Abstract
This paper constructs a footloose entrepreneur model with Diamond–Mortensen–Pissarides job search and matching frictions in the manufacturing sector. It captures unemployment adjustment both within the manufacturing sector and in the regional labor market. The within-sector unemployment rate is negatively affected by firm market access and is positively related to the intensity of firm screening among heterogeneous candidate workers. The regional unemployment rate, on the other hand, is related to the sectoral share of job searching across sectors within each region. We find the coexistence of a smaller within-sector unemployment rate and a larger local unemployment rate in the region with firm agglomeration. We also extend the analysis by examining the role of labor market frictions across sectors and the interdependence between agglomeration and unemployment.
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Notes
Our paper also relates to some recent trade literature about the effect of trade costs on unemployment and wage inequality (e.g., Egger and Kreickemeier 2009; Felbermayr et al. 2011). We simplify the firm heterogeneity issue while allowing for some labor mobility. This setup enables us to explore the spatial effects of trade costs on unemployment adjustment through identifying the different forces that work together with firm agglomeration to shape regional labor market outcomes.
Given the continuum measure of workers, the risk of unemployment faced by a worker is fully diversified at the family level and each worker acts as a risk-neutral individual. The family’s goal is to maximize its welfare by allocating workers to different sectors for job searching.
Note that families are risk neutral, and unemployment does not decrease the measure of consumers. In Sect. 5.3, we allow for the demand-downsizing effect of unemployment by considering a Cobb-Douglas utility function.
For empirical evidence of productivity complementarity within firms, see, for example, Mas and Moretti (2009).
In the process of firm screening, the productivity of each matched candidate worker is still unobservable to firms. Thus, screening only helps each manufacturing firm identify whether or not a matched candidate worker’s productivity is above \(a_{ci}\).
The property of constant returns to scale in the matching function is supported by many empirical studies using regional data. These include Coles and Smith (1996) and Petrongolo and Pissarides (2006) for the UK, Gorter and van Ours (1994) for the Netherlands, and Anderson and Burgess (2000) for the US, among others.
There is no risk premium if the family allocates some workers to the manufacturing sector for job searching. The family thus maximizes its welfare by comparing the expected wage income of job searching between the sectors.
We show in Sect. 4 that the curve between wage rate and local unemployment in our model is also negatively sloped. This result, however, arises from the sectoral allocation effect that responds to agglomeration and changes the weight of job searching across sectors.
The result of constant labor market tightness in equilibrium relies on our specification of labor market matching function. When there are increasing returns or externalities in matching technology, the labor market tightness measure is affected by the size of matching agents and the measure of productivity differences, as argued by Helsley and Strange (1990), Sato (2001) and Amiti and Pissarides (2005). The simplification of match-specific productivity and firm screening enables us to investigate the impact of industrial agglomeration on the unemployment of workers who are spatially immobile.
The denominator is positive in sign. The numerator term decreases with \(\delta \). When \(\delta >\kappa >2\), the numerator is always negative.
Note that once job search decisions are made, the agricultural sector cannot employ workers that have not found a job in the manufacturing sector; thus, Eq. (15) represents the job search allocation condition for the family in each region.
In Fig. 1a, the solid curve represents the case when \(\phi =0.3\), the dashed curve represents the case when \(\phi =0.23\), and the dot-dashed curve represents the case when \(\phi =0.2\).
The parameter values are as follows: \(\rho =0.75\), \(\sigma =4\), \(\gamma =1/3\), \(\kappa =2.01\), \(\delta =3.5\kappa \), \(b=1.05\), \(c=0.18\), \(H=1\), \(\theta =3\) and \(\beta =0.3\). See Helpman et al. (2008, pp. 51–52) for empirical studies in support of the values used in the simulation. These parameter values also ensure that the income of either the entrepreneur or the family is sufficiently larger than \(\beta \), the expenditure on manufacturing goods. In Sect. 4.2, we relax the parameter settings while satisfying the equilibrium conditions in Footnote 21. We show that the result of higher unemployment in the agglomerated region is robust such that regional unemployment disparities always increase under stronger agglomeration forces.
Comparing \(\phi _{B}\) in our setup with that in Pflüger (2004), we find numerically that labor market frictions per se decrease the tendency toward firm agglomeration. Setting the same parameters of \(\theta \) and \(\sigma \), \(\phi _{B}\) is 0.2255 in our model, while it is 0.2631 in Pflüger (2004). Similar results occur for the other parameter settings in Sect. 4.2.
First, we see that \(\sigma \Gamma \left( 1+\rho \psi \right) =1\) and that \(\sigma \Gamma >1\) always holds. Consequently, with \(\psi <0\), we obtain \(-1<\rho \psi <0\). Then, solving for \(\theta \) in the equation \(\left( 1+\theta \right) \left( s\theta -1\right) -\rho \psi =0\), the numerator term is positive if \(\theta >\frac{\left( 1-s\right) +\sqrt{\left( s-1\right) ^{2}+4s\left( 1+\rho \psi \right) }}{2s}\). Since the upper bound for \(\left( s-1\right) ^{2}+4s\left( 1+\rho \psi \right) \) is \(\left( s+1\right) ^{2}\), if \(\theta >1/s\), the no-black-hole condition is always satisfied.
For region 2, \(u_{2}^{\text {within}}\) is the same with full agglomeration as under asymmetry, as represented by the same values of firm profitability in both cases. First, \(x_{1}=x_{2}\) holds at \(\lambda =1/2\) while \(x_{1}=x_{2}/\phi \) if \(\lambda =0\). Second, substituting these equations into Eq. (16) and solving for \(x_{1}\) and \(x_{2}\), we see that \(\text {RMP}_{2}=\left[ \beta \left( 1+\theta \right) /k_{M}^{\rho }\right] ^{-1/\left( 1+\rho \psi \right) }\)when \(\lambda =0\) or \(\lambda =1/2\). Thus, even though all firms agglomerate in region 2, they obtain the same profitability as in the symmetry case and thus have the same intensity of screening. See Charlot et al. (2006, p. 333) for similar discussions.
Our model follows Pflüger (2004) so that when \(\phi \) is within the interval of \((\phi _{B},\phi _{S})\), there are interior firm shares at the spatial equilibrium. Given the lower price index in the core, the local firm profitability as well as entrepreneur nominal wages should also be lower. Otherwise, the entrepreneurs always prefer to locate in the core. This wage pattern persists in the partial agglomeration phases.
Handbury and Weinstein (2011) provide the first empirical evidence of the existence of forward linkages.
In this benchmark case, \(\tau \) is around 1.64, indicating a variable trade cost of about 64 %, a figure supported in many empirical trade studies.
These conditions include \(\kappa >2\), \(1-\kappa \gamma >0\), \(\delta >\kappa \), \(\Gamma >0\) and \(\theta >1/s\) where \(s=b^{\frac{\gamma \left( \gamma -\kappa \right) \rho ^{2}}{\Gamma }}\left( \frac{\rho }{1+\rho \gamma }\right) \).
With full employment in the agricultural sector, aggregate unemployment in the economy increases monotonically with \(u_{M}\).
We keep the parameters of \(\rho \), \(\delta \), \(\kappa \), \(\gamma \), \(c\), and \(\beta \) identical to our benchmark case, as shown in Footnote 13. In addition, we assume that \(\eta =1/2\) and examine how \(\zeta _{A}\) and \(\zeta _{M}\) may affect the unemployment rates in each region.
We still assume that when the symmetric equilibrium breaks up, region 1 happens to become a peripheral region with a smaller share of manufacturing firms.
References
Amiti M, Pissarides CA (2005) Trade and industrial location with heterogeneous labor. J Int Econ 67:392–412
Anderson P, Burgess S (2000) Empirical matching functions: estimation and interpretation using state-level data. Rev Econ Stat 82:93–102
Baldwin R, Forslid R, Martin P, Ottaviano G, Robert-Nicoud F (2003) Economic geography and public policy. Princeton University Press, Princeton
Blanchard O, Katz L (1992) Regional evolutions. Brookings Pap Econ Act 23:1–76
Bound J, Holzer HJ (2000) Demand shifts, population adjustments, and labor market outcomes during the 1980s. J Labor Econ 18:20–54
Charlot S, Gaigné S, Robert-Nicoud F, Thisse J-F (2006) Agglomeration and welfare: the core-periphery model in the light of Bentham, Kaldor, and Rawls. J Pub Econ 90:325–347
Coles M, Smith E (1996) Cross-section estimation of the matching function: evidence from England and Wales. Economica 63:589–597
Combes P-P, Mayer T, Thisse J-F (2008) Economic geography: the integration of regions and nations. Princeton University Press, Princeton
Dixit A, Stiglitz J (1977) Monopolistic competition and optimum product diversity. Am Econ Rev 67:297–308
Egger H, Kreickemeier U (2009) Firm heterogeneity and the labor market effects of trade liberalization. Int Econ Rev 50:187–216
Egger P, Seidel T (2008) Agglomeration and fair wages. Can J Econ 41:271–291
Elhorst JP (2003) The mystery of regional unemployment differentials: theoretical and empirical explanations. J Econ Surv 17:709–748
Epifani P, Gancia G (2005) Trade, migration and regional unemployment. Reg Sci Urban Econ 35:625–644
Felbermayr G, Prat J, Schmerer H (2011) Globalization and labor market outcomes: wage bargaining, search frictions, and firm heterogeneity. J Econ Theor 146:39–73
Forslid R, Ottaviano G (2003) An analytically solvable core-periphery model. J Econ Geogr 3:229–240
Francis J (2009) Agglomeration, job flows and unemployment. Ann Reg Sci 43:181–198
Fujita M, Krugman P, Venables A (1999) The spatial economy: cities, regions, and international trade. MIT Press, Cambridge, MA
Gorter C, van Ours J (1994) Matching unemployment and vacancies in regional labor markets: an empirical analysis for the Netherlands. Pap Reg Sci 73:153–167
Greenwood MJ (1997) Internal migration in developed countries. In: Mark RR, Oded S (eds) Handbook of population and family economics. Elsevier, Amsterdam, pp 647–720
Handbury J, Weinstein, D (2011) Is new economic geography right? Evidence from price data. NBER Working paper No. 17067
Harris J, Todaro M (1970) Migration, unemployment & development: a two-sector analysis. Am Econ Rev 60:126–142
Head K, Mayer T (2004) The empirics of agglomeration and trade. In: Henderson JV, Jacques-François T (eds) Handbook of regional and urban economics, vol 4. Elsevier, Amsterdam, pp 2609–2669
Helpman E, Itskhoki O, Redding S (2008) Inequality and unemployment in a global economy. NBER Working paper No. 14478
Helpman E, Itskhoki O, Redding S (2010) Inequality and unemployment in a global economy. Econometrica 78:1239–1283
Helsley R, Strange W (1990) Matching and agglomeration economies in a system of cities. Reg Sci Urban Econ 20:189–212
Krugman P (1991) Increasing returns and economic geography. J Polit Econ 99:483–499
Mas A, Moretti E (2009) Peers at work. Am Econ Rev 99:112–145
Nickell S, Bell B (1996) Changes in the distribution of wages and unemployment in OECD countries. Am Econ Rev 86:302–308
Ottaviano G, Thisse J-F (2004) Agglomeration and economic geography. In: Henderson JV, Jacques-François T (eds) Handbook of regional and urban economics, vol 4. Elsevier, Amsterdam, pp 2563–2608
Overman H, Puga D (2002) Unemployment clusters across Europe’s regions and countries. Econ Policy 17:117–147
Petrongolo B, Pissarides C (2006) Scale effects in markets with search. Econ J 116:21–44
Pflüger M (2004) A simple, analytically solvable, Chamberlinian agglomeration model. Reg Sci Urban Econ 34:565–573
Pflüger M, Südekum J (2008) A synthesis of footloose-entrepreneur new economic geography models: when is agglomeration smooth and easily reversible? J Econ Geog 8:39–54
Pflüger M, Südekum J (2011) On pitchforks and tomahawks. J Reg Sci 51:292–298
Sato Y (2001) Labor heterogeneity in an urban labor market. J Urban Econ 50:313–337
Shields G, Shields M (1989) The emergence of migration theory and a suggested new direction. J Econ Surv 3:277–304
Stole L, Zwiebel J (1996) Intra-firm bargaining under non-binding contracts. Rev Econ Stud 63:375–410
Südekum J (2005) Increasing returns and spatial unemployment disparities. Pap Reg Sci 84:159–181
Topel R (1986) Local labor markets. J Polit Econ 94:S111–S143
vom Berge P (2013) Search unemployment and new economic geography. Ann Reg Sci 50:731–751
Zierahn U (2013) Agglomeration, congestion and regional unemployment disparities. Ann Reg Sci 51:435–457
Acknowledgments
We thank the Editor and two anonymous reviewers for their very helpful comments and suggestions. We also benefited from comments by Shihe Fu, Nobuaki Hamaguchi, Tomoya Mori, Noritsugu Nakanishi, Se-il Mun, Laixun Zhao, and the workshop participants at Kobe University, Kyoto University and Xiamen University. Financial support from the National Natural Science Foundation of China (Grant No. 71303202) and MOE (Ministry of Education in China) Major Project of Humanities and Social Sciences (Grant No. 13JZD010) is gratefully acknowledged.