Seung C. Ahn

Efficient estimation of models for dynamic panel data

Abstract In this paper we consider a dynamic model for panel data. We show that, under standard assumptions, there are more moment conditions than are currently exploited in the literature. Some of these are linear, but others are quadratic, so that nonlinear GMM is required. We also show that exogenous regressors generate a larger number of relevant moment conditions in a dynamic model than they would in a static model.

Eigenvalue Ratio Test for the Number of Factors

This paper proposes two new estimators for determining the number of factors (r) in static approximate factor models. We exploit the well-known fact that the r largest eigenvalues of the variance matrix of N response variables grow unboundedly as N increases, while the other eigenvalues remain bounded. The new estimators are obtained simply by maximizing the ratio of two adjacent eigenvalues. Our simulation results provide promising evidence for the two estimators.

GMM estimation of linear panel data models with time-varying individual effects

Abstract This paper considers models for panel data in which the individual effects vary over time. The temporal pattern of variation is arbitrary, but it is the same for all individuals. The model thus allows one to control for time-varying unobservables that are faced by all individuals (e.g., macro-economic events) and to which individuals may respond differently. A generalized within estimator is consistent under strong assumptions on the errors, but it is dominated by a generalized method of moments estimator. This is perhaps surprising, because the generalized within estimator is the MLE under normality. The efficiency gains from imposing second-moment error assumptions are evaluated; they are substantial when the regressors and effects are weakly correlated.

Efficient estimation of dynamic panel data models: Alternative assumptions and simplified estimation

Abstract This paper considers the estimation of dynamic models for panel data. It shows how to count and express the moment conditions implied by a variety of covariance restrictions. These conditions can be imposed in a GMM framework. Many of the moment conditions are nonlinear in the parameters. We derive a simple linearized estimator that is asymptotically as efficient as the nonlinear GMM estimator, and convenient tests of the validity of the nonlinear restrictions.

Efficient estimation of panel data models with strictly exogenous explanatory variables

Abstract With panel data, exogeneity assumptions imply many more moment conditions than standard estimators use. However, many of the moment conditions may be redundant, in the sense that they do not increase efficiency; if so, we may establish the standard estimators’ efficiency. We prove efficiency results for GLS in a model with unrestricted error covariance matrix, and for 3SLS in models where regressors and errors are correlated, such as the Hausman–Taylor model. For models with correlation between regressors and errors, and with unrestricted error covariance structure, we provide a simple estimator based on a GLS generalization of deviations from means.

A reformulation of the Hausman test for regression models with pooled cross-section-time-series data

Abstract A Hausman test has been typically used to determine the consistency of the GLS estimator in static models with pooled cross-section-time-series data. Based on a GMM approach, we reformulate the Hausman test and find that it incorporates and tests only a limited set of moment restrictions. We also consider an alternative GMM statistic incorporating additional restrictions, which has power toward additional sources of model misspecification. Our Monte Carlo experiments demonstrate that while both the Hausman test and the alternative have good power detecting endogenous regressors, the alternative dominates if coefficients of regressors are nonstationary.

A separability result for GMM estimation, with applications to GLS prediction and conditional moment tests

Generalized method of moments estimates are unaffected by the addition of equal numbers of moment conditions and extra parameters. We prove thisresult and give examples of its use.

ORTHOGONALITY TESTS IN LINEAR MODELS

This paper considers several tests of orthogonality conditions in linear models where stochastic errors may be heteroskedastic or autocorrelated. It is shown that these tests can be performed with Wald statistics obtained from simple auxiliary regressions. Copyright 1997 by Blackwell Publishing Ltd

Major League Baseball Attendance Long-Term Analysis Using Factor Models

Although Major League Baseball has a long history, most studies of attendance have focused on recent years because important explanatory data, such as ticket prices, are often missing for earlier periods. This study fills gaps in the data by analyzing individual team attendance records between 1904 and 2012. If important missing variables are determined using common factors that can influence between-team attendance, the attendance function can be estimated by a panel factor model. Our results indicate that the determinants of fans’ attendance decisions have changed over time. In earlier years (1904-1957), the home team’s win record was the only significant team characteristic influencing attendance. However, in recent years (1958-2012), outcome uncertainty, size, and quality of the stadium, and playing styles have also influenced fan attendance.

Large-N and Large-T Properties of Panel Data Estimators and the Hausman Test

This paper examines the asymptotic properties of the popular within and GLS estimators and the Hausman test for panel data models with both large numbers of cross-section (N) and time-series (T) observations. The model we consider includes the regressors with deterministic trends in mean as well as time invariant regressors. Under general circumstances, we find that the within estimator is as efficient as the GLS estimator. Despite this asymptotic equivalence, however, the Hausman statistic, which is essentially a distance measure between the two estimators, is well defined and asymptotically χ 2-distributed under the random effects assumption. It is also found that the power properties of the Hausman test are sensitive to the size of T and the covariance structure among regressors and unobservable individual effects.