We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter θ and the decision maker can use a point-identified parameter μ to deduce restrictions on θ. Examples include treatment choice under partial identification and pricing with rich unobserved heterogeneity. Our notion of optimality combines a minimax approach to handle the ambiguity from partial identification of θ given μ with an average risk minimization approach for μ. We show how to implement optimal decision rules using the bootstrap and (quasi-)Bayesian methods in both parametric and semiparametric settings. We provide detailed applications to treatment choice and optimal pricing. Our asymptotic approach is well suited for realistic empirical settings in which the derivation of finite-sample optimal rules is intractable.

We document that consumption growth rates are far from i.i.d. and have a highly persistent component. First, we estimate univariate and multivariate models of cash‐flow (consumption, output, dividends) growth that feature measurement errors, time‐varying volatilities, and mixed‐frequency observations. Monthly consumption data are important for identifying the stochastic volatility process; yet the data are contaminated, which makes the inclusion of measurement errors essential for identifying the predictable component. Second, we develop a novel state‐space model for cash flows and asset prices that imposes the pricing restrictions of a representative‐agent endowment economy with recursive preferences. To estimate this model, we use a particle MCMC approach that exploits the conditional linear structure of the approximate equilibrium. Once asset return data are included in the estimation, we find even stronger evidence for the persistent component and are able to identify three volatility processes: the one for the predictable cash‐flow component is crucial for asset pricing, whereas the other two are important for tracking the data. Our model generates asset prices that are largely consistent with the data in terms of sample moments and predictability features. The state‐space approach allows us to track over time the evolution of the predictable component, the volatility processes, the decomposition of the equity premium into risk factors, and the variance decomposition of asset prices.

Researchers often hold out data from the estimation of econometric models to use for external validation. However, the use of holdout samples is suboptimal from a Bayesian perspective, which prescribes using the entire sample to form posterior model weights. This paper examines a possible rationale for the use of holdout samples: data-inspired modifications of structural models are likely to lead to an exaggeration of model fit. The use of holdout samples can, in principle, set an incentive for the modeler not to exaggerate model fit.

Policy analysis with potentially misspecified dynamic stochastic general equilibrium (DSGE) models faces two challenges: estimation of parameters that are relevant for policy trade-offs, and treatment of the deviations from the cross-equation restrictions. Using post-1982 US data, we study the robustness of the policy prescriptions from a state-of-the-art DSGE model with respect to two approaches to model misspecification pursued in the recent literature: (i) adding shocks to the DSGE model and/or generalizing the processes followed by these shocks; and (ii) explicit modeling of deviations from cross-equation restrictions (DSGE-VAR).

We compute a sunspot equilibrium in an estimated small-scale New Keynesian model with a zero lower bound (ZLB) constraint on nominal interest rates and a full set of stochastic fundamental shocks. In this equilibrium, a sunspot shock can move the economy from a regime in which inflation is close to the central bank’s target to a regime in which the central bank misses its target, inflation rates are negative, and interest rates are close to zero with high probability. A non-linear filter is used to examine whether the U.S. in the aftermath of the Great Recession and Japan in the late 1990s transitioned to a deflation regime. The results are somewhat sensitive to the model specification, but on balance, the answer is affirmative for Japan and negative for the U.S.

Kim, Minchul Shin, and Martin Weidner for research assistance. Moon gratefully acknowledges financial

Testing for Indeterminacy: An Application to U.S. Monetary Policy: Reply by Thomas A. Lubik and Frank Schorfheide. Published in volume 97, issue 1, pages 530-533 of American Economic Review, March 2007

This paper considers a prototypical New Keynesian model, in which the equilibrium is undetermined if monetary policy is “passive.” The likelihood-based estimation of dynamic equilibrium models is extended to allow for indeterminacies and sunspot fluctuations. We construct posterior weights for the determinacy and indeterminacy region of the parameter space and estimates for the propagation of fundamental and sunspot shocks. According to the estimated model, U.S. monetary policy post-1982 is consistent with determinacy, whereas the pre-Volcker policy is not. We find that before 1979 indeterminacy substantially altered the propagation of shocks.

In large-scale panel data models with latent factors the number of factors and their loadings may change over time. Treating the break date as unknown, this article proposes an adaptive group-LASSO estimator that consistently determines the numbers of pre- and post-break factors and the stability of factor loadings if the number of factors is constant. We develop a cross-validation procedure to fine-tune the data-dependent LASSO penalties and show that after the number of factors has been determined, a conventional least-squares approach can be used to estimate the break date consistently. The method performs well in Monte Carlo simulations. In an empirical application, we study the change in factor loadings and the emergence of new factors in a panel of U.S. macroeconomic and financial time series during the Great Recession.