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Article: Improving the Phillips Curve with an Interaction Variable

Here Is the link : https://www.frbsf.org/economic-research/files/el2019-13.pdf

A key challenge for monetary policymakers is to predict where inflation is headed. One promising approach involves modifying a typical Phillips curve predictive regression to include an interaction variable, defined as the multiplicative combination of lagged inflation and the lagged output gap. This variable appears better able to capture the true underlying inflationary pressure associated with the output gap itself. Including the interaction variable helps improve the accuracy of Phillips curve inflation forecasts over various sample periods. The Phillips curve is a key mathematical relationship that many economists use to predict where inflation is headed. The relationship presumes that near-term changes in inflation are partly driven by so-called gap variables. These may include the percent deviation of real GDP from potential GDP, known as the output gap, or the deviation of the unemployment rate from the natural rate of unemployment, known as the unemployment gap. Other drivers of inflation often included when estimating the Phillips curve are survey- based measures of expected inflation, lagged values of inflation, and special factors related to recent changes in oil or import prices. All else being equal, a larger output gap or a more negative unemployment gap implying a tighter labor market would predict rising inflation over the near term. Numerous studies have found that estimated versions of the Phillips curve have become flatter over time, implying that the standard relationship has less predictive power for future inflation than it once had. ThisEconomic Letterexamines a potential way to improve Phillips curve forecasts of future inflation by including an interaction variable, defined as the multiplicative combination of lagged inflation and the lagged output gap. Multiplying the output gap by inflation rescales the gap to produce a new variable that appears better able to capture the true underlying inflationary pressure associated with the output gap itself.

Figure 1 Estimated slope coefficient from 20-year rolling regressions Output gap coefficient Full sample estimate = 0.221 -0.4 1980 1985 1990 1995 2000 2005 2010 2015 Figure 2 Output gap versus inflation-output gap interaction variable Percent or percent2 30 20 10 1960 1970 1980 1990 2000 2010 Note: Shaded areas represent NBER recession dates. Figure 3 Estimated slope coefficient using interaction variable as gap Interaction coefficient 0.2 0.15 0.1 0.05 0 Full sample -0.05 estimate = 0.086 -0.1 1980 1985 1990 1995 2000 2005 2010 2015Figure 4 Comparing out-of-sample forecasts with interaction variable Percent 3 2 With inflation 1 x output gap O -1 Without -2 inflation x output gap 4-quarter change -3 in PCE inflation -4 -5 -6 2006 2008 2010 2012 2014 2016 2018