基于辅助回归模型的空间Hausman检验

 基于面板数据空间误差分量模型,提出空间Hausman检验,并通过数理推导,构造辅助回归模型的空间Hausman检验,进而通过Monte Carlo模拟实验,研究空间Hausman检验,以及辅助回归空间Hausman检验的有限样本性质。研究结果表明,空间Hausman检验能有效矫正空间面板数据下经典Hausman检验的水平扭曲,但随着空间相关性和样本量增大,其水平扭曲偏离理想值;辅助回归空间Hausman检验始终保持理想的水平扭曲。此外,二者均具有优越的检验功效。     

Bootstrapping the Hausman Test in Panel Data Models

In the article, it is shown that in panel data models the Hausman test (HT) statistic can be considerably refined using the bootstrap technique. Edgeworth expansion shows that the coverage of the bootstrapped HT is second-order correct.

The asymptotic versus the bootstrapped HT are compared also by Monte Carlo simulations. At the null hypothesis and a nominal size of 0.05, the bootstrapped HT reduces the coverage error of the asymptotic HT by 10–40% of nominal size; for nominal sizes less than or equal to 0.025, the coverage error reduction is between 30% and 80% of nominal size. For the nonnull alternatives, the power of the asymptotic HT fictitiously increases by over 70% of the correct power for nominal sizes less than or equal to 0.025; the bootstrapped HT reduces overrejection to less than one fourth of its value. The advantages of the bootstrapped HT increase with the number of explanatory variables.

Heteroscedasticity or serial correlation in the idiosyncratic part of the error does not hamper advantages of the bootstrapped version of HT, if a heteroscedasticity robust version of the HT and the wild bootstrap are used. But, the power penalty is not negligible if a heteroscedasticity robust approach is used in the homoscedastic panel data model.     

Panel data unit roots tests: The role of serial correlation and the time dimension

We investigate the influence of residual serial correlation and of the time dimension on statistical inference for a unit root in dynamic longitudinal data, known as panel data in econometrics. To this end, we introduce two test statistics based on method of moments estimators. The first is based on the generalized method of moments estimators, while the second is based on the instrumental variables estimator. Analytical results for the Instrumental Variables (IV) based test in a simplified setting show that (i) large time dimension panel unit root tests will suffer from serious size distortions in finite samples, even for samples that would normally be considered large in practice, and (ii) negative serial correlation in the error terms of the panel reduces the power of the unit root tests, possibly up to a point where the test becomes biased. However, near the unit root the test is shown to have power against a wide range of alternatives. These findings are confirmed in a more general set-up through a series of Monte Carlo experiments.     

动态广义最小二乘法在面板协整中的应用研究

在进行非平稳面板数据的协整分析时,使用动态最小二乘法（DOLS）可以有效消除内生性问题,从而得到具有渐进正态分布的统计量。但在小样本条件下,由于可使用解释变量差分项的阶数有限,导致模型中均衡误差项的序列相关,使得DOLS统计量出现严重的检验水平畸变。为此,本文将单一时间序列的动态广义最小二乘法（DGLS）应用于非平稳的同质面板数据模型。在序贯极限分布的条件下,DGLS统计量仍具有正态的条件极限分布。而仿真实验表明,对于非平稳的同质面板数据模型,即使在均衡误差项存在高序列相关的条件下,DGLS统计量仍具有较好的小样本性质。     

Simple Tests for Exogeneity of a Binary Explanatory Variable in Count Data Regression Models

This article investigates power and size of some tests for exogeneity of a binary explanatory variable in count models by conducting extensive Monte Carlo simulations. The tests under consideration are Hausman contrast tests as well as univariate Wald tests, including a new test of notably easy implementation. Performance of the tests is explored under misspecification of the underlying model and under different conditions regarding the instruments. The results indicate that often the tests that are simpler to estimate outperform tests that are more demanding. This is especially the case for the new test.     

A monte carlo comparison of tests based on the durbin-watson statistic with other autocorrelation tests in dynamic models

This paper examines the sampling properties of a number of serial correlation tests in dynamic linear models which include one or two lags of the dependent variable. Among the tests considered are the Durbin-Watson (DW) bounds test, modified versions of the DW proposed recently by King and Wu and Inder, Durbin's m test, Inder's point optimal test and a Hausman type test. Sampling designs include models with one or two lags of the dependent variable. The m, Hausman, and Inder's tests have the best performance, while Inder's modified DW test appears to be better than the other DW based tests. Results also suggest that tests are less powerful and more sensitive to design parameters in models with higher dynamics, with the DW-based tests being the most sensitive.     

单向面板回归模型中异方差类型的确定性检验框架

结合White检验和Hausman检验,在一个检验框架内对单向面板回归模型中异方差的七种类型进行研究,将误差项中的个体效应和时间效应进行分离,给出异方差类型的确定性检验方法和步骤。应用中国城镇居民总消费、居住消费和收入的数据进行实证分析,证实异方差类型确定性检验方法的实用性和可行性。     

A Criterion for Stepwise Regression

In “stepwise” regression analysis, the usual procedure enters or removes variables at each “step” on the basis of testing whether certain partial correlation coefficients are zero. An alternative method suggested in this paper involves testing the hypothesis that the mean square error of prediction does not decrease from one step to the next. This is equivalent to testing that the partial correlation coefficient is equal to a certain nonzero constant. For sample sizes sufficiently large, Fisher's z transformation can be used to obtain an asymptotically UMP unbiased test. The two methods are contrasted with an example involving actual data.     

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This paper examines the sampling properties of a number of serial correlation tests in dynamic linear models which include one or two lags of the dependent variable. Among the tests considered are the Durbin-Watson (DW) bounds test, modified versions of the DW proposed recently by King and Wu and Inder, Durbin's m test, Inder's point optimal test and a Hausman type test. Sampling designs include models with one or two lags of the dependent variable. The m, Hausman, and Inder's tests have the best performance, while Inder's modified DW test appears to be better than the other DW based tests. Results also suggest that tests are less powerful and more sensitive to design parameters in models with higher dynamics, with the DW-based tests being the most sensitive.     

Instrument endogeneity and identification-robust tests: Some analytical results

When some explanatory variables in a regression are correlated with the disturbance term, instrumental variable methods are typically employed to make reliable inferences. Furthermore, to avoid difficulties associated with weak instruments, identification-robust methods are often proposed. However, it is hard to assess whether an instrumental variable is valid in practice because instrument validity is based on the questionable assumption that some of them are exogenous. In this paper, we focus on structural models and analyze the effects of instrument endogeneity on two identification-robust procedures, the Anderson–Rubin (1949, AR) and the Kleibergen (2002, K) tests, with or without weak instruments. Two main setups are considered: (1) the level of “instrument” endogeneity is fixed (does not depend on the sample size) and (2) the instruments are locally exogenous, i.e. the parameter which controls instrument endogeneity approaches zero as the sample size increases. In the first setup, we show that both test procedures are in general consistent against the presence of invalid instruments (hence asymptotically invalid for the hypothesis of interest), whether the instruments are “strong” or “weak”. We also describe cases where test consistency may not hold, but the asymptotic distribution is modified in a way that would lead to size distortions in large samples. These include, in particular, cases where the 2SLS estimator remains consistent, but the AR and K tests are asymptotically invalid. In the second setup, we find (non-degenerate) asymptotic non-central chi-square distributions in all cases, and describe cases where the non-centrality parameter is zero and the asymptotic distribution remains the same as in the case of valid instruments (despite the presence of invalid instruments). Overall, our results underscore the importance of checking for the presence of possibly invalid instruments when applying “identification-robust” tests.     

Instrumental variable estimation of heteroskedasticity adaptive error component models

The linear panel data estimator proposed by Hausman and Taylor relaxes the hypothesis of exogenous regressors that is assumed by generalized least squares methods but, unlike the Fixed Effects estimator, it can handle endogenous time invariant explanatory variables in the regression equation. One of the assumptions underlying the estimator is the homoskedasticity of the error components. This can be restrictive in applications, and therefore in this paper the assumption is relaxed and more efficient adaptive versions of the estimator are presented.     

A NEW PROCEDURE FOR ASSESSING LARGE SETS OF CORRELATIONS

In this paper, a new test of the hypothesis that all the correlations between a set of variables are zero is proposed. It is based on the asymptotic behaviour of the largest of the observed correlation coefficients. Here “asymptotic” refers to the size of the correlation matrix considered. Simulations show that the critical levels, calculated using the asymptotic theory, are conservative but quite accurate, even for small correlation matrices.     

A test for the complete independence of high-dimensional random vectors

ABSTRACT

This paper discusses the problem of testing the complete independence of random variables when the dimension of observations can be much larger than the sample size. It is reported that two typical tests based on, respectively, the biggest off-diagonal entry and the largest eigenvalue of the sample correlation matrix lose their control of type I error in such high-dimensional scenarios, and exhibit distinct behaviours in type II error under different types of alternative hypothesis. Given these facts, we propose a permutation test procedure by synthesizing these two extreme statistics. Simulation results show that for finite dimension and sample size the proposed test outperforms the existing methods in various cases.     

空间面板杜宾模型的Bootstrap Wald-COMFAC检验研究

将共同因子约束(COMFAC)的Wald检验问题引入到空间面板模型中,讨论空间面板杜宾模型与空间面板误差模型的识别问题。蒙特卡洛模拟表明:在有限样本下,基于渐近临界值的Wald检验有着良好的检验功效,但存在着较为严重的尺度扭曲。进一步采用残差Bootstrap方法,在不损失检验功效的前提下,能够显著地降低检验的尺度扭曲。因此,残差Bootstrap方法是更为有效的检验方法。     

A robust test for testing the correlation coefficient

A test based on Tiku's MML (modified maximum likelihood) estimators is developed for testing that the population correlation coefficient is zero. The test is compared with various other tests and shown to have good Type I error robustness and power for numerous symmetric and skew bivariate populations.     

PARTIAL CORRELATION AND CONDITIONAL CORRELATION AS MEASURES OF CONDITIONAL INDEPENDENCE

This paper investigates the roles of partial correlation and conditional correlation as measures of the conditional independence of two random variables. It first establishes a sufficient condition for the coincidence of the partial correlation with the conditional correlation. The condition is satisfied not only for multivariate normal but also for elliptical, multivariate hypergeometric, multivariate negative hypergeometric, multinomial and Dirichlet distributions. Such families of distributions are characterized by a semigroup property as a parametric family of distributions. A necessary and sufficient condition for the coincidence of the partial covariance with the conditional covariance is also derived. However, a known family of multivariate distributions which satisfies this condition cannot be found, except for the multivariate normal. The paper also shows that conditional independence has no close ties with zero partial correlation except in the case of the multivariate normal distribution; it has rather close ties to the zero conditional correlation. It shows that the equivalence between zero conditional covariance and conditional independence for normal variables is retained by any monotone transformation of each variable. The results suggest that care must be taken when using such correlations as measures of conditional independence unless the joint distribution is known to be normal. Otherwise a new concept of conditional independence may need to be introduced in place of conditional independence through zero conditional correlation or other statistics.     

Semiparametric Smooth Coefficient Stochastic Frontier Model With Panel Data

ABSTRACT

We investigate the semiparametric smooth coefficient stochastic frontier model for panel data in which the distribution of the composite error term is assumed to be of known form but depends on some environmental variables. We propose multi-step estimators for the smooth coefficient functions as well as the parameters of the distribution of the composite error term and obtain their asymptotic properties. The Monte Carlo study demonstrates that the proposed estimators perform well in finite samples. We also consider an application and perform model specification test, construct confidence intervals, and estimate efficiency scores that depend on some environmental variables. The application uses a panel data on 451 large U.S. firms to explore the effects of computerization on productivity. Results show that two popular parametric models used in the stochastic frontier literature are likely to be misspecified. Compared with the parametric estimates, our semiparametric model shows a positive and larger overall effect of computer capital on the productivity. The efficiency levels, however, were not much different among the models. Supplementary materials for this article are available online.     

Testing Serial Correlation in Semiparametric Varying-Coefficient Partially Linear Models

We propose two test statistics for testing serial correlation in semiparametric varying-coefficient partially linear models. The proposed test statistics are not only for testing zero first-order serial correlation, but also for testing higher-order serial correlations. Under the null hypothesis of no serial correlation, the test statistics are shown to have asymptotic normal or chi-square distributions. By using R, some Monte Carlo experiments are conducted to examine the finite sample performances of the proposed tests. Simulation results show that the estimated size and power of the proposed tests behave well.     

Tests of specification in econometrics

This survey of recent developments in testing for misspecification of econometric models reviews procedures based on a method due to Hausman. Particular attention is given to alternative forms of the test, its relationship to classical test procedures, and its role in pre-test estimation.     

Generalized fixed‐T panel unit root tests

Panel data unit root tests, which can be applied to data that do not have many time series observations, are based on very restrictive error and deterministic component specification assumptions. In this paper, we develop a new, doubly modified estimator, based on which we propose a panel unit root test that allows for multiple structural breaks, linear and nonlinear trends, heteroscedasticity, serial correlation, and error cross‐section heterogeneity, when the number of time series observations is finite. The test has the additional perk that it is invariant to the initial condition.