“ Certainty Equivalence ” and “ Model Uncertainty ” Lars

Simon’s and Theil’s certainty equivalence property justifies a convenient algorithm for solving dynamic programming problems with quadratic objectives and linear transition laws: first, optimize under perfect foresight, then substitute optimal forecasts for unknown future values. A similar decomposition into separate optimization and forecasting steps prevails when a decision maker wants a decision rule that is robust to model misspecification. Concerns about model misspecification leave the first step of the algorithm intact and affect only the second step of forecasting the future. The decision maker attains robustness by making forecasts with a distorted model that twists probabilities relative to his approximating model. The appropriate twisting emerges from a two-player zero-sum dynamic game. Note: This paper was prepared for a conference at the Federal Reserve Board on March 26–27, 2004 to honor the work of our friends Dale Henderson, Richard Porter, and Peter Tinsley. An earlier version of this paper was presented at a conference to honor the memory of Henri Theil.