Estimating Econometric Models with Fixed Effects

2008

Since little is known about the degree of bias in estimated fixed effects in panel data models, we run Monte Carlo simulations on a range of different estimators. We find that Anderson-Hsiao IV, Kiviet's bias-corrected LSDV and GMM estimators all perform well in both short and long panels. However, OLS outperforms the other estimators when the following holds: the cross-section is small (N = 20), the time dimension is short (T = 5) and the coefficient on the lagged dependent variable is large (γ = 0.8).

Statistics & Probability Letters, 2013

ABSTRACT We consider the fixed effects panel data single-index model. For estimation of the link function and the index parameter, the local linear smoothing and the least squares method are used. We also propose a test for the presence of the fixed effects. Finite sample performances are illustrated using simulations.

2011

The paper introduces for the most frequently used three-dimensional fixed effects panel data models the appropriate Within estimators. It analyzes the behaviour of these estimators in the case of no-self-flow data, unbalanced data and dynamic autoregressive models.

2012

This paper describes the Stata implementation of series estimator of partially linear panel data models with fixed effects. After a brief description of the estimator itself, we describe the new command xtsemipar. We then simulate data to show that this estimator performs better than a fixed effect estimator if the relationship between two variables is unknown or quite complex.

The New Palgrave Dictionary of Economics, 2008

These notes summarize some recent, and perhaps not-so-recent, advances in the estimation of nonlinear panel data models. Research in the last 10 to 15 years has branched off in two directions. In one, the focus has been on parameter estimation, possibly only up to a common scale factor, in semiparametric models with unobserved effects (that can be arbitrarily correlated with covariates.) Another branch has focused on estimating partial effects when restrictions are made on the distribution of heterogeneity conditional on the history of the covariates. These notes attempt to lay out the pros and cons of each approach, paying particular attention to the tradeoff in assumptions and the quantities that can be estimated.

2008

This paper gives identification and estimation results for marginal effects in nonlinear panel models. We find that linear fixed effects estimators are not consistent, due in part to marginal effects not being identified. We derive bounds for marginal effects and show that they can tighten rapidly as the number of time series observations grows. We also show in numerical calculations that the bounds may be very tight for small numbers of observations, suggesting they may be useful in practice. We propose two novel inference methods for parameters defined as solutions to linear and nonlinear programs such as marginal effects in multinomial choice models. We show that these methods produce uniformly valid confidence regions in large samples. We give an empirical illustration.

Journal of Econometrics, 2013

This paper explores identification and estimation of a class of nonlinear panel data single-index models, which includes a class of single-index panel discrete-choice models. The model allows for unknown time-specific link functions, and semiparametric specification of the individual-specific effects. We develop an estimator for the parameters of interest that may be computed with any appropriate smoother, be it sieves or kernel smoothers. We propose a powerful new kernel-based modified backfitting algorithm to compute the estimator. The algorithm fully implements the identification restrictions of the model. We derive uniform rates of convergence results for the estimators of the link functions, and show the estimators of the finite dimensional parameters are root-N consistent with a Gaussian limiting distribution. We study the small sample properties of the estimator via Monte Carlo techniques. The results indicate that the estimator performs well in recovering the finite-dimensional parameters of interest.

MEDIA STATISTIKA

In linear models, panel data often violates the assumption that the error terms should be independent. As a result, the estimated variance is usually large and the standard inferential methods are not appropriate. The previous research developed an inference method to solve this problem using a variance estimator namely the Heteroskedasticity Autocorrelation Consistent of the Cross-Section Averages (HACSC), with some improvements. The test statistic of this method converges to the fixed-b asymptotic distribution. In this paper, the performance of the proposed inferential method is evaluated by means of simulation and compared with the standard method using plm package in R. Several comparisons regarding the Type I Error of these two methods have been carried out. The results showed that the statistical inference based on fixed-b asymptotic distribution out-perform the standard method, especially for the panel data with small number of individual and time dimension.

2011

In this paper we extend the fixed effects approach to deal with endogeneity arising from persistent unobserved heterogeneity to nonlinear panel data with nonparametric components. Specifically, we propose a nonparametric procedure that generalizes Chamberlain's (1984) conditional logit approach. We develop an estimator based on nonlinear stochastic integral equations and provide the asymptotic property of the estimator and an iterative algorithm to implement the estimator. We analyze the small sample behavior of the estimator through a Monte Carlo study, and consider the decision to retire as an illustrative application.

2013

This paper considers the maximum likelihood estimation of panel data models with interactive effects. Motivated by applications in economics and other social sciences, a notable feature of the model is that the explanatory variables are correlated with the unobserved effects. The usual within-group estimator is inconsistent. Existing methods for consistent estimation are either designed for panel data with short time periods or are less efficient. The maximum likelihood estimator has desirable properties and is easy to implement, as illustrated by the Monte Carlo simulations. This paper develops the inferential theory for the maximum likelihood estimator, including consistency, rate of convergence and the limiting distributions. We further extend the model to include time-invariant regressors and common regressors (cross-section invariant). The regression coefficients for the time-invariant regressors are time-varying, and the coefficients for the common regressors are cross-sectionally varying.

The Econometrics Journal, 2011

This paper is concerned with developing a nonparametric time-varying coefficient model with fixed effects to characterize nonstationarity and trending phenomenon in nonlinear panel data analysis. We develop two methods to estimate the trend function and the coefficient function without taking the first difference to eliminate the fixed effects. The first one eliminates the fixed effects by taking cross-sectional averages, and then uses a nonparametric local linear approach to estimate the trend function and the coefficient function. The asymptotic theory for this approach reveals that although the estimates of both the trend function and the coefficient function are consistent, the estimate of the coefficient function has a rate of convergence of (T h) −1/2 that is slower than that of the trend function, which has a rate of (N T h) −1/2 . To estimate the coefficient function more efficiently, we propose a pooled local linear dummy variable approach. This is motivated by a least squares dummy variable method proposed in parametric panel data analysis. This method removes the fixed effects by deducting a smoothed version of cross-time average from each individual.

2000

This paper shows that first-differences or fixed-effects models may understate the effect of interest because of the variation used to identify the model. For example, much of the recent research estimating the relationship between AFDC benefits and fertility has used fixed-effects models. If the cross-sectional variation in AFDC benefits is removed, then the variation over time within states left for identification will largely reflect transitory, idiosyncratic changes in welfare benefits, which are unlikely to affect fertility. In some sense, the independent variable as being measured with error, since it is contaminated with these temporary fluctuations. Estimates obtained using fixed-effects models are small because the “signal” of permanent changes is being overwhelmed by the “noise” of transitory changes. Two empirical examples are presented: one on the relationship between AFDC and fertility and the other on the relationship between local economic conditions and AFDC particip...

Social Forces, 2010

Fixed and random effects models for longitudinal data are common in sociology. Their primary advantage is that they control for time-invariant omitted variables. However, analysts face several issues when they employ these models. One is the uncertainty of whether to apply the fixed effects (FEM) versus the random effects (REM) models. Another less discussed issue is that the FEM and REM models as usually implemented might be insufficiently flexible. For instance, the effects of variables, including the latent time-invariant variable, might change over time rather than be constant as in the usual FEM and REM. The latent time-invariant variable might correlate with some variables and not others. Lagged endogenous variables might be necessary. Alternatives that move beyond the classic FEM and REM models are known, but they involve different estimators and software that make these extended models difficult to implement and to compare. This paper presents a general panel model that includes the standard FEM and REM as special cases. In addition, it provides a sequence of nested models that provide a richer range of models that researchers can easily compare with likelihood ratio tests and fit statistics. Furthermore, researchers can implement our general panel model and its special cases in widely available structural equation models (SEMs) software. The paper is oriented towards applied researchers with most technical details given in the appendix and footnotes. An extended empirical example illustrates our results.

It is well known that (quasi) MLE of dynamic panel data (DPD) models with short panels depends on the assumptions on the initial values; ignoring them or a wrong treatment of them will result in inconsistency or serious bias. This paper introduces a initial-condition free method for estimating the fixed-effects DPD models, through a simple modification of the quasi-score. An outer-product-of-gradients (OPG) method is also proposed for robust inference. The MLE of Hsiao, Pesaran and Tahmiscioglu (2002, Journal of Econometrics), where the initial observations are modeled, is extended to quasi MLE and an OPG method is proposed for robust inference. Consistency and asymptotic normality for both estimation strategies are established, and the two methods are compared through Monte Carlo simulations. The proposed method performs well in general, whether the panel is short or not. The quasi MLE performs comparably, except when model does not contain time-varying regressor, or the panel is not short and the dynamic parameter is small. The proposed method is much simpler and easier to apply.

Journal of Statistical Planning and Inference, 2018

In this paper local empirical likelihood-based inference for non-parametric varying coefficient panel data models with fixed effects is investigated. First, we show that the naive empirical likelihood ratio is asymptotically standard chi-squared when undersmoothing is employed. The ratio is self-scale invariant and the plug-in estimate of the limiting variance is not needed. Second, mean-corrected and residual-adjusted empirical likelihood ratios are proposed. The main interest of these techniques is that without undersmoothing, both also have standard chi-squared limit distributions. As a by product, we propose also two empirical maximum likehood estimators of the varying coefficient models and their derivatives. We also obtain the asymptotic distribution of these estimators. Furthermore, a non parametric version of the Wilk's theorem is derived. To show the feasibility of the technique and to analyse its small sample properties, using empirical likelihood-based inference we implement a Monte Carlo simulation exercise and we also illustrated the proposed technique in an empirical analysis about the production efficiency of the European Union's companies.