Nonparametric Specification Test Research Articles

SPECIFICATION TESTS FOR TIME-VARYING COEFFICIENT PANEL DATA MODELS

This paper provides nonparametric specification tests for the commonly used homogeneous and stable coefficients structures in panel data models. We first obtain the augmented residuals by estimating the model under the null hypothesis and then run auxiliary time series regressions of augmented residuals on covariates with time-varying coefficients (TVCs) via sieve methods. The test statistic is then constructed by averaging the squared fitted values, which are close to zero under the null and deviate from zero under the alternatives. We show that the test statistic, after being appropriately standardized, is asymptotically normal under the null and under a sequence of Pitman local alternatives. A bootstrap procedure is proposed to improve the finite sample performance of our test. In addition, we extend the procedure to test other structures, such as the homogeneity of TVCs or the stability of heterogeneous coefficients. The joint test is extended to panel models with two-way fixed effects. Monte Carlo simulations indicate that our tests perform reasonably well in finite samples. We apply the tests to re-examine the environmental Kuznets curve in the United States, and find that the model with homogenous TVCs is more appropriate for this application.

Two-step series estimation and specification testing of (partially) linear models with generated regressors

This paper studies three semiparametric models that are useful and frequently encountered in applied econometric work—a linear and two partially linear specifications with generated regressors, i.e., the regressors that are unobserved, but can be nonparametrically estimated from the data. Our framework allows for generated regressors to appear in linear or nonlinear components of partially linear models. We propose two-step series estimators for the finite-dimensional parameters, establish their -consistency (with sample size n) and asymptotic normality, and provide the asymptotic variance formulae that take into account the estimation error of generated regressors. Moreover, we develop a nonparametric specification test for the models considered. Numerical performances of the proposed estimators and test via simulation experiments and an empirical application illustrate the utility of our approach.

Partially linear functional-coefficient dynamic panel data models: sieve estimation and specification testing

We study the nonparametric estimation and specification testing for partially linear functional-coefficient dynamic panel data models, where the effects of some covariates on the dependent variable vary nonparametrically according to a set of low-dimensional variables. Based on the sieve approximation of unknown slope functions, we propose a sieve 2SLS procedure to estimate the model. The asymptotic properties of the estimators of both parametric and nonparametric components are established when sample size N and T tend to infinity jointly. A nonparametric specification test for the constancy of slopes is also proposed. We show that after being appropriately standardized, the test is asymptotically normally distributed under the null hypothesis. The asymptotic properties of the test is also studied under a sequence of local Pitman alternatives and global alternatives. A set of Monte Carlo simulations show that our sieve 2SLS estimators and specification test perform remarkably well in finite samples. We apply our method to study the impact of income on democracy, and find strong evidence of nonlinear/nonconstant effect of income on democracy.

Nonparametric Specification Testing of Conditional Asset Pricing Models

This article presents an adaptive omnibus specification test of asset pricing models where the stochastic discount factor is conditionally affine in the pricing factors. These models provide constraints that conditional moments of returns and pricing factors must satisfy, but most of them do not provide information on the functional form of those moments. Our test is robust to functional form misspecification, and also detects any relationship between pricing errors and conditioning variables. We give special emphasis to the test implementation and calibration, and extensive simulation studies prove the functioning in practice. Our empirical applications show a conditional counterpart of a well-known problem of unconditional models. The lack of rejection of consumption based conditional models seems to be due to a poor conditional correlation between consumption and stock returns.

Choosing the Best Performing Garch Model for Sri Lanka Stock Market by Non-Parametric Specification Test

This paper examines the performance of different kind of GARCH models with Gaussian, Student-t and generalized error distribution for Colombo Stock Exchange (CSE), in Sri Lanka. Analyzing the daily closing price index of CSE from January 02, 2007 to March 10, 2013. It was found that the Asymmetric GARCH models give better result than symmetric GARCH model. According to distributional assumption these models under Student-t as well as generalized error provided better fit than normal distributional assumption. The Non-Parametric Specification test suggest that the GARCH, EGARCH, TARCH and APARCH models with Student-t distributional assumption are the most successful model for CSE.

Sieve IV estimation of cross-sectional interaction models with nonparametric endogenous effect

In this study, we consider cross-sectional interaction models including spatial autoregressive models and peer effects models as special cases. Our model allows the endogenous effect – the effect of others’ outcomes on one’s own outcome – to be nonlinear and nonparametric. For the model estimation, we propose a sieve instrumental variable estimator and establish both its consistency and asymptotic normality. Furthermore, we propose a nonparametric specification test for the linearity of the endogenous effect. Under the null hypothesis of linearity, we show that the test statistic is asymptotically distributed as normal. As an empirical illustration, we focus on the data on regional economic performance investigated by Gennaioli et al. (2013). This empirical analysis highlights the usefulness of the proposed model and method.

Uniform nonparametric inference for time series using Stata

In this article, we introduce a command, tssreg, that conducts nonparametric series estimation and uniform inference for time-series data, including the case with independent data as a special case. This command can be used to nonparametrically estimate the conditional expectation function and the uniform confidence band at a user-specified confidence level, based on an econometric theory that accommodates general time-series dependence. The uniform inference tool can also be used to perform nonparametric specification tests for conditional moment restrictions commonly seen in dynamic equilibrium models.

Uniform nonparametric inference for time series

This paper provides the first result for the uniform inference based on nonparametric series estimators in a general time-series setting. We develop a strong approximation theory for sample averages of mixingales with dimensions growing with the sample size. We use this result to justify the asymptotic validity of a uniform confidence band for series estimators and show that it can also be used to conduct nonparametric specification test for conditional moment restrictions. New results on the validity of heteroskedasticity and autocorrelation consistent (HAC) estimators with increasing dimension are established for making feasible inference. An empirical application on the unemployment volatility puzzle for the search and matching model is provided as an illustration.

Uniform Nonparametric Series Inference for Dependent Data with an Application to the Search and Matching Model

This paper concerns the uniform inference for nonparametric series estimators in time-series applications. We develop a strong approximation theory of sample averages of serially dependent random vectors with dimensions growing with the sample size. The strong approximation is first proved for heterogeneous martingale difference arrays and then extended to general mixingales via martingale approximation, readily accommodating a majority of applications in applied econometrics. We use these results to justify the asymptotic validity of a uniform confidence band for series estimators and show that it can also be used to conduct nonparametric specification test for conditional moment restrictions. The validity of high-dimensional heteroskedasticity and autocorrelation consistent (HAC) estimators is established for making feasible inference. The proposed method is broadly useful for forecast evaluation, empirical microstructure, dynamic stochastic equilibrium models and inference problems based on inter-section bounds. We demonstrate the empirical relevance of the proposed method by studying the Mortensen–Pissarides search and matching model for equilibrium unemployment, and shed new light on the unemployment volatility puzzle from an econometric perspective.

Specification testing in random coefficient models

In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients, generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, that is, whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study, and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level. Nonparametric specification testing random coefficients unobserved heterogeneity sieve estimation characteristic function consumer demand C12 C14

Consistent nonparametric specification tests for stochastic volatility models based on the return distribution

This paper develops nonparametric specification tests for stochastic volatility models by comparing the nonparametically estimated return density and distribution functions with their parametric counterparts. Asymptotic null distributions of the tests are derived and the tests are shown to be consistent. Extensive Monte Carlo experiments are performed to study the finite sample properties of the tests. The proposed tests are applied in a number of empirical examples.

Sieve instrumental variable quantile regression estimation of functional coefficient models

In this paper we consider sieve instrumental variable quantile regression (IVQR) estimation of functional coefficient models where the coefficients of endogenous regressors are unknown functions of some exogenous covariates. We estimate the functional coefficients by the sieve-IVQR technique and establish the uniform consistency and asymptotic normality of the estimators. Based on the sieve estimates, we propose a nonparametric specification test for the constancy of the functional coefficients and study its asymptotic. We conduct simulations to evaluate the finite sample behavior of our estimator and test statistic, and apply our method to study the estimation of quantile Engel curves.

Nonparametric specification tests for stochastic volatility models based on volatility density

This paper develops a specification test for stochastic volatility models by comparing the nonparametric kernel deconvolution density estimator of an integrated volatility density with its parametric counterpart. L2 distance is used to measure the discrepancy. The asymptotic null distributions of the test statistics are established and the asymptotic power functions are computed. Through Monte Carlo simulations, the size and power properties of the test statistics are studied. The tests are applied to an empirical example.

Volatility Modeling of Emerging Foreign Exchange Market: A Case of Bangladesh

This paper examined the volatility models for exchange rate return, including Random Walk model, AR model, GARCH model and extensive GARCH model, with Normal and Student-t distribution assumption as well as nonparametric specification test of these models. We fit these models to Bangladesh foreign exchange rate index from January 1999 to December 31, 2012. The return series of Bangladesh foreign exchange rate are leptokurtic, significant skewness, deviation from normality as well as the returns series are volatility clustering as well. We found that student t distribution into GARCH model improves the better performance to forecast the volatility for Bangladesh foreign exchange market. The traditional likelihood comparison showed that the importance of GARCH model in modeling of Bangladesh foreign market, but the modern nonparametric specification test found that RW, AR and the model with GARCH effect are still grossly mis-specified. All these imply that there is still a long way before we reach the adequate specification for Bangladesh exchange rate dynamics.

Volatility Modeling of Emerging Foreign Exchange Market: A Case of Bangladesh

This paper examined the volatility models for exchange rate return, including Random Walk model, AR model, GARCH model and extensive GARCH model, with Normal and Student-t distribution assumption as well as nonparametric specification test of these models. We fit these models to Bangladesh foreign exchange rate index from January 1999 to December 31, 2012. The return series of Bangladesh foreign exchange rate are leptokurtic, significant skewness, deviation from normality as well as the returns series are volatility clustering as well. We found that student t distribution into GARCH model improves the better performance to forecast the volatility for Bangladesh foreign exchange market. The traditional likelihood comparison showed that the importance of GARCH model in modeling of Bangladesh foreign market, but the modern nonparametric specification test found that RW, AR and the model with GARCH effect are still grossly mis-specified. All these imply that there is still a long way before we reach the adequate specification for Bangladesh exchange rate dynamics.

A specification test for discrete choice models

In standard discrete choice models, adding options cannot increase the choice probability of an existing alternative. We use this observation to construct a simple nonparametric specification test by exploiting variation in the choice sets individuals face. We use a multiple testing procedure to determine the particular kind of choice sets that produce violations. We apply these tests to the 1896 US House of Representatives election and reject commonly used discrete choice voting models.

Comments on: An updated review of Goodness-of-Fit tests for regression models

We discuss the following two particular aspects of the paper of Gonzalez-Manteiga and Crujeiras ( 10.1007/s11749-013-0327-5 ): First, what changes if the null hypothesis is non- or semiparametric? For example, Rodriguez-Poo et al. (A practical test for misspecification in regression: functional form, separability, and distribution. Econom. Theory, 2013, under revision) considered optimal rates of adaptive nonparametric tests when the null model is semiparametric. A second, though related question is, how serious are the bandwidth and calibration problems? Sperlich (On the choice of regularization parameters in specification testing: a critical discussion. Empir. Econ., 2013, forthcoming) has shown that the unsolved bandwidth selection problems, in particular when calibrating, render nonparametric specification tests useless in practice. Two additional questions are only raised briefly and concern (a) the computational aspects, and (b) the problem that asymptotically, nonparametric omnibus tests might reject almost any null hypothesis as probably no parametric or semiparametric model is 100 % correct. But it is maybe a reasonable and useful approximation. To this aim we recall the idea of testing the problem of so-called ‘precise hypotheses’ as outlined in Dette (Ann. Stat. 27:1012–1040, 1999) for nonparametric goodness-of-fit tests.

Nonparametric Specification Testing in Nonlinear and Nonstationary Time Series Models: Theory and Practice

In this paper, we consider some specification testing problems in nonlinear time series models with nonstationarity. We propose using a nonparametric kernel test for specifying whether the regression is of a known parametric nonlinear form. The power of the proposed nonparametric test is systematically studied and an asymptotic distribution of the test statistic is shown to depend on the asymptotic behavior of the so called distance function under a sequence of general semiparametric local alternatives. The asymptotic theory developed in this paper differs from existing work on nonparametric specification testing in the stationary time series case. In order to implement the proposed test in practice, a computer-intensive bootstrap simulation procedure is introduced and asymptotic approximations for both the size and power functions are established. Furthermore, the bandwidth involved in the test is selected by maximizing the power while the size is controlled by a significance level. Meanwhile, both simulated and real data examples are provided to illustrate the proposed theory and methodology.

SPECIFICATION TEST FOR CONDITIONAL DISTRIBUTION WITH FUNCTIONAL DATA

In this paper we construct a statistic to test a specific form of the conditional density function. The main point of this work is to consider a functional explanatory variable, and the statistic is constructed following recent advances in nonparametric functional data analysis. The asymptotic behavior of the test statistic is studied under both the null hypothesis and some local alternative hypothesis. Then, the finite sample behavior of the method is studied through simulated examples. This paper is one of the first in the setting of nonparametric specification tests when functional data are involved.

Assessing parametric misspecification and heterogeneity in growth regression

A fully nonparametric analysis is applied to address the problems of nonlinearity and heterogeneity in classical growth regression models using original data from seminal contributions in this field. Nonparametric specification tests and in-sample goodness-of-fit measures, as well as cross-validation based out-of-sample measures provide considerable evidence for parametric misspecification and a superior performance of a nonparametric model, despite the small sample size. In contrast to recent contributions identifying heterogeneity as the primal source of misspecification, a formal and graphical analysis does not reveal evidence for heterogeneity in a parametric and nonparametric quantile regression framework.