Wednesday, January 29, 2020 at 11:40am to 1:10pm
Ives Hall, 115
B07 Tower Rd, Ithaca, NY 14853, USA
Chen Qiu - London School of Economics
Minimax Learning for Average Regression Functionals with an Application to Electoral Accountability and Corruption
Abstract: This paper proposes a new minimax methodology to estimate average regression functionals, which are relevant to many empirical problems including average treatment effects. Embedded in a penalized series space, this strategy exploits a minimax property of a key nonparametric component of the average regression functional and aims to directly control main remainder bias. I then construct a new class of estimators, called minimax learners, and separately study their asymptotic properties as the ratio of controls to sample size goes to zero, constant and infinity. Root-n normality is established under weak conditions for all three cases. Minimax learners are straightforward to implement due to their minimum distance representation. In simulations where selection bias is mild, minimax learners behave stably, maintain small mean square error and do not over control; if selection bias is substantial, minimax learners are able to correctly reduce mean square error as more relevant controls are added. When applied to the work of Ferraz and Finan (2011) on the effects of electoral accountability on corruption, minimax learners behave less erratically than OLS as well as other off-the-shelf shrinkage methods and lead to more coherent conclusions, even when the number of controls becomes very large.