A wide and established literature appears to agree on one essential ingredient of sound monetary policy: policy should be set to act aggressively against inflation (e.g. Taylor (1999), Clarida, Gali and Gertler (2000), Bernanke and Woodford (1997), Svensson and Woodford (2003), and Woodford (2003)). A basis for this finding is the New Keynesian monetary model, where adherence to an active monetary policy rule (a variant on the ‘Taylor principle’) results in a determinate model and thus a unique rational expectations equilibrium (REE). A determinate model is sometimes called “stable” because, due to its unique equilibrium, the economy is not subject to excessive volatility that can arise when agents’ beliefs are driven by self-fulfilling prophecies (e.g. sunspots). It is this sense of stability that motivates determinacy as a frequently advocated condition for good monetary policy.
Among the standard assumptions of the New Keynesian model is the macroeconomic benchmark of (homogeneous) rational expectations (R.E.). Recent empirical analysis, however, casts some doubt on this assumption’s validity. Using survey data, Branch (2004, 2005), Carroll (2003), and Mankiw, Reis, and Wolfers (2003) provide evidence that economic forecasters (both consumers and professional economists) have heterogeneous expectations and, importantly, the distribution of heterogeneity evolves over time in response to economic volatility.
Branch (2004), in particular, provides evidence that survey respondents in the Michigan survey of consumers are distributed across rational and adaptive expectations and these proportions evolve over time as a reaction to past mean square forecast errors: for instance, in periods of high economic volatility such as the 1970’s a higher proportion of agents used rational expectations than during periods of relatively low volatility. The standard monetary model under R.E. is not able to capture these empirical features.
Because the notion of determinacy is so closely connected to rational expectations equilibria, it is natural to question how a determinate (under R.E.) model might perform in the presence of boundedly rational agents. It is not difficult to see that with non-rational agents the concurrence between stability and determinacy may be broken. Recall that a determinate steady state is saddle-path stable, and therefore lies on the intersection of the associated dynamic system’s stable and unstable manifolds. Under the assumption of rationality, agents make initial choices so that the economy lies on the stable manifold and convergence to steady state obtains. Boundedly rational agents may not make such precise choices and so, in their presence, the associated steady state is dynamically unstable.
Now suppose the steady state is indeterminate. Then there are many initial choices by rational agents that result in convergence to the steady state. In fact, depending on the dimension of the unstable manifold, indeterminacy may yield dynamic stability in the presence of boundedly rational agents. If the unstable manifold is such that the steady state is a sink then regardless of the boundedly rational agents’ initial decisions the economy will converge to it. We come to the (somewhat uncomfortable) conclusion that in an economy with boundedly rational agents, determinacy may imply dynamic instability and indeterminacy may imply dynamic stability the opposite conclusion from what one would draw under the assumption of rationality.
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Dynamic Predictor Selection in a New Keynesian Model with Heterogeneous Expectations
