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The Annals of Regional Science

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17.07.2021 | Original Paper

Frictional unemployment, bargaining, and agglomeration

verfasst von: Xinmeng Li, Dao-Zhi Zeng

Erschienen in: The Annals of Regional Science | Ausgabe 1/2022

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Abstract

This paper examines how matching elasticity and labor bargaining power affect industrial agglomeration in an open economy with frictional labor markets. The analysis is based on a footloose capital model of two symmetric regions with a single industry and immobile labor. Unemployment is generated by a Diamond–Mortensen–Pissarides-type search and matching mechanism. We find that the agglomeration force caused by search frictions in the labor market may be strong enough to break the symmetric equilibrium when the matching elasticity with respect to job vacancies is large and/or labor bargaining power is strong. Matching elasticity is crucial for determining the configuration of economic geography.

Vorheriger Artikel The geography of COVID-19 in Sweden

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Empirical studies find that the range for the matching elasticity with respect to vacancies is quite large. For instance, Borowczyk-Martins et al. (2013) give a range from 0.33 to 0.84 with various estimating methodologies. In Coles and Petrongolo (2008), the estimated value could be pretty close to 1 under stock-flowing matching with specific filtered data. Fox (2002) reports an estimate of 0.98 in a linear regression model. Blanchard and Diamond (1989, p.31) also propose the possibility that manufacturing firms may have little trouble recruiting workers. Based on their empirical facts, we conclude that both symmetric and asymmetric equilibria are possible in the real world.

Another segment of the literature explores unemployment with the paradigm of fairness preference or efficiency wage in NEG frameworks, e.g., Suedekum (2005), Francis (2007), Egger and Seidel (2008), and Zierahn (2013).

Ago et al. (2017) construct a trade model with an elastic labor supply to investigate the economic impacts of technological progress. Nevertheless, the symmetric equilibrium is always stable in their framework.

There is also a growing body of literature on the trade–unemployment relationship within a framework of fair wages or efficiency wages, including Egger and Kreickemeier (2009, 2012) and Davis and Harrigan (2011).

This calculation is for deriving how a firm’s revenue is related to the employment level, $l_i$. Details are given in Appendix 1.

Details are given in Appendix 2.

In Appendix 4, we consider a more general case in which hiring costs are paid by both labor and capital. We show that our results are robust.

We assume that $1-m \left[ 2(\sigma -1)/(c \sigma )\right] ^{\mu }>0$ always holds, so that firms can always match sufficient workers with vacancies and the unemployment rate is nonnegative.

Using (4), the following differential equation of $w_i$ can be derived from (8):

$$\begin{aligned} \frac{\mathrm {d}w_i}{\mathrm {d}l_i}=\frac{\sigma -1}{\sigma }R_il_i^{-2}-\frac{w_i}{\beta l_i}. \end{aligned}$$

Using (3), the general solution to the above equation is $w_i=[\beta (\sigma -1)/(\sigma -\beta )]R_i/l_i +\mathcal{C}l_i^{-1/\beta }$, where $\mathcal{C}$ is a constant coefficient. Since $w_il_i$ is finite when $l_i\rightarrow 0$, we know that $\mathcal{C}=0$.

Researches with static matching setups include Helpman and Itskhoki (2010) and Helpman et al. (2010).

As in Baldwin et al. (2003, p.74), a straightforward assumption is imposed here that half of the employed capital in each region belongs to region 1 for any k. This simplifies our analysis of a short-run equilibrium because the capital returns to the owners in the two regions are equal for any k. Note that such an assumption does not change the results regarding a long-run equilibrium.

Since we have only two regions, the stability results derived from this specific dynamics can be generalized to any positive definite dynamics. See Tabuchi and Zeng (2004, p.644).

In Sect. 3, we show that a corner equilibrium exists if and only if $\mu =1$. Therefore, here we only focus on the case of $\mu <1$.

For $\mu =1$, full agglomeration occurs in the asymmetric equilibrium. We discuss the wage rate of this case in Sect. 3.

More wage payment with a larger $\beta$ also implies higher labor costs. Since the two regions have the same $\beta$, labor is more expensive in both regions with a larger $\beta$.

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Titel: Frictional unemployment, bargaining, and agglomeration
verfasst von: Xinmeng Li
Dao-Zhi Zeng
Publikationsdatum: 17.07.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: The Annals of Regional Science / Ausgabe 1/2022
Print ISSN: 0570-1864
Elektronische ISSN: 1432-0592
DOI: https://doi.org/10.1007/s00168-021-01072-z

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