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.
Linear mixed models provide a useful tool to fit continuous longitudinal data, with the random effects and error term commonly assumed to have normal distributions. However, this restrictive assumption can result in a lack of robustness and needs to be tested. In this paper, we propose tests for skewness, kurtosis, and normality based on generalized least squares (GLS) residuals. To do it, estimating higher order moments is necessary and an alternative estimation procedure is developed. Compared to other procedures in the literature, our approach provides a closed form expression even for the third and fourth order moments. In addition, no further distributional assumptions on either random effects or error terms are needed to show the consistency of the proposed estimators and tests statistics. Their finite-sample performance is examined in a Monte Carlo study and the methodology is used to examine changes in the life expectancy as well as maternal and infant mortality rate of a sample of OECD countries.
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.
This paper proposes a new approach to examine the relationship between CO2 emissions and economic developing. In particular, we propose to test the Environmental Kuznets Curve (EKC) hypothesis for a panel of 24 OECD countries and 32 non-OECD countries by developing a more flexible estimation technique which enables to account for functional form misspecification, cross-sectional dependence, and heterogeneous relationships among variables, simultaneously. We propose a new nonparametric estimator that extends the well-known Common Correlated Effect (CCE) approach from a fully parametric framework to a semiparametric panel data model. Our results corroborates that the nature and validity of the income–pollution relationship based on the EKC hypothesis depends on the model assumptions about the functional form specification. For all the countries analyzed, the proposed semiparametric estimator leads to non-monotonically increasing or decreasing relationships for CO2 emissions, depending on the level of economic development of the country.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.