Unemployment and Output Gaps in a New Keynesian DSGE

The output gap is big and negative; the unemployment gap is big and positive. From "Unemployment in an Estimated New Keynesian Model" (ungated version), by Jordi Galí, Frank Smets, and Rafael Wouters:

In this paper we have developed a reformulated version of the Smets-Wouters
(2007) framework that embeds the theory of unemployment proposed in Galí
(2011a,b). We estimate the resulting model using postwar U.S. data, while
treating the unemployment rate as an additional observable variable. This
helps overcome the lack of identification of wage markup and labor supply
shocks highlighted by Chari, Kehoe and McGrattan (2008) in their criticism
of New Keynesian models. In turn, our approach allows us to estimate a
"correct" measure of the output gap. In addition, the estimated model can
be used to analyze the sources of unemployment fluctuations.
A number of key results emerge from our analysis. First, we show that
wage markup shocks play a smaller role in driving output and employment
‡uctuations than previously thought. Secondly, ‡uctuations in our estimated
output gap are shown to be the near mirror image of those experienced by the
unemployment rate, and to be well approximated by conventional measures
of the cyclical component of GDP. Thirdly, demand shocks are the main
driver of unemployment fluctuations at business cycle frequencies, but wage
markup shocks are shown to be more important at lower frequencies. Finally,
our estimates point to an adverse risk-premium shock as the key force behind
the initial rise in unemployment during the Great Recession. The important
role uncovered for monetary policy and wage markup shocks at a later stage
may be interpreted as capturing the likely effects of the zero lower bound on
the nominal rate and of downward wage rigidities (as opposed to those of
truly exogenous shocks).

The major variation of this version of the SW model (which John Taylor has cited in his discussion of multipliers [1] [2]) is in the labor block:

First,
and regarding the data on which the estimation is based, we use employment
rather than hours worked, and rede…ne the wage as the wage per worker
rather than the wage per hour. We do so since the model focuses on variations
in labor at the extensive margin, in a way consistent with the conventional
de…nition of unemployment. Given that most of the variation in hours worked
over the business cycle is due to changes in employment rather than hours
per employee, this change does not have major consequences in itself. We
also combine two alternative wage measures in the estimation, compensation
and earnings, and model their discrepancy explicitly. Second, we generalise
the utility function in a way that allows us to parameterize the strength of
the wealth effect on labour supply, as shown in Jaimovich and Rebelo (2009).
This generalisation yields a better …t of the joint behavior of employment and
the labor force, as we discuss in detail. Third, for simplicity, we revert to
a Dixit-Stiglitz aggregator rather than the Kimball aggregator used in SW
(2007).

The paper is extremely interesting (as well as relevant) and definitely well-worth an in-depth reading. I will focus on three points: (1) the estimate of the output gap resulting from this approach is remarkably similar to the CBO's (and dissimilar to statistical methods such as HP and BK); (2) while the natural rate of unemployment rises noticeably, by 2010Q4, the cyclical component accounts for the greatest proportion of the increase in unemployment; and (3) the wage markup -- which the authors attribute to wage stickiness -- account for a large proportion of the increase in unemployment.

Source: "Unemployment in an Estimated New Keynesian Model"

Source: "Unemployment in an Estimated New Keynesian Model"

Source: "Unemployment in an Estimated New Keynesian Model"

Risk premium shocks are shocks in the consumption Euler equation, while investment shocks are productivity shocks specific to the investment equation. Monetary policy shocks are deviations from a Taylor rule; the authors interpret the increasing share of unemployment attributable to monetary policy shoks as arising from the zero interest rate bound.

Some Concluding Thoughts

I thought about this set of results when I read Professor Stephen Williamson's critical remarks about the relevance of Keynesian-inspired wage and price stickiness:

... what I do not like in any of the blog/mainstream news posts I have linked to above is the notion that we know exactly what is going on, and exactly what we should be doing about it. There are good reasons to question Keynesian orthodoxy in the current context. Even if we thought that sticky wages and prices were important factors in the recent recession (which I do not), it is hard to believe that the effects of this stickiness would matter 14 quarters after the onset of the recession. Those pushing the Keynesian narrative need to provide us with some more explicit evidence about wage and price stickiness as it relates to recent events.

What this paper demonstrates is that not all New Keynesian DSGE's yield the same results, and that wage stickiness could potentially explain high unemployment.