Aleksey Tetenov (Collegio Carlo Alberto)

“Statistical hypothesis testing and private information”

Abstract

This paper provides a rationalization for using classical one-sided hypothesis tests for approving innovations (e.g., new pharmaceuticals, new government programs). I consider this problem of statistical decision making in a setting where proponents of innovations (i) stand to benefit from approval decisions even if their innovations have a negative effect, (ii) possess private information about the idea’s quality, and (iii) must pay ex ante for collecting data on which the test is based. Lower test size deters proponents from attempting to gain approval of innovations that they ex ante know to be bad through trials. I show that test size equal to the ratio of the proponents’ cost of collecting data to their benefit from approval of a null innovation is optimal in a number of ways. It is a minimax decision rule for a regulator who prefers not to place a prior on the distribution of potential innovator types. It is also the limit of decision rules by Bayesian regulators as the assumed share of potential proponents with bad innovations converges to one.