consider a similar case with more general data observation mechanism—two cases considered are a probit binary response model and a Poisson regression. Both begin with an index function model,
where for the probit model, yi,t = 1[yi,t⁎ + ɛi,t > 0] while in the Poisson model, E[yi,t | xi,t] = exp(yi,t⁎). The model extension allows both i and t to grow, such that N/T converges to a constant. The authors focus on bias-corrected unconditional estimators. This enables estimation of partial effects as well as coefficients. Consistent with Greene’s (2004a, 2005) results, they find that the bias of estimators of APEs is much smaller than that of the coefficients themselves. For their case, with biases diminishing in both n and T simultaneously, they find the biases in the partial effects to be negligible.
Interactive effects of the form
were examined by Bai (2009). Chen et al. (2014) treat this as a fixed effects model, and derived a two-step maximum likelihood estimator for probit and Poisson regression models.
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