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Methodology for Determining the Economic Development Impacts of Transit Projects (2012)

Chapter: 4. MSA-level transit-agglomeration-productivity analysis

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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
Page 51
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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Suggested Citation:"4. MSA-level transit-agglomeration-productivity analysis." National Academies of Sciences, Engineering, and Medicine. 2012. Methodology for Determining the Economic Development Impacts of Transit Projects. Washington, DC: The National Academies Press. doi: 10.17226/22765.
×
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21 4. MSA­LEVEL TRANSIT­AGGLOMERATION­PRODUCTIVITY ANALYSIS  In the first empirical part of our study, we used data from all of the metropolitan areas in the United States to estimate how transit capacity is correlated with agglomeration, and how in turn agglomeration is correlated with productivity. In this section we describe that effort in detail, starting with the theory that is the basis for the study, describing data and analysis methods, and presenting our findings in summary form and then in greater detail. Theory  Transit improvements reduce travel time, and this may lead to increased access to central city areas, physical densification of employment, and population growth. In turn, those agglomeration changes may increase productivity. We conceptualized this relationship as a two- stage model, including the theoretical relationship between transit capacity and agglomeration, and the production relationship between agglomeration and productivity. In the first stage, changes in transit and road capacity may alter travel times and consequently affect both agglomeration interactions over space, by making them easier, as well as affecting physical agglomeration as measured spatially. But roads and transit infrastructure can also be expected to directly affect production, independent of agglomeration effects (Berechman et al., 2006). We distinguish them to avoid double-counting effects that are not included in our elasticity estimates. One of the first-stage models takes the form: ܦ௜ ൌ ߠ ௜ܶ ൅ ߬ܪ௜ ൅ ߪ ௜ܲ + XCi, (1) where D is employment density (one measure of agglomeration), T a measure of transit capacity, H the highway network supply, P population for each metro area i, and C a vector of other controls that might also affect employment density, including population and industry characteristics, and the employment density level from some previous period. This model is meant to measure the effect of transit capacity on central city employment density while controlling for other factors. Employment density may enable information spillovers and the potential knowledge networks that can form when firms and their employees are in close proximity. Another agglomeration mechanism is the increase in labor force size that can result in more efficient workers due to better matching of skills to needs, quicker filling of vacancies, and shorter unemployment spells. This is represented in our other first-stage model in which the population of the metropolitan area is specified as a function of transit and road capacity measures as well as a similar set of controls as for the employment density model: ௜ܲ ൌ ߩ ௜ܶ ൅ ߮ܪ௜ + XCi (2) Estimation of these equations results in elasticities that are dependent on the size of the transit (or road) network, the existing levels of employment density and of population, and other factors. The parameter θ provides an estimate of how employment density and population vary with transit supply. Elasticities of agglomeration with respect to transit supply are, for employment density, ்߳,ா ൌ ఏ்஽ , (3) and for population, ்߳,௉ ൌ ఘ்௉ . (4)

22 Next, we define a production function that includes a multiplier to account for any additional productivity effects from agglomeration. Similar to Graham (2007) we define our model as: ܻ ൌ ݃ሺݖሻ݂ሺܺሻ (5) Where g(z) is the Hicks multiplier, which incorporates any agglomeration effect, and f(X) is the production function. Graham (2007) goes on to specify this via a translog function, using effective density (ED) as the agglomeration term, where ED is based on travel times. Our approach differs in that we use in our empirical formulation more traditional measures of agglomeration to distinguish different possible agglomeration mechanisms: urbanized area employment density, central city employment density, and metropolitan area population. Most research uses a Cobb-Douglas production function, e.g. Abel et al. (2010) specify ௜ܻ௝ ൌ ܣ௜௝ܭ௜௝ఈܪ௜௝ఉܮ௜௝ଵିఈିఉ, (6) where Aij is the Hicks neutral parameter, Kij is physical capital, Hij is human capital and Lij is labor supply. Subscript i denotes metropolitan area, and j represents the larger region within which the metropolitan area is found (e.g. the state). Constant returns to scale are assumed in all inputs. Abel et al. assume that the rate of return on physical capital is constant and use this to redefine their model to factor out the physical capital input (which is generally not available at this scale of analysis, although Graham (2007), who used UK data, had a physical capital measure based on self reported firm-level capital depreciation). Thus Abel et al. reduce their model to the following: ௒೔ೕ ௅೔ೕ ൌ ߶௝ܣ௜௝ ംభ భషഀ ൬ு೔ೕ௅೔ೕ൰ ഁ భషഀ , (7) where øj is the rental price of capital for the larger region, j, is a constant and may vary across regions (or states). Aij is the measure of density (agglomeration). They take the log of the above to empirically estimate the model as, ݈݋݃ ௒೔ೕ௅೔ೕ ൌ ݈݋݃߶௝ ൅ ఊభ ଵିఈ ݈݋݃ܣ௜௝ ൅ ఉ ଵିఈ ݈݋݃ ൬ ு೔ೕ ௅೔ೕ൰ (8) We use this basic framework to estimate agglomeration elasticities using the three different agglomeration measures: principal city employment density, urbanized area employment density and MSA population. With the two models combined, we can estimate transit-agglomeration-productivity elasticities. Our models use both per capita wage rates and GDP as dependent variables for the productivity models. Thus we can calculate two estimates of the elasticity of productivity with respect to transit capacity, as follows: ߝ஽ ൌ ఏ்஽ ఊభ ଵିఈ, (9) representing the effect through densification of employment, and, ߝ௉ ൌ ఘ்௉ ఊభ ଵିఈ, (10) representing the agglomeration impact of increased city population. The overall elasticity of productivity with respect to transit capacity is then the sum of these two elasticities: ߝ ൌ ߝ஽ ൅ ߝ௉. (11) Our empirical analysis thus allows us to decompose the impact of transit capacity changes through both agglomeration mechanisms and on both wages and GDP per capita. We also explore equations restricted to particular industrial sectors to explore possible differences in transit-agglomeration-productivity relationships across sectors.

23 Data We compiled data for the 366 US metropolitan statistical areas (MSAs) as defined by the US Census for an eleven year period from 1998 to 2008, although we were not able to use all observations for our analysis, as we describe below. The dataset included transit capacity, as measured in several different ways; road network information; firm productivity measures, including GDP, average wages, and number of firms and workers; population; and measures of employment density for the MSA as a whole, the urbanized area portion of the MSA, and the urbanized area portion of the principal cities within the MSA. Transit capacity data were derived from two sources. First, we spent considerable effort to process a time-series of data from the National Transit Database (NTD). This is a rich data source of information for every transit agency in the country, but frequently suffers from lack of agency reporting for various years and for some variables. Data for both rail and bus revenue seat-miles, total revenue miles, and seat capacity were relatively complete. We obtained track mileage data by rail type from the American Public Transportation Association, supplemented by checking information on agency websites to compile a time-series of track mileage for commuter, heavy, and light rail modes. Aggregating transit agency data to the metropolitan area level was a non-trivial exercise. The NTD reports the location of transit service as the transit agency headquarters, but in some cases this did not match the primary metropolitan area that the agency served. For example, the Altamont Commuter Express rail service between Stockton and San Jose (California) is operated by the San Joaquin Regional Rail Commission, is headquartered in Stockton, but the primary flow of commuters is toward San Jose. In this case we allocated the system to the San Jose metropolitan area. We made similar corrections for a dozen other systems. There were 34 metropolitan areas with some form of rail transit in 2008, including 17 with commuter rail, 11 with heavy rail, and 27 with light rail (including a few relatively small trolley systems). Additional reallocations were made as noted in Appendix K. While the NTD contains a code identifying the primary MSA served, additional matching was done by manual inspection of the data files. This provided data for 333 MSAs, so our analyses using revenue seat-miles and total revenue miles had this as the maximum number of observations per year. Most MSAs had no transit service or incomplete data, and in some cases were served by transit agencies located in another MSA (e.g. Trenton, New Jersey MSA). Road network data were drawn from National Highway Planning Network (NHPN) files within the annually published National Transportation Atlas Database. NHPN provides a GIS record of virtually every road of federal significance, including those not within the National Highway System. From this we derived freeway and arterial road mileage for all 366 MSAs. One shortcoming of these data is that they are not updated every year (i.e., 2001 and post-2004) so it was problematic to use the data in time-series analysis, but based on our diagnostic tests with a time-series of road data for 88 MSAs taken from the Texas Transportation Institute dataset, we determined that it was not necessary to include road measures except in cross-sectional analysis. County Business Patterns data from the Census Bureau were used for our measures of worker productivity: average and total payroll. We aggregated county data to the MSA level to maintain consistent MSA boundaries, because many MSAs were created, expanded, or altered after definitional changes by the Census Bureau. These data between 1998 and 2007 were processed at the two-digit NAICS sector level. Data from the Bureau of Economic Analysis for GDP by two-digit NAICS sector was also processed at the MSA level between 2001 and 2007. We found there was incomplete data for most industrial categories, and so were only able to

24 evaluate total GDP data across the economy. Annual population and land area estimates by county were also obtained from the Census Bureau. One quirk in the data was the treatment of MSAs in Virginia. The Bureau of Economic Analysis (BEA) uses non-standard FIPS codes to deal with independent cities in Virginia, which are separate from their surrounding counties. We adjusted our data accordingly to aggregate to the relevant MSA level. We calculated two kinds of employment density-based measures of agglomeration: urbanized area employment density and central city employment density. We used primary- worker-at-place-of-work data from the Census Bureau’s Longitudinal Employer-Household Dynamics (LEHD) dataset, available at the census block level for the years 2002 to 2008, along with block-level land and water area from the 2009 Census TIGER shapefiles. The LEHD data (short for Longitudinal Employer-Household Dynamics) were developed by the Census Bureau in conjunction with state governments from a variety of federal and state data sources to estimate the number and characteristics of individuals employed within a given geographic area in areas as small as a census block. LEHD data were the basis for computing employment density of metropolitan areas and principal cities from 2002 on. Urbanized area employment density was calculated by dividing LEHD-estimated employment in census blocks within the Census-defined “urbanized area” boundary of the MSA by the land area of those blocks. Central city employment density was calculated by dividing LEHD-estimated employment in the urbanized blocks within Census-defined “principal cities” of the MSAs by the land area of those blocks. (For example, there are nine principal cities in the Dallas-Fort Worth MSA: Dallas, Fort Worth, Arlington, Plano, Irving, Carrollton, Denton, McKinney, and Richardson, accounting for 60 percent of employment and 9.5 percent of the urbanized area of the MSA.1 Data from the LEHD for Massachusetts, New Hampshire, Connecticut and the District of Columbia are not available for all years; some other states also have one-year gaps in the data. Two MSAs with rail transit—Boston, MA and New Haven, CT—were omitted from most of our analysis due to this limitation. Because the entire populated area of the District of Columbia is urbanized and within a principal city, we were able to include it by replacing the missing LEHD data with county-level data from the County Business Patterns database. ) Central city employment density is of particular interest here because we expect the clustering of economic activity around rail stops to be primarily in the main cities within the urbanized portions of metropolitan regions. The distribution of the employment density variables across all MSAs for the year 2008 are shown in FIGURE 1 and Figure 2. Central city employment density varies more than urbanized area employment density. The mean density of employees per square mile within central cities is 1,969, while for urbanized areas it is 932 employees per square mile. Central city employment density also has larger densities at the extreme of the distribution. Jaison Abel also kindly provided a measure of human capital used in Abel et al (2010): the fraction of people in each MSA of working age with a college degree, which we used as a control variable in the productivity models. 1 http://www.census.gov/population/www/metroareas/lists/2008/List2.txt.

25 FIGURE 1 Distribution of central city employment density (workers per square mile) FIGURE 2 Distribution of urbanized area employment density (workers per square mile) For a large majority of US metropolitan areas, their central cities make up less than 5 percent of their land area (Figure 3). Those whose central cities make up the largest share of their total metropolitan area —in the 10 to 20 percent range—include Los Angeles; El Paso, TX; Virginia Beach, VA; Carson City, NV; and Honolulu. The share of the metro area occupied by Census-defined urbanized blocks also varies widely (Figure 4). The most highly urbanized 0 2. 0e -0 4 4. 0e -0 4 6. 0e -0 4 8. 0e -0 4 D en si ty 0 2000 4000 6000 8000 Employment density - principal city 0 5. 0e -0 4 .0 01 .0 01 5 D en si ty 0 500 1000 1500 2000 2500 Employment density - urbanized area

26 MSAs include Honolulu; New York City; Trenton, NJ; Philadelphia; Providence, RI; and Los Angeles. FIGURE 3 Number of metropolitan areas by share of area occupied by central cities FIGURE 4 Urbanized share of MSAs

27 We also obtained some variables (“instruments”) that were needed to control for mutual causality, as described below. The first set of instruments included the population of the MSA in the year 1900 and a climate index (both kindly provided by Jaison Abel at the Federal Reserve Bank of New York, see Abel et al. 2010). The climate index is based on the average heating degree days and precipitation between 1970 and 2000, for each MSA (measured at the central city of each MSA). Two additional instruments were used. First, whether the state allows a township form of governance was included as an instrument for employment density in our productivity estimates. Township governance data were from the Census of Governments;2 we defined a dummy variable with a value of 1 for MSAs wholly within or primarily within in a state allowing town or township forms of governance, and a value of 0 otherwise. Twenty states enable this form of governance.3 In addition, we obtained MSA-level census data for nine variables that were included as control variables in the econometric analysis. These were: percent of residents aged under 18, aged 65 or over, aged 25+ holding a high school diploma, aged 25+ holding a Bachelor’s degree, identified as white, identified as Black/African-American, and identified as Hispanic/Latino, plus median household income, and the median value of owner-occupied housing units. These variables were only available for a cross-section and were included when we opted to examine cross-sectional instead of panel models. For the transit regressions we used three instruments: the climate index; the population in 1900 (described above); as well as another instrument, the percent water area in the MSA, from Census geographic files for 2009. We detail our use of these instruments in our discussion of statistical methods below. Methods There are several empirical issues associated with estimating our model. The choice of agglomeration measure is of particular interest, as discussed in the synthesis above. Abel et al. (2010) used population density. We explored three measures: total MSA population (rather than population density) and employment density measured both at the central city level and at the urbanized area level. Increasing public transit capacity may facilitate better labor pool matching by making larger populations possible; may cause densification of city centers by enabling more efficient use of space by transportation users accessing those centers; and may also affect the density of the larger urbanized portions of the metropolitan area. The clustering of employment and populations can also result in improved knowledge sharing and can allow for economies of scale in the production of urban amenities that attract high-quality labor (e.g. cultural activities and recreational facilities). State dummy variables (“fixed effects”) are one way to control for 2 The Census of Governments defines Township governments as follows: “Organized local governments authorized in state constitutions and statutes and established to provide general government for areas defined without regard to population concentration; includes those governments designated as towns in Connecticut, Maine (including organized plantations), Massachusetts, Minnesota, New Hampshire (including organized locations), New York, Rhode Island, Vermont, and Wisconsin, and townships in other states”. The definition varies between states, for example in some states townships are fully incorporated municipalities (e.g. New Jersey), whereas in others they are a junior partner of the county government with limited authority (e.g. Ohio), or are a layer of governance that overlaps with cities and provides a limited set of services (e.g. Indiana). 3 Data available at: https://www.census.gov/govs/cog/GovOrgTab03ss.html

28 physical capital as øj Our methodological strategy was to first model measures of agglomeration as a function of transit capacity; then to separately estimate productivity as a function of the agglomeration measures; and finally to trace the net effects of transit capacity on agglomeration-related productivity. We distinguished agglomeration-related productivity increases from the capitalization of transit travel time savings in wages or GDP by including transit capacity as an independent variable in our productivity models. Our method was to use the two separate sets of models to construct net transit-agglomeration-productivity elasticities via an implicit path analysis. We did not correct for error propagation between the two separate sets of models. is assumed constant for each state. However, these dummy variables were highly correlated with MSA population so they were omitted (see below); instead we used highway and transit capacity measures to proxy for physical capital. A particularly important statistical modeling issue is the problem of controlling for possible mutual causality. In addition to transit causing changes in levels of agglomeration, change in agglomeration could increase the likelihood that transit agencies improve capacity. And in addition to agglomeration causing changes in productivity, it could be that highly productive clusters of firms result in larger or denser agglomerations. The potential mutual causality requires statistical methods to avoid incorrect estimates of the effects of transit on agglomeration. Our initially preferred method was to use a statistical estimation routine called generalized method of moments (GMM) that specifies a dynamic model using multiple observations over time of the same MSAs. We spent a great deal of time constructing a ten-year panel dataset for this purpose. After substantial analysis of the panel data we abandoned this approach due to very poor diagnostics when using GMM that could not be solved with different model forms. The diagnostic tests indicated significant over-identification, and we were unable to draw any conclusions from these models. We switched to a series of cross-sectional regressions, relying on two methods to control for mutual causality: two-stage least squares and lagged independent variables. The two-stage least squares (or “instrumental variables”) approach was particularly important. To carry out this approach we predicted levels of transit service as a function of other variables that might be correlated with historical transit investment decisions, but not caused by recent levels of agglomeration. As previously mentioned, the transit capacity variables were instrumented using the population in 1900, a climate index (from Abel et al., 2010), and the percent of the metro area that is covered by water. In some models we omitted the climate index due to over- identification. We predicted levels of agglomeration using the population in 1900 and the climate index, as well as a dummy variable indicating whether the MSA is in a state that allows for township forms of government. We tested for weak instruments using the Cragg-Donald F test and the Stock-Yogo (2005) critical values. We tested for over-identification using either the Sargan test (for the first-stage transit-agglomeration models and for some of the second-stage agglomeration-productivity models), or the Hansen test (for the productivity models that corrected for robust standard errors, necessary when the state-varying township government instrumental variable was used). We treated track mileage as a regular normally distributed variable when carrying out two-stage least squares with instrumental variables. As Roodman (2009: 17-18) notes, “[two- stage least squares] and related linear methods are consistent in the presence of heteroskedasticity...whereas [maximum likelihood] estimation that explicitly models the censoring may not be.” Instrumenting track mileage is thus consistent, even though the variable is heteroskedastic (because it is equal to zero for 91 percent of US metropolitan areas). We also

29 tested a variation of this model in which we set predictions of track mileage that are less than zero to be equal to zero. This had differing but less statistically reliable results, and we do report those estimates. Analysis overview We carried out analysis of the MSA-level dataset in two stages. In the first stage, we investigated how agglomeration is correlated with transit capacity. In the second stage, we investigated how productivity is correlated with agglomeration. We modeled agglomeration in 2006 as a function of transit capacity two and four years prior; and we modeled 2008 productivity as a function of agglomeration in both 2006 and 2004. Our lag results for the two- and four-year periods were fairly similar, probably because there is not much variance in either transit capacity or in agglomeration in most cities in the US over a two- or four-year period. The strength of the MSA scale of analysis is that any redistribution of economic activity within a region that is occasioned by transit investments will be controlled for, to the extent that MSA boundaries correspond to economically self-contained regions. Looking at smaller measures of productivity (e.g., firm-level revenues) entails the problem of having to account for spatial shifts of economic productivity within economic regions. Regardless, we were unable to acquire firm-level revenue or wage data. Later in this report, we describe firm-level employment data for Portland and Dallas-Fort Worth that enable us to describe shifts of employment density at a small scale, but do not allow us to directly measure whether these shifts cause productivity changes. We tested a variety of measures of transit capacity: rail revenue miles; total revenue miles; rail and bus seat capacity per capita; and track mileage, specified in four ways (in absolute terms, per capita, per total CBSA area, and per urbanized portion of CBSA area). We also tested these four specifications of rail track mileage for three different types of rail: commuter rail, light rail, and heavy rail, specified in the same four ways. We tested three main measures of agglomeration: employment density in the urbanized portion of the metropolitan area; central-city employment density of the metropolitan area (defined as employment density within the urbanized portions of the metropolitan area’s census- designated “principal cities”); and the total population of the metropolitan area. Urbanized area employment density and central city employment density are used to test whether scale matters in agglomeration effects, while total population is used as a proxy for labor force size. These models also include a measure of road capacity (lane miles of arterials and freeways, normalized similar to the corresponding transit capacity variable) and a variety of control variables derived from census data. Models were tested with and without the control variables and we found the results on our transit and road capacity variables to be very robust. For productivity, our measures were gross domestic product and payroll, measured both per capita and in aggregate, measured at the MSA level (4 variables). Transit-agglomeration model results In this first stage of the MSA analysis, we examined whether transit capacity was correlated with agglomeration, as measured by both employment density and total MSA population. We regressed three measures of agglomeration—central city employment density, urbanized area employment density, and MSA population, measured in 2006—on measures of

30 transit capacity in 2004 and 2002, along with control variables including road capacity (lagged similarly) and population (observed contemporaneously). We examined several measures of transit capacity, including track mileage (as a total, per capita based on MSA population, per total area of the MSA, and per urbanized area of the MSA); track mileage for different rail modes (commuter rail, heavy rail and light rail); seat capacity totals and per capita (for rail and motorbuses); and revenue miles of service (both rail and total). All models included a measure of road capacity (the sum of freeway and arterial lane miles), in most cases normalized similar to the rail capacity measure. We also estimated models that omitted the New York metropolitan region because it is an outlier, accounting for a very high percentage of all transit use in the country, and by far the highest average central city density in our dataset at 8,813 employees per square mile. We also tested the inclusion of a dummy variable indicating whether the metro area had any kind of rail transit and we estimated difference regressions for changes in all variables between 2002 and 2007, the widest range possible given the availability of the employment density measures. The models with rail dummies did not show any major difference in results, while the difference models did not provide good statistical diagnostics; we omit both for brevity. A summary of our transit-agglomeration model estimates is presented here. The subsections give more technical details. First, transit capacity is associated with dispersion of employment at the urbanized area level, with a consistently negative and statistically significant coefficient. Second, we find an opposite effect when we analyze the impact of transit capacity on central city employment density; this is consistent with our expectation that transit will have a greater effect on spatial clustering of employment density in the vicinity of rail stations that are concentrated in central cities. Third, when we analyze the impact of transit capacity on total metropolitan population, we find a consistent and strong relationship with some transit variables. For example, each additional mile of track is associated with an additional 6,680 increase in population, and the effect is larger when the New York MSA is omitted. These results come with some caveats. First, heavy rail seems to be most influential, although light rail has some influences on central city employment density. Second, it appears that there is a nonlinear effect: an additional mile of track in an already-dense set of central cities or an already-populous metropolitan area has a bigger absolute impact. Third, there does not seem to be much difference in the two-year or the four-year impact, which suggests some caution since we would expect larger effects over time of a transit capacity investment; in fact our dataset has little variance over time, which is what probably gives rise to the need to use a cross- sectional approach rather than a dynamic panel approach. In the following subsections we provide more technical details on the effects of each of the transit capacity measures that we tested: total rail track mileage, rail track by type, seat capacity, and revenue-miles. Tables with model results are in Appendix B, and we refer to some of these tables in our discussion (all tables prefixed with ‘B’ are in Appendix B). In most cases we present both instrumental variable and ordinary least squares estimates. Total rail track mileage Track mileage is used as an unlogged dependent variable because models using logged track mileage were consistently over-identified. The per capita track mileage models were all consistently over-identified; thus, we cannot interpret the coefficient estimates and we do not show these results.

31 Track mileage is associated with dispersion of employment at the urbanized area level, with a consistently negative and statistically significant coefficient (Table B-1). However, when the New York City region is omitted (Table B-2) the coefficient is no longer statistically significant, suggesting that this outlier has a disproportionate impact on the analysis. The instrumental variable results, however, are over-identified as shown by the Sargan test, so we cannot claim a causal effect of track mileage on urbanized employment dispersion. In general this holds for the models in Table B-3 and B-4 for track miles normalized by CBSA square miles. Track mileage is associated with higher central city employment density, with good diagnostic tests on the instrumental variable models. One exception is the models that omit New York City (in Table 4) that have a weak instrument (as shown by the Cragg-Donald test). There are no major differences in the two- or four-year lags. Our second set of first-stage models estimated the effect of transit capacity on MSA population (Table B5 and Table B6). These models have somewhat different results. We used transit capacity per capita and per square mile, as total track miles gave weak diagnostic results. While the OLS models showed a strong association between population and track mileage in all cases, the instrumental variable models suffered from over-identification. Models with total track miles and track miles per area of the CBSA were both over-identified and could not be relied upon. Each model also includes a measure for road capacity, as this is likely to exert some additional influence on the spatial location of employment activity and on population growth. The variable is defined as the sum of freeway and arterial lane miles in the CBSA. Since we do not instrument road capacity there may be mutual causality at work. For our urbanized area models the coefficient is either statistically insignificant or negative (keeping in mind that the instrumental variable models have bad diagnostics). For the central city density models the coefficient is positive and significant, suggesting that road capacity could also have an agglomerative effect on central city employment density (in fact it is generally more significant in the instrumental variable models than in the OLS models). The road capacity variable was also lagged by two and four years, and no major differences were found. Finally, in the transit- population models we find that the total road capacity measure is negatively associated with population and most are statistically significant. There is a positive association in the OLS model in Table B-6 when normalized by MSA area. The negative effect could represent population dispersion to neighboring MSAs. It would require the development of additional spatial econometric models to examine this hypothesis more fully. The population of the metro area was also included as an independent variable in the transit-employment density models, and the coefficient was positive and statistically significant for the urbanized area employment density models, but in some cases not statistically significant in the central city employment density models. Principal cities account for just 2.4 percent of the metropolitan land area on average, ranging from less than one tenth of a percent to a high of 18 percent, so this difference is expected. We also ran some models that included a binary variable indicating the presence of rail transit (not shown here). The variable was statistically significant in both the central city and urbanized area employment density models, with a positive sign. This variable represents an additional shift of the intercept term for those areas with rail transit. We expected this variable to reduce the size of the rail capacity coefficient, but in fact the coefficient is slightly larger. We do not, however, display or use these models in elasticity estimates later, in order to err on the conservative side of effect sizes.

32 We omitted the New York metropolitan region from the final set of models to test their sensitivity to the inclusion of the MSA with the most pervasive rail transit and the highest central city employment density, exceeding the next highest MSA by 50 percent. We expected omission of the New York region to result in a reduced agglomeration effect. In the case of the transit- employment density models, our rail capacity coefficients are actually larger, but we did not test whether this difference was statistically significant. At a minimum, this clearly shows that New York City is not having a positive bias on the employment density results, and it may suggest a declining effect of transit capacity on central density densification. The effect in our transit- population models is the opposite: when New York City is omitted, the coefficients on rail capacity are slightly smaller. Table 4 summarizes overall results for the track mile density models. Track mile density is not correlated with urbanized area employment density, but it is with central city employment density. Table 5 summarizes results for the population models; track miles were found to be strongly positively correlated with metropolitan population, regardless of how that statistic was normalized (i.e. per capita or per urbanized square mile), while results regarding freeway and arterial lane-mile totals were more inconsistent.

33 TABLE 4 Summary of track mile regression results Urbanized area employment density Central city employment density Urbanized area employment density, omitting NYC Central city employment density, omitting NYC Regression diagnostics Total track miles Negative Positive Not statistically significant Positive, larger value Good instruments, some over-identification Track miles per CBSA area Negative Positive Not statistically significant Positive, larger value Urbanized area over- identified Freeway and arterial capacity Not statistically significant Positive Not statistically significant (except 1 case is negative) Positive Population Positive Not statistically significant, positive for OLS Positive Not statistically significant, positive for OLS TABLE 5 Track mile, population models Population (with and without NYC) Regression diagnostics Track miles per capita Positive Over-identified Track miles per UZA area Positive Over-identified Freeway and arterial capacity Per capita, negative; per square mile, positive in OLS NA

34 Rail track mileage by type  We also separately analyzed the impact of commuter rail (CR), heavy or metro rail (HR), and light rail (LR), using the standard APTA/NTD-defined categories. Each rail type has various different characteristics: speed, frequencies, number of stations, and network length. In each of these models we included all three rail types and instrumented each type in turn. Only the model with heavy rail instrumented did not suffer from a weak instrument problem, so we focus our discussion on those models (Table B7 and Table B8), both for total track miles and track miles per square mile of CBSA. We also analyzed track miles per square mile of urbanized area (UZA), but this model suffered from weak instruments for all three modes of operation. Omission of the New York region also resulted in weak instruments and we do not present those results either. We only include a reduced set of independent variables in these models as they were over-identified when the full set was included. Heavy rail is associated with dispersion of urbanized area employment, and concentration of central city employment (Table B7). Light rail and commuter rail have no statistically significant association with urbanized area employment density, but light rail is associated with concentration of central city employment, and commuter rail is associated with dispersion of central city employment. In these models, the road capacity variable is not statistically significant and population remains significant and positive only when urbanized area employment density is the dependent variable. Table B8 shows similar analysis, but with each mode normalized by square miles of land area for the CBSA. Only the results with heavy rail instrumented are presented. Other models were over-identified or had weak instruments. Heavy rail per square mile is associated with lower urbanized area employment density and higher central city employment density. Commuter rail per square mile has no statistically significant effects, while light rail per square mile is associated with higher urbanized area employment density. Both Table B7 and Table B8 also display population models. The model with total heavy track mileage (Table B7) is over-identified and thus the results are not reliable. Table B8, with heavy rail track miles per CBSA area, is well identified. In this model we see that increased density of heavy rail leads to greater population. Both light rail and commuter rail density, however, have no statistically significant effect. Overall results tend to be fairly consistent and similar to the total track mileage models. These are summarized in Table 6. Commuter rail is associated with higher urbanized area employment density, and lower central city employment density. In contrast, heavy rail is positively associated with central city employment density and total population and negatively associated with urbanized area employment density. Finally, light rail is positively associated with both scales of employment density. Note again that in these models only heavy rail was successfully instrumented.

35 TABLE 6 Summary of rail track associations by rail type   Urbanized area  employment density  Central city employment  density  Population  Commuter rail Small positive effect Negative effect No effect Heavy rail Negative effect Positive effect Positive effect Light rail Positive effect (NS for track miles) Positive (except for CBSA density) No effect Seat capacity   An alternative measure of transit capacity for which we have data is the seat capacity of both rail and buses. We specified these variables in the same model (with only the rail seat capacity variable instrumented) to calculate the effects of each in the same model. The bus seat capacity variable has the benefit of providing us with much more variability across our 351 metro areas (with full data), as virtually all have some amount of bus capacity, though in some cases the systems are very small. We estimated models that include measures of rail and bus capacity (both total and normalized by CBSA population), both with two-year and four-year lags, we also included an additional dummy variable if they have a rail system, and also tested models omitting the New York region (omitted here for brevity). One issue we encountered is that using total seat capacity as a measure, especially motor bus seat capacity, leads to large degree of multicollinearity with population. This made it difficult to determine whether it is population that is associated with the employment density or the seat capacity measure. For this reason we normalized the seat capacity measures by population and discuss those models. These also allowed us to estimate models where our agglomeration measure was population as the dependent variable. We estimated a set of models with seat capacity per capita, which are shown in Table B9. We used two instruments (population in 1900 and percent water area) as inclusion of the climate index led to over-identification. The models are well specified with only two instruments. There is a positive association of both rail seat capacity per capita and motor bus seat capacity per capita with central city employment density. Rail seat capacity is also positive and significant in the population model, but bus seat capacity is not. Note that only the rail seat measure is instrumented. We did not estimate urbanized area models, given the poor results in the track mile models. Revenue miles  We estimated models using revenue miles of both rail service and total revenue miles for all transit service, as a measure of the quantity of transit service. This variable is more highly endogenous than the other rail capacity variables, which are capital based. Given some level of capacity, more service may be provided in denser areas. The models for rail revenue miles were in line with the results from our other models: revenue miles were associated with lower urbanized area employment density and higher central city employment density. This held for the model omitting the New York region, although for the OLS model it is no longer significant. Test statistics indicated a good set of instruments and no over-identification for the principal city models, but not for the urbanized area models, which are over-identified. Results are in Table

36 B10 and Table B11. Population models show a high level of statistical significance and are shown in Table B12, although the instrumental variable model is over-identified. Models for total revenue miles (rail revenue miles plus bus revenue miles) were more problematic because the total revenue miles variable is very highly correlated with population. However, results are consistent with previous results. Our models without New York, however, suffer from weak instruments, and we can make no conclusions based on them. The population model is over-identified, but the coefficient values are similar to the OLS results. All results are in Table B13, Table B14, and Table B15. Agglomeration­productivity model results  In the second stage of our MSA-level analysis we modeled productivity as a function of our two significant measures of agglomeration: principal city employment density and total MSA population. For productivity measures, we used 2008 MSA-level data on payroll and GDP, in both total and per capita form. For agglomeration, we used the same measures as in the first step of the analysis: total MSA population, central city employment density, and urbanized area employment density, as measured in 2004 and 2006. Our control variables were human capital (share of population of working age with a college degree), transit and road capacity, demographic variables such as share of the population over the age of 65 and share Hispanic, and, in the employment density model, population. Good measures of physical capital are not available, but following other studies we proxied for physical capital with transportation capital measures: total freeway and arterial lane mileage per capita and transit track mileage per capita. We also included total track mileage as a measure of the quality of rail service, to minimize any double-counting of capitalization of transit time savings benefits. We present only those models with productivity and employment density measures specified in logarithmic form. Models specified without logging these variables did not provide satisfactory estimates and uniformly resulted in no statistical significance on the employment density variables. We tested state fixed effects but these models failed the over-identification test, and so were omitted. We corrected for robust standard errors on the first stage of the two- stage-least-squares procedure in order to account for clustering caused by the state-level “township form of government” instrument. Per capita wage and productivity models  We found that both central city employment density and total MSA population were highly significant predictors of average wages, but urbanized area employment density had no correlation. The agglomeration measures appear to have an initially large effect that attenuates over time, since coefficients on the two-year lagged agglomeration measures are larger than those on the four-year measures. Our initial estimates with GDP per capita models showed weak significance of central city employment density, but when we corrected for robust standard errors in the first stage of the 2SLS procedure (due to the need to correct for clustering by state on the “township form of government” variable) we found more highly significant results, so that GDP per capita was now significantly related to central city employment density and to MSA population. It is

37 unsurprising that the results are more robust for average payroll than for GDP, since most agglomeration mechanisms are related to labor productivity. Results of our first estimates are shown in Table B16. The instruments (which are drawn from those in Abel et al. 2010) were weak in all these models, as shown by the Cragg-Donald F- statistic which do not exceed the 10 percent critical value derived by Stock and Yogo (2005). The latter estimates are much improved and provide a stronger instrument, although just below the 10% Stock-Yogo maximal value in some cases. None of the estimates are over-identified as indicated by the Sargan test. We focus our discussion on the results of Table B17 because these are better estimates. There is a strong association between central city employment density and productivity as measured by wages. This is an important distinction from previous research, which has typically examined the entire metro area. Central cities are important to consider for this work; these contain the concentrations of employment within a city that are most likely to be affected by transit service, and where we expect to see accessibility changes from transit improvements. As mentioned previously, the two-year central city employment density lag has a stronger association with productivity than the four-year lag. This suggests a relatively fast productivity effect that is not critically linked to the timing of when densification occurs, but an effect that is attenuated over time, perhaps due to delayed firm competition between metropolitan areas or a delay in interurban labor migration that leads to more competition and a driving down of wages over time. Our measure of human capital (share of population of working age with a college degree) is statistically significant across all models. The population of the metro area also is positive and significant in our wage models, representing the benefits of a large labor market on productivity. As proxies for physical capital we also included measures for transit rail capacity (track mileage per capita) and road capacity (freeway and arterial lane mileage per capita). Our road mileage variables have a small effect on the GDP models but none on wages. The opposite is true of the transit capacity variable, although we note that these may not represent the investment in physical capital within the region. Industrial sub­sectors   The literature on productivity suggests that agglomeration benefits are more pronounced in some industries than in others. For example, the service sector is seen as benefiting from agglomeration and much research in the past has examined manufacturing. For this reason we estimated models for 20 sub-sectors of the economy, specifying agglomeration as own-sector employment density (Table B18). These models replicate the economy-wide wage and GDP models described above, using the same three instrumental variables and robust standard errors. We focus our discussion on those sectors where the models are well identified. These are shown in Table B19. We did not have sufficient detail on industry-specific GDP in our data and therefore could only estimate wage models. We regressed industry-specific wage levels on industry-specific employment density variables as well as population. For example, retail wages were regressed on central city retail density. Most models either had weak instruments or were over-identified. Three exceptions were the models for manufacturing (NAICS code 31-33), finance and insurance (code 52), and health and social assistance (code 62). We found a positive association and statistically significant association between manufacturing central city employment density and manufacturing productivity. The health and social assistance sector

38 actually shows a negative and statistically significant association between own-sector employment density and productivity. Finance and insurance was positive, but not statistically significant. Our tests of the other industry categories, including those we would most expect to have positive agglomeration-productivity effects—industries such as information (publishing and media); professional, scientific, and technical services; and retail trade—had poor test diagnostics and we cannot address whether there are any statistically significant associations in these industries. Total wage and productivity models  We also estimated models that use total GDP and total payrolls as the dependent variable. Many of these models were over-identified when our employment density measures were instrumented. However, in both OLS and IV estimates, the coefficients were similar in magnitude to our per capita models (described below). This serves as a good check on whether the per capita models (below) are biased by the failure to interactively control for MSA size. Central city employment density was positive and statistically significant in the wage model while urbanized area population density was not (in the IV model). In the GDP model effects were a bit smaller for central city employment density, at an 85-90% level of confidence (in the IV model), while urbanized area employment density was statistically insignificant. Population coefficients were near unity; we cannot separate a distinct agglomeration effect from population in these models. Nonlinearity  We also sought to determine whether there are marked differences in agglomeration- productivity effects depending on threshold levels. For example, there might be greater effects for changes in population from small to medium sized cities, or for changes from moderate to intense levels of employment density in central cities. To investigate this, we carried out spline regressions with density thresholds based on median or interquartile range of population and central city employment density (table not shown). The coefficients on different ranges were within 10 percent of each other and the differences were not statistically significant. This is a notable finding: it implies that the log-log model form, in which the model predicts percentage increases in productivity per percentage increases in agglomeration, is accurate. This implies metropolitan areas with higher per capita GDP or wages experience greater total agglomeration benefits from transit capacity increases than metropolitan areas with lower per capita productivity, when population or employment density increase in the same range. At the same time, this result implies that the largest per capita increases in productivity, all else equal, are for small cities. Demographic control variables  As mentioned previously we include various demographic control variables in most of the models. Models were tested with and without these controls and overall results on our key variables of interest were very robust. The behavior of the control variables showed some variation, depending on which term is tracked across specifications. Age variables were

39 consistent: youth population share was found to be negatively correlated with principal city density, while elderly population share was found to be negatively correlated with urbanized area density. Also, race was largely not a factor in the results, except that black population share was negatively correlated with urbanized area employment density. Education and income variables, however, showed no consistent pattern. The inclusion of these variables did, in general, improve the overall fit of the models. Linking transit capacity with productivity  Based on the above two stages of analysis, we estimated how transit capacity is associated with wages and GDP via the agglomeration-productivity pathway. The correlation between productivity and transit capacity is separate from any direct correlation between transit capacity and GDP or wages, due to (for example) reducing travel times. We avoid double- counting by including track mileage as an independent variable in the productivity equations. We calculated the net agglomeration-related productivity impacts of transit capacities by multiplying the calculated elasticities together. Our results do not account for eventual decreasing returns to productivity in central city employment density and in MSA population, which we believe exist but are difficult to explore with the limited data available on the just 29 MSAs which have rail capacity and for which employment density data are available. There may also be complex nonlinearity involved, including threshold effects of density levels and interactions (for example, between population and employment density, or between employment density and levels of transit service) but the small dataset precludes robust statistical tests of these hypotheses. Different effects for different metropolitan areas  We calculated correlations between transit and productivity for two agglomeration pathways: via MSA population increases and via central city employment densification. We found that these correlations—our best estimates of the effects of adding additional capacity— were dependent on current transit capacity, central city employment density, and MSA population. That is, they are not linear relationships, but depend on the starting point prior to the transit investment. The most reliable population models were those with per capita track mileage, while the most reliable central city employment density models used total track mileage. The largest correlations between transit and agglomeration were for increases to already large systems in already large cities (see Appendix G). There were relatively small yearly correlations per worker (ranging from $3 to over $100 per additional rail mile, for example) that often added up to larger figures when aggregated across all workers in the entire metropolitan area economy (ranging from $5 million to over $500 million per additional rail mile, see Appendix H). The average agglomeration “effect” of rail mileage is generally in the range of a 0.0009 to 0.04 percent net increase in productivity region-wide for every 1 percent increase in track mileage, with higher percentages in larger cities with more existing rail mileage. These are large figures in comparison to the total benefits associated with fixed-guideway transit investments. We calculated elasticities using mean values from our sample. These can be found in Table 7, Table 8, and Table 9 for the first stage, the second stage, and the combined effect, respectively. Similar elasticities are also calculated for each MSA, based on the value of each variable for that MSA, and are displayed in Appendix B.

40 Elasticity estimates give the effect of a one percent change in different measures of transit capacity upon average wages and GDP per capita. These are shown for the sample mean values in TABLE 10 (below). Appendix F lists these measures for each MSA. We likewise show the total effect on total wages and GDP multiplying per-person values by total workforce and total population, respectively. The results for each MSA in the US are shown in Appendix G. Summary of results   We found that in most of our tests, the transit capacity measures were significantly associated with three effects: increases in central city employment density, decreases in urbanized area employment density, and increases in total population. This is consistent with the hypothesis that increasing rail capacity causes both job dispersal (at the UZA level) and job density (at the central city level). In the second stage, we found that central city employment density was significantly correlated with higher productivity, both in wages and GDP per capita. We found even larger correlations between MSA population and productivity. The urbanized area employment dispersal caused by transit capacity is not correlated with any statistically significant differences in GDP or payroll. These results are consistent with a world in which increases in transit capacity simultaneously allow more far-flung non-residential development, outside of the core principal cities of the metropolitan area; greater densification in urban cores by enabling firms in those cores to draw from a wider labor pool; and metropolitan population growth, perhaps as a complement to the higher productivity from firms in densifying urban cores. Transit-related agglomeration mechanisms may work via the clustering of principal city (typically, polycentric) employment density and via the labor market increase, while there is no effect on productivity from urbanized area employment density. We analyzed a large number of regression models conducted in the first and second stages of analysis to make estimates of the relationship between transit capacity, population growth, central city employment density, and productivity. Because of the wide variety of models with different measures of transit capacity and of productivity, our results varied. In general, we found small per-worker relationships (ranging from $3 to over $100 per additional rail mile per year, for example), which translated into large effects when aggregated across all workers in the metropolitan economy (ranging from $5 million to more than $500 million per additional rail mile per year). If averaged over only those workers likely to have benefited from agglomeration economies, the per capita figures could be substantially higher. The average agglomeration effect of rail mileage is generally in the range of a 0.0009 to 0.04 percent net increase in productivity region-wide for every 1 percent increase in track mileage, with higher percentages in larger cities with more existing rail mileage. These are large effects in comparison to the total benefits associated with fixed-guideway transit investments. In general, larger cities have greater productivity impacts from an additional rail mile, and cities with larger amounts of existing transit capacity also have larger effects from additions to that capacity. Appendix F and G list elasticity results, and estimated effects at both the per-person level and aggregated across the population for each MSA for a variety of different transit measures, and for both OLS and instrumental variable results. There is a large range in these estimates, given both the different measures used and the analytical method used for estimation. However, the relative impacts between metropolitan areas are as expected. For example, the effect of an

41 additional mile of rail is larger in the Chicago region, which has a large population with an extensive rail network, than it is in Tampa-St. Petersburg, with less population and a minor streetcar system. In general, larger regions with more population and those regions with more extensive transit systems tend to have greater agglomeration-related productivity increases for an increase in transit investment. There are several caveats to mention, because the analysis, though groundbreaking, is not perfect. Our goal was to develop a causal model given the mutual causality among transit investment, density, and productivity benefits. Further analysis can likely refine the methods to increase our confidence in the magnitude of these results. The productivity models may not completely account for physical capital. Additional data (for example, on real estate rents) may be one way to control for this. Lack of this control is not uncommon within the literature on agglomeration economies, but examining it in more detail would increase the accuracy of the estimates. Finally, there may be other factors that influence central city employment density and population of MSAs in addition to transit capacity, highway capacity, and MSA demographics.

42 TABLE 7 Density elasticities w.r.t. transit capacity measures, calculated at the sample mean Total track mile coefficient elasticity (4 year lag) Employment density (principal city) Population Mean total track mile elasticity 0.01411 - 0.04827 Mean track mile per sqm CBSA area elasticity 0.01788 - 0.08705 Mean track mile per capita elasticity 0.30057 -0.66029 Mean track mile per sqm UZA elasticity 0.3451 -0.6454 Mean rail revenue miles 0.0296 - 0.04491 0.3656 - 0.4055 Mean total revenue miles 0.1004 - 0.1960 0.7083 - 0.7106 Mean rail seat capacity per capita 0.0200 - 0.0514 0.3049 - 0.4195 Mean bus seat capacity per capita 0.1372 - 0.1286 0.3165 - 0.1496 Note: range is based on OLS and IV estimates TABLE 8 Productivity elasticities w.r.t. agglomeration, calculated at the sample mean Average payroll (wages) elasticity GDP per capita elasticity Employment density of urbanized portion of principal city (2 year lag) 0.0554 – 0.114 0.152 - 0.135 Total population 0.0420 - 0.0344 0.0610 - 0.0633 Note: range is based on OLS and IV estimates TABLE 9 Productivity elasticities w.r.t. transit capacity measures, calculated at the sample mean Average payroll (wages) elasticity GDP per capita elasticity Average payroll (wages) elasticity GDP per capita elasticity Agglomeration mechanism Employment density (principal city) Population Total track miles 0.00078 - 0.00550 0.00214 - 0.00652 Track mile per sqm CBSA area 0.0010 - 0.0099 0.0027 - 0.0118 Track mile per capita 0.01262 -0.02271 0.01833 -0.04180 Track mile per sqm UZA 0.0145 -0.0222 0.0211 -0.0409 Rail revenue miles 0.0016 - 0.0056 0.0045 - 0.0066 0.0202 - 0.0462 0.0554 - 0.0547 Total revenue miles 0.0056 - 0.0223 0.0153 - 0.0265 0.0392 - 0.0810 0.1077 - 0.0959 Rail seat capacity per capita 0.0011 - 0.0059 0.0030 - 0.0069 0.0169 - 0.0478 0.0463 - 0.0566 Bus seat capacity per capita 0.0076 - 0.0147 0.0209 - 0.0174 0.0175 - 0.0171 0.0481 - 0.0202 Note: range is based on OLS and IV estimates from previous tables

43 TABLE 10 Estimated changes per unit based on mean elasticity estimates w.r.t transit capacity measures Change in average annual wage Change in GDP per capita Agglomeration mechanism Emp. Density (principal city) Population Total Emp. Density (principal city) Population Total OLS IV OLS IV OLS IV OLS IV OLS IV OLS IV Total track miles $0.34 $2.42 $0.94 $2.87 Track mile per sqm MSA $0.43 $4.36 $1.20 $5.18 Track mile per capita $5.54 $9.97 $8.08 $18.41 Track mile per sqm UZA $6.36 $9.75 $9.27 $18.00 Total track mi (per capita) $5.88 $12.39 $9.02 $21.28 Rail revenue mile $0.72 $2.46 $8.87 $20.29 $9.59 $22.75 $1.98 $2.46 $24.41 $24.11 $26.39 $27.03 Total revenue miles $2.44 $9.81 $17.23 $35.57 $19.67 $45.38 $6.72 $11.66 $47.43 $42.26 $54.15 $53.92 Rail seat capacity per capita $0.49 $2.57 $7.42 $21.00 $7.90 $23.57 $1.33 $3.05 $20.35 $24.86 $21.68 $27.91 Bus seat capacity per capita $3.34 $6.44 $7.70 $7.49 $11.04 $13.93 $9.16 $7.62 $21.12 $8.87 $30.28 $16.49 Note: range is based on OLS and IV estimates from previous tables.

44 Several features of our elasticity estimates are worth noting. First, we show a range of estimates based on different model types (ordinary least squares [OLS] and instrumental variables [IV]). In most cases, the IV estimated elasticity is much larger than that estimated with OLS, which is an unexpected result because the IV models are meant to control for overestimation. In a few cases, the OLS estimate is slightly larger. The correlation between transit capacity and agglomeration, for all of our transit capacity measures, is much larger for population than for central city employment density. Because of the large correlation with population, we ran a series of robustness tests using control variables drawn from the initial (2005-07) three-year American Community Survey (ACS): percent of residents aged under 18, aged 65 or over, aged 25+ holding a high school diploma, aged 25+ holding a Bachelor’s degree, identified as white, identified as Black/African- American, and identified as Hispanic/Latino, median household income, and the median value of owner-occupied housing units. In some specifications, only the second, fifth, and eighth of these variables were included to avoid potential collinearity. Inclusion of all nine terms did not generate variance inflation factors high enough to indicate inefficient estimates, and for most of our models we include all these additional controls, which significantly improved model fit. The coefficient estimates for the transit variables were remarkably stable. The other key policy variable, miles of freeway and arterial roadway (sometimes divided by MSA square mileage or population, depending on the nature of the specification), was positively correlated with principal city density, but was found to not be statistically significant when estimating urbanized area density. Conversely, MSA population was found to be positively correlated with urbanized area density, but was not significant in principal city regressions. Again, these findings are all consistent with and without demographic controls.

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TRB’s Transit Cooperative Research Program (TCRP) Web-Only Document 56: Methodology for Determining the Economic Development Impacts of Transit Projects explores development of a method for transit agencies to assess whether and under what circumstances transit investments have economic benefits that are in addition to land development stimulated by travel time savings.

As part of the project a spreadsheet tool was developed that may be used to help estimate the agglomeration-related economic benefits of rail investments in the form of new systems or additions to existing systems.

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