Journal of Econometrics 59 (1993) l-4. North-Holland

Editors’ introduction

The econometrics of panels and pseudo panels

Carlo Carraro Universitri di Udine. 33100 Udine, Italy

Franc0 Peracchi New York University, New York, NY 10003, USA

Guglielmo Weber IGIER. 20090 Opera, Milan, Italy

This collection of papers grew out of a three-day Conference on Panels and Pseudo Panels, held in Venice (Italy) in late October 1990. The conference was organized by CIDE (Consorzio Interuniversitario di Econometria) in conjunc- tion with GRETA (Gruppi di Ricerca di Economia Teorica e Applicata).

The papers in this volume can be divided into three groups. The first group deals with estimation and inference methods for genuine panels. The second group examines aspects of estimating linear and nonlinear models on repeated cross-sections and pseudo panels of cohort averages, while the third group of papers deals with some aspects of modelling duration data.

The first paper, by Christian Gourieroux and Alain Monfort, surveys recent developments in simulation-based inference, with special reference to panel data applications. The role of these methods is to approximate objective functions or estimating equations where multidimensional integrals appear for various rea- sons, such as transformations of latent variable models into observation models, missing data, random effects, heterogeneity, etc. Since quadrature methods for evaluating integrals are only tractable for very small dimensions, simulation methods based on random sampling from the distribution of the unobservables

Correspondence to: Franc0 Peracchi, Department of Economics, New York University, 269 Mercer Street, New York, NY 10003, USA.

0304-4076/93/SO6.00 0 1993-Elsevier Science. Publishers B.V. All rights reserved

2 C. Carraro et al.. Editors’ introduction

provide an attractive alternative. Gourieroux and Monfort consider the relative advantages of three estimation methods: simulated generalized method of mo- ments (simulated GMM), simulated maximum likelihood (simulated ML), and simulated pseudo ML, and establish their consistency and asymptotic normality under broad conditions. Simulated GMM and pseudo ML are particularly attractive, for they are consistent and asymptotically normal even if the number of simulations is fixed.

The next paper, by Bo Honor&, presents orthogonality conditions that can be used to construct GMM estimators for dynamic panel data Tobit models with fixed effects. It is well-known that in the case of nonlinear panel data models, the method of ML does not generally give consistent estimates of the parameters of interest, due to an incidental parameter problem. The method proposed by Honor6 exploits the fact that differences of independent and identically distrib- uted random variables are symmetrically distributed. It is this symmetry that leads to orthogonality conditions based on trimmed values of the response variable. The resulting GMM estimator is consistent if the orthogonality condi- tions are satisfied at a unique point in the parameter space. The results of a small Monte Carlo experiment indicate that the proposed estimator dominates ML in terms of mean squared error (MSE) if the coefficient on the dependent variables is the only parameter of interest, while ML may be preferable when this coefficient is a nuisance parameter. In the concluding remarks, Honor6 indicates a number of extensions of his approach, such as vector autoregressive models.

The paper by Hsiao, Appelbe, and Dineen presents a framework that unifies several single-equation linear panel data models. In this framework, some of the model coefficients are treated as fixed, although perhaps different for each individual, and others are treated as random in the cross-section dimension. Distributional assumptions on the random coefficients may be viewed as Bayesian priors. By combining this prior information with a conditional Gaus- sian likelihood for the response variable, the authors derive posterior distribu- tions for the models parameters, and show how some popular estimators (e.g., the generalized least squares estimator for the variance component model, Swamy’s random coefficients model estimator, etc.) can be viewed as Bayes estimators. They also discuss ways of generalizing from single-equation to simultaneous equations. An empirical application to long distance telephone service data in Canada provides an illustration of their methodology.

Manuel Arellano considers specification tests for linear panel data models where the unobservable individual effects are potentially correlated with the included covariates. He shows that a number of widely used specification tests can be derived within a unified framework as Wald tests in an extended model estimated by ordinary least squares. This framework allows a straightforward generalization of the tests to arbitrary heteroskedasticity and autocorrelation in the response variable. It also suggests a simple estimator that exploits prior

C. Carraro et al.. Editors’ introduction 3

knowledge about the nature of the correlation between the individual effects and the included covariates.

The next set of three papers deals with repeated cross-sections (RCS) and pseudo panels of cohort averages. In many countries, panel data are not available. Even when they are, they may be inferior to existing cross-sections in terms of sample size, attrition problems, and data quality. Cohort aggregation techniques have also been advocated to correct for measurement error problems in genuine panels, with year-cohort dummies used as instruments.

The paper by Robert Moffitt studies the nature of the restrictions that are necessary for consistent estimation of a class of dynamic models applied to RCS data. This class includes both linear and certain nonlinear models, with and without fixed effects. The critical problem of dynamic models applied to RCS is the unobservability of past and future values of the response variable and the covariates for the same individual. The estimators proposed by Moffitt are instrumental variables (IV) estimators that use functions of time and of broadly defined cohorts as instruments. An application to estimating the parameters of a Markov process for female labor force participation concludes the paper.

Grouping data to produce pseudo panels of cohort averages causes inconsist- ency of the standard within-group estimator, because of a measurement error problem. The nature of the asymptotic argument used to evaluate alternative estimators is also important.

The paper by Marno Verbeek and Theo Nijman considers the case when both the number of observations per cohort and the number of time periods are fixed, but the number of cohorts tends to infinity. They propose a class of estimators for linear fixed effects models, that contains Deaton’s original estimator as a special case. Deaton’s estimator is essentially a within-group estimator, where the moment matrices are adjusted by entirely eliminating the (estimated) measurement error variance. Verbeek and Nijman show that this leads to inconsistent estimates when the number of time periods T is fixed. The consis- tent estimator eliminates only a fraction (T - 1)/T of the measurement error variance. Since the choice of how much to eliminate also affects the variance of an estimator, a trade-off between variance and asymptotic bias arises. Verbeek and Nijman study this trade-off using an asymptotic MSE criterion, and show that it may be optimal to eliminate less than (T - 1)/T of the measurement error variance, since the implied bias is offset by a smaller variance.

The paper by Blundell, Meghir, and Neves provides an example of how to use RCS to estimate an intertemporal model of consumption and labor supply without imposing additive separability between consumption and hours of work, while allowing for uncertainty and corner solutions. The dynamic opti- mization problem is broken down in two stages, where the upper stage corre- sponds to the Euler equations that characterize the intertemporal allocation of consumption, and the lower stage describes the within-period trade-off between consumption and hours of work. Since the lower stage involves only decision

4 C. Carraro et al., Editors’ introduction

variables relating to one period alone, estimation on this case can be carried out using individual data, whereas upper stage equations require taking cohort averages. Instrumental variables methods are used to estimate the relevant model parameters at each stage. Their empirical application provides strong evidence of intertemporal substitution in the labor supply of married women, and of variation of the response to anticipated changes in wages over the life cycle.

The last two papers in this volume deal with aspects of modelling duration data. In their paper, Masako Kurosawa and Steve Pudney present a method for analyzing both the timing and the magnitude of events in a continuous time panel. Their data consist of a panel of negotiated wage settlements between UK bargaining groups over the period 1950 to 1973. Their model consists of one equation for the contract length and one for the wage change, conditional on the occurrence and timing of the settlement. Contract duration is modelled using a proportional hazard specification with time-varying covariates. The wage equation includes current and lagged duration and lagged wage changes as covariates. Since both equations include fixed effects for the bargaining groups, it is possible to distinguish between true duration dependence and heteroge- neity. After removing the fixed effects through a difference transformation, each equation is estimated by IV methods. The results presented in the paper show substantial effects of income policies on the frequency as well as the size of negotiated wage changes. Further, income policies appear to be more effective in moderating rather than delaying wage increases.

The paper by Nicola Torelli and Ugo Trivellato addresses the issue of how to model unemployment duration data when the use of retrospective questions leads to inaccurately measured job-search spells. The paper focuses on heaping effects, that is, abnormal concentration of response at certain durations. A model for the heaping effect is presented, and its implications for estimating the parameters of a proportional hazard specification are explored. As an empirical illustration, the paper presents results based on the Italian Labor Force Survey. The authors generate a short panel by matching individuals across two adjacent surveys. Their results indicate that, at least for some specification, ignoring heaping can lead to incorrect inference.