Maximum likelihood estimation and Lagrange multiplier tests for panel seemingly unrelated regressions with spatial lag and spatial errors: An application to hedonic housing prices in Paris

This paper proposes maximum likelihood estimators for panel seemingly unrelated regressions with both spatial lag and spatial error components. We study the general case where spatial effects are incorporated via spatial errors terms and via a spatial lag dependent variable and where the heterogeneity in the panel is incorporated via an error component specification. We generalize the approach of Wang and Kockelman (2007) and propose joint and conditional Lagrange multiplier tests for spatial autocorrelation and random effects for this spatial SUR panel model. The small sample performance of the proposed estimators and tests are examined using Monte Carlo experiments. An empirical application to hedonic housing prices in Paris illustrate these methods. The proposed specification uses a system of three SUR equations corresponding to three types of flats within 80 districts of Paris over the period 1990-2003. We test for spatial effects and heterogeneity and find reasonable estimates of the shadow prices for housing characteristics.     

The house price determination process: Rational expectations with a spatial context

Applying the rational expectations hypothesis, this essay models the current value of a house as the conditional expectation of the discounted stream of housing services accruing to the owner of the house. The value of housing services is determined by neighborhood effects as well as the physical attributes of the property itself. In the existing hedonic literature, future transactions have not been utilized to describe neighborhood effects. The rational expectations asset pricing model in this study accounts for expected future neighborhood effects as well as observed current neighborhood effects. The reduced form of the rational expectations model is a spatial autoregressive (SAR) model with two spatial lags. After employing the generalized method of moments (GMM) in estimating the spatial asset pricing model, I find that both expected future transactions and prior transactions in the neighborhood are significant. The inclusion of expected future transaction prices in the neighborhood takes into account the influence of expected changes in the community and factors these potential changes into the current house price. This is consistent with forward-looking households. The forward-looking model generates superior out-of-sample prediction performance relative to both the conventional hedonic model without considering neighborhood effects or the standard spatial hedonic model including only past transactions.     

Hedonic prices, price indices and housing markets

This paper extends hedonic price analysis to the formation of housing price indices measuring variation within a metropolitan area. In forming these indices fifteen submarkets, heterogeneous across time and space, are described within a short-run equilibrium model. Linear functional forms are generally rejected using a method proposed by Box and Cox. Aggregation of hedonic price coefficients into standardized units yields significantly higher housing prices in the central city than in its suburbs, as well as differential effects of structural and neighborhood improvements among submarkets.     

Measuring the diffusion of housing prices across space and over time: Replication and further evidence

Brady (Journal of Applied Econometrics, 2011, 26(2), 213–231) studies how fast and how long a change in housing prices in one region affects its neighbors by estimating the impulse response functions using a spatial autoregressive model (SAR). This paper replicates Brady's empirical results, but reports different SAR test statistics. Additional robustness checks are conducted by analyzing three different housing price indexes covering a more extensive period. Analysis shows that the model specifications and model estimates vary with the housing price indexes.     

Raising the bar (6)

Raising the bar (6). Spatial Economic Analysis. This editorial summarizes and comments on the papers published in issue 12(4) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper addresses the question of whether ‘jobs follow people’ or ‘people follow jobs’. The second paper develops a new methodology to determine functional regions. The third paper is a major contribution to the growing literature on new modelling approaches and applications of disaster impact models. The fourth paper focuses on the costs and benefits of higher education. The fifth paper develops a two-step procedure to identify endogenously spatial regimes in the first step using geographically weighted regression, and to account for spatial dependence in the second step. Finally, the sixth paper estimates a dynamic spatial panel data model to explain house prices and to show that restricted housing supply in the city of Cambridge, UK, has some undesirable labour market effects.     

FURTHER EVIDENCE ON THE SPATIO‐TEMPORAL MODEL OF HOUSE PRICES IN THE UNITED STATES

Holly, Pesaran, and Yamagata (Journal of Econometrics 2010; 158 : 160–173) use a panel of 49 states over the period 1975–2003 to show that state‐level real housing prices are driven by economic fundamentals, such as real per capita disposable income, as well as by common shocks, such as changes in interest rates, oil prices and technological change. They apply the common correlated effects estimator of Pesaran (Econometrica 2006; 74 (4): 967–101), which takes into account spatial interactions that reflect both geographical proximity and unobserved common factors. This paper replicates their results using a panel of 381 metropolitan statistical areas observed over the period 1975–2011. Our replication shows that their results are fairly robust to the more geographically refined cross‐section units, and to the updated period of study. Copyright © 2013 John Wiley & Sons, Ltd.     

A two-step approach to account for unobserved spatial heterogeneity

A two-step approach to account for unobserved spatial heterogeneity. Spatial Economic Analysis. Empirical analysis in economics often faces the difficulty that the data are correlated and heterogeneous in some unknown form. Spatial econometric models have been widely used to account for dependence structures, but the problem of directly dealing with unobserved spatial heterogeneity has been largely unexplored. The problem can be serious particularly if we have no prior information justified by economic theory. In this paper we propose a two-step procedure to identify endogenously spatial regimes in the first step and to account for spatial dependence in the second step. This procedure is applied to hedonic house price analysis.     

Normalized CES supply systems: Replication of Klump,McAdam, and Willman (2007)

The analysis of Klump, McAdam, and Willman (Review of Economics and Statistics, 2007, 89, 183–192) is replicated using alternative software. Their results are verified substantively and, in large measure, numerically. Contributions include a more explicit consideration of the nested testing structure than has appeared previously, and the appropriate means of imposing and testing the special case of logarithmic growth in technology. Also, plots of the likelihood serve to emphasize that maxima in the neighborhood of a unitary elasticity of substitution are often a spurious artifact of the singularity of the model at this point, of which empirical researchers should beware.     

Estimating the Demand for Housing, Land, and Neighbourhood Characteristics

This paper provides estimates of the structure of demand for individual housing and neighbourhood characteristics and for land in two British cities. We estimate a hedonic price function, and from this obtain the implicit prices of house attributes. These prices are used to estimate a demand system for each city. These perform well, and enable us to calculate price and income elasticities for each of the non-dichotomous characteristics and for land. To counteract criticisms of demand estimates derived within the hedonic framework a method is developed for selecting an appropriate set of instrumental variables. Estimates derived from this method, however, differ only slightly from those obtained using the conventional techniques. Several features of these estimates provide insights into the unusual characteristics of the British housing market, the effects of constraints imposed by land use planning, and the effects of changing income distribution on the structure of demand.     

Simultaneity in the market for housing characteristics

The nature of simultaneity in the markets for housing characteristics is examined. Simultaneity is found to arise in the implicit markets for individual characteristics because of the presence of nonlinearity in the market (hedonic) price function for housing. However, this simultaneity is not the kind discussed by S. Rosen [J. Political Econ. 82, 34–55 (1974)] between firm supplies and household demands. As a result, the Rosen suggestion of identifying demand with firm supply shifters is inappropriate. Among the alternative approaches to identification, the most desirable involve use of data over two or more markets in which residence for a given household is exogenous to the choice of housing.     

Hedonic versus repeat-sales housing price indexes for measuring the recent boom-bust cycle

Standard housing price indexes rely on strong constant-quality assumptions and often conflict. Hedonic price indexes overcome limitations of median price and repeat-sales indexes but their implementation has been limited by a lack of data. This paper constructs hedonic indexes at the zip code level for the Los Angeles and San Diego metropolitan areas using considerably more detailed data than previously available. Our sample was collected by a mortgage technology firm, and consists of almost 1.1 million transactions during the boom-bust cycle since 2000. Our hedonic regressions include new spatial models that capture correlations within submarkets (using zip codes as proxies) and allow temporal asymmetry. Compared to a repeat-sales price index constructed from the same data, the hedonic indexes indicate that the market peaked about 11 months later in Los Angeles and about 2 months earlier in San Diego, show less pre-peak appreciation and post-peak depreciation in low-tier housing and more pre-peak appreciation in high-tier housing. We also find that the intensity of the cycle varies greatly across zip codes and price-tiers in a pattern consistent with foreclosure activity.     

Crime and Racial Composition in Contiguous Communities as Negative Externalities: Prejudiced Household's Evaluation of Crime Rate and Segregation Nearby Reduces Housing Values and Tax Revenues

Abstract . How the level of amenities in surrounding communities affects the residential location decisions of households is considered. The amenities specifically taken into account are the crime and racial composition of the household's community and the contiguous communities. The theory of the household's valuation of neighborhood amenities through a housing value equation is expanded to include how the household's valuation of amenities is affected by the amenities in surrounding areas. An empirical model using data for 71 suburban communities in the Chicago Standard Metropolitan Statistical Area is specified to measure the simultaneous interaction between housing values, crime, and police effort. A revenue equation is included to determine how the household's valuation of crime and racial composition could affect the community's revenue-raising ability. The empirical results indicate that the crime and racial composition of surrounding communities as well as within the household's community have a statistically significant negative effect on housing values. While the magnitude of the effect is small, the empirical results suggest that households consider the crime rate and racial composition of surrounding communities as negative externalities.     

Estimating class‐specific parametric models under class uncertainty: local polynomial regression clustering in an hedonic analysis of wine markets

We introduce a method for estimating multiple class regression models when class membership is uncertain. The procedure—local polynomial regression clustering—first estimates a nonparametric model via local polynomial regression, and then identifies the underlying classes by aggregating sample observations into data clusters with similar estimates of the (local) functional relationships between dependent and independent variables. Finally, parametric functions specific to each class are estimated. The technique is applied to the estimation of a multiple‐class hedonic model for wine, resulting in the identification of four distinct wine classes based on differences in implicit prices of the attributes. Copyright © 2009 John Wiley & Sons, Ltd.     

Divergence in alternative Hicksian welfare measures: the case of revealed preference for public amenities

This paper investigates the divergence between the two Hicksian welfare measures of non‐traded amenity improvement associated with housing. First, the Hicksian surplus measures for amenity changes are analytically developed based on explicit specification of utility structures. A hedonic two‐stage approach is then applied to empirically show that, for quantity changes, in contrast to hypothetical markets, divergence in real market is small. The paper also analytically develops expressions for the income and substitution effects and empirically shows that for a given income effect, the greater the substitution effect the smaller the divergence between the two measures. Copyright © 2002 John Wiley & Sons, Ltd.     

Revealed preference for relative status: Evidence from the housing market

This paper investigates the value individuals place on their relative housing consumption as compared to absolute housing consumption. Using observed housing sales from three Ohio MSAs in 2000, a spatial Durbin hedonic price model provides total marginal willingness-to-pay estimates for both characteristics of housing units and those of its neighbors. Using this revealed-preference approach, we find evidence suggesting individuals do value relative house size, but the absolute effect dominates. For instance, the estimates indicate that if all homes in Columbus were to increase in size by 100 square feet, the net effect of impacts on absolute and relative consumption would be to increase house prices by $605 on average. This stands in contrast to the stated preference literature, which frequently find individuals to be willing to forgo absolute well-being in exchange for relative status gains.     

Raising the bar (7)

This editorial summarises the papers published in issue 13.1 so as to raise the bar in applied spatial economic research and highlight new trends. The first paper adopts a scale neutral approach to investigate the spatial mechanisms that cause regional innovation and growth. The second paper claims that population-weighting when calculating indices of regional inequality might lead to inconsistent outcomes. The third paper estimates the effect of distance between family residence and higher education institution on a student's academic performance, thereby accounting for endogenous regressors. The fourth paper shows an inverted U-shaped relationship between economic development at region of origin and the propensity to migrate using a multilevel approach. The fifth paper provides spatial econometric evidence of price competition between sellers of used books on Amazon.com. The last paper estimates a hedonic housing price equation and parameterizes the spatial weight matrix to determine how far back in time buyers, sellers and realtors are looking at the housing market.     

Tuning parameter selection in penalized generalized linear models for discrete data

In recent years, we have seen an increased interest in the penalized likelihood methodology, which can be efficiently used for shrinkage and selection purposes. This strategy can also result in unbiased, sparse, and continuous estimators. However, the performance of the penalized likelihood approach depends on the proper choice of the regularization parameter. Therefore, it is important to select it appropriately. To this end, the generalized cross‐validation method is commonly used. In this article, we firstly propose new estimates of the norm of the error in the generalized linear models framework, through the use of Kantorovich inequalities. Then these estimates are used in order to derive a tuning parameter selector in penalized generalized linear models. The proposed method does not depend on resampling as the standard methods and therefore results in a considerable gain in computational time while producing improved results. A thorough simulation study is conducted to support theoretical findings; and a comparison of the penalized methods with the L₁, the hard thresholding, and the smoothly clipped absolute deviation penalty functions is performed, for the cases of penalized Logistic regression and penalized Poisson regression. A real data example is being analyzed, and a discussion follows. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.     

Estimating dynamic equilibrium economies: linear versus nonlinear likelihood

This paper compares two methods for undertaking likelihood‐based inference in dynamic equilibrium economies: a sequential Monte Carlo filter and the Kalman filter. The sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. We report two main results. First, both for simulated and for real data, the sequential Monte Carlo filter delivers a substantially better fit of the model to the data as measured by the marginal likelihood. This is true even for a nearly linear case. Second, the differences in terms of point estimates, although relatively small in absolute values, have important effects on the moments of the model. We conclude that the nonlinear filter is a superior procedure for taking models to the data. Copyright © 2005 John Wiley & Sons, Ltd.     

The choice of functional forms for hedonic price equations: Comment

Rosen [13], Freeman [4], Halvorsen and Pollakowski [6], and others have stressed that economic theory does not suggest an appropriate functional form for hedonic price functions.¹ It consequently is reasonable to try several functional forms and utilize the multiple regression equation with the best performance. In this spirit, Halvorsen and Pollakowski [6] recommend using the Box-Cox flexible functional form for hedonic analysis and measuring best performance with a goodness of fit test. The Box-Cox methodology has also been adapted in hedonic studies by Goodman [5], Linneman [10], Blomquist and Worley [1], and Eberts and Gronberg [3].² The Box-Cox is particularly suited for testing functional forms because many familiar forms such as semilog, log linear, and translog are subsets of the flexible Box-Cox permitting nested hypothesis testing.In this note, we illustrate that the formal hypothesis testing advantage of the Box-Cox functional form is purchased at the expense of other important goals. The goal of most hedonic studies is to estimate the prices of the characteristics, to measure the response to changes in the prices, and/or to predict future expenditures. Using a best fit criterion to choose functional forms does not necessarily lead to more accurate estimates of characteristic prices. In fact, the large number of coefficients estimated with the Box-Cox functional form reduces the accuracy of any single coefficient which could lead to poorer estimates of specific prices. Second, because any negative number raised to a noninteger real power is imaginary, the traditional Box-Cox functional form is not suited to any data set containing negative numbers. Third, the Box-Cox functional form may be inappropriate for prediction. Since the mean predicted value of the untransformed dependent variable need not equal the mean of the sample upon which it is estimated, the predicted untransformed variable (housing value) will be biased. The predicted untransformed dependent variable may also be imaginary. Fourth, the nonlinear transformation results in complex estimates of slopes and elasticities which are often too cumbersome to use properly. We discuss each of these drawbacks and quantify them when possible in the remainder of this note.     

Estimating a Parsimonious Model of Inequality Aversion in Stackelberg Duopoly Experiments*

In the Stackelberg duopoly experiments in Huck et al. (2001) , nearly half of the followers’ behaviours are inconsistent with conventional prediction. We use a test in which the conventional self‐interested model is nested as a special case of an inequality aversion model. Maximum likelihood methods applied to the Huck et al. (2001) data set reject the self‐interested model. We find that almost 40% of the players have disadvantageous inequality aversion that is statistically different from zero and economically significant, but advantageous inequality aversion is relatively unimportant. These estimates provide support for a more parsimonious model with no advantageous inequality aversion.