Re: [Gretl-users] Question regarding the HIP function

On Wed, 19 Oct 2016, Juehui Shi wrote: Thanks, Prof. Cottrell. > > Professors, I have one additional question. > > Although the coefficient estimates of HIP match those of Stata IV Probit > exactly, I have found that the endogeneity test (Wald) result is a little > bit different. For example, the HIP give me Wald (t = 4.06864, p = > 0.0437), > but the Stata gives me Wald (t = 3.68, p = 0.0551). My sample size N = > 2204. Cragg-Donald shows 107.096 and both AR and Wald tests reject the > null > of weak instruments. > > As shown, this is a delicate situation. My question is that should I > reject > or not to reject the null of exogeneity in this case? and What might > attribute to the difference in the test? Thanks. > Stata and HIP compute the endogeneity test in a slightly different way, that is equivalent asymptotically but will give different results in finite samples. What I would do if I were you is keep in mind what a test statistic ultimately is: it's a number that should be "small" in "most" cases if your hypothesis was true. The p-value is just a rough indicator of how "small" your number is. In your case, your number is right on the threshold that we conventionally use to make a decision and even small modifications in irrelevant details can push your test either side of the boundary. This means that any decision you make should be considered as tentative and provisional. However, the hypothesis is in this case that your regressor is exogenous. Fortunately, the consequence of making the wrong decision are rather benign, because your IV estimates would be consistent anyway (assuming no other problems, of course). Using an IV estimator when the null is true only implies that your procedure could be a little inefficient compared to ordinary, non-IV probit; but OTOH, why care? In the end, you're just trading some (possible) inefficiency for the sake of robustness. HTH, ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------