The gravity model contains two sets of fixed effects that grow equally with the sample size. The incidental parameters problem, if there is one, is accommodated by using a conditional estimator. Fernandez-Val and Weidner (2016) 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,yi,t∗=αi+γt+β′xi,t,i=1,…,n;t=1,…,T,
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 formɛyi,t∗=αiγt+β′xi,t+ɛi,t
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. Boneva and Linton (2017) extend the model to allow multiple common latent factors.View chapterPurchase book