Semiparametric estimation of weak and strong separable models

In this paper we introduce a general method for estimating semiparametrically the different components in weak or strong separable models. The family of separable models is quite popular in economic theory and empirical research as this structure offers clear interpretation, has straight forward economic consequences and often is justified by theory. As will be seen in this article they are also of statistical interest since they allow to estimate semiparametrically high dimensional complexity without running in the so called curse of dimensionality. Generalized additive models and generalized partial linear models are special cases in this family of models. The idea of the new method is mainly based on a combination of local likelihood and efficient estimators in non or semiparametric models. Although this imposes some hypothesis on the error distribution this yields a very general usable method with little computational costs and high exactness even for small samples. E. g. it enables us to include models for censored and truncated variables which are quite common in quantitative economics. We give the estimation procedures and provide asymptotic theory for them. Implementation is discussed, simulations and an application demonstrate its feasibility in finite sample behavio

Testing for distributional features in varying coefficient panel data models

This article provides several tests for skewness and kurtosis for the error terms in a one-way fixed-effects varying coefficient panel data model. To obtain these tests, estimators of higher-order moments of both error components are obtained as solutions of estimating equations. Additionally, to obtain the nonparametric residuals, a local constant estimator based on a pairwise differencing transformation is proposed. The asymptotic properties of these estimators and tests are established. The proposed estimators and test statistics are augmented by simulation studies, and they are also illustrated in an empirical analysis regarding the technical efficiency of European Union companies.The authors would like to thank two anonymous referees for their very helpful comments and suggestions. Furthermore, the authors gratefully acknowledge financial support from the Programa Estatal de Fomento de la Investigaci´on Cient´ıfica y T´ecnica de Excelencia/Spanish Ministry of Economy and Competitiveness. Ref. ECO2016-76203-C2-1-P. In addition, this work is part of the Research Project APIE 1/2015-17: “New methods for the empirical analysis of financial markets” of the Santander Financial Institute (SANFI) of UCEIF Foundation resolved by the University of Cantabria and funded with sponsorship from Banco Santander. Stute’s work was partly done while he was on leave at BCAM, the Basque Center of Applied Mathematics in Bilba

Nonparametric estimation of fixed effects panel data varying coefficient models.

In this paper, we consider the nonparametric estimation of a varying coefficient fixed effect panel data model. The estimator is based in a within (un-smoothed) transformation of the regression model and then a local linear regression is applied to estimate the unknown varying coefficient functions. It turns out that the standard use of this technique produces a non-negligible asymptotic bias. In order to avoid it, a high dimensional kernel weight is introduced in the estimation procedure. As a consequence, the asymptotic bias is removed but the variance is enlarged, and therefore the estimator shows a very slow rate of convergence. In order to achieve the optimal rate, we propose a one-step backfitting algorithm. The resulting two-step estimator is shown to be asymptotically normal and its rate of convergence is optimal within its class of smoothness functions. It is also oracle efficient. Further, this estimator is compared both theoretically and by Monte-Carlo simulation against other estimators that are based in a within (smoothed) transformation of the regression model. More precisely the profile least-squares estimator proposed in this context in Sun et al. (2009). It turns out that the smoothness in the transformation enlarges the bias and it makes the estimator more difficult to analyze from the statistical point of view. However, the first step estimator, as expected, shows a bad performance when compared against both the two step backfitting algorithm and the profile least-squares estimator.The authors acknowledge fi nancial support from the Programa Estatal de Fomento de la Investigación Cien ica y Técnica de Excelencia/ Spanish Ministery of Economy and Competitiveness. Ref. ECO2013-48326-C2-2-P

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

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

Differencing techniques in semi-parametric panel data varying coefficient models with fixed effects: a Monte Carlo study.

Recently, some new techniques have been proposed for the estimation of semi-parametric fixed effects varying coefficient panel data models. These new techniques fall within the class of the so-called differencing estimators. In particular, we consider first-differences and within local linear regression estimators. Analyzing their asymptotic properties it turns out that, keeping the same order of magnitude for the bias term, these estimators exhibit different asymptotic bounds for the variance. In both cases, the consequences are suboptimal non-parametric rates of convergence. In order to solve this problem, by exploiting the additive structure of this model, a one-step backfitting algorithm is proposed. Under fairly general conditions, it turns out that the resulting estimators show optimal rates of convergence and exhibit the oracle efficiency property. Since both estimators are asymptotically equivalent, it is of interest to analyze their behavior in small sample sizes. In a fully parametric context, it is well-known that, under strict exogeneity assumptions the performance of both first-differences and within estimators is going to depend on the stochastic structure of the idiosyncratic random errors. However, in the non-parametric setting, apart from the previous issues other factors such as dimensionality or sample size are of great interest. In particular, we would be interested in learning about their relative average mean square error under different scenarios. The simulation results basically confirm the theoretical findings for both local linear regression and one-step backfitting estimators. However, we have found out that within estimators are rather sensitive to the size of number of time observations

Constrained nonparametric regression

Doctorat - UCL

Estimating the Time-of-Day Electricity Demand by Using the Constrained Smoothing Spline Estimator

The study of the time-of-day electricity demand motivates the introduction of a new class of nonparametric estimators: the constrained smoothing spline estimator. We compare the results obtained with this estimator against the classical Fourier and smoothing splines estimates.

An efficient marginal integration estimator of a semiparametric additive modelling

In this paper we introduce estimators for the nonparametric and the finite dimensional components of a partially additive model. In a first step the parametric part is estimated through an instrumental variable method. Then the nonparametric additive components are estimated by inserting the preliminary marginal integration estimator in a one step backfitting algorithm. The resulting estimators are efficient in the sense that it has the same asymptotic bias and variance as if the parametric and the other nonparametric components were known.Semiparametric additive model Root-n consistent semiparametric estimator Marginal integration techniques

A projection based approach for interactive fixed effects panel data models

This paper presents a new approach to estimation and inference in panel data models with interactive fixed effects, where the unobserved factor loadings are allowed to be correlated with the regressors. A distinctive feature of the proposed approach is to assume a nonparametric specification for the factor loadings, that allows us to partial out the interactive effects using sieve basis functions to estimate the slope parameters directly. The new estimator adopts the well-known partial least squares form, and its $\sqrt{NT}$-consistency and asymptotic normality are shown. Later, the common factors are estimated using principal component analysis (PCA), and the corresponding convergence rates are obtained. A Monte Carlo study indicates good performance in terms of mean squared error. We apply our methodology to analyze the determinants of growth rates in OECD countries