House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle

House Prices, Borrowing Constraints, and Monetary Policy in
                      the Business Cycle

                                            By MATTEO IACOVIELLO*

         I develop and estimate a monetary business cycle model with nominal loans and
         collateral constraints tied to housing values. Demand shocks move housing and
         nominal 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 supports
         two key model features: collateral effects dramatically improve the response of
         aggregate demand to housing price shocks; and nominal debt improves the sluggish
         response of output to inflation surprises. Finally, policy evaluation considers the
         role of house prices and debt indexation in affecting monetary policy trade-offs.
         (JEL E31, E32, E44, E52, R21)

   “The population is not distributed between                         A long tradition in economics, starting with
   debtors and creditors randomly. Debtors                         Irving Fisher’s (1933) debt-deflation explana-
   have borrowed for good reasons, most of                         tion of the Great Depression, considers financial
   which indicate a high marginal propensity                       factors as key elements of business cycles. In
   to spend from wealth or from current in-                        this view, deteriorating credit market condi-
   come or from any other liquid resources
   they can command. Typically their indebt-                       tions, like growing debt burdens and falling
   edness is rationed by lenders [...]. Business                   asset prices, are not just passive reflections of a
   borrowers typically have a strong propen-                       declining economy, but are themselves a major
   sity to hold physical capital [...]. Their de-                  factor depressing economic activity.
   sired portfolios contain more capital than                         Although this “credit view” has a long his-
   their net worth [...]. Household debtors are                    tory, most theoretical work on this subject had
   frequently young families acquiring homes                       been partial equilibrium in nature until the late
   and furnishings before they earn incomes to                     1980s, when Ben Bernanke and Mark Gertler
   pay for them outright; given the difficulty of                  (1989) formalized these ideas in a general equi-
   borrowing against future wages, they are                        librium framework. Following their work, var-
   liquidity-constrained and have a high mar-
   ginal propensity to consume.”                                   ious authors have presented dynamic models in
    —James Tobin, Asset Accumulation and                           which financing frictions on the firm side may
                            Economic Activity                      amplify or propagate output fluctuations in re-
                                                                   sponse to aggregate disturbances: examples in-
                                                                   clude the real models of Nobuhiro Kiyotaki and
   * Department of Economics, Boston College, Chestnut             John Moore (1997) and Charles Carlstrom and
Hill, MA 02467 (e-mail: I am deeply
indebted to my Ph.D. advisor at the London School of
                                                                   Timothy Fuerst (1997), and the sticky-price
Economics, Nobuhiro Kiyotaki, for his continuous help and          model of Bernanke et al. (1999). Empirically,
invaluable advice. I thank Fabio Canova, Raffaella Giaco-          various studies have shown that firms’ invest-
mini, Christopher House, Peter Ireland, Raoul Minetti,             ment decisions are sensitive to various measures
Claudia Oglialoro, François Ortalo-Magné, Marina Pavan,          of the firms’ net worth (see Glenn Hubbard,
Christopher Pissarides, Fabio Schiantarelli, two anonymous
referees, and seminar participants at the Bank of England,         1998, for a review). At the same time, evidence
Boston College, the European Central Bank, the Ente Luigi          of financing constraints at the household level
Einaudi, the Federal Reserve Bank of New York, the Fed-            has been widely documented by Stephen Zeldes
eral Reserve Bank of St. Louis, the London School of               (1989), Tullio Jappelli and Marco Pagano
Economics, the NBER Monetary Economics Meeting, and
Northeastern University for their helpful comments on var-
                                                                   (1989), John Campbell and Gregory Mankiw
ious versions of this work. Viktors Stebunovs provided             (1989), and Christopher Carroll and Wendy
superb research assistance.                                        Dunn (1997).
740                                       THE AMERICAN ECONOMIC REVIEW                                           JUNE 2005

   While these studies have highlighted the im-                 itive demand shock. When demand rises, con-
portance of financial factors for macroeconomic                 sumer and asset prices increase: the rise in asset
fluctuations, to date there has been no system-                 prices increases the borrowing capacity of the
atic evaluation of the extent to which a general                debtors, allowing them to spend and invest
equilibrium model with financial frictions can                  more. The rise in consumer prices reduces the
explain the aggregate time-series evidence on                   real value of their outstanding debt obligations,
the one hand, and be used for monetary policy                   positively affecting their net worth. Given that
analysis on the other. This is the perspective                  borrowers have a higher propensity to spend
adopted here. From the modeling point of view,                  than lenders, the net effect on demand is posi-
my starting point is a variant of the Bernanke et               tive, and acts as a powerful amplification mech-
al. (1999) new-Keynesian setup in which en-                     anism. However, while it amplifies the demand
dogenous variations in the balance sheet of the                 shocks, consumer price inflation dampens the
firms generate a “financial accelerator” by en-                 shocks that induce a negative correlation between
hancing the amplitude of business cycles. To                    output and inflation: for instance, adverse supply
this framework, I add two main features: collat-                shocks are beneficial to borrowers’ net worth if
eral constraints tied to real estate values for                 obligations are held in nominal terms. Hence, un-
firms, as in Kiyotaki and Moore (1997); and, for                like the previous papers, the financial accelerator
a subset of the households, nominal debt. The                   really depends on where the shocks come from:
reason for housing1 collateral is practical and                 the model features an accelerator of demand
substantial: practical because, empirically, a                  shocks, and a “decelerator” of supply shocks.
large proportion of borrowing is secured by real                   The transmission mechanism described above
estate; substantial because, although housing                   is at the root of the model’s success in explaining
markets seem to play a role in business fluctu-                 two salient features of the data. First, collateral
ations,2 the channels by which they affect the                  effects on the firm and the household allow match-
economy are far from being understood. The                      ing the positive response of spending to a housing
reason for having nominal debt comes from the                   price shock.3 Second, nominal debt allows the
widespread observation that, in low-inflation                   model to replicate the hump-shaped dynamics of
countries, almost all debt contracts are in nom-                spending to an inflation shock.4 Such improve-
inal terms, even if they appear hard to justify on              ments in the model’s ability to reflect short-run
welfare-theoretic grounds: understanding their                  dynamic properties are especially important,
implications for macroeconomic outcomes is a                    given that several studies (e.g., Jordi Galı́, 2004;
crucial task.                                                   Peter Ireland, 2004b) have stressed the role of
   In addition, I ask whether the model is able to              nontechnology and nonmonetary disturbances
explain both key business cycle facts and the                   in understanding business fluctuations.
interaction between asset prices and economic                      Finally, I address and answer two important
activity. To this end, I estimate the key struc-                policy questions. First, I find that allowing the
tural parameters by minimizing the distance be-                 monetary authority to respond to asset prices
tween the impulse responses implied by the                      yields negligible gains in terms of output and
model and those generated by an unrestricted                    inflation stabilization. Second, I find that nom-
vector autoregression. The estimates are both                   inal (vis-à-vis indexed) debt yields an improved
economically plausible and statistically signifi-               output-inflation variance trade-off for the cen-
cant. They also provide support for the two                     tral bank: this happens because the sources of
main features of the model (collateral con-                     trade-offs in the model do not get amplified,
straints and nominal debt). In the concluding                   since such shocks, ceteris paribus, transfer re-
part of the paper, therefore, I use the estimated               sources from lenders to borrowers during a
model for quantitative policy analysis.                         downturn.
   The model transmission mechanism works as
follows. Consider, for sake of argument, a pos-
                                                                      In the VAR below I document a significant two-way
                                                                interaction between housing prices and GDP. Aggregate de-
     With a slight abuse of notation, I use the terms “real     mand effects from changes in housing wealth have also been
estate,” “assets,” and “houses” interchangeably in the paper.   documented elsewhere; see, for instance, Case et al. (2001).
   2                                                                4
     See, for instance, International Monetary Fund (2000);           See, for instance, Jeffrey Fuhrer (2000), as well as the
Matthew Higgins and Carol Osler (1997); Karl Case (2000).       VAR evidence below.

                                    FIGURE 1. VAR EVIDENCE, UNITED STATES
Notes: VAR estimated from 1974Q1 to 2003Q2. The dashed lines indicate 90-percent confidence bands. The Choleski
ordering of the impulse responses is R, ␲, q, Y. Coordinate: percent deviation from the baseline.

   The paper is organized as follows. Section I          from a VAR with detrended real GDP (Y),
presents some VAR evidence on housing prices             change in the log of GDP deflator (␲), de-
and the business cycle. Section II presents the          trended real house prices (q), and Fed Funds
basic model. Section III extends the basic model         rate (R) from 1974Q1 to 2003Q2.5 I use this
by including a constrained household sector and          VAR to document the key relationships in
by allowing for variable capital. Section IV esti-       the data and, later in the paper, to choose the
mates the structural parameters of the model. Sec-
tion V analyzes its dynamics, while Section VI
looks at housing prices and debt indexation for the          5
formulation of systematic monetary policy. Con-                The Fed Funds rate is the average value in the first
                                                         month of each quarter. The house price series (deflated with
cluding remarks are contained in Section VII.            the GDP deflator) is the Conventional Mortgage Home
                                                         Price Index from Freddie Mac. The VAR included a time
  I. VAR Evidence on Housing Prices and the              trend, a constant, a shift dummy from 1979Q4, and one lag
               Business Cycle                            of the log of the CRB commodity spot price index. Two lags
                                                         of each variable were chosen according to the Hannah-
                                                         Quinn criterion. The logs of real GDP and real housing
  Figure 1 presents impulse responses (with              prices were detrended with a band-pass filter that removed
90-percent bootstrapped confidence bands)                frequencies above 32 quarters.
742                                THE AMERICAN ECONOMIC REVIEW                                            JUNE 2005

parameters of the extended model in a way to          estate is fixed in the aggregate, however, which
match the VAR impulse responses.                      guarantees a variable price of housing. This
   Here and in the rest of the paper, the variables   assumption is not crucial to the propagation
are expressed in percentages and in quarterly         mechanism: I will show below that collateral
rates. The shocks are orthogonalized in the or-       effects can generate sizeable amplification, even
der R, ␲, q, and Y. The ordering did not affect       when the share of real estate in production is
the results substantially: as I will show below,      small.
such an ordering also renders the VAR and the            As their activities are somewhat conven-
model more directly comparable. The results           tional, I start with the patient households’
suggest that a model of the interaction between       problem.
house prices and the business cycle has to de-
liver:                                                                A. Patient Households

(a) A negative response of nominal prices, real          The household sector (denoted with a prime)
    housing prices, and GDP to tight money            is standard, with the exception of housing (ser-
    (Figure 1, first row);                            vices) in the utility function.6
(b) A significant negative response of real              Households maximize a lifetime utility func-
    housing prices and a negative but small           tion given by
    response of output to a positive inflation

                                                            冘 ␤ 共ln c⬘⫹ j ln h⬘⫺ 共L⬘兲 /␩ ⫹ ␹ ln共M⬘/P 兲兲
    disturbance (second row); and                            ⬁
(c) A positive comovement of asset prices and                     t                              ␩
                                                      E0                t            t       t                 t   t
    output in response to asset price shocks                t⫽0
    (third row) and to output shocks (fourth
    row). Taken together, the two rows high-          where E0 is the expectation operator, ␤ 僆 (0, 1)
    light a two-way interaction between hous-         is the discount factor, c⬘t is consumption at t, h⬘t
    ing prices and output.                            denotes the holdings of housing, L⬘t are hours of
                                                      work (households work for the entrepreneurs),
  In the rest of the paper, I develop and esti-       and M⬘t /Pt are money balances divided by the
mate a model that is consistent with these facts      price level. Denote with qt ⬅ Qt/Pt the real
and that can be used for policy analysis. I start     housing price, with w⬘t ⬅ W⬘t /Pt the real wage.
with a basic model, which conveys the intuition.      Assume that households lend in real terms ⫺b⬘t
                                                      (or borrow b⬘t ⬅ B⬘t /Pt) and receive back
              II. The Basic Model                     ⫺Rt ⫺ 1B⬘t ⫺ 1/Pt, where Rt ⫺ 1 is the nominal in-
                                                      terest rate on loans between t ⫺ 1 and t, so that
   Consider a discrete time, infinite horizon         obligations are set in money terms. Denoting
economy, populated by entrepreneurs and pa-           with ⌬ the first difference operator, the flow of
tient households, infinitely lived and of measure     funds is
one. The term “patient” captures the assumption
that households have lower discount rates than        (1)         c⬘t ⫹ q t ⌬h⬘t ⫹ R t ⫺ 1 b⬘t ⫺ 1 / ␲ t
firms and distinguishes this group from the im-
patient households of the extended model (in                          ⫽ b⬘t ⫹ w⬘t L⬘t ⫹ Ft ⫹ T⬘t ⫺ ⌬M⬘t /Pt
Section III). Entrepreneurs produce a homoge-
neous good, hiring household labor and com-           where ␲t ⬅ Pt/Pt ⫺ 1 denotes the gross inflation
bining it with collateralizable real estate.          rate, Ft are lump-sum profits received from the
Households consume, work, and demand real
estate and money. In addition, there are retailers
and a central bank. Retailers are the source of          6
                                                           Javier Diaz-Gimenez et al. (1992) use a similar device
nominal rigidity. The central bank adjusts            in an OLG model of the banking and household sector. I do
money supply and transfers to support an inter-       not include imputed rents in my model definition of output;
est rate rule.                                        this does not affect the results of the paper in any significant
                                                      way. I also assume that housing and consumption are sep-
   In order to have effects on economic activity      arable: Bernanke (1984) studies the joint behavior of the
from shifts in asset holdings, I allow housing        consumption of durable and nondurable goods and finds that
investment by both sectors. I assume that real        separability across goods is a good approximation.

retailers (described below), and the last two                      b t ⱕ mE t 共q t ⫹ 1 h t ␲ t ⫹ 1 /R t 兲.
terms are net transfers from the central bank that
are financed by printing money. Solving this            To make matters interesting, one wants a
problem yields first-order conditions for con-       steady state in which the entrepreneurial return
sumption (2), labor supply (3), and housing          to savings is greater than the interest rate, which
demand (4):                                          implies a binding borrowing constraint. At the

                             冉               冊
                                                     same time, one has to ensure that entrepreneurs
                1              Rt                    will not postpone consumption and quickly ac-
(2)                 ⫽ ␤Et
                c⬘t       ␲ t ⫹ 1 c⬘t ⫹ 1            cumulate wealth so that they are completely
                                                     self-financed and the borrowing constraint be-
(3)                 w⬘t ⫽ 共L⬘t 兲 ␩ ⫺ 1c ⬘t           comes nonbinding. To deal with this problem, I
                                                     assume that entrepreneurs discount the future
                qt  j
                   ⫽ ⫹ ␤Et
                c⬘t h⬘t
                           qt ⫹ 1
                           c⬘t ⫹ 1
                                   .冉 冊              more heavily than households. They maximize

                                                                                  冘 ␥ ln c
   The first-order condition with respect to                                 E0          t
M⬘t /Pt yields a standard money demand equa-                                      t⫽0
tion. Since I focus in what follows on interest
rates rules, money supply will always meet           where ␥ ⬍ ␤,7 subject to the technology con-
money demand at the desired equilibrium nom-         straint, the borrowing constraint, and the fol-
inal interest rate. As utility is separable in       lowing flow of funds:
money balances, the quantity of money has no
implications for the rest of the model, and can      (6)        Y t /X t ⫹ b t ⫽ c t ⫹ q t ⌬h t
be ignored.
                                                                                   ⫹ Rt ⫺ 1 bt ⫺ 1 /␲t ⫹ w⬘t Lt
                  B. Entrepreneurs
                                                     where Rt ⫺ 1bt ⫺ 1/␲t in (6) reflects the assump-
   Entrepreneurs use a Cobb-Douglas constant         tion that debt contracts are set in nominal terms,
returns-to-scale technology that uses real estate    so that price changes between t ⫺ 1 and t can
and labor as inputs. They produce an interme-        affect the realized real interest rate. I use this
diate good Yt according to                           assumption on empirical grounds: in low-inflation
                                                     countries, almost all debt contracts are set in
(5)             Y t ⫽ A共h t ⫺ 1 兲 ␯ 共L t 兲 1 ⫺ ␯     nominal terms.8

where A is the technology parameter, h is real             Entrepreneurs are not risk neutral. Models of agency
                                                     costs and business cycles typically assume risk-neutral en-
estate input, and L is the labor input. Output       trepreneurs. Carlstrom and Fuerst (2001) discuss the issue.
cannot be transformed immediately into con-          In modeling firms’ behavior in a model of monetary shocks,
sumption ct: following Bernanke et al. (1999), I     agency costs, and business cycle, they consider two alter-
assume that retailers purchase the intermediate      natives. In one, entrepreneurs are infinitely lived, risk neu-
good from entrepreneurs at the wholesale price       tral, and more impatient than households: net worth sharply
                                                     responds to shocks, as the elasticity of entrepreneurial sav-
Pwt and transform it into a composite final good,    ings to changes in the real rate of interest is infinite. In the
whose price index is Pt. With this notation, Xt ⬅    other, a constant fraction of entrepreneurs dies each period, so
Pt /Pw
     t denotes the markup of final over interme-     that net worth responds passively and slowly to changes in the
diate goods.                                         real rate: in the aggregate, this is equivalent to a formulation in
                                                     which entrepreneurs are extremely risk averse. Log utility can
   As in Kiyotaki and Moore (1997), I assume a       be considered as shorthand between these two extremes.
limit on the obligations of the entrepreneurs.           8
                                                           With risk-averse agents, nobody seems to get any ben-
Suppose that, if borrowers repudiate their debt      efit in terms of expected utility from lack of indexation:
obligations, the lenders can repossess the bor-      presumably, if contracts were indexed, there would be wel-
rowers’ assets by paying a proportional trans-       fare gains. However, surprisingly few loan contracts are
                                                     indexed in the United States, where even 30-year govern-
action cost (1 ⫺ m) Et(qt ⫹ 1ht). In this case the   ment and corporate bonds are not indexed. In Sections II E
maximum amount Bt that a creditor can borrow         and VI A, I discuss how the results of the paper change
is bound by mEt(Qt ⫹ 1ht /Rt). In real terms:        when indexed debt is assumed.
744                                         THE AMERICAN ECONOMIC REVIEW                                     JUNE 2005

   Define ␭t as the time t shadow value of the             In this case, the model would become asymmet-
borrowing constraint. The first-order conditions           ric around its stationary state. In bad times,
for an optimum are the consumption Euler                   entrepreneurs would be constrained; in good
equation, real estate demand, and labor demand:            times, they might be unconstrained. In such a
                                                           case, a linear approximation around the deter-
             ⫽ Et    冉 冊
                  ␲t ⫹ 1 ct ⫹ 1
                                ⫹ ␭t Rt
                                                           ministic steady state might give misleading re-
                                                           sults. In the paper, I take as given that
                                                           uncertainty is “small enough” relative to degree

           qt ⫽ Et
                      冉 冉
                   ct ⫹ 1
                             Yt ⫹ 1
                            Xt ⫹ 1 ht
                                      ⫹ qt ⫹ 1       冊     of impatience so as to rule out this possibility.
                                                           In Appendix C, I present evidence from nonlin-
                                                           ear simulations that backs this assumption.9

                        ⫹ ␭t m␲t ⫹ 1 qt ⫹ 1   冊                                   C. Retailers

                                                              To motivate sticky prices I assume implicit
(9)          w⬘t ⫽ 共1 ⫺ ␯ 兲Y t /共X t L t 兲.                costs of adjusting nominal prices and, as in
                                                           Bernanke et al. (1999), monopolistic competi-
      Both the Euler and the housing demand                tion at the retail level. A continuum of retailers
equations differ from the usual formulations be-           of mass 1, indexed by z, buy intermediate goods
cause of the presence of ␭t, the Lagrange multi-           Yt from entrepreneurs at Pw    t in a competitive
plier on the borrowing constraint. ␭t equals the           market, differentiate the goods at no cost into
increase in lifetime utility that would stem from          Yt(z), and sell Yt(z) at the price Pt(z). Final
borrowing Rt dollars, consuming (equation [7]) or          goods are Y ft ⫽ (兰10 Yt(z)␧ ⫺ 1/␧ dz)␧/␧ ⫺ 1 where
investing (equation [8]) the proceeds, and reduc-          ␧ ⬎ 1. Given this aggregate output index,10 the
ing consumption by an appropriate amount the               price index is Pt ⫽ (兰10 Pt(z)1 ⫺ ␧ dz)1/1 ⫺ ␧, so that
following period.                                          each retailer faces an individual demand curve
   Without uncertainty, the assumption ␥ ⬍ ␤               of Yt(z) ⫽ (Pt(z)/Pt)⫺␧Y ft.
guarantees that entrepreneurs are constrained in              Each retailer chooses a sale price Pt(z) taking
and around the steady state. In fact, the steady-          Pwt and the demand curve as given. The sale
state consumption Euler equation for the house-            price can be changed in every period only with
hold implies, with zero inflation, that R ⫽ 1/␤,           probability 1 ⫺ ␪. Denote with P*t(z) the “reset”
the household time preference rate. Combining              price and with Y*t ⫹ k(z) ⫽ (P*t(z)/Pt ⫹ k)⫺␧Yt ⫹ k
this result with the steady-state entrepreneurial          the corresponding demand. The optimal P*t(z)
Euler equation for consumption yields: ␭ ⫽                 solves:
(␤ ⫺ ␥)/c ⬎ 0. Therefore, the borrowing con-
straint will hold with equality:                           (11)

                                                             冘 ␪ E 再 ⌳ 冉 PP*共z兲 ⫺ XX 冊 Y* 共z兲冎 ⫽ 0
(10)       b t ⫽ mE t 共q t ⫹ 1 h t ␲ t ⫹ 1 /R t 兲.            ⬁
                                                                    k              t
                                                                        t   t,k                        t⫹k
   Matters are of course thornier when there is                                    t⫹k         t⫹k
uncertainty. The concavity of the objective
function implies in fact that, in some states of
the world, entrepreneurs might “self-insure” by               9
                                                                The Appendix is available on the AER Web site (http://
borrowing less than their credit limit so as to   Specifically, I construct a
buffer their consumption against adverse                   partial equilibrium model of consumption and housing
                                                           choice which features an amount of volatility and a borrow-
shocks. That is, there is some target level of             ing limit similar to that assumed here. I show that the
their net worth such that, if their actual net             conditions under which precautionary saving arises are very
worth falls short of that target, the precautionary        restrictive if the volatility is parameterized to reflect the
saving motive might outweigh impatience, and               amount observed in macroeconomic aggregates.
entrepreneurs will try to restore some assets,                    The CES aggregate production function makes exact
                                                           aggregation difficult. However, a linear aggregator of the
borrowing less than the limit. Specifically, en-           form Y ft ⫽ 兰10 Yt(z) dz equals Yt within a local region of the
trepreneurs might not hit the borrowing limit              steady state. In what follows, I will consider total output
after a sufficiently long run of positive shocks.          as Yt.
VOL. 95 NO. 3       IACOVIELLO: HOUSE PRICES, BORROWING CONSTRAINTS, AND MONETARY POLICY                                                745

where ⌳t,k ⫽ ␤k(c⬘t /c⬘t ⫹ k) is the patient household                    forever. The equilibrium is an allocation {ht, h⬘t,
relevant discount factor and Xt is the markup,                            Lt, L⬘t, Yt, ct, c⬘t, bt, b⬘t}⬁
                                                                                                        t⫽0 together with the
which in steady state equals X ⫽ ␧/(␧ ⫺ 1). This                          sequence of values {w⬘t, Rt, Pt, P*t, Xt, ␭t, qt}⬁
condition states that P*t equates expected dis-                           satisfying equations (2) to (13) and the market
counted marginal revenue to expected dis-                                 clearing conditions for labor (Lt ⫽ L⬘t), real
counted marginal cost. Profits Ft ⫽ (1 ⫺ 1/Xt)Yt                          estate (ht ⫹ h⬘t ⫽ H), goods (ct ⫹ c⬘t ⫽ Yt), and
are finally rebated to patient households.                                loans (bt ⫹ b⬘t ⫽ 0), given {ht ⫺ 1, Rt ⫺ 1, bt ⫺ 1,
   As a fraction ␪ of prices stays unchanged, the                         Pt ⫺ 1} and the sequence of monetary shocks
aggregate price level evolution is                                        {eR,t}, together with the relevant transversality
(12) P t ⫽ 共 ␪ P t␧1−ε
                    ⫺ 1 ⫹ 共1 ⫺ ␪ 兲共P *
                                        1 ⫺ ␧ 1/共1 ⫺ ␧兲
                                             兲          .                    Appendix A describes the steady state. Let
                                                                          hatted variables denote percent changes from
   Combining (11) and (12) and linearizing                                the steady state, and those without subscript
yields a forward-looking Phillips curve, which                            denote steady-state values. The model can be
states that inflation depends positively on ex-                           reduced to the following linearized system
pected inflation and negatively on the markup Xt                          (which I solve numerically using the methods
of final over intermediate goods.                                         described by Harald Uhlig, 1999):

D. Central Bank Policy and the Interest Rate                              (L1)            Ŷ t ⫽ 共c/Y兲ĉ t ⫹ 共c⬘/Y兲ĉ⬘t
                                                                          (L2)                 ĉ⬘t ⫽ E t ĉ⬘t ⫹ 1 ⫺ rr
   The central bank makes lump sum transfers
of money to the real sector to implement a                                (L3)     cĉ t ⫽ bb̂ t ⫹ Rb共 ␲ˆ t ⫺ R̂ t ⫺ 1 ⫺ b̂ t ⫺ 1 兲
Taylor-type interest rate rule. The rule takes the
                                                                                            ⫹ 共␯Y/X兲共Ŷt ⫺ X̂t 兲 ⫺ qh⌬ĥt
                             1 ⫹ r␲                      1 ⫺ rR
(13) R t ⫽ 共R t ⫺ 1 兲 共 ␲
                             t⫺1      共Y t ⫺ 1 /Y兲 rr兲
                                                                  e R,t
                                                                          (L4)        q̂ t ⫽ ␥ e E t q̂ t ⫹ 1 ⫹ 共1 ⫺ ␥ e 兲E t
where rr and Y are steady-state real rate and
output, respectively. Here, monetary policy re-                                                ⫻ 共Ŷt ⫹ 1 ⫺ ĥt ⫺ X̂t ⫹ 1 兲
sponds systematically to past inflation and past
output.11 If rR ⬎ 0, the rule allows for interest                                              ⫺ m␤rr
                                                                                                   ˆt ⫺ 共1 ⫺ m␤兲Et⌬ĉt ⫹ 1
rate inertia. eR,t is a white noise shock process
with zero mean and variance ␴2e .                                         (L5) q̂ t ⫽ ␤ E t q̂ t ⫹ 1 ⫹ ␫ ĥ t ⫹ ĉ⬘t ⫺ ␤ E t ĉ⬘t ⫹ 1

                    E. Equilibrium                                        (L6)            b̂ t ⫽ E t q̂ t ⫹ 1 ⫹ ĥ t ⫺ rr

   Absent shocks, the model has a unique sta-                                                      ␩␯
tionary equilibrium in which entrepreneurs hit                            (L7)        Ŷ t ⫽               ĥ
the borrowing constraint and borrow up to the                                                  ␩ ⫺ 共1 ⫺ ␯ 兲 t ⫺ 1
limit, making the interest payments on the debt
and rolling the steady-state stock of debt over                                                       1⫺␯
                                                                                               ⫺              共X̂ ⫹ ĉ⬘t 兲
                                                                                                   ␩ ⫺ 共1 ⫺ ␯兲 t

                                                                                            ␲ˆ t ⫽ ␤ E t ␲ˆ t ⫹ 1 ⫺ ␬ X̂ t
      A backward-looking Taylor rule has the advantage of                 (L8)
isolating in a neat way the exogenous component of mon-
etary policy from its endogenous counterpart. As will be
shown later, given that the interest rate is assumed to re-               (L9) R̂ t ⫽ 共1 ⫺ r R 兲共共1 ⫹ r ␲ 兲 ␲ˆ t ⫺ 1 ⫹ r Y Ŷ t ⫺ 1 兲
spond only with one lag to all other variables, it offers some
convenient zero restrictions when taking the model to the                                 ⫹ rRR̂t ⫺ 1 ⫹ êR,t
data. Fuhrer (1997) shows that the data offer more support
for a backward rule than for a forward rule. Bennett Mc-
Callum (1999) has emphasized a related point, since output                where ␫ ⬅ (1 ⫺ ␤)h/h⬘, ␬ ⬅ (1 ⫺ ␪ )(1 ⫺ ␤␪ )/␪,
and inflation data are reported with a lag and therefore
cannot be known to the policymaker in the current quarter.                ␥e ⬅ m␤ ⫹ (1 ⫺ m)␥, and rrˆt ⬅ R̂t ⫺ Et␲ˆ t ⫹ 1 is
746                                 THE AMERICAN ECONOMIC REVIEW                                       JUNE 2005

the ex ante real rate. (L1) is total output. (L2) is   plays a role, too: as obligations are not indexed,
the Euler equation for household consumption.          deflation raises the cost of debt service, further
(L3) is the entrepreneurial flow of funds. (L4)        depressing entrepreneurial consumption and
and (L5) express the consumption/housing mar-          investment.
gin for entrepreneurs and households, respec-             How big are these effects? Figure 2 provides
tively. (L6) is the borrowing constraint. The          a stylized answer for three economies subject to
supply side includes the production function           the same shock, showing the total loss in output
(L7) (combined with labor market clearing) and         following a one-standard deviation increase
the Phillips curve (L8). Finally, (L9) is the          (0.29 percent on a quarterly basis) of the interest
monetary policy rule.                                  rate.12 The solid line illustrates the case when
                                                       both collateral and debt deflation effects are
 F. The Transmission Mechanism: Indexation             shut off, so that only the interest rate channel
           and Collateral Effects                      works (see Appendix B for the technical de-
                                                       tails): output falls by 3.33 percent. Here, the
   The basic model shows the key links between         output drop is mainly driven from intertemporal
the interest rate channel, the house price chan-       substitution in consumption. The dashed line
nel, and the debt deflation channel. I now focus       plots the response of output when the collateral
on one standard deviation (as estimated in the         channel becomes operational: the decline in
VAR) negative monetary shock; in the full              output is larger, and the total decline is 3.82
model, I will look at other disturbances, too, and     percent. Finally, in the starred line, both collat-
will estimate some of the structural parameters        eral and debt deflation channels are at work:
of the model. The parameters chosen here re-           output falls by 4.42 percent.13
flect the estimates and the calibration of the full
model.                                                         III. The Full Model: Household and
   The time period is one quarter. The entrepre-                      Entrepreneurial Debt
neurial “loan-to-value” ratio m is set to 0.89.
The probability of not changing prices ␪ is set to        The basic model assumes that all mortgaged
0.75. The discount factors are ␤ ⫽ 0.99 and ␥ ⫽        real estate is used by firms. In reality, financial
0.98. I set the elasticity of output to real estate    frictions apply to both firms and households.
␯ to 0.03. (With j ⫽ 0.1, this yields a steady         The previous section models entrepreneurial
state value of h, the entrepreneurial asset share,     consumption, but lacks the descriptive realism
of 20 percent.) The household labor supply             emphasized, for example, in the quote from
schedule is assumed to be virtually flat: ␩ ⫽          Tobin at the beginning of the paper. In addition,
1.01.                                                  investment occurs in the form of real estate
   For the Taylor rule, I set rY ⫽ 0, r␲ ⫽ 0.27,       transfers between agents, but net investment is
rR ⫽ 0.73. These are the parameters of an              zero. Before taking the model to the data, I
estimated policy rule for the VAR period, with         extend it along two dimensions. On the one
the exception of rY, which is reset to zero.           hand, I add a constrained, impatient household
Imposing rY ⫽ 0 amplifies the financial accel-         sector, that ends up facing a binding borrowing
erator since the central bank does not intervene       constraint in equilibrium. On the other, I allow
when output falls. However, it allows isolating        variable capital investment for the entrepre-
the exogenous component of the reaction func-          neurs. This allows a more realistic analysis of
tion from its endogenous component, while en-          the impact of a various range of disturbances: in
suring determinacy of the rational expectations
   The transmission mechanism is simple: con-             12
                                                             The figure shows the cumulative drop in output after
sider a negative monetary shock. With sticky           40 quarters. This is approximately the horizon at which
prices, monetary actions affect the real rate, and     output has returned to the baseline, so that the cumulative
its increase works by discouraging current con-        impulse responses level off.
sumption and hence output. The effect is rein-               It would be tempting to rank the two effects. There is
                                                       no way of doing so, however. For instance, depending on
forced through the fall in housing prices, which       how aggressive the central bank is on inflation, the debt
leads to lower borrowing and lower entrepre-           deflation effect can be larger or smaller than the collateral
neurial housing investment. Debt deflation             effect.
VOL. 95 NO. 3          IACOVIELLO: HOUSE PRICES, BORROWING CONSTRAINTS, AND MONETARY POLICY                                           747

                                       COMPARISON BETWEEN ALTERNATIVE MODELS
                   Notes: Ordinate: time horizon in quarters. Coordinate: percent deviation from initial steady

particular, I add inflation, technology, and taste                           symmetric for each agent: such a cost might
shocks. As before, a central bank and retailers                              proxy for transaction costs, conversion costs of
complete the model.                                                          residential housing into commercial housing
   The problems of patient households, retailers,                            and vice versa, and so on. The remainder of the
and the central bank are unchanged. I consider                               problem is unchanged: entrepreneurs maximize
therefore the slightly modified entrepreneurial                              E0 ¥⬁ t⫽0 ␥ log ct, where ␥ ⬍ ␤, subject to

problem and then move to impatient households.                               technology (14) and borrowing constraint (10),
                                                                             as well as the flow of funds constraint:

                      A. Entrepreneurs
                                                                             (15) Y t /X t ⫹ b t ⫽ c t ⫹ q t ⌬h t ⫹ R t ⫺ 1 b t ⫺ 1 / ␲ t
  Entrepreneurs produce the intermediate good
                                                                                                      ⫹ w⬘t L⬘t ⫹ w⬙t L⬙t ⫹ It
according to:
                                                                                                      ⫹ ␰e,t ⫹ ␰K,t .
(14) Yt ⫽ A t K t␮⫺ 1 h t␯⫺ 1 L⬘t ␣ 共1 ⫺ ␮ ⫺ ␯ 兲 L ⬙t 共1 ⫺ ␣ 兲共1 ⫺ ␮ ⫺ ␯ 兲

where At is random. L⬘ and L⬙ are the patient                                The first-order conditions for this problem
and impatient household labor (␣ measures the                                are fairly standard and are reported in Appen-
relative size of each group) and K is capital (that                          dix A.
depreciates at rate ␦) created at the end of each
period. For both housing and variable capital, I                                           B. Impatient Households
consider the possibility of adjustment costs:
capital installation entails a cost ␰K,t ⫽ ␺(It /                              Impatient households discount the future
Kt ⫺ 1 ⫺ ␦)2Kt ⫺ 1/(2␦), where It ⫽ Kt ⫺ (1 ⫺                                more heavily than the patient ones. They choose
␦) Kt ⫺ 1. For housing, changing the stock entails                           consumption c⬙t, housing h⬙t, labor L⬙t (and
a cost ␰e,t ⫽ ␾e(⌬ht /ht ⫺ 1)2qtht ⫺ 1/2, which is                           money M⬙t/Pt) to maximize
748                                              THE AMERICAN ECONOMIC REVIEW                            JUNE 2005

                                                                 moving to the estimation strategy, I present two
            冘 共␤⬙兲 共ln c⬙⫹ j ln h⬙⫺ 共L⬙兲 /␩

       E0               t                                ␩       direct implications of the main model features
                                t     t      t       t
                                                                 which can replicate key dynamic correlations in
                                                                 the data: the collateral effect allows pinning
                            ⫹ ␹ ln M⬙t /Pt )                     down the elasticity of consumption to a housing
                                                                 preference shock; the nominal debt effect allows
where ␤⬙ ⬍ ␤. Like for entrepreneurs, this guar-                 matching the delayed response of output to an
antees an equilibrium in which impatient house-                  inflation shock.
holds will hit the borrowing constraint. Here,
the subscript under jt allows for random distur-                     D. Collateral Effects and Effects on
bances to the marginal utility of housing, and,                     Consumption of a Housing Price Shock
given that it directly affects housing demand,
offers a parsimonious way to assess the macro                        Several commentators have expressed the
effects of an exogenous disturbance on house                     consideration that rising house prices have kept
prices.14 The flow of funds and the borrowing                    consumption growth high throughout the 1990s.
limit are                                                        Case et al. (2001) find long-run elasticities of
                                                                 consumption to housing prices of around 0.06
(16)     c ⬙t ⫹ q t ⌬h ⬙t ⫹ R t ⫺ 1 b ⬙t ⫺ 1 / ␲ t               for a panel of U.S. states. Morris Davis and
                                                                 Michael Palumbo (2001) estimate a long-run
            ⫽ b⬙t ⫹ w⬙t L⬙t ⫹ T⬙t ⫺ ⌬M⬙t /Pt ⫺ ␰h,t              elasticity of consumption to housing wealth of
                                                                 0.08. These positive elasticities are hard to rec-
(17)         b ⬙t ⱕ m⬙E t 共q t ⫹ 1 h ⬙t ␲ t ⫹ 1 /R t 兲           oncile with the traditional life-cycle model.
                                                                 Think about the simplest case, an exogenous
where ␰h,t ⫽ ␾h(⌬h⬙t/h⬙t ⫺ 1)2qth⬙t ⫺ 1/2 denotes the            increase in housing prices. If the gains were
housing adjustment cost (an analogous term                       equally distributed across the entire population,
also appears in the budget constraint of the                     if all agents had the same propensity to con-
patient households). The borrowing constraint                    sume, and if all agents were to spend these gains
is consistent with standard lending criteria used                on housing, total wealth less housing wealth
in the mortgage market, which limit the amount                   would remain unchanged, and so would the
lent to a fraction of the value of the asset. One                demand for non-housing consumption. However,
can interpret the case m⬙ ⫽ 0 as the limit situ-                 if liquidity-constrained households value current
ation when housing is not collateralizable at all,               consumption a great deal, they may be able to
so that households are excluded from financial                   increase their borrowing and consumption more
markets.                                                         than proportionally when housing prices rise, so
   Like for the entrepreneurs, the equations for                 that increases in prices might have positive ef-
consumption and housing choice (shown in Ap-                     fects on aggregate demand.
pendix A) hold with the addition of the multi-                       The mechanism described above is at work
plier associated with the borrowing restriction.15               in the paper, and it is straightforward in dem-
                                                                 onstrating its ability to produce an empiri-
              C. The Linearized Model                            cally plausible response of consumption to
                                                                 housing price shocks. Figure 3 displays the
   The equations describing the steady-state and                 impulse response of consumption to a persis-
the linearized model are isomorphic to those of                  tent housing price increase, generated from a
the basic model and are in Appendix A. Before                    shock to the marginal rate of substitution j
                                                                 between housing and consumption for all
                                                                 households. Such an experiment offers a par-
      I assume that the disturbance to jt is common to both      simonious way to model any kind of distur-
impatient and patient households. This way, variations in jt     bance that shifts housing demand, such as
can also proxy for exogenous variations in, say, the tax code    temporary tax advantages to housing invest-
that shift housing demand for all households.                    ment or a sudden increase in demand fuelled
      The money demand condition is redundant under in-
terest rate control, so long as the central bank respects, for   by optimistic consumer expectations. The pa-
each group, the equality between money injections and            rameters are those calibrated and estimated
transfers.                                                       using the method described in Section IV,

                                                  VALUES OF m AND m⬙
                Notes: Ordinate: time horizon in quarters. Coordinate: percent deviation from initial steady

except that here I compute responses for sev-                   loan-to-value ratios of 89 percent for entre-
eral values of the loan-to-values m and m⬙,                     preneurial loans and 55 percent for residential
and compare them with the impulse response                      loans, can generate responses of consumption
from a housing price shock in a VAR.                            (and income, as will be shown below) to a
   The VAR is estimated from 1974Q1 to                          housing price shock that are not only qualita-
2003Q2 on quarterly data for the federal                        tively but also quantitatively in line with the
funds rate, log real housing prices, log real                   VAR estimates. In particular, the impact elas-
personal consumption expenditures, log real                     ticity of consumption to a persistent 1-percent
GDP, and log change in the GDP deflator, in                     increase in housing prices is around 0.2. This
that order.16 The figure illustrates an impor-                  is slightly larger than reduced-form estimates
tant point: the greater the importance of col-                  found in the studies above; however, both in
lateral effects (higher m and m⬙), the closer                   the model and in the VAR, consumption falls
the simulated elasticity of consumption to a                    below the baseline during the transition,
housing price shock. A wage share of the                        hence the medium-run elasticities are some-
constrained sector (1 ⫺ ␣) of 36 percent, and                   what smaller. Instead, the model without collat-
                                                                eral effects (m, m⬙ 3 0) predicts a negative
                                                                response of consumption to housing prices—
      Consistent with the theoretical model, I allow for all
                                                                mainly driven by a substitution effect between
the variables (except the interest rate) to respond contem-     housing and consumption—which is clearly at
poraneously to a housing price shock. The results were,         odds with the data.
however, robust to alternative orderings. The lags and the         While I will conduct more formal estima-
set of exogenous variables are the same as in the VAR of
Section I. Consumption, GDP, and house prices were de-
                                                                tion and testing below, this pictures highlights
trended with a band-pass filter-removing frequencies above      the reason behind the success of the model in
32 quarters.                                                    tracking down the empirical positive elastic-
750                                       THE AMERICAN ECONOMIC REVIEW                                              JUNE 2005

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

ity of spending to housing prices. To better                      changes in q t can be rather large, and is
understand the result, it is useful to reinterpret                strongly increasing with m, the loan-to-value
the borrowers’ asset demand as determining                        ratio. Instead, as shown by equation (L5), for
consumption given asset prices and payoffs,                       lenders the effects of q t on c t are simply
rather than determining today’s asset prices                      one-for-one, and therefore much smaller in
in terms of consumption and payoffs. For                          magnitude.
entrepreneurs, for instance, the linearized op-
timality condition between housing and                             E. Debt Deflation and the Stabilizing Effects
consumption can be written (neglecting ad-                                    of an Inflation Shock
justment costs) as
                                                                     Starting from the steady state, I assume a
                              1                                   1-percent, persistent inflation surprise.17 It
(18) ĉ t ⫽ E t ĉ t ⫹ 1 ⫹                                        is informative to contrast the response of
                           1 ⫺ m␤
                                                                  output with nominal debt to the model with in-
             ⫻ 共q̂t ⫺ ␥e Etq̂t ⫹ 1 ⫺ 共1 ⫺ ␥e 兲EtŜt ⫹ 1 兲         dexed debt. Figure 4 displays the results of the
                   m␤                                                With nominal debt (the solid line), the rise in
             ⫹         ˆ
                       rr                                         prices reduces the desired supply of goods at a
                 1 ⫺ m␤ t

where ␥ e ⬅ m ␤ ⫹ (1 ⫺ m) ␥ and E t Ŝ t ⫹ 1 is
the expected marginal product of housing.                               The inflation shock shows up as a residual in
This equation clearly shows how, keeping                          the Phillips curve. It could be justified by assuming
                                                                  that the elasticity of demand for each intermediate
constant expected consumption, expected re-                       good is time-varying, and varies exogenously, as
turns on housing, and real interest rates, the                    done, for instance, by Frank Smets and Rafael Wouters
multiplier effect on consumption of given                         (2003).

given price level; at the same time, it transfers             Next, I set ␥ and ␤⬙. I match the reciprocal of
wealth from the lenders toward the borrowers,              ␥, which proxies for the firm’s internal rate of
who, ceteris paribus, have a higher propensity             return. I assume this is twice as big as the
to consume. Initially, the two effects go in op-           equilibrium real rate, and set ␥ ⫽ 0.98. I then
posite directions, and output falls by a small             pick a value for ␤⬙: Emily Lawrance (1991)
amount. Later, the first effect dominates, and             estimates discount factors for poor households
the output drop is larger: overall, output dis-            (which are more likely to be debtors) between
plays a hump-shaped pattern and a slow return              0.95 and 0.98 at quarterly frequency, depending
to its initial steady state.                               on the specification. Carroll and Andrew Sam-
   This contrasts with the responses that would            wick (1997) calculate an empirical distribution
occur in a model without debt deflation effects            of discount factors for all agents using informa-
(the dashed line): with indexed debt, the drop in          tion on the elasticity of assets with respect to
output is immediate and stronger in magnitude,             uncertainty: the two standard deviation bands
because the beneficial effects of inflation are            range in the interval (0.91, 0.99). Samwick
absent. Hence, the assumption of nominal debt              (1998) uses wealth holdings at different ages to
helps capture not only qualitatively but also              infer the underlying distribution of discount fac-
quantitatively the hump-shaped and persistent              tors: for about 70 percent of the households, he
response of output to inflation found in the VAR.          finds mean discount factors of about 0.99; for
   Interestingly, the negative correlation be-             about 25 percent of households, he estimates
tween inflation and output induced by an infla-            discount factors below 0.95. With ␤ set at 0.99,
tion shock acts as a built-in stabilizer for the           I choose ␤⬙ ⫽ 0.95, in the ballpark of these
economy. Debt deflation thus adds a new twist              estimates.
to the theories of financial accelerator men-                 I set ␯, the elasticity of output to entrepre-
tioned in the introduction: while it amplifies             neurial real estate, to 0.03. This number implies
demand-type disturbances, it can stabilize those           a plausible 62 percent for the steady-state value
that generate a trade-off between output and               of commercial real estate over annual output.
inflation. I will return to this issue in Section VI.      The parameter j mainly controls the stock of
                                                           residential housing over annual output (see Ap-
          IV. Econometric Methodology                      pendix A): j ⫽ 0.1 fixes this ratio at 140 percent,
                                                           in line with data from the Flow of Funds ac-
   I now discuss the methodology for evaluating            counts (see, e.g., Table B.100, row 4).
the model. I partition the model parameters in                I then pick values for the adjustment cost
three groups.                                              parameters. Preliminary attempts to estimate
                                                           these parameters (using the methods described
                   A. Calibration                          in Section IV C) led to estimates of the capital
                                                           adjustment cost ␺ around 2 and pushed the
   The first group includes the discount factors:          housing adjustment cost parameters ␾e and ␾h
␤, ␤⬙, ␥; the housing weight j; the technology             toward zero. These results suggest that the data
parameters ␮, ␯, ␦, ␺, ␾e, ␾h; the markup X; the           appear to favor a version of the model in which
labor disutility ␩; and the degree of price rigid-         variable capital moves more slowly than hous-
ity ␪. I calibrate these parameters on the basis of        ing in response to disturbances. Although this
the data sample means and other studies be-                finding is not in contradiction to the cyclical
cause they contain relatively more information             properties of the actual data,19 it is likely that
on the first moments of the data.
   For the standard parameters, I choose values
that are within the range considered in the mon-           studies would suggest, but has the virtue of rationalizing the
etary/real business cycle literature. Thus, ␤, ␦,          weak observed response of real wages to macroeconomic
␮, X, ␪, and ␩ equal 0.99, 0.03, 0.3, 1.05, 0.75,          disturbances. With ␩ approaching 1, the utility function
and 1.01, respectively.18                                  becomes linear in leisure, as proposed and explained in
                                                           Gary Hansen (1985).
                                                                 For the period 1974Q1–2003Q2, the standard devia-
                                                           tion of (a) structures investment, (b) residential investment,
      A value of ␩ ⫽ 1.01 implies a virtually flat labor   (c) equipment and software investment, and (d) change in
supply curve: this is higher than what microeconometric    inventories are, respectively, 0.8, 0.5, 0.58, and 0.94 per-
752                                        THE AMERICAN ECONOMIC REVIEW                                           JUNE 2005

the solution algorithm has difficulty in estimat-                  TABLE 1—CALIBRATED PARAMETERS         IN THE   EXTENDED
ing these parameters without data on the types                                        MODEL
of investment spending. At the same time, one                    Description                           Parameter       Value
has to consider that, ceteris paribus, the fixity of
the housing stock in the aggregate works by                      Preferences: Discount factors
itself as an adjustment cost on housing invest-                  Patient households                        ␤           0.99
ment: given that the total supply of structures is               Entrepreneurs                             ␥           0.98
fixed, additional housing investment in any                      Impatient households                      ␤⬙          0.95
given period drives up the price of the existing                 Other preference parameters
stock, so that, from each agent’s point of view,
                                                                 Weight on housing services                 j          0.1
every unit of new investment is more costly at                   Labor supply aversion                      ␩          1.01
the margin. In what follows, therefore, I esti-
mate the model by calibrating ␺ ⫽ 2 and ␾e ⫽                     Technology: Factors productivity
␾h ⫽ 0.20 The former implies an elasticity of 1⁄2                Variable capital share                     ␮          0.3
of investment to the capital shadow price, fol-                  Housing share                              ␯          0.03
lowing Robert King and Alex Wolman (1996):
                                                                 Other technology parameters
this value is well within the range of estimates
reported in the literature (see Robert Chirinko,                 Variable capital adjustment cost           ␺          2
1993). Table 1 summarizes the parameters.                        Variable capital depreciation rate         ␦          0.03
                                                                 Housing adjustment cost                    ␾          0

                     B. Policy Rule                              Sticky prices
                                                                 Steady-state gross markup                  X          1.05
   The second group includes the parameters                      Probability fixed price                    ␪          0.75
that can be recovered from the estimates of the
Taylor rule. For the period 1974Q1–2003Q2, an
OLS regression of the Fed Funds rate on its own                  eters by minimizing a measure of the distance
lag, past inflation, and detrended output yields                 between the empirical impulse responses (Sec-
rR ⫽ 0.73, rY ⫽ 0.13, r␲ ⫽ 0.27.21                               tion I) and the model responses, which were
                                                                 obtained from the reduced form of the model by
                     C. Estimation                               ordering and orthogonalizing the shocks as in
                                                                 the VAR.
   The third group includes the autocorrelation                     As is well known (see, e.g., Ireland, 2004a),
and the standard deviation of each shock (␳A, ␳j ,               the number of data series in the VAR represen-
␳u, ␴A, ␴j , ␴u), the loan-to-value ratios (m, m⬙),              tation cannot exceed the number of structural
and the wage income share of the patient house-                  disturbances in the model. With four distur-
holds, measured by ␣. I estimate these param-                    bances (monetary, inflation, taste, productivity),
                                                                 I select (R, ␲, q, Y) as the variables of interest.
                                                                 Denote with ⌿(␨) the vector collecting the
cent. (All variables were normalized by GDP. The data were       model orthogonalized impulse responses, ob-
then filtered using a band-pass filter that removed the low-     tained from the reduced form of the model by
frequency component above 32 quarters.)
       The results with ␾e, ␾h ⬎ 0 are qualitatively as fol-
                                                                 ordering and orthogonalizing the impulse re-
lows: housing adjustment costs reduce the fluctuations in        sponses as in the VAR. Let ⌿̂ be the n ⫻ 1
the housing stock variables but generate slightly larger         vector of empirical estimates of the VAR im-
changes in housing prices and output, which the data appear      pulse responses.22 I include the first 20 elements
to reject. Closer inspection of the impulse responses shows      of each impulse response function, excluding
that, when facing costs of adjusting both k and h, entrepre-
neurs vary labor input more strongly in response to distur-      those that are zero by the recursiveness assump-
bances, which in turn affects output.
       The standard deviation of the monetary shock ␴e is
taken from the standard error of the interest rate equation in
the VAR below, which equals 0.29. In principle, one could           22
                                                                       n ⫽ n21 ⫻ n2 ⫺ n3, where n1 is the number of variables
also obtain all the parameters of a more involved policy rule    in the VAR, n2 are the elements to match for each impulse
from the VAR. I use a shift dummy from 1979Q4 to capture         response, and n3 are the elements of ⌿ which are zero by
monetary policy changes that are known to have occurred          assumption (because of the zeros imposed by the Choleski
around that time.                                                ordering).

TABLE 2—ESTIMATED PARAMETERS AND THEIR STANDARD                  their wage share (1 ⫺ ␣) is around 36 percent
         ERRORS IN THE EXTENDED MODEL                            and is precisely estimated:24 interestingly, this
Description                          Parameter Value s.e.
                                                                 number is within the range of the various stud-
                                                                 ies that, since Campbell and Mankiw (1989),
Factor shares and loan-to-values                                 have estimated from consumption Euler equa-
Patient households wage share           ␣         0.64 0.03      tions the fraction of rule-of-thumb/constrained
Loan-to-value entrepreneur              m         0.89 0.02      agents in an economy. At the same time, they
Loan-to-value household                 m⬙        0.55 0.09
                                                                 support strong effects on demand from changes
Autocorrelation of shocks                                        in asset values, as shown by the high values of
                                                                 m and m⬙. The former is 89 percent, whereas the
Inflation                                ␳u       0.59 0.06
Housing preference                       ␳j       0.85 0.02      latter is 55 percent. Hence, the estimates suggest
Technology                               ␳A       0.03 0.10      that entrepreneurial real estate is more easily
                                                                 collateralizable than household real estate. A
Standard deviation of shocks                                     joint test of the hypothesis that collateral con-
Inflation                               ␴u        0.17 0.03      straints are unimportant—that the m and m⬙ are
Housing preference                      ␴j       24.89 3.34      equal to zero—is overwhelmingly rejected.
Technology                              ␴A        2.24 0.24
                                                                 High values of m and m⬙ are in fact needed to
                                                                 generate strong and persistent effects on aggre-
                                                                 gate demand from given changes in asset val-
tion. The estimate of ␨, a vector of parameters,                 ues, something that a model without these
solves                                                           effects cannot replicate.
                                                                    Finally, the estimate of the autocorrelation in
(19)      min共⌿共␨兲 ⫺ ⌿̂兲⬘⌽共⌿共␨兲 ⫺ ⌿̂兲                            the technology shock is low (␳A ⫽ 0.03) and
              ␨                                                  less precisely estimated: one explanation might
                                                                 be the detrending method used in the VAR,
where ⌽ is a n ⫻ n weighting matrix. Under the                   which takes away the low-frequency compo-
null hypothesis that the VAR model is true and                   nent of GDP. Instead, the autocorrelations in the
that the model fits the data, the optimal weight-                preference and in the inflation shock are pre-
ing matrix ⌽ would equal ⌽ ⫽ ⌼⫺1, the inverse                    cisely estimated and highlight moderate persis-
of the matrix with the sample variances of the                   tence in the shock processes (␳j ⫽ 0.85, ␳u ⫽
VAR impulse responses on the main diagonal.                      0.59). Interestingly, such autocorrelations are
Given that the cross-correlations between q and                  lower than what is found in estimates of stan-
Y are likely to be relatively more informative for               dard monetary business cycle models: one pos-
m, m⬙, and ␣, I specify ⌽ ⫽ ⍀⌼⫺1, where ⍀ is                     sibility is that the endogenous propagation
a n ⫻ n diagonal matrix of weights that gives a                  mechanisms that are at work in the model re-
weight four times larger to all the dynamic                      quire less persistent shocks to fit the second
cross-correlations involving q and Y. This way,                  moment properties of the data.
I still get consistent (yet inefficient) estimates of               While the estimates of ␣, m, and m⬙ are all
all the parameters, but at the same time I fit the               statistically significant,25 I reject the null
moments of highest interest.23 The results were,
however, robust to the choice of ⍀.
   Table 2 summarizes the estimates of the pa-                      24
                                                                       Standard errors were computed using the asymptotic
rameters in ␨. The results strongly support the                  delta function method applied to the first-order condition
presence of borrowing-constrained households:                    associated with the minimization problem.
                                                                       These findings are robust to changes in the estimation
                                                                 horizon and in the weighting matrix. As a robustness check,
                                                                 I included the discount factors among the parameters to
       As suggested by a referee, housing collateral is inter-   estimate. The resulting values for ␤⬙ and ␥ were, respec-
esting because of the potential spillovers to other consump-     tively, around 0.4 and 0.9; the other parameter estimates
tion goods as housing price increases relax borrowing            were unchanged, with the exception of m⬙, whose estimate
constraints. By focusing on the parameters that best match       was marginally positive. Loosely speaking, a reduction in
the dynamic cross-correlation between house prices and           the discount factor works to strengthen the preference for
output (and therefore consumption), the estimation proce-        current consumption, thus working in the same direction as
dure selects these particular moments as most informative at     an increase in the loan-to-value when it comes to explaining
the margin for the values of m, m⬙, and ␣.                       the high sensitivity of demand to aggregate shocks. How-
754                                       THE AMERICAN ECONOMIC REVIEW                                             JUNE 2005

                                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-percent

hypothesis of equality between the model and                               V. More on the Model Dynamics
the data. Perhaps the simplest explanation for
this finding is that the model lacks such features                   Figure 5 shows the model impulse responses
as expectational delays, inertial adjustment of                   and compares them with the VAR impulse re-
prices, or habit persistence, which elsewhere                     sponses. This way, I can assess the key proper-
authors have shown can help replicate the de-                     ties of the model and its consistency with
layed responses of macroeconomic variables to                     empirical evidence.26
various shocks (see, e.g., Julio Rotemberg and                       The top row shows a monetary tightening.
Michael Woodford, 1997; Galı́ and Gertler,
1999; Fuhrer, 2000).
                                                                         One caveat: the impulse responses from the VAR and
                                                                  those from the structural model are not strictly comparable,
                                                                  since the restrictions implied by the two representations are,
ever, although empirical estimates of the discount factor are     in general, different. See Fuhrer (2000) for a discussion: an
surrounded by large uncertainty, values below 0.9 appear          alternative could be to compare the autocorrelation func-
too low to be considered reasonable (see Carroll and Sam-         tions implied by the various models. The results using this
wick, 1997).                                                      representation were qualitatively similar.

The drop in output is immediate in the model,                  transmission mechanism: rather, it is the general
while it is delayed in the data, although the total            equilibrium effects working through the de-
output sacrifice is in line with the VAR esti-                 mand for all factors of production that affect the
mate. As in the basic model, money shocks have                 aggregate outcomes.28
heterogeneous effects: debtors bear most of the
brunt of the monetary contraction, while con-                     VI. Systematic Monetary Policy and Policy
sumption of lenders is mildly affected and can                                    Frontiers
be shown to rise above the baseline in the tran-
sition to the steady state. In turn, the real rate,               Shocks that generate a negative correlation be-
which prices lenders’ behavior, falls below the                tween output and inflation force the central bank
baseline in the transition. Real housing prices                to face a trade-off between the variability of out-
initially fall below the baseline, deepening the               put and that of inflation. A natural question is:
recession, and then overshoot above the base-                  how do different monetary policy rules and con-
line, preceding the economy’s recovery.                        tractual arrangements affect the cyclical properties
   The previous section has already shown how                  of output and inflation? This section gives an
nominal debt is successful in capturing the slug-              answer, based on the assumption that output and
gish response of output to an inflation shock.                 inflation volatility are the only two goals of mon-
The second row of Figure 5 shows that the model                etary policy. I consider whether interest rates
does very well at capturing the positive response              should respond to housing prices; and how differ-
of the interest rate and the negative response of              ent financing arrangements (nominal versus in-
housing prices to an inflation surprise.                       dexed debt) affect the volatility of the economy.
   For the preference shock, the third row of
Figure 5 shows that the model does well in                     A. Should Central Banks Respond to Housing
capturing the positive elasticities of demand and                                Prices?
inflation to a housing price shock. Figure 3 has
already shown how a model without collateral                      I compute the inflation-output volatility fron-
effects predicts a small, even negative, response              tiers for alternative parameterizations of the in-
of aggregate demand to a housing price shock.27                terest rate rule, as in Andrew Levin et al.
   The last row of Figure 5 shows the responses                (1999), subject to a constraint on interest rate
to a transitory productivity rise. Here it is harder           volatility.29 The class of rules I consider is
to compare the responses of the model with the
data, especially because it is harder to consider              (20) R̂ t ⫽ 0.73R̂ t ⫺ 1
the VAR disturbance as a pure productivity
shock: for instance, a government spending                                ⫹ 0.27共rqq̂t ⫹ 共1 ⫹ r␲ 兲␲ˆ t ⫺ 1 ⫹ rYŶt ⫺ 1 兲.
shock could be observationally equivalent. In the
model, output and asset prices peak only with a                  In other words, I assume that the central bank
delay following the improvement in productivity.               can respond to current asset price movements:
   In simulations not reported here, I find that
the model predicts a standard deviation for en-
trepreneurial housing investment that is twice                        One drawback of the model is that it predicts that
that of variable capital investment: this number               households’ housing holdings are countercyclical: with a
                                                               fixed supply, this sector absorbs in fact the reduction in the
is slightly bigger but roughly in line with the                demand by the entrepreneurs. This need not be unrealistic if
data (see footnote 19). Not shown in figure, I                 housing is given a broad interpretation, which also includes
find that in response to, say, a negative mone-                land. In Japan, for instance, households and the government
tary shock (positive preference shock), h falls                have traditionally been net purchasers of land in periods of
                                                               falling land prices (see the 2003 Annual Report on National
(rises) on impact by 4 percent (3 percent).                    Accounts of Japan).
Given that the elasticity of output to real estate                 29
                                                                      I compute the Taylor curves tracing out the minimum
is very small (0.03), this shows that changes in               weighted unconditional variances of output and inflation at
housing ownership per se are not crucial to the                different relative preferences for inflation versus output
                                                               variance. I constrain interest rate volatility by imposing an
                                                               upper bound 25 percent larger than the estimated standard
                                                               deviation generated by the benchmark model. I also impose
      Given the adjustment cost for capital, the initial re-   r␲, rY ⬎ 0 to generate a unique rational expectations equi-
sponse of output is roughly equal to that of consumption.      librium for each policy.
You can also read