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Fundación de Estudios de Economía Aplicada

The Role of Construction in the Housing Boom and Bust in Spain by Carlos Garriga DOCUMENTO DE TRABAJO 2010-09

February 2010

Federal Reserve Bank of St. Louis

The Role of Construction in the Housing Boom and Bust in Spain

Carlos Garriga Federal Reserve Bank of St. Louis

February 8th, 2010

Abstract

This paper describes a quantitative model developed to account for the change in the level of house prices (boom-and-bust cycle) in Spain. The driving forces behind the housing boom are residential investment, immigration, current account deÖcits, and the elimination of land regulation. The model emphasizes the interaction of housing supply (determined by the existing stock of residential investment and new construction) with market demand. A calibrated version of the model for the Spanish economy replicates the key aggregate of the economy in 1995. The model predicts that a change in observed fundamentals can rationalize at least 84 percent of the recent boom in the value of housing capital. The model suggests that without large current account deÖcits and demographic changes the housing boom could have been much smaller. With respect to the housing bust, the model suggests that the combination of increasing mortgage rates, unemployment, and low productivity can have large e§ects in the value of housing capital. Some conservative predictions quantify adjustments that range between 24 and 29 percent.

Keywords: Residential investment, mortgages rates, immigration J.E.L. codes: E2, E6

The author is grateful to the stimulating discussions with Samuel Bentolila, JosÈ GarcÌa Montalvo, Rody Manuelli, Robert F. Martin, Adrian Peralta-Alva, Don Schlagenhauf. The editorial comments from Judith Ahlers have been useful. The research has been supported by the National Science Foundation (grant No. SES-0649374) and the Spanish Ministerio de Ciencia y TecnologÌa (grant No. SEJ2006-02879). The views expressed herein do not necessarily reáect those of the Federal Reserve Bank of St. Louis nor those of the Federal Reserve System. Correspondence: Federal Reserve Bank of St. Louis, P.O. Box 442, St. Louis, MO 63166. Email: Carlos.Garriga@stls.frb.org.

Contents

1 Introduction ..... 3 2 Empirical Evidence ..... 6 3 The Economy ..... 11 3.1 House Price Fluctuations and Residential Investment ..... 12 3.2 Closed Economy ..... 15 3.3 Small Open Economy ..... 19 4 The Housing Boom-and-Bust Cycle in Spain ..... 20 4.1 Parameterization of the Model: 1995 ..... 20 4.2 Sources and Decomposition of the Housing Boom: 1995-2007 ..... 22 4.3 Counterfactual Experiments: 1995-2007 — An Alternative Story? ..... 27 4.4 Housing Bust: 2007-09 ..... 27 5 Housing Policy: Lessons Learned from the Literature ..... 31 6 Conclusions ..... 34 7 References ..... 34 8 Appendix ..... 36 8.1 First-Order Conditions of the Consumer Problem and Pricing Functions ... 36 8.2 Equilibrium with Housing Policy ..... 37

1. Introduction

In the past two decades, there have been important movements in real estate values and aggregate economic activities in many developed economies. These booms are characterized not only by a rapid increase in house prices, but also by an expansion in the proportion of households who own the house they occupy. The magnitude of these changes is signiÖcant. As Table 1 suggests, most countries in the Organisation for Economic Co-operation and Development (OECD) also had double-digit house price appreciation over an extended period. House prices in Spain have shown one of the biggest cumulative growth rates among the OECD countries over the past Öve years and, indeed, over a more extended period. The increases in house prices have been combined with simultaneous increases in home ownership. In some countries like Spain, Greece, Italy, France, and Sweden the expansion exceeds 800 basis points.

Table 1: House Prices and Ownership Rates in the OECD

D ata source for ow nership: U N E C E E nvironm ent and H um an Settlem ents D ivision, H ousing database, 2003 D ata source for nom inal house price appreciation: "C hecking the E ngine," E conom ist, June 7, 2007

These recent movements in housing prices have raised many concerns. To what extent are these housing price áuctuations consistent with fundamental conditions? In countries like the United States, part of the boom was fostered by important developments in housing Önance that include the introduction of new mortgage products, a reduction in the cost of providing mortgage services, and expansion of subprime lending and private securization. For example, instruments such as piggyback loans and option-adjustable rate mortgages (ARM)

accounted for 12.5 percent of the originations in 2004 and 32.1 percent in 2006. Chambers, Garriga, and Schlagenhauf (2009a, 2009b) use a quantitative model to explore the impact of innovation in housing Önance and changes in the demographic structure in the U.S. housing boom. Their Öndings suggest that these innovations account for roughly two-thirds of the boom in home ownership, whereas demographics account for the remaining one-third. More recently, Bernanke (2010) has discussed the same issues arguing, for the similar importance of mortgage innovations.

In Spain, the driving factors could be somewhat di§erent. Over the past decade, the Spanish economy has experienced by important structural changes. Some of these changes could have made an important contribution to the housing boom. First, the Spanish economy seen major demographic changes. The total population increased roughly 18 percent, and the workforce population increased 25 percent. Most of the growth (98 percent) was due to immigration áows from Eastern Europe, Latin America, and North Africa. Second, the integration into the European Monetary Union was a key factor in lowering the cost of borrowing. In real estate markets, mortgage rates in Spain sharply declined during this period (i.e. nominal mortgage rates were 12 percent in 1995, 3.5 percent in 2005, and 5 percent in 2007). The decline in mortgage rates was fueled by a sizable current account deÖcit that increased from 0 to 10 percent. This deÖcit has allowed Önance consumption and borrowing without relying on domestic savings. MartÌnez-PagÈs and Maza (2003) Önd that income and nominal interest rates are pivotal explanatory factors. Another important factor has been the liberalization of constructible land. In 2003, the government voted a to liberalize the real estate sector. The result was a 28 percent increase in the availability of land for construction.

The housing boom could also have been caused by other non-fundamental factors, such as speculators driven by the high yields in the sector, changes in family size, or home purchases by retired households from Northern Europe and the United Kingdom. Although all these factors could be relevant, the focus of this paper is restricted to the role played by the fundamental factors.

The paperís main objective is the development of a quantitative theory that accounts for the change in the level of house prices between 1995 and 2007 in Spain. Some necessary elements need to be formalized to understand the large increase in house prices in Spain. The paper argues that a key element is the evolution of the price of land and its contribution to the value of housing capital. Despite the land deregulation of the sector, most of the increase in the value of housing capital can be attributed to the price of land. This is a key driving force in the modeling strategy. With such a framework, it is also possible to (1) determine the relative importance of the di§erent contributing factors and (2) perform some counterfactual exercises to determine the magnitude of the housing boom and residential investment had these factors been di§erent. In addition, the model can be used to predict future changes in the levels of house prices when the economy is subject to changes in the same fundamental variables (i.e., higher mortgage rates, declines in employment, and lower productivity). The formal economy considers two productive sectors. One sector produces consumption goods and the other produces residential investment. Housing services are generated by combining structures and land. The quantitative version of the model considers a small open economy to accommodate capital áows. Appendix 8.2, shows some model extensions that consider the introduction of housing policy.¹

The baseline model can rationalize 84 percent of the increase in the real value of the housing stock and 82 percent of the increase in the real value of land as a response to the change in fundamentals (demographics, liberalization of land use, and lower interest rates). In a decomposition exercise, the contribution of each factor with respect to 1995 values assigns roughly 33 percent to immigration and low rate, respectively, and 7 percent to the elimination of land regulations. However, a single-factor decomposition analysis ignores the interaction of the combined e§ects essential to understanding the housing boom. For example, the model suggests that the combined e§ects of low mortgage rate and demographics are larger than the sum of the separate e§ects. These results are consistent with Gonzalez and Ortegaís (2009) empirical estimates. They Önd that immigration can account for roughly one-third of the housing boom, both in terms of prices and new construction.

The model also is used to perform some counterfactual experiments. The model predicts that a decline in mortgage rates from 9 percent to 6 percent should have generated a housing boom that is 20 percent smaller with respect to fundamentals and 32 percent with respect to the actual data. This experiment suggests that the current account deÖcits supporting the mortgage rate decline had an important contribution in the housing boom. Without such a áow of funds, the magnitude of the house price increase would have been much smaller.

Most experts seem to agree that house prices in Spain will need to adjust downward to align with income. The model can address the long-run e§ects of fundamental changes in house prices and the value of housing capital, and it suggests that the combined e§ects of higher mortgage rates, a decline in unemployment, and lower productivity can have signiÖ- cant e§ects in the value of housing capital. Some conservative predictions suggest declines between 24 and 29 percent. The current adjustment in house prices in Spain is still far from these magnitudes. However, it is not clear whether the current values will be sustainable in

¹LÛpez-Garcia (2004) studied the impact of housing policy on house prices in Spain. The model predictions suggest that the removal of housing subsidies implicit in the personal income tax would entail a substantial decline in the real price of housing and in the stock of housing. However, the quantitative results depend on the assumptions about the nature of land prices.

the long run.

This is not the Örst study to consider the impact of land or demographics on house prices. Several papers highlight the potential importance of the supply side of the market in understanding áuctuations in housing prices. For example, Kiyotaki, Michaelides, and Nikolov (2008) develop a quantitative general equilibrium model to study the interaction between housing prices and aggregate production. In their economy, land and capital are used to build residential and commercial real estate. They Önd that when the share of land in the value of real estate is large, housing prices react more to an exogenous change in expected productivity or the world interest rate, causing a large redistribution between net buyers and net sellers of houses. Davis and Heathcote (2006) document that the dynamics for the prices of residential land and residential structures are substantially di§erent. They Önd that the real price index for residential land almost tripled between 1975 and 2005, whereas the real price of structures increased by only 24 percent. Green, Malpezzi, and Mayo (2005) Önd that housing supply regulations are a key factor in explaining di§erences in housing supply elasticities across U.S. metropolitan areas. Van Nieuwerburgh and Weill (2006) argue that the increase in the dispersion of housing prices across regions can be quantitatively generated from an increase in the dispersion of earnings in the presence of planning restrictions.

In principle, changes in the demographic structure can have important e§ects on the demand for housing and ultimately on house prices. In a classic paper, Mankiw and Weil (1989) explore the connection between the baby boom in the United States and house prices. They argue that a demographic boom generates a level e§ect on demand because more individuals demand homes, but the boom also has a composition e§ect because the group of individuals purchasing also matters (i.e., young vs. middle-aged). Their Öndings suggest that the level e§ects should drive prices up in the short run, but as the baby boomers retire, home prices should be expected to fall because of insu¢ cient demand to purchase all the housing units from retired individuals. Although this argument is attractive, their predictions for the U.S. housing market and the baby boom generation (1978-85) proved to be incorrect. They predicted a large e§ect of the baby boomers on the housing market, but they had only a very small e§ect on home ownership and house prices, certainly less than the boom predicted by these economists. However, the model presented herein suggests a di§erent contribution of demographics to the housing boom.

2. Empirical Evidence

This section describes the evolution of the key variables in housing markets for the Spanish economy. The series for house prices and construction of new dwellings are collected from the Spanish Housing Ministry (http://www.mviv.es/es/). The house price data are available at a quarterly frequency. The data measure the nominal value of a square meter and include the sales of new and existing units. The data for residential investment include the total number of dwellings completed in a given year. Figure 1 shows an impressive boom in house prices and residential investment.

Figure 1: House Prices and Residential Investment in Spain (1995-2009)

Between 1998 and 2008, the house price index per square meter in Spain roughly tripled (345 percent) in nominal terms and more than doubled in real terms (221 percent).² This rapid increase implies an average annual appreciation of 11.5 percent in nominal terms and around 6.3 percent in real terms. These magnitudes are large both in nominal and real terms, especially from a historical perspective. The housing boom in Spain makes the boom in the United States appear small. In the case of the U.S. economy, the estimates of the di§erent price indices suggest that the implied annual nominal appreciation ranged between 4.2 and 6.1 percent (see Freddie Mac Conventional Mortgage Home Price Index (http://www.freddiemac.com/Önance/cmhpi/) and Case-Shiller House Price Index (http://www.standardandpoors.com)). These are clearly di§erent orders of magnitude.

The housing boom in Spain is even more surprising given the large increase in residential construction activity during the period. The number of new units put in place between 1998 and 2007 doubled, and the share of construction in Spainís Gross Domestic Product (GDP) increased by 4 percentage points, attaining 10.7 percent in 2008. For example, in the U.S.

²This aggregate number has some dispersion because some coastal areas such as Andalucia (243%), CataluÒa (214%), and Valencia (227%) had larger increases than inland locations such as Castilla-LÈon (138%) and Madrid (178%). The nature of the dispersion of prices is not discussed here, but the model could be extended to price the amenities from coastal areas.

the share of residential investment over GDP during the same time period grew from 4 to 6 percent (see Fisher and Quayyum, 2006).

Between 1995 and 2007, the increased value of the price per square meter and the expansion of the housing stock generated an increase in the nominal value of the housing stock by a factor of 4.3 and 2.78 in real terms. This increase is mainly due to an important component in the value of housing capital: the value of land. In Spain, Uriel et al. (2009) show that the share of land in house prices was 25 percent in 1995,but increased to 46 percent in 2008. They argue that during this period 84 percent of the increase in house prices is due to land costs. Figure 1b summarizes the evolution of the value of the housing stock, the value of the structures, the value of land, and the house price index in real terms.

Figure 1b: Components of the Value of Housing Capital in Spain (1995-2009)

The Ögure suggests that the increase in the value of housing capital is higher than the house price index. The di§erence is the expansion of the housing stock that resulted from the boom in residential investment as a fraction of GDP. Uriel et al. (2009) estimated that the value of land increase by a factor of 8.2 in nominal terms and 5.25 in real terms. The increase in the value of land is even more surprising considering that government liberalization of land use expanded the land available for construction by roughly 30 percent. The evolution of

Figure 2: The Role of Land in the Housing Boom in Spain (1995-2009)

Two important forces in housing Önance fueled the housing boom. In Spain, the housing market is very sensitive to mortgage rates. The rates are quite relevant since more than 80 percent of homeowners use ARMís to Önance the purchase of a house. This number is much larger in contrast with the 15 percent who use ARMs in the U.S. economy. According to the Bank of Spain, the average mortgage rates in Spain have steadily declined from 17 percent in 1991, to 10 percent in 1996, to 3.5 percent around 2004-05. An important factor lowering interest rates was the integration of Spain into the European Monetary Union. Nevertheless, the global Önancial crises that started in the summer of 2007 a§ected credit conditions across developed economies. In Spain this was reáected in an increase in mortgage rates to levels around 6 percent in 2009, which is particularly important given the majority of homeowners holding ARMs.

The expansion in housing Önance has been sustained by a large current account deÖcits as a fraction of GDP (Figure 3). The deÖcit has made it possible to Önance consumption and the purchase of homes without relying on domestic savings.

Figure 3: Current Account DeÖcits over GDP (1995-2009)

The lower rates and capital áows can be explained by the liberalization of the mortgage market. For example, the fraction of outstanding mortgage debt over GDP grew from 14 percent in 1990, to 29 percent in 2000, to more than 61 percent in 2007. The 2007 Ögure is closer to the aggregate leverage ratio of the U.S. economy roughly 97 percent of GDP.

The important changes in housing Önance have been accompanied by important changes in the demand side. In the past decade, the Spanish economy has experienced a large ináux of immigrants, particularly in the workforce. In absolute terms, the number of foreignborn population increased from 1.2 to 6 million in only 10 years. This change is very signiÖcant, given that the total number of native-born residents in the same period has only increased from 38.7 to 40.1 million. The relative importance of the foreign-born population is summarized in Figure 4.

Figure 4: Demographic Changes in Spain

In the past decade, the share of immigrants among the total population increased from 3 to 15 percent. Immigration accounts for most of the increase in total population. The áow of immigrants has had an important e§ect in the labor markets. In particular, the total working-age population has increased from 26.7 to 31.3 percent; however, 98 percent of that growth is due to immigrants. The magnitude of immigration áows can be important to reconcile the simultaneous increase in house prices and residential investment during this period. The addition of new workers increased the demand for housing goods and provides more workers for new construction. The combined e§ect is an increase in the level of e§ective workers from 41 percent to 56 percent of total population in 2008 ó a 37 percent increase in the size of the labor force. The change of the population structure in the workforce is summarized in the right panel in Figure 4. As a result, the reallocation of resources from the production of consumption goods into housing could be a contributing factor in the housing boom.

3. The Economy

The choice of the model is driven mainly by the goal of reconciling the change in the levels of house prices and the boom in residential investment. The model has two sectors. One sector produces consumption goods using a linear technology where labor is the only input, whereas the other produces residential investment. Housing services are generated by combining structures and land. The baseline formulation considers a closed economy. Later this assumption is relaxed to accommodate capital áows and discuss additional extensions.

3.1. House Price Fluctuations and Residential Investment

In this section a simple equilibrium model is developed to determine house prices. The model provides some basic intuition and is useful in understanding two ideas. The Örst is the connection between interest rates and house prices, whereas the second reáects the challenges faced in the literature to simultaneously understand the boom in house prices (the boom-bust cycle) and residential investment (changes in the housing supply). The model has limitations but is helpful in illustrating these key ideas.

Consider an economy where two investment opportunities are available. Individuals can either invest resources in (1) a riskless technology (i.e. bank deposit or savings accounts) earning a return denoted by r or (2) housing This second alternative requires the purchase of a house, which generates an income áow of housing services Rs; where R represents the market value of selling/renting one unit of space : The house can be sold in the market the following period without incurring any transaction costs. In the absence of frictions, the rate of return from both investments (bank and housing) must be the same. Formally,

\[1 + r _ {t} = R (1 + r _ {t}) + \frac {p _ {t + 1}}{p _ {t}},\tag{3.1}\]

where the purchase price and is the selling price. This expression states that the rate of return of investing one dollar ($1) and earning tomorrow must be equivalent to purchase a house today, receive some rental payments from the house that can be deposited in the bank, , and then sell the house tomorrow. Selling the house generates a capital gain (loss) that depends on the di§erence between the purchase price, ; and the selling price, : The return from purchasing a house has two components: the service áow from the property and the capital gains (losses). The expression can be used to determine the price to pay per unit of housing today. Formally,

\[p _ {t} = \underbrace {R _ {t}} _ {\text {User Cost} = R _ {t}} + \underbrace {\frac {p _ {t + 1}}{1 + r _ {t + 1}}} _ {\text {Resale Value}}.\tag{3.2}\]

The new expression decomposes the price paid for a unit of housing (this concept is di§erent than the rate of return) as a function of the rental price and the expected discounted resale value tomorrow. This expression ignores the presence of bubbles in the pricing equation that would cause the price to deviate from the asset fundamentals, transaction costs associated with the purchase and sale of the property, and any asymmetry in the tax treatment of tenant versus owner-occupied housing. In addition, when housing acts as collateral, the pricing equation should also include an additional term that captures the beneÖts and costs of changes in the value of the housing in the collateral constraint. Thus, it is useful to illustrate the key determinants of housing valuation. This expression can be iterated forward to compute the price in the event of sale in period

\[p _ {t} = R _ {t} + \frac {R _ {t + 1}}{1 + r _ {t + 1}} + \frac {p _ {t + 2}}{(1 + r _ {t + 1}) (1 + r _ {t + 2})},\tag{3.3}\]

and the same procedure can be used to determine the current price for di§erent buy, hold, and sell strategies. Two things become obvious: The longer you hold the property the more you should be willing to pay, whereas if the resale value is expected to decline, the current price should be lower. The expression encompasses most of the important elements that determine house prices: the value of the rental áow, expected appreciation, and the discount rate (i.e. opportunity cost of alternative investments). Consider a special case: when the house is viewed as an inÖnite console (where the growth rate of rental income is zero, . In this case, the pricing expression can be written as

\[p = \frac {R (1 + r)}{r - g} \approx \frac {R}{r}.\tag{3.4}\]

According to this expression house prices can rise (decline) as a result of two factors: a change in the rental prices and/or interest rates. A permanent increase in the market value of rental income should increase by more than one for one the house prices, since . Similarly, a decline in the interest rate should generate an increase in the house price, : A simple way to test the model is to regress the log of prices against the log of rental rates and interest rates. This regression presents several problems. First, data estimates for rental prices are di¢cult to obtain. In addition, houses have di§erent attributes and characteristics that are not captured by house size as the model predicts. A second problem with this analysis is that rental value is not independent of the interest rate. Changes in the interest rate are likely to modify the intertemporal allocation of consumption, which changes the implied user cost. Therefore, the Önal e§ect on house prices depends on the relative strength of both e§ects, : To understand the joint determination of rental prices and interest rate it is necessary to impose additional structure on the economy.

Letís now assume that there exists a Öxed supply of house, and each unit of housing generates a áow of housing services that depends on the size of the units purchased that period, : Individualís value consumption of goods, ; and housing services, and use a utility function, ; to rank di§erent bundles of goods. The utility function satisÖes the standard properties ; and the Inada conditions. These properties suggest that consuming either more consumption goods or housing services increases the individual well-being. However, each additional unit of consumption has diminishing returns, or decreasing contributions to the total level of utility, u:

In this economy, the consumer faces a trade-o§ between consumption goods and housing services. The optimal decision equates the marginal rate of substitution of these goods to the relative price, since the price of consumption goods has been normalized to 1. The price of one unit of housing is tight to consumer preferences:

\[p _ {t} = \underbrace {\frac {u _ {2} (c _ {t} , s _ {t})}{u _ {1} (c _ {t} , s _ {t})}} _ {\mathrm{UserCost} = R _ {t}} + \underbrace {\frac {p _ {t + 1}}{1 + r _ {t + 1}}} _ {\mathrm{FutureValue}}.\tag{3.5}\]

To illustrate the nature of changes in the level of house prices it is useful to make some additional assumptions about the model. Assume that preferences are characterized by ; where and : In a representative agent economy without capital, the optimal level of consumption is determined by labor income : In this case, the pricing equation becomes

\[p \approx \frac {\gamma}{r} \left[ \frac {w N}{A _ {H} H} \right] ^ {1 - \rho}.\tag{3.6}\]

The formula relates house prices to fundamentals and not bubbles. According to expression (3.6), house prices should increase (decrease) with wages, employment (or hours worked), a change in the relative importance of housing in the utility function, or a decline in interest rates. Therefore, each factor can be an important contributor to the housing boom and bust. For example, the U-shaped pattern of labor income and mortgage rates between 1998 and 2009 would be consistent with the boom-bust cycle observed in the Spanish economy.

One important challenge in a model based on economic fundamentals is rationalizing the simultaneous increase in house prices and residential investment. Equation (3.6) suggests that an increase in the stock of homes, H; should decrease the house prices, p: In the case of positive residential investment, prices and quantities work in opposite directions. An excess of supply can be an important factor in explaining the housing bust, the challenge is to explain the boom while the supply is expanding. To reconcile house price movements with sizable changes in residential investment it is necessary to introduce an additional Öxed factor: land. In the presence of land, a house becomes a composite good that depends on the price of the structure, ; and the market value of that land, vL: The next section develops a more complex economy to explore the role of residential investment in the boom-bust cycle

in Spain.

3.2. Closed Economy

In the economy the size of total population at a given time point is : Since the focus of the paper is the change in the house price index between 1998 and 2009, it is useful to normalize the population of the initial time period, ; to unity, ; and assume that the total level of the population remains constant in the long run, Following Martin (2005), the demographics in a representative agent are introduced by assuming that the time endowment varies through time, : This variable can be interpreted as either a time-varying endowment or as the number of individuals in the total population who are available to work. A change in the time endowment or the fraction of individuals who can work is equivalent to a change in the workforce due to demographics. In particular, the áow of immigrants will be modeled as a combined increase in total population, , and the time endowment,

As in the previous section, individual preferences are deÖned by a time-separable utility function, . The sequence of utilities is discounted at a rate : In addition to goods consumption and housing services, the representative consumer chooses a sequence of housing structures or housing capital, ; bond holdings, , and land holdings, A house in the model is complex object. Housing services are produced according to a technology ; that combines the physical structure (or building) and the land on which the structure sits. The technology has constant returns to scale and satisÖes ; but : The term is a reduced form of capturing the presence of land regulations that can limit the utilization of the existing stock of land over time.⁴ With this speciÖcation, homes in the model have two dimensions. One is the size of the dwelling or the livable space. The other element is the size of the lot (or land) where the structures are located. The ratio of land over structures, ; can be interpret as density.⁵ Formally, the representative consumer chooses the relevant variables for all

³Since the stock of land is Öxed, assuming a constant level of population in the long run eliminates the problem of having the share of land converges to zero. The purpose of the paper is to understand the change in house prices between di§erent time periods, not to deÖne the stationarity properties of an economy with a Öxed factor.

⁴This parameter is determined outside the model and is taken as given by the consumer.

h_t+1;

⁵Formally, a ìhouseî in the model is deÖned as a combination of infrastructures, and land, L_t+1; Lt+1 that produces a given amount of housing services. For simplicity and interpretation, the notion of a house is normalized to a single unit of housing services, s_t = 1: This notion can be interpreted as the price per St = 1 square meter. The price of a house can be computed by solving such that p = qh + vL: Any g(h; L) = 1 p = qh + vL combination of infrastructures and land can be priced using the above expression.

the individuals in the economy, : Formally,

\[\max \sum_ {t = 0} ^ {\infty} \beta^ {t} u (c _ {t}, s _ {t}) N _ {t},\]

\[\begin{array}{c} s. t. \qquad N _ {t} c _ {t} + B _ {t + 1} + q _ {t} H _ {t + 1} + v _ {t} (L _ {t + 1} - L _ {t}) = w _ {t} N _ {t} ^ {w} + \ldots \\ (1 + r _ {t}) B + q _ {t} (1 - \delta) H _ {t} + R _ {t} (g (H _ {t + 1}, \chi_ {t} L _ {t + 1}) - s _ {t} N _ {t}), \\ H _ {0}, L _ {0}, B _ {0} \geq 0 \end{array}\tag{3.7}\]

where is the price of infrastructures, is the land price, ; represents the wage rate, is the rate of return from bonds and, is the rental price of housing. Some features of the consumer deserve further explanation. The current speciÖcation allows land trading, ， and rental markets for tenant-occupied housing. In equilibrium, there is no trade in either market, but its formalization determines the implied equilibrium prices necessary to price the value of the stock of housing. In particular, formalizing the market of rental services makes explicit the opportunity cost of owner-occupied housing. When the production of housing services at the household level equals the level of consumption, the term drops from the budget constraint. In addition, labor income is expressed as a combination of total hours worked at market wage, but this term can be expressed as the labor income earned in each sector, for

The Örst-order conditions of the consumer problem are derived in Appendix (8.1), but the optimality conditions that result are characterized by expressions that determine the rental price and the interest rate as functions of allocations:

\[R _ {t} = \frac {u _ {2} (c _ {t} , s _ {t})}{u _ {1} (c _ {t} , s _ {t})}, \quad \forall t,\tag{3.8}\]

\[\frac {1}{(1 + r _ {t + 1})} = \frac {\beta u _ {1} (c _ {t + 1} , s _ {t + 1})}{u _ {1} (c _ {t} , s _ {t})}, \quad \forall t,\tag{3.9}\]

Equation (3.8) states that the rental price is determined by the ratio of marginal utilities between consumption goods and housing services. As usual, the interest rate is determined by the ratio of marginal utilities between consumption in periods t and : The model predicts no arbitrage between land investment opportunities and housing capital or infrastructures. Formally, the rate of return of both types of investments need to equalize:

\[\frac {q _ {t + 1} (1 - \delta)}{q _ {t} - R _ {t} g _ {1} (H _ {t + 1} , \chi_ {t} L _ {t + 1})} = \frac {v _ {t + 1}}{v _ {t} - R _ {t} g _ {2} (H _ {t + 1} , \chi_ {t} L _ {t + 1})}.\tag{3.10}\]

This expression is consistent with the ideas developed in the previous section. It is worth noting that the rate of return needs to be adjusted by the market value of the contribution of each input in the production of housing services. Using the implied (and endogenous) interest rate, it is possible to compute via recursion the value of housing capital and land:

\[q _ {t} = R _ {t} g _ {1} (H _ {t + 1}, \chi_ {t} L _ {t + 1}) + \frac {q _ {t + 1} (1 - \delta)}{1 + r _ {t + 1}},\tag{3.11}\]

and

\[v _ {t} = R _ {t} g _ {2} (H _ {t + 1}, \chi_ {t} L _ {t + 1}) + \frac {v _ {t + 1}}{1 + r _ {t + 1}}.\tag{3.12}\]

These expressions state that the current cost of purchasing a unit of housing structures (land) equals the contemporaneous return of housing services derived from the housing capital (land) valued at market prices, and the discounted selling price next period. In the case of structures, it is necessary to net out the depreciation cost of that particular unit. The formal expression for the prices are detailed in Appendix 8.1.

The production of consumption goods and houses is endogenous in the model. There are two di§erent types of Örms in this economy. The Örst type is a representative Örm that uses a linear technology to produce consumption goods, : The Örmís optimization problem is characterized by

\[\max _ {N _ {c t}} A _ {c t} N _ {c t} - w _ {c t} N _ {c t}, \quad \forall t,\]

where the price of consumption goods is normalized to 1. The constant returns to scale assumption implies zero equilibrium proÖts and marginal cost pricing for the labor input

\[w _ {c t} = A _ {c t}.\tag{3.13}\]

The other type of Örm produces residential investment, : This investment is combined with the existing undepreciated housing capital to produce the new level of structures. This technology is subject to irreversibility constraints, : The market value of residential investment is determined by : Then, the optimization problem is given by

\[\begin{array}{r l} & {\underset {(N _ {h t}, x _ {t}) \in R _ {+}} {\max} p _ {h t} x _ {t} - w _ {h t} N _ {h t},} \\ & {s. t. \qquad x _ {t} = A _ {h t} N _ {h t},} \end{array}\]

where the equilibrium price of new structures is given by

\[w _ {h t} = p _ {h t} A _ {h t}.\tag{3.14}\]

The consumer time allocation problem, ; implies : For this condition to hold the price of new structures must equate

\[p _ {h t} = \frac {A _ {c t}}{A _ {h t}}.\tag{3.15}\]

This speciÖcation assumes that this price depends on the path of e§ective productivities of each sector. In a stationary environment, this price is constant and the wage rate of both sectors equates : This result allows redeÖnition of the notion of labor income, ; and it also simpliÖes the number of prices that need to be solved in equilibrium. It is worth emphasizing that reáects the cost of producing new structures. However, the price of a house di§ers from this value since it depends on the relative value of structures and land.

DeÖnition (Competitive Equilibrium): Given ; equilibrium comprises allocations ; and prices that solve i) consumers solve the optimization problem, ii) Örms producing consumption goods and housing capital maximize proÖts; and iii) all markets clear: a) Labor markets: Goods markets: Land markets: Bond market: Rental market: Market for structures:

The objective of the paper is understanding the change in the level of house prices between 1998 and 2007, and the bust cycle in 2007-09. Therefore, it is useful to deÖne and characterize the steady state of the economy. In this equilibrium prices, allocations, and expectations over future variables are constant over time.

DeÖnition of Steady-State Equilibrium: For a given level of productivities a steady-state equilibrium is characterized by allocations and prices that solve the equilibrium conditions.

The steady-state conditions are used to determine the levels of house prices. In this case, the equilibrium interest rate is determined by the rate of time preference, : The rental price by the marginal utility is

\[R = u _ {2} (c, s) / u _ {1} (c, s).\tag{3.16}\]

The equilibrium prices for housing capital and land are determined by

\[q = \frac {(1 + r)}{(r + \delta)} R g _ {1} (H, \chi L),\tag{3.17}\]

and

\[v = \frac {(1 + r)}{r} R g _ {2} (H, \chi L).\tag{3.18}\]

In steady-state, there is no net investment in housing capital. All residential investment replaces the depreciated structures,

\[x = \delta H = A _ {h} (N ^ {w} - N _ {c}).\tag{3.19}\]

This expression is used to determine the steady-state level of structures, as a function of the employment allocation across sectors. Substituting the expression in the market-clearing condition for consumption goods,

\[A _ {c} N ^ {w} - q \delta h = A _ {h} (N ^ {w} - N _ {c}),\tag{3.20}\]

determines the steady-state price of structures

\[q ^ {*} = \frac {A _ {c}}{A _ {h}},\tag{3.21}\]

as a ratio of the productivity levels in each sector. To determine the value of land, rental prices, R; and employment, it is necessary to solve a system of nonlinear equations.

3.3. Small Open Economy

In a small open economy, households have access to international borrowing by accessing capital áows. A simple approach to formalize the access to the global credit market is to assume that consumption of goods is tradable, whereas housing services, housing capital, and land are non tradable goods and inputs. In this case, households can import consumption goods from abroad by borrowing, ; where the term represents imported goods. To simplify matters, the model considers capital áows with countries that use the same currency (i.e. European Monetary Union, EMU); therefore, the exchange rate between Spain and their counterparts is set to 1, . The consumption goods market clearing condition needs to be modiÖed accordingly,

\[N _ {t} c _ {t} = A _ {c t} N _ {c t} + D _ {t + 1} - (1 + r _ {t} ^ {*}) D _ {t}.\]

In this class of economies, any deviation in the implied interest rate determined by the rate time preference, and the world interest rate, ; generates permanent increasing deÖcits or surpluses. One way to solve the problem, ignoring default issues, it to bound the long-run level of sovereign debt, and consumption. The parameter sets the long-run level of indebtness and it can be determined to match the levels of the current account deÖcits. The introduction of capital áows and bounds on current account deÖcits modiÖes the intertemporal decision with respect to consumption

\[\frac {u _ {1} (c _ {t} , s _ {t})}{\beta u _ {1} (c _ {t + 1} , s _ {t + 1})} \geq (1 + r _ {t + 1} ^ {*}), \quad \forall t.\]

This condition holds with inequality when : The relevant long-run case for the Spanish economy implies permanent current account deÖcits, ; where the above expression becomes : In the open economy, the relevant discount rate is given by hence, the pricing equation must be evaluated at the EMU borrowing and lending rate. This rate is the relevant one to discount the future áows in the pricing equations.

4. The Housing Boom-and-Bust Cycle in Spain

4.1. Parameterization of the Model: 1995

The quantitative evaluation of the model requires specifying parameter values and functional forms. These are determined to match key properties of the Spanish economy before the housing boom. Some key parameters have a directly observable counterpart in the data. The remaining parameter values are determined using an exactly identiÖed method of moments approach. Once the economy is parameterized, it can be used to address the key forces driving the housing boom.

Three parameters that are determined directly are the size of total population, ; the share of the workforce in the population, ; and the current account position. In 1995, the current account of the Spanish economy was balanced. A simple way to capture the absence of deÖcits is to assume that the world interest rate coincided with the rate of time preference, : An alternative speciÖcation would imply that Spain had no access to credit markets,

The choice of functional forms is relatively standard. The utility function is consistent with unitary income elasticity,

\[U (c, s) = [ \gamma c ^ {\rho} + (1 - \gamma) s ^ {\rho} ] ^ {1 / \rho},\]

where the term represents the relative share of goods consumption in utility. The production of housing services is given by

\[g (H, \chi L) = H ^ {\alpha} (\chi L) ^ {1 - \alpha}.\]

where represents the relative weight of each input.

In the model, housing structures depreciate at a constant rate ; and the áow of utility is discounted at a rate The model key parameters are determined to match four targets in the data. The model targets are deÖned to be consistent with their data counterpart (i.e, output, value housing stock). For example, the model deÖnition of GDP includes the production of consumption goods, residential investment, and the market value of housing services. The data used to determine the targets are from three sources. The National Income and Products Accounts data are from the Instituto Nacional de Estadistica. The estimates of the real mortgage rate are from the Banco de EspaÒa, and the share of land in the housing stock is derived from the estimated series of Uriel et al. (2009). The parameters are determined to match a 9 percent interest rate (12 percent nominal minus 3 percent ináation), an 83 percent ratio between consumption and output, a 25 percent contribution of land in the value of the housing stock, and a 2.05 ratio between housing capital and GDP. Table 2, summarizes the results of the model parameterization

Table 2: Parameterization of the Model ó1995

The targets generated by the model solution along with the market-clearing equations are within less than 1% error in each target. The model can be evaluated in terms of housing characteristics that have not been targeted. The model predicts that the value of land relative to output is 68 percent, whereas the data predict 66 percent. Similarly, the value of housing relative to output is 2.73 in the model and 2.71 in the data.

4.2. Sources and Decomposition of the Housing Boom: 1995-2007

The objective of the paper is to understand the sources driving a housing boom of the magnitude experienced in Spain. A model capable of generating booms of sizable magnitude also can be used to decompose the quantitative impact of each variable. Before addressing any of these issues it is important to explore the change in the magnitude of the relevant housing variables in this period. Table 3 summarizes the change in house prices and the composition of value of housing capital relative to GDP observed in the data.

Table 3: Changes in House Prices and Value in Spain: 1995-2007

S o u r c e : U r ie l e t a l. ( 2 0 0 9 )

The house price index data show that prices more than doubled (tripled) in real (nominal) terms. The appreciation during the 12-year period is 6.3 percent in real terms and 10 percent nominal. The value of the housing stock relative to GDP was 2.71 in 1995 and 4.63 in 2007. Despite the extended period of growth, the appreciation of the housing stock (land plus structures) was much more rapid than output. The change in the value can be decomposed with changes in the values of structures and changes in the value of the land.

\[\frac {p ^ {h}}{G D P} = \frac {q H}{G D P} + \frac {v L}{G D P}.\]

In 1995, the contribution of structures to the total value was 75 percent. Surprisingly, this contribution declined by 28 percent to account only for 54 percent of the value. The mirror image is the importance of land in the formation of value, which increased from 25 percent to 46 percent. Land not only had an increasing weight in value, but it also had a much larger increase (318 percent) than the value of structures (122 percent). These facts are important because a model that captures a sizable magnitude in the value of housing capital should also be consistent in its composition (land vs. structures).

Three fundamental changes are used to understand the change in the value housing stock in 2007 (peak boom). These include demographic changes, the ability to borrow and better lending terms due to current account deÖcits, and relaxation of land restrictions.

1) Demographics: The demographic changes associated with the housing boom involve two terms: the total population and the size of the workforce relative to total population. In Spain, the total population increased roughly 18 percent, whereas the workforce increased 25 percent. Most of the growth (98%) is due to immigration áows. The combined e§ect is an increase in the level of e§ective workers from 41 percent to 56 percent of total population in 2008, which is a 37 percent increase in the size of the labor force.

2) Borrowing ability and better lending terms: In the past years homeowners in Spain were able to borrow with much better terms. The real mortgage rate was reduced from 9 percent to roughly 4 percent. Because it is di¢ cult to determine the precise value of the discount rate with capital áows, the paper also presents estimates for di§erent values for this rate. What is clear from the data is that part of the decline has been sustained with a large increase in the current account deÖcit. The deÖcit peaked after 2005 with values around 9 to 10 percent of GDP. A simple way to capture the decline in mortgage rates in the open economy requires reducing the world interest rate, r; to 4 percent. In addition to the interest rate decline, it is necessary to increase the access to credit markets by setting the term to values consistent with current account deÖcits.

3) Relaxation of land restrictions: During this period the Spanish government opted to deregulate the sale of existing land. The result of this deregulation process was an increase in the supply of land (measured in square meters) of 28 percent. The index of land use was summarized in Figure 2.

Table 4 summarizes the baseline model prediction to a change in fundamentals (demographic structure and the reduction of land restrictions) with di§erent assumptions about the mortgage rate and the cost of structures. The Örst two columns represents the change with respect to baseline values normalized to 100. The last column captures the change in the rental price with respect to the baseline economy in 1995.

Table 4: Contribution to House Prices: Joint E§ects

It is clear from Table 4 that the model makes di§erent predictions depending on the assumed mortgage rates. For a conservative estimate of 4 percent, the baseline economy suggests that the change in fundamentals can rationalize 84 percent of the increase in house prices (230/275), and 82 percent of the contribution of land value to output (260/318). Following the intuition of the simple model presented in the previous section, the increase in house prices is accompanied by a decline in the rental price or dividend payment of the house. Without this decline, the increase in house prices would have been larger. Therefore, the model is consistent with the idea that rental prices are not independent of interest rates because these change the relative price of present and the future consumption. Given the model speciÖcation a decline in consumption implies a decline in the rental price as well. For lower interest rates the magnitude of the housing booms increases and the model can rationalize 90 percent of the increment of the housing capital value. The model also captures the fact that most of the increase in the value of housing is associated with the increase in the price of land. The contribution of this factor can be decomposed by an increase in the price, v; which triples, and the expansion of available land, which increases 30 percent. The combined e§ect adjusted by the increase in output explains the change in the ratio.

Table 4 also includes the same simulations under the assumption that the relative price of structures, ; increases 10 percent. The price increase could be due to the cost of materials, time cost of hiring workers, or any factor that increases the cost of production unrelated to land. The objective is not to provide a precise estimate of a change (if any) but to understand how prices respond to such change. The model suggests that the same changes in fundamentals can be magniÖed with increasing costs of structures. Even though q increases only 10 percent, the Önal contribution of higher costs translates to an approximate increase in the value of housing capital of 10 percent. In the case of a 4 percent mortgage rate, the model accounts for 85 percent of the increase in value instead of percent. Other factors not included in the model could be important (i.e., bubbles, speculation, change in the value of housing preferences), but the results suggest that theories based on rationality should not be abandoned.

To understand the total e§ects of the change in fundamentals it is necessary to solve the model isolating the contribution of each factor. It is important to understand that each simulation is performed under the assumption that the households perceive the change in the fundamentals as permanent. The results of the decomposition are summarized in Table 5.

Table 5: Decomposition of the Housing Boom by Factors

The index of house prices in 1995 has been normalized to 100. Compared with the baseline model, the decomposition exercise suggests that the largest e§ects can be attributed to the decline in the interest rate (145 percent) and the change in the demographic structure brought about by immigration (143 percent). In relation to the total increase, each of the changes individually accounts for roughly one-third. Table 5 shows, decomposing contributions in a general equilibrium model is complicated because the contribution of two simultaneous factors is usually di§erent than the sum of these factors separately. In general equilibrium, some of these e§ects can either reinforce or cancel. The model suggests that the combined e§ects of demographics and low mortgage rate would increase 91 percent from the baseline period, and the contribution with respect to the total change in house prices is 67 percent. However, the sum of the separate contribution for immigration and low mortgage rates is 55 percent (33%+32%). This suggests that the general equilibrium e§ects generate a reinforcing e§ect of 22 percent. The increase in the supply of land should produce a decline in the value of land (v) of 21 percent, but the decline in the price does not compensate for the increase in the quantity of land , so the contribution associated with thr elimination of land restrictions is quite small.

The model seems to make some strong predictions about the key forces driving the increase in the value of the housing stock in Spain. The áow of immigrants and the decline of interest rates account for the majority of the housing boom. These two factors seem to reinforce each other. Whether the housing boom was driven by bubbles or irrational behavior remains to be proved. Nevertheless, the approach in this paper suggests that a parsimonious model with clear and testable assumptions can generate sizable housing booms such as the ones observed in the Spanish economy.

These results are consistent with those of Gonzalez and Ortega (2009) who Önd a sizable causal e§ect of immigration on both prices and quantities in the housing market. Their estimates suggest that the immigrant ináow increased house prices by about 52% and is responsible for 37% of the total construction of new housing units during the period. Overall, immigration can account for roughly one-third of the housing boom in terms of both prices and new construction.

One assumption in the model ó the existence of complete markets ó merits further attention. Some papers in the literature argue that the housing boom is partially due to innovations in housing Önance that relaxed down payment constraints and reduced the cost of purchasing a home. Although this paper abstracts from Önancial frictions, a direct implication of using complete markets is that any household that wants to purchase a home and can a§ord to do so will indeed buy a house. In some sense, the complete market paradigm eliminates all frictions and maximizes the access of the population to the housing market. This is particularly important in a framework where the total population and the workforce increase dramatically. That situation suggests that in a model with Önancial frictions, there would still be some individuals who cannot Önance their house purchases, thereby making the e§ect on house prices much smaller.

4.3. Counterfactual Experiments: 1995-2007 ó An Alternative Story?

This section uses the model to perform some counterfactual experiments. In particular, it considers the e§ects of the relaxation of credit markets on house prices. The exercise takes the áow of immigrants and relaxation of land regulations as given and asks what would have happened with 6 percent interest rates instead of the 4 percent observed.

Table 6: Counterfactual Experiments

The results in Table 6 suggest that the increase in the value of housing capital (structures and land) would have been much smaller. How much smaller? The model states 187 instead of 230, which is 20 percent less. The model suggests that the current account deÖcits supporting the mortgage rate decline had an important contribution in the housing boom. Without such a áow of funds, the house price increase would have had a di§erent order of magnitude. The model also predicts that without the immigration áows 2 the housing boom would been much smaller. These Öndings reinforce the idea that a combination of low mortgage rates with important changes in the demographic structure can be responsible for large changes in the level of house prices.

4.4. Housing Bust: 2007-09

Although the model is relatively stylized, it can be used to make predictions about the down ward response of house prices to changes in economic fundamentals. It may still too early to fully understand the nature and the impact of the Önancial crises in the Spanish economy. However, it is certainly important to be aware of the magnitude of the economic adjustment when conditions are deteriorating. For example, MartÌnez-PagÈs and Maza (2003) found that house prices in Spain were already above their long-term equilibrium level in 2003. However, their model does not allow them to make an estimate of the correction of future house prices.

The goal in this section is to derive predicted magnitudes using the model. Before proceeding further in the analysis, it is important to compare the evolution of house prices in Spain with the house prices in the U.S. The comparison is important because many economic commentators suggest that the U.S. economy already has had a severe adjustment in the housing market.⁶ In the case of the Spanish economy, it is not clear that the housing market has had a signiÖcant correction. Figure 6 compares the evolution of nominal house prices in Spain and the United States between 1995 and 2009. Both indices have been normalized to 100 in 1995.

Figure 6 House Prices in Spain and the United States (1995-2009)

Ssome of the features in Figure 6 are dramatic. Until 2005, the housing boom in both countries had similar magnitudes. However, in the United States this period represented the peak of nominal house prices, whereas in Spain prices continued to grow well into the Örst quarter of 2008. Not only the timing but the magnitudes of the peak di§er. In Spain the peak of house prices was 3.12 times larger than the 1995 counterpart, but it was only 2.5 times larger in the United States. In addition, the timing and magnitudes in the downward adjustment of prices also di§er. In the United States, house prices declined 30 percent, whereas in Spain prices continued to grow 25 percent more until 2008, but the decline has been much more modest ó between 8 and 10 percent at the national level. If the adjustment in Spain is of magnitude similiar to that of the United States (30 to 40 percent), the index still has to decline from 2.87 to somewhere between 1.87 and 2.18. Other estimates based on consumer price index (CPI) adjustment would suggest a further adjustment to 1.56.

⁶There is still some disagreement in markets. Recently, Moodyís agency revised upward its loss forecasts on option-ARM residential mortgage-backed securities (RMBS) issued between 2005 and 2007 in the U.S. The rating agency is now projecting cumulative loss rates of 20%, 41%, and 51% for 2005, 2006, and 2007 securitizations, respectively. The increasing losses are partially due to the expectation that the overhang of impending foreclosures is likely to adversely a§ect home prices going forward. As a result, some analysts generally expect another 10% decline in U.S. home prices, bringing the peak-to-trough drop to roughly 37%

The Önal adjustment of house prices will depend on the length of the Önancial crises and other factors. However, it is possible to use the model to make some predictions about the sensitivity of house prices to various factors.

Altough many combinations of factors can be considered, this section concentrates on only a few. In particular, it is interesting to explore the model response to increases in the mortgage rate (from 4 to 5 percent), declining employment (5 and 10 percent), and negative productivity shocks in the production of consumption goods (5 and 10 percent). The numbers are compared with the model predicted-peak based on fundamental variables. Of note, the baseline model with 4 percent mortgage rates accounts for only 84 percent of the run-up in the value of the housing stock. Table 7 summarizes the percentage change with benchmark predictions for 2007 levels (see Table 4).

Table 7: Model Predictions for House Price Declines

All the experiments share a common feature. The interest rate increases from 4 to 5 percent. There are di§erent ways to rationalize the increase in mortgage rates. One could be an increase in the cost of borrowing abroad, due to country-speciÖc risk premia (Öscal deÖcits that crowded private savings), liquidity shortages, or the credit crunch. The model predicts that an increase in the mortgage rates should decrease the long run value of the housing stock by roughly 11 percent. The decrease occurs despite the 6 percent increase in the market value of housing services; this suggests that the link between house prices and interest rates (i.e. is weak given that the rental price is an endogenous variable. The Öndings from Table 7 shows two di§erent cases where rental prices and house prices move in opposite directions. The higher interest rate increases the level of current consumption relative to housing services that are ultimately responsible for the increase in R:

Changes in the level of employment in the economy can be analyzed by reducing the size of the active population. The model predicts that declines in employment have important e§ects on the value of housing capital. A decline of 5 percent (in conjunction with higher mortgage rates) implies a 16 percent decline in value, whereas a 10 percent decline generates a 21 percent drop. The model suggests an almost one-for-one relationship between employment and house prices, but lesser relationship for rental prices.

In the traditional business cycle literature the sources of economic áuctuations are shocks to total factor productivity. A simple way to integrate some of these features is to consider an unexpected and permanent decline in the productivity of consumption goods, Declines of 5 and a 10 percent in productivity generates a declines similar declines in house values. The model linearity also suggests a one-for-one decline. However, in this case the response in the rental market is very di§erent than the case of employment. Figure 7 compares the levels of the value of housing capital for the data and the model predictions for di§erent scenarios.

Figure 7 Housing Boom-and-Bust Cycle: Data and Model Predictions

Depending on the assumption, it is clear that the model can generate boom-and-bust cycles of similar magnitude as the data. With respect to the bust cycle, the model also suggests that the combined e§ects of higher mortgage rates, lower levels of employment, and reduced productivity can have large and devastating e§ects on the value of housing capital. Some conservative predictions suggest declines between 24 and 29 percent. The current adjustment in house prices in Spain is still far from these magnitudes. However, it is not clear that the current values will be sustained in the long run.

5. Housing Policy: Lessons Learned from the Literature

The importance of housing policy has been neglected in the model. However, an extensive body of literature analyzes the macroeconomic and distributional e§ects of housing policy. For example, tax provisions, such as deductions of mortgage interest payments in taxable income or the exclusion of the imputed rental value of owner-occupied housing from taxable income, modify the incentives of owning property and a§ect housing tenure and investment decisions. Similarly, liberalization in the supply of land and acceleration in the concession of construction permits can modify developersíincentives to supply housing. This section summarizes some of the recent Öndings in the existing literature and relates them to Fedeaís proposal for a structural reform in the Spanish housing market, ìMaking the Housing Market Work.î ⁷ Housing policy in most developing economies shares common features: subsidies for housing, progressive taxation, and the deregulation of mortgages to name a few.

1) Subsidies to owner-occupied housing: In economics, subsidies are an optimal policy tool only in the presence of market imperfections. In the current environment with substantial deregulation in housing Önance and construction, the purpose of these subsidies is not clear. At the aggregate level, the countries with higher subsidies appear to have a larger fraction of the population in owner-occupied housing. At the micro level, these subsidies generate an asymmetry in the tax treatment of owner and tenant-occupied housing. Clearly, only those individuals who have access to owner-occupied housing can take advantage of the tax provisions. Therefore, the portfolio of homeowners is usually biased toward housing at the expense of other Önancial assets. In addition, renters (usually young and poor households) do not beneÖt from these tax provisions.

The evidence in the literature is mixed. Some studies suggest that the elimination of this asymmetry, by taxing the imputed rents of owner-occupied housing, should lead to the consumption of smaller homes and lower home ownership. For example, Berkovic and Fullerton (1992) Önd that the taxation of housing services should reduce average housing consumption between 3 and 6 percent, whereas Gervais (2002) Önds that taxing imputed rents of owneroccupied housing would increase the capital stock over 6 percent but decrease the housing stock 8 percent. However, Chambers, Garriga, and Schalgenhauf (2009b) argue that in a model with progressive taxation the elimination of the subsidies can be used to reduce the average and marginal tax rates. This e§ect, combined with an increase in average net income (more productive resources), can increase the home ownership rate particularly for young cohorts and low-income households. Despite the modest decline in housing consumption, the results suggest that an elimination of housing subsidies is not necessary incompatible with home ownership.

⁷Fedeaís proposal for a structural reform in the housing market suggests four main changes: 1) Strengthen the rental market by liberalizing contracts, increasing legal protection for owners and reducing obstacles for renters, 2) Abolish immediately all tax incentives for home purchase, 3) Abolish owneroccupied social housing and reorient social protection toward the rental market, 4) Abolish or strongly reduce the property transfer tax for home purchases and sales. Additional information is available at (http://crisis09.es/vivienda/index.html).

It is clear that given the current situation in the labor and housing market young people might Önd it di¢cult to leave the parental home. However, an increase in the homeownership rate beyond the current levels could constitute a serious obstacle to labor mobility. The empirical evidence suggests that labor mobility is seriously reduced in the presence of home ownership. Some of these issues have been addressed by government-sponsored initiatives (ComitÈ de Expertos de Vivienda, 1992; FundaciÛn de Estudios Inmobiliarios, 1999) or by other studies by Garcia and Mas (2000), and Taltavull (2001). In Spain, LÛpez-Garcia (2004) studies the impact of housing policy on house prices. The model predicts a substantial decline in the real price of housing and in the stock of housing resulting from the elimination of housing subsidies implicit in the personal income tax. However, the quantitative results depend on the assumptions about the nature of land prices. When the price of land is exogenous, the long-run decline in home prices ranges between 16 and 21 percent and 11 and 16 percent for stock (depending on the assumed value of the price elasticity of newly built homes). If land prices are endogenous, the decline is even larger.

2) Deduction of mortgage interest payments on taxable income: One of the hallmarks of housing policy across countries is the deductibility of mortgage interest payments. This deduction creates an incentive to both own and consume more homes, generating an asymmetry between housing and Önancial investment. The view among practitioners is that the removal of the interest deduction would result in lower owner-occupied housing consumption and thus smaller home sizes. Home ownership would be lower because the incentives to own have been reduced. From a macro perspective the elimination of the deduction should result in a tax reduction. The magnitude of the income e§ects implied from lower taxes can reverse the intuition implied from the partial equilibrium argument. Some papers in the literature support the Örst conjecture. For example, Rosen and Rosen (1980) use a reduced-form model and estimate a 400-basis-point decline in home ownership as a result of eliminating the deduction, whereas Gervais (2002) Önds that the elimination of the deduction reduces the aggregate homeownership by 420 basis points. Nevertheless, Chambers, Garriga, and Schalgenhauf (2009b) show that when the elimination of the deduction interacts with the progressivity of income taxation, its elimination does not necessarily imply a decline in homeownership. Their quantitative results provide support to Glaeser and Shapiroís (2002) conjecture that the mortgage deduction has little e§ect on home ownership.

3) Housing policy and the progressivity of income taxation: The asymmetric treatment of owner and tenant-occupied housing is magniÖed by the progressivity of income taxation. This is particularly important in Spain given the high marginal tax rates and the relatively low income that is taxed in the top brackets. Chambers, Garriga, and Schlagenhauf (2009b) explore the impact of reducing the progressivity of income taxation and its interaction with the tax provisions toward housing. The conventional wisdom suggests that a reduction in the degree of progressivity in the income tax code would mitigate the e§ects of tax provisions that favor owner-occupied housing and hence home ownership. However, in a model where markets (labor, capital, and rental markets) are allowed to adjust, the Öscal reform is not compatible with housing policy goals such as home ownership. In this case, the increase in disposable income increases aggregate savings and average income. These combined e§ects allow young and low-income households to purchase housing.

4) Deregulation of mortgage products: For most households, housing Önance is very important since the purchase of a house is typically the largest transaction in terms of income. The manner in which this purchase is Önanced (i.e. pay cash or use a mortgage) is equally important for expenditure patterns and asset accumulation. From a macroeconomic perspective, housing investment (both residential and nonresidential structures) accounts for a large fraction of gross private investment, and the liabilities from home mortgages are usually a large fraction of GDP. Historically, innovations in housing Önance have preceded important housing booms that have had ramiÖcations for prices and homeownership rates. Recently, Federal Reserve Chairman Bernanke (2010) argued that the developments in mortgage markets in the United States that increased the leverage and changed the repayment schedules of loans were the heart of the housing bubble. In Spain, the problem has been somewhat similar with the increased in leverage via manipulation of the appraised value of the properties. The mechanism allow borrowers to overcome lending caps and borrow (in some cases) the full value of the purchase. In both countries, it appears that the execution (or lack thereof) has been one source of the problem. To overcome these issues, it is important not only to monitor lending institution by institution, but also to be able to supervise the Önancial system as a whole to control correlated risks. However, this is an issue requiring a separate discussion.

5) Subsidies to producers: In the current environment with a large supply of unsold property, any subsidy to construction and housing development could result in a decline in house prices. For example, LÛpez-Garcia (2004) Önds that a policy of ìinvestment incentivesî in housing designed to promote newly built housing units would entail an increase in the housing stock accompanied by a reduction in prices of the existing housing stock. If the price of land is Öxed, the policy can generate a long-run rise in housing stock between 2.5 percent and 3.5 percent, while real prices of existing units would fall between 2 percent and

3.5 percent. When land prices adjust, the decline in house prices ranges between -1 percent and -2.5 percent. Given these results, it seems that the optimal strategy might be to do the opposite. These results also ignore the time and money cost of reallocating workers in the construction sector to other productive activities in the economy.

6. Conclusions

The paper develops a quantitative model to account for the change in the level of house prices in Spain. An important element in understanding the increase in the value of the residential capital stock is the existence of a Öxed factor ó land ó that interacts with residential investment. The proposed model can rationalize 84 percent increase in the value of the housing stock and an 82 percent in the increase in the value of land. The contribution of each factor with respect to 1995 prices assigns rougly 33 percent to demographics and low interest rates, respectively, and 7 percent to land restrictions. However, these single contributions ignore the interaction of the combined e§ects that is essential to understanding the housing boom. The model is used to perform some counterfactual exercises to determine the magnitude of the housing boom and residential investment had these factors been di§erent. The model suggests that the housing boom would have been 25 percent lower if mortgage rates had been 200 basis point higher.

One of the challenges going forward is understanding the housing bust. That process requires identifying the relevant sources that changed around 2007 and consequently modiÖed householdsíexpectations about the path of future prices. Some preliminary Öndings suggest that the combined e§ects of higher mortgage rates, unemployment, and low productivity can have large e§ects on the value of housing capital. Some conservative predictions suggest adjustments that can easily range between 24 and 29 percent.

7. References

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8. Appendix

8.1. First-Order Conditions of the Consumer Problem and Pricing Functions

Let represent the Lagrange multiplier of the budget constraint. The Örst-order conditions of the consumer problem with respect to imply in the case of an interior solution:

\[\beta^ {t} u _ {1} (c _ {t}, s _ {t}) = \lambda_ {t},\tag{8.1}\]

\[\beta^ {t} u _ {2} (c _ {t}, s _ {t}) = \lambda_ {t} R _ {t},\tag{8.2}\]

\[\lambda_ {t} = \lambda_ {t + 1} (1 + r _ {t + 1}),\tag{8.3}\]

\[q _ {t} \lambda_ {t} = \lambda_ {t} R _ {t} g _ {1} (H _ {t + 1}, \chi_ {t} L _ {t + 1}) + q _ {t + 1} (1 - \delta) \lambda_ {t + 1},\tag{8.4}\]

\[v _ {t} \lambda_ {t} = \lambda_ {t} R _ {t} g _ {2} (H _ {t + 1}, \chi_ {t} L _ {t + 1}) + v _ {t + 1} \lambda_ {t + 1}.\tag{8.5}\]

The characterization of the prices for structures and land requires substituting the values of the Lagrange:

\[q _ {t} = \frac {u _ {2} (c _ {t} , s _ {t})}{u _ {1} (c _ {t} , s _ {t})} g _ {1} (H _ {t + 1}, \chi_ {t} L _ {t + 1}) + q _ {t + 1} (1 - \delta) \frac {\beta u _ {1} (c _ {t + 1} , s _ {t + 1})}{u _ {1} (c _ {t} , s _ {t})},\tag{8.6}\]

\[v _ {t} = \frac {u _ {2} (c _ {t} , s _ {t})}{u _ {1} (c _ {t} , s _ {t})} g _ {2} (H _ {t + 1}, \chi_ {t} L _ {t + 1}) + v _ {t + 1} \beta \frac {u _ {1} (c _ {t + 1} , s _ {t + 1})}{u _ {1} (c _ {t} , s _ {t})}.\tag{8.7}\]

Iterating forward

\[q _ {t} = \sum_ {\tau = 0} ^ {\infty} (1 - \delta) ^ {\tau} m _ {t + \tau} \frac {u _ {2} (c _ {t + \tau} , s _ {t + \tau})}{u _ {1} (c _ {t + \tau} , s _ {t + \tau})} g _ {1} (H _ {t + \tau + 1}, \chi_ {t + \tau} L _ {t + \tau + 1}),\tag{8.8}\]

and

\[v _ {t} = \sum_ {\tau = 0} ^ {\infty} m _ {t + \tau} \frac {u _ {2} (c _ {t + \tau} , s _ {t + \tau})}{u _ {1} (c _ {t + \tau} , s _ {t + \tau})} g _ {2} (H _ {t + \tau + 1}, \chi_ {t + \tau} L _ {t + \tau + 1}).\tag{8.9}\]

Let represent the pricing kernel or the consumer-adjusted discount rate. In this economy, the equilibrium interest rate for any time period, ; is endogenously determined by the path of consumption over time:

\[\frac {1}{1 + r _ {t + \tau}} = \beta^ {\tau} \frac {u _ {c} (c _ {t + \tau} , s _ {t + \tau})}{u _ {c} (c _ {t} , s _ {t})}.\]

Since the model prices housing services (or rents), ; the current market value of these assets is

\[q _ {t} = \sum_ {\tau = 0} ^ {\infty} Q _ {h t + \tau} R _ {t + \tau} g _ {1} (H _ {t + \tau + 1}, \chi_ {t + \tau} L _ {t + \tau + 1}),\]

\[v _ {t + \tau} = \sum_ {\tau = 0} ^ {\infty} Q _ {L t + \tau} R _ {t + \tau} g _ {2} (H _ {t + \tau + 1}, \chi_ {t + \tau} L _ {t + \tau + 1}),\]

where and represent the Arrow-Debreu discount prices for : The depreciation term has been embedded in the term that represents the discount rates, where the indicator takes two values and

8.2. Equilibrium with Housing Policy

The baseline economy does not consider the role of housing policy. However, the basic model can easily accommodate the introduction of tax subsidies for consumers and producers.

DeÖnition (Competitive Equilibrium with Housing Policy): Given a sequence of productivity ; and housing policy ; an equilibrium comprises allocations and prices that solve the following conditions:

1. The consumerís optimization problem,

\[\max \sum_ {t = 0} ^ {\infty} \beta^ {t} u (c _ {t}, s _ {t}) N _ {t},\]

\[\begin{array}{c} s. t. \qquad N _ {t} c _ {t} + B _ {t + 1} + (1 + \tau_ {t} ^ {I V D}) q _ {t} H _ {t + 1} + v _ {t} (L _ {t + 1} (1 + \tau_ {t} ^ {L}) - L _ {t} (1 - \tau_ {t} ^ {L S})) = w _ {t} N _ {t} ^ {w} + \dots \\ (1 + r _ {t}) B + q _ {t} (1 - \delta) H _ {t} (1 - \tau_ {t} ^ {H S}) + R _ {t} (g (H _ {t + 1}, \chi_ {t} L _ {t + 1}) - (1 - \theta_ {t}) s _ {t} N _ {t}) + T _ {t}, \quad (8. 1 0) \\ H _ {0}, L _ {0}, B _ {0} \geq 0. \end{array}\]

2. Firmsíproducing consumption goods optimize proÖts,

\[\max _ {N _ {c t}} A _ {c t} N _ {c t} - w _ {c t} N _ {c t}, \quad \forall t.\]

3. Firmsíproducing housing capital maximize proÖts,

\[\max _ {N _ {h t} \in R _ {+}} (1 + s _ {x t}) p _ {h t} A _ {h t} N _ {h t} - w _ {h t} N _ {h t}.\]

4. Government budget constraints

\[T _ {t} + \theta_ {t} s _ {t} N _ {t} + s _ {x t} p _ {h t} x _ {t} = \tau_ {t} ^ {I V D} q _ {t} H _ {t + 1} + \tau_ {t} ^ {L} v _ {t} L _ {t + 1} + \tau_ {t} ^ {L S} v _ {t} L _ {t} + \tau_ {t} ^ {H S} q _ {t} (1 - \delta) H _ {t}.\]

5. All markets clear

R_t+

rt+τ

⁸In a closed economy, the sequences for and r_t+ are simultaneously determined.

1. Labor markets: 2

2. Goods markets: 2

3. Land markets:

4. Bond market: 2

5. Rental market: 2

6. Market for structures:

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