Computing Sunspots in Linear Rational Expectations Models

We provide computationally simple methods of analyzing the effects of fundamental and sunspot shocks in linear rational expectations models when the equilibrium is indeterminate Under indeterminacy sunspots can affect model dynamics through endogenous forecast errors that do not completely adjust to fundamental shocks alone Moreover the effect of fundamental shocks on forecast errors is not uniquely determined We characterize the full set of equilibria and show that some solution methods only generate subsets of all the rational expectations equilibria by imposing specific restrictions on the forecast errors However in most cases it is possible to recover the full set of equilibria from the output of these methods The solution algorithms are illustrated with a New Keynesian dynamic stochastic equilibrium model that can be solved analytically We show that under a passive interest-rate rule the response of output and inflation to an unanticipated interest rate cut is ambiguous: while output rises there are some equilibria in which inflation increases and other in which prices fall