Chapter 4Tests on Error Component Models

The double dimensionality of panel data allows for much richer specifications than simple cross sections or time series. This is both a blessing and a curse, given how much more complicated the specification may become. In fact, all possible features from either cross sections or time series, like distance‐decaying correlation in – respectively – space or time, can coexist with individual (time), time‐(individual‐) invariant heterogeneity. Moreover, diagnostic tests will usually have a hard time distinguishing between different forms of persistence along the same dimension unless explicitly designed to take the “other” effect into account.

The specification problem of panel models is typically associated with the presence or absence of individual effects, i.e., with the need to account for unobserved heterogeneity. Given that in the vast majority of cases it will be inappropriate to rule out individual heterogeneity altogether, the related issue emerges of whether it is safe to assume that the latter is uncorrelated with the explanatory variables (and therefore to proceed in a random effects framework) or rather to proceed estimating out (transforming out) the individual effects in a fixed effects fashion. Hence, tests for individual effects under either of the two approaches and Hausman‐type tests for determining which one is appropriate are among the most popular diagnostic procedures in this field.

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