توزیع درآمد و قیمت مسکن: یک رویکرد مدل تخصیص
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Economic Theory, Available online 28 January 2014
We present a framework for studying the relation between the distributions of income and house prices that is based on an assignment model where households are heterogeneous by incomes and houses by quality. Each household owns one house and wishes to live in one house; thus everyone is potentially both a buyer and a seller. In equilibrium, the distribution of prices depends on both distributions in a tractable but nontrivial manner. We show how the impact of increased income inequality on house prices depends on the shapes of the distributions, and can be inferred from data. In our empirical application we find that increased income inequality between 1998 and 2007 had a negative impact on average house prices in 6 US metropolitan areas.
A central feature of the housing market is that housing is not a fungible commodity but comes embedded in indivisible and heterogeneous units. What people refer to as “houses,” are really bundles of land and structures. The quality of land is inherently heterogeneous because locations differ in their attractiveness due to fixed factors such as distance from the center and view of the sea. The supply of structures is more or less fixed in the short term, and only partly adjustable in the medium term. Quality of structures can also have a fixed component, due to zoning restrictions or the scarcity value of vintage architecture. At the same time, housing is a normal good, as the more wealthy spend more on housing. Given the indivisibility and heterogeneity of houses, it is natural to consider the housing market as an assignment problem. Yet, assignment models are not a standard tool in applied work on housing economics. One reason may be that in the standard assignment model agents are ex ante divided into two distinct classes, such as “buyers” and “sellers”. The two-sidedness assumption is natural in many markets, for example when firms are matched with workers, but is problematic in the housing market where most households are potentially both sellers and buyers. Furthermore, standard assignment models assume transferable utility and so preclude income effects. In the housing market, however, income effects may be significant since housing takes up a large part of household expenditure. In this paper, we present a one-sided assignment model with non-transferable utility, where houses are heterogeneous by quality and households are heterogeneous by income. Each household owns one house and wishes to live in one house; thus householdsʼ reservation prices as sellers depend on the opportunities available to them as buyers. We model a single metropolitan region, where the set of households is fixed. The distributions of income and house quality are exogenous, while the distribution of house prices and therefore wealth is endogenous, with the exception of the cheapest or “marginal” house. In general, the initial joint distribution of houses and income is arbitrary, which results potentially in a lot of trading between households. Equilibrium prices depend on the properties of the joint distribution, not just on the marginal distributions of income and house quality. We show the existence of equilibrium prices under an arbitrary initial endowment. For most of the paper we focus on the equilibrium prices that emerge after all trading opportunities have been exploited. Equilibrium prices can then be solved explicitly from the joint distribution of wealth and house quality and the parameters of the utility function. We use the equilibrium conditions to derive analytical results for the impact of income distribution on the distribution of house prices. According to our theoretical results the impact of increased income inequality on top (as well as average) house prices is ambiguous. The intuition for why increase in income inequality leads to lower prices at the bottom of the quality distribution is clear: if low-income households have less income they bid less for low-quality houses. However, in equilibrium, any changes in prices spill upwards in the quality distribution. This is because the binding outside opportunity of any (inframarginal) household is that they must want to buy their equilibrium match rather than the next best house. The equilibrium price gradient—the price difference between two “neighboring” houses in the quality distribution—is pinned down by how much the households at the relevant part of the income distribution are willing to pay for the quality difference. The price of any particular house is then given by the summation of all price gradients below, plus the price of the marginal house. Thus, while an increase in incomes at the top increases the local price gradient, the lower prices at the bottom put downward pressure on prices above. It is therefore possible for all house prices to go down in response to an increase in inequality. In order to illustrate the mechanisms of the model and to evaluate their quantitative importance we apply our model to data from the American Housing Survey (AHS) in 1998 and 2007. We assume that all households prefer to live in their current house under current market prices. Under this “post-trade” interpretation of data the distribution of unobserved house qualities can be inferred as the distribution that gives rise to the observed price distribution as the equilibrium outcome of our model. The inferred distribution of house qualities can be used to generate counterfactuals. This setup is at its most useful in analyzing changes or policies that may be at least partly capitalized into house prices, such as income transfers and housing cost subsidies; we discuss other potential applications of our model in the end. We find that a suitably parametrized constant elasticity of substitution (CES) utility function allows us to roughly match the observed change in the price distribution under the assumption that it was caused by the observed change in incomes while unobserved house qualities remained unchanged. We first use the calibrated model to illustrate how the income elasticity of housing demand depends on the quality and income distributions, and varies between households, despite homogeneous CES preferences. Intuitively, how much more one would spend on housing following an increase in income depends on the additional housing quality that one extra dollar can buy; this in turn varies over the distribution, as it depends both on available qualities and on the incomes of competing buyers and sellers. We then consider counterfactual income distributions for 2007 where all incomes grow uniformly since 1998 at the same rate as the actual mean income in the same metropolitan region. We compare house prices that result from the counterfactual income distributions with the prices resulting from the actual income distributions, while holding constant the population and the housing supply in each city. This exercise can be seen as a way to disentangle the short or medium run impact of increased income inequality on house prices from changes in other house price determinants. Depending on the region, counterfactual income distributions result in house prices that are on average 0−10% higher than house prices resulting from actual income distributions. (This excludes any changes in the top 3% of the price distribution, which is excluded due to top coding). This implies that the increase in inequality has resulted in lower prices on average than would have prevailed under uniform income growth, but the impact is modest in magnitude compared to the overall change in prices. The contribution of uneven income growth on house prices has been positive only within the top decile, with magnitudes of up to 12%. We also compare our results to those that one would obtain using a two-sided model or a much simpler model without indivisibilities. In the next section we discuss related literature. In Section 3 we present the model and our theoretical results. In Section 4 we show how the model can be used for inference and counterfactuals. The empirical application is presented in Section 5, and Section 6 concludes.
نتیجه گیری انگلیسی
We have presented a new framework for studying the relationship between the income distribution and the housing price distribution. In the model houses are heterogeneous and indivisible. The key element is that all houses are owned by the households, and, due to concave utility, their reservation prices as sellers depend on the opportunities available to them as buyers, which in turn depend on their incomes and on the prices of other houses. Thus, our model provides a framework for analyzing how income differences get capitalized into house prices. The equilibrium is tractable under the assumption that households prefer to live in their current house. The equilibrium can be understood intuitively by considering the price gradient, which is, loosely, the price difference between “neighboring” houses in the quality distribution. The price gradient expresses how much households that inhabit a particular part of the quality distribution in equilibrium are willing to pay for the quality difference over next best house. This depends on their marginal rate of substitution between house quality and other goods, which in general depends on their level of wealth. The price level at any quantile in the distribution is the sum over all price gradients below. The natural comparative static in our setup is order-preserving changes in income distribution, as these have an impact on prices without generating trading. The model yields a number of theoretical implications about the relation of income and house price distributions. (Thus it also yields results about the relation of the progressivity of income taxation and house price distribution). Any increase in income levels will increase both the level and dispersion of house prices. An increase in income inequality will decrease house prices except (possibly) in a segment adjacent to the top. House prices at the top can go either way in response to an increase in income inequality, depending on the details of both supply and demand sides of the market. As an illustration of the model, we obtained a theory-driven estimate for the impact of recent increases in income inequality on house prices in the US. The equilibrium conditions of the model allow us to estimate the housing quality distribution without imposing restrictions on the shapes of the distributions. Specifically, we asked how the 2007 price distribution would differ from the actual price distribution if income of every household would have grown at the actual mean rate since 1998. We found that the impact of increased inequality on prices has been modest but negative on average, and positive only at the top decile. This is because the cumulative impact of reductions in the price gradient at the bottom households, whose income growth did not keep up with the mean growth, dominates the positive effects almost all the way to the top of the distribution. Our model opens the possibility for other applications. Most directly, it is a natural framework for studying how various housing and income subsidy schemes impact housing prices. The intuition of the price gradient makes it clear why housing subsidies targeted for the poor will not merely be capitalized into prices of low-quality housing but will spill upwards in the quality ladder. A serious empirical analysis of this issue will require the inclusion of non-owner-occupied housing. Other important and challenging directions include migration (choice between cities) and preference heterogeneity. Both one-sided and two-sided matching, when assumed in “pure form” are abstractions and extreme ends of a spectrum of possible assumptions about the population of households in the local market. In a one-sided setup the local market is a closed economy, while in a two-sided setup all sellers are locals who move out of the economy, and all buyers are outsiders who move in. A model of a local housing market that would combines both type of trades—households who both buy and sell within the local market, and households that in and out for exogenous reasons (such as preference shocks), would of course be more realistic and more complicated. The counterfactuals presented in this paper took the form of order-preserving changes in the exogenous income distribution. This was crucial for being able to apply the formulae derived under the assumption of no-trade equilibrium. The lack of trading also meant that price changes do not have welfare effects–they are merely changes in paper wealth. In order to have welfare effects, price changes have to generate trading. One interesting and challenging topic for further study is the welfare effects of regulations, for instance transaction taxes, which can be expected to distort the matching of houses and households. A particularly policy-relevant issue is the impact of repealing rent control, which would result in a simultaneous supply and demand shock. Again, the impact on the entire distribution of housing prices is likely to be nontrivial. Our characterization of the (no-trade) equilibrium should be helpful even in applications that involve trading, although these will require more involved numerical methods