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The Annals of Regional Science

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01.06.2013 | Original Paper

Search unemployment and new economic geography

verfasst von: Philipp vom Berge

Erschienen in: The Annals of Regional Science | Ausgabe 3/2013

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Abstract

This paper develops a general equilibrium geographical economics model, which uses matching frictions on the labor market to generate regional unemployment disparities alongside the usual core-periphery pattern of industrial agglomeration. In the model, regional wage differentials do not only influence migration decisions of mobile workers, but also affect the bargaining process on local labor markets, leading to differences in vacancies and unemployment as well. In a setting with two regions, both higher or lower unemployment rates in the core region are possible equilibrium outcomes, depending on transport costs and the elasticity of substitution. Stylized facts suggest that both patterns are of empirical relevance.

Vorheriger Artikel Endogenous Growth in an Aging Economy: Evidence and Policy Measures

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The original setup using interregional migration has been complemented by models using intraregional migration and intermediate inputs (e.g. Venables 1996). Puga (1999) merges both ideas in a more general framework. There are models that incorporate congestion (e.g., Brakman et al. 1996; Südekum 2006) and commuting costs (e.g., Tabuchi 1998; Borck et al. 2007). Other models deal with more than two regions (e.g., Brakman et al. 1996; Fujita et al. 1999, chapt. 6). Baldwin et al. (2003, part I) review analytically solvable variants of the model.

For a comprehensive review of the empirical literature on regional labor market differentials, see Elhorst (2003).

One example often made in this context are the rather low migration rates between European regions.

Monfort and Ottaviano (2002), Picard and Toulemonde (2001) and Picard and Toulemonde (2006) do not model unemployment.

Matusz (1996) has a related models that lacks agglomeration forces. Peeters and Garretsen (2004) deals with unemployment, but allows for it only in the home country.

In the case of Epifani and Gancia (2005), in-migration first increases unemployment in the core region. This effect is then reverted in the long run.

Obviously, these coefficients indicate correlation, not causality.

German data are split to account for the large divergence between East and West. Anchorage (AK) has been excluded from the US regression because of its very low density. This is due to an implausibly high number for surface area in the data.

Pissarides (1990, Chap. 1) presents a basic equilibrium unemployment model with search costs. This approach has been extended in the literature in several ways that are relevant to the model presented here. Ziesemer (2005) introduced monopolistic competition of the Dixit and Stiglitz (1977) type to it. Ortega (2000) and Sasaki (2007) consider international migration in models with constant-returns production technologies when matching frictions occur. Sato (2000) shows that a stable wage curve emerges in a search model if regions with a monocentric city structure and different productivity levels are included.

Both rates are measured as a fraction of the mobile labor force.

For details of the derivations in this section, readers are referred to Fujita et al. (1999, Chapter 4).

Thus we may call $k$ the “number” of varieties.

Nominal benefit payments $z$ are assumed to be constant over regions.

This has been shown by Ziesemer (2005). The result does not carry over to decisions between regions, because the tax might influence regional real wages and benefits differently. We will therefore reintroduce the tax system in Sect. 3.

Linking vacancy costs to wages has two advantages over fixing them to (the real value of) some arbitrary number. The first advantage is that the conditions for short-run equilibrium in Sect. 3 get more tractable. As a second advantage, we now explicitly specify where the vacancy costs go.

We use the concept of a large firm proposed by Pissarides (1990), so there is no uncertainty about the flow of labor.

See Appendix A.1 for details.

This is true if $\rho < \delta /(r+\delta )$.

Note that workers real wage $w^{W}$ and firms real wage $w^{F}$ might well be different in Eqs. (9) and (10). Fortunately, this is not a problem. Because of the structure of the bargain, one can always scale the value functions for workers in a way resulting in only one decision variable $w^{F}$ without changing incentives. From (8) and (9) one gets that $E-U = (w^{F}-rU)/(r+\delta )$. The supply condition is $V=0$. Equation (23) follows assuming that $\theta $ is given for a single bargain.

In the absence of any search costs, $\rho /c$ equals the average product. Here,

$$\begin{aligned} \rho /c = (\hat{x}/\hat{\ell }) \left[ 1 + \frac{\gamma r}{q(\theta )} \right] \left[ 1-\frac{\gamma \delta }{q(\theta )} \right]^{-1}, \end{aligned}$$

because a successful job match frees resources from search.

See Appendix A.2 for details.

See Blanchflower and Oswald (1994) for other explanations for such a relationship.

We assume that there are no transport costs for the traditional good.

To simplify notation, we choose units such that $\rho =c$ and $\mu =F$. Moreover, we introduce the function

$$\begin{aligned} \varOmega (\theta ) = \left(1-\rho +\frac{\gamma r}{q(\theta )}\right)^{1/\sigma } \left[ 1 + \frac{\gamma r}{q(\theta )} \right]^{-1} \left[ 1-\frac{\gamma \delta }{q(\theta )} \right]. \end{aligned}$$

(28)

We choose a two-region representation for ease of exposition. The model can be readily expanded to a multi-region case along the lines of Brakman et al. (1996) and Fujita et al. (1999, chap. 6).

$\mu $ and $\sigma $ are set like in Fujita et al. (1999) to ensure comparability. The labor market parameters are set in a range of plausibility according to empirical data (see Cahuc and Zylberberg 2004, chapter 9). $\gamma $ and $z$ are chosen to imply an unemployment rate of 8 to 10 % and a replacement ratio of 60–70 % to roughly match Germany (see OECD 2006, p. 60 and Table 1).

The scaling of the right figure is difference in percentage points.

For plotting the unemployment differentials, assume that region 1 comes out as the core in case of an agglomeration equilibrium.

Strictly speaking, there is no unemployment in the periphery when agglomeration is complete since there are no mobile workers present. The unemployment rate in region 2 is defined as the one that would result if a marginal worker decided to leave the core.

Simulation results are omitted.

See Pissarides (1990).

See, for example, Glaeser and Mare (2001) for the U.S. and Haas and Möller (2003) for Germany.

Even if the price for housing does not influence the workers relative fall-back position, it still has an effect on migration decisions, of course.

In our simple model, this just means to hold $z/W$ constant for all regions. In reality, this might be more complicated because incentives are not only influenced by wages and unemployment benefits.

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Titel: Search unemployment and new economic geography
verfasst von: Philipp vom Berge
Publikationsdatum: 01.06.2013
Verlag: Springer-Verlag
Erschienen in: The Annals of Regional Science / Ausgabe 3/2013
Print ISSN: 0570-1864
Elektronische ISSN: 1432-0592
DOI: https://doi.org/10.1007/s00168-012-0535-z

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