Panel data from time series of cross-sections

Abstract

In many countries, there are few or no panel data, but there exists a series of independent cross-sections. For example, in the United Kingdom, there are no panel data on consumers' expenditure or on household labor supply, but there are several large household surveys carried out every year. Samples for these surveys are drawn anew each year, so that it is impossible to track individual households over time. This paper considers the possibility of tracking ‘cohorts’ through such data. A ‘cohort’ is defined as a group with fixed membership, individuals of which can be identified as they show up in the surveys. The most obvious example is an age cohort, e.g. all males born between 1945 and 1950, but there are other possibilities (Korean war veterans or founding members of the Econometric Society). Consider any economic relationship of interest that is linear in parameters (but not necessarily in variables). Corresponding to individual behavior, there will exist a cohort version of the relationship of the same form, but with cohort means replacing individual observations. If there are additive individual fixed effects, there will be corresponding additive cohort fixed effects. Further, the sample cohort means from the surveys are consistent but error-ridden estimates of the true cohort means. Hence, provided errors-in-variables techniques are used (and error variances and covariances can be estimated from the surveys), the sample cohort means can be used as panel data for estimating the relationship. Such data are immune to attrition bias and can be extended for long time periods. There is also evidence to suggest that the errors in variables problems may be just as severe for genuine panel data; in the created panels considered here, the problem is controllable. The paper discusses appropriate errors in variables estimators, with and without fixed effects.