Ranking Information Systems without the First-Order Approach

We develop a new method to rank information systems in moral hazard principal-agent problems. We show a necessary and sufficient condition for ranking the efficiency of signals without the first-order approach, that is, a convex-linear order based on the global likelihood ratio. According to the new theory, the Holmstrom sufficient statistic criterion remains valid. However, the Kim mean-preserving spread criterion is not robust when the first-order approach is not valid. We thus propose several new criteria that are robust under the global incentive compatibility constraint. In particular, we show that the necessity of the well-known Blackwell criterion comes back when the signals are single-dimensional and satisfy the monotone likelihood property.