Semiparametric estimation of a hedonic price function

Previous work on the preferred specification of hedonic price models usually recommended a Box-Cox model. In this paper we note that any parametric model involves implicit restrictions and they can be reduced by using a semiparametric model. We estimate a benchmark parametric model which passes several common specification tests, before showing that a semiparametric model outperforms it significantly. In addition to estimating the model, we compare the predictions of the models by deriving the distribution of the predicted log(price) and then calculating the associated prediction intervals. Our data show that the semiparametric model provides more accurate mean predictions than the benchmark parametric model.     

On nonparametric estimation of a hedonic price function

Recently, using mixed data on Canadian housing, Parmeter, Henderson, and Kumbhakar (Journal of Applied Econometrics 2007; 22 : 695–699) found that a nonparametric approach for estimating a hedonic house price function is superior to formerly suggested parametric and semiparametric specifications. We carefully reanalyze these specifications for this dataset by applying a recent nonparametric specification test and simulation‐based prediction comparisons. For the case at issue our results suggest that a previously proposed parametric specification does not have to be rejected and we illustrate how nonparametric methods provide valuable insights during all modeling steps. Copyright © 2010 John Wiley & Sons, Ltd.     

Nonparametric state price density estimation using constrained least squares and the bootstrap

The economic theory of option pricing imposes constraints on the structure of call functions and state price densities. Except in a few polar cases, it does not prescribe functional forms. This paper proposes a nonparametric estimator of option pricing models which incorporates various restrictions (such as monotonicity and convexity) within a single least squares procedure. The bootstrap is used to produce confidence intervals for the call function and its first two derivatives and to calibrate a residual regression test of shape constraints. We apply the techniques to option pricing data on the DAX.     

Nonparametric estimation of a discontinuity in regression

We propose and study a new method to nonparametrically estimate a discontinuity of a regression function. The optimal rate of convergence n ⁻¹ is obtained under minimal assumptions. No smoothing is required.     

Choice of functional form for hedonic price equations

The appropriate functional form for a hedonic price equation cannot in general be specified on theoretical grounds. In this paper, a statistical procedure for the choice of functional form is proposed. A highly general functional form is specified that yields all other functional forms of interest as special cases. Likelihood ratio tests are used to test the appropriateness of alternative forms. The procedure is illustrated using cross section microdata for housing. For the case considered, the functional forms most commonly used in previous studies are strongly rejected.     

Convenient links for the estimation of hedonic price indexes: the case of unique,infrequently traded assets

Hedonic methods are a prominent approach in the construction of quality‐adjusted price indexes. This paper shows that the process of computing such indexes is substantially simplified if arithmetic (geometric) price indexes are computed based on exponential (log‐linear) hedonic functions estimated by the Poisson pseudo‐maximum likelihood (ordinary least squares) method. A Monte Carlo simulation study based on housing data illustrates the convenience of the links identified and the very attractive properties of the Poisson estimator in the hedonic framework.     

Nonparametric estimation of distribution functions

Summary Using Silverman and Young’s (1987) idea of rescaling a rescaled smoothed empirical distribution function is defined and investigated when the smoothing parameter depends on the data. The rescaled smoothed estimator is shown to be often better than the commonly used ordinary smoothed estimator.     

Some empirical results on the nature of the hedonic price function for the urban housing market

An attempt is made to develop a systematic statistical methodology for the analysis of the urban housing market The standard estimation procedures used for fitting hedonic price functions for the urban housing market are reviewed, and several potentially serious sources of bias are noted. An alternative estimator which capitalizes property values into flows and also searches for the appropriate functional form which avoids these biases is developed. The capitalization rate for owner-occupied housing in 1973 is found to be about 0.03. The magnitudes and seriousness of several of the estimation biases are examined within the context of inappropriate policy decisions which can result from the use of the standard estimators. The importance of neighborhood site characteristics in the determination of local site valuations is also examined and it is found that they explain between 15 and 50% of the standardized variation in site valuations. Further, it is found that these traits are capable of inducing valuation differentials as large as 100% between structurally identical sites.     

Nonparametric regression function estimation using interaction least squares splines and comlexity regularization

Let (X, Y) be a pair of random variables withsupp(X)⊆[0,1] ^l andEY ²<∞. Letm ^* be the best approximation of the regression function of (X, Y) by sums of functions of at mostd variables (1≤d≤l). Estimation ofm ^* from i.i.d. data is considered. For the estimation interaction least squares splines, which are defined as sums of polynomial tensor product splines of at mostd variables, are used. The knot sequences of the tensor product splines are chosen equidistant. Complexity regularization is used to choose the number of the knots and the degree of the splines automatically using only the given data. Without any additional condition on the distribution of (X, Y) the weak and strongL ₂-consistency of the estimate is shown. Furthermore, for everyp≥1 and every distribution of (X, Y) withsupp(X)⊆[0,1] ^l ,y bounded andm ^* p-smooth, the integrated squared error of the estimate achieves up to a logarithmic factor the (optimal) rate      

Nonparametric function estimation subject to monotonicity, convexity and other shape constraints

This paper uses free-knot and fixed-knot regression splines in a Bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log-concave likelihood functions. The shape constraints we consider include monotonicity, convexity and functions with a single minimum. A computationally efficient MCMC sampling algorithm is developed that converges faster than previous methods for non-Gaussian models. Simulation results indicate the monotonically constrained function estimates have good small sample properties relative to (i) unconstrained function estimates, and (ii) function estimates obtained from other constrained estimation methods when such methods exist. Also, asymptotic results show the methodology provides consistent estimates for a large class of smooth functions. Two detailed illustrations exemplify the ideas.     

Managing hedonic housing price indexes: The French experience

Despite their theoretical advantages, hedonic housing price indexes are not so commonly computed by statistical agencies or real estate professionals. Many published indexes still rely on mean or median prices, or favor repeat-sales methods, which require less information about the attributes of the housing units and less econometric expertise on the part of the index compilers, but may be less accurate and robust. In France as in other countries where housing sales have to be recorded in front of a notary, data on transaction prices and characteristics of dwellings are available. Such data have been centralized since 1994, and quarterly hedonic housing price indexes have been computed for more than 10 years. This paper describes the institutional setting of housing transactions in France, and the collaboration between the notaries and the national statistical agency (INSEE). The former are responsible for data collection and regular computation, whereas the latter takes scientific responsibility for the method. The detailed information on the individual properties transacted remains proprietary data, but disaggregated indexes are publicly and freely available. This organization and assignment of roles has proven effective and might be extended to countries with similar institutional settings.     

A mixed index approach to identifying hedonic price models

Recent literature suggests identifying house price hedonic regressions by using instrumental variables, spatial statistics, the borders approach, panel data, and other techniques. We present an empirical application of a mixed index model, first proposed by Bowden [Bowden, R.J., 1992. Competitive selection and market data: the mixed-index problem. The Review of Economic Studies 59(3):625–633.] to identify hedonic price regressions. We compare the performance of the mixed index model to a traditional hedonic model and to a hedonic model that includes characteristics of the buyer of each house. We find the mixed index model outperforms the other models based on bootstrap distributions of predicted housing values, prediction variance, and predicted policy effects. The mixed index model distributions are less skewed and kurtotic than the other models, suggesting it more closely satisfies the classical linear regression assumption of normally distributed errors. Compared to the mixed index model, the traditional hedonic overstates the importance of lot size and school quality to house price and understates the importance of environmental quality.     

Identification and stochastic specification in Rosen's hedonic price model

The use of an explicitly specified utility function to derive the inverse demand functions in S. Rosen's hedonic price model provides considerable insight into the correct stochastic specification of the model. It turns out that except in special cases, the inverse demand equations are nonlinear in parameters and cannot be formulated conveniently as regression models. Moreover, the inverse demand functions and the hedonic price function must be estimated simultaneously to obtain consistent estimates of the parameters of these functions. A tractable estimation technique is described. It is desirable to derive the inverse demand functions from a utility specification that is not a strongly separable function of houses' attributes since strong separability implies the existence of deterministic relations among incomes, prices, and observed housing attributes that may fail to hold in applications. Finally, it is shown that the use of an explicitly specified utility function does not guarantee identification of the parameters of Rosen's model.     

Nonparametric estimation of distributional policy effects

This paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest. In contrast to other methods, we do not restrict attention to the effect on the mean. In particular, our method can be used to conduct inference on the change of the distribution function as a whole, its moments and quantiles, inequality measures such as the Lorenz curve or Gini coefficient, and to test for stochastic dominance. The practical applicability of our procedure is illustrated via a simulation study and an empirical example.     

Nonparametric covariance estimation in multivariate distributions

The estimation problem of the unknown covariance matrix of a multivariate distribution with the known mean is studied under a matrix-valued quadratic loss function. The conditions on the sample sizes for the best unbiased estimator to have a smaller risk than the sample covariance matrix is established. The former estimator is completely (without exceptional sets of Lebesgue measure zero) characterized by its expectation in the class of all multivariate distributions with zero mean and finite fourth moments. Received: November 1998     

Nonparametric curve estimation with bernstein estimates

In this paper we propose a Bernstein type estimate of the regression functionm(x)=E[Y|X=x]. Various local and global asymptotic properties of this estimate are studied.     

Nonparametric density estimation with grouped observations

A smooth and detailed distribution is fitted to coarsely grouped frequency data by a nonparametric approach, based on penalized maximum likelihood. The estimated distribution conserves mean and variance of the data. The numerical solution is described and a compact and simplified algorithm is given. The procedure is applied to two empirical datasets.     

Nonparametric estimation of the determinants of inefficiency

We consider the benchmark stochastic frontier model where inefficiency is directly influenced by observable determinants. In this setting, we estimate the stochastic frontier and the conditional mean of inefficiency without imposing any distributional assumptions. To do so we cast this model in the partly linear regression framework for the conditional mean. We provide a test of correct parametric specification of the scaling function. An empirical example is also provided to illustrate the practical value of the methods described here.