This article develops tests of covariance restrictions after estimating by three-stage least squares a dynamic random effects model from panel data. The asymptotic distribution of covariance matrix estimates under nonnormality is obtained. It is shown how minimum chi-square tests for interesting covariance restrictions can be calculated from a generalized linear regression involving the sample autocovariances and dummy variables. Asymptotic efficiency exploiting covariance restrictions can also be attained using a generalized least squares estimator.

We study the identification of panel models with linear individual-specific coefficients, when T is fixed. We show identification of the variance of the effects under conditional uncorrelatedness. Identification requires restricted dependence of errors, reflecting a trade-off between heterogeneity and error dynamics. We show identification of the density of individual effects when errors follow an ARMA process under conditional independence. We discuss GMM estimation of moments of effects and errors, and introduce a simple density estimator of a slope effect in a special case. As an application we estimate the effect that a mother smokes during pregnancy on child’s birth weight.

We develop an empirical model of labour supply that is consistent with on-the-job search and which is identified and estimated by combining two data sets: the U.K. Family Expenditure Survey which contains information on income and expenditure and the U.K. Labour Force Survey, which has data on hours and job search behaviour. We provide statistical evidence on the compatibility of the two samples for the purposes of estimating our model. We find that search has a direct negative effect on hours of work and we establish a strong positive effect of wages on hours.

This paper presents specification tests that are applicable after estimating a dynamic model from panel data by the generalized method of moments (GMM), and studies the practical performance of these procedures using both generated and real data. Our GMM estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no strictly exogenous variables. We propose a test of serial correlation based on the GMM residuals and compare this with Sargan tests of over-identifying restrictions and Hausman specification tests.