Agglomeration of low-productive entrepreneurs to large regions: a simple model

ABSTRACT

This paper develops a simple model of spatial sorting where the least productive entrepreneurs are drawn to the large core region. This is an unusual feature. The literature on spatial sorting typically shows how the most productive individuals and firms agglomerate to the core. However, our model is consistent with empirical evidence that reveals that large agglomerations also attract the low skilled.

KEYWORDS:

• agglomeration
• heterogeneous firms
• spatial sorting

JEL:

• F12
• F15
• F21
• R12

DISCLOSURE STATEMENT

No potential conflict of interest is reported by the authors.

Notes

1 That the poor seem to live closer to the city center than the rich has previously been noted by, for example, Margo (1992), Mieszkowski and Mills (1993), and Mills and Lubuele (1997).

2 Only six out of 30 mega-cities are today located in high income countries (Glaeser, 2014).

3 For example, the slum in Ahmedabad, India, according to UN-Habitat (2003), has increased from 17% in 1971 to 21% in 1982, and for 1991, 40% of households lived in slums. For Karachi, Pakistan, the share of shacks increased from 37% to 50% between 1978 and 2000.

4 Thus, migration is driven by real wage differences in both cases, but our model focuses on a different margin.

5 For surveys, see Fujita et al. (1999), Baldwin et al. (2003) and Combes et al. (2008b).

6 The first paper introducing heterogeneous firms in this literature, Baldwin and Okubo (2006), shows that the most productive firms are the first to agglomerate to the core when using the ‘footloose capital’ (FC) model by Martin and Rogers (1995).

7 Several other papers generate a gradual relocation pattern. Helpman (1998) introduces a housing sector that dampens the agglomeration process. Tabuchi and Thisse (2002), Murata (2003), Zeng (2008) and Picard and Okubo (2012) introduce preference heterogeneity in different models, which generate a non-catastrophic relocation pattern, and there are also models with CES upper tier preferences may generate a gradual relocation pattern (Pflüger & Südekum, 2007, 2011).

8 Using Second World War data from Germany, Bosker et al. (2007) find instances of multiple equilibria.

9 Baldwin and Okubo (2006) assume two asymmetric regions. Okubo (2009) models vertical linkage in two symmetric regions.

10 Sor a sufficient condition, see Appendix A in the supplemental data online.

11 This is essentially a Pareto distribution that has been truncated (Forslid & Okubo, 2012, 2015).

12 Our breakpoint corresponds to that of Pflüger (2004) for $a_i=1,$ since $\underset{\underset{\_}{a}\to 1}{lim}\xi =1.$

13 Our ‘no-black-hole’ condition corresponds to that of Pflüger (2004) for $a_i=1,$ since $\underset{\underset{\_}{a}\to 1}{lim}\xi =1$. Our condition then simplifies to ${\displaystyle \frac{L}{H}>\frac{\sigma }{\sigma -1}}$ (i.e., ${\displaystyle \frac{2L}{H+H^{\ast }}>\frac{\sigma }{\sigma -1}}$). This is identical to Plfuger’s condition (p. 569, n. 9).

14 This is a difference compared with the FC model in Baldwin and Okubo (2006), which has the same sustain point as in the homogeneous firms’ model by Martin and Rogers (1995).

15 The break/sustain gap essentially disappears when non-negative consumption is imposed in the Pflüger (2004) model, as shown by Barde and Peirson (2011).

16 We have made sure that $L$ is sufficiently large to guarantee that $C_A>0$ holds in all our simulations. See Barde and Peirson (2011) for a discussion of this condition.

Additional information

Funding

Rikard Forslid is grateful for financial support from the Jan Wallander and Tom Hedelius Research Foundation and from the Swedish Research Council. Okubo is financially supported by the JSPS (Japan Society for the Promotion of Science) KAKENHI [grant number 19H01487] and RIETI (Research Institute of Economy, Trade and Industry).