Validating Approximate Slope Homogeneity in Large Panels

Abstract: Statistical inference for large data panels is omnipresent in modern economic applications. An important benefit of panel analysis is the possibility to reduce noise and thus to guarantee stable inference by intersectional pooling. However, it is wellknown that pooling can lead to a biased analysis if individual heterogeneity is too strong. In classical linear panel models, this trade-off concerns the homogeneity of slope parameters, and a large body of tests has been developed to validate this assumption. Yet, such tests can detect inconsiderable deviations from slope homogeneity, discouraging pooling, even when practically beneficial. In order to permit a more pragmatic analysis, which allows pooling when individual heterogeneity is sufficiently small, we present in this paper the concept of approximate slope homogeneity. We develop an asymptotic level $\alpha$ test for this hypothesis, that is uniformly consistent against classes of local alternatives. In contrast to existing methods, which focus on exact slope homogeneity and are usually sensitive to dependence in the data, the proposed test statistic is (asymptotically) pivotal and applicable under simultaneous intersectional and temporal dependence. Moreover, it can accommodate the realistic case of panels with large intersections. A simulation study and a data example underline the usefulness of our approach.