Unobservable factors and panel data sets

Abstract

This thesis addresses statistical issues related to linear panel data models with the joint occurrence of unobserved heterogeneity and measurement errors-in-variables. Specifically, it is concerned with hypothesis testing and estimation techniques in a static and in a dynamic framework respectively.

Chapter 1 presents a methodological revision of the use of the Hausman test (Hausman, 1978) for correlated effects with panel data.  The consequence of deviations from the basic assumptions underlying the construction of the Hausman statistic are investigated. In particular, the distribution of the Hausman statistic in cases of misspecification of the variance-covariance matrix of the errors is examined. It is shown that the size distortion may be serious.  An alternative robust formulation of the test with panel data, based on the use of an auxiliary regression, is proposed. This test, which we call the Hausman Robust  or HR-test gives correct significance levels in common cases of misspecification of the variance-covariance matrix of the errors and has a power comparable to the standard Hausman test when no evidence of misspecification is present. It can be easily implemented using a standard econometric package, e.g. Stata.

In Chapter 2 this robust version of the Hausman test (suitably tailored) is used to compare different pairs of panel data estimators in a particular sequence. The resulting two-step testing procedure is intended to distinguish between an endogeneity problem caused by correlation between repressors and individual effects, and an endogeneity problem due to measurement errors.  The statistical performance of the sequential test is assessed using simulated data.  This methodological is then applied to an empirical job-search matching model to investigate the effects of measurement errors and unobserved heterogeneity that, as is well-known, contaminate two of the variables extensively used in labour market research, namely the stock of unemployed and the stock of vacancies. The economic implications of the inference results using the proposed methodology are compared with those produced by a possible traditional analysis.

Chapter 3 presents consistent estimators (which differ in terms of efficiency) for an autoregressive (stationary) model of panel data that superimposes the errors-in-variables problem and the unobserved heterogeneity issue on a dynamic framework. Moreover, the measurement errors are not ‘classical’ (i.e., uncorrelated with everything else in the model included their own past values) but are assumed to have a more complicated structure. The analysis of an example demonstrates the empirical relevance of this modelling. Furthermore, because the cross sectional units in the panel data set considered have a spatial connotation (UK counties), spatial features are also incorporated in the econometric analysis. The resulting empirical model is a spatio-temporal panel data model with unobserved heterogeneity and systematic measurement errors.

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