Consistent Model Specification Test Research Articles

(Under)Mining local residential property values: A semiparametric spatial quantile autoregression

SummaryRock mining operations, including limestone and gravel production, have considerable adverse effects on residential quality of life due to elevated noise and dust levels resulting from dynamite blasting and increased truck traffic. This paper provides the first estimates of the effects of rock mining—an environmental disamenity—on local residential property values. We focus on the relationship between a house's price and its distance from a nearby rock mine. Our analysis studies Delaware County, Ohio, which, given its unique features, provides a natural environment for the valuation of property‐value‐suppressing effects of rock mines on nearby houses. We improve upon the conventional approach to evaluating adverse effects of environmental disamenities based on hedonic house price functions. Specifically, in the pursuit of robust estimates, we develop a novel (semiparametric) partially linear spatial quantile autoregressive model which accommodates unspecified nonlinearities, distributional heterogeneity, as well as spatial dependence in the data. We derive the consistency and normality limit results for our estimator as well as propose a consistent model specification test. We find statistically and economically significant property‐value‐suppressing effects of being located near an operational rock mine which gradually decline to insignificant near‐zero values at roughly a 10‐mile distance. Our estimates suggest that, all else equal, a house located a mile closer to a rock mine is priced, on average, at about 2.3–5.1% discount, with more expensive properties being subject to larger markdowns.

A martingale-difference-divergence-based test for specification

In this paper we propose a novel consistent model specification test based on the martingale difference divergence (MDD) of the error term given the covariates. The MDD equals zero if and only if error term is conditionally mean independent of the covariates. Our MDD test does not require any nonparametric estimation under the alternative and it is applicable even if we have many covariates in the regression model. We establish the asymptotic distributions of our test statistic under the null and a sequence of Pitman local alternatives converging to the null at the usual parametric rate. Simulations suggest that our MDD test has superb performance in terms of both size and power and it generally dominates several competitors. In particular, it is the only test that has well controlled size in the presence of many covariates and reasonable power against high frequency alternatives as well.

The Value-Undermining Effects of Rock Mining on Nearby Residential Property: A Semiparametric Spatial Quantile Autoregression

Rock mining operations, including limestone and gravel production, have considerable adverse effects on residential quality of life due to elevated noise and dust levels resulting from dynamite blasting and increased truck traffic. This paper provides the first estimates of the effects of rock mining — an environmental disamenity — on local residential property values. We focus on the relationship between a house’s price and its distance from nearby rock mine. Our analysis studies Delaware County, Ohio which, given its unique features, provides a natural environment for the valuation of property-value-suppressing effects of rock mines on nearby houses. We improve upon the conventional approach to valuating adverse effects of environmental disamenities based on hedonic house price functions. Specifically, in a pursuit of robust estimates, we develop a novel (semiparametric) partially linear spatial quantile autoregressive model which accommodates unspecified nonlinearities, distributional heterogeneity as well as spatial dependence in the data. We derive the consistency and normality limit results for our estimator as well as propose a consistent model specification test. We find statistically and economically significant propertyvalue-suppressing effects of being located near an operational rock mine which gradually decline to insignificant near-zero values at a roughly ten-mile distance. Our estimates suggest that, all else equal, a house located a mile closer to a rock mine is priced, on average, at about 2.3–5.1% discount, with more expensive properties being subject to larger markdowns.

Consistent model specification tests based on [formula omitted]-nearest-neighbor estimation method

We propose a simple consistent test for a parametric regression functional form based on k-nearest-neighbor (k-nn) method. We derive the null distribution of the test statistic and show that the test achieves the minimax rate optimality against smooth alternatives. A wild bootstrap method is used to better approximate the null distribution of the test statistic. We also propose a k-nn statistic which tests for omitted variables nonparametrically. Simulations and an empirical application using US economics new Ph.D. job market matching data show that the k-nn method is more appropriate than the kernel method to analyze unevenly distributed data.

Using the dependent wild bootstrap for the nonparametric goodness-of-fit test for density functions

In this paper, we consider the well-known nonparametric consistent model-specification test for the stationary density function (see [Aït-Sahalia Y. Testing continuous-time models of the spot interest rate. Rev Financ Stud. 1996;9:385–426; Li Q. Nonparametric testing of closeness between two unknown distribution functions. Econ Rev. 1996;15:261–274; Fan Y, Ullah A. On goodness-of-fit tests for weakly dependent processes using kernel method. J Nonparametric Stat. 2000;11:337–360]) and reinvestigate it carefully using asymptotics and simulation. Our work reveals that the test is subject to power and size distortions, which are mainly caused by dependence or convergence rate changes under the null and alternative hypothesis. A dependent wild bootstrap is newly suggested as a feasible remedy to such distortions. Our result provides a complete explanation as well as a solution to the problem that experienced by Aït-Sahalia [Testing continuous-time models of the spot interest rate. Rev Financ Stud. 1996;9:385–426], that is, that the test rejects true models too often when independent and identically distributed asymptotic critical values are used.

Can we reject linearity in an HAR-RV model for the S&P 500? Insights from a nonparametric HAR-RV

This article tests the linearity assumption underlying the popular heterogeneous autoregressive model for realized volatility (HAR-RV). We implement a consistent model specification test that is robust to both distributional and model misspecification. We find that, using a nonparametric HAR-RV (NPHAR-RV), we are unable to reject the null of linearity.

Validation tests for semi-parametric models

Tests are proposed for validation of the hypothesis that a partial linear regression model adequately describes the structure of a given data set. The test statistics are formulated following the approach of Fourier-type conditional expectations first suggested by Bierens [Consistent model specification tests. J Econometr. 1982;20:105–134]. The proposed procedures are computationally convenient, and under fairly mild conditions lead to consistent tests. Corresponding bootstrap versions are compared with alternative procedures for a wide selection of different estimators of the underlying partial linear model.

A consistent model specification test for a partial linear model with covariates missing at random

In this paper, we discuss the model checking problem for a partial linear model when some covariates are missing at random. A weighted model-adjustment method is applied to estimate the regression coefficients and the nonparametric function for the null hypothetical partial linear model. A testing procedure based on a residual-marked empirical process is developed to check the adequacy of the partial linear model. It is shown that the proposed test is consistent and can detect the local alternatives converging to the null hypothetical model at the rate n −1/2. Since the asymptotic null distribution of the testing statistics is case-dependent, an adjusted wild bootstrap method is used to decide the critical value, which is proved to be consistent. A simulation study and a real data analysis are conducted to show that the proposed procedure works well.

Consistent and Non-Degenerate Model Specification Tests against Smooth Transition and Neural Network Alternatives

Nous developpons un test de specification pour un modele de regression qui dirige une puissance maximale vers des formes fonctionnelles a transition douce et qui est convergent contre toute deviation par rapport a l'hypothese nulle. Nous precisions egalement la degeneration asymptotique des tests parametriques convergents de formes fonctionnelles: un test d'un processus autoregressif lineaire contre une alternative STAR n'est jamais degenere. De plus, un test d'une fonction exponentielle STAR possede une puissance entierement associee au choix du seuil. Dans une simulation ou tous les parametres sont choisis aleatoirement, le test propose possede une puissance presque identique a celle d'un test le plus puissant pour de vrais processus de type STAR, reseaux de neurones et SETAR, et domine tous les tests usuels. Nous appliquons ce test a des donnees americaines de niveaude production, de monnaie, de prix et de taux d'interets.

Nonparametric Econometrics: ThenpPackage

We describe the R <b>np</b> package via a series of applications that may be of interest to applied econometricians. The np package implements a variety of nonparametric and semiparametric kernel-based estimators that are popular among econometricians. There are also procedures for nonparametric tests of significance and consistent model specification tests for parametric mean regression models and parametric quantile regression models, among others. The <b>np</b> package focuses on kernel methods appropriate for the mix of continuous, discrete, and categorical data often found in applied settings. Data-driven methods of bandwidth selection are emphasized throughout, though we caution the user that data-driven bandwidth selection methods can be computationally demanding.

A consistent model specification test with mixed discrete and continuous data

In this paper we propose a nonparametric kernel-based model specification test that can be used when the regression model contains both discrete and continuous regressors. We employ discrete variable kernel functions and we smooth both the discrete and continuous regressors using least squares cross-validation (CV) methods. The test statistic is shown to have an asymptotic normal null distribution. We also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic, the bootstrap being our preferred method for obtaining the null distribution in practice. Simulations show that the proposed test has significant power advantages over conventional kernel tests which rely upon frequency-based nonparametric estimators that require sample splitting to handle the presence of discrete regressors.

An alternative series based consistent model specification test

This paper presents a series based test for regression functional forms. Compared with the tests of Hong and White [Hong, Y.M., and White, H., 1995. Consistent Specification Testing via Nonparametric Series Regression, Econometrica, 63, 1133–1159.], our test imposes weaker conditions on the approximating base functions, avoids non-zero center terms and allows for optimal smoothing.

A Consistent Model Specification Test with Mixed Discrete and Continuous Data

In this paper we propose a nonparametric kernel-based model specification test that can be used when the regression model contains both discrete and continuous regressors. We employ discrete variable kernel functions and we smooth both the discrete and continuous regressors using least squares cross-validation methods. The test statistic is shown to have an asymptotic normal null distribution. We also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic, the bootstrap being our preferred method for obtaining the null distribution in practice. Simulations show that the proposed test has significant power advantages over conventional kernel tests which rely upon frequency-based nonparametric estimators that require sample splitting to handle the presence of discrete regressors.

Some higher-order theory for a consistent non-parametric model specification test

We provide higher-order approximations for a smoothing-based model specification test. We derive the asymptotic cumulants and give the formal Edgeworth distributional approximation valid to a third order. We also prove the validity of the expansion in a special case where the error in the Edgeworth expansion is of order n − ε 2 for some 0<ε 2< 1 3 . The proof is based on new results for degenerate weighted U-statistics. There is a trade-off between size distortion and local power, so that large bandwidths are good for power and bad for size distortion, and vice-versa. One finding of practical importance is that this trade-off is not affected by the dimensionality of the regressors. This is because there are no smoothing bias terms under the null hypothesis and one can simply take larger bandwidth when dimensions are large. We provide an application to computing size-corrected critical values whose null rejection frequency improves on the normal critical values. Our simulations confirm the efficacy of this method in moderate sized samples.

Consistent specification tests for semiparametric/nonparametric models based on series estimation methods

This paper considers the problem of consistent model specification tests using series estimation methods. The null models we consider in this paper all contain some nonparametric components. A leading case we consider is to test for an additive partially linear model. The null distribution of the test statistic is derived using a central limit theorem for Hilbert-valued random arrays. The test statistic is shown to be able to detect local alternatives that approach the null models at the order of O p ( n −1/2 ). We show that the wild bootstrap method can be used to approximate the null distribution of the test statistic. A small Monte Carlo simulation is reported to examine the finite sample performance of the proposed test. We also show that the proposed test can be easily modified to obtain series-based consistent tests for other semiparametric/nonparametric models.

A CONSISTENT MODEL SPECIFICATION TEST BASED ON THE KERNEL SUM OF SQUARES OF RESIDUALS

ABSTRACT This paper constructs a consistent model specification test based on the difference between the nonparametric kernel sum of squares of residuals and the sum of squares of residuals from a parametric null model. We establish the asymptotic normality of the proposed test statistic under the null hypothesis of correct parametric specification and show that the wild bootstrap method can be used to approximate the null distribution of the test statistic. Results from a small simulation study are reported to examine the finite sample performance of the proposed tests.

Nonparametric model check based on local polynomial fitting

In this paper we propose a consistent model specification test based on local polynomial fitting. The Monte Carlo simulations show that the new test performs favorably with the existing local constant kernel tests.

Consistent model specification tests for time series econometric models

In this paper we consider general hypothesis testing problems for nonparametric and semiparametric time-series econometric models. We apply the general methodology to construct a consistent test for omitted variables and a consistent test for a partially linear model. The proposed tests are shown to have asymptotic normal distributions under their respective null hypotheses. We also discuss the problems of testing portfolio conditional mean-variance efficiency and testing a semiparametric single index model. Monte Carlo simulations are conducted to examine the finite sample performances of the nonparametric omitted variable test and the test for a partially linear specification.

Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms

In this paper, we develop several consistent tests in the context of a nonparametric regression model. These include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function, where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative. One common feature to the construction of all these tests is the use of the Central Limit Theorem for degenerate U-statistics of order higher than two. As a result, they share the same advantages over most of the corresponding existing tests in the literature: (a) They do not depend on any ad hoc modifications such as sample splitting, random weighting, etc. (b) Under the alternative hypotheses, the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications.

The Bierens test under data dependence

This paper generalizes the consistent model specification test proposed by Bierens to the framework of time series. The main problem encountered in this generalization is the fact that time series usually are functions of an infinite number of random variables. A simulation procedure that is capable of establishing asymptotically valid critical values for such a test is described.