Bargaining and Wage Rigidity in a Matching Model for the US

AuthorSophocles Mavroeidis,James M. Malcomson
DOIhttp://doi.org/10.1111/obes.12186
Date01 December 2017
Published date01 December 2017
997
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
doi: 10.1111/obes.12186
Bargaining and Wage Rigidity in a Matching Model
for the US*
James M. Malcomson† and Sophocles Mavroeidis
Department of Economics, University of Oxford, UK
(e-mail: james.malcomson@economics.ox.ac.uk)
Department of Economics and Institute for New Economic Thinking at the Oxford Martin
School, University of Oxford, UK (e-mail: sophocles.mavroeidis@economics.ox.ac.uk)
Abstract
This paper uses robust econometric methods to assess previous empirical results for the
Mortensen and Pissarides (1994) matching model. Assuming all wages are negotiatedeach
period is inconsistent with the history dependence in US wages, even allowing for hetero-
geneous match productivities, time to build vacancies and credible bargaining. Flexible
wages for job changers, with rigid wages for job stayers, allows the model to capture this
history dependence and is not inconsistent with parameter calibrations in the literature.
Such wage rigidity affects only the timing of wage payments over the duration of matches;
conclusions about other characteristics are unaffected by it.
I. Introduction
The Mortensen and Pissarides (1994) matching model is the basis for most recent discus-
sions of unemploymentand vacancies at the macroeconomic level in the US.1The empirical
implementations in Cole and Rogerson (1999),Yashiv (2000), Shimer (2005),Yashiv(2006)
and Hagedorn and Manovskii (2008) assume Nash bargaining of wages in all matches
each period. Hall (2005a, b) and Hall and Milgrom (2008) retain bargaining of wages in
all matches each period but replace Nash by other forms of bargaining. Others, such as
Shimer (2004), Gertler and Trigari (2009), Pissarides (2009), Rudanko (2009), Rudanko
(2011), Haefke, Sonntag and van Rens (2013), Kudlyak (2014) and Gertler, Huckfeldt and
Trigari (2016), argue that introducing some form of wage rigidity enables the matching
model to better capture the relationship between unemployment, vacancies and wages in
US data. There is also a substantial literature on New Keynesian models with search and
JEL Classification numbers: E2, J3, J6.
*Wethank participants in seminars at IZA/CEPR European Summer Symposium in Labour Economics, at LSE and
at Oxford for very helpful comments. Malcomson thanks Leverhulme Trust Major Research Fellowship F/08519/B
for financial support of this research. Mavroeidis thanks the European Commission for financial support of this
research under a FP7 Marie Curie Fellowship CIG 293675.
1There is also a growing literature applying disaggregated versions of the matching model with heterogeneous
firms and employees to micro data (see e.g. Cahuc, Postel-Vinay and Robin, 2006, Robin, 2011).
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 79, 6 (2017) 0305–9049
998 Bulletin
matching frictions that has looked at wage persistence (Christoffel, Kuester and Linzert,
2009, Krause and Lubik, 2007, Krause, Lopez-Salido and Lubik, 2008, Trigari, 2009).
In most of these studies, empirical results are based on calibration or full-information
estimation, both of which require strong assumptions to pin down the distribution of the
data. The studies using calibration rely on specific assumptions about the distribution of
shocks. Those using full-information estimation rely on other aspects of the full model
being correctly specified. In addition, all empirical results reported in the literature rely on
the assumption of strong identification, since none of the papers use methods that are robust
to weak identification or weak instruments. Hence the rejection of the spot market model,
and evidence on any of the proposed extensions, is conditioned on those assumptions.
The contribution of this paper is to assess the robustness of results in previous studies
to dropping those strong assumptions. We use limited-information analysis so that our
results do not rely on correct specification of the other aspects of the model.2Moreover,
the models we estimate are forward-looking rational expectations models and this charac-
teristic provides straightforward criteria for determining valid instruments. Furthermore,
our estimation is based on the generalized method of moments (GMM) making use of
methods of inference that are robust to weak instruments (see Stock and Wright, 2000).
This innovation relative to the literature on matching in wage determination is important
because weak instruments are known to pose a very serious threat to empirical validity
across many areas of economics (see e.g. Stock, Wright andYogo, 2002).
The paper establishes two main robust findings on the basis of these estimation meth-
ods. First, none of the formulations in the aforementioned literature with wages in all
matches negotiated each period satisfactorily captures the history dependence in wages.
Second, there is a formulation of wage rigidity that does so and, consistent with the micro
evidence reported in Pissarides (2009) and reiterated by Haefke et al. (2013), applies only
to continuing matches.
This second finding has important implications. If wage rigidity applies to new, as well
as continuing, matches, as in Gertler and Trigari (2009), it affects job creation and hence
vacancies and unemployment. But, as pointed out by Malcomson (1999, Section 4) and
Pissarides (2009), if it applies only to continuing matches, it affects onlythe timing of wage
payments over the duration of a match. So conclusions for vacancies and unemployment
drawn from studies without wage rigidity continue to apply.3
The underlying problem for capturing the history dependence of wages with models in
which wages in all matches are determined by the Nash bargainin every period is illustrated
in Figure 1.This compares the variation in the wage predicted by the calibration in Hagedorn
and Manovskii (2008) with the average wage in the data. The residuals are the difference
between these. It is apparent from the figure that the residuals are highly persistent (as
measured by the autocorrelation function), which is contrary to what one would expect if
the model captured adequately the history dependence of wages in the data.
Subsequent contributions have extended the model with all wages negotiated each pe-
riod to address this problem. Hall and Milgrom (2008) consider a different model of bar-
2This approach has been used successfully in many other areas of macroeconomics. For example, see Gali and
Gertler (1999) for the New Keynesian Phillips curve.
3Gertler et al. (2016) criticizes this conclusion but does not test for history-dependence in wages, the issue we
address in this paper.
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

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