Robustness by Lars Peter Hansen

By Lars Peter Hansen

The traditional concept of determination making below uncertainty advises the choice maker to shape a statistical version linking results to judgements after which to decide on the optimum distribution of results. This assumes that the choice maker trusts the version thoroughly. yet what should still a call maker do if the version can't be relied on? Lars Hansen and Thomas Sargent, major macroeconomists, push the sector ahead as they set approximately answering this query. They adapt powerful regulate concepts and observe them to economics. through the use of this conception to permit selection makers recognize misspecification in fiscal modeling, the authors improve purposes to quite a few difficulties in dynamic macroeconomics. Technical, rigorous, and self-contained, this e-book may be beneficial for macroeconomists who search to enhance the robustness of decision-making approaches.

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2. Certainty equivalence. 6 ), the scalar p = β 1−β traceP CC . The volatility matrix C influences the value function through p, but not through P . 9 ) that the optimal decision rule F is independent of the volatility matrix C . 1 ), we have normalized C by setting Eˇt ˇt = I . Therefore, the matrix C determines the covariance matrix CC of random shocks impinging on the system. The finding that F is independent of the volatility matrix C is known as the certainty equivalence principle: the same decision rule ut = −F yt emerges from stochastic (C = 0) and nonstochastic (C = 0) versions of the problem.

Y0 ]. 4 ) as a statistical measure of the discrepancy between the distorted and approximating models. The alternative models differ from the approximating model by having shock processes whose conditional means are not zero and that can feed back in potentially complicated ways on the history of the state. Notice that our specification leaves the conditional volatility of the shock, as parameterized by C , unchanged. We adopt this specification for computational convenience. We show in chapter 3 the useful result that our calculations for a worstcase conditional mean wt+1 remain unaltered when we also allow conditional volatilities C to differ in the approximating and perturbed models.

4) where ∗ denotes next period’s value, and ∼ N (0, I). 3 ) the decision maker pretends that a malevolent nature chooses a feedback rule for a model misspecification process w. 4 ). 2 ), we mention a kind of certainty equivalence that applies to the multiplier problem. 1. Modified certainty equivalence principle On page 29, we stated a certainty equivalence principle that applies to the linear quadratic dynamic programming problem without concern for model misspecification. It fails to hold when there is concern about model misspecification.

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