Urban Form and Productivity: What is the Shape of Latin American Cities?

This paper examines the linkages between urban form and city productivity, using alternative metrics for urban form and applying them to a comprehensive sample of Latin American cities. Although most of the literature has concentrated on the effects of population density (compact versus sprawling urban development), this paper seeks to assess whether different dimensions of a city's urban form, such as shape, structure, and land-use, affect its economic performance. The paper finds that the shape of the urban extent, the inner-city connectedness, and fullness have a statistically significant influence on the productivity level of the city.


Introduction
Early work on urban economics Parr (1979Parr ( , 1987 recognized the links between urban form and economic performance. The spatial structure of cities or urban form is thought to have important influence on the emergence of agglomeration economies and congestion costs, and, hence, on a city's level of productivity, but also the sustainability of cities and their quality of life (Squires, 2002). The same channels -matching, learning and sharing -that are used to explain the emergence of agglomeration economies (Duranton and Puga, 2004) are also thought to be at the core of the links between urban form and city productivity. Holding city size constant, cities can use land and space in very different ways. Local governments, through land use regulations and other urban policy instruments, can influence the way economic activities, urban infrastructure, and households are located (World Bank, 2009).
These differences in the occupation of urban space have consequences in terms of the transport modes used (i.e. favoring the use of private vehicles versus public transport), commuting times in cities, as well as on the type and intensity of human interaction. Denser cities are thought to improve labor productivity through better matching of firms and workers and enhanced interactions which facilitate the spread of tacit knowledge, both of which are thought to occur more easily the closer are people and firms located together (Ciccone and Hall, 1996;Rosenthal and Strange, 2004;Cervero, 2001). However, despite the links being well established through a theoretical framework, there are few empirical studies that examine the relationship between urban form and economic performance; further, there is still little evidence linking the presence of agglomeration economies with the form that cities take.
With over 80 percent of LAC's population living in cities, understanding the links between city form and productivity is of paramount importance for policy makers in the region. The challenges of topography may have prevented dense development in some cases, as many Latin American cities are located in rugged topographies with natural barriers. Furthermore, rapid urbanization combined with limited infrastructure investments may have also led to urban forms that pose a barrier to the rise of agglomeration economies, limit firm interaction, and make it hard for workers to reach their jobs. Better understanding the links between urban J.C. Duque, N. Lozano-Gracia, J.E. Patino, P. Restrepo / LCR Flagship Report on Cities and Productivity 3 form and productivity can shed light on whether urban policy has a role to play in supporting city productivity and through that, economic growth.
In this paper we examine the linkages between urban form and city productivity using different urban form metrics for a comprehensive sample of Latin American cities with more than 50,000 inhabitants in the year 2010. We use a consistent time series of Defense Meteorological Satellite Programs -Operational Linescan System (DMSP-OLS) nighttime lights (NTL) imagery to identify city extents, characterize urban structure and create a proxy measure of a city's economic performance. In terms of methodological approach, our first base model includes the estimation of urban productivity using time-lagged measures of urban form and other control variables. In a second model we follow Harari (2016) and explore the use of synthetic instruments that use the potential shape of city as a starting point, and calculate the city form indicators based on such potential form. The contribution of this paper is twofold. First, the analysis of linkages between urban form and city productivity has important policy implications in regards to the potential benefits or consequences of land use, transport and other city planning policies that can influence city form. Second, it contributes to the advancement in the measurement of urban form, by using open data available at a global scale that allow for benchmarking of cities across the globe.
The rest of the paper is organized as follows. Section 2 provides a literature review. Section 3 presents the empirical models. Section 4 describes the source data and the construction of the proxy measure of a city's economic performance, the measures of urban form, and the construction of the synthetic instrument. Section 5 presents the empirical results. Finally, section 6 presents our conclusions.

Literature review
Density, size and sprawl have been commonly referenced in economic literature as some of the key aspects of urban productivity. The most recurrent conclusion is that less dense cities face high commuting rates (Wheeler, 2001), have higher marginal costs of transporting intermediate goods (Ciccone and Hall, 1996), and lower knowledge spillovers (Lynch, 1981;Jaffe et al 1993 andGlaeser 1998). All of which can affect a city's productivity levels. However some authors argue that achievements such as improved highways, public transit services (Glaeser, 2014;Chatman and Noland, 2014) and advances in communication technologies (Partridge et al, 2009) have helped to reduce the productivity costs of sprawling.
When thinking of urban form, urban economists commonly use population density and city size as proxies. However, the main limitation of this kind of variables is that they assume a uniform distribution of people across space. Such an assumption ignores the fact that the urban form is the result of the interaction of individuals, firms, and government decisions on where to live, where to locate, and where to place infrastructure. Such interactions are often reflected in the layout of the city, e.g. the street layout, and the land use patterns across the urban space. In other words, urban form and land use patterns cannot be properly identified from density (Melo, et al., 2017). Nowadays, the evolution of areas such as Geographic Information Science and Computational Geometry, which has been reflected in friendlier and inexpensive analysis tools, together with the increase of availability of georeferenced data, has allowed economists to look beyond density and size when thinking of the effect of urban form on city productivity. 1 An example of this trend can be found in Harari (2016) Other studies on urban form, that do not necessarily use the libraries mentioned above, are: Bertaud and Malpezzi (2003) calculate a range of measures of urban form for 48 major metropolitan areas around the world, and analyzed the impact of income, population, and the nature of the regulatory regime as potential determinants of urban form; Huang et al (2007) calculate seven spatial metrics of urban form for 77 metropolitan areas in Asia, US, Europe, Latin America and Australia; they found that urban agglomerations in the developing world are more compact and dense than their those in Europe or North America.
Urban planners, in the search of an integrated theory of city planning, have explored multidisciplinary approaches that integrate areas such as economics, network science, and geometry, to understand the impact of size, scale, and shape on city sustainability (Batty, 2008). This process led them to have a more elaborated concept of urban form. As in Batty and Longley (1994), urban form, from an urban planning perspective, "represent the spatial pattern of elements composing the city in terms of its networks, buildings, spaces, defined through its geometry mainly, but not exclusively, in two rather than three dimensions" [pp :42]. Thus, a proper characterization of city form should include not only information on the shape of its border, but also characteristics of its urban texture and land use planning (a similar warning is made by Prosperi et al., 2009). In fact, the characterization of urban form as a combination of external shape and internal structure was suggested for the very first time 6 J.C. Duque, N. Lozano-Gracia, J.E. Patino, P. Restrepo / LCR Flagship Report on Cities and Productivity by Whyte (1968). Based on these characteristics, the authors differentiate between natural/organic and planned/regular/artificial/geometric cities. Planned cities are characterized by straight streets forming a grid, which can include some radiality with the incorporation of streets that symmetrically converge to a point in the city. They also show a clear segregation of uses and are the result of large-scale planning processes. They also tend to have circular borders. Organic cities grow slower than those that are planned, and their geometry is the result of individual decisions and follows more closely the natural landscape.
It has curved roads and open spaces randomly located. The pattern shows no evidence of planned growth and it is radially concentric in structure (Batty, 2008).
Our contribution to the literature consists of using the multidimensional definition of urban form from urban planning to attain an integral understanding of the influence of urban form on city productivity. We also contribute with new empirical evidence of this relationship using a large set of Latin American cities.

Models
To examine the effect of urban form on productivity, we estimate the following model: where measures productivity of city i at time t; is a vector of urban shape variables; is a vector of urban texture variables; represents the land use pattern within the city; and is a vector of control variables, included the intercept; are the city fixed effects; and is the error term.
One of the main challenges to be tackled in this paper is the endogeneity of urban form when estimating the relationship between productivity and city shape; city form in fact, can be thought of as being the result of the interaction between decisions taken by firms, households, and government, and hence both urban form and productivity result from the interplay between agglomeration economies and congestion forces. In the simplest example, cities that grow dense (or in a concentric pattern around a central business district) can facilitate agglomeration economies by easing proximity of firms and, hence, fostering productivity. But highly productive cities are also more likely to have governments willing to invest in city centers, and hence promote denser growth patterns. For identification purposes, this work will explore two alternative strategies: Strategy 1: We implemented instrumental variables techniques for a cross-section of cities.
The productivity variable is measured using information from the latest available year, and the explanatory variables use data from an earlier year, to mitigate the direct simultaneity between the dependent and independent variables.
Strategy 2: We use an instrumental variables approach, exploiting both temporal and crosssectional variation in city shape. In this step, we use the time variation of the NTL data to build a panel of time-city observations. In defining the instrumental variable, we follow Harari (2016) and construct a synthetic instrument that uses the potential shape of the city as a starting point, and calculates the city form indicators based on such potential form.
Following Harari (2016), the identification relies on the fact that exogenous changes in city form over time can result from encountering topographic obstacles along its expansion path.
The estimation has the following form: , where is a vector of city shape indicators derived from the potential urban extent, are the city fixed effects; are the time fixed effects; and is the error term.
For completeness, we present the steps proposed by Harari (2016) to estimate the potential urban extent when assuming a common average expansion rate across all cities: 1. For the first year, the potential urban extent is the largest patch of developable land (i.e., excluding water bodies and steep terrains) within the minimum-bounding circle of that first year.
2. Estimate the predicted area of city i in year t, area , , with the following regression: where and are city and year fixed effects. In order to estimate this regression, it is necessary to have the actual areas of the urban extents of all the studied cities for, at least, two different years.
3. The estimated urban extent of city i in year t consists of the largest patch of developable land within the circle of ratio , calculated as: , ,
There are two different nighttime light products from DMSP-OLS that can be used to delineate urban areas: the stable or ordinary product (NTL), and the radiance-calibrated (RC) product. For this work we use the latter, given that such data include a correction for the saturation issue likely to be an important issue for most large cities in the region. Further, previous work has suggested that the RC information provides a better proxy for socioeconomic variables than the stable products (Hsu et al., 2015;Ma, Wu, Li, Peng, & Liu, 2014). Radiance-calibrated yearly composites for 1996, 2000 and 2010 obtained from NOAA National Centers for Environmental Information were used to delineate urban extents. These composites have a spatial resolution of 30 arc-seconds (about 1 km at the Equator).
Another known issue of the DMSP-OLS products is the "overglow" effect: dim lighting detected from light in surrounding areas of cities because the scattering of lights in the atmosphere (Wu, Ma, Li, Peng, & Liu, 2014). A novel deblurring process was applied to address the issue of over glow in the radiance-calibrated products. This process involves the use of two sequential filters, a standard deconvolution and the frequency of illumination maxima, to withdraw the light from the surroundings back and restacking it vertically on its source pixels at city centers (Abrahams, Lozano-Garcia and Oram, 2016).

Calibration and interannual correction of DMSP-OLS RC NTL images
We use the deblurred DSMP-OLS RC yearly composites for the years 1996, 2000 and 2010 to delineate urban extents in Latin America. DMSP-OLS RC NTL from different years 10 J.C. Duque, N. Lozano-Gracia, J.E. Patino, P. Restrepo / LCR Flagship Report on Cities and Productivity cannot be compared because of the lack of the sensor's on-board calibration (Cao et al., 2016;Hsu et al., 2015;Pandey et al., 2013;Zhang & Seto, 2011). An empirical intercalibration was performed to enable the comparison of these images. We follow (Hsu et al., 2015) and used the same area as reference: Los Angeles metropolitan area. This area was selected for two reasons: it has for long been a mature metropolis and hence the light change is negligible; second, because of its size and the large variability of light intensity within its extent, it provides samples of high DN values in the city center, as well as low DN values in suburban areas. We use the 2000 image as reference, and estimate linear regression models and secondorder regression models. The second-order models showed only negligible improvements compared to the linear model, which is preferred for its simplicity (Table 1). We set the intercept as 0 in the calibration models to ensure that all the background areas have the same zero value in the three images. While the calibration solves the comparison issue, there are additional inconsistences in lit pixels among the three dates that need to be addressed. These inconsistences are seen as lit pixels that change to unlit pixels in the next date image at the same geographic location, and as abnormal fluctuations in pixel values across dates (Cao et al., 2016). We applied the inter-annual series correction proposed by (Cao et al., 2016) to ensure that the lit pixels detected in an image do not disappear in a later date, and that the lit pixel DN values for each date are not smaller than the pixel DN value at the same location of a previous date. The inter-annual correction model after intercalibration is composed of two rules: (1) when a pixel DN value is equal to zero in an image, that pixel DN value for the previous date at the same geographic location should also be equal to zero, and (2) when a pixel DN value is not equal to zero in an image, the pixel DN value must be greater than the DN value of the lit pixel in the same geographic location in the previous date.
This correction model is described in equation (7).
Where DN(n-1, i), DN(n i), and DN(n+1. i) are the DN values of the i-th lit pixel in the deblurred RC NTL image after intercalibration in the (n-1)-th, the n-th, and (n+1)-th years, respectively. And n = 1996, 2000, and 2010.

Urban extent delineation
We use the inter-annual corrected deblurred DMSP-OLS NTL RC images to outline urban extents in Latin America and the Caribbean. We applied a DN threshold to define what is considered an urban area in the NTL imagery. Threshold-based methods have been 12 J.C. Duque, N. Lozano-Gracia, J.E. Patino, P. Restrepo / LCR Flagship Report on Cities and Productivity extensively used to extract urban areas from NTL data (Ellis and Roberts, 2015;Harari, 2016;Li and Zhou, 2017;Pandey et al., 2013;Sutton, et al., 2010;Zhang and Seto, 2011). The central premise in this method is that urban areas are generally a concentration of people and income such as there is a DN value (a threshold) that can be used to define and delineate urban areas from NTL imagery (Tewari et al., 2016  . For this work we found a threshold of DN equal to 110 in the processed NTL images (i.e., after

deblurring, and interannual calibration and correction). Because the GHS built-up layer uses
Landsat images as input and does not consider at any point layers of NTL, we feel confident using it as an independent data source to set the threshold. Figure 1 shows three examples of the extracted urban extent and the built-up layer used as reference. We applied the threshold and obtained binary images of urban areas in LAC. The three images were converted to vector format to create the polygons that outline the extent of cities.
Further, we applied a buffer of 10 meters to the outlined polygons to encompass all the image cells that belonged to the same urban area. We used the LandScan 2012 data set (Bright et al., 2013) as reference to identify and extract the NTL urban extents with more than 50,000 people in 2010. We obtained 940 urban extents with more than 50,000 people in Latin J.C. Duque, N. Lozano-Gracia, J.E. Patino, P. Restrepo / LCR Flagship Report on Cities and Productivity 13 America for the year 2010 and extracted the urban extents for the same locations from the processed NTL images of the years 1996 and 2000 ( Figure 2). According to (Chuvieco, 2016), an object must be several times larger than the pixel size to be delineated properly from a remote sensing image. Since the pixel size of the DMSP-OLS NTL RC images is 30 arc seconds (almost 1 by 1 Km near the Equator), we feel justified to exclude those urban extents that were smaller than 3 Km 2 in 1996. That resulting final sample therefore includes 919 urban extents in each year ( Figure 2).

Measuring urban productivity
The use of NTL in socioeconomic studies emerged as a way to address the lack of economic measures at disaggregated scales. The pioneer contribution by Henderson et al (2012) shows that NTL data can be used as a proxy of GDP within and across countries. Since then, other authors have used light density from NTL imagery to measure economic performance and welfare (Bleakley and Lin, 2012;Michalopoulos and Papaioannou, 2013;Lowe, 2014;Storeygard, 2016;Pinkovskiy, 2013).
In this paper we follow Tewari et al. (2016) to calculate a measure of productivity (Y) from NTL data. We use the density of radiance within the urban extent, dr_ntl_2010, as our

Measuring urban form
Following the literature on urban planning, we adopt an integral definition of urban form that includes three dimensions: Shape of the urban extent, internal urban structure and land use pattern (Prosperi et al., 2009 andBatty, 2008). In this subsection we present our proposal for measuring urban form within the framework of these three dimensions. For each dimension we present the variables proposed for its measurement, the rationale about the potential mechanisms through which each variable impacts economic performance, and the hypothesis to be tested in the empirical results.
According to Thompson (1952) a perfect circle has geometric properties such as minimum surface area, and maximum accessibility from and to any interior point. Angel et al. (2010) translate these geometric concepts to city shape and argue that the shape of a city affects its Productivity 15 efficiency, equitability and sustainability. It is also proven that the city's annual costs, per household, of public infrastructure and services are lower for circular/compact cities compared to fragmented/irregular/sprawling cities. Thus, circular cities can reach efficiency at lower cost. Based on those premises, we hypothesize that cities whose shape approaches a perfect circle can reach economic efficiency cheaper and faster. It is important to make clear that measuring the geometric shape of the city using its boundary does not capture what is happening within the city in terms of accessibility or land use. (For example, a geometrically compact city may have an inefficient transport network that prevents taking full advantage of being a circular city.) These internal characteristics of the city are covered by the dimensions urban structure and land use.
From a geometric perspective, a shape metric is usually focused in one of the three following geometric characteristics: degree of roundness, smoothness of its perimeter, and fullness (Angel et al., 2010). None of those geometric characteristics can be captured via the usual density-based measures of urban sprawl, but they affect aspects such as trip lengths and accessibility, and through that, have the potential of affecting productivity levels in a city.
We used the Shape Metrics Toolbox 4 to calculate the shape metrics of the urban extent polygons. This tool is a Python script that runs out of ArcToolbox in ArcGIS 9.3, and we and productivity, we would expect a "full-city" to be one that is also a more compact city, hence allowing for greater interaction and therefore higher agglomeration economies which ultimately increase productivity. However, a city that is "too-full" might also be suggestive of lack of public space, which can both be a dissamenity and reflect lack of planning. For these reasons we can expect a non-linear relationship between fullness and productivity.
Following the above-mentioned rationale, our hypotheses regarding the effect of these indicators of city shape on productivity are as follows:  H1: An increase of the Exchange_index suggests a more circular urban extent, which is expected to be associated with higher productivity levels of the city.
 H2: An increase of the Perimeter_index implies smooth perimeters that are associated with higher productivity levels of the city.
 H3: An increase of the Fullness_index implies a less fragmented urban layout that increases productivity levels of the city, but at extremely high levels of fullness can affect productivity.
As mentioned in Section 2, the internal structure of the city may play a considerable role in its productivity levels. Natural/organic cities have different dynamics than planned/regular/artificial/geometric cities; thus, it is important to include variables that capture the different urban structures in order to quantify its impact on productivity. Such structures affect the way in which people and products move within the city. Previous J.C. Duque, N. Lozano-Gracia, J.E. Patino, P. Restrepo / LCR Flagship Report on Cities and Productivity 17 literature has found empirical evidence between urban structure and economic performance; for example, Mills and Hamilton (1989) and Bogart (1998) found that better accessibility to labor force and efficient transport infrastructure reduces time and costs, which increases productivity levels; and Bertaud (2004) shows that shorter, and therefore cheaper, internal trips increase the levels of urban efficiency.
In order to capture such characteristics of the city structure, we used the OSMnx Python library (Boeing, 2017) to compute three geometry-based network topology variables: Circuity_avg, Intersection_density and Street_density. 5 The Circuity_avg divides the sum of the length of all edges of the street network by the sum of the great-circle distances between nodes incident to each edge (Boeing, 2017). If all the streets in the network are straight, the value of the circuity average (Circuity_avg) is 1. Higher values account for the presence of curvy streets, indicating a more organic urban layout. As shown in Giacomin and Levinson (2015), for the most populated Metropolitan Statistical Areas in the United States, low circuity is associated with more efficient and shorter trips. Using also metropolitan areas in the US, Huang and Levinson (2015) show that transit circuity affects accessibility of transit networks.
The second and third variables are the Intersection_density and the Street_density. These two variables inform about how fine grained and connected the network is, thus informing about the ease of movement across the city (Boeing, 2017). The existence of dense intersection patterns may allow for high rates of walking and non-motorized modes use, taking into account the possibility of having more controlled street crossings and more available access points (Cervero, 1997).
From the discussion above, we formulate the following hypotheses related to the structure of the urban extent: 18 J.C. Duque, N. Lozano-Gracia, J.E. Patino, P. Restrepo / LCR Flagship Report on Cities and Productivity  H4: Regular urban structures (associated to low values of Circuity_avg) are usually associated with more efficient and shorter trips, which reduce agglomeration costs and may lead to higher levels of productivity.
 H5: An increase of either Intersection_density or Street_density implies higher levels of street coverage that facilitates the mobility of people and products increasing the connectivity levels, and therefore, leading to higher productivity levels of the city.
Finally, as shown in Fallah et al (2011), the consideration of the distributional aspects of the population within the urban extent provides information on the land use pattern of the city.
The authors proposed a measure of urban sprawl that allows differentiating between cities with an even distribution of its population, from cities with highly concentrated population.
For completeness, we present in equation (8)   H6: The distribution of population density within a city affects its economic performance. According to Fallah et al (2011), an uneven distribution of population density, associated with high levels of Sprawl, can be linked to deteriorating socioeconomic outcomes, inefficient provision of public goods, and lower productivity levels.
As a summary, Table 2 presents the proposed variables, their description, and data source for calculation, and Table 3 presents examples of urban areas with high, medium and low values of these seven variables that describe urban form. Based on our hypotheses, our benchmarkhighly efficient city would have the following values for our variables:  Exchange_index = 1 and Perimeter_index = 1; suggesting a perfectly circular border of the urban extent.
 Sprawl = 0; suggesting a homogeneously distributed population across the urban extent.  Normalized difference between the share of areas with population density below the regional average density and the share of areas with population density above the regional average density (Fallah et al., 2011(Fallah et al., ) 1990 Population count at pixel level from from GHS (GHS_POP_GPW41990_G LOBE_R2015A_54009_250_v1_0 at 250 meters of spatial resolution) within the urban extents from deblurred and corrected DMSP-OLS NTL RC 1996 data.

Potential shape of urban extents
As stated in section 3, we follow Harari (2016) to obtain a panel of city-time potential urban extents and to calculate their shape metrics. Harari (2016) considered "undevelopable" terrain the areas that are occupied by a body of water, or that have a slope above 15%. We version 4, with a resolution of 90 meters (Jarvis, Reuter, Nelson, & Guevara, 2008), to calculate slopes; and the Global MODIS Raster Water Mask (Carroll, Townshend, DiMiceli, Noojipady, & Sohlberg, 2009a, 2009b to account for the presence of bodies of water. We implemented the process to define the potential urban extent in ArcGIS from the extracted urban extents for 1996, considered as the real urban extents. We first determine the "minimum-bounding circle" that contains the real urban extent and locate its centroid. Then we use the , estimated from equations (5) and (6) with the buffer function to obtain the estimated circles for each date. In all cases we use the estimated radius for the first date (1996). This is because we observed contraction of the potential urban extents when using the minimum-bounding circle for the first date (1996) and the estimated ratio for the following two dates (2000 and 2010). Second, we defined the developable terrain. Initial tests with a 15% slope threshold proved to produce fragmented patches of developable land in many cities, resulting in potential urban extents that were extremely small compared to reality. While architectural development guidelines in developed countries typically use the 15% slope threshold as constraint threshold for urban development (Saiz, 2010), given that the Andean Mountain Range crosses many countries in Latin America, in the region, urban development guidelines have been more tolerant and cities have grown in areas with considerably steeper slopes. An analysis of the distribution of slope values in a sample of urban extents extracted for the year 1996 suggested that in fact the median slope in the areas considered is 21%; hence, in the analysis we use a threshold of 20% slope to delimitate the undevelopable land areas. Finally, we manually select the largest patch within the circle as the potential urban extent for each date. Figure 3 shows an example of an actual urban extent and its potential shapes in the three dates.  Pesaresi et al., 2016). Natural amenities were calculated using several GIS layers. Average annual temperature and precipitation were obtained from the WorldClim web portal (Hijmans et al., 2005). Topographic variation was computed from the Topographic Ruggedness Index global gridded data 6 (Nunn & Puga, 2012). Water bodies and elevation data were used to code constraints to urban expansion, and to calculate dummy variables for location near the sea (coast) or inland bodies of water such as large rivers and lakes. We used the 250 meters resolution raster MODIS Water Mask (Carroll et al., 2009a(Carroll et al., , 2009b Table 6 presents the correlations between the seven variables that we use to describe the three dimensions of urban form, and Table 7 presents a series of 10 alternative specifications for equation (2). 9 The main equation is estimated using OLS and assuming intra-group correlation; i.e., that the residuals are correlated within geographical clusters, but uncorrelated between clusters. We cluster at the country level and have a total of 32 countries in the sample.

Strategy 1: Lagged model
Even though the three indexes used to describe the shape of the urban extent seek to measure different aspects of urban form (roundness, smoothness and fullness), the correlations in Table 6 show that there is very high positive correlation between exchange_index and perimeter_index (0.74). We also found high correlation between the variables intersection_density and street_density. Both variables measure the level of connectivity within a city and therefore have a very high correlation of 0.95. For this reason, we test alternative specifications, as shown in Table 7 where columns 1 to 5 use intersection_density and columns 6 to 10 use street_density. Finally, there is a high and negative correlation between fullness and sprawl (-0.71); for this reason we use them separately. Sum of population counts within the urban extent 1990 Population count at pixel level from GHS (GHS_POP_ GPW41990_GLOBE_R2015A_54009_250_v1_0 at 250 meters of spatial resolution) within the urban extents from deblurred and corrected DMSP-OLS NTL RC 1996 data.

Pop_1990_2
The square of population counts within the urban extent II. Location Dist_Border_kms_1996 Distance to the near international border Country borders from the World Bank LAC Spatial Database and urban extents from deblurred and corrected DMSP-OLS NTL RC 1996 data. III. Natural Amenities Temp_2010 Average annual temperature (C) WorldClim, Bioclimatic variables, BIO1: annual mean temperature within the urban extents from deblurred and corrected DMSP-OLS NTL RC 2010 data. Precip_2010 Average annual precipitation (mm) WorldClim, Bioclimatic variables, BIO12: annual precipitation within the urban extents from deblurred and corrected DMSP-OLS NTL RC 2010 data. TRI_2010 Topographic ruggedness index Topographic ruggedness index global gridded data (Nunn & Puga, 2012) within the urban extents from deblurred and corrected DMSP-OLS NTL RC 2010 data. C o a s t _2010 Dummy for location at the coast MODIS Water Mask (Carroll et al., 2009a(Carroll et al., , 2009b and urban extents from deblurred and corrected DMSP-OLS NTL RC 2010 data. Water2_2010 Dummy for location near a large river or lake The results confirm the convenience of having a more integral definition of urban form that goes beyond the use of population density. Regarding the shape of the perimeter of the urban extent, the models show that, ceteris paribus, a higher level of compactness is associated with higher productivity levels. The coefficients of exchange_index and perimeter_index are both positive and significant. These results provide support for hypotheses H1 and H2 regarding the shape of the perimeter of the urban extent. Changing our focus from the periphery to the inner city, we covered four aspects: the level of urbanization (fullness), the urban structure (circuity), the level of connectivity (intersection density or street density) and the land use pattern (sprawl):  The models show a nonlinear relation between the level of fullness and productivity: the coefficient of fullness is positive and significant, showing how less interrupted urban layout (i.e., low urban sprawl) increases the productivity levels. Yet, the coefficient of fullness 2 is negative and statistically significant, suggesting that an excessive fullness may reflect a lack of public space and/or a lack of planning, setting the conditions for the appearance of diseconomies of agglomeration. Thus, this finding supports hypothesis H3.
 Regarding the urban structure of the city, the results show no evidence in favor of hypothesis H4. The coefficient of circuity is not significant in all specifications presented in Table 7. This implies that the level of productivity of the city does not depend on whether the city has a reticular or an organic urban structure.
 Connectivity, measured as either the street_density or the intersection_density, appears positive and highly significant at the 1 percent level, suggesting that, ceteris paribus, a well-connected city is a more productive city. These results support hypothesis H5.
 We also find empirical evidence in favor of our hypothesis H6: the sprawl variable, as measured by Fallah et al (2010), is negative and statistically significant, at the 10 percent level. Therefore, there is some evidence that the distribution of population density within Latin American cities can affect their level of productivity. It is important to note that the average level of sprawling in our sample is very similar to Finally, surprisingly and as shown in the results summarized in Table 7, we do not find evidence of the existence of economies of agglomeration or congestion costs, since the variables population and population 2 are not significant. After performing an outlier analysis, 10 we found that these specific results were driven by eight extreme outliers: Ciudad to H6 remain unchanged. The results of the estimations without outliers are presented in Table A3.  (6) -0.1993* -0.1172* -0.0586 -0.3901* -0.4351* 1 1990 sprawl (7) 0.0422 0.2216* -0.7122* -0.5454* -0.5939* 0.2032* 1 Note: * Denotes significance at 5%

Strategy 2: Instrumental variables
The implementation of instrumental variables techniques was carried out using the two-stage least squares estimator (2SLS), allowing intra-group correlation at the country level. In Table   8 we report the 2SLS estimations, which use the log of normalization of potential urban form Productivity 31 (exchange_index and perimeter_index) as instruments for actual urban form (the results without outliers are reported in Table A6). We present in Tables A4 and A5 the estimates of the first stage, with and without outliers. 11 We began by discussing the instruments diagnostic test reported at the bottom of Table 8.
Regarding the relevance of the instruments, the first stage of regressions results show that the instruments for actual urban form have considerable explanatory power. The explanatory power is tested using the F-tests, and we found values above 10 indicating that these instruments are strongly related to actual urban form. In fact, the results from estimating the first stage, reported in Tables A4 and A5, show that the potential urban form is a highly significant and positive predictor of the actual urban form, for the exchange_index as well as the perimeter_index. To further inspect the relevance of the instruments we carried out the Kleibergen-Paap test of under-identification (Kleibergen and Paap, 2006)  Note: Robust standard errors clustered at the country level in parentheses. *** p<0.01, ** p<0.05, * p<0.1; All models include geographical characteristics as measured of natural amenities, namely, distance in km to international border, temperature, precipitation and coast indicator. Intersection_density has been divided by 100; street_density has been divided by 1,000; population has been divided by 100,000; and the control dist_border_kms has been divided by 1,000.

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We now turn to consider the estimates of the impact urban form on productivity. For the case of exchange_index, we note that both the OLS and 2SLS estimates reveal that a higher level of urban compactness is associated with higher levels of productivity. The coefficient on exchange_index is positive and highly significant at the 5% level and the 2SLS coefficient is higher than what was found with the OLS estimate. The 2SLS coefficient on exchange_index suggests that a one standard deviation increase in the level of urban compact shape is associated with an 8-percentage point increase in productivity. Regarding perimeter_index estimates, the results show that while the OLS estimate is positive and significant in statistical terms, the 2SLS coefficient is not significant.  Stock and Yogo (2005). The values of this test are higher than the Stock and Yogo (2005) critical values, suggesting that the instruments are not weak.

Conclusions
This paper proposes a more integral way to measure urban form and its relationship with economic performance, measured as the density of radiance within the urban extent, dr_ntl_2010, computed as the sum of the NTL DN values in 2010 divided by area, in square kilometers, of the urban extent in 2010. Instead of using population density as a proxy for urban form, we use seven variables that cover the three dimensions of urban form: shape of the urban extent, structure of the urban texture and land use pattern. For the empirical evidence we use two strategies for dealing with the endogeneity between urban form and productivity: First, using lagged explanatory variables as in Fallah et al (2010); and second, using instrumental variables as in Harari (2015).
Using information from 919 urban extents in Latin America, the results show that the shape of the urban extent, the inner-city connectedness, the level of urbanization and the population level have a statistically significant influence over the productivity level of the city. We also found evidence of the presence of a congestion effect on productivity since the results for population 2 and fullness 2 are both significant and negatively associated with productivity. According to these results, a compact, dense and well-connected city meets important conditions to be highly productive.
An important consequence of decomposing the concept of urban form into three dimensions is that a non-compact city can reach high levels of productivity by guaranteeing a high level of inner-city connectedness; or, it may happen that a compact city that is poorly connected can show low levels of productivity. Another feasible situation using our way to characterize urban form is that compact cities that are poorly urbanized can have low productivity. In summary, our empirical evidence shows that each city can find its way towards a higher productivity level by analyzing the status of each dimension of its urban form and implementing the corresponding strategies to improve its current conditions.
Intersection_density has been divided by 100; street_density has been divided by 1,000; population has been divided by 100,000; and the control dist_border_kms has been divided by 1,000.  Note: Robust standard errors clustered at the country level in parentheses. *** p<0.01, ** p<0.05, * p<0.1 All models include geographical characteristics as measured of natural amenities, namely, temperature and coast indicator.  Stock and Yogo (2005). The values of this test are higher than the Stock and Yogo (2005) critical values, suggesting that the instruments are not weak.