In a “crazy travelling week” (dixit my daughter), I gave a talk at an IYS 2013 conference organised by Stephen Senn (formerly at Glasgow) and colleagues in the city of Luxembourg, Grand Duché du Luxembourg. I enjoyed very much the morning train trip there as it was a misty morning, with the sun rising over the frosted-white countryside. (I cannot say much about the city of Luxembourg itself though as I only walked the kilometre from the station to the conference hotel and the same way back. There was a huge gap on the plateau due to a river in the middle, which would have been a nice place to run, I presume…)
One of the few talks I attended there was about an econometric model with instrumental variables. In general, and this dates back to my student’s years at ENSAE, I do not get the motivation for the distinction between endogenous and exogenous in econometrics models. Especially in non-parametric models as, if we do not want to make parametric assumptions, we have difficulties in making instead correlation hypotheses… My bent would be to parametrise everything under the suspicion of this everything being correlated with everything. The instrumental variables econometricians seem so fond of appear to me like magical beings, since we have to know they are instrumental. And because they seem to allow to always come back to a linear setting, by eliminating the non-linear parts. Sounds like a “more for less” free-lunch deal. (Any pointer would be appreciated.) The speaker there actually acknowledged (verbatim) that they are indeed magical and that they cannot be justified by mathematics or statistics. A voodoo part of econometrics then?!
A second talk that left me perplexed was about a generalised finite mixture model. The model sounded like a mixture along time of individuals, ie a sort of clustering of longitudinal data. It looked like it should be easier to estimate than usual mixtures of regressions because an individual contributed to the same regression line for all the times when it was observed. The talk was uninspiring as it missed connections to EM and to Bayesian solutions, focussing instead on a gradient method that sounded inappropriate for a multimodal likelihood. (Funny enough, the choice in the number of regressions was done by BIC.)