The E¤ects of Housing Prices and Monetary
Policy in a Currency Union
Oriol Aspachs-Braconsy

Pau Rabanalz

August 27, 2010

Abstract

The recent boom-and-bust cycle in housing prices has refreshed the debate
on the drivers of housing cycles as well as the appropriate policy response. We
analyze the case of Spain, where housing prices have soared since it joined the
EMU. We present evidence based on a VAR model, and we calibrate a New
Keynesian model of a currency area with durable goods to explain it. We …ndthat labor market rigidities provide stronger ampli…cation e¤ects to all type ofshocks than …nancial frictions do. Finally, we show that when the central bankreacts to house prices, the non-durable sector su¤ers an important contraction,and hence it is not obvious that if Spain had remained outside the EMU theboom-and-bust cycle would have been avoided.
Keywords: Housing, Monetary Policy, Financial Constraints.
JEL Classi…cation: E44, E52, F41.

We thank Jordi Galí and two anonymous referees for useful comments. This paper should not
be reported as re‡ecting the views of Caixa d’Estalvis i Pensions de Barcelona ("la Caixa") or of
the International Monetary Fund. Any errors and omissions are our own.
yCorresponding author. Research Department, Caixa d’Estalvis i Pensions de Barcelona.
Avinguda Diagonal 621-629, 08028 Barcelona. Email: oaspachs@lacaixa.es.
zResearch Department, International Monetary Fund. 700 19th St. NW, Washington DC
20431, USA. Email: prabanal@imf.org.

1

1

Introduction

The recent boom and bust cycle in housing prices in many advanced economies
has refreshed the debate on the drivers of housing cycles and the role of the housing sector in amplifying economic volatility, as well as the appropriate response of
the monetary authorities. The case of Spain is of special interest since its recent
economic expansion has been characterised by sustained growth of residential investment, private consumption, credit and housing prices for more than a decade.
Moreover, during this period nominal and real interest rates fell to exceptionally
low levels during the convergence period in order to enter the european Economicand Monetary Union (EMU). As a result, a large current account de…cit emerged,
reaching almost 10 percent of GDP at the peak of the cycle in 2007.
In addition to growing external imbalances, a special source of concern for the Spanish economy was the loss of monetary policy autonomy after entering the EMU. In
countries with their own national currency and monetary policy, such as the US,
the UK, Australia and New Zealand, the central bank can increase interest rates
to slow down the growth rate of housing prices (although in practice they were notsuccessful in doing so in the most recent cycle), and also respond to a housing pricecollapse.1 However, Spain belongs to the EMU, and the European Central Bank sets
rates according to the in‡ation rate of the Harmonised Index of Consumer Prices(HICP) of the Euro area as a whole. This means that monetary policy cannot be
the …rst line of defense in response to negative sector- and country-speci…c shocks.
The recent evolution of the Spanish economy since 1996, including the housing market boom-bust cycle, is shown in Figures 1 thru 4. The period of convergence toand adoption of the euro (1996-2007) was characterized by declining interest rates,
and increased residential investment and house price growth rates. The demand for
housing was further increased by the high levels of inmigration and the baby boom
generation (which peaked in the early 1970s in Spain) turning into adulthood, fuelling residential investment and even further increasing house prices. This increasein housing prices raised wealth and borrowing capacity of house owners who, in
principle, could use these mechanisms to …nance other consumption.2 The growing
1

Mishkin (2007) suggested that in response to a 20 percent housing price drop in the UnitedStates, the Federal Reserve should cut interest rates between 75 and 175 basis points, dependingon the assumptions about the transmission mechanism.
2
However, we should note that estimates of the marginal propensity to consume out of housing
wealth in Spain are lower than in other countries. Bover (2005) obtains estimates of about 0:01-

2

current account de…cit is the other indicator of the magnitude of the consumption
and borrowing boom, and the large savings-investment imbalance was …nanced fromabroad. Since late-2007, the boom cycle has turned into a bust.
Hence, in this paper we study the response of a small economy in a currency union(such as the Spanish one) to ‡uctuations in housing prices and residential investment.
First, we present VAR evidence that shows the response of private consumption,
residential investment, aggregate GDP, and real house prices to an interest rate
shock and to a housing demand shock. We show that a decrease of interest rates
and a positive housing demand shock lead to a rise in both …nal consumption andresidential investment, a …nding labelled as “comovement” in the literature whenstudying US data.
Then, we rationalize our …ndings by building a two-country, two-sector model ofa currency union in the spirit of Benigno (2004) and Rabanal (2009). The model
includes durable and non-durable goods. Holding durables (i.e. housing) not only
provides utility to the consumer but is also a vehicle for savings. In addition, theinternational dimension of the model implies that the savings and investment balanceneed not hold period per period at the country level. This will allow us to explain
how increased credit demand in one country of a currency union can be met throughfunds coming elsewhere in the union. We calibrate the model, and examine thereaction of domestic variables and the nominal interest rate to a monetary policy
shock and a demand/preference shock in the durable sector. Overall, the demand
shock and the interest rate shock produce e¤ects on the main aggregates of theeconomy similar to the ones observed in the VAR. Then, we conduct a robustness
exercise to understand how important are labor market and credit market rigidities
in understanding the transmission of housing demand and monetary shocks in theeconomy. As opposed to the existing literature that stresses the role of …nancial
frictions and borrowing constraints to explain comovement, we …nd that the e¤ectof labor market rigidities has important implications for the persistent responseof variables to shocks, and to explain the comovement between consumption andresidential investment.
In the last section of the paper we study the policy options for a small open economy
such as the Spanish one, that faces large sector-speci…c shocks. In addition to
our benchmark currency union model, we consider two additional cases. In the
0:02.

3

…rst one, we assume that Spain follows a Taylor rule which is similar to the one
followed by the rest of the EMU. In the second case, we examine what would have
happened if the Spanish authorities, outside the euro, had tried to "lean against thewind" and included house price in‡ation in their reaction function. We …nd that if
Spain had followed an in‡ation targeting regime with a pure ‡oating exchange rate,
the monetary policy reaction to a domestic demand shock would not have beenvery di¤erent than that of belonging to a currency union. If we allow the central
bank to react to house prices, the initial boom in housing in‡ation and residential
investment can be reduced. However, to achieve stability in the housing market
using the nominal interest rate as a policy tool leads to an important and persistentcontraction in the non-durable sector. Hence, even if the Spanish authorities had
kept monetary policy management, it is not clear that they would have chosen to"lean against the wind".
The rest of the paper is organized as follows. In section 2, we present some VARbased evidence. In section 3, we present the model, and in section 4 we discussat length the quantitative implications of the model. The robustness checks arepresented in section 5 and in section 6 we analyze the e¤ects of belonging to the
EMU. We leave section 7 for concluding remarks.

2

The VAR Response to Housing Demand andInterest Rate Shocks

In this section, we present evidence on the response of main macroeconomic variables
to housing demand and interest rate shocks with the help of a Vector Autoregressive(VAR) model. Several papers in the literature have studied the response of durable
and non-durable consumption to a monetary policy shock using a VAR and therecursive identi…cation scheme of Christiano, Eichenbaum, and Evans (1999, 2005).
This approach consists of identifying the e¤ect of the monetary policy shock byusing the Cholesky decomposition of the variance-covariance matrix of the reduced
form residuals of the VAR. Papers following this approach include Erceg and Levin(2006) and Monacelli (2009).
In addition, we seek to identify a housing demand shock from the VAR. We do so by
assuming that the housing demand shock a¤ects the real price of housing within a4period, but it does not a¤ect its quantity: in the short run the supply of housing is…xed, and demand shocks must be absorbed via price movements. In practice, thisshock leads to an increase of residential investment and prices, thereby con…rming
our labeling. In the last part of the section, we discuss several robustness resultsthat include: introducing euro area variables into the system, extending the sample
period, and using sign restrictions to identify the housing demand shock.
We estimate the following VAR using k variables:
Yt = C +LX

Aj Yt j + But

j=1

where Yt is a kx1 vector of observable variables, C is a kx1 vector of constants,
Aj are kxk matrices that collect the e¤ect of endogenous variables at lag j on
current variables, L is the lag length in the VAR, B is a kxk lower triangular matrix
with diagonal terms equal to unity, and ut is a kx1 vector of zero-mean, serially
uncorrelated shocks with diagonal variance-covariance matrix.
The vector of endogenous variables is divided as follows: Yt =

h

Y1t

Rt

Y2t

i0

,

where Y1t is a group of macroeconomic variables predetermined when monetary
policy decisions are taken, Rt is a relevant interest rate, and Y2t contains the variables
a¤ected contemporaneously by monetary policy decisions. As is customary in theliterature, to identify the interest rate shock we place the nominal interest rate after
the macroeconomic variables. On the other hand we assume that house prices can
respond to changes in monetary policy within a period: as an asset price, housing
prices are likely to respond contemporaneously to changes in the nominal interest
rate, so we include them in Y2t . Hence, we identify the housing demand shock as
the shock that a¤ects housing prices within a period, after taking into account thee¤ect that changes in the interest rate have on housing prices.3

2.1

Data

The vector of observable variables is divided the following way. In Y1t we include: (i)real household consumption of …nal goods in Spain, (ii) real residential investment
in Spain, and (iii) real GDP in Spain. We use as a relevant interest rate (Rt ) the3

We have also estimated a VAR with the ordering Yt =very similar to the ones we present.

5

Y1t

Y2t

Rt

0

and the results arereference interbank rate. Finally, we include in Y2t real house prices in Spain. Allvariables are introduced in the VAR in levels after taking natural logarithms, except
for the nominal interest rate that we introduce directly in levels.
Private consumption, residential investment and GDP come from Spanish national
accounts data and are de‡ated by the Spanish GDP de‡ator. Nominal housing prices
come from the OECD and are de‡ated by the HICP in Spain. In studies involving
US data the Federal Funds rate is typically the variable used as an indicator of
the stance of monetary policy, following the study of Bernanke and Blinder (1992).
Spain relinquished its monetary policy autonomy when it joined the EMU January
1st, 1999, and hence a domestic reference rate is no longer available. We choose
the 3-month interbank rate as the reference interest rate. From 1999 we use the
3-month Euribor rate, and before the EMU period we use the 3-month MIBOR rate(the Madrid Interbank rate). Note that because of this reason, we call our shock aninterest rate shock rather than a monetary policy shock in the VAR.
The relevant interbank interest rate for mortgages in Spain is the 12-month rate.
In practice, using the 3-month or the 12-month rate delivers the same results, since
the reference rate set by the European Central Bank, the 3-month interbank rate
and the 12-month interbank rate move very closely together. We estimate the VAR
from 1997:01 to 2008:04 at a quarterly frequency, with 2 lags. While the euro
was launched in 1999, monetary policy in Spain followed its european counterparts
closely in 1997-1998, and this allows us to include 8 more observations in the system.

2.2

Results

In Figures 5 and 6 we present the impulse responses of the …ve variables to an increase
in interest rates and a housing demand shock. We present the mean and 85 percent
con…dence bands.4 With respect to a monetary policy shock, the impulse responses
are qualitatively similar to those shown by Monacelli (2009) for the US economy.
The interest rate shock takes the form of an increase of about 25 basis points inthe nominal interest rate. It takes some time for the e¤ects of the shock to build
up in the economy: household consumption peaks after 12 quarters and residential
investment peaks after 7 quarters. The peak response of residential investment isabout 5 times larger than that of private consumption. Real house prices decline
4

Given the short sample, it is di¢ cult to obtain signi…cance at the conventional 95 percent
interval.

6

with an increase in the nominal interest rate.
On the other hand, following a housing demand shock, real house prices immediately
increase by 1.2 percent, and residential investment increase by a similar magnitude
one period later (because of the assumptions built in to identify the shock). Interestingly, household consumption also increases over time, peaking after 12 quarters
at about 0.25 percent. While the e¤ect is small, it is statistically signi…cant at the85 percent level. These are the features that our model will reproduce, in particular the comovement in the response of both private consumption and residential
investment to shocks.

2.3

Robustness

We have conducted several robustness exercises with our VAR-based evidence, which
are not presented here to save space, but are available upon request. In the …rst
extension, we include the Harmonized Index of Consumer Prices (HICP) in‡ation
and real GDP growth in the euro area to control for the endogenous response ofinterest rates. In this case, we …nd that the qualitative results do not change. Thissuggests that, from the Spanish perspective, changes in interest rates can be seen as
purely exogenous shocks. Second, we have also experimented by using the sample
period 1980-2008. All the results are very similar to the ones presented here, except
in the response of real house prices to a monetary policy shock, which is small
and nonsigni…cant. Finally, we have used sign restrictions as in Uhlig (2005) andCardarelli et al (2009) to identify the e¤ects of housing demand, housing supply andmonetary policy shocks, and found that the main message of Figures 5 and 6 does
not change.

3

The Model

The theoretical framework consists of a general equilibrium two country, two sector
model in a single currency area. The countries are of size n and 1

n, and each ofthem produces two types of goods, durables and non-durables, under monopolisticcompetition and nominal rigidities. Only the non-durable goods are tradable. Producers of the …nal durable good sell its product to domestic households only in eachcountry, which allows them to increase their housing stock. For this reason, we use
7the terms “durable good production”and “residential investment”interchangeably
throughout the paper.
Since our VAR analysis has only focused on the e¤ects of monetary and demand
shocks on the housing sector and the spillover e¤ects to the macroeconomy, themodel will only include these shocks, so we leave aside technology shocks in thecurrent analysis. In what follows, we present the home country block of the model.
The analogous foreign country variables will be denoted by an asterisk.

3.1

Households

Each household j in the home country maximizes the following utility function:

E0

(1
X

t

t=0

"

1+

log(Ctj"Ct 1 ) + (1)

jD
t log(Dt )

Ljt
1+

#)

(1)

where Ctj denotes consumption of non-durable goods, Dtj denotes consumption ofdurable goods and Ljt is the labor disutility index.

Dt is a housing preference shock,which follows an AR(1) process in logs.
The utility function denotes external habit formation, as in Smets and Wouters(2003) and Iacoviello and Neri (2010).

is the discount factor andis the inverse

elasticity of labor supply. The parameter " denotes the importance of the habit stock,which is last period’s aggregate consumption (Ct 1 ). In addition, consumption of
non-durables is an index composed of home and foreign consumption goods:

Ctj =

1
C

j
CH;t

C 1
C

+ (1

)

1
C

j
CF;t

C 1
C

C
C 1

; where C > 0

(2)

j
j
where CH;tand CF;tare, respectively, consumption of the home non-durable goods

and consumption of foreign non-durable goods by the home agent, andis thefraction of domestically produced non-durables at home. Finally, following Iacovielloand Neri (2010), we assume that there is imperfect substitutability of labor supply
across sectors, such that the labor disutility index can be written as:
Ljt =

L

LC;j
t

1+ L

+ (1

)

L

8

LD;j
t

1+ L

1
1+ L

; where L > 0(3)

where Li;jt denotes hours worked by household j in each sector i = C; D, andis theeconomic size of each sector. This imperfect substitutability implies that there is acostly labor reallocation across sectors following a shock. Note that when L = 0 theaggregator is linear in hours worked in each sector, so there are no costs of switchingfrom working in one sector to the other.
The budget constraint of the home agent, in nominal terms, is given by:
PtC Ctj +PtD ItD;j +PtA Ajt +Btj

C

C;j

D

D;j

~ t 1 Btj 1 + Wt Lt + Wt Lt
R
XtC
XtD

+(RtA +PtA )Ajt 1 +

j
t

(4)

where PtC and PtD are the price indices of durable and non-durable goods, to bede…ned below, Wti is the nominal wage in each sector i = C; D, and Btj denotes
uncontingent nominal assets that are traded among households across the monetary~ t > 1: Following
union, and that pays (or costs) a gross nominal interest rate R
Iacoviello and Neri (2010), Xtj denotes the mark up (due to monopolistic competitionin the labor market) between the wage paid by intermediate …rms and the wagethat households receive (the details of the nominal rigidities in the labor market are
discussed below).

jt denotes nominal pro…ts, because …rms are ultimately owned byhouseholds. At denotes the level of land owned by households, which is purchased ata price PtA and which is rented to durable intermediate goods producers at a rental
rate of RtA .
ItD;j denotes residential investment to increase the housing stock. We assume thatthe law of motion of the housing stock evolves as follows:

Dtj = (1
where")Dtj 1 + 1

S

ItD;j
ItD;j1

!#

ItD;j

(5)

denotes the rate of depreciation of the housing stock and, following Chris-tiano, Eichenbaum, and Evans (2005), we introduce an adjustment cost function,
S (:), which is convex (i.e. S 00 () > 0). Furthermore, in the steady state S = S = 0
and S 00 > 0: The aim of introducing this cost is to allow for the possibility that themodel can generate hump-shaped responses of residential investment to shocks.
We assume that households in the home country have to pay a premium above theunion-wide riskless nominal interest rate as the country’s debt level as a percentage
of GDP increases. This assumption is needed to obtain a well-de…ned steady state9

for the aggregate level of debt.5 The relevant interest rate for the home-country
households and the union-wide interest are related as follows:~ t = RtR

Bt
P t Yt

exp

B
PY

1

(6)

where Pt is the aggregate price level, to be de…ned below, and Yt is real GDP, also to
be de…ned below. Rt is the riskless interest rate andis the risk premium elasticity.

This risk premium depends on aggregate variables, such that each household takes
this e¤ect as given when choosing between consuming durables, non-durables, andsaving. Note that the risk premium is declining in the net foreign asset position of
the country as a percentage of GDP, PBt Yt t .
We can separate the household’s decision in a two stage process. First, households
choose the amount of labor to supply to each sector, and the consumption of durables
and non-durables. Second, they allocate how much to spend on home and foreign
produced goods, taking into account that,PtC Ct = PH;t CH;t + PF;t CF;twhere PH;t denotes the price of home non-durable consumption goods and PF;t theprice of foreign non-durable consumption goods. The variables corresponding to theforeign country are denoted with an asterisk, but the prices of foreign non-durable
consumption goods do not carry it because they are also set in euros, and there is
no price discrimination across countries.
The …rst order conditions to the household problem are given by:6

UCt =

UDt =
5
6

t

(1

C
t Pt

(7)

)Et t+1

See Schmitt-Grohé and Uribe (2003).
Since all households behave the same way, we drop the j subscripts in what follows.

10

(8)

D
t Pt =

t

1

S

ItD
ItD 1

ItD
ItD 1

S0

ItD
ItD 1

"

+ Et t+1 S 0

D
It+1
ItD

D
It+1
ItD

2

#

:

(9)
Absent adjustment costs to residential investment, these three equations can be
reduced to the following condition:
D
t (Ct

1
PtD
=
C
Pt

"Ct 1 )Dt

+ (1Ct "Ct 1
Ct+1 "Ct)Et

Note that if the durable good was in fact non-durable (i.e.

D
Pt+1
:
C
Pt+1

= 1), this condition

simply states that the marginal utilities of consumption should equal relative prices.
Since the durable good has a residual value the following period, this induces theextra-term of holding an additional unit of the durable good.
A standard Euler equation for the consumption of non-durable goods is:~ t Et
1= R

PtC
C
Pt+1

Ct "Ct 1
Ct+1 "Ct(10):

A similar Euler equation for land is as follows:~ t = Et
RA
A
+ Pt+1
Rt+1
PtA

(11)

such that households are indi¤erent between investing in land and riskless bonds.
The allocation of nondurable consumption expenditures between home and foreignproduced goods is:
CH;t =
CF;t = (1

PH;t
PtC
PF;t
PtC

)

C

(12)

Ct
C

(13)

Ct :

The price index for non-durables is (the CPI):
PtC

1

C

=

(PH;t )1C+ (1) (PF;t )1

C

:

(14)

The utility maximization problem of foreign country households is quite similar. We
assume that the functional forms for preferences are the same across countries, butallow for di¤erent parameter values. That is,11

is the weight of non-durables in theutility function, and3.2

the fraction of domestically produced non-durables.

Wage Setting

Nominal wage stickiness is introduced as in Smets and Wouters (2007) and Iacovielloand Neri (2010), so we omit most functional forms here and refer the interested
reader to those papers. Households supply homogeneous labor services to unions.
These unions di¤erentiate these labor services and set wages subject to a Calvo-type
restriction, where the probabilities in each sector of not being able to readjust wages
in a given period are

C;W

and

D;W .

They o¤er these labor services to wholesalelabor packers, who reassemble these services into homogeneous labor composites,
which are in turn hired by intermediate …rms from these packers.
Under Calvo wage setting and with partial indexation to past non-durable (CPI)in‡ation (with coe¢ cients 'C;W and 'D;W ), the wage-setting equations can be loglinearized into the following wage Philips curves, where lower case variables denote
percent deviations from steady-state values:

!C
t

!C
t 1+
+ C;W

where

C;W

!D
t

=

(1

pC
t
ct

"ct 1
+ [('
1 "

C;W )(1
C;W

!D
t 1+
+ D;W
(1

pC
t
ct

C;W )

D;W )(1

D;W

3.3

Producers

D;W) + ] ltC + ('

!C
t +
)(1

pC
t+1
)ltD

'C;W pC
t
!C
t

(15)

, and

D
'D;W pC
t 1 = Et ! t+1

"ct 1
+ [('
1 "

where

=

C
'C;W pC
t 1 = Et ! t+1

D;W )

)(1

!D
t +

) + ] ltD + ('

pC
t+1
) ltC

'D;W pC
t
!D
t

(16)

.

There is a continuum of intermediate goods producers, indexed by h 2 [0; n] inthe home country, and by f 2 [n; 1] in the foreign country, that are imperfect
substitutes of each other, and that supply …nal goods producers in each sector.
12There is a continuum of …nal goods producers in the two sectors that operate under
perfect competition and ‡exible prices. Producers of the …nal durable good sell
their products to domestic households only in each country. Producers of the …nal
non-durable good sell their products to domestic and foreign households. Hence,
it is important to distinguish the price level of domestic non-durable consumption
goods, PH;t , which does not coincide with the price level of non-durables or CPI(PtC ) because of the presence of imported non-durable goods, whose price is PF;t .

3.3.1

Final Goods Producers

In the durable sector, …nal goods producers purchase intermediate goods producers
and aggregate them according to the following production function:

YtD

"

1
D

1
n

Z n

YtD (h)

D 1
D

#

D
D 1

(17)

dh

0

Pro…t maximization delivers the following demand for individual, intermediate nondurable goods:

YtD (h) =PtD (h)
PtD

D

YtD ;

(18)

where the price level is given by imposing the zero-pro…t condition,
1
n

PtD

Z n

1

PtD (h)

1

D

1

dh

D

:

0

In the non-durable goods sector, expressions are similar but with an appropiatechange of notation since the price level of domestic non-durables and of a basket of
durables is not the same. The aggregate production function is:

YtC

"

1
n

1
C

Z n

YtC (h)

C 1
C

dh

0

individual intermediate non-durable goods demand is:

13

#

C
C 1

;

(19)

YtC (h) =PtH (h)PtH

Z n1
PtH (h)

C

YtC ;

(20)

where the price level is:

PtH

3.3.2

1
n

1
C

1

dh

C

:

0

Intermediate Goods Producers

There is a continuum of intermediate goods producers, indexed by h 2 [0; n] in thehome country, and by f 2 [n; 1] in the foreign country, that are imperfect substitutesof each other, and that supply …nal goods producers in each sector. Intermediate
goods producers face a Calvo-type restriction when setting their price. In eachperiod, a fraction 1

i in each sector (i = C; D) receives a signal to reset prices

optimally. In addition, a fractioni (i = C; D) index their price to last period’s

sectorial in‡ation rate whenever unable to reoptimize.
Intermediate nondurable goods in both countries are produced with labor:
YtC (h) = LCt (h); for all h 2 [0; n]:(21)

YtC (f ) = LCt (f ); for all f 2 [n; 1]:
Intermediate goods in the durable sector are produced combining land and laborwith the following Cobb-Douglas production function:

where

YtD (h) = (At 1 )1

D

LD
t (h)

D

YtD (f ) = (At 1 )1DLDt (f ); for all h 2 [0; n]:D; for all f 2 [n; 1];(22)

D denotes the labor share in the housing sector. In the remaining part of thissubsection, we work out the conditions for the home country …rms’pricing decisions.
In the nondurable sector, cost minimization implies that the real marginal cost of
production equals the real wage:
M CtC =

14

WtC
:
PtC

(23)

In the durable sector, after imposing that the supply of land is …xed (At = A), themarginal cost is given by:
1 WtD D 1
Lt
D PC
t

M CtD =

D

D)

(1

A

(24)

;

where we have substituted for the optimal expression of the rental rate of land:7
D

1

RtA =

D

WtD LDt:A

Firms in the durable sector face the following maximization problem:

M axPtD (h) Et

1
X

k
D

k=0

subject to future demand

82
PD 1
>
< PtD (h) Pt+k
D
6
t 1
4
t;t+k
D
>
Pt+k
:

D
Yt+k
(h) =

where

t;t+k =

k

t+k
t

"

PtD (h)
D
Pt+k

D
Pt+k
1
D
Pt 1

9
>
=
D 7 D
M Ct+k 5 Yt+k (h)
>
;
3

D

D

#

D

D
Yt+k
;

is the stochastic discount factor, andt is the marginal utilityof non-durable consumption.
The optimal choice is given by:
8
1
>
X
>
>
>
>
<

k k
D t+k

P^tD
D
=
Et k=0
D1( D 1) >
Pt
> X
>
>
>
:

k
Y
( D
s=1

k k
D t+k

t+s 1
D
t+s

k
Y
( D
s=1

k=0

)

!

D

)

t+s 1
D
t+s

D

D

!1

9
>
>
D
D >
>
M Ct+k
Yt+k
>
=
>
>
>
>
>
;

D

D
Yt+k

(25)

Given the assumptions about Calvo pricing, the evolution of the price level is:
PtD =

D

h

PtD 1

D
t 1

D

i1

D

+ (1

^D
D ) Pt

1

1
D

1

D

:

(26)

Firms in the non-durable sector face a similar maximization problem, and hence theoptimal price and the evolution of the price level have similar expressions, with the7

We choose the level of A, such that the level of real wages is the same across sectors in thesteady-state.

15

appropiate change of notation.

3.4

Closing the Model

3.4.1

Market Clearing Conditions

In each intermediate good, supply equals demand. We write the market clearing
conditions in terms of aggregate quantities. Hence, we multiply per-capita quantities
by population size of each country. Total production in the non-durable sector isequal to total domestic consumption and exports:

YtC = nCH;t + (1(27)n) CH;twhile residential investment is used to increase the domestic housing stock:
YtD = n [Dt

(1

(28)

)Dt 1 ] :Total hours worked equals labor supply in each sector:
Z nLCt (h)dh

=

0

Z n

Z n

LC;j
t dj

(29)

LD;j
t dj:

(30)

0

LD
t (h)dh

=

Z n
0

0

Market clearing in the international bonds market is:
nBt + (1(31)n)Bt = 0:

Finally, the evolution of aggregate net foreign assets is:~ t 1 Bt 1 + (1nBt = nR

3.4.2n) PH;t CH;tnPF;t CF;t :(32)

Monetary Policy Rule

In order to close the model, we need to specify a rule for monetary policy, whichis conducted by the European Central Bank with an interest rate rule that targets

16

CPI in‡ation and also exhibits interest rate inertia:
1

U
PtEM U =PtEM
1

Rt = RR

Rt R1 exp("m
t ):

EM U

(33)

where the euro area CPI is given by a geometric average of the home and foreigncountry CPIs, using the country size as a weight:n

PtEM U = PtC

4

1 n

PtC

:

Calibration

In the steady state, we assume zero in‡ation, a trade balance of zero, and that the
net international position of both economies is zero. Therefore, we only need tosolve for the per-capita values of the home country, which are the same as those in
the foreign country. We also assume that the degree of monopolistic competition inboth types of goods is the same ( C =), and hence the ratio of prices isD =one. Now, we solve for the levels of consumption of durables, non-durables, hours,
and the economic size of each sector. The optimal steady-state ratio of durable tonon-durable consumption is:
C
=
D

[1

(1

)]

= :

1

(34)

The fraction of spending allocated to non-durable consumption over total spending( ) is equal to:
C
= :
C+ D
Note thatandcannot be calibrated independently. Given values for , , , wecan solve for the value ofin the utility function.

To ensure that the level of real wages in both sectors is the same (despite di¤erent
labor shares), we need to calibrate A =

1
D

1
1

D

LD

. As a result, from the labor

supply conditions by households,(1)LC = LD ;which means that agents spend a fraction
sector, and a fraction 1of time working in the non-durable

in the durable sector.
17

(35)

Table 1 summarizes the values of the exogenous and endogenous parameters of themodel. We set as the home country Spain, and the foreign country the rest of the
EMU. Hence, we set the size of the home economy to n = 0:1. We set the size ofthe construction sector at 1

= 0:1, both in Spain and in the EMU, which isroughly the average size for the value added of the construction sector in the last
decade. We calibrate the bilateral trade parameter ( ) based on total imports fromthe EMU to Spain over total spending, and calibrate its analogous parameter in the
EMU ( ) in a similar way.
For the parameter capturing the debt elasticity to the domestic interest rate, thetechnology, preference and nominal rigidities parameters, we use the estimated values in a companion paper of ours.8 In that paper, we imposed the same parametervalues across countries (except the bilateral imports ratio), so we follow this strategy
here. Therefore, the value foris …xed to 0:02, which captures the idea that interest

rates spreads between Spain and the EMU have been negligible during this period.
In Aspachs-Bracons and Rabanal (2010), the posterior mean estimate for the labormarket rigidities,

L ; is 1:2, a value which is very similar to the one estimated by

Iacoviello and Neri (2010) using US data. We also calibrate the degree of habit
formation ", the elasticity of labor supply , the elasticity of substitution between
home and foreign goods C , and the investment adjustment cost parameter , fromour companion paper.
Having calibrated the real side of the economy, we now proceed to discuss the calibration of the degree of nominal rigidity in each sector and country. In the literature,
there is a long standing debate on the degree of nominal rigidities between housing
and the other sectors of the economy, and how this might a¤ect the transmission
mechanism of monetary policy. For instance, Carlstrom and Fuerst (2007) use theevidence on frequency of price adjustments in the durable and non-durable sectorsof Bils and Klenow (2004) to argue that prices in the housing sector are more ‡exible than in the consumption goods sector. Using this calibration is problematic
because, in the model, a monetary contraction leads to an expansion of residential
investment that is at odds with the data. This result arises because the di¤ering
degree of nominal rigidity across sectors causes a strong movement of relative prices.
We also use the values estimated in Aspachs-Bracons and Rabanal (2010) to calibrate
8

In Aspachs-Bracons and Rabanal (2009), we use standard Bayesian methods to estimate a
DSGE model similar to the one presented here for Spain and the rest of the EMU using data
between 1995 and 2008.

18

the nominal rigidities. Hence, we set prices to be more sticky in the non-durable
sector,C = 0:87, than in durable goods,

D = 0:34. Nominal rigidities parameters

are assumed to be the same between Spain and the rest of the EMU.9 We assume
that the Calvo lotteries for wage setting imply average durations of wage contractsof one year ( C;W =D;W = 0:75) and we also assume full indexation to last period’sin‡ation, given the way wage contracts are set in Spain.10 Finally, we also calibrate
the parameters of the Taylor rule according to the estimates in our companion paper.

4.1

Impulse response functions

In this section, we discuss the main features of the model by presenting the impulse
response functions of a monetary policy shock and a housing preference shock. We
obtain the model’s dynamics by taking a log-linear approximation around the steadystate. In Appendix A we detail the full set of linear equations of the model.

4.1.1

Monetary policy ("mt ) shockFigure 7 presents the impulse response functions of the main variables in Spain to
an expansionary monetary policy shock in the euro area. We choose the size ofthe shock "mt in the Taylor rule expression (33) to simulate an increase of 25 basis
points on impact in the nominal interest rate. Following the shock, consumptionof both good types declines. Similar to what we obtained in the VAR, the e¤ect isquantitatively stronger in the durable sector, although we have trouble matching thelong lags in the transmission mechanism present in the data. Note that we obtain astrong comovement between both sectors even though the degrees of nominal rigidity
in price setting are di¤erent across sectors. Why is this the case? After a monetary
policy tightening, and in response to lower demand, durable good producers candecrease prices faster than the non-durable producers and, hence, the relative pricebetween durables and non-durables decreases (just as in the VAR-based evidence).
Wage stickiness limits the degree to which real unit labor costs di¤er across sectors
and, hence, the movement in relative prices is lower even under asymmetric nominal
9

Assuming that durable prices are ‡exible does not change the qualitative results of our analysis.
Aspachs-Bracons and Rabanal (2009) use information contained in survey evidence for the euroarea in, as explained in Fabiani et al. (2006), as priors.
10
Smets and Wouters (2003) obtain a posterior mean of 0:66 for backward looking wage indexation in the euro area. Using this paramter value instead of full indexation does not change theresults.

19

rigidities in price setting.11 In addition, costly labor reallocation limits the degree towhich sectorial output can di¤er due to di¤erent labor inputs. Hence, as we discussin the following section, labor market and wage rigidities are key to explaining the
data.

4.1.2

Housing preference shock ( Dt )Next, we examine the e¤ects of a housing preference shock in Figure 8. In theirstudy of the US economy, Iacoviello and Neri (2010) conclude that these type ofshocks explain a signi…cant fraction of the volatility of house prices and residential
investment. Darracq-Parriès and Notarpietro (2009) reach a similar conclusion whenlooking at euro area data, and Aspachs-Bracons and Rabanal (2010) …nd a similar
result when using data for Spain and the euro area. In the context of our model, one
could see these demand pressures as stemming from population changes: increased
immigration, the “baby boom” generation that in Spain peaked in the 1970s, andchanges in social attitudes that reduce the number of persons per households andincrease the number of household units.
The housing demand shock is normalized such that residential investment increases
about 10 percent above its long-run value, and the shock has an AR(1) coe¢ cientof 0.9. The preference shock in the durables sector also leads to an increase in
the relative price of durables. Given the small size of the Spanish economy withrespect to the Euro area, interest rates barely react to developments in the Spanish
economy, allowing it to experience a long-lived expansion in this sector. Note alsothat non-durable output slightly increases with the housing demand shock, whichcoincides with the VAR evidence presented above. However, as in Iacoviello and Neri(2010), the positive response of non-durable consumption is quantitatively small. In
the following subsection, we seek to understand which mechanism in the model
generates the comovement between the two sectors.

5

Robustness checks

As argued by Calstrom and Fuerst (2007) and Monacelli (2009), if prices are ‡exible
in one sector but sticky in the other, then a monetary policy contraction will imply
11

Di Ceccio (2009) …nds a similar result in a two-sector RBC model.

20

that output falls in the sticky price sector but will increase in the ‡exible price sector,
contradicting VAR evidence using US data. These papers suggest that introducing
credit constraints and/or labor market rigidities might help solve the comovement
problem even under heterogeneous degrees of nominal rigidity. Hence, in this section
we study how the impact of monetary and demand shocks changes for di¤erent
degrees of labor market rigidities and …nancial frictions in the context of our model.
The key to explaining the VAR evidence is the lack of ‡exibility in the labor market.
This is crucial when there are sector-speci…c shocks.

5.1

The role of labor market frictions

In Figures 9 and 10 we plot how the e¤ect of both shocks changes as we remove
wage stickiness and indexation in both sectors (by setting

C;W=

D;W = 0), and the degree of labor market reallocation (by setting

D;W=

L = 0).

C;W

=

When

we removed a rigidity we do so for both countries. The …rst result to note is that
we do not …nd lack of comovement under a monetary policy shock. Even when bothtypes of rigidities are eliminated, i.e. wages are allowed to be fully ‡exible and thework force can be reallocated instantaneously across sectors, non-durable output anddurable output decrease after a monetary policy tightening. Sticky wages are key toexplaining the fact that residential investment reacts more strongly than non-durable
consumption to a monetary policy shock. When there are no labor market rigidities,
real house prices experience a larger decline, and this tends to push demand for
housing upwards because: a) housing becomes cheaper and b) it is expected toappreciate from a low level. By limiting the variability in real unit labor costs acrosssectors and hence the relative price di¤erential, wage stickiness helps in lowering the
response of residential investment and helps explain its higher sensitivity to interest
rate changes. But it does not a¤ect the comovement properties of the model. Given
that the shock symmetrically a¤ects both sectors, the introduction of labor market
reallocation rigidities does not a¤ect the results in an important way.
On the other hand, since the housing preference shock is asymmetric by nature, themodel needs the labor market reallocation rigidities to explain the VAR evidence. In
Figure 10, we still calibrate the shock to deliver a 10 percent increase of residential
investment under the benchmark calibration. We keep the same size of the shock as
we change features of the model. When the workforce is allowed to be reallocatedinstantaneously after the shock, non-durable output decreases while durable output
21

increases by a larger amount, making it impossible to explain comovement. Wage
stickiness helps in increasing the persistent response of the endogenous variables
to the shocks, but does not a¤ect the comovement properties of the model underhousing demand shocks. Therefore, the conclusion to this subsection is that eachrigidity (wage stickiness and costly labor reallocation) helps explain the comovement
between consumption and residential investment to a di¤erent type of shock. Hence,both rigidities are needed.

5.2

The e¤ects of …nancial frictions

An important reason for concern for policy makers is the accelerator e¤ect associatedwith ‡uctuations in housing prices. The nominal (and real) growth of the housing
sector increases the amount of collateral available, allowing households to borrow
more (or to save less in other instruments) and hence stimulates consumption. Thereis a well established literature that highlights the role of collateral as a key element in
the ampli…cation in the transmission mechanism of shocks through business investment (see Kiyotaki and Moore, 1997; and Bernanke, Gertler and Gilchrist, 1999).
More recently, a new strand of the literature has focused on the role of residential
investment in the transmission mechanism (see Aoki et al., 2004; Iacoviello, 2005;
Iacoviello and Neri, 2009; and Monacelli, 2009). We therefore proceed with ouranalysis by studying how the impact of each shock changes when the fraction of
credit-constrained agents increase, and/or their borrowing capacity changes.
To evaluate the importance of …nancial frictions we analyze how the impact ofa monetary policy and housing preference shocks varies as the fraction of agentswith limited borrowing capacity increases, and their pledging capacity changes. We
extend the model of section 3 by assuming that a fraction 1of agents face credit

constraints. In particular, we assume that these agents, which are typically labelled
as borrowers in the literature (see Monacelli, 2009), are more impatient than theregular agents, whose mass is , and that now we label as savers.
We denote all variables for borrowers with a superscript B.

E0

8
>
1
<X
>
: t=0

2

B;t 6

B;j
4 log(Ct"CtB 1 ) + (1

22

B;j
) D
t log(Dt )

LB;j
t

1+'

1+'

39
>
=
7
5
>
;

where all the indices of consumption and hours worked, and the law of motion of the
housing stock are the same as for the case of savers. Note that borrowers are more
impatient and discount the future at a lower rate:B< . Their budget constraint

in nominal terms is given by:~ t 1 StB;j1
PtC CtB;j + PtD ItB;j + R

StB;j +

WtC LB;C;j
LB;D;j
t
t
+
:
XtC
XtD

(36)

While borrowers can invest in housing, they do not own land as savers do. Also,borrowers do not have access to international capital markets, and hence they obtain
credit from savers, who can trade in international bonds subject to an interest ratedi¤erential, just as in Section 3. Borrowers face a collateral constraint that is tied
to the current value of durable goods (i. e. the housing stock they own):
StB;j
One can interpret the fraction)DtB;j PtD :(1

as a down-payment rate, and hence (1(37)) is theloan-to-value (LTV) ratio. When house prices increase, borrowers are able to borrow
more in order to …nance additional durable and non-durable consumption.12
We present the impact e¤ect of monetary and housing demand shocks as a functionofandin Figures 11 and 12. All other parameter values are set to those in

Table 1. We study an economy where= 0:5 and that includes two levels ofindebtedness of borrowers: a low level (= 0:5, corresponding to an LTV ratioof 50 percent) and a high level (= 0:1, which implies an LTV of 90 percent).

We obtain similar results to those reported in the existing literature: the responsesof both non-durables and durables consumption are larger when …nancial frictions
are tighter. By …nancial frictions being tighter we mean that either there is a larger
fraction of credit constrained agents (lower ) in the economy and/or their borrowing
capacity is more restricted (higher ).
After a monetary policy shock, the response of non-durable consumption does notappear to be sensitive to di¤erent levels of …nancial frictions. The e¤ects on residential investment are more important, especially to di¤erent speci…cations of the LTV,
. The tighter the credit conditions (lower LTV), the larger is the response of1

durable output to a monetary contraction. The conclusions are similar when we analyze the housing preference shock. The response of consumption is barely a¤ected
12

In an appendix available upon request we detail the full set of log-linearized equations.

23

by the presence of …nancial frictions, especially when agents can borrow against it,
but the numerical di¤erences are very small when comparing the response of nondurable consumption to residential investment. The tightness of credit conditions
implicit in the LTV ratio a¤ects the response of durable output, while the fraction of constrained agents in the economy does not appear to play a major role inamplifying the shock.
Overall, even if …nancial frictions seem to amplify the monetary and preference
shocks, their quantitative e¤ects are rather small when compared with a model withhomogeneous agents and no credit constraints (but with labor market frictions). In
Aspachs-Bracons and Rabanal (2010) we estimated that the fraction of …nanciallyconstraints individuals in the Spanish economy was low and it did not improvemodel …t. In the same spirit, Darracq-Parriès and Notarpietro (2009) have di¢ culty
identifying the fraction of credit-constrained individuals in a DSGE model of theeuro area, and show that this extension does not improve model …t.
This does not mean credit constraints are not present in the spanish or EMU data.
But they need to be modelled in a di¤erent way than has been included in theliterature since Iacoviello (2005). One avenue to study would be to allow agents toborrow against their labor income, in addition to housing collateral.

6

The e¤ects of belonging to the EMU

The tools available to Spanish policymakers to react to shocks were reduced substantially when Spain joined the EMU. To analyze the consequences of having abandoned
monetary policy independence, we extend the model of Section 3 by assuming thatboth countries can run their own monetary policy with di¤erent national currencies as units of account.13 We therefore introduce Taylor rules for both countries(Spain, and a hypothetic EMU without Spain) and an uncovered interest rate parity condition, and we assume producer currency pricing for imports and exports of
non-durable goods, as in Lubik and Schorfheide (2006). The goal is to study thereaction of a small open economy in a two country model when faced with housing
demand shocks.
13

Of course, the model abstracts from other potential bene…ts of joining a monetary union, likethe disappearance of exchange rate risk and the lowering of risk premia.

24In log linear terms, the uncovered interest rate parity reads as follows:rtrt = Et nert+1

nert

(38)

bt

where nert is the (log deviation from the steady state) of the nominal exchange
rate, de…ned as units of home country currency per unit of foreign country currency.
This equation links the interest rate di¤erential to the expected depreciation of
the currency, and also includes the endogenous risk premium depending on the net
foreign asset position as percent of GDP of the economy (bt ).
In this case, the domestic interest rate becomes rt , while the foreign interest rate is
rt , and both follow Taylor rules targeting domestic CPI in‡ation:rt =R rt 1 + (1R)

pC
t + (1rt

R rt 1 + (1

R)

pC
t :

=

R) D

pD
t

(39)
(40)

Note that we assume that the coe¢ cients of the Taylor rule ( R and) are thesame across countries. In addition, we consider that the home country can either
run a strict in‡ation targeting regime ( D = 0), or react to deviations in the durable
price in‡ation rate,

D > 0.

Finally, since we have assumed that there is producer currency pricing and that thelaw of one price holds, non-durables in‡ation in both countries is given by:

pC
=
t
pC
t

= (1

pH;t + (1)( pH;t)( pF;t +

st )

(41)

st ) +

pF;t(42)

such that movements in the nominal exchange rate a¤ect directly the price of imports
and exports.
In Figure 13 we compare the impulse response functions of a housing demand shock
under a …xed exchange rate, a pure ‡oating in‡ation targeting regime and a pure‡oating regime with housing in‡ation targeting. We use the same calibrations discussed in Table 1. When we refer to the "No EMU" we set the parameter
while in the "No EMU-HP targeting" we set the parameter

25

D = 0,

D = 0:5. We have also

studied the case in which the Spain Taylor rule targets the nominal exchange rate,
which results in an intermediate case between joining the EMU and running strictin‡ation targeting.
Under a housing demand shock of the same size, the response of output is almost
the same when Spain belongs to the EMU or not. The small impact of this shock
into the euro area economy produces no reaction from the monetary authority, andthe Spanish economy experiences high growth rates in the durable sector, while thenon-durable sector barely reacts, and CPI-in‡ation does not change either. This
explains why the response of the main variables is almost the same because thedi¤erence in the CPI in‡ation paths does not justify a stronger reaction from themonetary authority outside the EMU.
Finally, we analyze the implications of having a monetary authority that not only
reacts to CPI in‡ation, but also to deviations in housing prices. The rationale forthis case is that we assume that the hypothetical monetary policy in Spain would try
to "lean against the wind" when faced with increasing house prices. After a housing
demand shock, in‡ation in the durable sector increases. Therefore, the responseof the monetary authority in this case consists of increasing interest rates, which
reduces non-durable consumption and residential investment, and CPI in‡ation.
Nominal house prices decline but real house prices increase. The collapse in nondurable consumption comes from two channels. The …rst channel is higher interest
rates, and the second is the nominal exchange rate appreciation that comes withhigher interest rates.
Therefore, the monetary policy trade-o¤ is the following: to o¤set the e¤ects ofa housing demand shock, a recession in the non-durable sector of the economy isnecessary, a politically unacceptable consequence to many central banks. To theextent that these reduced form demand shocks are capturing other developments inthe credit or housing markets (for instance, lax credit practices or tax breaks forhome ownership), using another tool directed at those imperfections would be better
than having monetary policy address these distortions directly.

7

Concluding Remarks

In this paper we have studied the recent evidence on interest rates, housing prices andresidential investment in Spain. We have presented some evidence based on a VAR
26

model, and have rationalized our …ndings with a two-country, two-sector model withhousing demand and monetary shocks. One important caveat to the VAR evidence
is that the sample period for the VAR only includes a decade of data during aperiod of transition, and hence the empirical analysis may be subject to nontrivial
small-sample bias— an issue recently emphasized by Chari, Kehoe, and McGrattan(2008). Perhaps one direction for further research would be to use arti…cial data
drawn from stochastic simulations of the DSGE model in order to obtain a roughgauge of the small-sample properties of the empirical analysis.
We have also examined the key features of the model in order to help explain the
results. Of all the mechanisms suggested in the literature, labor market rigidities arenecessary to obtain the right comovement between the two sectors of the economy.
The introduction of …nancial frictions helps in increasing the response of non-durable
goods consumption to both shocks, but this increase can also be achieved under othermodeling assumptions. The model is linearized around a steady state, assuming no
imbalances in trade or the current account. While this approach simpli…es theanalysis considerably, it does seem to be a important departure from reality. Future
research regarding the implications of linearizing the model around a qualitativelydi¤erent steady state.should be considered.
We have studied the cost of losing monetary autonomy (i.e. through currency union
membership). We conclude that the behavior of the Spanish economy under its
own monetary policy or under euro membership does not change the outcome to a
housing demand shock due to the following reason: even if the shock has importante¤ects on residential investment and house prices, Spanish CPI in‡ation does notchange, and hence an in‡ation targeting monetary authority remains passive ineither case. However, if the Spanish monetary authority reacts to housing pricechanges, the response of the main variables di¤ers substantially, with high costsin the non-durable sector: non-durable output su¤ers an important and persistentcontraction. Hence, it is not clear at all that if Spain had not belonged to the
EMU the boom-and-bust cycle in housing prices between 1996-2007 could have been
avoided by using monetary policy.
The case of other advanced economies provides additional evidence to support thisargument. Fatás et al. (2009) and Dokko et al. (2009) study the relationshipbetween the stance of monetary policy (proxied by Taylor rule residuals) and realhouse price increases during 2002-2006. Both studies …nd that the cross-country27relationship between the two variables is statistically weak. Both studies single out
the case of Spain, where monetary policy was about 300 basis points on average
below the prescriptions of a standard Taylor rule, and house prices appreciatedabout 80 percent. But both studies also mention the cases of the United Kingdom,
New Zealand and Australia where monetary policy was not loose and yet the housing
price boom was sizable.14 Finally, Dokko et al. (2009) provide simulations basedon the FRBUS model and conclude, as we have shown in this paper, that monetary
policy tightening would likely only have marginal e¤ects in containing a house pricebubble and might well be detrimental to other sectors of the economy.

14

In this context, it might be interesting to note the position of the newly elected government
in the U.K. who is inclined to incorporate housing prices in a comprehensive measure of consumer
prices. In his letter of May 18, 2010 to the Governor of the Bank of England, the Chancellor of the
Exchequer George Osborne mentioned that “As we have discussed, over the longer term I would
welcome your views on how we might accelerate the process of including housing costs in the CPI in‡ation target.”The letter is available at http://www.hm-treasury.gov.uk/ukecon_mon_index.htm

28

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29

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Reserve System.
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30

[23] Lubik T. and F. Schorfheide, 2006. A Bayesian look at new open economy
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381-419.

31

A

Appendix: Linear approximation

Here we present the loglinear conditions. Also, we de…ne the relative price of
PD

P

F;t
durables in terms of non-durables as Qt = PtC , and the terms of trade as Tt = PH;t.
tAlso, ! it denotes deviations from the real wage from steady-state values, de…ned asnominal wage (Wti ) divided by the CPI (PtC ), for i = C; D:
From the optimal decisions by savers we get the following:
ct

qt
where

"ct 1
+ (it
1 "

it 1 ) =t+(Et it+1

(43)

it )

= S"(:).

[1)] ( Dt(1dt ) =

q t = qt 1 +" ct = Et ct+1

(1

t

pD
t

(1

(44)

)Et t+1

pC
t

")(~
rt

(45)

Et pC
t+1 )

(46)

Under Calvo wage setting and with partial indexation to past non-durable (CPI)in‡ation (with coe¢ cients 'C;W and 'D;W ), the wage-setting equations can be loglinearized into to the following wage Philips curves:

!C
t

!C
t 1+
+ C;W

where

C;W

!D
t

=

(1

ct

C;W )(1

pC
t

!D
t 1+

D;W

=

(1

ct

C
'C;W pC
t 1 = Et ! t+1

"ct 1
+ [('
1 "

C;W

+ D;W
where

pC
t

C;W )

D;W

)(1

pC
t+1
)ltD

'C;W pC
t
!C
t

(47)

, and

D
'D;W pC
t 1 = Et ! t+1

"ct 1
+ [('
1 "

D;W )(1) + ] ltC + ('

!C
t +

D;W )

)(1

.

32

!D
t +

) + ] ltD + ('

pC
t+1
) ltC

'D;W pC
t
!D
t

(48)

The relationship between the domestic and the EMU-wide interest rates is as follows:^bt

r~t = rt(49)

where ^bt =(Bt =Yt Pt ) denotes the deviation of foreign assets as percent of GDP fromits steady-state value of zero.
The evolution of net foreign assets is:^bt = 1 ^bt 1 + (1

n)(1
n

)

cH;t

tt

(1

(50)

)cF;t

The evolution of domestic and imported non-durable consumption iscH;t = (1cF;t =)tt + ct(51)

tt + ct(52)

Here we list the evolution of the foreign country variables for households:
ct

qt

[1

"ct 1
+ (it
1 "

(1

)] ( Dt

it 1 ) =dt ) =

!C
t

C;W

!C
t 1+

ct

pC
t

t

pD
t

qt = q t 1 +" ct = Et ct+1

t +

(1

)

")(rt

+ ] ltC + ('

33

(1

(53)

it )

(54)

)Et t+1

pC
t

C'W C pC
t 1 = Et ! t+1

"ct 1
+ [('
1 "

(Et it+1

(55)

Et pC
t+1 )

!C
t +

)(1

(56)

pC
t+1

)ltD

'C;W pC
t

!C
t

+

(57)

!D
t

!D
t 1+

D;W

where

C;W

ct

pC
t

D
'D;W pC
t 1 = Et ! t+1

"ct 1
+ [('
1 "

and

D;W

!D
t +

) + ] ltD + ('

)(1

pC
t+1

)

ltC

'D;W pC
t

+

!D
t

(58)

are the same as in the home country. The demand for foreignand domestic goods is:cH;t =
cF;t =(59)

tt + ct(1(60))tt + ct

where we have used the de…nition of the terms of trade, the fact that tt =tt , andthe evolution of the terms of trade is given by:
pFt

pH
t :

(61)

pC
t + (1

) pD
t

(62)

pC
t + (1

) pD
t

(63)

pH;t + (1) pF;t

(64)

pF;t

(65)

tt = tt 1 +The de‡ators of the …nal goods are

pt =

pt =
where CPI in‡ation is given by

pC
t =
pC
t = (1) pH;t +The production functions are given by:
ytC = ltC

34

(66)

D D
lt

ytD =

(67)

ytC = ltC

(68)

ytD =

(69)

D D
lt

And the pricing equations are given by
pH
t
C

where

pD
t
where

D

= (1

H
'C pH
t 1 = Et ( pt+1
C )(1
C

C)

D )(1
D

C

!C
t + (1

(70)

)tt

.

D
'D pD
t 1 = Et ( pt+1

= (1

'C pH
t )+

D)

'D pD
t )+

D

!D
t + (1

D

)ltD

qt

(71)

.

For the foreign country, after assuming symmetric Calvo parameters, we get that:
pFt

pD
t

'C pFt 1 = Et ( pFt+1

D'D pD
t 1 = Et ( pt+1

'C pFt ) +

'D pD
t )+

D

C

!C
t

!D
t + (1

(1

D

(72)

)tt

)ltD

qt

(73)

The market clearing conditions for the goods sectors read as follows:
ytC = cH;t +
ytC =

(1

n)(1
n

cF;t +

)

cH;t

n(1
)
cF;t
1 n

(74)

(75)

dt = (1)dt 1 + ytD(76)

dt = (1)dt 1 +

ytD

(77)

ytD = it(78)

ytD = it(79)35

while for the labor market it is:lttot = ltC + (1lttot; =ltC + (1

)ltD

(80)

)ltD

(81)

To close the model, we specify a monetary policy Taylor rule conducted by the ECB:rt =R rt 1 + (1

R )(

U
pEM
) + "mtt(82)

where the euro area CPI is given byU= n pCpEM
t + (1
t

36

n) pC
t

(83)

B

Tables and Figures
Table 1: Calibrated Parameters of the Model
Size of Spain inside the EMU

0:1

Share of the non-durable sector in the GDP

0:9

1

Fraction of EMU imports consumed in Spain

0:15

1

Fraction of Spain imports goods consumed in the EMU 0:015

nDebt elasticity of the domestic interest rate

0:02

Elasticity of substitution between intermediate goods

10

Discount factor

0:99

Depreciation rate of housing stock

0:025

Habit formation

0:4

Labor supply elasticity

0:9

C

Elasticity of subs. between goods

4:4

L

Costly labor reallocation

1:3

Share of non-durable consumption in the CPI

0:82

Investment adjustment costs

0:3

C

Calvo lottery for the non-durable sector, prices

0:87

D

Calvo lottery for the durable sector, prices

0:34

C;W

Calvo lottery for the non-durable sector, wages

0:75

D;W

Calvo lottery for the durable sector, wages

0:75

C

Price indexation, non-durables

0:5

DPrice indexation, durables

0:7

C;W

Wage indexation, non-durables

1

D;W

Wage indexation, durables

1In‡ation parameter of the Taylor rule

1:25

Interest rate smoothing parameter of the Taylor rule

0:77

C;

"

R

D

37

Figure 1: Nominal house prices and interest rates.

Figure 2: Residential Investment and interest rates.

38

Figure 3: Mortgage credit and the current account.

Figure 4: Demographic patterns

39

Figure 5: Impulse response from VAR, monetary policy shock.

40

Figure 6: Impulse response from VAR, housing demand shock.

41

Figure 7: Impulse response to monetary policy shock. X axis: quarters after shock.
Y axis: percent deviation from steady-state values.

42Figure 8: Impulse response to a housing preference shock. X axis: quarters after
shock. Y axis: percent deviation from steady-state values.

43

Figure 9: Impulse response to a monetary shock. The role of labor market frictions.

44

Figure 10: Impulse response to a housing preference shock. The role of labor market
frictions.

45

Figure 11: Impulse response to a monetary shock. The role of …nancial frictions.

46

Figure 12: Impulse response to a housing preference shock. The role of …nancial
frictions.

47

Figure 13: Impulse response to housing preference shock. The e¤ects of belonging to
the EMU. X axis: quarters after shock. Y axis: percent deviation from steady-statevalues.

48