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Indeterminacy and Imperfect Information

with Thomas A. Lubik and Christian Matthes 

(Revised November 2019)
  • draft: pdf
  • supplementary appendix: pdf
  • slides: pdf


We study equilibrium determination in an environment where two kinds of agents have different information sets: The fully informed agents know the structure of the model and observe histories of all exogenous and endogenous variables. The less informed agents observe only a strict subset of the full information set. All types of agents form expectations rationally, but agents with limited information need to solve a dynamic signal extraction problem to gather information about the variables they do not observe. In this environment, we identify a new channel that leads to equilibrium indeterminacy: Optimal information processing of the less informed agent introduces stable dynamics into the equation system that lead to self-fulling expectations. For parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium is indeterminate. We illustrate our framework with a monetary policy problem where an imperfectly informed central bank follows an interest rate rule.

Inflation and Professional Forecast Dynamics: An Evaluation of Stickiness, Persistence and Volatility

(Revised May 2019)

This paper studies the joint dynamics of U.S. inflation and a term structure of average inflation predictions taken from the Survey of Professional Forecasters (SPF).  We combine an unobserved components (UC) model of inflation and a sticky information forecast mechanism to study these dynamics.  The UC model decomposes inflation into a trend and a gap component and measurement error. We innovate by endowing inflation gap persistence and the frequency of sticky information inflation forecast updating with drift. Stochastic volatility is imposed on the innovations to trend and gap inflation. The result is a non-linear state space model.  The model is estimated on a sample from 1968:Q4 to 2018:Q3 using sequential Monte Carlo methods that include a particle learning filter and a Rao-Blackwellized particle smoother. Our estimates show that (i) longer horizon average SPF inflation predictions inform estimates of trend inflation; (ii) inflation gap  persistence is procyclical before the Volcker disinflation and acyclical afterwards; (iii) by 1990 sticky information inflation forecast updating is less frequent than it was earlier in the sample; and (iv) the drop in the frequency of the sticky information forecast updating occurs at the same time persistent shocks become less important for explaining fluctuations in inflation. All told, the data calls for drift in inflation gap persistence and in the frequency of updating sticky information forecasts. 


On the Reliability of Output Gap Estimates in Real Time


Real-time estimates of the Output Gap — defined as the cyclical component of GDP — have previously been shown to be unreliable, since they are subject to large revisions when new data comes in. However, this result has so far only been derived for constant parameter models. This paper uses statistical models where the volatility of shocks to trend and cycle can vary over time. In this case, output gap estimates derived from data vintages going back to the 1970s are much closer to “final” estimates derived from all available sample data. The final estimates not only fall mostly within the credible intervals generated by the real-time data. When generated from a model with stochastic volatility, these credible sets are also tighter, at least over low-volatility periods.

Discreet Commitments and Discretion of Policymakers with Private Information


This papers presents general methods to compute optimal commitment and discretion policies, when a policymaker is better informed about the realization of some shocks than the public. In this situation, public beliefs about the hidden information emerge as additional state variables, managed by the policymaker.

Under commitment, policy is additive in two components: The optimal policy, as if the government shared the public's information set and the systematic manipulation of that information set. Even under discretion, belief management imparts history dependence.

Illustrated in a New Keynesian economy with time-varying output targets of the policymaker, belief management improves outcomes compared to symmetric information. At the margin, the policymaker tries to be intransparent about policy objectives by engineering disturbances which lower public beliefs about the persistence of output targets.

Three Essays on the Determinants of Output, Inflation and Interest Rates (2007, Study Center Gerzensee) 

Ph.D. Thesis. University of Lausanne, 18 October 2007 (Dissertation Committee)