The multidimensional Mundlak estimator

Mundlak (1978) shows that the fixed effects estimator is equivalent to the random effects estimator in the one-way error component model once the random individual effects are modeled as a linear function of all the averaged regressors over time. In the spirit of Mundlak, this paper shows that this result also holds for the multidimensional error component model. This is a generalization of Baltagi (2023) from the two-way Mundlak model to higher order multidimensional error components model, see Balazsi et al. (2024a) for the multidimensional fixed effects model and Balazsi et al. (2024b) for the multidimensional random effects model. The F test suggested by Mundlak (1978) to test for this correlation between the random effects and the regressors generate Hausman (1978) type tests that are easily generalizable to the multi-dimensional Mundlak regression.