Housing market cycles a disequilibrium model and its calibration to the Warsaw housing market

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1 Housing market cycles a disequilibrium model and its calibration to the Warsaw housing market Hanna Augustyniak 1, Jacek Łaszek 2 and Krzysztof Olszewski 3, July Work in progress preliminary draft Abstract We present a disequilibrium model of the housing market, which allows us to analyze and explain cycles in this market. Cycles are a permanent feature of the real estate market and can be mainly explained by elastic demand which meets inelastic supply. Further on, market participants tend to extrapolate expectations from past observations. This leads to frequent cycles, which under specific conditions lead to boom and bust cycles and potentially result in a crisis. We propose a simple disequilibrium model, which we calibrate to the Warsaw housing market. We first explain the past cycle and further show how the multiplication of marginal shocks can lead to strong fluctuations. We consider this model as useful for central banks and financial supervisors in the analysis of different monetary, regulatory or fiscal policy changes, as it better replicates the reality than usually applied equilibrium models do. Key words: Housing market cycles; disequilibrium; banking sector; regulation; JEL Classification Numbers: E32, E44, E37, R21, R31; 1 Introduction While most models on the housing market assume that it is in equilibrium, the long construction lag and fast changing demand, which is largely driven by credit supply and credit affordability makes it oscillate around the equilibrium, which changes over time. In this paper we propose a formal model which incorporates the usual assumptions on the household utility and captures the fact that supply is fixed in the short run and reacts only with a lag, while demand is flexible. It allows us to study how the housing cycle changes when there is a shock 1 Economic Institute, National Bank of Poland. 2 Warsaw School of Economics and Economic Institute, National Bank of Poland. 3 Economic Institute, National Bank of Poland. Ul. Świętokrzyska 11/21, Warszawa, Poland. Krzysztof.Olszewski@nbp.pl. Corresponding author. The paper presents the personal opinions of the authors and does not necessarily reflect the official position of the National Bank of Poland or the Warsaw School of Economics. 1

2 to the nominal interest rate or household preferences. We present the housing demand and supply model in Chapter 2 and calibrate it to the Warsaw housing market in Chapter 3. We apply shocks to the model in Chapter 4 and Chapter 5 concludes the paper. 2 The housing demand and supply model We present a disequilibrium model of housing demand and supply, where expectations are based on the extrapolation of past observations. The main driving force of price movements is increased demand for housing, which is largely determined by credit supply. In this article we focus on flats that are bought on the primary market and which are usually financed with a loan. The secondary market and the primary market are usually strongly correlated, but the prices on the secondary market are usually lower. More details about the relationship between those two markets can be found in NBP (2011a,b). The model economy consists of households that take loans and buy flats on the primary market. Empirical evidence shows that many households do not buy already created houses, but they buy contracts from developers. Developers sell a contract and commit to deliver a flat, which they already have started to build. Usually, contracts are sold two years after the construction process has stared. Then it takes another two years until the construction is finalized, but this does not have any effect on the market. While pre-sales are not very usual in Western Europe, they are often used in Poland but also have a long history in Asia (see Chang and Ward 1993). In fact such contracts make supply more elastic and help to shorten the cycle and lower its amplitude. Sometimes, especially when demand is very high, households buy contracts for virtual projects. Developers can sell pre-sale contracts around one year after they have started the construction process and the households virtually buy a hole in the ground. Such a forward contract is always associated with some risk, but it helps the supply side to respond quicker to strongly increasing demand. The advantage for the buyer is that he buys a flat at a fixed price, while the developer gets financing throughout the project without the need to obtain it from a bank. The disadvantage is that the buyer takes a higher risk (the developer might default), while the developer cannot easily adjust the price upwards if the market price rises in the future (see Chang and Ward 1993). 2.1 Housing demand We focus only on the primary market and assume that the majority of households needs to finance the purchase with a loan. Burkham (1972) quotes a study by the FED 2

3 according to which credit supply is the major determinant of house constructions. We observe that all around the globe housing demand is strongly driven by credit supply, and this also holds for Poland (see NBP 2011a,b). Another important determinant for housing demand are consumer's preferences about the consumption of other goods C and housing H. We describe his utility with a CES utility function, where θ is the weight on utility from consumption of goods and µ is the inverse of the elasticity of substitution between consumption and housing. We also incorporate the fact that consumers have expectations about the future house price (see Dunsky and Follain (1997) or Sommervoll et al. (2010)). The appreciation is captured by. The households utility takes the form: The consumer has to split his income between the consumption of other goods and the repayment of the housing loan. We solve the consumers problem subject to the budget constraint,, where r is the interest rate and p the price of square meter of housing, which gives us the optimal allocation of housing and consumption in every period. Combining this solution with the budget constraint, we obtain the optimal allocation of housing and consumption, which depends on the budget, the nominal interest rate and the price of housing. Lin and Lin (1999) state that income elasticity is close to 1, thus an increase of income should lead to a proportional increase in housing demand. The household, however is not only constrained by its budget, but also by its credit affordability and bank limits. As stated earlier, credit supply is seen as the main driver of housing demand. The bank calculates the household's credit affordability basing on the nominal interest rate and its income. Also the initial down payment has a significant impact on the housing demand (see for example, Stein (1995), Ortola-Magne and Rady (2006)). If the household is constrained and will be allowed to use only a part of its income to finance housing (repay the monthly debt), 3

4 its choice will not always be the optimal allocation C* and H*, but it will choose: This constrained choice is a second best choice, because the household consumes more than it wants to, while it has a smaller flat than it would like to have. The consumers choice under a normal budget constraint and under the restricted budget constraint is presented in figure 1. Figure 1. Consumer's choice under normal budget constraint (left) and credit restricted budget constraint (right). H H A A B C C This case is interesting from the monetary policy or regulatory point of view, because even small changes in the credit affordability or credit regulations can generate strong shifts in consumer's optimal choice. An unconstrained consumer reacts, to an increased budget or to higher credit affordability, as stated above, with unit elasticity. However, if suddenly low interest rates or regulatory changes make more credit affordable, the constrained household will jump from one optimal consumption point to another, where it gives up a lot of consumption of other goods to buy a larger flat. On the other hand, increases in prices or interest rates will not necessarily make the household to buy a smaller flat, it might give up more consumption of other goods to buy the same amount of housing. 4

5 2.2 Housing supply - construction The supply of housing (the construction of new housing) depends on lagged excess demand, reflected in past price growth of housing, and on the costs that developers have to bear. A broad literature review about the supply side can be found in DiPasquale (1999). Moreover, a detailed discussion of the developer and construction sector in general and with special focus on Poland will be presented soon in NBP (2012, forthcoming). In this paper we base on the model proposed by Tse, Ho and Ganesan (1999), where house supply (construction) S depends on some autonomous supply (its long run equilibrium level) and also reacts with some elasticity to the past price changes and the cost of construction. Unlike in the Tse, Ho and Ganesan model, we lag the effect of the price change ( P) to capture the construction time, which we consider as crucial to make the model be closer to reality. The developer usually sells a housing contract when the construction process is around its half-time (which is 4 years in total). Thus, under normal conditions the developer currently sells construction contracts, which he started around two years earlier. Therefore, the current supply of housing contracts depends on the developers decision that he made two years earlier, observing the price developments at that time. Further on, basing on our empirical observations we add another parameter, which captures risky home contracts, namely very early pre-sale contracts. When the demand goes up very strongly, developers start to sell holes in the ground. Those are projects which consist of nothing more than the permit to build a house and land owned by the developer. This kind of contracts can enter the market already one year after the construction process has started. We have to remember that the houses will be finished later, but the current contract fully satisfies the households need for housing. Lastly, construction costs C_t (material, labour, etc.) will affect the developers decision negatively. The housing supply function takes the following form. We see that besides the autonomous supply of housing contracts more contracts will be sold by developers if the price was growing in the past. Contrary, supply will slow down, when developers observe price stagnating or even declining prices. 2.3 Price adjustments The motion in the economy stems from changes in prices. One option to explain price changes is to look at the current mismatch between demand D and supply S, as Tse, Ho and Ganesan (1999). In our model we look at deviations from long run supply, as this is more 5

6 convenient for our analysis. The price change is determined by the current mismatch between long-run supply which equals long run demand and current demand, thus we write: The parameter ρ describes how fast the price adjusts. Empirical evidence tells us that the reaction is asymmetric, that is prices are elastic upwards but quite rigid downwards. The explanation is as follows. The price is usually set by developers. Buyers can sometimes negotiate, but have relatively little information and bargaining power. The developer can ask a higher price when demand exceeds supply. Further on, he can expect that costs of intermediary goods and services will rise. On the other hand, when there is excess supply the developer can wait until he sells his construction contract or even a finished flat. The developer will lower the price slowly, hoping to find a buyer who is willing to pay the price. This is indeed what we observe in the Polish housing market. The situation would change drastically if developers were highly leveraged and would need to get financing very quickly. Then they might lower the price drastically to sell the flat as quick as possible. 2.4 Moving towards a new equilibrium We assume that the market is initially in equilibrium. For simplicity one can say that if price changes are very little, demand and supply deviate only marginally and the economy is close to an equilibrium. But we want to study the impact of meaningful price changes. Assume that credit supply increases, as indeed happened in Poland due to access to FX denominated loans. Demand for housing will increase instantly, but developers will be able to deliver more flats with a time lag. When current demand exceeds supply, housing prices will grow, which will make developers to construct more housing in the future. However, the households ability to buy housing depends strongly on credit supply, which is determined by interest rates. Thus, at some point households will not be able to afford more housing, while there will be still construction in the pipeline. This should lead to price reductions. Developers will slow down production and they will slowly move towards a new equilibrium. Due to the construction lag the equilibrium is just a step away, but it changes before the developers or the households can reach it. To sum up, the model allows to explain the rich dynamics that lead to significant cycles in the real estate market. The model suggests that the only way to make the catch-up process towards the equilibrium faster and the oscillations flatter is to slow down the credit boom, thus control demand and make it more stable. We check the models implications by calibrating it to the Warsaw housing market. 6

7 3 Calibration of the model to the Warsaw housing market We calibrate the model to the Warsaw market to show how variations in the interest rate or other parameters affect housing demand, which in turn affects the housing supply with a certain lag. We show how the market oscillates around the equilibrium point. The analysis of the Warsaw housing market over the recent years shows us that, similarly as in other housing markets, the increase in demand leads to a quite fast increase in prices and finally in the production of new housing. We have too short time series of data to perform a long-term analysis like it is done for Switzerland over a 33 years period ( ) by Steiner (2010) or to perform an analysis of the disequilibrium as proposed by Fair and Jaffee (1972). Instead, we use our expert knowledge and perform some calibration and rule of thumb estimations basing on data4 for the last 10 years ( ). The data allows us to capture the recent cycle, which starts with a three years period of stable prices , which accelerated due to increased income and lower interest rates during and started to decline during due to the slowdown in the world economy, excessive housing supply and constrained credit supply. Figure 2. Dwelling starts and dwelling prices. Source: Central Statistical Office, NBP BaRN and PONT Info. 4 Data on house prices origins for from PONT Info (offer prices), for from NBP BaRN (transaction prices). Construction and income data origins from the Central Statistical Office of Poland. Data on interest rates and credit availability estimates origin from NBP (see NBP 2011b for details). 7

8 We find that the price elasticity of housing construction is slightly above 1 over the whole period. It seems to be more elastic upwards than downwards, as indicated already in the theoretical considerations about the model. We look, similarly to Steiner (2010) at the long run equilibrium of housing demand and supply and study the fluctuations around it. Our data indicate that over the considered period the average demand and supply was around housing units annually. We consider this level as the equilibrium level. Starting from the equilibrium, demand increased drastically after 2004 due to an increased credit supply. This lead to an increase in prices as described by the price adjustment equation. In consequence, developers started new construction projects, which entered the market with a lag of around one to two years. The price and construction of new dwellings continued until 2007, but due to the global economic crisis demand for housing declined. We see that new construction went down much faster than prices. This shows that prices are less elastic downwards than upwards. [TO BE CONTINUED] 4 Analysis of the impact of various shocks In this section we apply small shocks to the interest rate and consumer preferences and analyse how they affect the housing market cycle. Further, we apply a positive interest rate shock and a change in consumer preferences to show that even small but combined shocks can have a significant impact on the market cycle. This lead to an increase in prices and consequently the number of new dwellings started to rise. Those are sold with a lag of one or two years on the market [TO BE ADDED] 5 Conclusions We presented a relatively simple and tractable model that helps to understand the cyclicality of the housing market. After calibrating it to the Warsaw market, we show how different shocks affect the market. We further show that the combination of small shocks can lead to significant price swings. The model is useful for policymakers, central banks and regulators to analyse the impact of various policies on the housing market. One central feature of our model is that we consider the market, as empirical evidence clearly shows, to be in disequilibrium. The permanent adjustment towards an equilibrium which changes continuously leads to very interesting cycles. We would like to stress that the common assumption, which one can find in most models, that the market is in equilibrium 8

9 might lead to misleading results and thus give wrong signals to policymakers. We also think that our model might help to augment existing macroeconomic models that try to explain the effects of monetary policy GDP on growth and inflation and usually treat the housing market only as a residual variable. Literature Aoki K., J. Proudman and G. Vlieghe (2002). House prices, consumption, and monetary policy: a financial accelerator approach. Bank of England Working Paper no Bernanke B., M. Gertler and S. Gilchrist (1999). The financial accelerator in a quantitative business cycle framework. Handbook of macroeconomics (North Holland). Bracke P. (2011) How Long Do Housing Cycles Last? A Duration Analysis for 19 OECD Countries. IMF Working Paper WP/11/231. Chang C.-O. and C.W.R. Ward (1993) Forward pricing and the housing market: the pre-sales housing system in Taiwan. Journal of Property Research V 10, p DiPasquale D. and W. C. Wheaton (1992). The markets for Real Estate Assets and Space: A A Conceptual Framework. Journal of the American Real Estate and Urban Economics Association. V20, 1. p DiPasquale D. (1999). Why Don t We Know More About Housing Supply? The Journal of Real Estate Finance and Economics V18, 1, p Dunsky R.M. and J.R. Follain (1997). The demand for mortgage debt and the income tax. Journal of Housing Research V8, Lambertini L., C. Mendicino and M. T. Punzi (2012). Expectations-Driven Cycles in the Housing Market. Bank of Finland Research Discussion Paper Levin E. J. and G. Pryce (2009). What Determines the Responsiveness of Housing Supply? The Role of Real Interest Rates and Cyclical Asymmetries. Centre for Public Policy for Regions Discussion Paper no. 20. Lin C. and S. Lin (1999). An Estimation of Elasticities of Consumption Demand and Investment Demand for Owner-Occupied Housing in Taiwan: A Two-Period Model. International Real Estate Review, V2, 1, p NBP (2011a). Report on the residential and commercial real estate market in Poland in NBP (2011b). Information on home prices and the situation in the residential and commercial real estate market in Poland in 2011 (Q1- Q4). NBP (2012, forthcoming). Report on the residential and commercial real estate market in Poland in Ortola-Magne F. and S. Rady (2006). Housing Market Dynamics: On the Contribution of Income Shocks and Credit Constraints. Review of Economic Studies, V73, p Phang S. Y., K. H. Kim and S. Wachter (2010). Supply Elasticity of Housing. Forthcoming in: International Encyclopedia of Housing and Home, Published by Elsevier and Science Direct. Sanchez A. C. and A. Johansson (2011). The Price Responsiveness of Housing Supply in OECD Countries. OECD Economics Department Working Papers, No Sommervoll D. E., T.-A. Borgensen and T. Wennemo (2010). Endogenous housing market cycles. Journal of Banking & Finance V34, p Stein, J. (1995). Prices and trading volume in the housing market: a model with downpayment constraints. Quarterly Journal of Economics, 110(2), p

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