Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

Journal of Economic Surveys

2016

In this paper, we provide an intensive review of the recent developments for semiparametric and fully nonparametric panel data models that are linearly separable in the innovation and the individual-specific term. We analyze these developments under two alternative model specifications: fixed and random effects panel data models. More precisely, in the random effects setting, we focus our attention in the analysis of some efficiency issues that have to do with the so-called working independence condition. This assumption is introduced when estimating the asymptotic variance-covariance matrix of nonparametric estimators. In the fixed effects setting, to cope with the so-called incidental parameters problem, we consider two different estimation approaches: profiling techniques and differencing methods. Furthermore, we are also interested in the endogeneity problem and how instrumental variables are used in this context. In addition, for practitioners, we also show different ways of avoiding the so-called curse of dimensionality problem in pure nonparametric models. In this way, semiparametric and additive models appear as a solution when the number of explanatory variables is large.

Section: Semiparametric Panel Data Models With Random Effectsmentioning

confidence: 99%

Nonparametric and Semiparametric Panel Data Models: Recent Developments

Journal of Economic Surveys

2016

“…We could relax this assumption by assuming some dependence based on second-order moments. For example, heteroscedasticity of unknown form can be allowed and, in fact, under more complex structures in the variancecovariance matrix, a transformation of the estimator proposed by You et al (2010) can be developed in our setting. This type of assumption also rules out the existence of endogenous explanatory variables and imposes strict exogeneity conditions.…”

Section: Asymptotic Properties and The Oracle Efficient Estimatormentioning

confidence: 99%

Direct semi-parametric estimation of fixed effects panel data varying coefficient models

The Econometrics Journal

2014

In this paper, we present a new technique to estimate varying coefficient models of unknown form in a panel data framework where individual effects are arbitrarily correlated with the explanatory variables in an unknown way. The estimator is based on first differences and then a local linear regression is applied to estimate the unknown coefficients. To avoid a non-negligible asymptotic bias, we need to introduce a higher-dimensional kernel weight. This enables us to remove the bias at the price of enlarging the variance term and, hence, achieving a slower rate of convergence. To overcome this problem, we propose a one-step backfitting algorithm that enables the resulting estimator to achieve optimal rates of convergence for this type of problem. It also exhibits the so-called oracle efficiency property. We also obtain the asymptotic distribution. Because the estimation procedure depends on the choice of a bandwidth matrix, we also provide a method to compute this matrix empirically. The Monte Carlo results indicate the good performance of the estimator in finite samples.

“…We could relax this assumption by assuming some dependence based on second order moments. For example, heteroskedasticity of unknown form can be allowed and in fact, under more complex structures in the variancecovariance matrix a transformation of the estimator proposed in You et al (2010) can be developed in our setting. This type of assumption also rules out the existence of endogenous explanatory variables and imposes strict exogeneity conditions.…”

Section: Asymptotic Properties and The Oracle Efficient Estimatormentioning

confidence: 99%

Direct Semiparametric Estimation of Fixed Effects Panel Data Varying Coefficient Models

2012

SSRN Journal

Summary In this paper we present a new technique to estimate varying coefficient models of unknown form in a panel data framework where individual effects are arbitrarily correlated with the explanatory variables in an unknown way. The estimator is based in first differences and then a local linear regression is applied to estimate the unknown coefficients. To avoid a non-negligible asymptotic bias, we need to introduce a higher dimensional kernel weight. This enables us to remove the bias at the price of enlarging the variance term and hence, achieving a slower rate of convergence. To overcome this problem we propose a one step backfitting algorithm that enables the resulting estimator to achieve optimal rates of convergence for this type of problems. It exhibits also the so called oracle efficiency property. We also obtain the asymptotic distribution. Since the estimation procedure depends on the choice of a bandwidth matrix, we also provide a method to compute this matrix empirically. Monte Carlo results indicates good performance of the estimator in finite samples.