Berk-Nash Equilibrium and Pseudo MLE

The Berk-White statistics/econometrics tradition is alive and well, appearing now as Berk-Nash equilibrium in cutting-edge economic theory. See for example Kevin He's Harvard job-market paper here and the references therein, and the slides from yesterday's lunch talk by my Penn colleague Yuichi Yamamoto. But the connection between Berk-Nash equilibrium of economic theory and KLIC-minimizing pseudo-MLE of econometric theory is under-developed. When the Berk-Nash people get better acquainted with Berk-White people, good things may happen. Effectively Yuichi is pushing in that direction, working toward characterizing log-run behavior of likelihood maximizers rather than beliefs.