Panel Models with Interactive Effects

The multiplication of individual specific effects, λ˜ i, and time-specific effects, f ˜ t, λ˜ i f ˜ t, provides a more general formulation than the traditionally used additive form to capture the unobserved heterogeneity in panel data modeling. It is also a useful approach for dimension reduction or for modeling cross-section dependence. However, λ˜ i and f ˜ t are unobservable. We explore the implications for econometric modeling under various formulations of the interactive effects models and suggest a quasi-likelihood approach as a common framework to study issues of estimation and statistical inference when regressors are either strictly exogenous or predetermined and under different combinations of the data size of cross-sectional dimension, N, and time series dimensions, T. We also review some popular estimation methods in light of the quasi-likelihood approach. Monte Carlo studies are conducted to highlight the issues involved