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The idea for this paper dates back to the time when the authors were working on the IMF’s World Economic Outlook. We would like to thank Marco Terrones and David Robinson for useful suggestions.
To be fair, the central role of public responses has been emphasized in extreme situations such as the end of hyper-inflations (Sargent, 1993) and the Great Depression in the United States (Friedman and Schwartz, 1963). However, this lesson does not seem to have been more generally absorbed.
The existence of a positive association between the average level of inflation and its volatility has long been recognized (Friedman, 1977, and Taylor, 1981). This trend can be observed from measures of inflation uncertainty derived from surveys of consumers or professional forecasters (Diebold and others, 1999; IMF, 2002).
For example, Ahmed, Levin, and Wilson (2002) and Stock and Watson (2003) suggest that over half of the decline in output volatility is the result of smaller common international shocks. Other possible causes include better inventory management (McConnell and Pérez-Quirós, 2000) and shifts in output composition (Alcalá and Sancho, 2004).
Rudebusch and Svensson (1999) estimate that 7 percent of the reduction in output variance since 1984 reflects improved monetary policy. Blanchard and Simon (2001) find a strong correlation between output volatility and the level and volatility of inflation across G-7 countries. Cecchetti, Flores-Lagunes, and Krause (2001) document this effect across a wider range of countries.
See, for example, Woodford (2001) and Amato and Shin (2003) based on the original insights of Lucas (1972) and Phelps (1983). Mankiw and Reis (2001) develop a slightly different imperfect information pricing model.
For an overview across industrial countries, see IMF (2002). In a cross-country analysis, Corbo and others (2001) point out the role of inflation targeting in weakening the weight of past inflation inertia.
Sack and Wieland (1999) provide an in depth discussion of interest rate smoothing. On the issue of gradualism as optimal response to uncertainty, see Brainard (1967) as canonical reference on the theory side, Woodford (1999) and Levin, Wieland, and Williams (1999) for recent applications, and Walsh (2004) for an exhaustive review.
Most models suggest these coefficients should sum to the discount factor. This is so close to unity in quarterly data that we chose to let the coefficients add to one.
Using overlapping relative real wage contracts, Buiter and Jewitt (1989), and Fuhrer and Moore (1995) argue that there is a structural interpretation for a backward-looking element involving past inflation. An alternative approach has been to assume that some agents use simple autoregressive rules of thumb to forecast inflation (Roberts, 1998; Galí and Gertler, 1999, Ball, 2000; Ireland, 2000) or respond to non-credible announcements by the monetary authority (Ball, 1995). Departures from an optimizing-agent framework are, however, unpalatable to some involved in the microfoundation approach to macroeconomics (Rotemberg and Woodford, 1997).
IMF (2002) examined the link between monetary policy and inflation interia, while Erceg and Levin (2003) suggest that combining a staggered contracts model with information uncertainty about the implicit target for inflation can generate sluggish expectations adjustment. The link between inflation persistence and learning about regime shifts in a monetary reaction function has been analyzed by Fuhrer and Hooker (1993) using stochastic simulations. Cogley and Sargent (2001) use spectral analysis and estimates from a nonlinear Bayesian VAR to investigate the correlation between the degree of inflation persistence and the strength of the monetary response to inflation.
We experimented with various windows. Fifty quarters struck the best balance between the desire to lengthen the window to provide more accurate parameter estimates and keep the window short to illustrate movements in coefficients over time.
Our Generalized Method of Moments (GMM) estimates use a Newey-West weighting matrix to allow for up to four-quarter of serial correlation. The set of instruments includes the first four quarters of annual inflation, output gap, and effective federal funds rate. For a discussion of GMM estimator and identifying restrictions in the case of monetary policy rules, see Clarida, Gali, and Gertler (1998).
We would like to thank Athanasios Orphanides for providing us with the “real time” output gap data. He also provided us with a real time series on inflation, but the results from this series were essentially identical to those using inflation expectations in the Michigan survey, and we chose to use the latter.
The coefficient estimates obtained using a Hodrick-Prescott filter rather than real time data are relatively close, and generate broadly similar conclusions (results are available upon request). The main reason for using the real time data is that the coefficient on forward-looking inflation in the Phillips in the 1990s seems more sensible.
The coefficient on the output gap in the monetary response function for the 1970s was perverse and, as it was not statistically significant at conventional levels, was set to zero.
As the model is linear (in logs), it can be analyzed using solution methods such as Blanchard and Kahn (1980) or Klein (2000). In all sub-periods (that is, 1960s, 1970s, 1980s, and 1990s), the number of eigen values outside the unit circle (two) is equal to the number of ‘non-predetermined’ variables of the model, hence the model is saddlepath stable. Our model was solved in Matlab, using McCallum’s routines for rational expectation models (http://wpweb2k.gsia.cmu.edu/faculty/mccallum/Software%20for%20RE%20Analysis.pdf).