A bivariate count data model for household tourism demand

Households' choice of the number of leisure trips and the total number of overnight stays is empirically studied using Swedish tourism data. A bivariate hurdle approach separating the participation (to travel and stay the night or not) from the quantity (the number of trips and nights) decision is employed. The quantity decision is modelled with a bivariate mixed Poisson lognormal model allowing for both positive as well as negative correlation between count variables. The observed endogenous variables are drawn from a truncated density and estimation is pursued by simulated maximum likelihood. The estimation results indicate a negative correlation between the number of trips and nights. In most cases own price effects are as expected negative, while estimates of cross‐price effects vary between samples. Copyright © 2005 John Wiley & Sons, Ltd.     

Change point estimation in panel data with time-varying individual effects

Existing panel data methods remove unobserved individual effects before change point estimation through data transformations such as first-differencing. In this paper, we show that multiple change points can be consistently estimated in short panels via ordinary least squares. Since no data variation is removed before change point estimation, our method has better small-sample properties compared to first-differencing methods. We also propose two tests that identify whether the change points found by our method originate in the slope parameters or in the covariance of the regressors with individual effects. We illustrate our method via modeling the environmental Kuznets curve and the US house price expectations after the financial crisis.     

Nonparametric estimation and testing of fixed effects panel data models

In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We introduce an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model. Simulations are used to examine the finite sample performance of the proposed estimators and the test statistics.     

Fixed effects instrumental variables estimation in correlated random coefficient panel data models

We provide a set of conditions sufficient for consistency of a general class of fixed effects instrumental variables (FE-IV) estimators in the context of a correlated random coefficient panel data model, where one ignores the presence of individual-specific slopes. We discuss cases where the assumptions are met and violated. Monte Carlo simulations verify that the FE-IV estimator of the population averaged effect performs notably better than other standard estimators, provided a full set of period dummies is included. We also propose a simple test of selection bias in unbalanced panels when we suspect the slopes may vary by individual.     

Robust penalized quantile regression estimation for panel data

This paper investigates a class of penalized quantile regression estimators for panel data. The penalty serves to shrink a vector of individual specific effects toward a common value. The degree of this shrinkage is controlled by a tuning parameter λ$\lambda$. It is shown that the class of estimators is asymptotically unbiased and Gaussian, when the individual effects are drawn from a class of zero-median distribution functions. The tuning parameter, λ$\lambda$, can thus be selected to minimize estimated asymptotic variance. Monte Carlo evidence reveals that the estimator can significantly reduce the variability of the fixed-effect version of the estimator without introducing bias.     

A general framework for frontier estimation with panel data

The main objective of the paper is to present a general framework for estimating production frontier models with panel data. A sample of firms i = 1, ..., N is observed on several time periods t = 1, ... T. In this framework, nonparametric stochastic models for the frontier will be analyzed. The usual parametric formulations of the literature are viewed as particular cases and the convergence of the obtained estimators in this general framework are investigated. Special attention is devoted to the role of N and of T on the speeds of convergence of the obtained estimators. First, a very general model is investigated. In this model almost no restriction is imposed on the structure of the model or of the inefficiencies. This model is estimable from a nonparametric point of view but needs large values of T and of N to obtain reliable estimates of the individual production functions and estimates of the frontier function. Then more specific nonparametric firm effect models are presented. In these cases, only NT must be large to estimate the common production function; but again both large N and T are needed for estimating individual efficiencies and for estimating the frontier. The methods are illustrated through a numerical example with real data.     

Small sample considerations in estimation from panel data

Recent interest in statistical inference for panel data has focused on the problem of unobservable, individual-specific, random effects and the inconsistencies they introduce in estimation when they are correlated with other exogenous variables. Analysis of this problem has always assumed the variance components to be known. In this paper, we re-examine some of these questions in finite samples when the variance components must be estimated. In particular, when the effects are uncorrelated with other explanatory variables, we show that (i) the feasible Gauss-Markov estimator is more efficient than the within groups estimator for all but the fewest degrees of freedom and its variance is never more than 17% above the Cramer-Rao bound, (ii) the asymptotic approximation to the variance of the feasible Gauss-Markov estimator is similarly within 17% of the true variance but remains significantly smaller for moderately large samples sizes, and (iii) more efficient estimators for the variance components do not necessarily yield more efficient feasible Gauss-Markov estimators.     

Estimates of technical inefficiency in stochastic frontier models with panel data: generalized panel jackknife estimation

Estimates of technical inefficiency based on fixed effects estimation of the stochastic frontier model with panel data are biased upward. Previous work has attempted to correct this bias using the bootstrap, but in simulations the bootstrap corrects only part of the bias. The usual panel jackknife is based on the assumption that the bias is of order T ⁻¹ and is similar to the bootstrap. We show that when there is a tie or a near tie for the best firm, the bias is of order T ^−1/2, not T ⁻¹, and this calls for a different form of the jackknife. The generalized panel jackknife is quite successful in removing the bias. However, the resulting estimates have a large variance.     

Minimax estimation for the bounded mean of a bivariate normal distribution

A bivariate normal distribution is considered whose mean lies in an equilateral triangle. We show by a convexity argument that the three point prior having mass 1/3 at each of the edges is least favourable if the length of a side of the equilateral triangle is less than or equal to . Thus the corresponding Bayes estimator is minimax in that case. Numerical studies are given as well.     

Residual‐based IV estimation of dynamic panel data models with fixed effects

In dynamic panel regression, when the variance ratio of individual effects to disturbance is large, the system‐GMM estimator will have large asymptotic variance and poor finite sample performance. To deal with this variance ratio problem, we propose a residual‐based instrumental variables (RIV) estimator, which uses the residual from regressing Δy_i,t?1 on as the instrument for the level equation. The RIV estimator proposed is consistent and asymptotically normal under general assumptions. More importantly, its asymptotic variance is almost unaffected by the variance ratio of individual effects to disturbance. Monte Carlo simulations show that the RIV estimator has better finite sample performance compared to alternative estimators. The RIV estimator generates less finite sample bias than difference‐GMM, system‐GMM, collapsing‐GMM and Level‐IV estimators in most cases. Under RIV estimation, the variance ratio problem is well controlled, and the empirical distribution of its t‐statistic is similar to the standard normal distribution for moderate sample sizes.     

Estimating efficiency effects in a panel data stochastic frontier model

Journal of Productivity Analysis - This paper proposes a panel data based stochastic frontier model which accommodates time-invariant unobserved heterogeneity along with efficiency effects. The...     

Nonparametric dynamic panel data models: Kernel estimation and specification testing

Motivated by the first-differencing method for linear panel data models, we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors. The estimators utilize the additive structure of the first-differenced model—the fact that the two additive components have the same functional form, and the unknown function of interest is implicitly defined as a solution of a Fredholm integral equation of the second kind. We establish the uniform consistency and asymptotic normality of the estimators. We also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the _L2$L_2$ distance of our nonparametric estimates and the parametric estimates under the linear restriction. We derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of Pitman local alternatives, and prove its consistency against global alternatives. Simulations suggest that the proposed estimators and tests perform well for finite samples. We apply our new method to study the relationships among economic growth, the initial economic condition and capital accumulation, and find a significant nonlinear relation between economic growth and the initial economic condition.     

Testing for heteroskedasticity and serial correlation in a random effects panel data model

This paper considers a panel data regression model with heteroskedastic as well as serially correlated disturbances, and derives a joint LM test for homoskedasticity and no first order serial correlation. The restricted model is the standard random individual error component model. It also derives a conditional LM test for homoskedasticity given serial correlation, as well as, a conditional LM test for no first order serial correlation given heteroskedasticity, all in the context of a random effects panel data model. Monte Carlo results show that these tests along with their likelihood ratio alternatives have good size and power under various forms of heteroskedasticity including exponential and quadratic functional forms.     

Bias corrections for two-step fixed effects panel data estimators

This paper introduces large-T bias-corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity. These models include systems of equations with limited dependent variables and unobserved individual effects, and sample selection models with unobserved individual effects. Our two-step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity/selection bias. We then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable. The fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity. Since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem. This problem is exacerbated by the two-step nature of the procedure. As these two-step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large-T bias adjustments to an important class of models. Simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator.     

Quantile regression for dynamic panel data with fixed effects

This paper studies a quantile regression dynamic panel model with fixed effects. Panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors. To reduce the dynamic bias, we suggest the use of the instrumental variables quantile regression method of Chernozhukov and Hansen (2006) along with lagged regressors as instruments. In addition, we describe how to employ the estimated models for prediction. Monte Carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias, and the empirical levels for prediction intervals are very close to nominal levels. Finally, we illustrate the procedures with an application to forecasting output growth rates for 18 OECD countries.     

Individual effects and dynamics in count data models

In this paper we examine the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables. Use of a linear feedback model is proposed. A quasi-differenced GMM estimator is consistent for the parameters in the dynamic model, but when series are highly persistent, there is a problem of weak instrument bias. An estimator is proposed that utilises pre-sample information of the dependent count variable, which is shown in Monte Carlo simulations to possess desirable small sample properties. The models and estimators are applied to data on US patents and R&D expenditure.     

A Lagrange Multiplier test for cross-sectional dependence in a fixed effects panel data model

It is well known that the standard Breusch and Pagan (1980) LM test for cross-equation correlation in a SUR model is not appropriate for testing cross-sectional dependence in panel data models when the number of cross-sectional units (n)$\left(n\right)$ is large and the number of time periods (T)$\left(T\right)$ is small. In fact, a scaled version of this LM test was proposed by Pesaran (2004) and its finite sample bias was corrected by Pesaran et al. (2008). This was done in the context of a heterogeneous panel data model. This paper derives the asymptotic bias of this scaled version of the LM test in the context of a fixed effects homogeneous panel data model. This asymptotic bias is found to be a constant related to n$n$ and T$T$, which suggests a simple bias corrected LM test for the null hypothesis. Additionally, the paper carries out some Monte Carlo experiments to compare the finite sample properties of this proposed test with existing tests for cross-sectional dependence.     

Two tests for strict exogeneity in a correlated random effects panel data Tobit model

This paper presents two tests for strict exogeneity of the covariates in a correlated random effects panel data Tobit model. The tests are applied in an analysis of hours of work of US women. Estimation procedures when a model does not pass a test for strict exogeneity are discussed.     

Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.     

Parameter estimation for a bivariate lifetime distribution in reliability with multivariate extensions

Bivariate lifetime distributions are considered which describe physically motivated dependencies like those proposed by Freund (1961) and Marshall and Olkin (1967a). Such distributions arise in reliability problems with two-component systems. Generalizations of some previous models are investigated and the maximum likelihood estimates for a combined bivariate exponential distribution are given. The case of dependent random censorship is considered in connection with two-component series systems. Some simulations show how censorship affects the parameter estimates.