Indeterminacy and fundamental reduced form representations of DSGE models

Dynamic stochastic general equilibrium (DSGE) models are known to exhibit indeterminacy—that is, equilibrium nonuniqueness—under realistic parameterizations. This paper studies how the potential for indeterminacy impacts on the possibility of recovering a DSGE model's structural shocks via empirical vector autoregressions (VARs), which in turn requires the model's reduced form representation to be fundamental. By means of a simple example, we first establish that indeterminacy is neither necessary nor sufficient for (non)fundamental representations to arise. We then investigate the relationship between indeterminacy and nonfundamentalness in the context of a general class of linearized DSGE models, which nests the New Keynesian framework as a special case. It is shown that an indeterminate equilibrium model may generically admit a fundamental moving average representation, even when its determinate counterpart always involves nonfundamentalness. As a main implication, checking for existence of a VAR representation of a DSGE model's equilibria cannot be regarded as an indirect test for the indeterminacy hypothesis.