Housing Market and Current Account Imbalances in a Two-Sector Open Economy Model

Transcription

1 Housing Market and Current Account Imbalances in a Two-Sector Open Economy Model Maria Teresa Punzi April 25, 2006 First draft and Incomplete 1 Abstract This paper analyzes the contribution of the housing market to the external unbalances of a country. The external deficit may depend on the combination of high net worth of US households and low investment in other countries. In U.S. economy, volatility of residential investment is more than twice that of non-residential investment and a residential investment can lead to higher loan-to-value ratio with more procyclical debt capacity; the procyclical increase in the housing value will itself allow households to further increase borrowing and the collateral-based spending cycle gets amplified, that means when housing is more expensive, collateral constraints are less likely to bind. These facts contribute to increase net worth, and therefore, to have a strong impact on current account deficit. I build a two-sector small open economy to study the effect of housing price shocks to the current account and exchange rate. Because an house can be a consumption good and an investment asset, I treat the real estate sector as a separated sector from the standard goods production sector. Contact information: Boston College - Department of Economics Commonwealth Avenue, Chestnut Hill, MA USA; punzi@bc.edu 1 I am grateful to Fabio Ghironi, Matteo Iacoviello, and Peter Ireland for their guidance and advice. I also would like to thank Susanto Basu, Luisa Lambertini, Vittorio Santaniello, Franco Peracchi, Federico Mandelman and Alberto Bagnai for useful comments and suggestions. All the errors are mine. 1

2 1 Introduction A number of economies have experienced substantial appreciation in house prices over the past decades, with the appreciation particularly strong in recent years. Various housing indicators in those countries, such as the affordability ratio, price-to-rent ratio, mortgage loans-to-gdp ratio, and ownership ratio are at historical highs, suggesting a peak in the value of houses relative to the underlying economic fundamentals. Moreover, indications of possible bubbles in house prices, at least in some countries, are also visible from the increase in speculative activities. For example, in the United States, turnover in housing markets has increased, the share of investment-oriented house purchases has risen and novel mortgage products such as interest-only loans, innovative forms of adjustable rate mortgages and the allowance for a limited amount of negative amortization have been proliferating, thus enabling many marginally qualified and highly leveraged borrowers to purchase homes at inflated prices. Meanwhile, the booming housing sector has been a major driver for GDP growth in many developed countries. For example, in the United States, home equity extraction, namely cash taken out during refinancing, has financed 30 to 40 per cent of the increase in consumer spending in recent years, accounting for one percentage point or more of total real GDP growth, with the residential building sector contributing another 0.6 of a percentage point. Part of the housing boom in recent years can be attributed to various country-specific features, but low interest rates and easier access to mortgage loans seem to be the common factors for most of these countries. Therefore, an increase in interest rates can lead to a fl attening or reversal in the growth of house prices, turning the positive growth contributions of the housing sector into negative ones. As an example, the recent notable growth moderation in Australia and the United Kingdom of Great Britain and Northern Ireland was unambiguously attributable to a cooling down of the housing sector. At the same time, house prices have a substantial impact on the banking sector, as mortgage loans account for a sizable pro- portion of total bank loans. Declining house prices will heighten the risk of default and can trigger bank crises, as has happened in a number of countries in the past. For the global economy, the risks associated with the housing sector are serious, not only because of the large size of the economies concerned, but also because of an inextricable linkage between the increase in house prices and global imbalances. A number of economies that have 2

3 seen a substantial appreciation in house prices are also running large external deficits (relative to their GDP) and experiencing a decline in household savings to very low levels. In that regard, the housing boom in those countries has been to some extent financed by borrowing from the highsaving countries running external surpluses. Therefore, a burst in house prices is likely to lead to an abrupt and contractionary adjustment of the global imbalances. The determinants of property prices are in many ways similar to those of other assets, namely the expected service stream (consumption service) or expected future cash flow (rents) and the required rate of return (the long-term interest rate plus the risk premium) as a discount factor. In the long run, property prices therefore depend on demand factors, such as national income and average discount rates, and on supply factors, such as cost of construction, land availability and the quality of the existing stock. Nevertheless, property markets also have a number of distinctive features compared with other types of asset. The supply of property is intensively local; delivery of the new stock can take quite a long time owing to the length of the planning and construction phases; rents can be very sticky because of the use of long-term rental contracts; market prices lack transparency and most transactions occur through bilateral negotiations; the liquidity of the market is constrained because of the existence of high transaction costs; borrowers rely heavily on external finance; real estate is widely used as collateral; and short sales are usually not possible. These features cause property prices to behave differently. In particular, in the short run, property prices are more likely to deviate from their long-term fundamentals. And fluctuations in property prices can arise not only owing to cyclical movements in economic fundamentals, interest rates and the risk premium, but also as a result of the intrinsic characteristics of the property market itself. The business cycle causes property price fluctuations for obvious reasons. Improvements in overall economic conditions tend to increase the average income of households and therefore boost the demand for new homes, putting upward pressure on house prices. Similarly, businesses see profitable opportunities and seek to expand the scale of their investments. Such an expansion implies a higher demand for office space and storage, driving up commercial property prices. In addition, the market perception of risk changes with the phases of the cycle. During a booming phase, the risk involved in a given project is considered to be lower than in a downward phase. The 3

4 changing risk premiums, in combination with time-varying interest rates (decided by policymakers), determine the discount rates and by extension have a sizeable impact on real estate prices. Property price oscillations are also driven by endogenous factors, most notably supply lags and the historical dependence of investment decisions. On the one hand, the supply response in the property market is much slower compared with that of other goods, mainly as a result of limited land supply and the length of the approval process and the construction phase. On the other hand, the flow of information in the property market is usually inefficient. Because the turnover rate of properties is usually very low, the price information is rather limited and often inaccurate. In particular, much of the information that is important to understand the dynamics of property prices is related to knowledge of local markets, which is accessible only at a substantial cost. Therefore, it is usually very difficult, if not impossible, for market participants to forecast the future movements of property prices. In practice, market forecasts either rely heavily on current property prices or are computed by extrapolating past trends. This so-called myopic or rule of thumb expectation (Hendershott (1994) and Herring and Wachter (1999)) can contribute to endogenous oscillation of property prices or deviations from their long-run equilibrium values. The argument for the wealth effect goes back to the permanent income hypothesis of the life cycle model. According to this hypothesis, the level of household consumption is determined by permanent income, which is the present value of all future incomes of the household. Given that housing and equity are the two most important financial assets for an average household in most industrial countries, with housing typically the greater of the two, an increase in house prices implies that household wealth increases. As a result, owner-occupiers may reduce their savings and increase their expenditure. Bank lending is the primary source of real estate funding; not surprisingly, there are close connections between real estate prices and bank credit. On the one hand, sharp falls in property prices can lead to a large-scale deterioration in asset quality and in the profitability of the banking industry, particularly for those banks that are deeply involved in property or property-related lending businesses. They also undermine the value of bank capital, reducing the banks lending capacity. On the other hand, banks lending attitude has important implications for property prices. 4

5 Bank credit to property buyers and constructors may change the balance between the demand and the supply side and cause property prices to fluctuate. This paper analyzes the contribution of the housing market to the external unbalanced of a country. The external deficit depends on the combination of high net worth of US households and low investment in other countries. In U.S. economy, volatility of residential investment is more than twice that of non-residential investment and a residential investment can lead to higher loanto-value ratio with more procyclical debt capacity; the procyclical increase in the housing value will itself allow households to further increase borrowing and the collateral-based spending cycle gets amplified, that means when housing is more expensive, collateral constraints are less likely to bind. These facts contribute to increase net worth, and therefore, to have a strong impact on current account deficit. I construct a two-sector small open economy to study the effect of housing price shocks to the current account. The two-sector model is justified by the need to keep separated the real estate sector from the rest of the production and investment sector. Producing and investing in housing implies different effort and risk, so I treat this sector as a special non-tradable and durable sector, and because an house can be a consumption good and an investment asset, I treat the real estate sector as a separated sector from the standard goods production sector. Furthermore, I allow at the economic agent to have access to domestic and international financial assets, to consume domestic and foreign final goods, and to have access to real mortgage debt. In this way I will evaluate the impact of housing price shock on the current account and real exchange rate. 2 Related Literature Recent theoretical research proposes that endogenous developments in financial markets can greatly amplify and propagate small income or interest rate shocks throughout the economy (Kiyotaki and Moore, 1997; and Bernanke, Gertler, and Gilchrist, 1996, 1999). Bernanke et al. (1996) call this amplification mechanism the financial accelerator or credit multiplier. The key idea behind the financial accelerator is the notion that shocks to the net worth of firms and households have a procyclical effect on their borrowing capacity. This could happen either because the information 5

6 cost wedge between external and internal finance moves countercyclically (Bernanke and Gertler, 1989), or because a procyclical change in the value of collateralizable assets changes the amount of collateralized external finance in the same direction (Kiyotaki and Moore, 1997). Following a positive income shock, agents should be able to raise more external finance and the increase in borrowing capacity would further boost investment spending. According to this view, financial mechanisms such as the endogenous procyclicality of external financing capacity can help explain important features of the business cycle and the transmission of monetary policy. There is little direct evidence on the amplification mechanism which underlies the financial accelerator. Most empirical studies use firm data to explore one insight behind the accelerator: income shocks should affect corporate spending only when firms have imperfect (constrained) access to external finance. Empirically, the investment spending of nancially constrained firms should be more sensitive to changes in net worth than the investment spending of unconstrained firms (Fazzari, Hubbard, and Petersen, 1988).1 In the same vein, constrained firms. spending and borrowing should fluctuate relatively more in the aftermath of monetary and other macroeconomic shocks (Gertler and Gilchrist, 1993, 1994). Unfortunately, while comparisons between constrained and unconstrained firms may indicate whether one group.s spending is more dependent on current income following an economic shock, they will not identify whether differences in spending stem from an endogenous financial amplification mechanism: because constrained firms are more dependent on current income for investment funding, they should be more sensitive to a shock that affects income even when the shock has no cyclical effect on their borrowing capacity. Iacoviello (2003) introduces real estate in an economy composed of agents facing binding borrowing constraints and where real estate plays the role of a collateral used to secure loans. Similarly, Aoki, Proudman and Vliegh (2002) construct a financial accelerator model where house prices amplify fluctuations in consumption and housing investment over the business cycle. As explained by Iacoviello (2003), this literature is based on the view that deteriorating credit market conditions, such as growing debt burden and falling asset prices, are not simply passive reflections of a declining economy, but are themselves a major factor depressing the economy. Following the home production literature [seebenhabib,rogerson andwright (1991), Greenwood 6

7 and Hercowitz (1991)] in addition to the multi-sector growth literature that begins with Long and Plosser (1983), Davis and Heathcote (2003) build a neoclassical multi-sector stochastic growth model in order to explain the dynamics of residential investment. While successful in explaining the behavior of the main macroeconomic aggregate as well as the behavior of residential and nonresidential investment, the model developed by these authors fails to account for the observed volatility of house prices in the USA. In their model, house prices are found to be less than half as volatile as output while in the data house prices are more volatile than output. As for residential investment and house prices, Jin and Zeng (2003) develop a three-sector model driven by three different productivity shocks and one monetary shock. While the model is quite successful at accounting for some of the salient business cycle properties concerning residential investment and house prices, the fact that a large number of exogenous shocks are needed to generate these conclusions is somewhat unsatisfying. Moreover, the dynamics of some key macroeconomic variables such as aggregate consumption are not studied. There is another strand of literature that considers the role of housing in incomplete market environments. These models typically either focus on steady states [see Platania and Schlagenhauf (2000) or Fernandez-Villaverde and Krueger (2002)] or else abstract from the production side of the economy [see Diaz-Gimenez, Prescott, Fitzgerald and Alvarez (1992), Peterson (2003), and Ortalo-Magne and Rady (2001)]. But, as explained by Davis and Heathcote (2003), while frictions such as poorly functioning rental and mortgage markets are likely to be important in accounting for cross-sectional issues, it is not obvious that they are important for housing dynamics at the aggregate level. Part of the literature review focus on the current account dynamics showing its increasing umbalanced deficit and trying to capture the causes that determine this change. Obstfeld & Rogoff (2000a) argue that the United States current account deficit was on an unsustainable trajectory over the medium term, and that its inevitable reversal would precipitate a change in the real exchange rate. Always Obstfeld & Rogoff (2004) develop a general equilibrium model in the global economy, and they show that faster growth abroad helps only if it is relatively concentrated in nontradeble goods and faster productivity growth in foreign tradable goods is more likely to exacerbate the US 7

8 adjustment problem. Obstfeld (2004) shows how fluctuations in asset value render the national income and product account measure of the current account balance increasingly inadequate as a summary of the change in a country s net foreign assets. Mercereau (2003) tests a model of the role of stock markets in current account dynamics and his results also suggest that stock markets matter to the current account dynamics. Roubini & Setser (2004) found that the sharp rise in U.S. net external debt since 2001 has financed a fund a boom in goverment borrowing, a boom in consumption and a boom in residential construction, not a boom in investment, let alone investment in the export sector; the U.S. has become increasingly dependent on foreign purchases of fixed income debt securities, and in particular purchases of U.S. treasuries by Asian central banks, to finance huge U.S. current account deficit that are absorbing an enormous fraction of all cross-border capital flows. Under this direction, it looks reasonable to look at the housing market behavior, and the recent literature offers a lot of empirical works that include the real estate market in the economic cycle and showing how this arket is related to the fundamentals of economy. Flavin (2001) examines the portfolio choice problem of an agent who invests in both financial and assets and real estate. Campbell & Cocco (2003) examine a household s mortgage choice between a fixed rate loan and an adjustable rate loan. All those last papers focus on the effect of housing positions and house price risk on household portfolio choice. Also I consider Schmitt-Grohe and Uribe (2003) to evaluate and solve stationarity problems. 3 Model I develop a general equilibrium model that incorporates housing market imperfections into an international business cycle model. The simple fact that agents can collateralize their homes value, this generates financial friction through the financial accelerator mechanism. The model combines heterogeneity of time preference with collateral constraints. The basic model corresponds to a two-sector small open economy under flexible exchange rate regimes, without money. Housing is treated as a durable good where the demand depends on both the service flow and the asset value of housing units and the stock od house is assumed to be proportional to the service flow; the return from housing equals the return of other alternative 8

9 assets. The economy is composed of heterogeneous agents, as well as two sectors. The first sector produces a consumption good using capital and labor, and capital is owned by the household who rent to the firm, while the second sector produces a composite real estate good using residential structures and labor as inputs. I assume that the utility gains from holding real money are zero and therefore omit real money balances from the utility function. 3.1 Household Sector The household sector is composed by to type of agents: Saver and Borrower. The model combines heterogeneity of time preference with collateral constraints. Household debt reflects intertemporal trade between an impatient borrower and a patient saver. In equilibrium, the saver holds all the capital stock and the borrower s debt. Savers are more patient and do not work. The first assumption generates a concentration of assets in a relatively small number of households as in Krusell and Smith s (1998). Because of their small number and large wealth, had savers an endogenous labor supply decision, their contribution to aggregate labor supply would have been small. Savers and borrowers sell capital services and labor to a representative firm and borrow from each other. All debt is collateralized by durable goods. Borrowers face an external borrowing constraint. The constraint is not de- rived endogenously but it is consistent with standard lending criteria used in the mortgage and consumer loans market. The borrowing constraint is introduced through the assumption that households cannot borrow more than a fraction of the value of their houses. Mortgage loans re.nancing takes place every period and the household repays every new loan after one period. It seems quite realistic that the overall value of the loan cannot be higher than a fraction of the expected value of the collateral. The fraction m, referred to as loan to value ratio, should not exceed one. This can be explained thinking of the overall judicial costs which a creditor incurs in case of the debtor default. Since housing prices affect the collateral value of the houses, fluctuations in the price plays a large role in the determination of borrowing conditions at household level. Borrowing against an higher value of the house is used to.nance both investment in housing and consumption. The other source of 9

10 mortgage equity withdrawal is given by an increase in the value of the collateral due to a rise the loan to value ratio. 3.2 The Saver s Problem In this model, the saver does not work, she consume non-durable goods and housing service, she also owns all the capital, which rents to firms. She extends financial credit to the borrower and has access to international asset. The saver maximizes this utility function subject to: [ ] U t = E t β t ln C t + ln j t h t t=0 C t + q t [h t (1 δ h )h t 1 ] + k ct + k ht + R t 1b t 1 b t R ct 1 k ct 1 + R ht 1 k ht 1 R t 1 b t 1 + b t + ψ 3 2 (b t b t )2 where R t and R t are the domestic interest rate and the international interest rate, respectively. Following Schmitt-Grohe and Uribe, ψ 3 and b t are constant parameters defining the portfolio adjustment cost function. As we will see in the first order condition, the portfolio adjustment cost helps to solve non-stationarity problem, and it is assumed that if the household chooses to borrow an additional unit, then current consumption increases by one unit minus the marginal portfolio adjustment cost ψ 3 2 (b t b t )2. Next period, the household must repay the additional unit of debt plus interest. At the optimum, the marginal benefit of a unit debt increase must equal its marginal cost. The nn-separability between goods and housing holdings means that shocks to the real estate sector have spillover effects on traded goods consumption, and hence the current account. For instance, in the case that traded goods consumption rises together with real estate holdings consumption, a boom in the real estate can cause an increase in demand for imports and a current account deficit (i.e. an increase in the real estate sector may increase demand for furniture). 10

11 The optimality conditions are: [ 1 Capital-Goods Allocation C t = βe t [ 1 Capital-Houses Allocation C t = βe t [ 1 Consumption/Saving C t = βe t ] R ct C t+1 ] R ht C t+1 ] R t C t+1 ( 1 Foreign Bond Holdings C t [1 + ψ 3 (b t b t ] = βe t ) Rt c t+1 Housing Demand Allocation q t C t = jt h t + β(1 δ h )E t [ q t+1 C t+1 ) ] 3.3 The Borrower s Problem The borrower consumes non-durable goods and housing services, she can decide to work in the non-residential or residential sector. In equilibrium the two sector offer the same wage. The borrower maximizes this utility function subject to: [ ] U t = E t γ t ln C t + ln j t h t η (L1/ν ct + L 1/ν ht )ν ν t=0 C t + q t [h t (1 δ h )h t 1] + R t 1 b t 1 w ct L ct + w ht L ht + b t and b t mq t h t where γ β to distinguish between patient and impatient. I assume ν to be equal to 1 to make the labor market perfectly substitute. 11

12 Labor-Goods Allocation w ct C t = η(l ct ) 1/ν 1 [L 1/ν ct + L 1/ν ht ]ν 1 Labor-House Allocation w ht C t = η(l ht ) 1/ν 1 [L 1/ν ct + L 1/ν ht ]ν 1 Borrowing Allocation 1 C t = γe t ( R t C t+1 ) + λ t Housing Demand Allocation qt C t = jt h t [ ] q + γ(1 δ h )E t+1 t ) + mq C t λ t t Firms Recent works have been showed the importance to incorporate the real estate sector into the business cycle,a nd there are good reasons for distinguishing between residential and non-residential sector. This is because different durable assets are produced using different technologies and residential investment leads the business cycle, whereas nonresidential investment lags. Previous research have estimated that the percentage standard deviation of residential investment is twice that of nonresidential investment, and consumption, nonresidential investment, residential investment, and GDP all co-move positively. In addition, the model economy can account for the facts that hours worked and output are most volatile in the construction sector and least volatile in the services sector, and that hours worked and output in all intermediate sectors co-move positively. The reason to address the dynamics of residential investment and house prices, and in part because there are important differences between housing and other durables. Housing is an important component of wealth and is a much better store of value than consumer durables since residential structures depreciate at a rate of only 1.6 % per year, compared to 21.4 % for other durables. Then, the technology for producing new houses is more land intensive and more construction intensive than the technology for producing consumer durables. We shall argue that these details of depreciation rates and production technologies are crucial in accounting for residential investment 12

13 dynamics. Firms produce non-durable goods and new houses. Both sector follow a Cobb-Douglas production function, but with different capital and labor intensity. They repay back capital to the savers and pay wage to the borrowers. Max y t + q t N t + (1 δ k )(k ct 1 + k ht 1 ) [w ct L ct + w ht L ht + R ct 1 k ct 1 + R ht 1 k ht 1 ] where h t (1 δ h )h t 1 + h t (1 δ h )h t 1 = N t N t = A ht L 1 µ h ht k µ h ht 1 The optimal conditions are: y t = A ct L 1 µc ct k µc ct 1 {k c,t 1 } : µ c y t k c,t 1 + (1 δ k ) = R c,t 1 {k c,t 1 } : µ h q tn t k h,t 1 + (1 δ k ) = R h,t 1 {L c,t } : (1 µ c ) yt L c,t = w c,t {L h,t } : (1 µ h ) qtnt L h,t = w h,t 13

14 3.5 Current Account Equation The current account is the changing in the net asset position of one country respect the other one. CA t = (b t b t 1) = (R t 1)b t 1 + y t + (1 δ k )(k ct 1 + k ht 1 ) C t + C t k ct k ht 3.6 Exogenous Factors The foreign sector is assumed to be exogenous, as well both technology process to produce final goods and new houses. Each exogenous variable follows an autoregressive process of order one, as: A ct+1 = ρ c A ct + ε ct A ht+1 = ρ h A ht + ε ht j t+1 = ρ j j t + ε jt 3.7 Market Clear Condition b t + b t = 0 h t (1 δ h )h t 1 + h t (1 δ h )h t 1 = N t C t + C t + k ct + k ht + R t 1b t 1 = y t + (1 δ k )(k ct 1 + k ht 1 ) + b t 4 Results A standard VAR system is the reduced form of a linear dynamic simultaneous equation model in which all variables are treated as endogenous. This framework is employed in this paper to study 14

15 the behaviour of property prices and current account. I construct a VAR where each variable is regressed on a number of lags (4 quarters in this study) of itself and of all other variables in the information set. In the next step the aim is to provide some quantitative estimates of the dynamic interaction among the variables of interest. To do this, I orthogonalise the estimated reducedform model to identify the effect of the innovations of the variables in the system in isolation from each other. In this paper the identification uses Sims lower triangular ordering (the standard Choleski decomposition), and the ordering of the variables is: current account, trade balance (GDP, consumption, investment and government spending) and residential prices. The ordering is justified by the fundamental equation of the current account derived in the appendix. For the three countries I analyzed, I found that an housing price shocks drives a current account deficit in response. The basic results found so far include the impulse response to technology change shock to the goods sector and the impulse response to the technology change shock to the real estate sector, I mean an improvement in building new houses. We expect an increase in consumption due to an improvement in producing goods, also output increase and this leads to an increasing in the current account, small one because both output and consumption increase. This sector is able to influence the real estate sector because firms create new capital, either goods capital and real estate capital, so real estate sector will produce more houses. In the case of a technology real estate sector shock, the goods sector is not really affected, and consumption is a little bit reduced because people switch buying new house, since the prices go down. Current account show a very marginal increase. In case of house preference shock, we can expect an increasing in the current account due to an increase of housing supply to respond to the high demand, so investment increase and consumption decrease because people demand more houses. This is the benchmark case with no borrowing constraint. If we apply the borrowing constraint we can see that a preference house shock push up the demand side with an increasing in the price, this leads in an increase on the borrowing level with the consequential wealth effect, and current account deficit. 15

16 5 Conclusions This paper analyzes a two-sector small open economy with a goods production sector and a real estate sector. The purpose is to predict what kind of shocks determine a change in the current account dynamic when we include housing in our economic model. We expect to find that mostly house preference shocks generate an increase in the current account deficit. People are willing to buy more house, and this push up the prices leading to a wealth effect because of the financial accelerator mechanism generated by the mortgage borrowing constraint. 16

17 5.1 Parametrization β = 0.99 γ = 0.98 Subject Discount Factor of Saver Subject Discount Factor of Borrower 1/β = R = 1.01 Steady State Real Gross Interest rate δ k = δ h = κ = 2.5 j = 0.1 m = 0.89 χ = 0.5 ψ 3 = Depreciation Rate of Capital Depreciation Rate of House Scale Factor for Labor Supply Weight on Housing Services Loan-to-value ratio Elasticity of Labor Supply to Wage Bond Adjustment Cost µ c = 0.37 Capital Share for Good Sector µ h = 0.13 Capital Share for House Sector η = 2.32 ν = 1 ρ σ Scale Factor for Labor Supply Elasticity of Labor Supply to Wage AR(1) Parameter on Shock Standard Deviation of the Shock 17

18 6 Appendix 6.1 The Baseline Model with Houses The model considers a small open economy which faces a given world interest rate and has no capital controls. A representative household, which also represents the national economy, maximizes the lifetime expected utility function U = E 0 [ u(t)], with 0 < β < 1, (1) t=0 where E 0 [ ] denotes the expectations conditional upon the information available at time 0, and β is the subjective discount factor. Instantaneous utility u depends on general consumption (C), and durables consumption representaed by holding housing, H. Utility function is represented by the following form: U(t) = γlog(c t ) + (1 γ)log(h t ). (2) The model only allows for a one-period bond, and thus assumes incomplete international securities markets. Also in the model houses purchases are reversible and can be undertaken instantaneously without incurring adjustment costs. The household can accumulate external assets B which evolve according to B t+1 = (1 + r)b t + Y t C t I t G t p h t [H t (1 δ)h t 1 ], (3) which represent the budget constraint. p h t is the purchase price of houses relative to the rest of good which is considered to be the numeraire in each period; B t is the stock of external assets at the beginning of time period t; r t is the world interest rate measured in terms of the numeraire; Y t I t G t can be rewritten as the net output (NO t ), meaning the GDP minus the sum of investment and government expenditures. Maximization of the household s intertemporal utility function leads to the Euler equations that describe optimal intertemporal consumption decisions for t = β(1 + r t )E t [ ], (4) C t C t+1 and 18

19 γ ph t C t = 1 γ H t + β(1 δ)e t [ ph t+1 C t+1 ]. (5) Assuming that both the relative price of houses, and the consumption based real interest rate in terms of the consumptions are constant, the relationship between house stock and consumption can be expressed as: C t H t = γ r + δ 1 γ 1 + r ph. (6) Plugging both Euler-equations in the intertemporal budget constraint, we can obtain the optimal allocation for consumption and housing holdings: and C t = H t = where i t p h t γr 1 + r [(1 + r)b t + (1 δ)p h t H t 1 + (1 γ)r i t (1 + r) [(1 + r)b t + (1 δ)p h t H t ( 1 + r )s t (Y s G s I s )] (7) s=t 1 ( 1 + r )s t (Y s G s I s )], (8) s=t 1 δ 1+r t+1 p h t+1 represents the implicit date t rental price, or user cost, of the house. Given a resale market with no transaction costs, user cost equals the net expense of buying the house in one period, using it in the same period, and selling it the next. Finally, we can derive the current account for period t: CA t = B t+1 B t = rb t + NO t C t p h t [H t (1 δ)h t 1 ] Making use of equation (7), we can rewrite: CA t = B t+1 B t = NO t r 1 + r now use equation (6) to get rid of C t, and we can obtain: 1 ( 1 + r )s t NO s r 1 + r (1 δ)ph t H t 1 + (1 γ)c t p h t H t +(1 δ)p h t H t 1, γ s=t CA t = (NO t NO) (i p h )[H t H t 1 ]. (9) The current account not only reacts revisions about future net output, but also contains a stock adjustment term. This new component has an important consequence: whereas in the standard model a permanent decrease in net output has no impact on the current account, in the specification with houses it leads to a temporary current account surplus. This is due to fact that, after the 19

20 realization of the permanent decline in net output, households find themselves temporarily holding a high stock of durables. In response to that, they adjust their durables stock downward by depleting the existing stock to levels that are optimal given the new net output. This leads to a decline in aggregate consumption spending and a temporary current account surplus. Similarly, a temporary decrease in net output leads to a smaller current account deficit because of the ability of the households to smooth their consumption through the stock of durables. The model also has implications for the volatility of the current account. This is related to the fact that consumption expenditures on durables (flow) are much more variable than the stock of durables and nondurables consumption. Despite the fact that durables purchases impart an additional adjustment component to the current account, the precise influence of durables expenditures on the volatility of the current account depends on a host of factors. In the above model, these factors include the preponderance of permanent versus temporary shocks (to net output) and their correlations with the determinants of durables expenditures. Other modelling choices, such as adjustment costs and tradability, may also a affect current account volatility in different ways. If some durables are nontraded (as in Matsuyama 1990), or durables purchases are irreversible, then durable goods induced variability may dampen because such factors moderate the effects of unanticipated permanent income shocks on desired durables stock. In contrast, if some durables require fixed stock adjustment costs, households may bunch their durables expenditures, which leads to more variable current account dynamics. None of these modelling choices, of course, has been considered in the derivation of the fundamental equation as they lead to nonlinear environments and aggregate results are available only in very special cases (Leahy and Zeira 1998). 20

21 References [1] M. Gertler, S. Gilchrist and F. Natalucci (2003). External Constraints on Monetary Policy and the Financial Accelerator. Nber Working Paper, [2] J. Greenwood and Z. Hercowitz (1991). The Allocation of Capital and Time over the Business Cycle. Journal of Political Economy, 99 (6): [3] J. Greenwood, Z. Hercowitz and P. Krussel (2000). The Role of Investment-Specific Technological Change in the Business Cycle. European Economic Review, 44 (1): [4] M. Iacoviello (2004). House Prices, Borrowing Constraints and Monetary Policy in the Business Cycle. American Economic Review, 95 (3): [5] M. Iacoviello and R. Minetti (2004) International Business Cycles with Domestic and Foreign Lenders. forthcoming, Journal of Monetary Economics. [6] Y. Jin and Z. Zeng (2004) Residential Investment and House Prices in a Multisector Monetary Business Cycle Model. Journal of Housing Economics 13: [7] W. D. Lastrapes (2002). The Real Price of Housing and Money Supply Shocks: Time Series Evidence and Theoretical Simulations. Journal of Housing Economics, 02 (11): [8] B. Mercereau (2003). The Role of Stock Markets in Current Account Dynamics: Evidence from the United States. Economic Journal, 84 (2): [9] J. Muellbauer and A. Murphy (1997). Booms and busts in the UK housing market. Economic Journal, 84 (2): [10] M. Obstfeld and K. Rogoff (2004). The Unsustainable US Current Account Position Revisite. NBER working paper [11] M. Piazzesi, M. Schneider and S. Tuzel (2003). Housing, Consumption and Asset Pricing. Working paper. 21

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