Compact cities and economic productivity in Mexico

Abstract

Chinese

This paper examines the contingent nature of agglomeration economies. Existing empirical evidence that compact cities are more productive is mostly from countries and regions with highly productive service sectors, such as the USA or Europe. We hypothesise that this relationship will differ in countries where land-intensive manufacturing activities are more productive than services. In this paper, we test this hypothesis using data from the 100 largest cities in Mexico in 1990, 2000 and 2010. Under a number of specifications, we find that the most common measures of urban compactness are, in fact, negatively associated with economic productivity. This holds even when instrumenting urban spatial structure with the underlying geology of urban areas. The findings suggest a need for greater attention to national economic structure in the study of agglomeration economies, and that policy agendas focused on compact urbanisation take account of the needs of the manufacturing sector.

Keywords

agglomeration economic processes land use productivity urban spatial structures urbanisation

Introduction

Urban agglomeration plays a fundamental role in economic development, but not a static one. The productivity benefits of concentrating economic activity in urban areas has been recognised for over a century (Marshall, 1890), yet scholars continue to unpack the details of how these benefits accrue. A recent review of research shows that larger, more economically dense urban areas are more productive (Ahlfeldt and Pietrostefani, 2017a). Yet beyond the size or density of cities, many questions about the role of urban spatial structure remain unanswered. For example, how does the national economic structure shape the role of urban spatial structure in agglomeration economies?

Policy debates around urban spatial structure often simplify to sprawl versus compactness. The primary set of arguments against policies that promote sprawl are based on its environmental impacts, centring on the inefficiency of travel in less compact cities (Newman and Kenworthy, 1989) and the preservation of rural environments (Jabareen, 2006). Increasingly, however, advocates for urban compactness also point to its productivity benefits (Haddaoui, 2018). Research in the USA and Europe provides ample evidence of higher productivity in places with greater economic density (Ahlfeldt and Pietrostefani, 2017a).

Evidence of the productivity benefits of urban compactness in developing countries, however, is minimal. For example, in the review of 189 studies by Ahlfeldt and Pietrostefani (2017a), only 36 are from developing countries. Of these, 18 are focused in Asia (mostly China), five from India, two from the Middle East, and 11 from Latin America. Not one is from Mexico, Central America or the Caribbean. In this paper, we examine the relationship between urban spatial structure and economic productivity in Mexico. We ask a basic question: Are compact urban areas more productive in Mexico?

This research has direct implications for urban policy. Around the world, local governments enact strict urban growth boundaries and greenbelts to stop what they call ‘chaotic’ or ‘uncontrolled’ urban growth. Governments use them for theorised environmental and economic benefits (Angel and Blei, 2016). Critics, however, assert they exacerbate negative externalities such as congestion and raise the price of land and housing unnecessarily (Quigley and Rosenthal, 2005). Recent federal policy in Mexico, for example, seeks to curtail urban expansion through urban containment perimeters for economic and sustainability reasons (Monkkonen and Giottonini, 2017).

Yet research from developing countries on urban compactness and productivity is limited. In countries such as Mexico, manufacturing jobs are much more productive (almost two times more) than service sector jobs on average (INEGI, 2015). Moreover, the manufacturing sector benefits less from the face-to-face interaction of dense urban environments than the services sector, and often is more land intensive. It is generally associated with a dispersed rather than compact urban spatial structure.

We hypothesise that the relationship between urban spatial structure and productivity across cities¹ in Mexico, therefore, may differ from that in high-income countries. We test this hypothesis using three decades of data for the 100 largest urban areas in Mexico, and find that larger cities are more economically productive, but compact urban areas are less productive. In a cross-section, the negative relationship between compactness and productivity is robust to a model that instruments urban spatial structure with the underlying geology of an urban area’s land. The relationship does not persist in a statistically significant manner in a fixed-effects panel model, however.

The results raise questions for urban policy and for the conventional understanding of productive urbanisation. One important caveat is that, given data limitations, these results are compelling associations rather than causal evidence. Nonetheless, the evidence from Mexico raises the question: will other countries with similar economies exhibit a similar relationship between compactness and productivity?

We organise the paper as follows. The next section reviews the state of knowledge about urban spatial structure and economies of scale and urban agglomeration. Then, we examine recent industrial dynamics and changes in the spatial structure of urban areas in Mexico. The fourth section is a research framework, presenting the metrics of urban spatial structure and our modelling strategy. We discuss the outcomes in the penultimate section. Finally, we draw some preliminary conclusions connecting this empirical work and a broader theory of how national economic structure shapes agglomeration economies.

Theory and evidence on the role of urban spatial structure in urban productivity

Agglomeration economies are the multitude of benefits derived from a proximate location between firms and people in urban areas. They increase individual economic productivity in multiple ways. Most directly, larger urban areas generate economies of scale because they support larger firms, reducing costs per produced unit (Camagni, 2005). Firms in large cities also benefit from a larger, more specialised labour pool (Chinitz, 1961), from reductions in transportation costs between firms (Glaeser, 2010) and from lower costs for shared inputs. Infrastructure costs are also lower in larger cities (Strogatz, 2009). Knowledge-spillovers within and between firms can foster innovation (Quigley, 1998).

There is a size limit to agglomeration. Congestion costs reduce efficiency advantages above a certain population size. Diseconomies of agglomeration are the reason urban areas do not indefinitely increase in size. They also vary. Urban areas with worse urban management, public services and infrastructure are less able to mitigate diseconomies of scale, and less likely to harness the productivity advantages of agglomeration (Puga, 2010). Recent evidence shows that India, for example, does not benefit from agglomeration in the same way higher-income countries do (Chauvin et al., 2016).

With the dramatic decline in transportation costs during the 20th century and the rapid increase in the quality of communication technologies, many hypothesised that cities would lose their importance (Cairncross, 2001). Clearly, this was not the case. Although transportation costs decreased, the cost of moving people is still relatively high, especially for face-to-face interactions (Glaeser, 2010). These interactions, however, are more important in knowledge-based, service industries. Distance is less relevant for industrial location decisions than for the location of service-sector firms (Camagni, 2005), suggesting that agglomeration economies depend on national economic structure.

Empirical evidence on the connection between the size of urban areas and productivity

The most common and simplest ways to measure agglomeration are through urban populations or economic density. The connection between density and labour productivity is clear for the most-studied nations. In the 1970s, researchers found that a doubling of the urban population size in the USA led to an increase in productivity of between 3% and 8% (Shefer, 1973). Studies in the following decades found productivity increases of between 6% and 10% when urban populations doubled (Ciccone and Hall, 1996; Fallah et al., 2011; Fogarty and Garofalo, 1988; Glaeser and Maré, 2001; Meijers and Burger, 2010). The recent meta-analysis of the elasticity of density with respect to over a dozen outcomes, from productivity to crime reduction to pollution, by Ahlfeldt and Pietrostefani (2017b), finds a roughly 4% wage elasticity.

Glaeser and Resseger (2010) highlight that agglomeration economies are stronger in cities with more highly skilled workers. They argue that knowledge spillovers make urban density vital for highly productive service sectors. The sorting of workers with different skills and unobserved qualities has led empirical analyses to increasingly rely on individual-level microdata rather than city-level averages. As Combes et al. (2010) demonstrate in France, higher skilled workers sort into productive cities, but they are also more productive there than they would be elsewhere.

Evidence of larger cities’ higher productivity in the US and Europe is prevalent, but less common in developing countries. Prud’homme and Lee (1999), for example, find that French cities’ labour productivity is a function of the size of their labour pool, which in turn depends on their population size. Recently, Ahrend and colleagues at the OECD (2014) estimated the benefits of scale economies based on the differentials on urban productivity across Germany, Mexico, Spain, the UK and the USA. They find that productivity increases with city size in all five countries (Ahrend et al., 2014).

Empirical evidence on the connection between urban spatial structure and productivity

Evidence for a connection between urban spatial structure (e.g. compactness or monocentricity) and productivity is less ample, partly because of the greater measurement challenges. Additionally, the main dimension of spatial structure – density – tends to correlate closely with population size and other dimensions such as centralisation and contiguity. This complicates modelling efforts. Nonetheless, studies do find a positive relationship between compactness and productivity in US and European metropolitan areas.

Early work on this topic examined manufacturing density gradients in US metropolitan areas, testing the hypothesis that agglomeration economies depend not only on population size but also on spatial structure and the age of the city (Fogarty and Garofalo, 1988). Fogarty and Garofalo differentiated between two types of density externalities: diminished communication costs leading to improved information flows and reductions in transportation costs. They found that the central density of manufacturing and the density gradient related positively to productivity in manufacturing. Beyond a certain population size, however, density began to reduce productivity.

Using a different measure of urban structure, Meijers and Burger (2010) find that polycentricity is associated with higher labour productivity in the USA. Doubling the degree of polycentricity increases metropolitan labour productivity by over 5%. They also posit that more polycentric cities will diminish the relative importance of agglomeration. They reject this hypothesis, finding that dispersion is not necessarily harmful to labour productivity and speculate that diseconomies of scale are lower in polycentric regions.

Studies in Europe and Asia confirm the productivity benefits of density found in the USA. Prud’homme and Lee (1999) also find that the effective size of the labour market increases with density, and that when people are closer to their workplace they are more productive. In the case of France, Combes et al. (2010) confirm that denser areas are more productive. They use a two-part identification strategy, which we borrow from in this study.

Azari et al. (2016) find the role of agglomeration in productivity is less direct in the Korean manufacturing sector. They find that job density has a negative effect on productivity but the density of production has a positive impact. These results are consistent with Ke’s (2010) study of agglomeration in China, which finds that the spatial concentration of industrial production had a positive effect on productivity. Ke emphasises the importance of congestion diseconomies in the Chinese context, however.

With a few exceptions, empirical studies of agglomeration economies in Latin America do not address the question of urban spatial structure. One study provides suggestive evidence about the unusual relationship between compactness and labour productivity in Mexico (Kim and Zangerling, 2016). Another, Quintero and Roberts (2017), assesses the role of agglomeration across 16 Latin American countries. They use individual data in a wage equation to account for human capital and sorting effects. They find a measure of density to be significantly associated with incomes, though most of the location premium disappears after controlling for sorting. Their model is similar to that of Duranton (2015), who estimates these parameters for Colombia, and Chauvin et al. (2016), who study Brazil, China and India.

A gap in the literature: The land use needs of different economic sectors

Ciccone and Hall (1996) point out that the relationship between density and labour productivity is ambiguous a priori, and that density likely affects productivity in high-end services jobs differently than in the manufacturing sector. The benefits of in-person interactions are stronger in knowledge-based service industries. Software firms, for example, tend to locate in central areas because they benefit more from the concentration of human capital found there (Glaeser and Resseger, 2010). There is a positive correlation between the number of patents per capita and employment density in US metropolitan areas (Carlino et al., 2007).

Even within the manufacturing sector, different types of firms will benefit in different ways from urban structures. Large car manufacturers need space for production, and benefit more from economies of scale than do high-end clothing producers, for example, who seek proximity to designers and marketing teams. Land-intensive manufacturing firms tend to locate in peripheral areas where large parcels are available (Méndez and Caravaca, 1996). For these reasons, we expect the overall relationship between urban spatial structure and economic productivity to depend partly on the economic base of regions.

The economic and urban context of Mexico

The inter-urban evolution of manufacturing in Mexico

Until the 1970s, Mexican manufacturing was highly concentrated in space and sector. Just four manufacturing subsectors (out of 20) represented almost 50% of the gross industrial product and Mexico City produced 46% of the gross industrial product (Garza, 1980). The primacy of this metropolitan area prompted the Federal Government to attempt to disperse economic activity across the country. They actively promoted the construction of industrial parks, industrial polygons and industrial cities outside of Mexico City between 1953 and 1986 (Garza, 1988).

The dispersion of economic activity did eventually occur. Starting in the 1980s, manufacturing began to boom in the states along the northern border and the outskirts of the greater Mexico City region (Dávila, 2004; Sobrino, 2002). Older industrial centres such as Puebla, Hidalgo, Tlaxcala and Mexico City have gradually lost manufacturing jobs as cities in the central and northern regions gain in relative importance.

There are two probable explanations. First, the opening of Mexico to international trade and investment weakened the spatial concentration of manufacturing jobs in the centre of the country by encouraging factory construction near the US border (Dávila, 2004). Second, diseconomies of scale in Mexico City began pushing manufacturing from older regions. Local governments were unable to provide adequate public infrastructure (Mendoza-Cota and Pérez-Cruz, 2007).

In spite of the industrial boom in the northern border states during the 1980s and 1990s, and the decentralisation process of the Mexico City metropolitan area, the share of jobs in manufacturing has been quite stable at the national level, at roughly 25%. Manufacturing as a share of GDP has also held steady, at nearly 20% of GDP in 1981 and 2013. In our sample of 100 cities, manufacturing accounts for roughly 30% of jobs and over 40% of gross value added.

Comparing labour productivity across the three broad economic sectors in Mexico from 1985 to 2010 reveals that productivity per worker is consistently about two times higher in the manufacturing sector (INEGI, 2015).

Urbanisation in Mexico

Mexico’s most dramatic period of urbanisation occurred in the second half of the 20th century, but urban areas continue to grow rapidly. In fact, in the 1990s and 2000s, the 100 largest cities in Mexico grew by roughly 20% in land area and population. Overall, urban population density increased slightly during this period.

A massive expansion of Mexico’s government-run housing finance system starting in the early 1990s led to a rapid urban expansion that has not yet abated. The country’s housing production system also transitioned from a primarily incremental, self-help construction process to one based on speculative building by large private companies (Monkkonen, 2011b). This change created higher-density urban expansion and has been linked to high levels of housing vacancy (Monkkonen, 2019) and population loss in urban centres (Monkkonen and Comandon, 2016).

Research framework

We first measure the urban spatial structure of the 100 largest urban areas in Mexico using various metrics, described below. The smallest of the urban areas had over 50,000 residents in 1990, the base year for our sample. Many urban areas span multiple municipalities. They include the more than 50 official metropolitan areas as classified by the federal government of Mexico in its National Urban System (CONAPO/INEGI/SEDESOL, 2012). Conveniently for this study, urban census tracts in Mexico are delimited only for urbanised land, thus the boundaries of urban areas are built into the census data we rely on (for more, see Montejano et al., 2019).

We then examine the relationship between urban spatial structure and economic productivity in a cross section and time series. One challenge is the correlation between population size and some measures of spatial structure, such as population density. A second challenge is the endogeneity between agglomeration and productivity. Combes et al. (2010) clearly outline the two potential threats. Productive urban areas attract more people at the same time as larger urban areas become more productive. Additionally, more ambitious and innately skilled workers sort into productive cities, although in Mexico only 5% of adults in our sample moved to an urban area between 2010 and 2015, and only 2% moved from one city to another (INEGI, 2015).

We partly address these threats by first running two-stage least squares models, instrumenting urban spatial structure with indicators of a city’s underlying geology. This follows from Rosenthal and Strange (2008) and Combes et al. (2010), who argue that geology can constrain or abet density, but does not directly affect economic productivity. We also take advantage of the longitudinal nature of our data to examine changes in form and productivity. Nonetheless, future work with microdata on human capital will be important to assess the impact of sorting in Mexico.

Measuring urban spatial structure

The spatial structure of cities is complex. Reis and colleagues (2016) group measures of urban form into four categories. The first is landscape metrics, which in turn have four basic types: shape irregularity, fragmentation, diversity and connectivity. The second is geo-spatial metrics, mostly indicators developed in an ad hoc manner for specific cases. The third is spatial statistics, which seek to measure the distribution of events across space, and include regression metrics and measures of the evenness of distribution. Finally, accessibility metrics assess the distance from people to locations or the number of opportunities available to a location, including cumulative opportunity and gravity-based measures (Handy and Niemeier, 1997).

We measure urban structure considering the particularities of urban areas in Mexico. For example, unlike the low-density, fragmented, leapfrog, single-use development that characterises urban sprawl in the USA (Galster et al., 2001), suburban developments in Mexico are relatively high-density, fragmented and single-use (Monkkonen, 2011a).

We consider nine of the most common measures to capture the five key dimensions of spatial structure. The dimensions (and their measures) are (1) density (of population and jobs), (2) centrality (Density Gradient and Centrality Index (Galster et al., 2001)), (3) compactness (Proximity Index (Angel et al., 2010) and Compactness (Amindarbari and Sevtsuk, 2015)), (4) fragmentation (Discontiguity (Amindarbari and Sevtsuk, 2015)) and (5) evenness (Gini Coefficient, Clustering Index (Pereira et al., 2013) and Moran’s I (Tsai, 2005)). A technical Appendix includes formulas for each of the nine metrics.

Density

1. The simplest measure of urban population density is the number of residents or jobs in an urban area divided by its land area. The Mexican census bureau, INEGI, distinguishes between urban and rural census tracts such that urban census tracts create boundaries for urbanised areas.

Centrality

2. The density gradient measures a city’s central tendency. Density is highest near city centres and the gradient measures the rate at which density falls as one travels away from the city centre, using a negative exponential. First developed by Clark in 1951, the density gradient is used by scholars to measure monocentricity (Mills, 1972).

3. The centrality index (Galster et al., 2001) measures whether people or jobs are located near the city centre. Unlike the density gradient, it does not measure decay over distance. It is equal to the inverse distance of each census tract from the city centre, weighted by its population. We divide this ‘average distance’ by the square root of the total urban area to normalise it by city size.

Compactness

4. The proximity index is essentially a measure of a city’s circularity (Angel et al., 2010). It takes the value of 1 when the city is a circle, and 0 under perfect linearity. We improve on the measure by removing non-developable land, such as bodies of water or steep hills, from the calculation. The proximity index is effective in its simplicity, but does not consider the distribution of people or activities.

5. Amindarbari and Sevtsuk (2015) measure how accessible different parts of the city are to each other using a gravity model as a base. The more accessible different locations are within a city, the more compact it is. Population, geographical constraints, or the density of the reference city can normalise the index. We use population, manufacturing jobs and total jobs to compare cities with one another. Calculating compactness using census tract data is robust when compared with calculations using smaller geographic scales.

Fragmentation

6. Amindarbari and Sevtsuk’s (2015) discontinuity measure is the most straightforward measure of fragmentation we find in the literature. Galster et al. (2001) propose a continuity measure, the inverse of which would be discontinuity or the extent to which urban areas develop in a leapfrog pattern. However, it is quite complex to implement. Other fragmentation measures dependent on satellite imagery data are preferable in some ways but require extensive processing.

Evenness of distribution

7. The Gini coefficient measures the evenness of a distribution across units, for example, people or jobs across parts of a city. A low coefficient reflects a more equal distribution across a city.

8. The Clustering Index developed by Pereira et al. (2013) also measures the evenness of a distribution across a city. It is similar to the Gini coefficient but uses tracts as the unit of observation, assuming each to be equally sized, and considers whether similar tracts are next to one another.

9. A global spatial autocorrelation measure, the Moran’s I, also measures whether tracts with high values of a variable are clustered, dispersed or randomly distributed.² It does not distinguish among different distributions of density, but Tsai (2005) argues this index can effectively characterise compactness on its own. Higher values match monocentric conditions.

We calculate all nine measures of urban spatial structure for jobs (using data from the economic censuses 1999 and 2009 at the census-tract level) and population (using data from the population and housing censuses of 1990, 2000 and 2010). Tract-level jobs data are not available for 1990, so we only compute metrics related to the population distribution and the ‘pure form’ metric, the proximity index, for that year. Table 1 presents summary statistics.

Table 1.

Measures of urban spatial structure for 100 urban areas in Mexico, 1990–2010.

Measure	Year
	1990		2000		2010
	Mean	Standard deviation	Mean	Standard deviation	Mean	Standard deviation
Population
Density	37.20	12.45	39.33	13.81	42.67	12.78
Gradient	0.20	0.29	0.18	0.18	0.15	0.17
Centrality	0.49	0.18	0.71	0.24	0.83	0.30
Proximity^a	0.51	0.25	0.61	0.21	0.63	0.19
Compactness	744.84	898.02	538.39	646.48	994.37	952.86
Discontiguity	0.55	1.13	0.57	1.04	0.54	0.97
Gini	0.30	0.06	0.35	0.08	0.35	0.07
Clustering	0.30	0.06	0.31	0.07	0.36	0.08
Moran’s I	0.19	0.44	0.17	0.13	0.27	0.16
Employment
Density			39.40	13.20	41.80	12.20
Gradient			−0.30	0.29	−0.35	0.36
Centrality Index			0.98	0.33	0.87	0.30
Compactness			43.69	78.54	31.84	159.07
Discontiguity			0.57	1.03	0.63	1.11
Gini			0.46	0.06	0.51	0.06
Clustering			0.58	0.06	0.57	0.06
Moran’s I			0.33	0.13	0.17	0.19

Notes: ^aProximity is a pure form metric thus applies to neither population nor employment.

Source: Authors, with INEGI (1990, 2000, 2010).

The measures point to an increasing average level of centralisation across cities in Mexico, despite their rapid expansion. The 1990s saw greater changes. To assess the interrelationship between these different dimensions of urban structure, Table 2 presents their correlations for the year 2000. With a few exceptions, the correlations are not high. Average density correlates with Centrality, the Density Gradient with Proximity, and Clustering with Centrality and Compactness.

Table 2.

Correlation of measures of urban spatial structure (population), 2000.

Measure	Dens.	Grad.	Cent.	Prox.	Comp.	Disc.	Gini	Clus.	Mor.
Gradient	−0.025	1
Centrality	0.588	0.191	1
Proximity	0.140	0.678	0.155	1
Compactness	0.032	0.237	0.001	0.063	1
Discontiguity	0.198	−0.366	−0.063	−0.276	−0.108	1
Gini	−0.216	0.021	−0.019	0.019	0.004	−0.033	1
Clustering	0.067	0.266	0.499	−0.069	0.059	−0.074	−0.015	1
Moran’s I	0.001	−0.066	0.251	−0.055	−0.132	−0.057	0.104	0.131	1
Pop. (log)	0.485	−0.467	0.070	−0.076	−0.298	0.516	0.107	−0.28	0.091

The relationship between urban spatial structure and productivity in Mexico

Our dependent variable is the average economic productivity per worker in a given urban area. We calculate the average Gross Value Added (GVA) per worker using the economic census, excluding workers and GVA of the mining and extractive industries. Productivity is very high in these sectors, though employment is very low in most cities. They are not theoretically related to agglomeration.

The most significant factor in shaping a city’s productivity in Mexico – apart from the composition of industries – is its size. Based on evidence from other countries, we also expect population density to be positively associated with population. In fact, it is, a correlation of roughly 0.5 (see Table 2 above).

Nonetheless, productivity does not correlate positively with density or other measures of compactness. In fact, a simple visualisation of the relationship between urban centralisation (as measured by the population density gradient) and economic productivity reveals a negative relationship. Figure 1 shows this alongside the aforementioned relationship between population and productivity.

Figure 1.

Relationship between productivity, density gradient and population 2010.

In all regressions of productivity on the different measures of urban spatial structure, therefore, we control for population size and a city-level measure of economic specialisation, the Herfindhal-Hirschman Index (HHI). The HHI ranges from one – total concentration in one of three sectors (manufacturing, services and commerce), to zero – an equal distribution across sectors.

The first set of models use pooled data from 1990, 2000 and 2010. Four of the nine measures of urban spatial structure are statistically significant: density gradient, centrality, proximity and clustering. These are the more prevalent measures in the literature, and the most conceptually reliable. The coefficients show that more sprawling cities are less productive.

Table 3 presents the results of four models. Results of the other five models are available upon request. The signs on the coefficients in Table 3 indicate that more compact, centralised and clustered Mexican cities are less productive. The density gradient’s coefficient indicates it has higher values in more centralised-monocentric cities.³ For example, cities with one standard deviation more centralised structures than average are 2% less productive. Sectoral concentration also has a negative relationship to productivity but, all else equal, more manufacturing is positive.

Table 3.

OLS regression results: Average productivity (1990, 2000 and 2010 pooled).

Variable	Model 1	Model 2	Model 3	Model 4
Population (ln)	0.008 (0.036)	0.071 (0.034)^**	0.058 (0.034)^*	0.026 (0.034)
% Jobs mfg.	0.633 (0.139)^***	0.501 (0.144)^***	0.638 (0.140)^***	0.683 (0.138)^***
HHI	−3.090 (0.614)^***	−3.287 (0.605)^***	−3.245 (0.613)^***	−3.145 (0.610)^***
Density Gradient	−0.611 (0.165)^***
Centrality		−0.614 (0.143)^***
Proximity			−0.525 (0.156)^***
Clustering				−1.977 (0.502)^***
Constant	6.101 (0.521)^***	5.645 (0.492)^***	5.700 (0.500)^***	6.353 (0.539)^***
Observations	300	300	300	300
R-squared	0.20	0.22	0.20	0.21

Notes: Includes year fixed effects. Mining productivity and employees not included. All measures of spatial structure are calculated using population. Standard errors in brackets. ^***, ^**, and ^* indicate significance at p < 0.001, p < 0.01, and p < 0.05 levels.

We also run three additional sets of models to assess potentially confounding factors (full results of which are available upon request). First, models that control for the wide regional variation across cities in Mexico using regional fixed effects find they do not affect the models of urban structure and productivity. Parameter estimates are less than 10% different and retain significance. Although concerns about the role of human capital and sorting across cities are best addressed using microdata, we ran models identical to those reported above, controlling for the share of a city’s adult population with education beyond high school and a college degree. Parameter estimates of interest changed very little, and the coefficients on education variables were essentially zero with large standard errors.

Finally, models that differentiate between productivity in the manufacturing sector and in the service sector show that urban spatial structure has a very different relationship to the two sectors. By several measures, compact cities have more productive service sectors. Kim and Zangerling (2016) provide suggestive evidence and discussion of this as well.

Next, we run two-stage least squares models, instrumenting the measures of urban spatial structure with four indicators of an urban area’s underlying geology: two measures of earthquake risk, a measure of landslide risk based on soil composition, and a measure of flooding risk. Table 4 presents the results of these four models. Results from the first stage are available upon request.

Table 4.

2SLS regression results: average productivity (1990, 2000 and 2010 pooled).

Variable	Model 1	Model 2	Model 3	Model 4
Population (ln)	−0.041 (0.057)	0.094 (0.039)^**	0.061 (0.035)^*	0.025 (0.046)
% Jobs mfg.	0.589 (0.146)^***	0.251 (0.234)	0.580 (0.154)^***	0.684 (0.137)^***
HHI	−2.807 (0.670)^***	−3.180 (0.640)^***	−3.059 (0.655)^***	−3.141 (0.643)^***
Density Gradient	−1.246 (0.586)^**
Centrality		−1.496 (0.649)^**
Proximity			−1.356^* (0.754)
Clustering				−2.014 (2.103)
Constant	6.738 (0.772)^***	5.869 (0.541)^***	6.035 (0.597)^***	6.369 (1.040)^***
Observations	300	300	300	300
R-squared	0.16	0.12	0.12	0.21

Notes: Includes year fixed effects. Urban spatial structure variables are instrumented with HHI, % jobs in manufacturing, population, two measures of earthquake risk, a measure of landslide risk and a measure of flooding risk. Mining productivity and employees not included. All measures of spatial structure are calculated using population. Standard errors in brackets. ^***, ^**, and ^* indicate significance at p < 0.001, p < 0.01, and p < 0.05 levels.

In the two-stage least squares models, the coefficients on the density gradient, the index of centralisation and proximity/circularity retain statistical significance, but the measure of clustering does not. Coefficients on the urban spatial structure measures are larger. While theoretically strong, the instruments are somewhat mathematically weak according to the first stage. The relatively small F statistics on the first stage models prompt us to run the instrumental variables models using limited information maximum likelihood models. In these models, only the density gradient and the centralisation index retain significance.

Changing urban spatial structure and productivity from 1990 to 2010

We also examine the relationship between spatial structure and productivity over time, in a limited manner. Tract-level employment data are only available in 2000 and 2010 so we concentrate on measures of urban spatial structure using population data from 1990, 2000, 2010. We use a panel model from 1990 to 2010, with fixed effects and the population-based measures of urban spatial structure. A Hausman test indicates that a fixed effects model is preferred over a random effects model. The fixed effects model has the advantage of controlling for all time-invariant features of urban areas but therefore precludes using geology instruments.

Table 5 reports the results of the four models for those urban spatial structure measures that were statistically significant in the pooled cross-section models. Although three of the four measures of urban spatial structure – density gradient, centralisation and clustering – have similar but smaller signs, their coefficients are not statistically significant. Cities that became less centralised, less circular and less clustered apparently did not become more or less productive.

Table 5.

Results of fixed effects panel models, 1990–2010.

Variables	Model 1	Model 2	Model 3	Model 4
Population (ln)	−0.248 (0.122)^**	−0.142 (0.135)	−0.235 (0.120)^*	−0.223 (0.123)^*
% Jobs mfg.	−0.182 (0.248)	−0.160 (0.247)	0.177 (0.249)	−0.165 (0.250)
HHI (GVA)	−1.671 (0.590)^***	−1.906 (0.610)^***	−1.642 (0.617)^***	−1.733 (0.612)^***
Density Gradient (Pop.)	−0.129 (0.198)
Centrality (Pop.)		−0.233 (0.160)
Proximity (Pop.)			0.028 (0.200)
Clustering				−0.196 (0.482)
Constant	8.899 (1.659)^***	7.789 (1.734)^***	8.685 (1.629)^***	8.637 (1.633)^***
Observations	300	300	300	300
R-squared	0.05	0.05	0.04	0.04

Notes: Models include year and city fixed effects. The dependent variable is Log(Gross Value Added per Job). Standard errors in brackets. ^***, ^**, and ^* indicate significance at p < 0.001, p < 0.01, and p < 0.05 levels.

Population growth is associated with decreasing productivity in the panel model. One possible explanation for this is that inter-urban migration in Mexico results more from push factors, such as a lack of jobs, or violence in rural areas, than pull factors, such as a booming urban economy (Hanson, 2003). While this explanation is speculative, the results are compelling in that they provide a new perspective on the contingency of agglomeration economies and invite further research in order to explain them more comprehensively. The avenues for future work include a more explicit consideration for the sorting of individuals with different levels of human capital and the potential impacts of polycentric urban forms.

Conclusion

The majority of empirical research on the link between urban spatial structure and productivity is for the USA and Europe, which differ in key aspects from much of the developing world. Less land-intensive activities, such as professional services, drive their urban economies. Additionally, they generally have better quality infrastructure and urban governance, which likely mitigate agglomeration diseconomies. Scholars have begun to highlight the variation in the benefits of agglomeration across countries and metrics (Ahlfeldt and Pietrostefani, 2017a; Chauvin et al., 2016; Quintero and Roberts, 2017). Case studies from a variety of countries are important to provide nuance to our understanding of cities and economic growth, often oversimplified.

This study looks at a nation with an economic structure different from that of service-oriented developed nations. In our analysis of the relationship between urban spatial structure and productivity in the 100 largest cities in Mexico, we confirm that larger cities are more productive. However, in contrast with much empirical work from high-income nations, we find that the various measures of compact urban spatial structure correlate negatively with productivity. The density gradient of cities and an index of centralisation – calculated using population and employment by census tract – are consistently significantly associated with productivity, even when estimated using instrumental variables.

The results of this study demonstrate the contingent nature of agglomeration economies and the importance of the structure of the national economy in determining the relationship between urban spatial structure and productivity. In Mexico, manufacturing workers are more productive than those in the service sector. Manufacturing also tends to be more land intensive. Thus, overall productivity is, perhaps unsurprisingly, higher in cities with a more decentralised urban spatial structure. The results invite more research in nations where land-intensive manufacturing is relatively more productive than the service sector.

The results also raise questions about federal urban policy in Mexico. The recently created Secretary for Urban, Territorial and Agricultural Development (SEDATU), along with the National Housing Commission (CONAVI), have been advancing an agenda of urban containment and growth control (SEDATU, 2013). We recognise the potential environmental and social benefits of compact cities, yet suggest that the government incorporate productivity considerations into its approach. The federal government should better specify the goals of urban containment policy taking into account the needs of decentralised manufacturing.

Footnotes

Appendix

Density

(A1)

Density = \frac{\sum Population}{\sum Urbanized Area}

Centrality

(A2)

D (u) = D_{0} e^{- rue}

where $D_{0}$ is the density in the urban centre, $u$ is the distance to the city centre, $r$ is an exponential decay parameter (the gradient), and $e$ represents an error term. Higher values indicate greater centrality.

(3)

CI = \frac{T (i) u (A^{\frac{1}{2}})}{\sum_{m = 1}^{M} F (k, m) T (i) m}

where $T (i) u$ is the total number of observations (population) of land use I in Urban Area u; $A^{\frac{1}{2}}$ is the square root of the Urban Area for normalisation purposes; $F (k, m)$ is the distance between the centroids of grid k and grid m; $T (i) m$ is the total number of observations (population) of land use i in land area m.

Compactness

(4)

PI = \frac{2 \sqrt{A / π}}{3 d_{CS}}

where A is the circle area, $d_{CS}$ is the average distance to the proximate centre, the $\frac{2}{3}$ factor is to compute the average distance to the centre in a circle of radius $\sqrt{A / π}$ .

(5)

G_{i} = \sum_{j \in G - {i}} \frac{W [j]}{e^{β \cdot d [i, j]}}

where $G_{i}$ is the Gravity index for census tract i; $W [j]$ is the weight if the j density, and $d [i, j]$ is the distance between centroids of census tracts i and j. $β$ is the decay. The weight can be population or jobs, so the spatial relationships between larger distances have a proportional stronger effect over the index than smaller locations. The index is then normalised by population, geographical constraints or by the density of the reference city.

Fragmentation

(6)

DC = \frac{\sum_{n = 1}^{N} (\frac{\sum_{i = n + 1}^{N} A_{i}}{A_{n}} \cdot A_{n})}{A_{total}}

where $N$ is the number of urbanised clusters and $A_{n}$ the area of cluster n, and $A_{total}$ the joint area of the urban area (Amindarbari and Sevtsuk, 2015: 20). Lower values indicate less fragmentation.

Evenness of distribution

(7)

Gini = 0.5 \sum_{i = 1}^{N} | X_{i} - Y_{i} |

where $N$ is the number of census tracts or sub-areas; $X_{i}$ the proportion of land area in sub-area i; and $Y_{i}$ the proportion of population, employment or dwellings in sub-area i (Burt et al., 2009; Tsai, 2005). Gini was calculated for population, total jobs, and manufacturing jobs.

(8)

CLI = 0.5 \sum_{i = 1}^{n} | s_{i} - 1 / n |

where $n$ is the number of census tracts of a city, and $s_{i}$ is the share of the city’s population or jobs in a given tract. Higher values indicate greater clustering.

(9)

I = \frac{N}{\sum_{i} \sum_{j} w_{ij}} \frac{\sum_{i} \sum_{j} w_{ij} (X_{i} - \bar{X}) (X_{j} - \bar{X})}{\sum_{i} {(X_{i} - \bar{X})}^{2}}

where N is the number of spatial units indexed by i and j; $X$ is the variable of interest; $\bar{X}$ is the mean of $X$ and $w_{ij}$ is an element of a matrix of spatial weights.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was made possible by support from the Lincoln Institute of Land Policy.

ORCID iD

Paavo Monkkonen

Notes

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