metadata: authors: 0: author: Grover,Arti Goswami
1: author: Lall,Somik V.
2: author: Timmis,Jonathan David
count: China,Africa,India,World
docna: 0: docna: Agglomeration Economies in Developing
            Countries : A Meta-Analysis
docty: Policy Research Working Paper
subtopic: Crime and Society,Food & Beverage Industry,General Manufacturing,Business Cycles and Stabilization Policies,Textiles, Apparel & Leather Industry,Pulp & Paper Industry,Common Carriers Industry,Construction Industry,Plastics & Rubber Industry,Labor Markets
teratopic: Macroeconomics and Economic Growth,Social Development,Industry,Social Protections and Labor
abstracts: cdata!: Recent empirical work suggests that
            there are large agglomeration gains from working and living
            in developing country cities. These estimates find that
            doubling city size is associated with an increase in
            productivity by 19 percent in China, 12 percent in India,
            and 17 percent in Africa. These agglomeration benefits are
            considerably higher relative to developed country cities,
            which are in the range of 4 to 6 percent. However, many
            developing country cities are costly, crowded, and
            disconnected, and face slow structural transformation. To
            understand the true productivity advantages of cities in
            developing countries, this paper systematically evaluates
            more than 1,200 elasticity estimates from 70 studies in 33
            countries. Using a frontier methodology for conducting
            meta-analysis, it finds that the elasticity estimates in
            developing countries are at most 1 percentage point higher
            than in advanced economies, but not significantly so. The
            paper provides novel estimates of the elasticity of
            pollution, homicide, and congestion, using a large sample of
            developing and developed country cities. No evidence is
            found for productivity gains in light of the high and
            increasing costs of working in developing country cities.
geo_reg_key: 517198,517212,517191,119225
repnme: repnme: Agglomeration Economies in Developing
            Countries : A Meta-Analysis
display_title: Agglomeration Economies in
            Developing Countries : A Meta-Analysis
listing_relative_url: /research/2021/07/33278844/agglomeration-economies-developing-countries-meta-analysis
topicv3: Manufacturing Sectors m1326521 1281,Population, Aging and Health m1327736 640,Crime m1439217 3041,Homicide m1439222 HOM-3046,Labor Productivity m1504060 2756
publishtoextweb_dt: 2021-07-19T00:00:00Z
dois: 10.1596/1813-9450-9730
historic_topic: Macroeconomics and Economic Growth,Social Development,Industry,Social Protections and Labor
origu: EFI-FCI-TIC-Firms,Entrep,&Innov. (ETIFE)
no_of_pages: 47
author_keys: 0: author_key: 1066720
1: author_key: 124534
2: author_key: 1808241
model_extractions: Policy Research Working Paper 9730 Agglomeration Economies in Developing Countries A Meta-Analysis _Arti Grover Somik V. Lall Jonathan Timmis_ Finance, Competitiveness and Innovation Global Practice Urban, Disaster Risk Management, Resilience and Land Global Practice & East Asia and the Pacific Region Office of the Chief Economist July 2021
Policy Research Working Paper 9730

# **Abstract**

Recent empirical work suggests that there are large agglomeration gains from working and living in developing country cities. These estimates find that doubling city size is associated with an increase in productivity by 19 percent in China, 12 percent in India, and 17 percent in Africa. These agglomeration benefits are considerably higher relative to developed country cities, which are in the range of 4 to 6 percent. However, many developing country cities are costly, crowded, and disconnected, and face slow structural transformation. To understand the true productivity advantages of cities in developing countries, this paper systematically evaluates more than 1,200 elasticity estimates from 70 studies in 33 countries. Using a frontier methodology for conducting meta-analysis, it finds that the elasticity estimates in developing countries are at most 1 percentage point higher than in advanced economies, but not significantly so. The paper provides novel estimates of the elasticity of pollution, homicide, and congestion, using a large sample of developing and developed country cities. No evidence is found for productivity gains in light of the high and increasing costs of working in developing country cities.

This paper is a product of the Finance, Competitiveness and Innovation Global Practice, the Urban, Disaster Risk Management, Resilience and Land Global Practice, and East Asia and the Pacific Region Office of the Chief Economist. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank. org/prwp. The authors may be contacted at agrover1@worldbank.org, slall1@worldbank.org; and jtimmis@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **_Agglomeration Economies in Developing Countries: A Meta-Analysis_**

Arti Grover, Somik V. Lall and Jonathan Timmis World Bank JEL Classification: R11, R12, R30, O18 Keywords: Meta-analysis, Agglomeration, Developing Countries, Productivity, Elasticity _Acknowledgements_ : We thank Gilles Duranton and Bill Maloney for insightful discussions; Somya Bajaj for research assistance; Mark Roberts, Luis Quintero, Patricia C. Melo, Daniel J. Graham, Robert B. Noland, Gabriel M. Ahlfeldt, and Elisabetta Pietrostefani for generously sharing the underlying data for their meta-analysis studies, Nancy Lozano Gracia, Olivia D’aoust, Maria Edisa Soppelsa, Hogeun Park, Katie McWilliams, for pointing us to complementary data sources on urban costs.
# 1. Introduction

There is a growing body of academic literature highlighting the productivity enhancing agglomeration economies from living and working in dense cities (Ahlfedt and Pietrostefani, 2019). Duranton and Puga (2004) outline the micro-foundations of agglomeration economies based on sharing, matching, and learning mechanisms. Dense cities encourage _sharing_ of indivisible public goods, production facilities, and marketplaces, a greater variety of inputs and individual specialization, and the pooling of risk; improve the quality and possibility of _matching_ between firms and workers; and increase opportunities for _learning_ from the generation, diffusion, and accumulation of knowledge.

Economists have used the elasticity of wages with respect to urban density as a canonical measure of agglomeration economies. A recent meta-analysis of empirical work by Ahlfedt and Pietrostefani (2019) covering 347 estimates shows a of doubling urban density is associated with a wage premium of 4 percent. In the United States, the elasticity of wages with respect to city size is 0.043; in France it is 0.03-- implying that doubling density could increase productivity by 3-4 percent. (Combes and Gobillon 2015, Melo et al. 2009, and Rosenthal and Strange 2004).

While these estimates suggest strong productivity enhancing agglomeration economies in dense urban environments, a major knowledge gap arises from the limited knowledge of agglomeration economies in developing country settings. The empirical reviews (Melo et al., 2009 and Ahlfeldt and Pietrostefani, 2019) and a recent literature survey (Duranton and Puga, 2020) primarily draw on developed country estimates. Further, there has been no attempt to systematically quantify the differences in estimates between advanced and developing countries. Filling this knowledge gap is important as most of future urban growth is expected in developing country cities (United Nations 2018) and these cities are growing in people but without the commensurate investments in human and physical capital that enhance the returns from density (Lall, Henderson and Venables 2017; Ellis and Roberts 2016).

Avner and Lall (2016) find that jobs are often located far from where people live; heavy congestion and high rates of walking and informal transportation fragment the labor market and lead to low employment rates and the misallocation of labor in Nairobi. For instance, _Matatu_ (privately owned minibuses) users on average can access only 4 percent of jobs within 30 minutes, 10 percent within 45 minutes, and 20 percent within 60 minutes. In metropolitan Buenos Aires, equivalent accessibility figures using public transportation are only 7 percent, 18 percent, and 34 percent for the same time thresholds (PeraltaQuiros 2015). In Ugandan cities, 70 percent of work trips are on foot (Uganda Bureau of Statistics 2010), with only 19 percent of the city’s jobs being accessible within a one hour commute (Bernard 2016). Further, many cities particularly in Sub-Saharan Africa and South Asia produce non-tradable goods and services (Lall, Henderson and Venables 2017, Venables 2017). This is consistent with what has been called “pre-mature urbanization” (see for e.g. Gollin et al., 2016), that is, people are concentrating in developing country cities but not because industrial dynamism is attracting them.

To shed light on the productivity advantages of agglomeration in developing country cities, we make the following contributions. _First_ , we expand the sample size of existing meta-analyses to systematically examine 1,242 elasticity estimates, originating from 70 studies covering 21 developing and 12 advanced countries. _Second,_ we construct novel estimates of density elasticity on urban costs, with respect to crime, congestion and pollution by collecting data from hundreds of cities around the world, including several in developing countries. This fills a critical knowledge gap as relative to studies measuring the 2
benefits of agglomeration, the evidence base on urban costs is underdeveloped. _Third,_ using frontier methodology for conducting meta-analysis, we control for a variety of differences across studies to provide a robust assessment. This allows us to contextualize country specific estimates showing large agglomeration economies: 0.19 in China, 0.12 in India, 0.17 in Africa, and between 0.06-0.16 in Latin America (Chauvin et al., 2017 (India, China), Combes et al. 2019 (China), Henderson et al. 2019 (six African countries: Ethiopia, Nigeria, Ghana, Malawi, Tanzania and Uganda) and Quintero and Roberts 2018 (Latin America)).

Our meta-analysis highlights that while elasticity estimates for developing countries are nearly 1 percentage point higher than that for developed countries, the estimates are not statistically different. Nonetheless, estimates using nominal wages, the canonical measure of agglomeration economies, are higher than those using TFP. This suggests that part of the wage premium is driven by higher capital intensity, perhaps a result of thicker capital markets in urban areas, rather than efficiency or spillovers per se.

Further, studies controlling for urban costs find elasticities to be 4.2 percentage points lower than studies that do not, implying a net agglomeration elasticity of 0.1 percent when using labor productivity as an outcome measure. Our novel estimates of urban dis-amenities suggest that although the elasticity of pollution and congestion in developing countries is comparable with developed countries, their levels are much higher. For the average city density in our data, 19-30 percent fewer hours are spent in traffic congestion in developed countries, pollution is 16-28 percent lower, and the homicide rate is around 4 times lower.

Our analysis confirms high wage elasticities with respect to density; however we find no evidence for efficiency gains in light of high and increasing costs of working in developing country cities. This is partly driven by bad design and lack of capital investment in cities, but also by the fact that their growth is not driven by the process of structural transformation, which would create a mass of industrial or service firms that benefit from sharing, matching, and learning. Many developing country cities are not dense and productive—they are just crowded.

The rest of the paper is organized as follows. Section 2 reviews the relevant literature. Section 3 describes data collected for the meta-analysis. Section 4 discusses the estimation strategy, Section 5 presents the meta-analysis results on agglomeration elasticities, and Section 6 presents the results on urban costs. Section 7 concludes.

# 2. Density, productivity and agglomeration elasticities

There is a higher wage premium associated with working in dense cities. Meta-analysis carried out by Ahlfeldt and Pietrostefani (2019) suggests an elasticity of productivity with respect to density of 0.04, based on a citation-weighted average of 347 estimates. To set the stage for our subsequent metaanalysis, and inform our choice of study characteristics included as meta-controls, we draw on the vast literature estimating agglomeration elasticities.

## _Agglomeration measures_

Agglomeration or city size can be measured using population, density and measures of market potential or access. The use of population or economic density is preferred relative to population mass 3
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While r _eal_ wages may be a natural indicator of city wage premia, the main challenge is the availability of price data at a local level. Even if prices are available, it is not clear whether the estimated agglomeration economies with respect to real wages represent sorting on human capital or compensation for adverse urban amenities rather than true productivity premia of cities (Chauvin et al., 2017). Wages are usually only proportional to and not equal to labor productivity by a factor that depends on the local monopsony power of the firm. Thus, the use of total factor productivity (TFP) is preferred since urban costs do not play a role and it avoids making any assumption about the relationship between the local monopsony power and agglomeration economies (Combes and Gobillon, 2015).

Melo et al. (2009) show that elasticities of TFP with respect to density are on average estimated to be larger than those obtained for wages, typically around 50 percent larger. In France, for example, the elasticity of TFP with respect to density of 0.035-0.040 whereas with the same data, the elasticity is 0.027 for wages (Combes et al., 2012). It is difficult to interpret the difference between the two types of estimates. In wage equations, all the effects are re-scaled by the share of labor in the production function. Moreover, agglomeration economies percolating through the cost of inputs other than labor, such as land and intermediate inputs affect wages, but not TFP. A further possible reason for the difference in estimates obtained from wage and TFP regressions is that most researchers have not managed to successfully control for worker skills in wage regressions.

# _Underlying data_

Elasticity estimates vary by the underlying data used for analysis. Spatially aggregated industry- or worker-level data might yield different elasticity estimates relative to micro firm- or worker-level data because with spatial aggregation the information on industry, firm and worker attributes is lost. Even within micro data, productivity measures derived from firm level data versus those collected through household or labor force surveys vary. This may be due to the type of firms in the data set. For instance, some countries have a cut-off on employee size in their firm census data, while comparable wage elasticity using household surveys may have a different threshold or criterion. In particular, elasticity estimates using firm level data might be lower than worker level data. For instance, Chun et al. (2019) find the wage elasticity for China to be negative 0.113 using firm level data compared to other studies that find huge estimates of ranging from 0.07 to 0.29 when using worker-level data (Combes et al. 2019).

# _Spatial scale_

Studies evaluate the spatial extent of local spillovers ranging from the broadest administrative level (regions) to the finest administrative level (e.g. villages and neighborhood). Most studies end up somewhere in the middle – administrative level 2 or 3 (e.g. municipalities or districts). The spatial scope of agglomeration effects depends on the nature of activity. For example, while knowledge and technology intensive activities will need to be co-located, other interactions such as input–output linkages can take place at a larger scale. A common approach is to consider an individual or location defined at a fine scale and to draw rings with increasing radius around it. Agglomeration benefits dissipate with distance and are rarely significant beyond a threshold distance and hence broader spatial scales yield lower benefits (See Rosenthal and Strange, 2003; Desmet and Fafchamps, 2005 for evidence on the US and Rice et al., 2006 for the UK ; Di Addario and Patacchini, 2008 for Italy).

5
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density (Ciccone and Hall 1996)<sup>1</sup> and geological variables such as land fertility (Combes et al. 2010), land suitability for the construction of tall buildings (Rosenthal and Strange 2008; Combes et al. 2010), and (ii) including location or plant fixed effects to capture any unobserved attributes that may have attracted more establishments to a given city (Henderson 2003).

Evidence suggests that the large estimated benefits are not a reflection of exogenous shocks or reverse causality. It could have been the case that some places may be intrinsically more productive, attract more workers, and thereby causing city size or population density to rise (“quantity” effects). Estimates that use instruments to control for endogeneity due to “quantity” effects do not drastically change the elasticity magnitudes. For example, in the U.S., Brazil China, India and Brazil, the elasticity estimates remain stable when instrumenting current agglomeration with historical values. This dispels the fear that correlation between city size and productivity is caused by, for instance, in China by the post- 1980 political shocks to particular areas, like the special economic zones (Chauvin et al., 2017). Likewise, Duranton (2016) does not find significant differences in elasticity estimates in Colombia with an IV estimation that use past population density or geological variables as an instrument.

# _Returns to skills, worker and firm sorting_

Agglomeration elasticity estimates may also be biased due to sorting of more educated workers or productive firms to large locations (“quality” effect). While education and other observable characteristics of workers and firms can be controlled, unobservable traits that affect productivity may differ systematically across cities. Glaeser and Maré (2001) and Combes, Duranton, and Gobillon (2008) suggest introducing worker fixed-effects when relating individual earnings to density. The productivity benefits of density for workers is then identified from the changes in earnings that a given worker experiences when changing work location. Plant relocations are much less frequent than worker relocations and hence firm sorting is more difficult to control for.

Several approaches have been used to measure returns to skills. Chauvin et al. (2017) estimate elasticity of real wages as returns to human capital and find that the elasticity of density is lower for the US and China, suggesting that the nominal-wage premium in dense locations does not reflect sorting of higher-ability people. By comparison, the nominal and real wage elasticities are not very different in India, which may be interpreted as large returns to human capital, given the wide heterogeneity of skills across space and low migration rates. Other studies have used observable skills and parental education and worker/individual fixed effects. Studies on the US find lower estimates of elasticity once controlling for skills (e.g. Glaeser and Mare, 2001). In Colombia, the elasticity of wages with respect to city size drops from 11 percent to 5.4 percent when individual worker characteristics such as education are included, implying that about half this relationship is explained by larger cities hosting more educated workers. This is consistent with the greater representation of more educated workers in larger cities and the view that workforce composition effects account for a sizeable fraction of spatial wage disparities (Combes and Gobillon, 2015).

In France, there is a high correlation between density and worker characteristics (0.44), and the associated elasticity of wage premium is cut by about one-half when worker fixed-effects are included (Combes et al., 2008; 2010). Worker sorting is slightly weaker in Italy, where the correlation between

> 1 The validity of the instruments rely on the past populations being uncorrelated with unobserved drivers of contemporaneous wages conditional on the other controls. While a good case can be made for this (Combes et al.,2010), it is by no means decisive.

7
individual fixed effects and density is 0.21 (Mion and Naticchioni, 2009). There is also evidence of spatial sorting in Spain and in the United Kingdom (de la Roca and Puga, 2012; D’Costa and Overman, 2014).<sup>2</sup>

## _Urban costs_

Systematic evidence about urban costs is nearly absent - most agglomeration studies use nominal wages, rather than real wages that account for local urban costs . Urban costs take a variety of forms. In larger cities, housing is more expensive, commutes are longer, and the bundle of amenities that these cities offer may differ. Residential mobility implies that urban (dis)amenities and commuting costs are reflected into land prices. The elasticity of urban costs with respect to city population is the product of three quantities: the elasticity of unit land prices at the city center with respect to population, the share of land in housing, and the share of housing in consumption expenditure. It is critical to estimate the elasticity with respect to urban cost because, _first_ , city size is an outcome of a tradeoff between agglomeration economies and urban costs (Henderson, 1974; Fujita and Ogawa, 1982). The costs of agglomeration can partly explain why firms and workers do not move to larger cities. _Second_ , urban policies such as barriers to labor mobility and zoning limits (e.g. Duranton, 2008) are imposed to curb population growth and costs such as housing and congestion in cities. An estimation of the association of urban cost with city size helps understand the efficacy of these policies in achieving their stated objectives.<sup>3</sup> The topic remains underexplored because of a lack of an integrated framework to guide empirical work and appropriate data.

Although agglomeration benefits are higher, urban costs may explain why cities do not expand further. Urban costs have been estimated for France and Colombia using land and housing price data (Combes et al., 2013; Combes et al., 2019; Duranton, 2016). In France, the elasticity of urban costs with respect to population ranges from 0.016 to 0.05, while the estimates for agglomeration effects in France range from 0.015 to 0.03 (Combes _et al._ , 2010). Similar results on the elasticity of urban costs are obtained for Colombia as well (Duranton, 2016). In both these countries, cities operate at near aggregate constant returns to scale, suggesting that the benefits of agglomeration are balanced by their costs.

The costs of density on outcomes such as pollution, crime, and congestion is significantly high, and often higher than productivity elasticities. Ahlfeldt and Pietrostefani (2019) suggest that a log- point increase in density is associated with higher rents (0.15), pollution concentration (0.13), mortality risk (0.09) and crime (0.085). Thus, to understand the true advantages of larger cities, it is critical to estimate agglomeration costs alongside benefits. Cities in developing countries face the same downsides of density, that is, congestion, crime and diseases, however, they lack the financial resources to invest in infrastructure such as transport network, clean water and air, and sewerage to mitigate these risks. They also lack the public capacity to enforce urban regulations (Glaeser and Porteba, 2020).

# 3. Data

We rely on two separate datasets: one for the meta-analysis of agglomeration elasticities, and another for the analysis of urban costs. First, we discuss the construction of the sample of papers used for the meta-analysis, and second, the urban cost data.

> 2 For more evidence see Bacolod et al. 2009; Abel et al., 2012; Lindley and Machin, 2014 for the United States; Di Addario and Patacchini, 2008 for Italy; Groot and de Groot, 2014 for the Netherlands.

> 3 In France Combes et al. (2013) find that urban costs are much lower when the physical growth of cities is not restricted.

8
# Meta-analysis data

The primary focus of our paper is a meta-analysis of agglomeration productivity elasticities differentiating between developing and developed countries, where our paper follows the approach outlined in Stanley et al (2013) to construct the sample of studies (further details are given in the Appendix).

We build on the meta-analysis data of Melo et al. (2009) and Ahlfeldt and Pietrostefani (2019) by extending their sample on elasticity estimates for developing countries. We use a combination of keywords, such as “agglomeration” or “density” or “urban”, and “elasticity” or “productivity” or “wages”, applied to the academic databases EconLit, Web of Science, and Google Scholar. We supplement the keyword search by conducting an analysis of citation trees of key published and working papers by eminent researchers in the field and papers that inspired the study.<sup>4</sup> We also consulted with experts in academia (including the University of Pennsylvania, Johns Hopkins University, and Oxford) and practice (including the World Bank) to identify ongoing work in the field. The initial sample included peer-reviewed papers, working papers of universities, research institutes and international organizations (World Bank, NBER, CEPR, CESIfo, and IZA), chapters in books and conference proceedings.

We restrict the initial sample to papers with one of four outcome variables --- labor productivity, wages or earnings, TFP and output using a production function -- and four agglomeration measures: population size, population density, economic density and market potential. To ensure comparability, we only retain studies that either estimate unit-free agglomeration elasticities, or those that could be converted to an elasticity (e.g. semi-elasticities). Estimates reporting analysis pooled across several countries are excluded; country specific estimates are retained.

To test and correct for publication bias, we also collect standard errors of estimates either from the papers or by requesting the authors. Studies without the standard errors needed for precisionweighting are excluded from the meta-analysis. Most studies are empirical; however, studies estimating structural models are also included provided they report agglomeration elasticities and standard errors. To avoid double counting several versions of the same study, in particular for working papers, we include only the latest version.

Our resulting sample comprises of 1,242 elasticity estimates sourced from 70 studies across 33 countries covering 1973 to 2020. Of the 70 studies, 29 are reported in Melo et al. (2009), 16 are drawn from Ahlfeldt and Pietrostefani (2019), with 25 additional studies included here. Table A5 in the Appendix reports the full list of 70 studies. Among the estimates, 388 are for developing countries.

Even within a single study or a single country in our data there are often a wide range of estimates, highlighting substantial heterogeneity in data and estimation methods. Figure 3 reports a forest plot of the estimated 1,242 agglomeration elasticities across the 33 countries. The figure suggests that countries show a broad range of elasticities, with some reporting both large positive and negative estimates. While some of the variation is likely a result of differences in time period, spatial scale, estimation methods and so on across papers, Appendix Figure A1 shows a similar spread in estimates within individual studies. The wide range of estimates strongly suggests key differences in underlying factors within and across studies, highlighting the importance of controlling for such distinctions

> 4 Melo et al. (2009), Chauvin et al., (2017) and Ahlfeldt and Pietrostefani (2019).

9
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|Urban Cost|Urban Cost<br>Control|= 1 if estimations include a<br>local measure of urban costs,<br>e.g. land rents, house prices,<br>localprice indices|estimations do not include<br>an urban cost control|0.032|0.177|
|---|---|---|---|---|---|
|Industry|Manufacturing<br>Sector<br>Services Sector|=1 if estimates reflect the<br>manufacturingsector<br>=1 if estimates reflect the<br>services sector|estimates are not specific<br>to manufacturing or<br>services|0.382<br>0.155|0.486<br>0.362|
|Skill|Skilled workers<br>Unskilled workers|= 1 if estimates reflect skilled<br>workers (including managers,<br>scientists or non-routine<br>occupations)<br>= 1 if estimates reflect<br>unskilled workers (routine<br>occupations)|estimates are not specific<br>to skilled or unskilled<br>workers|0.021<br>0.027|0.143<br>0.161|
|Time Period|Post-1990|= 1 if mid-point of data is 1990<br>onwards|mid-point of data is before<br>1990|0.782|0.413|
||Published|= 1 if study is published in a<br>peer-reviewed journal|study is unpublished|0.712|0.453|
|Study Quality|Number of<br>Citations (as of<br>April 2020)|Log number of citations -<br>normalized by study<br>publicationyear|-|0.000|1.349|
|Spatial<br>Measure|City - Level<br>Sub City - Level|=1 if study uses city-level<br>spatial units<br>= 1 if study uses sub-city-level<br>spatial units|study uses regional level<br>spatial units|0.521<br>0.310|0.500<br>0.463|
|Agglomeration|Density Measure|= 1 if agglomeration is<br>measured by population or<br>employment density|agglomeration is<br>measured by size, such as|0.452|0.498|
|Measure|Market Potential<br>Measure|= 1 if agglomeration is<br>measured by effective density<br>or marketpotential|total employment or<br>population|0.257|0.437|
|Localization|Localization<br>Control|= 1 if a localization control is<br>included (reflecting the size of<br>own industry)|estimations do not include<br>a localization control|0.312|0.464|
||Panel Data|= 1 if study uses panel data|study uses cross-section<br>data|0.590|0.492|
|Data|Firm Data|= 1 if study uses firm-level<br>micro data|study does not use micro|0.352|0.478|
||Worker Data|= 1 if study uses worker-level<br>micro data|data|0.388|0.488|
||Panel Fixed<br>Effects|= 1 if panel fixed effects are<br>included or estimation is in<br>differences|study does not use fixed<br>effects|0.209|0.407|
|Endogeneity|IV estimation -<br>contemporaneous|= 1 if estimates reflect IV<br>estimation, using<br>contemporaneous or short-<br>lagged instruments (including<br>GMM)|study does not use IV<br>estimation|0.069|0.254|

11
||IV estimation -<br>historic|= 1 if estimates reflect IV<br>estimation, using historic or<br>geological instruments||0.177|0.382|
|---|---|---|---|---|---|
|Firm<br>Heterogeneity|Industry control<br>Firm size control|= 1 if estimates include an<br>industry dummy variable<br>= 1 if estimates include a firm<br>size control|study does include<br>industry or firm size<br>controls|0.275<br>0.366|0.446<br>0.482|
|Worker|Local area human<br>capital|= 1 if study includes a local<br>area human capital measure|study does not control for|0.189|0.392|
|Sorting|Individual-level<br>human capital|= 1 if study includes worker-<br>level controls|human capital|0.261|0.439|

Note: Number of observations for each variable is equal to 1,242. We normalize patents by publication year, common practice in the patent literature, by using the residual from a regression of citations on publication year<sup>5</sup> . We reported unweighted means and standard errors. Country-income is captured by a dummy variable reflecting whether the country is non-highincome country, using the mid-point of the study’s data sample.<sup>6</sup>

# Urban cost data

We also provide novel estimates of urban cost elasticities across developing and developed countries. While Ahlfeldt and Pietrostefani (2019) provide a good synthesis of the available literature, they focus on developed countries. We use three measures of city-level urban costs: congestion (hours lost due to traffic), pollution (PM2.5 emissions) and crime (homicide rate).

Congestion information is sourced from TomTom, which provides real time traffic statistics for over 600 million users around the world. Congestion reflects the average annual additional hours spent driving in rush hours in 2018 and is available for 337 cities, of which 69 cities are in developing countries. Pollution, measured using PM2.5 emission levels, is sourced from the World Health Organization and is available from 2008 to 2015. We use pollution data for 2014, the most recent year covering a sample of 298 cities (with 78 in developing countries). We exclude China from the pollution analysis because of potential data reporting concerns highlighted in Greenstone et al. (2020). Crime is measured using the homicide rate obtained from United Nations Office on Drugs and Crime (UNODC) global study on homicide (2019) and is available from 2003 to 2017. We utilize crime data for 2015, the latest year comprising 124 cities (with 63 in developing countries). Summary statistics of these variables are provided in Table 2. Figure 4 shows how pollution, congestion and crime vary across levels of economic development.

City-level population density is calculated as the population per square kilometer of _built up density_ using 2015 data from the Global Health Settlement (GHS). Unfortunately, this data is only available at irregular intervals (1975, 1990, 2000 and 2015), which combined with limited time horizon of our urban cost measures, limits us to a cross-section analysis. We also examine robustness to population density from country census data that are available for approximately half the cities in our baseline sample.

> 5 An alternative approach of demeaning citations using the mean citations of publications in that year is not possible, due to few observations in some publication years.

> 6 The analysis is robust to defining country income using the first or last period of the study sample.

12
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# 4. Estimation

We first discuss the estimation strategy for the meta-analysis of agglomeration elasticities, followed by the methodology for estimating urban cost elasticities.

## Meta-analysis estimation

There are several estimation challenges in conducting a meta-analysis (see Florax, 2001; Stanley, 2005).

_First_ , selective reporting can lead to bias in meta analyses. Publication bias can reflect a preference among researchers and journals to selectively report statistically significant coefficients in a desirable direction, for instance, those in agreement with established theory. Such selective reporting implies that the reported estimates are truncated, that is, we primarily observe estimates that are statistically significant. This introduces a systematic relationship between reported estimate for study _i_ and the reported standard errors, . More formally, as Stanley and Doucouliagos (2014) note, the first-order ii approximation of the conditional expectation of a truncated normal distribution implies the reported ee ii estimates will be a linear function of the estimates’ standard errors. We follow standard practice and ssee test for publication bias using the funnel asymmetry test (FAT) (e.g. Card and Kreuger, 1995; Egger et al., 1997; Stanley, 2008): 0 0 (1) The null hypothesis of no publication bias corresponds to 0 = 0, i.e. no relationship between the reported study effects and the reported standard errors. To test for publication bias, equation 1 can be estimated using a variety of models: unweighted OLS, meta-random effects, meta-fixed effects and ββ precision-weighted least squares (WLS).<sup>7</sup> Traditional methods, including precision-weighted regressions, are particularly sensitive to publication bias (Stanley and Doucouliagos, 2014; 2019). We deploy state of the art estimators that outperform these approaches. More specifically, Precision-effect estimate with standard error (PET-PEESE) has been shown to outperform several estimators, such as unrestricted WLS or WAAP or random effects estimation under publication bias (Stanley and Doucouliagos, 2015; 2019). PET-PEESE, uses a quadratic approximation to the conditional expectation of a truncated normal distribution, to proxy publication bias. So, PET-PEESE includes the square of the estimates’ standard errors, in place of a linear relationship as in equation 1. We use PET-PEESE as our preferred specification.

Our baseline specification, PET-PEESE, involves estimation the following precision-weighted regression: 0 1l + γ 0 2 1 2n (2) ii ii ii ii ii ii where, l is a dummy variable for studies of developing countries and eê = ee + αα ll + ββ . ssee + ββ . ssee nnhiill 1+ uu is our coefficient of interest and reflects differences in agglomeration elasticities across developing and developed countries. All ii 2 regressions are weighted by the inverse of the estimates’ variances (ll αα), 0 is the constant term, and ii ssee ee

> 7 Note that we use the terms meta-random effects and meta-fixed effects to reflect “random effects” and “fixed effects” meta analyses, in order to distinguish them from the similarly named (but distinct) panel estimators.

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in addition to the estimates’ variance term to capture publication bias, we add interactions with l , given our interest in understanding the differences between countries in the two income groups.<sup>8</sup> Z ii is a vector of study characteristics to allow for heterogeneity across studies, outlined in Table 1. All ll estimations include cluster-robust standard errors, clustered within studies, to allow for correlation across estimates within a study and also mitigate potential type I errors (as suggested by Stanley and Doucouliagos, 2019).

_Second_ , since reported estimates can vary by estimation methods, country, time period, unit of analysis, and degree of spatial aggregation among many other elements, the specification of included study characteristics can critically affect results. The vector of controls, Z are listed in Table 1. The broad set of potentially relevant study characteristics extends those included by the previous meta-analyses of Melo et al. (2009) and Ahlfeldt and Pietrostefani (2019) to encompass the recent literature as discussed in section 2. However, the choice of which sub-set of study controls to include as metaregressors is not straight-forward.

We employ two techniques to strip-off researcher judgement and potential biases in selecting study controls. First, Bayesian Model Averaging (BMA) estimates millions of regressions consisting of subsets of the potential explanatory variables and weights them by model fit and model complexity (following Havranek et al., 2017; Steel, 2020). BMA reports an average of these many underlying regressions. The only covariates required to be included in each regression are the variance terms (to control for publication bias) and the non-interacted developing country dummy and post-1990 terms – we estimate nearly 17 million regressions for every combination of other covariates. We use as a robustness of our variable selection, since BMA does not report clustered standard errors – which can help control for type I errors (De Luca and Magnus, 2011; Havranek et al., 2017). Second, we run all 17 million combinations of covariates, with standard errors clustered at the study-level, and choose the parsimonious models that minimize the Bayesian Information Criteria or the Akaike Information Criteria. Both BIC and BMA are consistent, meaning that they converge to the true model, and BIC provides a good approximation of many linear models (van Erven et al., 2012, Fragoso et al., 2018). Cluster-robust estimation using BIC model selection is our preferred specification.

_Third_ , meta-analyses that take a single “preferred” estimate per study have the risk of overweighting smaller studies that contribute to only a small number of estimates (and underweighting larger studies that produce multiple estimates). This also raises complications in choosing a single “best” estimate from each study, particularly when even within a single study there can be a range of estimation methods or data sample restrictions employed (e.g. manufacturing vs services, worker skill). Selecting a single estimate also requires researcher judgement, which may inadvertently introduce bias in the meta-analysis.

Instead, for our focal analysis, we follow the most common practice and retain multiple estimates per study and include an exhaustive set of potential covariates to explain heterogeneity across estimates and address issues of within-study autocorrelation by clustering at the paper-level. Our sample of 1,242 elasticity estimates are drawn from 70 studies and range from a single estimate in some papers to up to 80 estimates in a given study. To ensure our results are not driven by a few studies with a large number of estimates, we do a robustness check by taking a single estimate per combination of

> 8 In section 5a, we also add interactions between the estimates’ variances and other data characteristics, to test for heterogeneous publication bias across data samples.

15
meta controls. To avoid introducing researcher biases in choosing this estimate, the single estimate is the mean elasticity reported in the study.

## Urban cost estimation

We estimate urban cost elasticities across developed and developing countries using city-level OLS regressions of (log) urban cost against (log) population density (equation 3). We use three measures of city-level urban costs: congestion (hours lost due to traffic), pollution (PM2.5 emissions) and crime (homicide rate).

A developing country dummy is included to reflect difference in urban costs in _levels_ , and interact the dummy with population density to estimate the difference in urban cost _elasticities_ across income groups. We normalize density relative to the mean value, such that constant terms can be interpreted as the levels at the mean city density.

Specifically, we estimate: 1. n 2 3. l (3) ii oo ii ii ii ii ii where llnnsscc is the log urban cost for city i, urban costs reflect either the log average annual additional = δδ + δδ nnhiill + δδ . lleennssiiccdd + δδ ll ∗lleennssiiccdd + uu hours spent driving in rush hours in 2018, log PM2.5 emissions for 2014 or log homicide rates in 2015. ii l is a dummy variable reflecting cities in developing countries, llnnsscc is the log population density for city i in 2015. Developing countries reflects non-high-income status as defined in 2015, ii ii using the World Bank classification. ll lleennssiiccdd

# 5. Meta-analysis: Estimation of Agglomeration Benefits

This section presents the results of the meta-analysis of agglomeration elasticities. We first examine potential publication bias, present overall meta-estimates and then examine the role of heterogeneity by study characteristics.

## a) Publication Bias

The results from Funnel Asymmetry Test (FAT) for publication bias, are presented in Table 3. For all estimation methods we find robust evidence of a highly significant positive relationship between the estimated agglomeration elasticity and the corresponding standard error, suggestive of publication bias.

**_Table 3: Funnel Asymmetry Test for Publication Bias_**

||**(1)**|**(2)**|**(3)**|
|---|---|---|---|
|Estimation Method:|Meta RE|Meta FE|WLS|
|Standard error (publication bias)|1.225***|3.824***|3.824***|
||(0.087)|(0.030)|(0.566)|

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However, publication quality, as measured by the number of citations or publication in a journal, is not significant (columns 3 and 4). At first glance it appears publication bias is more severe for studies using micro-data (column 5), but more recent studies are more likely to use micro-data and study developing countries. A full specification model with the characteristics together suggests that differences in publication bias are driven by the time period of study and the country’s income level (column 6).<sup>10</sup>

|**_Table 4: Funnel Asymmetry Te_**|**_st for Hetero_**<br>|**_geneity in Pu_**<br>|**_blication Bia_**<br>|**_s across Stu_**<br>|**_dy Characte_**<br>|**_ristics_**<br>|
|---|---|---|---|---|---|---|
||**(1)**|**(2)**|**(3)**|**(4)**|**(5)**|**(6)**|
|Estimation Method:|||W|LS|||
|Standard error|4.386***|-0.349|3.540***|4.118***|1.968***|0.618|
||(0.719)|(1.066)|(0.981)|(0.536)|(0.520)|(1.521)|
|Standard error *|-2.437***|||||-2.563***|
|Developing Country|(0.883)|||||(0.900)|
|Standard error * Post-1990||4.980***<br>(1.216)||||5.782***<br>(1.580)|
|Sdd * Pblihd|||-0.576|||0.333|
|tanar error use|||(1.052)|||(1.072)|
|Standard error * Number of||||-0.796||-0.391|
|Citations||||(0.666)||(0.360)|
|Standard error * Micro Data|||||2.593***|-2.211|
||||||(0.836)|(1.853)|
|Constant|0.011***|0.038***|0.029***|0.006**|0.010*|0.039**|
||(0.004)|(0.014)|(0.008)|(0.003)|(0.006)|(0.017)|
|Observations|1,242|1,242|1,242|1,242|1,242|1,242|

Notes: Outcome is the reported agglomeration elasticity. WLS is precision-weighted least squares estimates, using the inverse of the reported estimate’s variances as weights. WLS estimation of equation 1, but interacting the estimates’ standard errors with different study characteristics to allow for heterogeneous publication bias across studies. Non-interacted study characteristics are included in the estimation, but not reported for parsimony. Study characteristics are defined in Table 1. Reported agglomeration elasticity expressed as absolute values. Robust standard errors clustered at the study level are in parentheses. ***, ** and * reflect significance at the 1, 5 and 10 percent levels respectively.

# b) Homogenous meta-estimates

In this section, we present meta-estimates examining agglomeration elasticities across developed and developing economies. To this end, Table 5 presents results from estimating equation (2), with country level income as the only source of heterogeneity in elasticity estimate. Traditional metaanalysis techniques that do not control for publication bias (columns 1 to 3) suggest significant positive agglomeration elasticities for developed countries ranging from 1.4 percent to 5.1 percent, as 10 Interacting the standard error with study characteristics allows testing of significant differences in publication bias. In Table A2 in the Appendix we estimate FAT using different sub-samples of studies, and find evidence of publication bias in both high and non-high-income subsamples, across published and un-published studies and across studies using both micro and macro-data. Only for the pre-1990 studies do we fail to find evidence of publication bias.

18
reflected in the constant term. For developing countries, agglomeration elasticities appear to be significantly higher than developed countries – of the range 1.1 to 2.3 percentage points.

The pervasive evidence of publication bias suggests that the raw meta-estimates cannot be taken at their face value. The state of the art methodology, PET-PEESE, that outperforms other estimations under publication bias is presented in columns 4 and 5 of Table 5. We start with PET-PEESE estimation in column 4. Given that the publication bias is stronger for studies post-1990, we augment our estimating equation (2) to allows for publication bias that differs across studies based on these variables (column 5).<sup>11</sup> We find that controlling for publication bias in PET-PEESE does not substantially change the results relative to estimates that do not control for the bias. Agglomeration elasticities appear to be significantly higher than developed countries by around 2.1 to 2.2 percentage points (column 4 and 5).<sup>12</sup>

**_Table 5: Homogeneous meta-estimates – agglomeration elasticities across developed and developing countries_**

||**(1)**|**(2)**|**(3)**|**(4)**|**(5)**|
|---|---|---|---|---|---|
|Estimation Method:|Meta RE|Meta FE|WLS|PET-|PEESE|
|Publication Bias Correction:||N|||Y|
|Developing Country|0.011***|0.023***|0.023**|0.022**|0.021**|
||(0.004)|(0.001)|(0.009)|(0.009)|(0.010)|
|Post-1990s|||||-0.025*<br>(0.013)|
|Constant|0.051***|0.014***|0.014***|0.014***|0.037***|
||(0.002)|(0.000)|(0.004)|(0.004)|(0.013)|
|Observations|1,242|1,242|1,242|1,242|1,242|

Notes: Outcome is the reported agglomeration elasticity. Meta RE reflects meta-analysis random effects estimation, Meta FE reflects meta-analysis fixed effects estimation, WLS are precision weighted least squares estimates, using the inverse of the reported estimate’s variance as the weight. PET-PEESE are “precision-effect estimates with standard errors” following Stanley and Doucouliagos (2019), which to correct for publication bias includes a squared standard error term in column 6, and its interaction with a developing country dummy, and with a post-1990s dummy in column 7. The standard error terms are omitted for parsimony. PET-PEESE and WLS are precision-weighted, using the inverse of the reported estimate’s variance as the weight. Robust standard errors are presented in parentheses, these are clustered at the study level for all except Meta RE and FE estimation. ***, ** and * reflect significance at the 1, 5 and 10 percent levels respectively.

11 Our results are robust, although somewhat less precisely estimated, when not allowing for heterogeneous publication bias.

> 12 A robustness check using Andrews and Kasy (2019) estimator finds similarly meta estimates are around 2 percentage points higher in non-high income countries.  Depending on the choice of cutoff for probability of publication, the estimator finds a mean high-income true elasticity of 1.6 percent to 2.0 percent, compared to 3.8 percent to 4.8 percent for non-high income.  The estimator is available at

<u>https://maxkasy.github.io/home/metastudy/</u> . We employ PET-PEESE as our preferred estimator it is readily adaptable to heterogeneity by study characteristics.

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# c) Heterogeneity by study characteristics

Considering the wide range of differences within and across studies on characteristics pertaining to estimation methods, sector of study, skills of workers spatial scale, underlying data and so on, we augment our meta-analysis by controlling for a broad set of study characteristics outlined in Table 1.

Table 6 presents our preferred PET-PEESE specification where we deploy a variety of model selection methods to objectively arrive at the sub-set of controls included as meta-regressors. In addition to the general model including all controls, we experiment with Bayesian Model Averaging (BMA) to examine robustness of our variable selection (Steel, 2020). We report the posterior inclusion probability (PIP) for each variable under BMA in square brackets (see column 2). Our preferred specification, in column 4, involves estimating all 17 million combinations of covariates to choose the models that minimizes the Bayesian Information Criteria (BIC). The variables included in our preferred BIC specification, is broadly similar to that proposed by BMA, excluding all variables with a PIP of less than 50 percent and including all those with a PIP of more than 80 percent. We also examine robustness to using the Akaike Information Criteria (AIC) in column 3.

Table 6 suggests that the agglomeration premia in developing countries is about 1 percentage point higher than developed countries, after controlling for not only publication bias, but also differences in time period, agglomeration or productivity measures, estimation methods and underlying data (columns 1 to 4). Across all specifications, the difference between elasticities in developed and developing countries ranges from 0.8 to 1.0 percentage points across all specifications. However, in all specifications except BMA, the difference in agglomeration premia is not statistically significant. The significance in BMA may be driven by the fact that we are not able to cluster BMA standard errors within papers. To examine if the small overall differences between agglomeration premia in developing and developed countries is driven by a few outlier countries, we re-estimate the specification in column 4 (BIC) replacing income level dummy with indicator variables for each country. The estimated country coefficients, with the United States as the reference category, are presented in the Appendix Figure A2. While there are differences across individual countries, as expected, we find that most developed and developing countries are clustered around the reference category. The small differences between agglomeration premia across developed and developing countries broadly holds across the countries in our sample, and is not driven by one or two outlier countries.

Table 6 suggests that while the agglomeration elasticities may be comparable across country income groups, many other differences in data or estimation methods across studies matter much more. More specifically, we make the following observations. _First_ , the productivity measure matters when it comes to measuring agglomeration premia. Estimated nominal wages or labor productivity premia are much higher than studies using TFP – by 6.5 and 4.3 percentage points respectively. _Two_ , one possible reason for the difference is urban costs. Urban costs increase local prices and the cost of inputs, which feed through into higher nominal wages or labor productivity, however, TFP elasticities are theoretically independent of urban costs (Combes and Gobillon, 2015).<sup>13</sup> Studies that estimate _real_ wages or labor productivity – controlling for urban costs – have 4.2 percentage point lower estimates

> 13 Note also that TFP estimates need to be scaled up by the labor share to be comparable with wages or labor productivity.

20
than those that use nominal values.<sup>14</sup> Accounting for urban costs and labor share explains the majority of the difference we find between nominal wage and labor productivity estimates and TFP.

_Three,_ agglomeration premia differ substantially across industries. The agglomeration premia in services is on average much higher, around 3.5 percentage points higher than estimates encompassing all industries (column 4). _Four,_ controlling for heterogeneity in firm or worker traits and underlying data also yields interesting results. Studies that control for firm size tends to reduce agglomeration premia, likely because larger firms tend to be more productive and hire more skilled workers. More spatially disaggregated studies tend to find around 1.1 percentage point smaller agglomeration benefits, perhaps because of spillovers on surrounding areas. Skilled workers disproportionately benefit from density, although the strength of the statistical significance depends on the model selection. Skilled workers have between 1.1 to 1.7 percentage point higher productivity than workers as a whole. _Five_ , controlling for sorting of skilled workers in cities either at the local level or using individual’s education reduces agglomeration premia by 1.0 and 1.3 percentage points respectively (column 4). Similarly, more productive firms may choose to locate in cities and agglomeration premia may reflect local characteristics that are hard to measure. Employing panel fixed effects leads to lower estimates of around 1.8 percentage points (column 4). _Six,_ controlling for the so-called endogeneity via instrumental variable estimation typically does not materially impact the results.

_Lastly,_ there are no robust differences for agglomeration premia estimated in higher and lower quality publications, or across different agglomeration measures (although there is some evidence localization controls matter).

In the Appendix Table A3 we examine robustness of our main results to alternative estimation approaches and sample restrictions. The main findings shown in Table 6 remain intact, that is, the differences in agglomeration premia across developed and developing countries are small, once publication bias and other study differences are considered. It becomes clearer that underlying data or estimation choices matter far more that country-income. In Appendix Table A3, we decompose the panel fixed effects, industry, firm size and local area human capital controls into those separately reflecting spatial, worker and firm data (column 1). In general, we fail to find that these controls matter differentially across data sources. In column 2, we mitigate any residual risk that our results are driven by a few papers with a large number of estimates (although note we cluster standard errors at the study-level in the baseline estimation). To do so we take a single mean estimate per combination of meta controls in each paper, which reduces the sample substantially to only 310 observations. We now find there is weak evidence that agglomeration premia are somewhat _higher_ in developed countries. This confirms the message of our baseline results that differences across country income groups are small, and other data or estimation choices matter far more. Finally, columns 3 to 6 repeat our preferred specification (from Table 6 column 4) but exclude two developed and developing countries with the largest number of estimates, Brazil, China, UK, USA. The results are unchanged.

> 14 This is broadly in line with differences between real wage and nominal wage elasticities within the same papers, e.g. Chauvin et al. (2017) or Faberman and Freedman (2016).

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**_Table 6: Heterogeneous meta-estimates by study characteristics_**

|||**(1)**|**(2)**||**(3)**|**(4)**|
|---|---|---|---|---|---|---|
||Estimation Method:||P|ET-PEESE|||
||Model Selection:|General|BMA||AIC|BIC|
|Country|DevelopingCountry|0.009|0.009***||0.008|0.010|
|Income||(0.007)|(0.003)|_[1.00]_|(0.007)|(0.008)|
||Wages|0.067***|0.065***||0.065***|0.063***|
|Productivity||(0.013)|(0.005)|_[1.00]_|(0.014)|(0.012)|
|Measure|Labor Productivity|0.045***|0.043***||0.045***|0.042***|
|||(0.010)|(0.004)|_[1.00]_|(0.010)|(0.012)|
|Urban Cost|Urban Cost Control|-0.039***|-0.042***||-0.041***|-0.045***|
|||(0.013)|(0.005)|_[1.00]_|(0.013)|(0.012)|
||ManufacturingSector|0.012*|0.011***||0.012|0.011|
|Industry|Services Sector|(0.007)<br>0.035***|(0.003)<br>0.034***|_[1.00]_|(0.007)<br>0.035***|(0.008)<br>0.035***|
|||(0.010)|(0.004)|_[1.00]_|(0.011)|(0.011)|
||Skilled workers|0.014***|0.011||0.015***|0.017***|
|Skill|Unskilled workers|(0.004)<br>-0.002***|(0.009)<br>-0.001|_[0.66]_|(0.004)<br>-0.002***|(0.004)|
|||(0.001)|(0.001)|_[0.31]_|(0.001)||
|Time Period|Post-1990s|-0.001|-0.004||-0.001|-0.007|
|||(0.008)|(0.003)|_[1.00]_|(0.008)|(0.007)|
||Published|-0.005|-0.003||-0.005|-0.005|
|Study Quality||(0.005)|(0.003)|_[0.54]_|(0.005)|(0.005)|
||Number of Citations|0.001|0.000||0.001||
|||(0.002)|(0.000)|_[0.04]_|(0.003)||
||City- Level|0.002|0.000||||
|Spatial||(0.002)|(0.001)|_[0.09]_|||
|Measure|Sub City- Level|-0.008|-0.011***||-0.009*|-0.011***|
|||(0.006)|(0.002)|_[1.00]_|(0.005)|(0.003)|
||DensityMeasure|-0.007|-0.001||-0.010||
|Agglomeration||(0.009)|(0.002)|_[0.08]_|(0.009)||
|Measure|Market Potential Measure|-0.007|-0.001||-0.010||
|||(0.007)|(0.003)|_[0.10]_|(0.007)||
|Localization|Localization Control|0.009|0.010***||0.009|0.009***|
|||(0.007)|(0.002)|_[1.00]_|(0.006)|(0.003)|
||Panel Data|-0.005|-0.006||||
|||(0.006)|(0.004)|_[0.77]_|||
|D|Firm Data|0.047***|0.049***||0.046***|0.046***|
|ata||(0.012)|(0.005)|_[1.00]_|(0.013)|(0.012)|
||Worker Data|-0.021**|-0.021***||-0.022**|-0.021***|
|||(0.009)|(0.003)|_[1.00]_|(0.009)|(0.008)|

22
||Panel Fixed Effects|-0.019***<br>(0.007)|-0.018***<br>(0.002)|_[1.00]_|-0.020***<br>(0.007)|-0.018**<br>(0.008)|
|---|---|---|---|---|---|---|
|Endoeneit|IV estimation -|-0.002|-0.000||||
|gy|contemporaneous|(0.005)|(0.001)|_[0.05]_|||
||IV estimation - historic|-0.001|-0.000||||
|||(0.007)|(0.000)|_[0.03]_|||
||Industrycontrol|0.012**|0.012***||0.011***|0.010***|
|Firm||(0.005)|(0.002)|_[1.00]_|(0.004)|(0.004)|
|Heterogeneity|Firm size control|-0.004*|-0.004***||-0.004*|-0.004*|
|||(0.002)|(0.001)|_[0.99]_|(0.002)|(0.002)|
||Local area human capital|-0.012***|-0.010***||-0.012***|-0.010**|
|Worker Sortin||(0.004)|(0.002)|_[1.00]_|(0.004)|(0.004)|
|g|Individual-level human capital|-0.014**|-0.013***||-0.014**|-0.011*|
|||(0.006)|(0.003)|_[1.00]_|(0.006)|(0.006)|
||Constant|-0.002|-0.005||0.000|-0.004|
|||(0.010)|(0.005)|_[1.00]_|(0.010)|(0.009)|
||Observations|1,242|1,242||1,242|1,242|

Notes: Outcome is the reported agglomeration elasticity. All models are estimated under PET-PEESE, “precision-effect estimates with standard errors” following Stanley and Doucouliagos (2019), which to correct for publication bias includes a squared standard error term, and its interaction with a developing country dummy, and with a post-1990 dummy. The standard error terms are not reported for parsimony. PET-PEESE estimates are precision-weighted, using the inverse of the reported estimate’s variance as the weight. Robust standard errors are presented in parentheses, these are clustered at the study level for all model selection methods except Bayesian Model Averaging (BMA). The square brackets reflect the probability of each variable’s model inclusion under BMA. The General model includes all control variables. BIC and AIC are the specifications (from all 17million combinations of controls) that minimize the Bayesian and Akaike Information Criteria respectively. ***, ** and * reflect significance at the 1, 5 and 10 percent levels respectively.

# 6. Estimating urban costs

Our meta-analysis in section 5 suggests that urban costs play a major role in explaining differences in agglomeration benefits across studies. Most studies measure “gross” agglomeration benefits of density rather than advantages of locating in crowded, congested and crime prone places that “net” out these benefits. In sum, the evidence base for urban costs is underdeveloped. Using novel data on crime, congestion and pollution from hundreds of cities around the world, including those in developing countries, we present estimates of density elasticity of urban costs in Table 7. The table makes the following points: First, urban costs are significantly higher in _levels_ in developing countries, and this is true across our measures of congestion and crime, and depending on the specification, pollution, suggested by the positive developing country dummy (and mirroring Figure 4). In levels, for the average city density in our data, pollution is on average 16-28 percent higher (although not significantly different from zero in column 1), 19-30 percent more hours are lost hours to congestion and homicides are 4 times as likely.

Second, although developing countries have higher urban cost levels, their cost _elasticities_ may not be different than that observed in developed countries. Relative to developed countries, the elasticity of 23
urban dis-amenities in developing countries are similar for pollution and congestion. Our results point to an elasticity of pollution and congestion with respect to city density to be 45 percent and 16 percent respectively in developing countries (compared to 48 percent and 18 percent for developed countries).<sup>15</sup> By contrast, the elasticity of crime, measured by the homicide rate, with respect to city built-up density is significantly higher at +24 percent in developing countries compared with -56 percent in developed countries. The latter suggests that if crime is accounted for in measuring the advantages of locating agglomerations, the net benefits in developing countries would be much smaller.

As a robustness exercise we use city population density from census data (instead of build-up density) for each country.<sup>16</sup> . The results are presented in the Appendix Table A4. Although we find somewhat lower urban cost elasticities for pollution (18 percent overall) and higher for congestion (26 percent), the key messages do not change. We find that the levels of congestion, crime and pollution are larger in developing economies, but the urban cost elasticities are not discernibly different between developing and developed countries.

**_Table 7: Urban cost elasticities and cost levels - across developed and developing countries_**

|Outcome:|**Log PM2.5**|**Pollution**|**Log Hours L**<br>**Ti**|**ost to Travel**<br>**me**|**Log Hom**|**icide Rate**|
|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|(6)|
|Developing Country|0.150|0.252**|0.176***|0.264***|1.578***|1.686***|
||(0.097)|(0.118)|(0.060)|(0.073)|(0.212)|(0.201)|
|Log Population Density|0.453***|0.481***|0.158***|0.177***|0.006|-0.566**|
||(0.052)|(0.056)|(0.039)|(0.043)|(0.166)|(0.259)|
|Log Population Density *<br>||-0.145||-0.140||0.807**|
|Developing Country||(0.136)||(0.094)||(0.331)|
|Constant|2.525***|2.534***|4.627***|4.631***|0.428***|0.220*|
||(0.040)|(0.042)|(0.023)|(0.024)|(0.122)|(0.125)|
|Observations|298|298|337|337|188|188|

Note: City-level pollution reflects PM2.5 data for 2014 for 298 cities (78 in developing countries). Congestion reflects the annual additional hours spent driving in rush hours, measured in 2018, and contains data for 337 cities (69 in developing countries). Homicide rate data reflects 124 cities (63 in developing countries) in 2015. Population density reflects population per square km of built up area in 2015. The top and bottom 1 percent of population density observations are excluded. Non-HIC reflects a dummy variable for developing countries using World Bank country classifications in 2015. Log population density is demeaned such that the constant terms are interpreted at the mean city density. Robust standard errors in parentheses, ***, ** and * reflect significance at the 1, 5 and 10 percent levels respectively.

# 7. Conclusions

15 Our estimate is somewhat higher than Ahlfeldt and Pietrostefani (2019) who report the pollution elasticity to be +22 percent, using OLS estimation and OECD data. They also find a congestion elasticity of +8 percent, using a different measure of congestion to our paper, average travel speeds using OECD data. Their meta-analysis of 13 high income country studies of crime elasticities (not focusing on homicides as we do) finds a mean elasticity of -24 percent.

16 Census data is available for only about half the cities in our sample.

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We examine more than 1,200 estimates of agglomeration elasticities from 70 studies covering 33 countries over the period 1973 to 2020. While raw agglomeration elasticities are positive and high in China, India and countries in Africa, countries such as Chile have negative elasticity estimates. Overall, raw estimates tend to suggest that developing countries reap huge benefits from urban density, nearly 5 points higher than developed countries. Further, these estimates are not driven by reverse causality.

These aggregate estimates, however, hide substantial heterogeneity. The differences in estimates can be attributed to estimation set-up (outcome and agglomeration measure), consideration of urban costs in estimating net benefits, and the variation in pay-off across sectors and skills. Studies using wages as an outcome variable have higher estimated elasticities compared to those using TFP measures, while studies using population size or density have larger estimates relative to market access measures. Service sector estimates are on average higher than manufacturing, while skilled workers disproportionately benefit from density relative to others. These findings are broadly consistent with the literature.

Our most important finding is that nominal wages, the canonical measure of agglomeration economies, seldom capture the costs of working and living in cities. These costs include higher housing costs, time lost in commuting as well as dis-amenities such as pollution or crime. Our metaanalysis shows that studies controlling for urban costs find elasticities to be 4.2 percentage points lower than studies that do not, implying a net agglomeration elasticity of 0.1 percent for developed countries, when using labor productivity as an outcome measure. Although our analysis confirms the relatively higher “gross” wage elasticities with respect to density; we find no evidence for “net” gains in light of high and increasing costs of working in developing country cities.

Further, rather than developing country agglomeration estimates being much higher than advanced countries as noted in country studies using wage data from China and India (e.g. Chauvin et al., 2017), there is no statistically significant difference between developing country and developed country estimates. Our novel estimates of urban dis-amenities suggest that although the elasticity of pollution and congestion in developing countries is comparable with developed countries, their levels are much higher. Higher costs in developing country cities are partly due to bad design and lack of capital investment, but also the fact that their growth is not driven by the process of structural transformation, which would create a critical mass of more productive firms that benefit from sharing, matching, and learning. Many developing country cities are not dense and productive—they are just crowded.

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