House Prices, Borrowing Constraints, and Monetary Policy ... · John Moore (1997) and Charles Carlstrom and Timothy Fuerst (1997), and the sticky-price model of Bernanke et al. (1999)

House Prices, Borrowing Constraints, and Monetary Policy inthe Business Cycle

By MATTEO IACOVIELLO*

I develop and estimate a monetary business cycle model with nominal loans andcollateral constraints tied to housing values. Demand shocks move housing andnominal prices in the same direction, and are amplified and propagated over time.The financial accelerator is not uniform: nominal debt dampens supply shocks,stabilizing the economy under interest rate control. Structural estimation supportstwo key model features: collateral effects dramatically improve the response ofaggregate demand to housing price shocks; and nominal debt improves the sluggishresponse of output to inflation surprises. Finally, policy evaluation considers therole of house prices and debt indexation in affecting monetary policy trade-offs.(JEL E31, E32, E44, E52, R21)

“The population is not distributed betweendebtors and creditors randomly. Debtorshave borrowed for good reasons, most ofwhich indicate a high marginal propensityto spend from wealth or from current in-come or from any other liquid resourcesthey can command. Typically their indebt-edness is rationed by lenders [...]. Businessborrowers typically have a strong propen-sity to hold physical capital [...]. Their de-sired portfolios contain more capital thantheir net worth [...]. Household debtors arefrequently young families acquiring homesand furnishings before they earn incomes topay for them outright; given the difficulty ofborrowing against future wages, they areliquidity-constrained and have a high mar-ginal propensity to consume.”—James Tobin, Asset Accumulation and

Economic Activity

A long tradition in economics, starting withIrving Fisher’s (1933) debt-deflation explana-tion of the Great Depression, considers financialfactors as key elements of business cycles. Inthis view, deteriorating credit market condi-tions, like growing debt burdens and fallingasset prices, are not just passive reflections of adeclining economy, but are themselves a majorfactor depressing economic activity.

Although this “credit view” has a long his-tory, most theoretical work on this subject hadbeen partial equilibrium in nature until the late1980s, when Ben Bernanke and Mark Gertler(1989) formalized these ideas in a general equi-librium framework. Following their work, var-ious authors have presented dynamic models inwhich financing frictions on the firm side mayamplify or propagate output fluctuations in re-sponse to aggregate disturbances: examples in-clude the real models of Nobuhiro Kiyotaki andJohn Moore (1997) and Charles Carlstrom andTimothy Fuerst (1997), and the sticky-pricemodel of Bernanke et al. (1999). Empirically,various studies have shown that firms’ invest-ment decisions are sensitive to various measuresof the firms’ net worth (see Glenn Hubbard,1998, for a review). At the same time, evidenceof financing constraints at the household levelhas been widely documented by Stephen Zeldes(1989), Tullio Jappelli and Marco Pagano(1989), John Campbell and Gregory Mankiw(1989), and Christopher Carroll and WendyDunn (1997).

* Department of Economics, Boston College, ChestnutHill, MA 02467 (e-mail: [email protected]). I am deeplyindebted to my Ph.D. advisor at the London School ofEconomics, Nobuhiro Kiyotaki, for his continuous help andinvaluable advice. I thank Fabio Canova, Raffaella Giaco-mini, Christopher House, Peter Ireland, Raoul Minetti,Claudia Oglialoro, Francois Ortalo-Magne, Marina Pavan,Christopher Pissarides, Fabio Schiantarelli, two anonymousreferees, and seminar participants at the Bank of England,Boston College, the European Central Bank, the Ente LuigiEinaudi, the Federal Reserve Bank of New York, the Fed-eral Reserve Bank of St. Louis, the London School ofEconomics, the NBER Monetary Economics Meeting, andNortheastern University for their helpful comments on var-ious versions of this work. Viktors Stebunovs providedsuperb research assistance.

739

While these studies have highlighted the im-portance of financial factors for macroeconomicfluctuations, to date there has been no system-atic evaluation of the extent to which a generalequilibrium model with financial frictions canexplain the aggregate time-series evidence onthe one hand, and be used for monetary policyanalysis on the other. This is the perspectiveadopted here. From the modeling point of view,my starting point is a variant of the Bernanke etal. (1999) new-Keynesian setup in which en-dogenous variations in the balance sheet of thefirms generate a “financial accelerator” by en-hancing the amplitude of business cycles. Tothis framework, I add two main features: collat-eral constraints tied to real estate values forfirms, as in Kiyotaki and Moore (1997); and, fora subset of the households, nominal debt. Thereason for housing1 collateral is practical andsubstantial: practical because, empirically, alarge proportion of borrowing is secured by realestate; substantial because, although housingmarkets seem to play a role in business fluctu-ations,2 the channels by which they affect theeconomy are far from being understood. Thereason for having nominal debt comes from thewidespread observation that, in low-inflationcountries, almost all debt contracts are in nom-inal terms, even if they appear hard to justify onwelfare-theoretic grounds: understanding theirimplications for macroeconomic outcomes is acrucial task.

In addition, I ask whether the model is able toexplain both key business cycle facts and theinteraction between asset prices and economicactivity. To this end, I estimate the key struc-tural parameters by minimizing the distance be-tween the impulse responses implied by themodel and those generated by an unrestrictedvector autoregression. The estimates are botheconomically plausible and statistically signifi-cant. They also provide support for the twomain features of the model (collateral con-straints and nominal debt). In the concludingpart of the paper, therefore, I use the estimatedmodel for quantitative policy analysis.

The model transmission mechanism works asfollows. Consider, for sake of argument, a pos-

itive demand shock. When demand rises, con-sumer and asset prices increase: the rise in assetprices increases the borrowing capacity of thedebtors, allowing them to spend and investmore. The rise in consumer prices reduces thereal value of their outstanding debt obligations,positively affecting their net worth. Given thatborrowers have a higher propensity to spendthan lenders, the net effect on demand is posi-tive, and acts as a powerful amplification mech-anism. However, while it amplifies the demandshocks, consumer price inflation dampens theshocks that induce a negative correlation betweenoutput and inflation: for instance, adverse supplyshocks are beneficial to borrowers’ net worth ifobligations are held in nominal terms. Hence, un-like the previous papers, the financial acceleratorreally depends on where the shocks come from:the model features an accelerator of demandshocks, and a “decelerator” of supply shocks.

The transmission mechanism described aboveis at the root of the model’s success in explainingtwo salient features of the data. First, collateraleffects on the firm and the household allow match-ing the positive response of spending to a housingprice shock.3 Second, nominal debt allows themodel to replicate the hump-shaped dynamics ofspending to an inflation shock.4 Such improve-ments in the model’s ability to reflect short-rundynamic properties are especially important,given that several studies (e.g., Jordi Galı, 2004;Peter Ireland, 2004b) have stressed the role ofnontechnology and nonmonetary disturbancesin understanding business fluctuations.

Finally, I address and answer two importantpolicy questions. First, I find that allowing themonetary authority to respond to asset pricesyields negligible gains in terms of output andinflation stabilization. Second, I find that nom-inal (vis-a-vis indexed) debt yields an improvedoutput-inflation variance trade-off for the cen-tral bank: this happens because the sources oftrade-offs in the model do not get amplified,since such shocks, ceteris paribus, transfer re-sources from lenders to borrowers during adownturn.

1 With a slight abuse of notation, I use the terms “realestate,” “assets,” and “houses” interchangeably in the paper.

2 See, for instance, International Monetary Fund (2000);Matthew Higgins and Carol Osler (1997); Karl Case (2000).

3 In the VAR below I document a significant two-wayinteraction between housing prices and GDP. Aggregate de-mand effects from changes in housing wealth have also beendocumented elsewhere; see, for instance, Case et al. (2001).

4 See, for instance, Jeffrey Fuhrer (2000), as well as theVAR evidence below.

740 THE AMERICAN ECONOMIC REVIEW JUNE 2005

The paper is organized as follows. Section Ipresents some VAR evidence on housing pricesand the business cycle. Section II presents thebasic model. Section III extends the basic modelby including a constrained household sector andby allowing for variable capital. Section IV esti-mates the structural parameters of the model. Sec-tion V analyzes its dynamics, while Section VIlooks at housing prices and debt indexation for theformulation of systematic monetary policy. Con-cluding remarks are contained in Section VII.

I. VAR Evidence on Housing Prices and theBusiness Cycle

Figure 1 presents impulse responses (with90-percent bootstrapped confidence bands)

from a VAR with detrended real GDP (Y),change in the log of GDP deflator (�), de-trended real house prices (q), and Fed Fundsrate (R) from 1974Q1 to 2003Q2.5 I use thisVAR to document the key relationships inthe data and, later in the paper, to choose the

5 The Fed Funds rate is the average value in the firstmonth of each quarter. The house price series (deflated withthe GDP deflator) is the Conventional Mortgage HomePrice Index from Freddie Mac. The VAR included a timetrend, a constant, a shift dummy from 1979Q4, and one lagof the log of the CRB commodity spot price index. Two lagsof each variable were chosen according to the Hannah-Quinn criterion. The logs of real GDP and real housingprices were detrended with a band-pass filter that removedfrequencies above 32 quarters.

FIGURE 1. VAR EVIDENCE, UNITED STATES

Notes: VAR estimated from 1974Q1 to 2003Q2. The dashed lines indicate 90-percent confidence bands. The Choleskiordering of the impulse responses is R, �, q, Y. Coordinate: percent deviation from the baseline.

741VOL. 95 NO. 3 IACOVIELLO: HOUSE PRICES, BORROWING CONSTRAINTS, AND MONETARY POLICY

parameters of the extended model in a way tomatch the VAR impulse responses.

Here and in the rest of the paper, the variablesare expressed in percentages and in quarterlyrates. The shocks are orthogonalized in the or-der R, �, q, and Y. The ordering did not affectthe results substantially: as I will show below,such an ordering also renders the VAR and themodel more directly comparable. The resultssuggest that a model of the interaction betweenhouse prices and the business cycle has to de-liver:

(a) A negative response of nominal prices, realhousing prices, and GDP to tight money(Figure 1, first row);

(b) A significant negative response of realhousing prices and a negative but smallresponse of output to a positive inflationdisturbance (second row); and

(c) A positive comovement of asset prices andoutput in response to asset price shocks(third row) and to output shocks (fourthrow). Taken together, the two rows high-light a two-way interaction between hous-ing prices and output.

In the rest of the paper, I develop and esti-mate a model that is consistent with these factsand that can be used for policy analysis. I startwith a basic model, which conveys the intuition.

II. The Basic Model

Consider a discrete time, infinite horizoneconomy, populated by entrepreneurs and pa-tient households, infinitely lived and of measureone. The term “patient” captures the assumptionthat households have lower discount rates thanfirms and distinguishes this group from the im-patient households of the extended model (inSection III). Entrepreneurs produce a homoge-neous good, hiring household labor and com-bining it with collateralizable real estate.Households consume, work, and demand realestate and money. In addition, there are retailersand a central bank. Retailers are the source ofnominal rigidity. The central bank adjustsmoney supply and transfers to support an inter-est rate rule.

In order to have effects on economic activityfrom shifts in asset holdings, I allow housinginvestment by both sectors. I assume that real

estate is fixed in the aggregate, however, whichguarantees a variable price of housing. Thisassumption is not crucial to the propagationmechanism: I will show below that collateraleffects can generate sizeable amplification, evenwhen the share of real estate in production issmall.

As their activities are somewhat conven-tional, I start with the patient households’problem.

A. Patient Households

The household sector (denoted with a prime)is standard, with the exception of housing (ser-vices) in the utility function.6

Households maximize a lifetime utility func-tion given by

E0 �t � 0

�

�t�ln c�t � j ln h�t � �L�t��/� � � ln�M�t /Pt��

where E0 is the expectation operator, � � (0, 1)is the discount factor, c�t is consumption at t, h�tdenotes the holdings of housing, L�t are hours ofwork (households work for the entrepreneurs),and M�t /Pt are money balances divided by theprice level. Denote with qt � Qt/Pt the realhousing price, with w�t � W�t /Pt the real wage.Assume that households lend in real terms �b�t(or borrow b�t � B�t /Pt) and receive back�Rt�1B�t�1/Pt, where Rt�1 is the nominal in-terest rate on loans between t � 1 and t, so thatobligations are set in money terms. Denotingwith � the first difference operator, the flow offunds is

(1) c�t � qt�h�t � Rt � 1 b�t � 1 /�t

� b�t � w�tL�t � Ft � T�t � �M�t /Pt

where �t � Pt/Pt�1 denotes the gross inflationrate, Ft are lump-sum profits received from the

6 Javier Diaz-Gimenez et al. (1992) use a similar devicein an OLG model of the banking and household sector. I donot include imputed rents in my model definition of output;this does not affect the results of the paper in any significantway. I also assume that housing and consumption are sep-arable: Bernanke (1984) studies the joint behavior of theconsumption of durable and nondurable goods and finds thatseparability across goods is a good approximation.


retailers (described below), and the last twoterms are net transfers from the central bank thatare financed by printing money. Solving thisproblem yields first-order conditions for con-sumption (2), labor supply (3), and housingdemand (4):

(2)1

c�t� �Et� Rt

�t 1 c�t 1�

(3) w�t � �L�t �� 1c �t

(4)qt

c�t�

j

h�t� �Et�qt 1

c�t 1� .

The first-order condition with respect toM�t /Pt yields a standard money demand equa-tion. Since I focus in what follows on interestrates rules, money supply will always meetmoney demand at the desired equilibrium nom-inal interest rate. As utility is separable inmoney balances, the quantity of money has noimplications for the rest of the model, and canbe ignored.

B. Entrepreneurs

Entrepreneurs use a Cobb-Douglas constantreturns-to-scale technology that uses real estateand labor as inputs. They produce an interme-diate good Yt according to

(5) Yt � A�ht � 1 ��Lt �1 � �

where A is the technology parameter, h is realestate input, and L is the labor input. Outputcannot be transformed immediately into con-sumption ct: following Bernanke et al. (1999), Iassume that retailers purchase the intermediategood from entrepreneurs at the wholesale pricePt

w and transform it into a composite final good,whose price index is Pt. With this notation, Xt �Pt /Pt

w denotes the markup of final over interme-diate goods.

As in Kiyotaki and Moore (1997), I assume alimit on the obligations of the entrepreneurs.Suppose that, if borrowers repudiate their debtobligations, the lenders can repossess the bor-rowers’ assets by paying a proportional trans-action cost (1 � m)Et(qt1ht). In this case themaximum amount Bt that a creditor can borrowis bound by mEt(Qt1ht /Rt). In real terms:

bt mEt �qt 1 ht�t 1 /Rt �.

To make matters interesting, one wants asteady state in which the entrepreneurial returnto savings is greater than the interest rate, whichimplies a binding borrowing constraint. At thesame time, one has to ensure that entrepreneurswill not postpone consumption and quickly ac-cumulate wealth so that they are completelyself-financed and the borrowing constraint be-comes nonbinding. To deal with this problem, Iassume that entrepreneurs discount the futuremore heavily than households. They maximize

E0 �t � 0

�

tln ct

where �,7 subject to the technology con-straint, the borrowing constraint, and the fol-lowing flow of funds:

(6) Yt /Xt � bt � ct � qt�ht

Rt � 1bt � 1 /�t � w�tLt

where Rt�1bt�1/�t in (6) reflects the assump-tion that debt contracts are set in nominal terms,so that price changes between t � 1 and t canaffect the realized real interest rate. I use thisassumption on empirical grounds: in low-inflationcountries, almost all debt contracts are set innominal terms.8

7 Entrepreneurs are not risk neutral. Models of agencycosts and business cycles typically assume risk-neutral en-trepreneurs. Carlstrom and Fuerst (2001) discuss the issue.In modeling firms’ behavior in a model of monetary shocks,agency costs, and business cycle, they consider two alter-natives. In one, entrepreneurs are infinitely lived, risk neu-tral, and more impatient than households: net worth sharplyresponds to shocks, as the elasticity of entrepreneurial sav-ings to changes in the real rate of interest is infinite. In theother, a constant fraction of entrepreneurs dies each period, sothat net worth responds passively and slowly to changes in thereal rate: in the aggregate, this is equivalent to a formulation inwhich entrepreneurs are extremely risk averse. Log utility canbe considered as shorthand between these two extremes.

8 With risk-averse agents, nobody seems to get any ben-efit in terms of expected utility from lack of indexation:presumably, if contracts were indexed, there would be wel-fare gains. However, surprisingly few loan contracts areindexed in the United States, where even 30-year govern-ment and corporate bonds are not indexed. In Sections II Eand VI A, I discuss how the results of the paper changewhen indexed debt is assumed.


Define �t as the time t shadow value of theborrowing constraint. The first-order conditionsfor an optimum are the consumption Eulerequation, real estate demand, and labor demand:

(7)1

ct� Et� Rt

�t 1 ct 1� � �t Rt

(8)1

ctqt � Et�

ct 1��

Yt 1

Xt 1 ht� qt 1�

�tm�t 1qt 1�(9) w�t � �1 � ��Yt /�Xt Lt �.

Both the Euler and the housing demandequations differ from the usual formulations be-cause of the presence of �t, the Lagrange multi-plier on the borrowing constraint. �t equals theincrease in lifetime utility that would stem fromborrowing Rt dollars, consuming (equation [7]) orinvesting (equation [8]) the proceeds, and reduc-ing consumption by an appropriate amount thefollowing period.

Without uncertainty, the assumption �guarantees that entrepreneurs are constrained inand around the steady state. In fact, the steady-state consumption Euler equation for the house-hold implies, with zero inflation, that R � 1/�,the household time preference rate. Combiningthis result with the steady-state entrepreneurialEuler equation for consumption yields: � �(� � )/c � 0. Therefore, the borrowing con-straint will hold with equality:

(10) bt � mEt �qt 1 ht�t 1 /Rt �.

Matters are of course thornier when there isuncertainty. The concavity of the objectivefunction implies in fact that, in some states ofthe world, entrepreneurs might “self-insure” byborrowing less than their credit limit so as tobuffer their consumption against adverseshocks. That is, there is some target level oftheir net worth such that, if their actual networth falls short of that target, the precautionarysaving motive might outweigh impatience, andentrepreneurs will try to restore some assets,borrowing less than the limit. Specifically, en-trepreneurs might not hit the borrowing limitafter a sufficiently long run of positive shocks.

In this case, the model would become asymmet-ric around its stationary state. In bad times,entrepreneurs would be constrained; in goodtimes, they might be unconstrained. In such acase, a linear approximation around the deter-ministic steady state might give misleading re-sults. In the paper, I take as given thatuncertainty is “small enough” relative to degreeof impatience so as to rule out this possibility.In Appendix C, I present evidence from nonlin-ear simulations that backs this assumption.9

C. Retailers

To motivate sticky prices I assume implicitcosts of adjusting nominal prices and, as inBernanke et al. (1999), monopolistic competi-tion at the retail level. A continuum of retailersof mass 1, indexed by z, buy intermediate goodsYt from entrepreneurs at Pt

w in a competitivemarket, differentiate the goods at no cost intoYt(z), and sell Yt(z) at the price Pt(z). Finalgoods are Y t

f � (�01 Yt(z)��1/� dz)�/��1 where

� � 1. Given this aggregate output index,10 theprice index is Pt � (�0

1 Pt(z)1�� dz)1/1��, so thateach retailer faces an individual demand curveof Yt(z) � (Pt(z)/Pt)

��Y tf.

Each retailer chooses a sale price Pt(z) takingPt

w and the demand curve as given. The saleprice can be changed in every period only withprobability 1 � . Denote with P*t(z) the “reset”price and with Y*tk(z) � (P*t(z)/Ptk)

��Ytkthe corresponding demand. The optimal P*t(z)solves:

(11)

�k � 0

�

kEt� t,k�P*t �z�

Pt k�

X

Xt k�Y*t k �z�� 0

9 The Appendix is available on the AER Web site (http://www.aeaweb.org/aer/contents). Specifically, I construct apartial equilibrium model of consumption and housingchoice which features an amount of volatility and a borrow-ing limit similar to that assumed here. I show that theconditions under which precautionary saving arises are veryrestrictive if the volatility is parameterized to reflect theamount observed in macroeconomic aggregates.

10 The CES aggregate production function makes exactaggregation difficult. However, a linear aggregator of theform Y t

f � �01 Yt(z) dz equals Yt within a local region of the

steady state. In what follows, I will consider total outputas Yt.


where t,k � �(c�t /c�tk) is the patient householdrelevant discount factor and Xt is the markup,which in steady state equals X � �/(� � 1). Thiscondition states that P*t equates expected dis-counted marginal revenue to expected dis-counted marginal cost. Profits Ft � (1 � 1/Xt)Ytare finally rebated to patient households.

As a fraction of prices stays unchanged, theaggregate price level evolution is

(12) Pt � � Pt � 1� � �1 � ��P*t �

1 � ��1/�1 � ��.

Combining (11) and (12) and linearizingyields a forward-looking Phillips curve, whichstates that inflation depends positively on ex-pected inflation and negatively on the markup Xtof final over intermediate goods.

D. Central Bank Policy and the Interest RateRule

The central bank makes lump sum transfersof money to the real sector to implement aTaylor-type interest rate rule. The rule takes theform

(13) Rt � �Rt � 1 �rR��t � 11 r��Yt � 1 /Y�rY rr�1 � rReR,t

where rr and Y are steady-state real rate andoutput, respectively. Here, monetary policy re-sponds systematically to past inflation and pastoutput.11 If rR � 0, the rule allows for interestrate inertia. eR,t is a white noise shock processwith zero mean and variance �e

2.

E. Equilibrium

Absent shocks, the model has a unique sta-tionary equilibrium in which entrepreneurs hitthe borrowing constraint and borrow up to thelimit, making the interest payments on the debtand rolling the steady-state stock of debt over

forever. The equilibrium is an allocation {ht, h�t,Lt, L�t, Yt, ct, c�t, bt, b�t}t�0

� together with thesequence of values {w�t, Rt, Pt, P*t, Xt, �t, qt}t�0

�

satisfying equations (2) to (13) and the marketclearing conditions for labor (Lt � L�t), realestate (ht h�t � H), goods (ct c�t � Yt), andloans (bt b�t � 0), given {ht�1, Rt�1, bt�1,Pt�1} and the sequence of monetary shocks{eR,t}, together with the relevant transversalityconditions.

Appendix A describes the steady state. Lethatted variables denote percent changes fromthe steady state, and those without subscriptdenote steady-state values. The model can bereduced to the following linearized system(which I solve numerically using the methodsdescribed by Harald Uhlig, 1999):

(L1) Yt � �c/Y�ct � �c�/Y�c�t

(L2) c�t � Etc�t 1 � rrt

(L3) cct � bbt � Rb��t � Rt � 1 � bt � 1 �

��Y/X��Yt � Xt� � qh�ht

(L4) qt � e Etqt 1 � �1 � e �Et

� �Yt 1 � ht � Xt 1�

� m�rrt � �1 � m��Et�ct 1

(L5) qt � �Etqt 1 � �ht � c�t � �Etc�t 1

(L6) bt � Etqt 1 � ht � rrt

(L7) Yt ��

� � �1 � ��ht � 1

�1 � �

� � �1 � ��Xt � c�t�

(L8) �t � �Et�t 1 � �Xt

(L9) Rt � �1 � rR ��1 � r� ��t � 1 � rYYt � 1 �

rRRt � 1 � eR,t

where � � (1 � �)h/h�, � � (1 � )(1 � � )/ ,e � m� (1 � m), and rrt � Rt � Et�t 1 is

11 A backward-looking Taylor rule has the advantage ofisolating in a neat way the exogenous component of mon-etary policy from its endogenous counterpart. As will beshown later, given that the interest rate is assumed to re-spond only with one lag to all other variables, it offers someconvenient zero restrictions when taking the model to thedata. Fuhrer (1997) shows that the data offer more supportfor a backward rule than for a forward rule. Bennett Mc-Callum (1999) has emphasized a related point, since outputand inflation data are reported with a lag and thereforecannot be known to the policymaker in the current quarter.


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the ex ante real rate. (L1) is total output. (L2) isthe Euler equation for household consumption.(L3) is the entrepreneurial flow of funds. (L4)and (L5) express the consumption/housing mar-gin for entrepreneurs and households, respec-tively. (L6) is the borrowing constraint. Thesupply side includes the production function(L7) (combined with labor market clearing) andthe Phillips curve (L8). Finally, (L9) is themonetary policy rule.

F. The Transmission Mechanism: Indexationand Collateral Effects

The basic model shows the key links betweenthe interest rate channel, the house price chan-nel, and the debt deflation channel. I now focuson one standard deviation (as estimated in theVAR) negative monetary shock; in the fullmodel, I will look at other disturbances, too, andwill estimate some of the structural parametersof the model. The parameters chosen here re-flect the estimates and the calibration of the fullmodel.

The time period is one quarter. The entrepre-neurial “loan-to-value” ratio m is set to 0.89.The probability of not changing prices is set to0.75. The discount factors are � � 0.99 and �0.98. I set the elasticity of output to real estate� to 0.03. (With j � 0.1, this yields a steadystate value of h, the entrepreneurial asset share,of 20 percent.) The household labor supplyschedule is assumed to be virtually flat: � �1.01.

For the Taylor rule, I set rY � 0, r� � 0.27,rR � 0.73. These are the parameters of anestimated policy rule for the VAR period, withthe exception of rY, which is reset to zero.Imposing rY � 0 amplifies the financial accel-erator since the central bank does not intervenewhen output falls. However, it allows isolatingthe exogenous component of the reaction func-tion from its endogenous component, while en-suring determinacy of the rational expectationsequilibrium.

The transmission mechanism is simple: con-sider a negative monetary shock. With stickyprices, monetary actions affect the real rate, andits increase works by discouraging current con-sumption and hence output. The effect is rein-forced through the fall in housing prices, whichleads to lower borrowing and lower entrepre-neurial housing investment. Debt deflation

plays a role, too: as obligations are not indexed,deflation raises the cost of debt service, furtherdepressing entrepreneurial consumption andinvestment.

How big are these effects? Figure 2 providesa stylized answer for three economies subject tothe same shock, showing the total loss in outputfollowing a one-standard deviation increase(0.29 percent on a quarterly basis) of the interestrate.12 The solid line illustrates the case whenboth collateral and debt deflation effects areshut off, so that only the interest rate channelworks (see Appendix B for the technical de-tails): output falls by 3.33 percent. Here, theoutput drop is mainly driven from intertemporalsubstitution in consumption. The dashed lineplots the response of output when the collateralchannel becomes operational: the decline inoutput is larger, and the total decline is 3.82percent. Finally, in the starred line, both collat-eral and debt deflation channels are at work:output falls by 4.42 percent.13

III. The Full Model: Household andEntrepreneurial Debt

The basic model assumes that all mortgagedreal estate is used by firms. In reality, financialfrictions apply to both firms and households.The previous section models entrepreneurialconsumption, but lacks the descriptive realismemphasized, for example, in the quote fromTobin at the beginning of the paper. In addition,investment occurs in the form of real estatetransfers between agents, but net investment iszero. Before taking the model to the data, Iextend it along two dimensions. On the onehand, I add a constrained, impatient householdsector, that ends up facing a binding borrowingconstraint in equilibrium. On the other, I allowvariable capital investment for the entrepre-neurs. This allows a more realistic analysis ofthe impact of a various range of disturbances: in

12 The figure shows the cumulative drop in output after40 quarters. This is approximately the horizon at whichoutput has returned to the baseline, so that the cumulativeimpulse responses level off.

13 It would be tempting to rank the two effects. There isno way of doing so, however. For instance, depending onhow aggressive the central bank is on inflation, the debtdeflation effect can be larger or smaller than the collateraleffect.


particular, I add inflation, technology, and tasteshocks. As before, a central bank and retailerscomplete the model.

The problems of patient households, retailers,and the central bank are unchanged. I considertherefore the slightly modified entrepreneurialproblem and then move to impatient households.

A. Entrepreneurs

Entrepreneurs produce the intermediate goodaccording to:

(14) Yt � At Kt � 1� ht � 1

� L�t��1 � � � ��L �t

�1 � ��1 � � � ��

where At is random. L� and L� are the patientand impatient household labor (� measures therelative size of each group) and K is capital (thatdepreciates at rate �) created at the end of eachperiod. For both housing and variable capital, Iconsider the possibility of adjustment costs:capital installation entails a cost �K,t � �(It /Kt�1 � �)2Kt�1/(2�), where It � Kt � (1 ��)Kt�1. For housing, changing the stock entailsa cost �e,t � �e(�ht /ht�1)2qtht�1/2, which is

symmetric for each agent: such a cost mightproxy for transaction costs, conversion costs ofresidential housing into commercial housingand vice versa, and so on. The remainder of theproblem is unchanged: entrepreneurs maximizeE0 ¥t�0

� tlog ct, where �, subject totechnology (14) and borrowing constraint (10),as well as the flow of funds constraint:

(15) Yt /Xt � bt � ct � qt�ht � Rt � 1 bt � 1 /�t

w�tL�t � w�tL�t � It

�e,t � �K,t .

The first-order conditions for this problemare fairly standard and are reported in Appen-dix A.

B. Impatient Households

Impatient households discount the futuremore heavily than the patient ones. They chooseconsumption c�t, housing h�t, labor L�t (andmoney M�t/Pt) to maximize

FIGURE 2. TOTAL OUTPUT LOSS IN RESPONSE TO A MONETARY SHOCK IN THE BASIC MODEL:COMPARISON BETWEEN ALTERNATIVE MODELS

Notes: Ordinate: time horizon in quarters. Coordinate: percent deviation from initial steadystate.


E0 �t � 0

�

��t�ln c�t � jtln h�t � �L�t��/�

� ln M�t /Pt)

where �� . Like for entrepreneurs, this guar-antees an equilibrium in which impatient house-holds will hit the borrowing constraint. Here,the subscript under jt allows for random distur-bances to the marginal utility of housing, and,given that it directly affects housing demand,offers a parsimonious way to assess the macroeffects of an exogenous disturbance on houseprices.14 The flow of funds and the borrowinglimit are

(16) c �t � qt�h �t � Rt � 1 b �t � 1 /�t

� b�t � w�tL�t � T�t � �M�t /Pt � �h,t

(17) b �t m�Et �qt 1 h �t�t 1 /Rt �

where �h,t � �h(�h�t/h�t�1)2qth�t�1/2 denotes thehousing adjustment cost (an analogous termalso appears in the budget constraint of thepatient households). The borrowing constraintis consistent with standard lending criteria usedin the mortgage market, which limit the amountlent to a fraction of the value of the asset. Onecan interpret the case m� � 0 as the limit situ-ation when housing is not collateralizable at all,so that households are excluded from financialmarkets.

Like for the entrepreneurs, the equations forconsumption and housing choice (shown in Ap-pendix A) hold with the addition of the multi-plier associated with the borrowing restriction.15

C. The Linearized Model

The equations describing the steady-state andthe linearized model are isomorphic to those ofthe basic model and are in Appendix A. Before

moving to the estimation strategy, I present twodirect implications of the main model featureswhich can replicate key dynamic correlations inthe data: the collateral effect allows pinningdown the elasticity of consumption to a housingpreference shock; the nominal debt effect allowsmatching the delayed response of output to aninflation shock.

D. Collateral Effects and Effects onConsumption of a Housing Price Shock

Several commentators have expressed theconsideration that rising house prices have keptconsumption growth high throughout the 1990s.Case et al. (2001) find long-run elasticities ofconsumption to housing prices of around 0.06for a panel of U.S. states. Morris Davis andMichael Palumbo (2001) estimate a long-runelasticity of consumption to housing wealth of0.08. These positive elasticities are hard to rec-oncile with the traditional life-cycle model.Think about the simplest case, an exogenousincrease in housing prices. If the gains wereequally distributed across the entire population,if all agents had the same propensity to con-sume, and if all agents were to spend these gainson housing, total wealth less housing wealthwould remain unchanged, and so would thedemand for non-housing consumption. However,if liquidity-constrained households value currentconsumption a great deal, they may be able toincrease their borrowing and consumption morethan proportionally when housing prices rise, sothat increases in prices might have positive ef-fects on aggregate demand.

The mechanism described above is at workin the paper, and it is straightforward in dem-onstrating its ability to produce an empiri-cally plausible response of consumption tohousing price shocks. Figure 3 displays theimpulse response of consumption to a persis-tent housing price increase, generated from ashock to the marginal rate of substitution jbetween housing and consumption for allhouseholds. Such an experiment offers a par-simonious way to model any kind of distur-bance that shifts housing demand, such astemporary tax advantages to housing invest-ment or a sudden increase in demand fuelledby optimistic consumer expectations. The pa-rameters are those calibrated and estimatedusing the method described in Section IV,

14 I assume that the disturbance to jt is common to bothimpatient and patient households. This way, variations in jtcan also proxy for exogenous variations in, say, the tax codethat shift housing demand for all households.

15 The money demand condition is redundant under in-terest rate control, so long as the central bank respects, foreach group, the equality between money injections andtransfers.


except that here I compute responses for sev-eral values of the loan-to-values m and m�,and compare them with the impulse responsefrom a housing price shock in a VAR.

The VAR is estimated from 1974Q1 to2003Q2 on quarterly data for the federalfunds rate, log real housing prices, log realpersonal consumption expenditures, log realGDP, and log change in the GDP deflator, inthat order.16 The figure illustrates an impor-tant point: the greater the importance of col-lateral effects (higher m and m�), the closerthe simulated elasticity of consumption to ahousing price shock. A wage share of theconstrained sector (1 � �) of 36 percent, and

loan-to-value ratios of 89 percent for entre-preneurial loans and 55 percent for residentialloans, can generate responses of consumption(and income, as will be shown below) to ahousing price shock that are not only qualita-tively but also quantitatively in line with theVAR estimates. In particular, the impact elas-ticity of consumption to a persistent 1-percentincrease in housing prices is around 0.2. Thisis slightly larger than reduced-form estimatesfound in the studies above; however, both inthe model and in the VAR, consumption fallsbelow the baseline during the transition,hence the medium-run elasticities are some-what smaller. Instead, the model without collat-eral effects (m, m� 3 0) predicts a negativeresponse of consumption to housing prices—mainly driven by a substitution effect betweenhousing and consumption—which is clearly atodds with the data.

While I will conduct more formal estima-tion and testing below, this pictures highlightsthe reason behind the success of the model intracking down the empirical positive elastic-

16 Consistent with the theoretical model, I allow for allthe variables (except the interest rate) to respond contem-poraneously to a housing price shock. The results were,however, robust to alternative orderings. The lags and theset of exogenous variables are the same as in the VAR ofSection I. Consumption, GDP, and house prices were de-trended with a band-pass filter-removing frequencies above32 quarters.

FIGURE 3. RESPONSE OF AGGREGATE CONSUMPTION TO A HOUSING PRICE SHOCK: VARIOUS

VALUES OF m AND m�

Notes: Ordinate: time horizon in quarters. Coordinate: percent deviation from initial steadystate.


ity of spending to housing prices. To betterunderstand the result, it is useful to reinterpretthe borrowers’ asset demand as determiningconsumption given asset prices and payoffs,rather than determining today’s asset pricesin terms of consumption and payoffs. Forentrepreneurs, for instance, the linearized op-timality condition between housing andconsumption can be written (neglecting ad-justment costs) as

(18) ct � Etct 1 �1

1 � m�

� �qt � eEtqt1 � �1 � e�EtSt1�

m�

1 � m�rrt

where e � m� (1 � m) and EtSt 1 isthe expected marginal product of housing.This equation clearly shows how, keepingconstant expected consumption, expected re-turns on housing, and real interest rates, themultiplier effect on consumption of given

changes in qt can be rather large, and isstrongly increasing with m, the loan-to-valueratio. Instead, as shown by equation (L5), forlenders the effects of qt on ct are simplyone-for-one, and therefore much smaller inmagnitude.

E. Debt Deflation and the Stabilizing Effectsof an Inflation Shock

Starting from the steady state, I assume a1-percent, persistent inflation surprise.17 Itis informative to contrast the response ofoutput with nominal debt to the model with in-dexed debt. Figure 4 displays the results of thesimulation.

With nominal debt (the solid line), the rise inprices reduces the desired supply of goods at a

17 The inflation shock shows up as a residual inthe Phillips curve. It could be justified by assumingthat the elasticity of demand for each intermediategood is time-varying, and varies exogenously, asdone, for instance, by Frank Smets and Rafael Wouters(2003).

FIGURE 4. RESPONSE OF OUTPUT TO AN INFLATION SHOCK: NOMINAL VERSUS INDEXED DEBT

Notes: Ordinate: time horizon in quarters. Coordinate: percent deviation from initial steady state.


given price level; at the same time, it transferswealth from the lenders toward the borrowers,who, ceteris paribus, have a higher propensityto consume. Initially, the two effects go in op-posite directions, and output falls by a smallamount. Later, the first effect dominates, andthe output drop is larger: overall, output dis-plays a hump-shaped pattern and a slow returnto its initial steady state.

This contrasts with the responses that wouldoccur in a model without debt deflation effects(the dashed line): with indexed debt, the drop inoutput is immediate and stronger in magnitude,because the beneficial effects of inflation areabsent. Hence, the assumption of nominal debthelps capture not only qualitatively but alsoquantitatively the hump-shaped and persistentresponse of output to inflation found in the VAR.

Interestingly, the negative correlation be-tween inflation and output induced by an infla-tion shock acts as a built-in stabilizer for theeconomy. Debt deflation thus adds a new twistto the theories of financial accelerator men-tioned in the introduction: while it amplifiesdemand-type disturbances, it can stabilize thosethat generate a trade-off between output andinflation. I will return to this issue in Section VI.

IV. Econometric Methodology

I now discuss the methodology for evaluatingthe model. I partition the model parameters inthree groups.

A. Calibration

The first group includes the discount factors:�, ��, ; the housing weight j; the technologyparameters �, �, �, �, �e, �h; the markup X; thelabor disutility �; and the degree of price rigid-ity . I calibrate these parameters on the basis ofthe data sample means and other studies be-cause they contain relatively more informationon the first moments of the data.

For the standard parameters, I choose valuesthat are within the range considered in the mon-etary/real business cycle literature. Thus, �, �,�, X, , and � equal 0.99, 0.03, 0.3, 1.05, 0.75,and 1.01, respectively.18

Next, I set and ��. I match the reciprocal of, which proxies for the firm’s internal rate ofreturn. I assume this is twice as big as theequilibrium real rate, and set � 0.98. I thenpick a value for ��: Emily Lawrance (1991)estimates discount factors for poor households(which are more likely to be debtors) between0.95 and 0.98 at quarterly frequency, dependingon the specification. Carroll and Andrew Sam-wick (1997) calculate an empirical distributionof discount factors for all agents using informa-tion on the elasticity of assets with respect touncertainty: the two standard deviation bandsrange in the interval (0.91, 0.99). Samwick(1998) uses wealth holdings at different ages toinfer the underlying distribution of discount fac-tors: for about 70 percent of the households, hefinds mean discount factors of about 0.99; forabout 25 percent of households, he estimatesdiscount factors below 0.95. With � set at 0.99,I choose �� 0.95, in the ballpark of theseestimates.

I set �, the elasticity of output to entrepre-neurial real estate, to 0.03. This number impliesa plausible 62 percent for the steady-state valueof commercial real estate over annual output.The parameter j mainly controls the stock ofresidential housing over annual output (see Ap-pendix A): j � 0.1 fixes this ratio at 140 percent,in line with data from the Flow of Funds ac-counts (see, e.g., Table B.100, row 4).

I then pick values for the adjustment costparameters. Preliminary attempts to estimatethese parameters (using the methods describedin Section IV C) led to estimates of the capitaladjustment cost � around 2 and pushed thehousing adjustment cost parameters �e and �htoward zero. These results suggest that the dataappear to favor a version of the model in whichvariable capital moves more slowly than hous-ing in response to disturbances. Although thisfinding is not in contradiction to the cyclicalproperties of the actual data,19 it is likely that

18 A value of � � 1.01 implies a virtually flat laborsupply curve: this is higher than what microeconometric

studies would suggest, but has the virtue of rationalizing theweak observed response of real wages to macroeconomicdisturbances. With � approaching 1, the utility functionbecomes linear in leisure, as proposed and explained inGary Hansen (1985).

19 For the period 1974Q1–2003Q2, the standard devia-tion of (a) structures investment, (b) residential investment,(c) equipment and software investment, and (d) change ininventories are, respectively, 0.8, 0.5, 0.58, and 0.94 per-


the solution algorithm has difficulty in estimat-ing these parameters without data on the typesof investment spending. At the same time, onehas to consider that, ceteris paribus, the fixity ofthe housing stock in the aggregate works byitself as an adjustment cost on housing invest-ment: given that the total supply of structures isfixed, additional housing investment in anygiven period drives up the price of the existingstock, so that, from each agent’s point of view,every unit of new investment is more costly atthe margin. In what follows, therefore, I esti-mate the model by calibrating � � 2 and �e ��h � 0.20 The former implies an elasticity of 1⁄2of investment to the capital shadow price, fol-lowing Robert King and Alex Wolman (1996):this value is well within the range of estimatesreported in the literature (see Robert Chirinko,1993). Table 1 summarizes the parameters.

B. Policy Rule

The second group includes the parametersthat can be recovered from the estimates of theTaylor rule. For the period 1974Q1–2003Q2, anOLS regression of the Fed Funds rate on its ownlag, past inflation, and detrended output yieldsrR � 0.73, rY � 0.13, r� � 0.27.21

C. Estimation

The third group includes the autocorrelationand the standard deviation of each shock (�A, �j,�u, �A, �j, �u), the loan-to-value ratios (m, m�),and the wage income share of the patient house-holds, measured by �. I estimate these param-

eters by minimizing a measure of the distancebetween the empirical impulse responses (Sec-tion I) and the model responses, which wereobtained from the reduced form of the model byordering and orthogonalizing the shocks as inthe VAR.

As is well known (see, e.g., Ireland, 2004a),the number of data series in the VAR represen-tation cannot exceed the number of structuraldisturbances in the model. With four distur-bances (monetary, inflation, taste, productivity),I select (R, �, q, Y) as the variables of interest.Denote with �(�) the vector collecting themodel orthogonalized impulse responses, ob-tained from the reduced form of the model byordering and orthogonalizing the impulse re-sponses as in the VAR. Let � be the n � 1vector of empirical estimates of the VAR im-pulse responses.22 I include the first 20 elementsof each impulse response function, excludingthose that are zero by the recursiveness assump-

cent. (All variables were normalized by GDP. The data werethen filtered using a band-pass filter that removed the low-frequency component above 32 quarters.)

20 The results with �e, �h � 0 are qualitatively as fol-lows: housing adjustment costs reduce the fluctuations inthe housing stock variables but generate slightly largerchanges in housing prices and output, which the data appearto reject. Closer inspection of the impulse responses showsthat, when facing costs of adjusting both k and h, entrepre-neurs vary labor input more strongly in response to distur-bances, which in turn affects output.

21 The standard deviation of the monetary shock �e istaken from the standard error of the interest rate equation inthe VAR below, which equals 0.29. In principle, one couldalso obtain all the parameters of a more involved policy rulefrom the VAR. I use a shift dummy from 1979Q4 to capturemonetary policy changes that are known to have occurredaround that time.

22 n � n12 � n2 � n3, where n1 is the number of variables

in the VAR, n2 are the elements to match for each impulseresponse, and n3 are the elements of � which are zero byassumption (because of the zeros imposed by the Choleskiordering).

TABLE 1—CALIBRATED PARAMETERS IN THE EXTENDED

MODEL

Description Parameter Value

Preferences: Discount factors

Patient households � 0.99Entrepreneurs 0.98Impatient households �� 0.95

Other preference parameters

Weight on housing services j 0.1Labor supply aversion � 1.01

Technology: Factors productivity

Variable capital share � 0.3Housing share � 0.03

Other technology parameters

Variable capital adjustment cost � 2Variable capital depreciation rate � 0.03Housing adjustment cost � 0

Sticky prices

Steady-state gross markup X 1.05Probability fixed price 0.75


tion. The estimate of �, a vector of parameters,solves

(19) min�

��

where � is a n � n weighting matrix. Under thenull hypothesis that the VAR model is true andthat the model fits the data, the optimal weight-ing matrix � would equal � � ��1, the inverseof the matrix with the sample variances of theVAR impulse responses on the main diagonal.Given that the cross-correlations between q andY are likely to be relatively more informative form, m�, and �, I specify � � ��1, where � isa n � n diagonal matrix of weights that gives aweight four times larger to all the dynamiccross-correlations involving q and Y. This way,I still get consistent (yet inefficient) estimates ofall the parameters, but at the same time I fit themoments of highest interest.23 The results were,however, robust to the choice of �.

Table 2 summarizes the estimates of the pa-rameters in �. The results strongly support thepresence of borrowing-constrained households:

their wage share (1 � �) is around 36 percentand is precisely estimated:24 interestingly, thisnumber is within the range of the various stud-ies that, since Campbell and Mankiw (1989),have estimated from consumption Euler equa-tions the fraction of rule-of-thumb/constrainedagents in an economy. At the same time, theysupport strong effects on demand from changesin asset values, as shown by the high values ofm and m�. The former is 89 percent, whereas thelatter is 55 percent. Hence, the estimates suggestthat entrepreneurial real estate is more easilycollateralizable than household real estate. Ajoint test of the hypothesis that collateral con-straints are unimportant—that the m and m� areequal to zero—is overwhelmingly rejected.High values of m and m� are in fact needed togenerate strong and persistent effects on aggre-gate demand from given changes in asset val-ues, something that a model without theseeffects cannot replicate.

Finally, the estimate of the autocorrelation inthe technology shock is low (�A � 0.03) andless precisely estimated: one explanation mightbe the detrending method used in the VAR,which takes away the low-frequency compo-nent of GDP. Instead, the autocorrelations in thepreference and in the inflation shock are pre-cisely estimated and highlight moderate persis-tence in the shock processes (�j � 0.85, �u �0.59). Interestingly, such autocorrelations arelower than what is found in estimates of stan-dard monetary business cycle models: one pos-sibility is that the endogenous propagationmechanisms that are at work in the model re-quire less persistent shocks to fit the secondmoment properties of the data.

While the estimates of �, m, and m� are allstatistically significant,25 I reject the null

23 As suggested by a referee, housing collateral is inter-esting because of the potential spillovers to other consump-tion goods as housing price increases relax borrowingconstraints. By focusing on the parameters that best matchthe dynamic cross-correlation between house prices andoutput (and therefore consumption), the estimation proce-dure selects these particular moments as most informative atthe margin for the values of m, m�, and �.

24 Standard errors were computed using the asymptoticdelta function method applied to the first-order conditionassociated with the minimization problem.

25 These findings are robust to changes in the estimationhorizon and in the weighting matrix. As a robustness check,I included the discount factors among the parameters toestimate. The resulting values for �� and were, respec-tively, around 0.4 and 0.9; the other parameter estimateswere unchanged, with the exception of m�, whose estimatewas marginally positive. Loosely speaking, a reduction inthe discount factor works to strengthen the preference forcurrent consumption, thus working in the same direction asan increase in the loan-to-value when it comes to explainingthe high sensitivity of demand to aggregate shocks. How-

TABLE 2—ESTIMATED PARAMETERS AND THEIR STANDARD

ERRORS IN THE EXTENDED MODEL

Description Parameter Value s.e.

Factor shares and loan-to-values

Patient households wage share � 0.64 0.03Loan-to-value entrepreneur m 0.89 0.02Loan-to-value household m� 0.55 0.09

Autocorrelation of shocks

Inflation �u 0.59 0.06Housing preference �j 0.85 0.02Technology �A 0.03 0.10

Standard deviation of shocks

Inflation �u 0.17 0.03Housing preference �j 24.89 3.34Technology �A 2.24 0.24


hypothesis of equality between the model andthe data. Perhaps the simplest explanation forthis finding is that the model lacks such featuresas expectational delays, inertial adjustment ofprices, or habit persistence, which elsewhereauthors have shown can help replicate the de-layed responses of macroeconomic variables tovarious shocks (see, e.g., Julio Rotemberg andMichael Woodford, 1997; Galı and Gertler,1999; Fuhrer, 2000).

V. More on the Model Dynamics

Figure 5 shows the model impulse responsesand compares them with the VAR impulse re-sponses. This way, I can assess the key proper-ties of the model and its consistency withempirical evidence.26

The top row shows a monetary tightening.

ever, although empirical estimates of the discount factor aresurrounded by large uncertainty, values below 0.9 appeartoo low to be considered reasonable (see Carroll and Sam-wick, 1997).

26 One caveat: the impulse responses from the VAR andthose from the structural model are not strictly comparable,since the restrictions implied by the two representations are,in general, different. See Fuhrer (2000) for a discussion: analternative could be to compare the autocorrelation func-tions implied by the various models. The results using thisrepresentation were qualitatively similar.

FIGURE 5. RESPONSES TO ALL SHOCKS, MODEL VERSUS VAR

Note: Coordinate, percent deviation from steady state. Solid lines: estimated model. Dotted lines: VAR model with 90-percentbands.


The drop in output is immediate in the model,while it is delayed in the data, although the totaloutput sacrifice is in line with the VAR esti-mate. As in the basic model, money shocks haveheterogeneous effects: debtors bear most of thebrunt of the monetary contraction, while con-sumption of lenders is mildly affected and canbe shown to rise above the baseline in the tran-sition to the steady state. In turn, the real rate,which prices lenders’ behavior, falls below thebaseline in the transition. Real housing pricesinitially fall below the baseline, deepening therecession, and then overshoot above the base-line, preceding the economy’s recovery.

The previous section has already shown hownominal debt is successful in capturing the slug-gish response of output to an inflation shock.The second row of Figure 5 shows that the modeldoes very well at capturing the positive responseof the interest rate and the negative response ofhousing prices to an inflation surprise.

For the preference shock, the third row ofFigure 5 shows that the model does well incapturing the positive elasticities of demand andinflation to a housing price shock. Figure 3 hasalready shown how a model without collateraleffects predicts a small, even negative, responseof aggregate demand to a housing price shock.27

The last row of Figure 5 shows the responsesto a transitory productivity rise. Here it is harderto compare the responses of the model with thedata, especially because it is harder to considerthe VAR disturbance as a pure productivityshock: for instance, a government spendingshock could be observationally equivalent. In themodel, output and asset prices peak only with adelay following the improvement in productivity.

In simulations not reported here, I find thatthe model predicts a standard deviation for en-trepreneurial housing investment that is twicethat of variable capital investment: this numberis slightly bigger but roughly in line with thedata (see footnote 19). Not shown in figure, Ifind that in response to, say, a negative mone-tary shock (positive preference shock), h falls(rises) on impact by 4 percent (3 percent).Given that the elasticity of output to real estateis very small (0.03), this shows that changes inhousing ownership per se are not crucial to the

transmission mechanism: rather, it is the generalequilibrium effects working through the de-mand for all factors of production that affect theaggregate outcomes.28

VI. Systematic Monetary Policy and PolicyFrontiers

Shocks that generate a negative correlation be-tween output and inflation force the central bankto face a trade-off between the variability of out-put and that of inflation. A natural question is:how do different monetary policy rules and con-tractual arrangements affect the cyclical propertiesof output and inflation? This section gives ananswer, based on the assumption that output andinflation volatility are the only two goals of mon-etary policy. I consider whether interest ratesshould respond to housing prices; and how differ-ent financing arrangements (nominal versus in-dexed debt) affect the volatility of the economy.

A. Should Central Banks Respond to HousingPrices?

I compute the inflation-output volatility fron-tiers for alternative parameterizations of the in-terest rate rule, as in Andrew Levin et al.(1999), subject to a constraint on interest ratevolatility.29 The class of rules I consider is

(20) Rt � 0.73Rt � 1

0.27�rqqt � �1 � r��t � 1 � rYYt � 1�.

In other words, I assume that the central bankcan respond to current asset price movements:

27 Given the adjustment cost for capital, the initial re-sponse of output is roughly equal to that of consumption.

28 One drawback of the model is that it predicts thathouseholds’ housing holdings are countercyclical: with afixed supply, this sector absorbs in fact the reduction in thedemand by the entrepreneurs. This need not be unrealistic ifhousing is given a broad interpretation, which also includesland. In Japan, for instance, households and the governmenthave traditionally been net purchasers of land in periods offalling land prices (see the 2003 Annual Report on NationalAccounts of Japan).

29 I compute the Taylor curves tracing out the minimumweighted unconditional variances of output and inflation atdifferent relative preferences for inflation versus outputvariance. I constrain interest rate volatility by imposing anupper bound 25 percent larger than the estimated standarddeviation generated by the benchmark model. I also imposer�, rY � 0 to generate a unique rational expectations equi-librium for each policy.


this way, I shift the bias in favor of finding anon-zero coefficient on asset prices in the reac-tion function.

I compute two efficient frontiers. In the firstone, I fix rq � 0; in the second, I allow Rt torespond to qt. This way, I investigate the extentto which responding to asset prices can yieldlower output and inflation volatility. Altogether,responding to asset prices does not yield signif-icant gains in terms of output and inflation sta-bilization. As shown by Figure 6, the frontierobtained by responding to asset prices shiftsinward only marginally: keeping inflation stan-dard deviation constant, the decrease in thestandard deviation of output is a rather smallnumber, about 0.7 percent of its baseline value.The optimal rq is positive and slightly increas-ing in the weight given to output stabilization inthe loss function, ranging between 0.1 and 0.15.However, such a weight is small compared tothe optimal responses to output and inflation.30

The unimportance of responding to assetprices is reminiscent of the findings of Bernankeand Gertler (2001) and Simon Gilchrist andJohn Leahy (2002). They look at whether cen-tral banks should respond to stock prices in aversion of the Bernanke et al. (1999) modelwhich allows for fundamental and nonfunda-mental asset price changes. They find no casefor responding to stock prices, although they donot calculate a complete efficient frontier fordifferent policy rule specifications. In theirsetup, the signal-to-noise ratio of asset prices istoo low for asset prices to be informative for thecentral bank. Here, asset prices matter in thatthey transmit and amplify a range of distur-bances to the real sector. Despite this, if thecentral bank wants to minimize output andinflation fluctuations, little is gained by re-sponding to asset prices, even if their currentmovements are in the policymaker informationset.

30 The “optimal” coefficients on output and inflation arelarger than those estimated from the historical rule. If therelative weight on output stabilization is around, say, 10percent, the optimal r� and rY should be around 4 and 1.5,

respectively. For this reason, the estimated policy rule in-dicated in the figure performs worse than the optimal two-parameter rule for the model.

FIGURE 6. POLICY FRONTIERS AND ASSET PRICE RESPONSES

Note: The triangle indicates the performance of the rule estimated for the period 1974Q1–2003Q2.


B. Does Debt Indexation Reduce EconomicVolatility?

As shown earlier, the model can deliver asmaller response of output to monetary shockswhen debt contracts can be indexed to the pricelevel, but indexed debt does not dampen outputresponses to inflation or technology shocks. Con-sider a positive inflation surprise: this shockcauses a stronger output decline in the indexeddebt model since, while demand drops in bothcases, borrowers do not get the benefit of lowerreal repayments as before. Hence, indexed debtstabilizes only the type of disturbances that mon-etary policy can offset. In the presence of “supply”shocks, the Taylor curve in an economy withindexed debt lies above that for an economy withnominal debt (Figure 7). This result is somewhatsurprising and goes counter the widely held wis-dom that high levels of household and firm debtmay threaten economic stability. However, it is anatural consequence of two causes: first, theshocks that matter for the trade-off are only thosethat move the target variables in opposite direc-tions; second, the accelerator of demand shocks

gives more leverage to the central bank, and im-plies that smaller interest rate changes are neededto stabilize the economy for given demanddisturbance.

It is interesting to consider how the resultschange when the trade-off involves inflation andoutput gap, defined as the shortfall of output fromits equilibrium level under flexible prices (as prox-ied by Xt, the time-varying markup). The maindifference with the baseline case concerns tech-nology shocks. Consider, say, a favorable technol-ogy shock: for a given drop in prices, output risesless with nominal debt than with indexed debtbecause of the negative deflation effect; however,output gap rises more with nominal debt than withindexed debt because, while in both cases down-ward price stickiness prevents aggregate demandfrom rising enough to meet the higher supply,debt-deflation implies that demand rises even lessif debt is not indexed. Hence the gap is biggerunder nominal debt and, if the technology shockswere the only source of supply-side fluctuations,the trade-off would be worsened under nominaldebt. Quantitatively, whether nominal debt isbetter than indexed debt depends on the relative

FIGURE 7. POLICY FRONTIERS: NOMINAL VERSUS INDEXED DEBT

Note: The triangle indicates the performance of the rule estimated for the period 1974Q1–2003Q2.


standard deviation of inflation versus technologyshocks and on the policymaker’s preferences.31

Figure 8 shows the two Taylor curves in outputgap/inflation standard deviation space: if theweight on inflation stabilization is large, the cen-tral bank can offset technology shocks better thaninflation shocks, and nominal debt dominates in-dexed debt. If the weight on output stabilization islarge, the reverse is true, and indexed debt yieldsa better trade-off.

VII. Concluding Remarks

My model adds two important dimensions tothe literature on financial frictions and the mac-roeconomy: (a) nominal debt contracts, and (b)collateral constraints tied to housing values onboth the firm and the household side. It then takesthem to the data. The improvements afforded bythese features arise in two important and distinctways. First, collateral effects allow the model to

match the positive response of real spending to ahousing price shock. Second, nominal debt allowsthe model to accurately replicate the sluggish dy-namics of real spending to an inflation surprise.32

Given that the model is quite successful inmatching some key properties of the data, onecan conduct quantitative policy analysis. In par-ticular, I show how the fact that debt-deflationamplifies demand shocks but stabilizes supplyshocks yields an improved output-inflation vari-ance trade-off for the central bank. I also showthat responding to asset prices does not yieldsignificant welfare gains.

One limitation of the model is that it rules outbuffer-stock behavior: key to this result is thataggregate uncertainty is small relative to thedegree of impatience of borrowers. In Appen-dix C,33 I investigate this issue in a partialequilibrium model of consumption and housinginvestment with borrowing constraints that fea-

31 In practice, a large response of the interest rate to thegap would stabilize the gap itself as well as inflation, butmight violate the volatility bound on the interest rate: how-ever, this could not hold under cost-push shocks, whichwould require either keeping inflation constant (but a largevariance in the gap) or keeping the gap constant (but a largevariance in inflation).

32 In a variant of the model developed by Bernanke et al.(1999) calibrated to U.K. data, Kosuke Aoki et al. (2004)assess the impact of monetary policy on the real economythrough its effect on consumption and housing prices. Theyfall short, however, of providing a full analysis of theinteractions between house prices and the macroeconomy.

33 The Appendix is available on the AER Web site(http://www.aeaweb.org/aer/contents).

FIGURE 8. POLICY FRONTIERS WITH OUTPUT GAP: NOMINAL VERSUS INDEXED DEBT


tures an amount of uncertainty sufficient to rep-licate the aggregate output volatility in the data.The nonlinear solution shows how such uncer-tainty is small enough to generate nonnegligiblebuffer-stock behavior. In particular, agents bor-row up to the limit in all states unless thestandard deviation of the underlying aggregateshock rises to about four times more than what

is needed to replicate the actual data. Whilethese results are suggestive, ideally one wouldlike to embed this extension in a full-blowngeneral equilibrium model which endogenizesquantities as well prices, and which introducesidiosyncratic risk in addition to aggregate risk.Assessing this is an important task for futureresearch.34

APPENDIX A: STEADY STATE AND LOG-LINEARIZATIONS

Steady State of the Basic Model. Assuming zero inflation (so that R � 1/�), the steady state willbe described by

h

H�

��1 � ��

��1 � �� j��X � ��1 � e � � ��1 � ��m�

qh

Y�

�

1 � e

1

X

b

Y�

�m�

1 � e

1

X

c

Y�

�

X� �1 � ��m

qh

Y� �

�1 � ��1 � �m�

1 � e

1

X

c�

Y�

X � �

X� �1 � ��m

qh

Y� �X � � �

��1 � ��m

1 � e� 1

X

where e � (1 � m) m� is the average discount factor for the returns to entrepreneurial realestate investment.

The Impatient Household Problem in the Extended Model. Denoting with �� the multiplier on theborrowing constraint, the first-order conditions are

1

c �t� Et� ��Rt

�t 1 c �t 1� � � �t Rt

qt

c �t�1 � �h

�h �th �t � 1

� �jt

h �t� Et��qt 1

c �t 1�1 � �h

�h �t 1

h �t� � � �t m�qt 1�t 1�

w �t /c �t � �L �t �� 1.

34 Carroll and Dunn (1997) develop a dynamic partial equilibrium model of consumption and debt-financed housingpurchases with idiosyncratic and aggregate uncertainty. They find that variations in uncertainty, combined with lumpyhousing and transaction costs, can explain the timing of housing purchases over the cycle. Unlike theirs, my model, whichdoes not have idiosyncratic risk, assumes that uncertainty is small and linearizes around the nonstochastic steady state. Despitethese differences, my model also predicts that higher debt-to-income ratios (in the form of smaller down-payment constraints)may account for the increased sensitivity of expenditure to adverse (demand) shocks.


IACOVIEL

Cross-Out

The Entrepreneurial Problem in the Extended Model. The first-order conditions are

vt �1

ct��

� � It

Kt � 1� �� It

Kt � 1�

�

2� � It

Kt � 1� ��2� � Et� �Yt 1

ct 1Xt 1Kt� vt 1�1 � ��

w�t � ��1 � � � ��Yt /�Xt L�t �

w �t � �1 � ��1 � � � ��Yt /�Xt L �t �

where vt � (1/ct){(1 (�/�)[(It/Kt�1) � �]}, together with (7) and (8), the latter modified to includethe adjustment cost terms.

The first equation says that the shadow price of capital vt must equal the capital’s marginal productnext period plus the capital contribution to lower installation costs, plus the shadow value of capitalin the next period. In addition, there are two labor demand schedules.

Steady State of the Extended Model. The values of commercial real estate and commercial debtover output (qh/Y and b/Y) are unchanged from the basic model. Let s� � (�(1 � � � �) X �1)/X, s� � (1 � �)(1 � � � �)/X be the income shares of patient and impatient households. The realestate shares for each household are

qh�

Y�

j

1 � �s� �

jm�

1 � e

1

X�

j

1 � �� m�� j�1 � ��m�s�

qh�

Y�

j

1 � �� m�� j�1 � ��s�.

The debt-to-output and the consumption-to-output ratio for the impatient household are

b�

Y�

j�m�

1 � �� m�� jm��1 � ��s�

c�

Y�

1 � �� m��

1 � �� m�� jm��1 � ��s�.

The consumption-to-output ratio for the entrepreneurs is

c

Y� ��

��

1 � �1 � ��

�1 � ��m�

1 � e� 1

X.

The Complete Log-Linearized Model. To save on notation, I drop the expectation operator beforevariables dated t 1, which must be intended in expected value conditional on the informationavailable at time t. The model can be expressed in six blocks of equations:

1. Aggregate demand

(A1) Yt �c

Yct �

c�

Yc�t �

c�

Yc�t �

I

YIt

(A2) c�t � c�t 1 � rrt

(A3) It � Kt � 1 � � It 1 � Kt � �1 � �1 � ��

��Yt 1 � Xt 1 � Kt � �

1

��ct � ct 1 �


2. Housing/consumption margin

(A4) qt � eqt 1 � �1 � e ��Yt 1 � Xt 1 � ht � � m�rrt � �1 � m��ct 1

� �e ��ht � �ht 1 �

(A5) qt � hqt 1 � �1 � h �� j t � h �t � � m��rrt � �1 � m��c �t � �c �t 1 �

� �h ��h �t � ��h �t 1 �

(A6) qt � �qt 1 � �1 � �� j t � �ht � ��h �t � c�t � �c�t 1

�h

h��h�ht � h��h �t � �h�ht 1 � �h��h �t 1 �

3. Borrowing constraints

(A7) bt � qt 1 � ht � rrt

(A8) b �t � qt 1 � h �t � rrt

4. Aggregate supply

(A9) Yt ��

� � �1 � � � ��At � �ht�1 � �Kt�1� �

1 � � � �

� � �1 � � � ��Xt � �c�t � �1 � ��c�t �

(A10) �t � ��t 1 � �Xt � ut

5. Flows of funds/evolution of state variables

(A11) Kt � � It � �1 � ��Kt � 1

(A12)b

Ybt �

c

Yct �

qh

Y�ht �

I

YIt �

Rb

Y�Rt � 1 � bt � 1 � �t � � �1 � s� � s��Yt � Xt �

(A13)b�

Yb �t �

c�

Yc �t �

qh�

Y�h �t �

Rb�

Y�b �t � 1 � Rt � 1 � �t � � s��Yt � Xt �

6. Monetary policy rule and shock processes

(A14) Rt � �1 � rR ��1 � r� ��t � 1 � rY �1 � rR �Yt � 1 � rRRt � 1 � eR,t

j t � �jj t � 1 � ej,t

ut � �uut � 1 � eu,t

At � �AAt � 1 � eA,t


where � � (�� m��)/(1 � m��), � � (1 � �)h/h�, �� (1 � �)h�/h�, h � �� m�(� � ��),and rrt � Rt � Et�t 1 is the ex ante real rate.

(A1) is the goods market clearing. (A2) is the patient household’s first-order conditions forconsumption. (A3) is the investment schedule. The entrepreneurial optimality condition for con-sumption/housing is (A4), the impatient household’s is (A5), and the patient household’s demand(incorporating market clearing) is (A6) (the last brackets in each equation account for the adjustmentcost). The borrowing constraint for firms is (A7) and for households is (A8). (A9) is the productionfunction together with labor market clearing; (A10) is the Phillips curve. (A11) is the law of motionfor capital. (A12) and (A13) describe the net worth dynamics of entrepreneurs and constrainedhouseholds, respectively. (A14) is the monetary policy rule. The last three equations specify thestochastic AR(1) processes for preferences, inflation, and technology.

APPENDIX B: ALTERNATIVE MODELING ASSUMPTIONS

Indexed Debt. If debt is indexed to the price level, the entrepreneur borrows Bt and pays back therealized real value of his debt, that is, Rt�1(Pt/Pt�1)Bt�1. In the basic model, the entrepreneurialflow of funds becomes

Yt /Xt � bt � ct � qt�ht � Rt � 1 bt � 1 � w�t Lt .

The entrepreneurial new Euler equation is

1/ct � Et �Rt /ct 1 � � �t Rt

whereas the Euler equation for the unconstrained households is

1/c�t � �Et �Rt /c�t 1 �

so that now lenders’ behavior prices nominal bonds.

No Asset Price Channel. The borrowing limit is Bt � PtB� /R, where B� /R is a constant independentfrom the asset value. The first-order conditions for consumption and housing choice become

1

ct� Et� Rt

�t 1 ct 1� � �t R

1

ctqt � Et� 1

ct 1��

Yt 1

Xt 1 ht� qt 1�� .

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