  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.
