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The Annals of Regional Science

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12.10.2015 | Original Paper

Agglomeration, search frictions and growth of cities in developing economies

verfasst von: Chul-In Lee

Erschienen in: The Annals of Regional Science | Ausgabe 2-3/2015

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Abstract

We study agglomeration economies from a dynamic search-matching perspective to account for the growth of cities in developing economies. Agglomeration economies are not only the cause but also the consequence of migratory inflows. Without frictions, however, agglomeration economies as a labor-pull factor will attract workers instantaneously to a region, which is inconsistent with the data. We argue that agglomeration benefits combined with search and additional frictions (e.g., fixed costs and imperfect recognition of the benefits) can generate a transitory endogenous growth path that is consistent with the set of empirical regularities observed over the economic development process: gradual rural-to-urban migration and the resulting urban concentration, productivity improvement, urban unemployment, and wage and unemployment gaps across regions, which diminish with economic development. We also characterize optimal urbanization and draw some policy implications including the necessity of regulating urban concentration.

Vorheriger Artikel Regional well-being indicators and dispersion from a multidimensional perspective: evidence from Italy

Nächster Artikel Segregation patterns in cities: ethnic clustering without skill differences

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Since Marshall (1890), economists have noted that urban agglomerations can create technological externalities: the information spillover benefits in input and output markets of having economic agents in close spatial proximity where information decay over space is rapid. In addition, the NEG literature (e.g., Krugman 1991) develops the idea that spatial proximity generates pecuniary externalities, which reduces the costs of trade of intermediate and final goods. Recently, the economic growth literature has offered further insight into urban agglomeration by viewing cities as promoting human capital accumulation through active learning (e.g., Lucas 1988; and Glaeser and Mare 2001). See the survey about urbanization and growth by Henderson (2004). Rosenthal and Strange (2004) provide an extensive survey of the evidence on the nature and sources of agglomeration economies. See also Duranton (2008) for a survey of developing countries.

Endogenous growth often refers to the case in which the shares of accumulating factors sum up to unity or above, and thus per capita income growth does not stop even in the long run. As we will see later, our model can cover both the case mentioned and the case in which per capita income growth eventually stops.

The motivation for HT models comes from accounting for the stylized fact that high urban unemployment has been widely observed in LDCs together with a substantial wage gap between urban and non-urban sectors. HT’s rural–urban migration model has long been invoked to explain the migration and urban unemployment of developing countries: typical developing countries exhibit large and sustained migration flows from rural areas to cities, while urban unemployment rates are high. Their model postulates that migration proceeds in response to differences in urban and rural “expected” wages, and this HT equilibrium holds when the expected wages are equalized. A partial list of recent studies on this literature includes Partridge and Rickman (1997), Krichel and Levine (1999), Sato (2004), Zenou (2008) and Lee (2008; 2010).

The consequences of rural–urban migration in recent decades are still dramatic: e.g., between 1990 and 2014 the share of the urban population in the total population of less developed countries rose from 35 to 48 % (United Nations 2014). The comparable figures for the period of 1950–1975 are from 16.7 to 28 % (Williamson 1988), indicating a gradual urbanization process toward a long-run equilibrium.

Strictly speaking, urbanization is a concept different from urban concentration. But considering the established Zipf’s law for cities in most countries (i.e., a systematic empirical relationship between the size of a city and its ranking) (e.g., Gabaix 1999), it seems harmless to say that urbanization and urban concentration are highly correlated, lending support to the statement in the text.

From a political economy perspective, urban agglomeration in developing economies is often viewed excessive because urban residents are more accessible to labor unions, lobbying and corruption to pressure governments to protect their interests, which is referred to as “urban bias” (see Lipton 1977).

Henderson (2003) finds weak evidence linking the extent of urbanization to either economic or productivity growth or levels and views urbanization as something that emerges as part of the growth process. In contrast, Gallup et al. (1999) suggest that urbanization may cause growth. Our view may be seen as combining these two views. In our endogenous growth model, urbanization emerges as part of the growth process, and at the same time, advancement of urbanization creates agglomeration externalities for developing economies, which fosters productivity growth at least transitorily along the transition path.

As will be shown later, the urban unemployment rate of Korea in 1963, a typical developing country at that time, is 16.3 % compared to the non-urban counterpart of 2.9 %. Ball et al. (2013) also report regional unemployment gaps among 17 countries from Latin America and the Caribbean: average urban unemployment rate of 6.3 % versus rural unemployment rate of 3.2 %.

Hertz et al. (2009) report a substantial wage gap between rural and urban sectors: a 21 % gap between rural and urban non-agriculture wages and a 56 % gap between the agriculture sector wage and the urban sector wage (see Table 1 on page 19). See also Hatton and Williamson (1992) for an earlier survey.

We note that this positive relationship between wage and unemployment is in contrast to the wage curve literature which finds a negative relationship [see e.g., Nijkamp and Poot (2005)]. There is still some controversy regarding which view is more consistent with the data, ranging from Freeman (2010) who criticizes empirical relevance of HT models to Card (1995) who finds its validity in a between-regions context and Partridge and Rickman (1997) who argue that the wage curve phenomenon is not inconsistent with HT models.

Earlier contributions include Krugman (1991) and Bencivenga and Smith (1997). Unlike Krugman (1991), we focus on typical developing economies that face sectoral/regional reallocation of labor and subsequent search frictions, and conceptualize the optimal regional policy in the presence of agglomeration externalities in part of regions. In a study related to this study, Bencivenga and Smith (1997) propose a neoclassical growth model with rural–urban migration and urban underemployment in the informal sector, which arises from a typical adverse selection problem in labor markets for workers with heterogeneous abilities. In contrast, our endogenous growth model focuses on agglomeration economies as a source of growth in the economic development process and offers the optimal growth path and policy implications in a search-matching framework.

da Mata et al. (2007) show that Brazilian cities are on the decreasing part of the net wage curve, lending empirical support to the latter half of the bell-shaped agglomeration benefits.

See Duranton (2008) for details on the bell-shaped net wage curve (the gap between the wage curve and the cost-of-living curve) that yields non-optimal urban concentration. The wage curve is shaped such that the wage in a city is increasing in the size of the urban labor force, reflecting the existence of urban agglomeration externalities, which also rely on urban infrastructure and institutions. In contrast, the cost-of-living curve reflects the costs arising from commuting, housing and other consumption goods, which rises rapidly with urban population: negative congestion externalities. See also Henderson (2003) and Brülhart and Sbergami (2009) for evidence from growth regression analysis.

We will later qualify the function g to ensure reasonable equilibrium.

Henderson points out that “the benefits of increasing primacy—enhanced local scale economies contributing to productivity growth—should be compared with the costs—more resources diverted away from productive and innovative activities to shoring up the quality of life in congested primate cities.” Based on this, he finds an optimal degree of primacy at each level of development that declines as development proceeds.

This is to reflect that search frictions in the rural sector are less severe than the urban counterpart. Based on the data that rural unemployment is less serious than the urban counterpart in typical developing economies, we take this simplifying assumption for analytical convenience as in HT models. The intuition behind the assumption is that unlike the rural sector, the urban sector faces complex industrial and labor market structures that entail search and matching and hence the resulting frictional unemployment (e.g., Lee 2008). While this view has been taken in the rural-to-urban migration for developing economies, there are recent NEG studies which try to account for a contrasting observation: agglomerated regions tend to exhibit both high productivity/wage and low unemployment, i.e., the so-called wage curve phenomenon (e.g., vom Berge 2013). See also footnote 10 for this controversy between the two views.

The CRS matching technology is: \(m (sL,\;vL)=m (s,\;v)\;L\), where v is the aggregate level of vacancy; s is the aggregate search intensity of urban unemployed workers: \(s=eu_1 \); e is the search intensity of urban unemployed workers with size \(u_1 \)(henceforth, e is normalized at unity); and L is the urban workforce. Using this, we can define a measure of job market tightness by the ratio of the number of vacancies to that of searchers, \(\theta (t)\equiv v(t)/u_1 (t)\). The probability that a firm with a vacancy will find a worker (i.e., the worker-arrival rate) therefore becomes \(q(\theta (t))\equiv m\left( {s(t)/v(t),\;1} \right) \). By the properties of the matching technology, \(q^{\prime }(\theta )<0\) and the elasticity of \(q(\theta )\) is a number between 0 and \(-\)1. Meanwhile, urban unemployed workers can obtain an urban job with probability \(\theta (t)q(\theta (t))\). It is often called the unemployment hazard rate or the job arrival rate. See Pissarides (2000) for details.

We can interpret the aggregate good as a composite of agricultural and manufacturing goods and examine how production and consumption move across regions due to agglomeration benefits. Alternatively, we can set up our model such that the non-urban sector produces agricultural goods and the urban sector produces manufacturing goods with individuals consuming both types of goods as in the NEG literature (e.g., Krugman 1991; vom Berge 2013). Since this type of two-sector model does not change the main findings of our study, we adopt the simplest possible specification.

We also consider the case in which the long-run equilibrium urbanization rate converges to 100 %, but the main properties of the transition path do not change.

Our steady-state HT equilibrium is consistent with the one in Lee (2008), who establishes an HT-type equilibrium under no economic growth.

In the case of \(W>R+\delta >U\) or \(W>U>R+\delta \), urban unemployed workers move to the non-urban sector, or non-urban workers move to the urban sector to become unemployed workers, respectively, until \(W(t)>R(t)+\delta =U(t)\) is established.

More precisely, \(\mathrm{d}w/\mathrm{d}p>0\) is always true if \(\mathrm{d}\theta q(\theta )/\mathrm{d}p\ge 0\) [(see Eq. (16)]. \(\mathrm{d}\theta q(\theta )/\mathrm{d}p\ge 0\) is because \(\mathrm{d}\theta /\mathrm{d}p>0\) [see Eq. (18)] and the elasticity of \(q(\theta )\) with respect to \(\theta \) is a number between 0 and \(-\)1 under the CRS matching technology.

This interior long-run equilibrium is empirically supported. If our model is alternatively set up such that the non-urban sector produces agricultural and the urban sector produces manufacturing goods with individuals consuming both types of goods, urban manufacturing productivity updating arising from agglomeration leads to the expansion of both production and consumption of manufacturing goods. But a certain fraction of non-urban agricultural consumption has to persist, supporting the imperfect urbanization more naturally as a long-run equilibrium.

That is, the g function has a small negative curvature around the steady state such that migration does not create divergence from the steady state. \({G}'\left( p \right) <-1\) would create a diverging dynamic.

Because of the Inada condition, the non-urban marginal productivity at \(u_2 =0\) goes to infinity, and therefore convergence to the perfect urbanization \(l_1 +u_1 \rightarrow 1\) occurs only in the long run.

This is because “additional” technical and pecuniary externalities get smaller with urban concentration due to rising congestion externalities. At the long-run interior urbanization rate, \(g\left( {l_1^*+u_1^*} \right) =0\) should hold, implying no further agglomeration-based growth.

The programs for this calibration exercise are available from the author upon request.

The specification of agglomeration benefits is set by \(g=\varphi \cdot \left( {l_1 -l_1^0 } \right) \cdot \left( {l_1 -l_1^*} \right) \) while still satisfying \(l_1^*+u_1^*=0.8\).

We present transitional dynamics where variables can be defined at economically sensible levels, excluding negative values or rates greater than unity.

Differences in the job-matching process across sectors imply sectoral differences in job-matching costs and entail underutilization of scarce resources in the urban sector ex post, i.e., unemployment. In our model, the social planner cannot implement exact matching between workers and firms. Controlling the search-matching process is beyond the planner’s ability.

Given that individuals maximize their wealth, which comes from production in the general equilibrium setting, the utilitarian social optimum is achieved when we maximize the present value of overall production in all periods.

Rural marginal labor productivity falls because of the added labor \(\varepsilon \), but the total non-urban output rises, a gain to the society.

This is an approximation. The urban employed population would change after relocating the urban unemployed workers to the rural sector because the equilibrium ratio of vacancy to unemployed changes.

We need the following condition: \(-\frac{1}{r}{g}'\cdot \left( {1-u_1^*-u_2^*} \right) +\beta {u_2^*}^{\beta -1}>\psi \).

This is intended to improve urban job creation while reducing the size of migrants, i.e., urban job searchers.

This result may be seen as a dynamic implication of Baldwin and Krugman (2004).

Note that \(q^{\prime }(\theta )<0\) in the CRS matching technology.

See footnote 22.

\(\mathrm{d}\theta q(\theta )/\mathrm{d}\theta =q(\theta )\left( {1+\varepsilon _{q,\theta } } \right) >0\) is derived because the elasticity of \(q(\theta )\) is bounded between \(-\)1 and 0 in the CRS matching technology: \(-1\le \varepsilon _{q,\theta } \le 0\).

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Titel: Agglomeration, search frictions and growth of cities in developing economies
verfasst von: Chul-In Lee
Publikationsdatum: 12.10.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: The Annals of Regional Science / Ausgabe 2-3/2015
Print ISSN: 0570-1864
Elektronische ISSN: 1432-0592
DOI: https://doi.org/10.1007/s00168-015-0708-7

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