Nonparametric estimation and testing of fixed effects panel data models

In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We introduce an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model. Simulations are used to examine the finite sample performance of the proposed estimators and the test statistics.     

Estimating dynamic panel data discrete choice models with fixed effects

This paper considers the estimation of dynamic binary choice panel data models with fixed effects. It is shown that the modified maximum likelihood estimator (MMLE) used in this paper reduces the order of the bias in the maximum likelihood estimator from O(T^-1) to O(T^-2), without increasing the asymptotic variance. No orthogonal reparametrization is needed. Monte Carlo simulations are used to evaluate its performance in finite samples where T is not large. In probit and logit models containing lags of the endogenous variable and exogenous variables, the estimator is found to have a small bias in a panel with eight periods. A distinctive advantage of the MMLE is its general applicability. Estimation and relevance of different policy parameters of interest in this kind of models are also addressed.     

Testing for a unit root in a random coefficient panel data model

This paper proposes new unit root tests in the context of a random autoregressive coefficient panel data model, in which the null of a unit root corresponds to the joint restriction that the autoregressive coefficient has unit mean and zero variance. The asymptotic distributions of the test statistics are derived and simulation results are provided to suggest that they perform very well in small samples.     

Robust penalized quantile regression estimation for panel data

This paper investigates a class of penalized quantile regression estimators for panel data. The penalty serves to shrink a vector of individual specific effects toward a common value. The degree of this shrinkage is controlled by a tuning parameter λ$\lambda$. It is shown that the class of estimators is asymptotically unbiased and Gaussian, when the individual effects are drawn from a class of zero-median distribution functions. The tuning parameter, λ$\lambda$, can thus be selected to minimize estimated asymptotic variance. Monte Carlo evidence reveals that the estimator can significantly reduce the variability of the fixed-effect version of the estimator without introducing bias.     

Testing for random effects in panel models with spatially correlated disturbances

In the empirical analysis of panel data the Breusch–Pagan (BP) statistic has become a standard tool to infer on unobserved heterogeneity over the cross-section. Put differently, the test statistic is central to discriminate between the pooled regression and the random effects model. Conditional versions of the test statistic have been provided to immunize inference on unobserved heterogeneity against random time effects or patterns of spatial error correlation. Panel data models with spatially correlated error terms are typically set out under the presumption of some known adjacency matrix parameterizing the correlation structure up to a scaling factor. This paper delivers a bootstrap scheme to generate critical values for the BP statistic allowing robust inference under misspecification of the adjacency matrix. Moreover, asymptotic results are derived for the case of a finite cross-section and infinite time dimension. Finite sample simulations show that misspecification of spatial covariance features could lead to large size distortions, while the robust bootstrap procedure retains asymptotic validity.     

Generalized least squares inference in panel and multilevel models with serial correlation and fixed effects

In this paper, I consider generalized least squares (GLS) estimation in fixed effects panel and multilevel models with autocorrelation. The presence of fixed effects complicates implementation of GLS as estimating the fixed effects will typically render standard estimators of the covariance parameters necessary for obtaining feasible GLS estimates inconsistent. I focus on the case where the disturbances follow an AR(p) process and offer a simple to implement bias-correction for the AR coefficients. The usefulness of GLS and the derived bias-correction for the parameters of the autoregressive process is illustrated through a simulation study which uses data from the Current Population Survey.     

Nonparametric fixed effects model for panel data with locally stationary regressors

We develop methods for inference in nonparametric time-varying fixed effects panel data models that allow for locally stationary regressors and for the time series length $T$ and cross-section size $N$ both being large. We first develop a pooled nonparametric profile least squares dummy variable approach to estimate the nonparametric function, and establish the optimal convergence rate and asymptotic normality of the resultant estimator. We then propose a test statistic to check whether the bivariate nonparametric function is time-varying or the time effect is separable, and derive the asymptotic distribution of the proposed test statistic. We present several simulated examples and two real data analyses to illustrate the finite sample performance of the proposed methods.     

Testing a linear dynamic panel data model against nonlinear alternatives

The most popular econometric models in the panel data literature are the class of linear panel data models with unobserved individual- and/or time-specific effects. The consistency of parameter estimators and the validity of their economic interpretations as marginal effects depend crucially on the correct functional form specification of the linear panel data model. In this paper, a new class of residual-based tests is proposed for checking the validity of dynamic panel data models with both large cross-sectional units and time series dimensions. The individual and time effects can be fixed or random, and panel data can be balanced or unbalanced. The tests can detect a wide range of model misspecifications in the conditional mean of a dynamic panel data model, including functional form and lag misspecification. They check a large number of lags so that they can capture misspecification at any lag order asymptotically. No common alternative is assumed, thus allowing for heterogeneity in the degrees and directions of functional form misspecification across individuals. Thanks to the use of panel data with large $N$ and $T$, the proposed nonparametric tests have an asymptotic normal distribution under the null hypothesis without requiring the smoothing parameters to grow with the sample sizes. This suggests better nonparametric asymptotic approximation for the panel data than for time series or cross sectional data. This is confirmed in a simulation study. We apply the new tests to test linear specification of cross-country growth equations and found significant nonlinearities in mean for OECD countries’ growth equation for annual and quintannual panel data.     

Labour adjustment costs: Estimation of a dynamic discrete choice model using panel data for Greek manufacturing firms

In this paper we estimate a dynamic structural model of employment at firm level. Our dataset consists of a balanced panel of 2790 Greek manufacturing firms. The empirical evidence of this dataset stresses three important stylized facts: (a) there are periods in which firms decide not to change their labour input, (b) there are periods of large employment changes (lumpy nature of labour adjustment) and (c) the commonality is employment spikes to be followed by smooth and low employment growth periods. Following Cooper and Haltiwanger [Cooper, R.W. and Haltiwanger, J. “On the Nature of Capital Adjustment Costs”, Review of Economic Studies, 2006; 73(3); 611–633], we consider a dynamic discrete choice model of a general specification of adjustment costs including convex, non-convex and “disruption of production” components. We use a method of simulated moments procedure to estimate the structural parameters. Our results indicate considerable fixed costs in the Greek employment adjustment.     

Nonparametric testing for smooth structural changes in panel data models

Detecting and modeling structural changes in time series models have attracted great attention. However, relatively little effort has been paid to the testing of structural changes in panel data models despite their increasing importance in economics and finance. In this paper, we propose a new approach to testing structural changes in panel data models. Unlike the bulk of the literature on structural changes, which focuses on detection of abrupt structural changes, we consider smooth structural changes for which model parameters are unknown deterministic smooth functions of time except for a finite number of time points. We use nonparametric local smoothing method to consistently estimate the smooth changing parameters and develop two consistent tests for smooth structural changes in panel data models. The first test is to check whether all model parameters are stable over time. The second test is to check potential time-varying interaction while allowing for a common trend. Both tests have an asymptotic $N(0,1)$ distribution under the null hypothesis of parameter constancy and are consistent against a vast class of smooth structural changes as well as abrupt structural breaks with possibly unknown break points alternatives. Simulation studies show that the tests provide reliable inference in finite samples and two empirical examples with respect to a cross-country growth model and a capital structure model are discussed.     

Technical efficiency measures for dairy farms using panel data: A comparison of alternative model specifications

This article examines the impact of fixed effects production functions vis-à-vis stochastic production frontiers on technical efficiency measures. An unbalanced panel consisting of 96 Vermont dairy farmers for the 1971–1984 period was used in the analysis. The models examined incorporated both time-variant and time-invariant technical efficiency. The major source of variation in efficiency levels across models stemmed from the assumption made concerning the distribution of the one-sided term in the stochastic frontiers. In general, the fixed effects technique was found superior to the stochastic production frontier methodology. Despite the fact that the results of various statistical tests revealed the superiority of some specifications over others, the overall conclusion of the study is that the efficiency analysis was fairly consistent throughout all the models considered.     

Estimating panel data models in the presence of endogeneity and selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.     

A Lagrange Multiplier test for cross-sectional dependence in a fixed effects panel data model

It is well known that the standard Breusch and Pagan (1980) LM test for cross-equation correlation in a SUR model is not appropriate for testing cross-sectional dependence in panel data models when the number of cross-sectional units (n)$\left(n\right)$ is large and the number of time periods (T)$\left(T\right)$ is small. In fact, a scaled version of this LM test was proposed by Pesaran (2004) and its finite sample bias was corrected by Pesaran et al. (2008). This was done in the context of a heterogeneous panel data model. This paper derives the asymptotic bias of this scaled version of the LM test in the context of a fixed effects homogeneous panel data model. This asymptotic bias is found to be a constant related to n$n$ and T$T$, which suggests a simple bias corrected LM test for the null hypothesis. Additionally, the paper carries out some Monte Carlo experiments to compare the finite sample properties of this proposed test with existing tests for cross-sectional dependence.     

Forecasting and turning point predictions in a Bayesian panel VAR model

We provide methods for forecasting variables and predicting turning points in panel Bayesian VARs. We specify a flexible model, which accounts for both interdependencies in the cross section and time variations in the parameters. Posterior distributions for the parameters are obtained for hierarchical and for Minnesota-type priors. Formulas for multistep, multiunit point and average forecasts are provided. An application to the problem of forecasting the growth rate of output and of predicting turning points in the G-7 illustrates the approach. A comparison with alternative forecasting methods is also provided.     

p2: a random effects model with covariates for directed graphs

A random effects model is proposed for the analysis of binary dyadic data that represent a social network or directed graph, using nodal and/or dyadic attributes as covariates. The network structure is reflected by modeling the dependence between the relations to and from the same actor or node. Parameter estimates are proposed that are based on an iterated generalized least-squares procedure. An application is presented to a data set on friendship relations between American lawyers.     

经济适用住房挤出效应研究——基于2006-2010年29个大中城市的面板数据分析

国内学者在经济适用房对商品住房的挤出效应问题上一直存有争议。基于2006-2010年29个大中城市面板数据回归,对经济适用房的挤出效应进行实证检验,结果表明：（1）经济适用房销售量的系数显著不为0,说明经济适用房对商品住房的挤出效应存在;（2）挤出效应的值为-0．86,即经济适用房销售量每增加1个单位量,商品住房销售量将会减少0．86个单位量。结果表明,经济适用房政策存在较大的挤出效应。     

Testing homogeneity in a random intercept model using asymptotic, posterior predictive and plug-in p-values

In this paper three statistics and three discrepancy measures with which homogeneity in the random intercept model can be investigated will be evaluated. The first two can be used to test the homogeneity of level one residual variances across level two units and the third can be used to test whether effects should be fixed or random. Each statistic and discrepancy measure will be evaluated using asymptotic (if available), posterior predictive and plug in p -values. A simulation study will be used to investigate the frequency properties of these p -values. In the discussion it will be indicated how the results obtained for the random intercept model with one explanatory variable can be useful during the construction of general two level models.     

On marginal estimation in a semiparametric model for longitudinal data with time-independent covariates

We consider M-estimators for a class of semiparametric mixed-effect models without time-dependent covariates and show that the simple marginal estimation method is generally better than the same M-estimator applied to the de-correlated response based on a known or estimated covariance matrix for each subject.     

Joint estimation of technical efficiency and production risk for multi-output banks under a panel data cost frontier model

This article generalizes production risk from a single output production function to a multiple output cost frontier, which is able to examine input-oriented technical efficiencies and production risk simultaneously in the context of a panel data. Furthermore, the joint confidence interval estimates for technical efficiencies are constructed by means of multiple comparisons with the best approach. Whether taking production risk into account or not offers quite dissimilar implications in terms of the average technical efficiency measure and the identification of multiple efficient banks achieving the optimal cost frontier. It is suggested that inferences drawn on the basis of the confidence intervals of technical efficiency provide much more fruitful and insightful information than the point estimation alone. Bank specific risk parameters are found to be highly and positively correlated with fixed-effect estimates, implying that the more risk-averse a bank is, the more technically efficient it will be.

2SLS and OLS in a spatial autoregressive model with equal spatial weights

The paper considers a Cliff–Ord type spatial model with a spatially lagged dependent variable and a row normalized weighting matrix with equal weights. We show that the 2SLS and OLS estimators are inconsistent unless panel data are available. The weighting matrix in question is one which would naturally be considered if all units are neighbors to each other, and there is no other reasonable or observable measure of distance between them.