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Prepared by Pau Rabanal. A fuller description of the results is available from the author.
See Woodford (2003) and Clarida, Galí and Gertler (1999). Earlier work by Kydland and Prescott (1977) and Barro and Gordon (1983) emphasized how a rules-based approach reduces the inflationary bias in monetary policy.
The existing literature generally tests for differences in coefficients over subsamples. For instance, Clarida, Galí and Gertler (2000), in a forward looking version of the Taylor rule, find significant differences in the coefficients of the Taylor rule between the 1960–79 and 1982–99 periods.
Following Erceg and Levin (2003), it is assumed that the Taylor rule reacts to output growth rather than the output gap, which has the advantage that all variables in the right hand side are observable, avoiding the complications associated with uncertainty about estimation of the output gap.
The variances of the shocks are estimated using maximum likelihood. The Kalman filter is subsequently used to obtain the one-step ahead forecasts and the smoothed series for the coefficients, as in Hamilton (1994).
Bayoumi and Sgherri (2004) present similar evidence on time-varying coefficients in the Taylor rule.
Expansions are associated with positive output growth, and recessions with negative growth. The model is estimated using quarterly data from 1960 to 2003, assuming that transitions from one state to another follow a first-order Markov process.
The results are obtained using weighted least-squares regressions, using the probabilities of being in each state as a weight. Starting in 1960 allows a sufficiently large number of recessions to be able to get an accurate reading of the impact of the cycle on monetary response.
The coefficients are (1-.).p and (1-.).g in the nomenclature of equation 1.