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This is a revised version of a paper that was prepared for the March 2011 Brookings Panel on Economic Activity. We are grateful for excellent research assistance from Indra Astrayuda, Kue Peng Chuah, Xu Lu, Prathi Seneviratne, and Hou Wang, and for suggestions from the editors, Karen Dynan, Jon Faust, Robert Gordon, Jeremy Rudd, James Stock, Eric Swanson, Jonathan Wright, and participants at the Brookings Panel. We are also very grateful to Brent Meyer for assistance with the Cleveland Fed’s data on inflation. Ball: Visiting Scholar, International Monetary Fund, firstname.lastname@example.org; and Department of Economics, Johns Hopkins University, email@example.com. Mazumder: Department of Economics, Wake Forest University, firstname.lastname@example.org.
The assumption that u −u* is uncorrelated with the error in the Phillips curve, implying that OLS estimates of the equation are unbiased, is standard in the literature but rarely examined. We interpret the error term as summarizing the effects of relative price changes, which influence inflation when some nominal prices are sticky (see Section 3). We assume that these relative-price effects are uncorrelated with the aggregate variable u −u*. We maintain this assumption when π is a measure of core inflation, which strips away effects of relative price changes but does so imperfectly. In this case, the error summarizes the relative-price effects that are not removed from core inflation.
This approach to identification ignores the problem of measurement error. The variable u is an imperfect measure of the activity variable in the Phillips curve, and u*is an imperfect measure of the natural rate. These problems bias our estimates of the coefficient α toward zero. Future work should investigate the size of this bias and more generally the identification problem for the Phillips curve.
The easiest way to derive this result is to numerically calculate the path of inflation following an increase in unemployment.
Some economists (including one of our discussants) question median CPI as an inflation measure because the median price change in the Cleveland Fed data is often one of the regional OERs. It is not clear to us why the validity of the Cleveland Fed’s approach depends on which industry is the median. Nonetheless, as a robustness check, we have constructed median non-housing inflation by discarding the regional OERs and computing the median price change for all other industries. A four-quarter average of this series falls by 2.1 percentage points between 2007Q4 and 2010Q4 (from 3.1% to 1.0%); the fall in the Cleveland Fed’s median, 2.6 percentage points, is somewhat larger. Yet housing prices have a greater effect on the other leading measure of core inflation, XFE. This variable falls by 1.7 percentage points between 2007Q4 and 2010Q4; if the OERs are removed along with food and energy, the resulting inflation measure falls by only 0.9 percentage points.
The Cleveland Fed website provides a different measure of quarterly inflation: the average of median inflation over the three months of the quarter.
As a robustness check, we also estimate a time-varying α with a simpler technique: rolling regressions with five-year windows. The qualitative results are the same.
The results do not change significantly if start the sample a year or two later. They are less robust when we move the start date earlier, with observations before 1985 proving influential.
Note that, in these regressions, we use the original median through 1985 even though the revised median is available starting in 1983Q2. This choice ensures that our measure of median inflation is consistent over the 1973-1984 subsample.
Rudd and Whelan and Kleibergen and Mavroeidis (2009) also demonstrate technical problems with the studies supporting the Gali-Gertler model, such as weak instruments.
More precisely, we use the inflation series we constructed to estimate the accelerationist Phillips curve over 1960-2010: the Cleveland Fed’s revised median for 1983-2010, the original median for 1968-1982, and XFE inflation for1960-1967.
Data on core inflation starts in 1957, therefore this regression actually starts in 1964.