In a regression model for count data, with a dependent variable yi taking non-negative integer values, suppose that yi = ????xi + ui, where xi ≥ 0 is a non-stochastic explanatory variable and E(ui) = 0. Assume that yi is Poisson-distributed, so that p(yi

|xi) =

????yi i e −????i yi!

where ????i = E(yi) = ????xi.

(a) Given a random sample of n pairs (yi, xi), what is the maximum likelihood estimator of ?????

(b) Compare the ML estimator of ???? with the OLS regression of yi on xi. Show that both estimators are unbiased, but that the MLE has smaller variance.