This paper studies dynamic identification of parameters of a dynamic stochastic general equilibrium model from the first and second moments of the data. Classical results for dynamic simultaneous equations do not apply because the state space solution of the model does not constitute a standard reduced form. Full rank of the Jacobian matrix of derivatives of the solution parameters with respect to the parameters of interest is necessary but not sufficient for identification. We use restrictions implied by observational equivalence to obtain two sets of rank and order conditions: one for stochastically singular models and another for nonsingular models. Measurement errors, mean, long-run, and a priori restrictions can be accommodated. An example is considered to illustrate the results.

This paper proposes a method for testing complementarities between explanatory and dependent variables in a large class of economic models. The proposed test is based on the monotone comparative statics (MCS) property of equilibria. Our main result is that MCS produces testable implications on the (small and large) quantiles of the dependent variable, despite the presence of multiple equilibria. The key features of our approach are: (1) we work with a nonparametric structural model of a continuous dependent variable in which the unobservable is allowed to be correlated with the explanatory variable in a reasonably general way; (2) we do not require the structural function to be known or estimable; (3) we remain fairly agnostic on how an equilibrium is selected. We illustrate the usefulness of our result for policy evaluation within Berry, Levinsohn, and Pakes’s (AER, 1999) model.

In this paper, we propose a new family of multivariate loss functions to test the rationality of vector forecasts without assuming independence across variables. When only one variable is of interest, the loss function reduces to the flexible asymmetric family proposed by Elliott, Komunjer, and Timmerman (2008). Following their methodology, we derive~a GMM test for multivariate forecast rationality that allows the forecaster's loss to be nonseparable across variables and takes into account forecast estimation uncertainty. We use our test to study the joint rationality of macroeconomic forecasts in the growth rate of nominal output, CPI inflation rate, and short-term interest rate.

In situations where a sequence of forecasts is observed, a common strategy is to examine “rationality” conditional on a given loss function. We examine this from a different perspective— supposing that we have a family of loss functions indexed by unknown shape parameters, then given the forecasts can we back out the loss function parameters consistent with the forecasts being rational even when we do not observe the underlying forecasting model? We establish identification of the parameters of a general class of loss functions that nest popular loss functions as special cases and provide estimation methods and asymptotic distributional results for these parameters. This allows us to construct new tests of forecast rationality that allow for asymmetric loss. The methods are applied in an empirical analysis of IMF and OECD forecasts of budget deficits for the G7 countries. We find that allowing for asymmetric loss can significantly change the outcome of empirical tests of forecast rationality.