Long-Term Unemployment and the Dual Mandate

The Federal Reserve's mandate from Congress, as described in the Federal Reserve Act, is to promote "maximum employment, stable prices, and moderate long-term interest rates." In January 2012, the FOMC clarified that a PCE inflation rate of 2% was most consistent with the price stability part of the so-called "dual mandate." The FOMC's Statement on Longer-Run Goals and Monetary Policy Strategy says:

In setting monetary policy, the Committee seeks to mitigate deviations of inflation from its longer-run goal and deviations of employment from the Committee's assessments of its maximum level. These objectives are generally complementary. However, under circumstances in which the Committee judges that the objectives are not complementary, it follows a balanced approach in promoting them, taking into account the magnitude of the deviations and the potentially different time horizons over which employment and inflation are projected to return to levels judged consistent with its mandate.

Lately, PCE inflation has been well below 2%. There is no similarly-specific definition of maximum employment, but I think it is safe to say that we are not there yet. So we seem to be in a situation in which the objectives are complementary--employment-boosting policies that also put some upward pressure on prices would get us closer to maximum employment and stable prices at the same time. This is supposed to be the "easy case" for monetary policymakers, earning the name "divine coincidence." The tougher case would come if inflation were to get up to or above 2% and employment were still too low. Then there would be a tradeoff between the employment and price stability objectives, making the Committee's balancing act more difficult.

San Francisco Federal President John Williams presents the case that the rise in the share of long-term unemployment should affect the approach that Committee members take when faced with such a balancing act. Williams and SF Fed Economist Glenn Rudebusch have a new working paper called "A Wedge in the Dual Mandate: Monetary Policy and Long-Term Unemployment." In this paper, they document key empirical facts about the share of long-term unemployment and explain how it alters the relationship between employment and inflation.

Source: Rudebusch and Williams 2014, p. 4.

First, the key empirical facts about long-term unemployment share in the U.S.:

1. It has trended upward over the past few decades.
2. It is countercyclical.
3. Its countercyclicality has increased in recent decades.

Fact 1 has been attributed to the aging population, women's rising labor force attachment, and increasing share of job losses that are permanent separations rather than temporary layoffs (Groshen and Potter 2003, Aaronson et al. 2010, Valletta 2011).

The long-term unemployed appear to place less downward pressure on wages and prices than the short-term unemployed. This may be because the long-term unemployed are less tied to the labor market and search less intensely for a job as they grow discouraged (e.g., Krueger and Mueller 2011). Stock (2011) and Gordon (2013) find that distinguishing between long- and short-term unemployment can help account for the puzzling lack of disinflation following the Great Recession. Rudebusch and Williams find a similar result by running Phillips Curve regressions that include short-term and long-term unemployment gaps as regressors. Only the coefficient on the short-term unemployment gap is negative and statistically significant, implying that short-run unemployment exerts downward pressure on prices while long-run unemployment does not.

The finding that long-term and short-term unemployment have different implications for price dynamics is very relevant for the Fed's pursuit of its dual mandate.  When the long-term unemployment share is high, this introduces a "wedge" between the employment and price stability portions of the mandate. Employment and inflation won't be as prone to moving in the same direction, because employment can get very low without much downward pressure on wages (and prices). To formalize what this means for monetary policy decisions, Rudebusch and Williams build a stylized model economy (skip ahead if not interested in the details) in which the central bank's objective is to minimize a quadratic loss function:
\begin{equation}
L=\tilde \pi + \lambda \tilde u,
\end{equation}
where pi tilde and u tilde are deviations of inflation from its target and unemployment from the natural rate, and lambda is the weight that policymakers place on unemployment stabilization versus inflation stabilization. Let the unemployment deviation depend on a demand shock v and the deviation of the short-term interest rate from the natural rate (IS equation):
\begin{equation}
\tilde u = \eta \tilde i + v
\end{equation}
 Let deviations in inflation depend on an inflation shock e and the deviation of the short-run unemployment rate s from its natural rate:
\begin{equation}
\tilde \pi = -\kappa \tilde s + e
\end{equation}
The short-run unemployment rate is a fraction of the overall unemployment rate u,
\begin{equation}
s=\theta u,
\end{equation} where
\begin{equation}
\theta=\bar \theta -\delta \tilde u + z,
\end{equation}
where z is a shock to the short-run unemployment share. If we substitute these equations into the loss function and take first order conditions, we arrive at an expression for the optimal deviation of inflation from its target:
\begin{equation}
\tilde \pi*=\frac{\lambda}{\lambda+\kappa^2 \theta^2}e-\frac{\lambda \kappa \bar u}{\lambda+\kappa^2 \theta^2}z
\end{equation}

The first thing to notice here is that the demand shock v does not show up in the optimal policy decision. This is the divine coincidence-- demand shocks impose no tradeoff between the employment and inflation objectives.

The second thing to notice is how the inflation shock e and the short-run unemployment share z. The first term is standard, and shows how the optimal policy partially offsets a positive (negative) inflation shock by raising (lowering) unemployment. The other term is new to this paper. A positive shock to theta acts like a negative inflation shock in the sense of prescribing a higher short-run unemployment rate and lower inflation rate. Another policy implication arises because theta affects the slope of the Phillips curve with respect to aggregate unemployment. This creates an asymmetry in the optimal policy response to inflation shocks that depends on theta.

During the Great Recession, the short-run unemployment share theta reached historic lows. Rudebusch and Williams simulate their model starting in the first quarter of 2014, using actual data from 2013 as initial conditions. They compare the optimal policy response implied by their model to that implied by a standard model (i.e. one that does not distinguish between short-run and long-run unemployment). The figure below displays the results. The quantitative results are not meant to be taken too seriously, since the models involve drastic oversimplifications, but the qualitative differences are  illustrative.The model that distinguishes between short-run and long-run unemployment (shown as black lines) prescribes a higher inflation rate--temporarily above 2%--than the standard model (shown as dashed red lines).

Source: Rudebusch and Williams 2014, p. 22

The authors conclude (emphasis added):

During the recent recession and recovery, the number of discouraged jobless excluded from the unemployment rate and the number of part-time employees wanting full-time work have reached historic highs. If the true measure of labor underutilization included these individuals, even though they have little or no eff ect on wage and price setting, then the wedge in the Fed's dual mandate would be even wider. Based on the analysis in this paper, the implications are clear: Optimal policy should trade off a transitory period of excessive inflation (beyond what is calculated using this paper's model) in order to bring the broader measure of underemployment to normal levels more quickly.

This is a very interesting and intuitive result, and is highly relevant to the policymaking environment in both the United States and elsewhere, particularly Europe. However, I'm not sure that the FOMC as a whole will take this paper's implications seriously. The committee does not share a single "loss function" like the quadratic function presented in the paper, which treats overshooting and undershooting of the inflation target symmetrically. Mark Thoma's comment on the paper is, "I'll believe the Fed will allow *intentional overshooting* of its inflation target when I see it."