The recent behavior of US inflation has puzzled economists. The accelerationist Phillips curve of textbooks says that a high level of unemployment causes inflation to fall over time. For common calibrations of this relationship, the high unemployment rates during the Great Recession and subsequent weak recovery should have pushed the inflation rate well below zero. Yet by many measures, the current rate of core inflation – excluding the transitory effects of supply shocks - is close to its pre-2008 level. How can we explain the ‘missing deflation’ (Stock 2011)?

Two answers to this question have become popular.

- The first, emphasised by Fed officials among others, is that inflation expectations have become anchored (e.g. Bernanke 2010). According to this story, the Fed’s commitment to a 2% inflation target has kept expected inflation near 2%, which in turn has prevented actual inflation from falling very far below that level.
- The second answer is that inflation depends not on the aggregate unemployment rate (as in textbook Phillips curves), but rather on the short-term unemployment rate – typically defined as the percentage of the labor force unemployed for 26 weeks or less. The story here is that the short-term unemployed put downward pressure on wages but the long-term unemployed do not, because their attachment to the labor force is weak (e.g. Krueger et al. 2014). This helps explain why inflation has not fallen further, because short-term unemployment rose less sharply than total unemployment over 2008-2009, and has since returned to pre-recession levels.

## An updated Phillips curve

The anchored-expectations and short-term unemployment stories are sometimes presented as competing explanations for recent inflation behavior. In a new paper, we argue that both ideas are on the right track (Ball and Mazumder 2014). In fact, they are complementary. Neither of the ideas can resolve the missing deflation puzzle by itself, but together they do.

We capture the two ideas in a highly parsimonious Phillips curve. In our specification, the core inflation rate depends only on a constant - which depends on a fixed level of expected inflation - and on the average level of short-term unemployment over the previous four quarters. We fit this equation to data starting in 2000, which is approximately the date that long-term inflation expectations became anchored at the Fed’s target, according to the Survey of Professional Forecasters. We measure core inflation with the weighted median inflation rate from the Federal Reserve Bank of Cleveland.

For the period from 2000 through 2014Q2, the estimated slope coefficient in our Phillips curve is approximately -1.0. This means that a one percentage point rise in average short-term unemployment over the previous four quarters reduces core inflation by about one percentage point. The fit of our simple equation is excellent: the Ṝ^{2} is 0.81.

Figure 1 illustrates this fit by comparing the path of median inflation to fitted values from our equation. Since 2000 median inflation has gone through two cycles of decline and recovery, with troughs during the ‘deflation scare’ of 2003 and in 2010. These two inflation cycles correspond closely to movements in short-term unemployment in the opposite direction.

**Figure 1**. Median inflation vs. fitted values from updated Phillips curve

## More traditional Phillips curves

Our recent paper compares our preferred Phillips curve to more traditional specifications that include past inflation and/or total unemployment. These equations fit the data poorly, primarily because they cannot reconcile the behavior of inflation before and after the financial crisis. To illustrate this point we examine forecasts of median inflation over 2008-2014 based on Phillips curves estimated over 2000-2007.

For our preferred Phillips curve, the predicted path of inflation over 2008-2014 is close to the actual path. In contrast, when we replace short-term unemployment with total unemployment (but maintain the assumption of anchored expectations), predicted inflation is considerably lower than actual inflation. This deviation peaks in 2011Q3, when predicted and actual inflation are 0.3% and 2.3%, respectively. These results reflect the fact that the Great Recession raised total unemployment more sharply and persistently than short-term unemployment.

We also consider specifications in which expected inflation is proxied by the average inflation rate over the previous four quarters. These accelerationist Phillips curves produce the missing-deflation puzzle: when estimated with pre-2008 data, they predict that inflation falls steadily from 2008 to the present. Predicted inflation in 2014Q2 is -0.6% if the Phillips curve includes short-term unemployment, and -2.1% with total unemployment.

## Alternative measures of core inflation

Our primary measure of core inflation is the weighted median inflation rate from the Cleveland Fed. A common alternative measure is the inflation rate for the consumer price index excluding food and energy (CPIX). As a robustness check, we estimate Phillips curves with CPIX as the dependent variable, and reach two conclusions.

- First, our main results about the Phillips curve are robust. For CPIX inflation – as for median inflation - the fit to recent data improves if we assume anchored expectations, and if we include short-term rather than total unemployment.
- Second, for a given specification of the Phillips curve, replacing median inflation with CPIX worsens the equation’s fit. For our preferred specification with anchored expectations and short-term unemployment, the Ṝ
^{2}is only 0.41 when core inflation is measured by CPIX, compared to 0.81 with median inflation.

Figure 2 shows the path of CPIX inflation, and fitted values from our preferred specification. Comparing Figures 1 and 2, we see that median inflation filters out short-term noise in the inflation rate more effectively than CPIX. This finding suggests that the median is a good measure of core inflation, which more researchers should adopt.

**Figure 2**. CPIX inflation vs. fitted values from updated Phillips curve

## Conclusion

US core inflation has not fallen greatly since 2008 despite high unemployment rates. Many observers are puzzled; Krugman (2014), for example, says “we don’t have a very good story about inflation and unemployment these days.” Our research explains recent inflation behavior by combining two popular ideas: that inflation expectations are anchored, and that labor-market slack is captured by the level of short-term unemployment.

Anchored expectations are a feature of the current monetary regime, in which the Fed targets a fixed level of inflation (specifically, 2%). In the future, expectations could become unmoored from their anchor if the Fed changes its target, or if actual inflation deviates greatly from the target. If that happens, future Phillips curves will need to incorporate the new behaviour of expectations.

## References

Ball, L and S Mazumder (2014), “A Phillips Curve with Anchored Expectations and Short-Term Unemployment”, Working Paper 20715, National Bureau of Economic Research.

Bernanke, B (2010), “The Economic Outlook and Monetary Policy”, Speech At the Federal Reserve Bank of Kansas City Economic Symposium, Jackson Hole, Wyoming.

Krueger, A, J Cramer, and D Cho (2014), “Are the Long-Term Unemployed on the Margins of the Labor Market?”, *Brookings Papers on Economic Activity*, 229–280.

Krugman, P (2014), “Inflation, Unemployment, Ignorance”, *The New York Times* Blog.

Stock, J (2011), Discussion of Ball and Mazumder, “Inflation Dynamics and the Great Recession” *Brookings Papers on Economic Activity*, 387–402.