Non‐parametric models in binary choice fixed effects panel data

In this paper, we explore identification and efficient semiparametric estimation of a class of nonlinear panel data index models with small-T, which includes a class of single-index panel discrete-choice models. The model allows for the inclusion of predetermined variables, lagged dependent variables, and a nonparametric specification of the individual-specific effects. The paper provides a root-N consistent, asymptotically normal and efficient estimator for the finite-dimensional parameters, and a consistent estimator of the unknown index function. The estimator developed in this paper may be computed with any 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 identifying restrictions of the model. 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. The simulation results also show that, in small samples, the estimator outperforms more parametric models with various mis-specifications of the index function.

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.

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.

Journal of Business & Economic Statistics, 2013

In this paper, we consider semiparametric estimation in a partially linear singleindex panel data model with fixed effects. Without taking the difference explicitly, we propose using a semiparametric minimum average variance estimation (SMAVE) based on a dummy-variable method to remove the fixed effects and obtain consistent estimators for both the parameters and the unknown link function. As both the cross section size and the time series length tend to infinity, we not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. The asymptotically normal distributions of the proposed estimators are similar to those obtained in the random effects case. In addition, we study several partially linear single-index dynamic panel data models. The methods and results are augmented by simulation studies and illustrated by an application to a cigarettedemand data set in the US from 1963-1992.

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.

Economics Letters, 2002

This paper proposes some new semiparametric instrumental variable estimators for estimating a dynamic panel data model. Monte Carlo experiments show that the new estimators perform much better than the existing ones.

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.

2002

This paper presents an extension to the fixed-effect Logit for panel-data discrete-choice models, where the error component structure is multiplicative (individual effects multiplied by time effects). In linear models with such an error-component structure as investigated by Ahn, Lee and Schmidt , usual fixed-effect estimators are generally inconsistent. We propose a conditional Logit estimator based on a different sufficient statistic, for the case where multiplicative time effects are known. When not the case, we discuss the implementation of the Modified Profile Likelihood based on a transformation of incidental parameters. The last estimator is an extension of Honoré and Lewbel (2000) semiparametric estimator. We investigate smallsample properties of these estimators with a Monte Carlo experiment. Phone +33 (0)5 61 12 85 21, Fax +33 (0)5 61 12 85 20.

Journal of Econometrics, 2007

This paper considers the problem of identi…cation and estimation in panel-data sample-selection models with a binary selection rule when the latent equations contain possibly predetermined variables, lags of the dependent variables, and unobserved individual e¤ects. The selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations. We derive a set of conditional moment restrictions that are then exploited to construct a three-step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample-selection term. In the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of Berkson's minimum chi-square sieve method and a …rst-step kernel estimator for the selection probability. This second-step estimator is of interest in its own right. It can be used to semiparametrically estimate a panel-data binary response model with a nonparametric individual speci…c e¤ect without making any other distributional assumptions. We show that both estimators (second and third stage) are p n-consistent and asymptotically normal.

The Econometrics Journal, 2006

This paper presents an extension of fixed effects binary choice models for panel data, to the case of heterogeneous linear trends. Two estimators are proposed: a Logit estimator based on double conditioning and a semiparametric, smoothed maximum score estimator based on double differences. We investigate small-sample properties of these estimators with a Monte Carlo simulation experiment, and compare their statistical properties with standard fixed effects procedures. An empirical application to land renting decisions of Russian households between 1996 and 2002 is proposed.