Unemployment in an Estimated
New Keynesian Model
Jordi Galí
y
Frank Smets
z
Rafael Wouters
x
June 27, 2011
Abstract
We reformulate the Smets-Wouters (2007) framework by embed-
ding 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. Our ap-
proach overcomes the lack of identi…cation of wage markup and labor
supply shocks highlighted by Chari, Kehoe and McGrattan (2008) in
their criticism of New Keynesian models, and 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 ‡uctuations.
JEL Classi…cation: D58, E24, E31, E32.
Keywords: nominal rigidities, unemployment ‡uctuations, Phillips
curve, wage markups shocks, output gap.
Prepared for the NBER Macroeconomics Annual 2011 Conference, held in Cambridge,
MA on April 8-9, 2011. We have bene…ted from comments by Larry Christiano, Marco del
Negro, Keith Kuester, Richard Rogerson, Carlos Thomas, and participants at the NBER
Summer Institute, SED Conference (Montréal), Banque de France, Harvard, EUI (Flo-
rence), Bank of Cyprus, CREI-UPF, ECB, Leuven, Insead and PSE. Galí acknowledges
the …nancial support from the European Research Council through an Advanced Grant
(Project Reference #229650).
y
CREI, Universitat Pompeu Fabra and Barcelona GSE.
z
European Central Bank, CEPR and University of Groningen
x
National Bank of Belgium
1 Introduction
Over the past decade an increasing number of central banks and other pol-
icy institutions have developed and estimated medium-scale New Keynesian
DSGE mo dels.
1
The combination of a good empirical …t with a sound, mi-
crofounded structure makes these models particularly suitable for forecasting
and policy analysis. However, as highlighted by Galí and Gerter (2009) and
others, one of the shortcomings of these models is the lack of a reference
to unemployment. This is unfortunate because unemployment is an impor-
tant indicator of aggregate resource utilization and the central focus of the
policy debate. Recently, a number of papers have started to address this
shortcoming by emb edding in the basic New Keynesian model various the-
ories of unemployment based on the presence of labor market frictions (e.g.
Blanchard and Galí (2007), Christo¤el et al (2007), Gertler, Sala and Tri-
gari (2008), Christiano, Trabandt and Walentin (2009), and de Walque et al
(2008)).
The present paper takes a di¤erent approach. Following Gali (2011a,b),
it reformulates the Smets and Wouters (2007; henceforth, SW) model to
allow for involuntary unemployment, while preserving the convenience of
the representative household paradigm. Unemployment in the model results
from market power in labor markets, re‡ected in positive wage markups.
Variations in unemployment over time are associated with changes in wage
markups, either exogenous or resulting from nominal wage rigidities.
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1
See, for example, Smets et al. (2010) for a short description of the two aggregate euro
area models used at the ECB. Two of the DSGE models used at the Federal Reserve are
described in Edge et al. (2007) and Erceg et al. (2006).
2
The general approach builds on Galí (1996). See also Blanchard and Galí (2007),
1
The proposed reformulation allows us to overcome an identi…cation prob-
lem pointed out by Chari, Kehoe and McGrattan (2008; henceforth, CKM)
and interpreted by these authors as an illustration of the immaturity of New
Keynesian models for p olicy analysis. Their observation is motivated by the
SW …nding that wage markup shocks account for almost 50 percent of the
variations in real GDP at horizons of more than 10 years. However, with-
out an explicit measure of unemployment (or, alternatively, labor supply),
these wage markup shocks cannot be distinguished from preference shocks
that shift the marginal disutility of labour. The policy implications of these
two sources of ‡uctuations are, however, very di¤erent. Variations in wage
markup shocks are ine¢ cient and a welfare-maximising government should
be interested in stabilising output ‡uctuations resulting from those shocks
(at least partly). In contrast, output and employment ‡uctuations driven
by preference shocks shifting the labor supply schedule, should in princi-
ple be accommodated. Put it di¤erently, the relative importance of those
two shocks will in‡uence the extent to which ‡uctuations in output during
a given historical episode should or should not be interpreted as re‡ecting
movements in the welfare relevant output gap (i.e. the distance between the
actual and e¢ cient levels of output). By including unemployment as an ob-
servable variable, this identi…cation problem can be overcome, and "correct"
measures of the output gap can be constructed, as we show in Section 4.
When we estimate the reformulated SW model using unemployment as an
observable variable, we …nd a much diminished role for wage markup shocks
Casares (2010), and Zanetti (2007) for related applications to the New Keynesian model.
After having circulated a …rst draft of the present paper we became aware of Casares,
Moreno and Vázquez (2011), which contains an exercise close in spirit (but with substantial
di¤erences in details) to the one presented here.
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as a source of output and employment ‡uctuations, even though those shocks
preserve a large role as drivers of in‡ation. Our estimates lead us to classify
the multiple shocks in the model in three categories (which we label "de-
mand", "supply", and "labor market" shocks), on the basis of their implied
joint comovement among output, employment, the labor force, unemploy-
ment, in‡ation and the real wage, as captured by their associated impulse
response functions (IRFs). In addition, we show how the implied measure
of the welfare-relevant output gap is to a large extent the mirror image of
the unemployment rate, and resembles conventional measures of the cyclical
component of log GDP, based on statistical detrending methods (though the
correlation is far from perfect).
Our estimates of the reformulated SW model allow us to address a num-
ber of additional questions of interest which could not be dealt with using the
model’s original formulation. Thus, in section 5 we assess quantitatively the
relative importance of di¤erent shocks as sources of unemployment ‡uctua-
tions and their role during speci…c historical episodes, including the recent
recession. Also, our approach allows us to uncover a measure of the natural
rate of unemployment (i.e. the ‡exible wage counterfactual) and to study
its comovement with actual unemployment. That comovement is shown to
be particularly strong at low frequencies, as expected, but the gap between
the two caused by wage rigidities is estimated to be large and persistent. We
also revisit the evidence on the joint behavior of in‡ation and unemployment
under the lens of our estimated model. This allows us to give a structural
interpretation to empirical Phillips curves, both for wage and price in‡ation.
In section 6 we discuss the robustness of our …ndings to the use of alternative
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sample period and data. Section 7 concludes.
In addition to reformulating the wage equation in terms of unemployment,
our model shows a number of small di¤erences with that in SW (2007). 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, comp ensation
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 e¤ect 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 rest of the paper is structured as follows. Section 2 describes the
modi…ed Smets-Wouters model. Next, Section 3 presents the data and es-
timation. Section 4 contains the discussion of the CKM critique. Section 5
analyses di¤erent aspects of unemployment ‡uctuations which the reformu-
lation of the SW model makes possible. Section 6 presents some robustness
exercises and, …nally, Section 7 concludes.
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