Spatial dependencies in German matching functions

Abstract

This paper proposes a spatial panel model for German matching functions to avoid possibly biased and inefficient estimates due to spatial dependence. We provide empirical evidence for the presence of spatial dependencies in matching data. Based on an official data set containing monthly information for 176 local employment offices, we show that neglecting spatial dependencies in the data results in upward-biased coefficients. For the incorporation of spatial information into our model, we use data on commuting relations between local employment offices. Furthermore, our results suggest that a dynamic modeling is more appropriate for matching functions.

Introduction

In 2009, there were about 9.25 million people that became unemployed in Germany. But, during the same time, about 9 million people left the state of inactivity while the average unemployment stock amounted to 3.42 million in 2009. These numbers illustrate that labor markets are characterized by large flows between the states of activity and inactivity. In macroeconomic research, a standard tool to analyze these dynamics is the matching function which describes how the flow of new hires (matches) is related to the unemployment stock and to the stock of vacancies. The matching function allows to analyze the determinants of job creation and the structure of underlying search frictions in labor markets.

However, as shown in this paper, labor market activity is correlated over space. The presence of spatial (auto-)correlation implies that the extent of matching in one particular region is correlated with that in neighboring regions. Neglecting spatial correlation when modeling the matching process yields biased and inefficient estimates of the matching function. This is widely ignored in the empirical matching literature as matching functions are mostly specified according to models assuming cross-sectional independence among observations. This independence assumption is questionable with respect to both the labor supply and the labor demand side. On the one hand, the search behavior of workers is not limited to one particular region resulting in migration and commuting of workers. On the other, the agglomeration literature shows that there are economies of scale due to spatial concentration of activity of firms within industries (see Ciccone and Hall, 1996, for example). According to Rosenthal and Strange (2001), one reason for agglomeration is labor pooling, i.e. firms of the same industry tend to cluster in space in order to profit from a pool of specialized workers in this region.

The aim of this paper is the estimation of matching functions taking into account spatial dependencies in order to obtain unbiased and efficient estimates. For the estimation, we use an official data set that provides monthly information on 176 local employment offices (Arbeitsagenturen) for the period from 2000 until 2009. To exploit the panel structure of the data, we specify the matching function using a spatial panel model. In addition to a static model, we use a dynamic model for the matching function to capture the positive (temporal) autocorrelation in the data. Most contributions in the empirical matching literature apply only a static modeling to the matching function. The combination of both spatial econometric methods and dynamic modeling is novel to this literature.

The estimation of matching functions has been subject of intensive research in the literature. In their seminal paper, Blanchard and Diamond (1989) estimate matching functions using aggregated time series for the United States. After that, other authors provide studies on aggregated matching functions for different countries. Van Ours (1991) analyzes the Netherlands, Berman (1997) estimates aggregate matching functions for Israel and Burda and Wyplosz (1994) investigate the labor markets of Germany, Spain, France and the United Kingdom. Utilizing aggregated time series assumes that the national economy acts as a single labor market (Coles and Smith, 1996). Due to many factors that hamper mobility, as individual preferences, social ties, differences in real income, etc., it is more reasonable to consider the national economy as a collection of spatially distinct labor markets (Coles and Smith, 1996). Therefore, authors turned to estimating matching functions using regional data sets. Burda (1993) uses data on Czech and Slovak employment offices, Coles and Smith (1996) use regional labor market data for the United Kingdom and Anderson and Burgess (2000) use state-level data for the United States. However, these contributions do not model cross-sectional dependencies explicitly. The contributions by Fahr and Sunde, 2001, Fahr and Sunde, 2006a, Fahr and Sunde, 2006b, Fahr and Sunde, 2009 also deal with data on German labor markets. Our paper extends the range of their analysis by using data for both West and East Germany covering a more recent period.

To our best knowledge, only a few contributions deal with spatial dependencies in the empirical matching context as Burgess and Profit, 2001, Hynninen, 2005, Fahr and Sunde, 2006a, Fahr and Sunde, 2006b, Dmitrijeva, 2008. These authors introduce spatial interactions into their model using spatially lagged exogenous variables. This is a simple way of modeling a spatial process since estimation of such models requires no specific estimation methodology. As suggested by test results on cross-sectional dependence in the residuals, this model does not capture the spatial autocorrelation in the data in a sufficient way. Therefore, we apply panel models including a spatial lag and a spatial error term to the matching function. Lee and Yu (2010b) propose a quasi-maximum likelihood approach for the static spatial autoregressive panel data model with fixed effects which we adopt here. For the estimation of the dynamic model, we employ the estimation methodology suggested by Lee and Yu (2010c).

An important component of spatial econometric modeling is the spatial weights matrix. In addition to the binary contiguity matrix that is mostly used in the literature, we exploit a data set on commuting relations between local employment offices to construct both binary spatial weights matrices with entries zero and one and spatial weights matrices with general weights. We believe that the amount of commuting captures the actual spatial relations on labor markets better than the binary contiguity matrix.

We extend the existing literature by the following three aspects: Firstly, we estimate matching functions controlling for both temporal and spatial (auto-)correlation by applying recent estimation methodologies for spatial panel models. Secondly, we find that ignoring spatial dependencies in matching data when modeling the matching function results in upward-biased matching elasticities. As the estimated matching elasticities reflect the structural features of the matching process, this finding is important. Thirdly, our results suggest that compared to a static model, a dynamic approach results in a better fit of the data.

The structure of the paper is as follows: The second section presents the basic matching model while the third presents the data set and explains how the spatial weights matrix is defined. In order to motivate the spatial econometric approach, the fourth section provides test results of the (global) Moran I test for spatial autocorrelation. Section five presents the econometric model and the sixth section is dedicated to the estimation results. Finally, the last section concludes.