Optimal policy with limited commitment
This paper uses Whiteman's(1986) frequency-domain optimization methodology to parameterize the precommitment period in a standard rational expectations policy design model. This allows researchers to adopt an empirical approach to the time consistency issue. That is, the operative commitment horizon in a given policy setting can be estimated along with the other parameters characterizing the preferences and constraints of the agents in the model. It is shown that the commitment horizon can be estimated by running (restricted) regressions of the policymaker's instrument variable on past values of its target variable. ; Parameterizing the commitment horizon also delivers a mapping between welfare (or the value of the policymaker's objective function) and the length of the commitment horizon. The paper shows that the rate of convergence to the perfect precommitment value can be either quite slow or quite rapid, suggesting that the severity of the time consistency constraint can be sensitive to variation in the assumed commitment horizon. ; Finally, the results are applied to U.S. and German monetary policy during the post-Bretton Woods era. Assuming the monetary authority attempts to stabilize inflation using a Federal Funds like interest rate as an instrument, the results point to a one-month ahead commitment horizon for the U.S. Federal Reserve, and to a twelve-month ahead commitment horizon for the German Bundesbank. However, these horizons are estimated very imprecisely.
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