencies. These ﬁndings are
consistent with Kocherlakota (2000) and Cordoba and Ripoll (2004), who report weak
ﬁnancial multiplier eﬀects following TFP a shock in a model with credit constraints.
TFP shocks do drive business cycle ﬂuctuations, but they do not work through the
ﬁnancial channel created by credit constraints because these shocks do not move the
asset prices much.
In contrast, the housing demand shock, which has the second largest standard deviation and is very persistent, stands out as the most important source of the ﬂuctuations
in the land price: it accounts for over 90% of the land price ﬂuctuations. Working
through the endogenous credit constraint, the housing demand shock also drives a
substantial fraction of ﬂuctuations in investment (36 − 46%) and in output (22 − 38%).
It does not follow that an economic shock directly inﬂuencing the borrowing capacity
will have an important impact on both asset prices and investment ﬂuctuations. The
collateral shock is the case in point: the shock is very persistent and has the third
largest standard deviation, but it has little impact on the dynamics of the land price
and that its impact on output is modest (about 10%). The results are evident in
Figures 4 and 5 by comparing the relative scales of the two ﬁgures: the estimated peak
eﬀect of a housing demand shock on the land price exceeds that of a collateral shock
by an order of magnitude (0.042 vs. 0.003).
As we have discussed in Section IV, there are two reasons why credit constraints
produce much stronger ampliﬁcation for the housing demand shock than for the collateral shock. First, the housing demand shock directly drives up the household’s land
demand and the resulting increase in the land price raises the entrepreneur’s net worth
and therefore the entrepreneur’s land demand as well. As the two sectors compete
for the ﬁxed amount of land, the land price rises. The rise in the land price raises
the collateral value for the entrepreneur and generates a powerful dynamic ﬁnancial
multiplier that ampliﬁes and propagates the initial housing demand shock. In contrast,

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21

the collateral shock does not shift the household’s land demand curve, but only the
entrepreneur’s demand curve. Consequently, the collateral shock has a smaller eﬀect
on the land price than does the housing demand shock.
Second, the collateral shock expands the entrepreneur’s borrowing capacity and the
resulting increase in leverage reduces the entrepreneur’s future net worth. The reduction in future net worth hampers the entrepreneur’s ability to invest in productive
factors such as land and capital and thus oﬀsets the initial increase in land demand
and the land price. In contrast, as we have argued in Section IV, the housing demand
shock has a direct impact on the land price and thus on the collateral value. It leads to
a persistent increase in the entrepreneur’s net worth. Figure 6 conﬁrms this intuition.
The ﬁgure shows that a positive housing demand shock leads to a persistent increase
in the entrepreneur’s net worth, whereas a positive collateral shock leads a small initial
increase and subsequent persistent declines in the net worth.
VI.3. The housing price and real aggregate variables. Some empirical studies
document positive comovements between the housing price and consumption (Campbell and Mankiw, 1989; Zeldes, 1989; Case, Quigley, and Shiller, 2005). These comovements are consistent with our ﬁndings (see, for example, the impulse responses to the
technology, collateral, and housing shocks in Figures 3-5). But the question of how
important these comovements are relative to the comovements between the housing
price and business investment remains unanswered. In this section, we address this
important question by comparing our model results with the data.
We begin with the data. The ﬁrst column of Figure 7 reports the impulse responses
of the housing price and consumption in response to a shock to the housing price
series, estimated from the same recursive bivariate BVAR model as in the ﬁrst column
of Figure 1, except that investment is now replaced by consumption. A comparison of
the ﬁrst columns in these two ﬁgures reveals that while consumption and the housing
price move together, the size of these comovements is not nearly as important as the
comovements between investment and the housing price.
We now show that the two types of ﬁnancial shocks—the collateral shock and the
housing demand shock—identiﬁed in our structural model can explain most of these
facts. For this purpose, we need to calculate what would have happened if only the
ﬁnancial shocks had occurred throughout the history. Since our model is structural,
it is internally coherent to perform the counterfactual exercise by turning oﬀ all the
estimated structural shocks bar the two types of ﬁnancial shocks and then using our
estimated model to generate the time paths of the housing price, consumption, and

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investment by conditioning on the estimated initial state variables and the estimated
sequence of ﬁnancial shocks. We then compare the simulation to the data.
The second column of Figure 1 reports the impulse responses of the housing price
and investment based on the simulated data from the DSGE model conditioned on the
historical housing demand shock only. The third column reports the same set of impulse responses based on the simulated data conditioned on both the housing demand
shock and the collateral shock. The way the impulse responses are calculated is exactly
the same as the bivariate BVAR applied to the actual data. Note that the BVAR is a
statistical, atheoretical device used only for the purpose of summarizing the comovements between an aggregate real variable and the housing price. By construction, had
all the other shocks in our DSGE model been left in place, the simulations would have
matched the observed data exactly and the impulse responses from the BVAR applied
to these simulated data would have been exactly the same as those in the data reported
in the ﬁrst column of the ﬁgure. Thus, the diﬀerences between the ﬁrst column and
the second (third) column reﬂect the missing histories contributed by the shocks other
than the housing demand shock (the ﬁnancial shocks).
Figure 1 shows that the magnitude of investment responses implied by the simulated
data conditioned on the housing demand shock only would be much stronger than that
implied by the data. Together with the collateral shock, however, the model is able
to generate the magnitude of investment responses and the persistent comovements
between the housing price and business investment comparable to the data. The results
indicate that the two types of ﬁnancial shocks, working through the endogenous creditconstraint channel, can explain most of the comovements between the housing price
and investment observed in the data.
The second column of Figure 7 reports the impulse responses of the housing price
and consumption implied by the simulated data conditioned on the housing demand
shock only and the third column reports those implied by the simulations conditioned
on both ﬁnancial shocks. Again, the ﬁnancial shocks in our structural model explain
most of the observed comovements between the housing price and consumption.
In summary, the ﬁnancial shocks identiﬁed in our structural model explain most
of the observed comovements between the housing price and real aggregate variables.
Based on the simulated time series conditioned on the two types of ﬁnancial shocks in
our model, we are able to reproduce the impulse responses of business investment that
are much larger than the responses of consumption, as we document in the U.S. data.

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VII. Conclusion
We have established that credit constraints can substantially amplify and propagate
macroeconomic ﬂuctuations in a DSGE framework. We argue that, for credit constraints to play an important role in macroeconomic ﬂuctuations, the model needs to
have a mechanism to explain the observed positive and persistent comovements between housing prices and business investment. We have identiﬁed such a mechanism.
By matching these comovements, we demonstrate that the ﬁnancial channel through
credit constraints, as developed by by Kiyotaki and Moore (1997), is not only theoretically elegant but also empirically important.
To focus on our main message that credit constraints provide an important transmission mechanism, our analysis abstracts from a number of factors to which our model
can be extended in future research. One extension is to apply our analysis to a broader
set of collateral assets such as intangible and working capital. Another ambitious task
is to extend our model to an explicit evaluation of policy intervention in the throes of
ﬁnancial crisis.

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Table 1. Prior distributions and posterior modes of structural parameters
Prior
Parameter

Distribution

a

γh

Beta(a,b)

γe

Beta(a,b)

Ω

Posterior
b

Low

High

Mode

Low

High

1.00 2.00 0.025

0.776

0.4655 0.4176 0.5340

1.00 2.00 0.025

0.776

0.6050 0.3577 0.8074

Gamma(a,b) 1.00 0.50 0.102

5.994

0.1881 0.1614 0.2646

100(gγ − 1) Gamma(a,b) 1.86 3.01 0.100

1.500

0.3682 0.2411 0.4652

100(λ̄q − 1) Gamma(a,b) 1.86 3.01 0.100

1.500

1.2530 1.1035 1.3776

β

Simulated

0.9563 0.9946

0.9870 0.9844 0.9905

λ̄a

Simulated

0.0000 0.0509

0.0068 0.0020 0.0105

ϕ̄

Simulated

0.0000 0.0697

0.0497 0.0424 0.0593

φ

Simulated

0.0655 0.0701

0.0697 0.0694 0.0700

δ

Simulated

0.0291 0.0485

0.0369 0.0354 0.0391

α

Calibrated

0.3000 0.3000 0.3000

θ̄

Calibrated

0.7500 0.7500 0.7500

Note: “Low” and “High” denote the bounds of the 90% probability interval for the
prior distribution.

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Table 2. Prior Distributions and posterior modes of shock parameters
Prior
Parameter Distribution

Posterior
a

b

Low

High

Mode

Low

High

ρa

Beta(a,b)

1.0000 2.0000 0.0256 0.7761

0.9108 0.8558 0.9327

ρz

Beta(a,b)

1.0000 2.0000 0.0256 0.7761

0.4743 0.2899 0.6143

ρνz

Beta(a,b)

1.0000 2.0000 0.0256 0.7761

0.0074 0.0081 0.4428

ρq

Beta(a,b)

1.0000 2.0000 0.0256 0.7761

0.6078 0.4989 0.7003

ρνq

Beta(a,b)

1.0000 2.0000 0.0256 0.7761

0.2920 0.0711 0.6215

ρϕ

Beta(a,b)

1.0000 2.0000 0.0256 0.7761

0.9998 0.9988 0.9999

ρψ

Beta(a,b)

1.0000 2.0000 0.0256 0.7761

0.9799 0.9708 0.9914

ρθ

Beta(a,b)

1.0000 2.0000 0.0256 0.7761

0.9790 0.9736 0.9876

σa

Inverse gamma(a,b) 0.3543 0.0002 0.0001 1.0000

0.1387 0.0955 0.5453

σz

Inverse gamma(a,b) 0.3543 0.0002 0.0001 1.0000

0.0036 0.0028 0.0046

σνz

Inverse gamma(a,b) 0.3543 0.0002 0.0001 1.0000

0.0038 0.0034 0.0049

σq

Inverse gamma(a,b) 0.3543 0.0002 0.0001 1.0000

0.0037 0.0031 0.0045

σνq

Inverse gamma(a,b) 0.3543 0.0002 0.0001 1.0000

0.0025 0.0019 0.0032

σϕ

Inverse gamma(a,b) 0.3543 0.0002 0.0001 1.0000

0.0543 0.0500 0.0655

σψ

Inverse gamma(a,b) 0.3543 0.0002 0.0001 1.0000

0.0073 0.0067 0.0087

σθ

Inverse gamma(a,b) 0.3543 0.0002 0.0001 1.0000

0.0126 0.0116 0.0144

Note: “Low” and “High” denote the bounds of the 90% probability interval for the
prior distribution.

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

26

Table 3. Variance decompositions of aggregate quantities

Horizon Patience Ngrowth Nlevel Bgrowth Blevel Housing Labor Collateral
land price
1Q

3.86

1.14

1.12

0.01

0.01

91.94

1.90

0.01

4Q

3.15

1.99

0.29

0.04

0.01

92.79

1.66

0.08

8Q

2.80

2.47

0.19

0.06

0.00

92.53

1.77

0.18

16Q

2.23

3.22

0.14

0.04

0.00

92.17

1.95

0.25

24Q

1.75

3.80

0.11

0.10

0.00

92.08

1.95

0.20

Consumption
1Q

5.91

42.49

6.85

0.26

0.12

1.08

42.32

0.97

4Q

2.05

55.84

1.33

0.38

0.03

1.24

38.74

0.39

8Q

1.28

53.87

1.17

0.59

0.01

6.67

34.47

1.95

16Q

2.82

52.38

1.09

0.42

0.01

10.77

29.66

2.87

24Q

2.82

56.25

0.89

1.38

0.00

9.16

27.35

2.15

Investment
1Q

18.86

0.35

12.39

3.29

1.35

40.63

10.38

12.76

4Q

18.44

3.21

4.36

0.87

0.25

46.46

10.28

16.11

8Q

17.42

6.12

3.33

3.03

0.19

44.36

10.92

14.64

16Q

15.50

9.23

2.87

8.86

0.17

39.38

11.41

12.58

24Q

14.25

10.81

2.64

12.83

0.15

36.26

11.10

11.96

Output
1Q

12.36

4.16

15.17

5.09

0.32

32.90

20.26

9.76

4Q

11.71

11.89

4.49

1.84

0.06

37.90

19.19

12.92

8Q

10.56

19.14

3.12

1.04

0.04

34.61

20.40

11.10

16Q

8.58

29.42

2.34

1.54

0.03

27.71

22.29

8.08

24Q

7.13

36.83

1.92

2.46

0.03

22.68

22.47

6.48

Note: Columns 2 to 9 reports the contributions of the patience shock (Patience), the
permanent and transitory shocks to the neutral technology (Ngrowth and Nlevel), the
permanent and transitory shocks to the biased technology (Bgrowth and Blevel), the
housing demand shock (Housing), the labor supply shock (Labor), and the collateral
shock (Collateral).

27

−0.02

−0.01

0

0.01

0.02

0.04

0.05

0.06

0.02

0.03

0.04

0.05

0.06

0.03

Investment

0.07

4

8

Data

16
Quarters

20

4

8

Housing

16
Quarters

20

4

8

16
Quarters

Housing & Collateral

20

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

Housing price

Figure 1. Impulse responses from a recursive bivariate BVAR model
with the housing price ordered ﬁrst. Solid lines represent the estimated
responses and dotted-dashed lines represent the 68% probability bands.
The ﬁrst column is based on the actual data. The second column on
the counterfactual data generated with housing shocks only. The third
column on the counterfactual data generated with both housing and
collateral shocks.

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

ql

Le

Lh

E
C
B
A

Le

Lh

Figure 2. Dynamic ﬁnancial multiplier: an illustration. Lh denotes
the household’s holding of land, Le denotes the entrepreneur’s holding
of land, and ql denotes the price of land.

28

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

29

0.025

0.01

0.02

0.008

0.015

0.006

Investment

Ct

Tech shock
0.012

0.01

0.004

0.005

0.002

0

0

−0.005

0.014

12

−3

x 10

11

0.012

10
0.01
0.008
0.006

Housing price

Output

9
8
7
6
0.004
5
0.002
0

4
3

4

8

16
Quarters

Figure 3. Impulse responses to a positive (one-standard-deviation)
shock to neutral technology growth. Thick solid lines represent the estimated responses in the economy with the endogenous credit limit and
thin dotted-dashed lines give the 68% probability bands. Thick dashed
lines represent the responses in the economy with the ﬁxed credit limit.

24

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?
−3

3

x 10

30

Collateral shock
0.035
0.03

2.5

0.025
2
Investment

0.02

C

t

1.5
1

0.015
0.01
0.005

0.5
0
0

−0.005

−0.5

−0.01

−3

10

−3

x 10

3

x 10

2.5

8

2

4

2

Housing price

Output

6

1.5
1
0.5
0

0

−2

−0.5
−1

4

8

16
Quarters

Figure 4. Impulse responses to a positive (one-standard-deviation) collateral shock. Thick solid lines represent the estimated responses in the
economy with the endogenous credit limit and thin dotted-dashed lines
give the 68% probability bands. Thick dashed lines represent the responses in the economy with the ﬁxed credit limit.

24

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?
−3

5

x 10

31

Housing shock
0.06
0.05

4

0.04

2

Investment

C

t

3
0.03
0.02

1
0.01
0

0

−1

−0.01

0.015

0.046

0.044

0.042

Output

Housing price

0.01

0.005

0.04

0.038

0.036

0

0.034

4

8

16
Quarters

Figure 5. Impulse responses to a positive (one-standard-deviation)
shock to housing demand. Thick solid lines represent the estimated
responses in the economy with the endogenous credit limit and thin
dotted-dashed lines give the 68% probability bands. Thick dashed lines
represent the responses in the economy with the ﬁxed credit limit.

24

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?
Housing shock

32

Collateral shock

0.06

0.05

Entrepreneur Net Wealth

0.04

0.03

0.02

0.01

0

−0.01

−0.02
4

8

16
Quarters

24

4

8

16
Quarters

Figure 6. Impulse responses to the entrepreneur’s net worth to a positive, one-standard-deviation, shock to housing demand (left panel) and to
a positive, one-standard-deviation, collateral shock (right panel). Thick
solid lines represent the estimated responses from the model with the
endogenous credit limit and thin dotted-dashed lines give the 68% probability bands.

24

33

−0.02

−0.01

0

0.01

0.02

0.04

0.05

0.06

0.02

0.03

0.04

0.05

0.06

0.03

Consumption

0.07

4

8

Data

16
Quarters

20

4

8

Housing

16
Quarters

20

4

8

16
Quarters

Housing & Collateral

20

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

Housing price

Figure 7. Impulse responses from a recursive bivariate BVAR model
with the housing price ordered ﬁrst. Solid lines represent the estimated
responses and dotted-dashed lines represent the 68% probability bands.
The ﬁrst column is based on the actual data. The second column on
the counterfactual data simulated with housing shocks only. The third
column on the counterfactual data generated with both housing and
collateral shocks.

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

34

Appendix A. Data Description
All data are either taken directly from the Haver Analytics Database or constructed
by Patrick Higgins at the Federal Reserve Bank of Atlanta. The construction methods
are described below.
The model estimation is based on six U.S. aggregate variables: the relative price
of land (qltData ), the inverse of the relative price of investment (QData
), real per capita
t
consumption (CtData ), real per capita investment in consumption units (ItData ), real per
). All these series
capita nonﬁnancial business debt (BtData ), and per capita hours (LData
t
are constructed to be consistent with the corresponding series in Greenwood, Hercowitz,
and Krusell (1997), Cummins and Violante (2002), and Davis and Heathcote (2007).
These series are deﬁned as follows:
LiqLAND_PI_OFHEO
;
PriceNonDurPlusServExHous
PriceNonDurPlusServExHous
Data
Qt
= GordonPriceCDplusES ;
;
CtData = (NomConsNHSplusND)/PriceNonDurPlusServExHous
LNNReviseQtr
(CD@USECON + FNE@USECON)/PriceNonDurPlusServExHous
Data
;
It
=
LNNReviseQtr
BtData = (PL10TCR5@FFUNDS + PL11CRE5@FFUNDS)/PriceNonDurPlusServExHous
;
LNNReviseQtr
LXNFH@USECON
Data
Lt
= LNNReviseQtr .

• qltData =
•
•
•
•
•

The original data, the constructed data, and their sources are described below.
LNNReviseQtr: civilian noninstitutional population with ages 16 years and over
(NSA, Thous) by eliminating breaks in population from 10-year censuses and
post 2000 American Community Surveys using “error of closure” method. This
fairly simple method is used by the Census Bureau to get a smooth monthly population series to reduce the unusual inﬂuence of drastic demographic changes.
The detailed explanation can be found in
http://www.census.gov/popest/archives/methodology/intercensal_nat_meth.html.
Source: BLS.
PriceNonDurPlusServExHous: the consumption deﬂator. The Tornqvist procedure is used to construct this deﬂator as a weighted aggregate index from
nondurables consumption and services consumption excluding housing services.
Source: BEA.
LiqLAND_PI_OFHEO: the liquidity-adjusted price index for residential land
from Davis and Heathcote (2007) ( http://www.marginalq.com/morris/landdata.html).
The adjustment methods of Quart and Quigley (1989, 1991) are used to be consistent with the volatility measure provided by Lin and Liu (2008).

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

35

GordonPriceCDplusES: the quality-adjusted price index for consumer durable
goods, equipment investment, and software investment. This index is a weighted
one from a number of individual price series within this category. For each individual price series from 1947 to 1983, we use Gordon (1990)’s quality-adjusted
price index. Following Cummins and Violante (2002), we estimate an econometric model of Gordon’s price series as a function of a time trend and a
few macroeconomic indicators in the National Income and Product Account
(NIPA), including the current and lagged values of the corresponding NIPA
price series; the estimated coeﬃcients are then used to extrapolate the qualityadjusted price index for each individual price series for the sample from 1984
to 2008. These constructed price series are annual. We use Denton (1971)’s
method to interpolate these annual series on a quarterly frequency. We then
use the Tornquist procedure to construct the quality-adjusted price index from
the interpolated individual quarterly price series. Source: BEA.
NomConsNHSplusND: nominal personal consumption expenditures: non-housing
services and nondurable goods. Source: BEA.
CD@USECON: nominal personal consumption expenditures: durable goods.
Source: BEA.
FNE@USECON: nominal private nonresidential investment: equipment & software. Source: BEA.
PL10TCR5@FFUNDS: nonfarm nonﬁnancial corporation business liabilities:
credit market debt. Source: BEA.
PL11CRE5@FFUNDS: nonfarm nonﬁnancial noncorporate business liabilities:
credit market instruments. Source: BEA.
LXNFH@USECON: nonfarm business sector: hours of all persons (1992=100).
Source: BLS.

DO CREDIT CONSTRAINTS AMPLIFY MACROECONOMIC FLUCTUATIONS?

36

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