Varying Coefficient Panel Data Models Research Articles

Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England

The contribution of this paper is twofold. Firstly, it introduces novel regression models that combine two important areas of the methodological development in panel data analysis, namely a varying coefficient specification and spatial error dependence. The former allows relatively flexible nonlinear interactions; the latter enables spatial correlations of the disturbance and thus differ significantly from the other random effect models in the literature. To estimate the model, a new estimation procedure is established that can be viewed as a generalization of the quasi-maximum likelihood method for a spatial panel data model to the well-known conditional local likelihood procedure. Novel inference methods, particularly variable selection and hypothesis testing of the parameter constancy, are introduced and are shown to be effective under the complex spatial error dependence. Equally importantly, this paper makes a substantial contribution to the understanding of financing and expenditure for health and social care. In particular, we empirically analyze and explain the effects of political ideologies on the local fiscal policy in England, especially the expenditure on mental health services.

Quasi Maximum Likelihood for MESS Varying Coefficient Panel Data Models with Fixed Effects

The study of spatial econometrics has developed rapidly and has found wide applications in many different scientific fields, such as demography, epidemiology, regional economics, and psychology. With the deepening of research, some scholars find that there are some model specifications in spatial econometrics, such as spatial autoregressive (SAR) model and matrix exponential spatial specification (MESS), which cannot be nested within each other. Compared with the common SAR models, the MESS models have computational advantages because it eliminates the need for logarithmic determinant calculation in maximum likelihood estimation and Bayesian estimation. Meanwhile, MESS models have theoretical advantages. However, the theoretical research and application of MESS models have not been promoted vigorously. Therefore, the study of MESS model theory has practical significance. This paper studies the quasi maximum likelihood estimation for matrix exponential spatial specification (MESS) varying coefficient panel data models with fixed effects. It is shown that the estimators of model parameters and function coefficients satisfy the consistency and asymptotic normality to make a further supplement for the theoretical study of MESS model.

Semiparametric inferences for panel data models with fixed effects via nearest neighbor difference transformation

In this paper, we propose a simple method to estimate a partially varying-coefficient panel data model with fixed effects. By taking difference upon the nearest neighbor of the smoothing variables to remove the fixed effects, we employ the profile least squares method and local linear fitting to estimate the parametric and nonparametric parts, respectively. Moreover, a functional form specification test and a nonparametric Hausman type test are constructed and their asymptotic properties are derived. Monte Carlo simulations are conducted to examine the finite sample performance of our estimators and test statistics.

Fitting partially linear functional-coefficient panel-data models with Stata

In this article, we describe the implementation of fitting partially linear functional-coefficient panel models with fixed effects proposed by An, Hsiao, and Li [2016, Semiparametric estimation of partially linear varying coefficient panel data models in Essays in Honor of Aman Ullah ( Advances in Econometrics, Volume 36)] and Zhang and Zhou (Forthcoming, Econometric Reviews). Three new commands xtplfc, ivxtplfc, and xtdplfc are introduced and illustrated through Monte Carlo simulations to exemplify the effectiveness of these estimators.

Network-Based Clustering for Varying Coefficient Panel Data Models

In this article, we introduce a novel varying-coefficient panel-data model with locally stationary regressors and unknown group structure, in which the number of groups and the group membership are left unspecified. We develop a triple-localization approach to estimate the unknown subject-specific coefficient functions and then identify the latent group structure via community detection. To improve the efficiency of the first-stage estimator, we further propose a two-stage estimation method that enables the estimator to achieve optimal rates of convergence. In the theoretical part of the article, we derive the asymptotic theory of the resultant estimators. In the empirical part, we present several simulated examples together with an analysis of real data to illustrate the finite-sample performance of the proposed method.

Empirical likelihood based inference for varying coefficient panel data models with fixed effect

In this paper, the empirical likelihood-based inference is investigated with varying coefficient panel data models with fixed effect. A naive empirical likelihood ratio is firstly proposed after the fixed effect is corrected. The maximum empirical likelihood estimators for the coefficient functions are derived as well as their asymptotic properties. Wilk’s phenomenon of this naive empirical likelihood ratio is proven under a undersmoothing assumption. To avoid the requisition of undersmoothing and perform an efficient inference, a residual-adjusted empirical likelihood ratio is further suggested and shown as having a standard chi-square limit distribution, by which the confidence regions of the coefficient functions are constructed. Another estimators for the coefficient functions, together with their asymptotic properties, are considered by maximizing the residual-adjusted empirical log-likelihood function under an optimal bandwidth. The performances of these proposed estimators and confidence regions are assessed through numerical simulations and a real data analysis.

Estimation in single-index varying-coefficient panel data model

In this paper, we study the single-index varying-coefficient panel data model. Combining the refined minimum average variance estimation (RMAVE) method with the local linear regression, we estimate the parameters in single index and link function, and explain the steps of the iterative algorithm. Under certain regularity conditions, the asymptotic properties of the estimators of the parameters and link functions are derived. Finally, numerical simulations are presented and our model is shown to perform better than the single-index panel data model in a real-data example.

Model detection and estimation for varying coefficient panel data models with fixed effects

In this paper, we study the model detection and estimation for varying coefficient panel data models with fixed effects. We first propose a data transformation approach to eliminate fixed effects. Then, using the basis function approximations and the group SCAD penalty, we develop a combined penalization procedure to select the significant covariates, detect the true structure of the model, i.e., identify the nonzero constant coefficients and the varying coefficients, and estimate the unknown regression coefficients simultaneously. Under some mild conditions, we show that the proposed procedure can identify the true model structure consistently, and the penalized estimators have the oracle properties. At last, we illustrate the finite sample performance of the proposed methods with some simulation studies and a real data application.

Varying Coefficient Panel Data Model with Interactive Fixed Effects

In this paper, we propose a varying coefficient panel data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function by B-spline, and propose a robust nonlinear iteration scheme based on the least squares method to estimate the coefficient functions of interest. We also establish the asymptotic theory of the resulting estimators under certain regularity assumptions, including the consistency, the convergence rate and the asymptotic distribution. Furthermore, we develop a least squares dummy variable method to study an important special case of the proposed model: the varying coefficient panel data model with additive fixed effects. To construct the pointwise confidence intervals for the coefficient functions, a residual-based block bootstrap method is proposed to reduce the computational burden as well as to avoid the accumulative errors. Simulation studies and a real data analysis are also carried out to assess the performance of our proposed methods.

Efficient nonparametric three-stage estimation of fixed effects varying coefficient panel data models

Efficient nonparametric three-stage estimation of fixed effects varying coefficient panel data models

Varying-Coefficient Panel Data Models With Nonstationarity and Partially Observed Factor Structure

In this article, we study a varying-coefficient panel data model with both nonstationarity and partially observed factor structure. Two approaches are proposed. The first approach proposed in the main text considers a sieve based method to estimate the unknown coefficients as well as the factors and loading functions simultaneously, while the second approach proposed in the online supplementary document involving the principal component analysis provides an alternative estimation method. We establish asymptotic properties for them, compare the asymptotic efficiency of the two estimation methods and examine the theoretical findings through extensive Monte Carlo simulations. In an empirical study, we use our newly proposed model and the first method to study the returns to scale of large U.S. commercial banks, where some overlooked modeling issues in the literature of production econometrics are addressed. Supplementary materials for this article are available online.

Estimation for varying coefficient panel data model with cross-sectional dependence

This paper describes a method for estimation and inference with a nonparametric varying coefficients panel data model that allows for cross-sectional dependence and heteroscedasticity, wherein the time series length T is larger than the cross-sectional size N. We first eliminate fixed effects by taking the cross-sectional average, and then use a local linear approach to obtain the initial estimator of the unknown coefficient functions. However, the initial estimator ignores the cross-sectional dependence and heteroscedasticity, which will lead to a loss of efficiency. Thus, we propose a weighted local linear method to obtain a more efficient estimator. In the theoretical part of the paper, we derive the asymptotic theory of the resulting estimator. Simulation results and a real data analysis are provided to illustrate the finite sample performance of the proposed method.

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.

Empirical likelihood based inference for a categorical varying-coefficient panel data model with fixed effects

In this paper local empirical likelihood-based inference for nonparametric categorical varying coefficient panel data models with fixed effects under cross-sectional dependence is investigated. First, we show that the naive empirical likelihood ratio is asymptotically standard chi-squared using a nonparametric version of Wilks’ theorem. The ratio is self-scale invariant and the plug-in estimate of the limiting variance is not needed. As a by product, we propose also an empirical maximum likelihood estimator of the categorical varying coefficient model and we obtain the asymptotic distribution of this estimator. We also illustrated the proposed technique in an application that reports estimates of strike activities from 17 OECD countries for the period 1951–85.

Varying-Coefficient Panel Data Models with Partially Observed Factor Structure

In this paper, we study a varying-coefficient panel data model with nonstationarity, wherein a factor structure is adopted to capture different effects of time invariant variables over time. The methodology employed in this paper fills a gap of dealing with the mixed I(1)/I(0) regressors and factors in the literature. For the purpose of comparison, we consider both of the scenarios where the factors are observable and unobservable, respectively. We then propose semiparametric estimators and establish the corresponding theory. We evaluate the finite-sample performance of proposed estimation theory through extensive Monte Carlo simulations. In an empirical study, we use our newly proposed model and method to study the returns to scale of large commercial banks in the U.S.. Some overlooked modelling issues in the literature of production econometrics are addressed.

Empirical likelihood based inference for fixed effects varying coefficient panel data models

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 likelihood 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.

A varying-coefficient panel data model with fixed effects: Theory and an application to US commercial banks

In this paper, we propose a semiparametric varying-coefficient categorical panel data model in which covariates (variables affecting the coefficients) are purely categorical. This model has two features: first, fixed effects are included to allow for correlation between individual unobserved heterogeneity and the regressors; second, it allows for cross-sectional dependence through a general spatial error dependence structure. We derive a semiparametric estimator for our model by using a modified within transformation, and then show the asymptotic and finite properties for this estimator under large N and T. The Monte Carlo study shows that our methodology works well for both large N and T, and large N and small T cases. Finally, we illustrate our model by analyzing the effects of state-level banking regulations on the returns to scale of commercial banks in the US. Our empirical results suggest that returns to scale is higher in more regulated states than in less regulated states.

Cross-country output convergence and growth: Evidence from varying coefficient nonparametric method

This article uses a nonparametric varying coefficient panel data model to study the convergence of real GDP per capita among 120 world economies for the sample period of 1980–2010. The estimates show that the indirect contribution of initial income via the control variables is important. The mediating effect of control variables to affect growth is positive. The conditional speed of convergence is larger than the absolute counterpart at all levels of initial income. The convergence hypothesis does not hold for economies with extremely low level of development. The conclusion is robust for regional subsamples of Europe, Asia, Latin America and Africa.

Varying coefficient panel data model in the presence of endogenous selectivity and fixed effects

This paper considers a flexible panel data sample selection model in which (i) the outcome equation is permitted to take a semiparametric, varying coefficient form to capture potential parameter heterogeneity in the relationship of interest, (ii) both the outcome and (parametric) selection equations contain unobserved fixed effects and (iii) selection is generalized to a polychotomous case. We propose a two-stage estimator. Given consistent parameter estimates from the selection equation obtained in the first stage, we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time. The selection bias term is then “asymptotically” removed from the equation along with fixed effects using kernel-based weights. The proposed estimator is consistent and asymptotically normal. We showcase our estimator by applying it to study production technologies of US retail credit unions from 2002 to 2006.

A Varying-Coefficient Panel Data Model with Fixed Effects: Theory and an Application to U.S. Commercial Banks

In this paper, we propose a panel data semiparametric varying-coefficient model in which covariates (variables affecting the coefficients) are purely categorical. This model has two features: first, fixed effects are included to allow for correlation between individual unobserved heterogeneity and the regressors; second, it allows for cross-sectional dependence through a general spatial error dependence structure. We derive a semiparametric estimator for our model by using a modified within transformation, and then show the asymptotic and finite properties for this estimator. Finally, we illustrate our model by analyzing the effects of state-level banking regulations on the returns to scale of commercial banks in the U.S.. Our empirical results suggest that returns to scale is higher in more regulated states than in less regulated states.