Mismatch and the Forecasting Performance of Matching Functions

AuthorEnzo Weber,Christian Hutter
Date01 February 2017
Published date01 February 2017
DOIhttp://doi.org/10.1111/obes.12142
101
©2016 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
Mismatch and the Forecasting Performance of
Matching Functions*
Christian Hutter† and Enzo Weber†,‡
Institute for Employment Research, Weddigenstr. 20-22, D-90478 Nuremberg, Germany
(e-mail: christian.hutter@iab.de)
University of Regensburg, D-93040 Regensburg, Germany (e-mail: enzo.weber@iab.de)
Abstract
This paper investigates the role of structural imbalance between job seekers and job open-
ings for the forecasting performance of a labour market matching function. Starting from
a Cobb–Douglas matching function with constant returns to scale (CRS) in each frictional
micro market shows that on the aggregate level, a measure of mismatch is a crucial in-
gredient of the matching function and hence should not be ignored for forecasting hiring
figures. Consequently, we allow the matching process to depend on the level of regional,
qualificatory and occupational mismatch between unemployed and vacancies. In pseudo
out-of-sample tests that account for the nested model environment, we find that forecast-
ing models enhanced by a measure of mismatch significantly outperform their benchmark
counterparts for all forecast horizons ranging between one month and a year. This is es-
pecially pronounced during and in the aftermath of the Great Recession where a low level
of mismatch improved the possibility of unemployed to find a job again. The results show
that imposing CRS helps improve forecast accuracy compared to unrestricted models.
I. Introduction
Many approaches for relating unemploymentand vacancies to job findings rely on matching
theory (see, e.g. Mortensen and Pissarides, 1994; Petrongolo and Pissarides, 2001) and thus
consider vacancies and unemployed as inputs into the production function of job findings.
Most studies, however, assume the efficiency parameter to be constant over time. Only in
recent years has this strong assumption been called into question. For instance, Sedlacek
(2014), Klinger and Weber (2014) and Barnichon and Figura (2015) allow for time-varying
matching efficiency. One source is given by mismatch (Sahin et al., 2014), denoting the
degree of structural imbalance between supply and demand.
We contribute to the literature by applying the concept of mismatch and, thus, a time-
varying efficiency parameter from a forecasting perspective. Employing a mismatch index
JEL Classification numbers: C22, C52, C53, E24, E27
*We are grateful to two anonymous referees,Anja Bauer as well as participants of the DIW Macroeconometric
Workshop2013, the IWH-CIREQ Macroeconometric Workshop 2013 and the UR-IAB seminar 2014 in Regensburg
for helpful suggestions and valuable input.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 79, 1 (2017) 0305–9049
doi: 10.1111/obes.12142
102 Bulletin
in forecasting regressions is an economically attractive way of modelling structural change
in the relationship among unemployment, vacancies and job findings. Furthermore, asking
whether a measure of imbalance helps improve hiring forecasts is a relevant question
because it is usually far more difficult to prove a theory useful for forecasting exercises
than it is to prove its in-sample significance. To date, the existing theoretical models have
rarely been tested for their practical usefulness with respect to forecasting exercises. As
a consequence, one hardly knows whether models that rely on matching theory truly can
serve as a base for forecasting hirings.
In the literature, a variety of indices and interpretations coexist for the concept of
mismatch.1Early approaches consider mismatch to be only a temporary phenomenon. For
instance, the mismatch index developed by Lilien (1982) is based on the assumption that
short-run shocks can lead to a change in the composition of sectoral demand in an economy.
Because labour markets only adjust slowly,mismatch occurs when both unemployment (in
the contracting sectors) and vacancies (in the expanding sectors) temporarily rise during
the period of transition. Another concept (applied by Franz, 1991, for instance) considers
mismatch to be not solely a temporary phenomenon. It is built on a disequilibrium model
in which the short side of any distinct labour market determines its level of employment.
Under the assumption that the short side is not the same in all micro markets, unemployment
and vacancies coexist at the aggregate level, which leads to employment being below
the minimum of the aggregate supply and demand. As a consequence, a higher level of
mismatch is attributable to a higher variance betweenthe markets at the micro level. A main
disadvantage of this approach to mismatch is that it rules out the coexistence of vacancies
and unemployed within each micro market (usually called frictional unemployment). In
contrast, the approach to mismatch that was embraced by Jackman and Roper (1987)
accepts that frictional unemployment is inevitable within each distinct labour market.
Therefore, incongruence at the micro level is measured relative to a more realistic (i.e.,
attainable) size of unemployment. Hence, the respective mismatch index measures how
much structural unemployment contributes to total unemployment, i.e., ‘the proportion
of unemployment attributable to structural imbalance’ (Jackman and Roper, 1987, p. 14).
However, this interpretation only holds under the assumption that the matching technology
followsa Cobb–Douglas production function with constant retur ns to scale (CRS) and equal
elasticity of 0.5. Hence, in addition to the Jackman/Roper mismatch index, we investigate
the performance of a more general mismatch indicator in which the assumption of equal
elasticities is lifted.
We use data for Germany from the statistics department of the Federal Employment
Agency (FEA), which allowfor the disagg regationof unemployed and registered vacancies
at the levels of 21 occupational segments, 50 labour market regions and three qualification
groups. This enables us to gain detailed empirical evidence on the size and development
of mismatch in Germany in the past 13 years, including the years after the Hartz labour
market reforms.
After log-linearization of the matching function, the mismatch indicator appears in an
additivefor m in our forecasting equations.As a consequence, the usual out-of-sample test of
1For an overview of various concepts for measuring mismatch, see, e.g., Schioppa (1991) or Canon, Chen and
Marifian (2013).
©2016 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

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