局部平稳部分线性面板数据模型的统计推断

部分线性模型是一类非常重要的半参数回归模型,由于它既含有参数部分又含有非参数部分,与常规的线性模型相比具有更强的适应性和解释能力。文章研究带有局部平稳协变量的固定效应部分线性面板数据模型的统计推断。首先提出一个两阶段估计方法得到模型中未知参数和非参数函数的估计,并证明估计量的渐近性质,然后运用不变原理构造出非参数函数的一致置信带,最后通过数值模拟研究和实例分析验证了该方法的有效性。     

Statistical Inference for Single‐index Panel Data Models

We study estimation and hypothesis testing in single‐index panel data models with individual effects. Through regressing the individual effects on the covariates linearly, we convert the estimation problem in single‐index panel data models to that in partially linear single‐index models. The conversion is valid regardless of the individual effects being random or fixed. We propose an estimating equation approach, which has a desirable double robustness property. We show that our method is applicable in single‐index panel data models with heterogeneous link functions. We further design a chi‐squared test to evaluate whether the individual effects are random or fixed. We conduct simulations to demonstrate the finite sample performance of the method and conduct a data analysis to illustrate its usefulness.     

Iterated Feasible Generalized Least-Squares Estimation of Augmented Dynamic Panel Data Models

This article provides the large sample distribution of the iterated feasible generalized least-squares (IFGLS) estimator of an augmented dynamic panel data model. The regressors in the model include lagged values of the dependent variable and may include other explanatory variables that, while exogenous with respect to the time-varying error component, may be correlated with an unobserved time-invariant component. The article compares the finite sample properties of the IFGLS estimator to that of GMM estimators using both simulated and real data and finds that the IFGLS estimator compares favorably.     

Testing for Slope Heterogeneity Bias in Panel Data Models

ABSTRACT

Standard econometric methods can overlook individual heterogeneity in empirical work, generating inconsistent parameter estimates in panel data models. We propose the use of methods that allow researchers to easily identify, quantify, and address estimation issues arising from individual slope heterogeneity. We first characterize the bias in the standard fixed effects estimator when the true econometric model allows for heterogeneous slope coefficients. We then introduce a new test to check whether the fixed effects estimation is subject to heterogeneity bias. The procedure tests the population moment conditions required for fixed effects to consistently estimate the relevant parameters in the model. We establish the limiting distribution of the test and show that it is very simple to implement in practice. Examining firm investment models to showcase our approach, we show that heterogeneity bias-robust methods identify cash flow as a more important driver of investment than previously reported. Our study demonstrates analytically, via simulations, and empirically the importance of carefully accounting for individual specific slope heterogeneity in drawing conclusions about economic behavior.     

Tests for Symmetric Error Distribution in Linear and Nonparametric Regression Models

In linear and nonparametric regression models, the problem of testing for symmetry of the distribution of errors is considered. We propose a test statistic which utilizes the empirical characteristic function of the corresponding residuals. The asymptotic null distribution of the test statistic as well as its behavior under alternatives is investigated. A simulation study compares bootstrap versions of the proposed test to other more standard procedures.     

Fixed Effects and Bias Due to the Incidental Parameters Problem in the Tobit Model

The maximum likelihood estimator (MLE) in nonlinear panel data models with fixed effects is widely understood (with a few exceptions) to be biased and inconsistent when T, the length of the panel, is small and fixed. However, there is surprisingly little theoretical or empirical evidence on the behavior of the estimator on which to base this conclusion. The received studies have focused almost exclusively on coefficient estimation in two binary choice models, the probit and logit models. In this note, we use Monte Carlo methods to examine the behavior of the MLE of the fixed effects tobit model. We find that the estimator's behavior is quite unlike that of the estimators of the binary choice models. Among our findings are that the location coefficients in the tobit model, unlike those in the probit and logit models, are unaffected by the “incidental parameters problem.” But, a surprising result related to the disturbance variance emerges instead - the finite sample bias appears here rather than in the slopes. This has implications for estimation of marginal effects and asymptotic standard errors, which are also examined in this paper. The effects are also examined for the probit and truncated regression models, extending the range of received results in the first of these beyond the widely cited biases in the coefficient estimators.     

Small-Sample Methods for Cluster-Robust Variance Estimation and Hypothesis Testing in Fixed Effects Models

ABSTRACT

In panel data models and other regressions with unobserved effects, fixed effects estimation is often paired with cluster-robust variance estimation (CRVE) to account for heteroscedasticity and un-modeled dependence among the errors. Although asymptotically consistent, CRVE can be biased downward when the number of clusters is small, leading to hypothesis tests with rejection rates that are too high. More accurate tests can be constructed using bias-reduced linearization (BRL), which corrects the CRVE based on a working model, in conjunction with a Satterthwaite approximation for t-tests. We propose a generalization of BRL that can be applied in models with arbitrary sets of fixed effects, where the original BRL method is undefined, and describe how to apply the method when the regression is estimated after absorbing the fixed effects. We also propose a small-sample test for multiple-parameter hypotheses, which generalizes the Satterthwaite approximation for t-tests. In simulations covering a wide range of scenarios, we find that the conventional cluster-robust Wald test can severely over-reject while the proposed small-sample test maintains Type I error close to nominal levels. The proposed methods are implemented in an R package called clubSandwich. This article has online supplementary materials.     

Bayes Estimation Based on Random Censored Data for Some Life Time Models Under Symmetric and Asymmetric Loss Functions

Censored data arise naturally in a number of fields, particularly in problems of reliability and survival analysis. There are several types of censoring; in this article, we shall confine ourselves to the right randomly censoring type. Under the Bayesian framework, we study the estimation of parameters in a general framework based on the random censored observations under Linear-Exponential (LINEX) and squared error loss (SEL) functions. As a special case, Weibull model is discussed and the admissibility of estimators of parameters verified. Finally, a simulation study is conducted based on Monte Carlo (MC) method for comparing estimated risks of the estimators obtained.