Transit Service,Physical Agglomeration and Productivity in US Metropolitan Areas

Abstract

Public transit improvements could cause more clustered and higher-density employment and enable urban growth, giving rise to agglomeration economies by improving labour market accessibility, increasing information exchange and facilitating industrial specialisation. Using data on US metropolitan areas, this paper traces the links from transit service to central city employment density, urbanised area employment density and population; and from these physical agglomeration measures to average wages and per capita GMP. Significant indirect productivity effects of transit service are found. For example, in the case of central city employment density, estimated wage increases range between $1.5 million and $1.8 billion per metropolitan area yearly for a 10 per cent increase in transit seats or rail service miles per capita. Firms and households likely receive unanticipated agglomeration benefits from transit-induced densification and growth, and current benefit–cost evaluations may therefore underestimate the benefits of improving transit service, particularly in large cities with existing transit networks.

1. Introduction

Along with internal economies of scale in production, and the invention of elevators and structural steel, streetcars and underground rail lines enabled the creation of central business districts and the rapid growth of large cities in the late 1800s (Jackson, 1985; Mills and Hamilton, 1989). Agglomerations—such as dense downtown districts, clusters near transit stops and larger cities—are physical changes in city form that could give rise to external economies of scale in production, known as ‘agglomeration economies’ (Marshall, 1920/1997; Anas et al., 1998).

Do public transit services continue to enable the increased productivity that agglomerations may bring, even in the face of ubiquitous road networks and auto ownership? By reducing the rate of growth in road congestion to let cities grow larger, transit services could create larger labour markets, leading to better sharing of the labour pool among industries and better matches between the needs of a job and the skills and interests of workers. Transit services could concentrate development near transit stops in employment centres, lowering the transactions costs associated with intermediate inputs (Scott, 1988) and causing information spillovers that happen when workers in innovation-based industries mix and mingle with each other (Arzaghi and Henderson, 2008).

Yet it is an open question whether and how city size or employment density change in response to transit improvements in modern-day US cities. If transit services provide a significant-enough accessibility advantage, higher-density employment clusters and larger cities could develop. However, by reducing transport costs, transit improvements could instead lead to cheaper land, sprawl and de-densification, and reduced proximity of firms, workers and consumers to each other. Which of these things happens is partly contingent upon how firms produce their goods and how transport affects the costs of their production inputs and outputs.

It is also an open question whether firm productivity will increase in response to transit-induced changes in physical agglomeration. Transit services may enable tighter spatial clustering for firms that desire access to each other, and thus increase agglomeration economies. Yet any such densification could instead be largely because firms capitalize upon lower transport costs.

Thus it is helpful to distinguish between two fundamental questions. First, what effect does public transit have on physical agglomeration measures like employment density? Secondly, what effect do any such changes have on economic productivity? There is also a third important question: what direct effect does increased public transit accessibility have upon productivity, regardless of any physical changes it may cause? Establishing a research design to credibly answer these causal questions is non-trivial, as there is no truly exogenous variation in public transit services. This article addresses the first two questions to the limit of available data at the metropolitan area level in the US. It only indirectly addresses the third question, which has been the subject of most previous relevant studies (Graham, 2007; Venables, 2007).

2. Literature Review

Empirical research on the links between transport investments, agglomeration and productivity is limited. Research is particularly scarce for transit, which is likely to have different effects on agglomeration than roads and highways because of its different service characteristics (Chatman and Noland, 2011) and because it may reduce diseconomies of agglomeration from road congestion (Wheaton, 2004). Those few estimates available suggest that the agglomeration-related productivity benefits of significant rail projects in large urban areas can add as much as a 25 per cent increment to a conventional benefit–cost ratio (Graham, 2007; Vickerman, 2008).

Few studies have related transit services to physical agglomeration measures. A study of Seoul, South Korea, defined intrametropolitan industry clusters using spatial hot spot analysis and analysed whether agglomeration status, measured for spatial units (villages) within the metro area, were correlated with measures of subway and road accessibility when controlling for population density and average rent (Song et al., 2012). Own-village subway accessibility and spatially lagged subway accessibility were both significantly associated with agglomeration status. It is not clear whether the correlation is causal in the direction of subways influencing agglomeration, or the reverse, given the use of cross-sectional data with few controls.

Other studies have made engineering and service-based assumptions about how transit can influence agglomeration economies. For example, Shefer and Aviram (2005) assumed that the extra capacity enabled by a new light rail line serving the central city of Tel Aviv would enable growth that would otherwise go to an outlying area. They used agglomeration elasticities found in other studies to estimate an increase in the benefit–cost ratio of 1.1 to 1.4.

A number of studies have related physical measures of agglomeration to direct measures of productivity such as wages, gross metropolitan product, or firm revenues, and indirect measures such as rents and property values. Much of this research has focused on agglomeration economies in manufacturing sectors, but transit services tend to be focused on central business districts with non-manufacturing industries including information, producer services and finance/insurance. Drennan and Kelly (2011) studied how office rents were related to the amount of producer services employment. Using an 18-year panel of 120 office markets in 49 US metropolitan areas, they found a positive relationship when controlling for other factors, but only in large ‘strong core’ cities.

Abel et al. (2011) found elasticities of metropolitan population-weighted population density with respect to productivity of between 1 and 3 per cent, controlling for endogeneity with instrumental variables. They found that the agglomeration influence was mediated by human capital; for example, population densification in low-education metropolitan areas had little or no relationship with per capita GMP, but had a strong relationship in higher-education metros. In a recent working paper, Melo et al. (2012) modelled wages as a function of both employment accessibility and employment density for a selection of 51 US urbanised areas (UZAs) observed in four years using national travel survey data from the Nationwide Personal Transportation Survey and its successor, the National Household Travel Survey. To calculate average UZA-wide employment accessibility, they used estimated network speeds from the same datasets and specified isochronic measures yielding the number of jobs within a given time band. They found a positive relationship between urbanised area employment density and wages, increasing with higher levels of density.

A meta analysis of 729 agglomeration–productivity estimates found an average elasticity of about 0.06 for US studies with metro-level agglomeration measures that control for human capital (Melo et al., 2009). Most of these studies used physical agglomeration measures, some industry-specific and others measured for all industries or the entire population of a metropolitan area.

A related set of literature has correlated employment accessibility (often called ‘effective density’) with measures of productivity such as firm revenues (for example, Graham, 2007; Holl, 2011), or demonstrated in mathematical models how better employment accessibility could increase employment search success and reduce vacancies (Venables, 2007; Pilegaard and Fosgerau, 2008). These studies have typically resulted in estimates of agglomeration elasticities that are similar in size to estimates from studies of physical agglomeration measures (Melo et al., 2009).

Model Specification and Methods

Previous research has concluded that higher employment accessibility is associated with higher wages and firm revenues, but has not explicitly investigated the causal chain implicit in the hypothesis that public transit services increase agglomeration economies by influencing city size and density. Our work builds on this body of research by using physical agglomeration measures; explicitly tracing links from transit to three measures of physical agglomeration; relating the same three agglomeration measures to per capita productivity as measured with both wages and GMP; and controlling for the capitalisation of transit service as a separate phenomenon from increasing returns to scale enabled by agglomeration. We then estimated net transit–productivity elasticities, which has not been done previously for physical agglomeration measures.

Our three measures of agglomeration are central city employment density, as a measure of densification in transit-served cores of metropolitan areas; urbanised area employment density, as a measure of overall employment concentration in the metropolitan area; and metropolitan area population, as a measure of labour force size. Previous studies have usually used a single convenient measure of ‘agglomeration’ as though the term denotes a single phenomenon that can be measured in different ways with little loss of precision. Different correlated agglomeration measures may have different effects on productivity. Central city employment density may be associated with informational spillovers and other firm-to-firm mechanisms (for example, fashion and finance in Manhattan); urbanised employment density with industrial specialisation, vertical disaggregation and access to suppliers (for example, information technology in Silicon Valley, auto manufacturing in Michigan); and metropolitan area population with labour force access and firm-to-worker matching (Chatman and Noland, 2011).

Total population and urbanised area employment density have been tested in previous agglomeration–productivity studies, although not together. No other study that we are aware of has tested the fine-scale central city employment density measure used here. Such measures are needed given the multiple agglomeration mechanisms that have been hypothesised to be at work (for example, see Duranton and Puga, 2004).

We estimated two sets of two-equation regressions for almost all US metropolitan areas: one estimating relationships between different measures of transit service and physical agglomeration; the second set, between measures of physical agglomeration and productivity. To the extent that census-defined metropolitan area boundaries correspond to economically self-contained regions, any intraregional redistribution of economic activity is controlled for by the fact that we use metropolitan-level measures. These estimates are for ‘urbanisation’ or ‘Jacobsian’ agglomeration economies, since the measures are metropolitan in scale and do not distinguish classes of worker or particular industries.

Because we hypothesise that different kinds of transit service might affect agglomeration in different ways, we tested a number of different transit service measures. Connectivity and coverage might affect physical agglomeration more than does total system size. Rail might affect intensity of development more than bus service, and different kinds of rail service might have more or less efficacy because of differences in service characteristics.

In specifying the models, we had to address two estimation problems. The first is that transport services can directly affect common productivity measures, independent of agglomeration effects (for example, Berechman et al., 2006), by reducing commuting costs for labour, freight costs for physical inputs and outputs, and travel time for other factors in the production process. Any such capitalisation is entirely separate from increasing returns of scale due to the various agglomeration mechanisms made possible by clustering, densification or growth. Previous literature has not addressed this distinction. We accounted for direct effects of transit service on productivity and indirect effects via agglomeration by controlling for both in the agglomeration–productivity models.

The second estimation issue is endogeneity. Transit services may cause agglomeration, and agglomeration may increase the productivity of firms and workers. Yet other possible relationships complicate matters. Higher-productivity areas may stimulate transit agencies to provide more services as travel demand increases. Productive cities might grow faster, and more densely. Denser areas may receive better transit services. These relationships can be represented in three simultaneous equations

t = f (a, p, c, x)

(1)

a = g (t, p, c, y)

(2)

p = h (t, a, c, z)

(3)

where, t represents transit service; a some measure or measures of agglomeration; p a productivity measure such as per capita wages or GMP; c a vector of influences upon transit, agglomeration and productivity; and x, y and z vectors of variables that are exogenous influences upon transit, agglomeration, and productivity respectively.

We addressed the endogeneity inherent in this system of equations primarily by using instrumental variables, in which equation (1) is used to predict transit values t in equation (2), and equation (2) is used to predict logged agglomeration values a for use in equation (3), as described in more detail later. We also included multiple related agglomeration measures, transit measures and productivity measures as right-hand-side variables to control for this simultaneity, and we lagged independent variables by four years.

3.1 Transit–Agglomeration Series

We specified three sets of models in the transit–agglomeration series, corresponding to three agglomeration measures: employment density in the principal or ‘central’ cities (CCED); employment density in the urbanised area (UZED); and the population of the metropolitan area (POP). Since there are up to 21 transit measures being tested in each model set, the transit measures and all of the coefficients are subscripted with j

C C E D_{i} = β_{1 j} {\hat{T}}_{i j} + β_{2 j} H_{i} + β_{3 j} UZE D_{j} + β_{4 j} PO P_{i} + β_{5 j} Y_{i} + Γ_{1 j} D_{i} + Φ_{1 j} S_{i}

(4)

U Z E D_{i} = β_{6 j} {\hat{T}}_{i j} + β_{7 j} H_{i} + β_{8 j} C C E D_{i} + β_{9 j} P O P_{i} + β_{10 j} Y_{i} + Γ_{2 j} D_{i} + Φ_{2 j} S_{i}

(5)

P O P_{i} = β_{11 j} {\hat{T}}_{i j} + β_{12 j} H_{i} + β_{13 j} C C E D_{i} + β_{14 j} U Z E D_{i} + β_{15 j} Y_{i} + Γ_{3 j} D_{i} + Φ_{3 j} S_{i}

(6)

For each equation, the other two agglomeration measures appear as endogenous right-hand-side variables, along with GDP or wages per capita $Y_{i}$ . The main variables of interest were $\hat{T_{j}}$ , predicted measures of transit service, estimated from a first-stage equation corresponding to equation (1). (These first-stage equations have the same regressors appearing in equations (4), (5) and (6), with the addition of exogenous instruments described later.) The control variables included H, a measure of highway and arterial road capacity, and D, a vector of metropolitan area population characteristics that might affect population and employment density. Finally, to control for differences in employment density and city size that might be correlated with different industries, we included a vector of variables S representing shares of employment in different industrial sectors. Without an a priori theoretical basis for model form, we tested log–log, semi-log and unlogged, and based on diagnostics chose the latter.

3.2 Agglomeration–Productivity Series

The second set of models relates productivity to physical agglomeration. We define a production function that includes a multiplier to account for additional productivity effects from agglomeration, similar to Graham (2007)

W = g (z) f (X)

(7)

where, W is gross metropolitan product (GMP) or wages; g(z) is the Hicks multiplier, implying an external agglomeration benefit if greater than one; and f(X) is the production function.

Most research on productivity uses a Cobb–Douglas function, which assumes a non-linear relationship between inputs, corresponding to firm production theory in microeconomics. Following this convention, and converting from aggregate to per capita to factor out labour, (7) can be restated as follows

Y_{i} = g (z_{i}) K_{i}^{α} E_{i}^{1 - α}

(8)

where, Y_ij is per capita GMP (or wages); K_ij is per capita physical capital; and E_ij is average education (a human capital measure). Subscript i denotes the metropolitan area. We do not formally convert the Hicks multiplier from aggregate to per capita terms, but the multiplier is conceptually appropriate for per capita use, as it denotes a change in the scale of productivity per unit of input.

Abel et al. (2011) assume that the rate of return on physical capital is constant within states, and use this to redefine their model to factor out the physical capital input while adding fixed effects for states. We use instead a measure of per capita highway capital, H. To control for the role that transit service might play directly in affecting GMP or wages, we also include a separate term for per capita transit supply, T, to capture any direct effect of transit on per capita productivity

Y_{i} = g (z_{i}) H_{i}^{ρ} E_{i}^{φ} T_{i}^{1 - ρ - φ}

(9)

This model distinguishes two measures of labour’s impact on productivity per capita: human capital or education, E, and labour accessibility due to per capita transit services, T.

The Hicks multiplier defined in (7) provides a way to introduce agglomeration into the equation. We use three physical agglomeration measures, CCED, UZED and POP (see earlier), such that the Hicks multiplier function $g (z_{i})$ is defined as follows:

g (z_{i}) = α_{i} {C C E D}_{i}^{τ_{1}} {U Z E D}_{i}^{τ_{2}} {P O P}_{i}^{τ_{3}}

(10)

To control for endogeneity, we predicted values for CCED, UZED and POP from a simultaneous set of three equations, corresponding to (2), earlier. Denoting this change from actual to predicted values with hats on the agglomeration variables, substituting (10) into (9), and taking logs of both sides provides the following equation

l n Y_{i} = α + τ_{1} l n {\hat{C C E D}}_{i} + τ_{2} l n {\hat{U Z E D}}_{i} + τ_{3} l n {\hat{P O P}}_{i} + ρ l n H_{i} + φ l n E_{i} + δ l n T_{i} + Θ S_{i}

(11)

where, τ₁ is the elasticity of central city employment density (CCED) with respect to per worker wages or per capita GMP, Y; τ₂ and τ₃ the elasticities for urbanised area employment density (UZED) and metropolitan population (POP) respectively; ρ the elasticity of physical capital as measured by highway/arterial road length per capita; φ the elasticity of human capital; and δ the elasticity of transit accessibility. Because wages and GMP could be higher in denser, larger cities, since that is where particular high-paid industries are concentrated (such as finance), we also included S. This vector of variables consists of shares of employment by industry (for the two-digit NAICS codes), to control for industry-specific differences in per capita wages or GMP.

3.3 Transit–Agglomeration–Productivity Estimates

We used the two sets of models to construct net transit–productivity elasticities via the three agglomeration channels for various measures of transit service. Because the transit–agglomeration models are linear, we estimated average point elasticities for each of j transit measures by multiplying the agglomeration-transit coefficients $β_{1 j}$ , $β_{6 j}$ and $β_{11 j}$ (from equations (4), (5) and (6)) by the value for each of the j transit measures, divided by the value of each of the agglomeration measures in turn, to yield the percentage change associated with a doubling of the transit measure (that is, the point elasticity for that metropolitan area). Each of these was then averaged across all metropolitan areas with non-zero values for the transit measure. Finally, we multiplied the three metropolitan-average transit–agglomeration elasticities by the agglomeration–productivity elasticities $τ_{1}$ , $τ_{2}$ and $τ_{3}$ (from equation (11)). The complete calculation for each of the three physical agglomeration measures, for each of j transit measures, T, is:

ϵ_{T_{j} C C E D} = (\frac{\sum \frac{β_{1 j} T_{i j}}{C C E D_{i}}}{n}) τ_{1}

(12)

ϵ_{T_{j} U Z E D} = (\frac{\sum \frac{β_{5 j} T_{i j}}{U Z E D_{i}}}{n}) τ_{2}

(13)

ϵ_{T_{j} P O P} = (\frac{\sum \frac{β_{9 j} T_{i j}}{P O P_{i}}}{n}) τ_{3}

(14)

3.4 Controls for Endogeneity, and Model Diagnostics

As noted earlier, we relied on three methods to control for mutual causality in the two model series: (1) two-stage least squares with instrumental variables; (2) lagged independent variables, observed four years prior to the year in which the dependent variable was measured; and (3) the inclusion of endogenous factors on both sides of both model series: measures of productivity as independent variables in the transit–agglomeration series; measures of transit as independent variables in the agglomeration–productivity series; and multiple measures of agglomeration in both model series—in the first case as independent variables and in the second case in a simultaneous system of first-stage equations.

In carrying out two-stage least squares, we predicted levels of transit service and levels of agglomeration as a function of instruments correlated with historical transit investments but not caused by recent levels of agglomeration, or correlated with historical levels of agglomeration but not caused by recent levels of productivity. The instruments are described later. We tested for underidentification with the Kleibergen–Paap Wald statistic; for weak instruments using the Kleibergen–Papp rank F statistic and the Stock–Yogo (2005) critical values; and for overidentification using the Hansen J statistic.

4. Data

We collected data on transit services, agglomeration and productivity, along with control variables and instruments, for about 90 per cent of the 364 metropolitan areas¹ in the continental United States. The number of metropolitan areas included in the regressions varied between 319 and 354, depending on missing values for some transit service measures, employment density measures and instruments.

4.1 Transit Service

The American Public Transportation Association provided track length data for the 27 metropolitan areas with some form of rail transit in 2003 (a year used in order to allow a four-year lag between transit service levels and physical agglomeration measures). Bus and rail seats in all vehicles, and bus and rail service miles (the distance driven by vehicles in revenue service), were from the National Transit Database. There were 290 metropolitan areas with bus service in 2003. We tested these transit service variable types in total, per capita in the metropolitan area, and per land area within the UZA (Table 1).

Table 1.

Principal variables used in the models

Variable type	Transit service^a→	Agglomeration →	Productivity
Variables tested	Total rail track length	Metro area population	Wages per capita
	Rail track length per capita	Central city employment density	Gross metropolitan product (GMP) per capita
	Rail track density^b	Urbanised area employment density
	Bus + rail seats
	Bus seats
	Rail seats
	Bus + rail seats per capita
	Bus seats per capita
	Rail seats per capita
	Bus + rail seat density^b
	Bus seat density^b
	Rail seat density^b
	Bus + rail service miles
	Bus service miles
	Rail service miles
	Bus + rail service miles per capita
	Bus service miles per capita
	Rail service miles per capita
	Bus + rail service mile density^b
	Bus service mile density^b
	Rail service mile density^b

The seven per capita transit service measures were excluded from the metro area population models, since, all else equal, increases in population will reduce transit per capita.

Per square mile in the urbanised area.

4.2 Agglomeration

We constructed three measures of agglomeration, for both the year 2007 (when used as dependent variables in the agglomeration–transit models) and the year 2004 (when used as lagged, instrumented independent variables in the productivity–agglomeration models). The density of employment in the urbanised area and the central cities were calculated using block-level worker-at-place-of-work data from the Census Bureau’s Longitudinal Employer–Household Dynamics (LEHD) dataset, along with block-level land and water area from the Census TIGER shapefiles; we used LEHD data from the years 2007 and 5as these had the fewest missing values at time of analysis.² Central city employment density was calculated only for the urbanised portions of the census-defined ‘principal cities’ of the metropolitan areas. For example, there are three principal cities in the Milwaukee–Waukesha–West Allis metropolitan area, the urbanised portions of which accounted for 46 per cent of employment and 9 per cent of the urbanised land in the metropolitan area in 2007 (Figure 1).

Figure 1.

Metro area, UZA and principal cities—Milwaukee example.

Metropolitan area population data were from the US census, aggregated from county level data.

4.3 Productivity

Average wages were from the County Business Patterns data from the Census Bureau, aggregated from county data using the 2008 metropolitan area definitions. GDP data at the metropolitan area level (i.e. GMP data) were obtained from the US Bureau of Economic Analysis.

Table 1 lists the main variables of interest that were tested in the models: 21 transit service measures, three physical agglomeration measures and two measures of productivity.

4.4 Controls

Highway/arterial road network data were drawn from National Highway Planning Network files in the National Transportation Atlas Database. Jaison Abel kindly provided a measure of human capital used in Abel et al. (2011): the share of the working-age population with a college degree. Seven census data variables were also included as controls: the share of the population aged under 18, aged 65 or over, aged 25+ and holding a high school diploma, aged 25+ holding a bachelor’s degree, and the share identified as White, Black/African American and Hispanic/Latino. The share of the metropolitan area workforce in each of the two-digit NAICS industry categories was calculated using LEHD data.

4.5 Instruments

As exogenous predictors of contemporary levels of transit in 2003, we used the passenger rail right-of-way in 1898 (infrastructure that may still influence transit supply today); the population of the metropolitan area in 1900 (as an early indicator of transit service demand); the percentage of the metropolitan area covered in water (as a proxy for constrained land availability that might make transit service more feasible); and an index of climate (as a proxy for transit demand and hence supply, as climate has been shown to be correlated with ridership in previous literature). We calculated the sum of the length of passenger rail right-of-way in each city using a 1898 map of US passenger and freight rail, provided to us by Matthew Turner (see Duranton and Turner, 2011), that we geocoded to match our geography. We calculated the percentage of the metropolitan area covered by water using census data in a GIS. Two other instruments—the population in 1900 and the climate index—were kindly provided by Jaison Abel (Abel et al., 2011). As exogenous predictors of current levels of agglomeration, in addition to using these same instruments we included an indicator variable representing whether the metropolitan area has some form of metropolitan-level governance and another for metropolitan areas where the state permits township forms of governance (both from the US Census of Governments). These may both influence urban fragmentation and therefore lead to lower employment density and population.

5. Results

5.1 Transit–Agglomeration Models

We estimated three sets of transit–agglomeration regressions, one set for each of the agglomeration measures, with each regression in the set varying only by the transit service measure included. We report only the successfully instrumented models, although the results are qualitatively and quantitatively similar even for those models that did not pass diagnostic tests. We did not simultaneously test multiple transit measures, although undoubtedly different kinds of transit service could play distinct and simultaneous roles in physical agglomeration.

Each transit service measure was predicted using a first-stage instrumental variables regression on all of the endogenous variables in the main model, including wages or GMP per capita, as well as one or more of the following instruments described earlier: the population in 1900, the length of rail track in 1898, the percentage of area covered by water and an index of climate. We present models excluding New York City, since it is an outlier on multiple dimensions. The models were specified with robust standard errors and limited information maximum likelihood (LIML) estimation to correct for heteroscedasticity. We also estimated ordinary least squares (OLS) models for comparison, although these models are not shown.

Central city employment density

Our first set of models tested the relationship between transit service and central city employment density. We found strong positive correlations between most transit service measures and central city employment density in the OLS models, although just six of 21 instrumental variables models passed all diagnostic tests. In all cases, the transit service coefficients increased in size and significance when instrumented. Two measures, per capita rail track length and rail service mile density, were successfully instrumented only when a single instrument, population in 1900, was used. Those results are not shown here in preference to models with two instruments, for which overidentification tests can be performed, but the effect sizes were similar to the remaining models. Models using the three per capita seat capacity measures—bus + rail, rail and bus per 1000 population—were more robust, with well or adequately instrumented measures for all; we show only the model with bus + rail seats per capita (Table 2, column 1). For a median-value increase of 3.66 seats per 1000 metropolitan area residents, the coefficient of 87.6 translates into about 320 additional employees per square mile in the central cities, or an increase of about 19 per cent. The seat density models perform well for bus + rail seat density, but not for either rail or bus seats in isolation (Table 2, column 2). A median-value increase in bus + rail seat density of 9.62 seats per square mile is associated with an additional 298 employees per square mile in the central city, about an 18 per cent increase. Rail service miles per capita was also successfully instrumented (Table 2, column 3). For a mean-value increase of 85 rail service miles per capita, the coefficient of 1.314 implies an additional 112 employees per square mile, an increase of about 7 per cent.

Table 2.

Central city employment density, urbanised area employment density and metropolitan area population (2007) as a function of lagged, instrumented transit service variables (2003), selected models

Model number	1	2	3	4	5	6	7	8	9	10
Dependent variable	CCED^a	CCED^a	CCED^a	UZED^a	UZED^a	Pop^b	Pop^c	Pop^d	Pop^c	Pop^d
Bus + rail seats per 1000 capita^a	87.63***			−35.96**
Bus + rail seats per 1000 capita^a	(3.61)			(−3.29)
Bus + rail seat density (per UZA square miles)^a		30.99**
Bus + rail seat density (per UZA square miles)^a		(3.01)
Rail service miles per 1000 capita^a			1.314***
Rail service miles per 1000 capita^a			(3.39)
Rail service mile density (per UZA square miles)^a					−0.166**
Rail service mile density (per UZA square miles)^a					(−2.73)
Bus seats (1000s)^b						−0.0371
Bus seats (1000s)^b						(−0.16)
Bus + rail service miles (100,000s)^c,d							0.0615***	−0.00129
Bus + rail service miles (100,000s)^c,d							(4.76)	(−0.05)
Bus service miles (100,000s)^c,d									0.0537***	−0.00139
Bus service miles (100,000s)^c,d									(4.44)	(−0.06)
Freeway/arterial length per 1000 population	−127.4*	−108	−122.1*	6.305	5.899	−0.228	−0.405*	−0.222	−0.343*	−0.223
Freeway/arterial length per 1000 population	(−2.18)	(−1.95)	(−2.45)	(0.34)	(0.32)	(−1.17)	(−2.27)	(−1.18)	(−2.12)	(−1.18)
GMP per capita, logged	266.8	523.8**	211.8	245.0***	244.3***	0.353	0.536	0.338	0.559	0.337
GMP per capita, logged	(1.35)	(2.60)	(1.10)	(3.89)	(4.34)	(0.39)	(0.64)	(0.41)	(0.72)	(0.41)
Employment density–central cities				0.166***	0.134***	−0.000275	−0.000385	−0.000301	−0.000323	−0.000303
Employment density–central cities				(3.76)	(3.92)	(−0.77)	(−0.99)	(−0.84)	(−0.94)	(−0.82)
Employment density–urbanised area	0.547*	−0.0473	0.789***			0.00242	−0.00197	0.00229	−0.00125	0.0023
Employment density–urbanised area	(2.51)	(−0.12)	(3.88)			(1.35)	(−1.24)	(1.23)	(−0.87)	(1.26)
Population of metro area (100,000s)	−0.948	−6.768	−5.294	8.876***	11.60***
Population of metro area (100,000s)	(−0.21)	(−1.15)	(−0.88)	(4.16)	(3.63)
Population of metro area, 1970 (100,000s)						1.31**	0.349*	1.26***	0.543***	1.26***
Population of metro area, 1970 (100,000s)						(3.14)	(2.00)	(3.38)	(3.83)	(3.72)
Constant	1026.2	652	2663	2461.5***	2208.6**	9.714	−1.502	9.275	−1.816	9.308
Constant	(0.69)	(0.38)	(1.82)	(3.76)	(2.66)	(0.67)	(−0.19)	(0.81)	(−0.25)	(0.79)
N	350	340	350	350	340	350	350	347	350	347
Adjusted R²	0.40	0.28	0.38	0.34	0.27	0.90	0.91	0.90	0.93	0.90
Underidentification test (Kleibergen– Paap rank Wald)	13.2	11.9	6.8	8.7	4.7	8.1	7.7	9.0	6.6	6.7
Underidentification probability	0.001	0.003	0.034	0.013	0.097	0.018	0.053	0.011	0.087	0.035
Weak identification test (Kleibergen– Paap)	22.6	16.2	12.0	14.5	7.4	8.8	12.8	9.5	14.9	6.2
Weak identification probability (Stock–Yogo)	<0.10	<0.10	<0.10	<0.10	<0.15	<0.10	<0.10	<0.10	<0.10	<0.15
Overidentification test (Hansen’s J)	0.01	0.37	0.61	0.002	0.11	2.55	5.79	0.22	7.05	0.22
P value for over-ID null hypothesis	0.91	0.54	0.44	0.97	0.74	0.11	0.06	0.64	0.03	0.64

Instruments for models 1–5: percentage area covered in water; population in 1900.

Model 6 instruments: length of freight and passenger rail track in 1898; percentage water coverage.

Model 7 and 9 instruments: 1900 population, water, climate index.

Model 8 and 10 instruments: 1898 rail, climate index.

Notes: * p<0.05; ** p<0.01; *** p<0.001; t statistics in parentheses. CCED: central city employment density. UZED: urbanised area employment density. Pop: metropolitan area population.‘L4’ refers to a four-year lag (measured for the year 2003). Robust standard errors on all models. IV models estimated with limited information maximum likelihood (LIML). Included, not shown: shares of employment in 2-digit NAICS categories from LEHD 2007 (for example, agricultural, manufacturing, retail, professional services, education, arts and 14 others); demographic variables from American Community Survey 2005–07 metropolitan area data (share of metropolitan population under 18, over 65, with high-school degree, college-educated, White, Black, Hispanic).

Urbanised area employment density

Urbanised area employment density was the dependent variable in our next set of models (Table 2, columns 4–5). Although only a few models robustly passed diagnostic tests, those with poor diagnostics yielded similar point elasticities. When the transit service measures were instrumented, there was typically a change in sign from positive to negative. That is, transit service was negatively associated with urbanised area density when controlling for central city employment density and population. Urbanised area employment density is highly correlated with population and this may be part of the reason for the change in sign. Variance inflation is reduced in the two-stage models, and population becomes statistically significant, suggesting that the instrumental variables models are more reliable. The result is also intuitive when taking into account the presence of the two other agglomeration measures, central city employment density and metropolitan area population. Transit service may reduce urbanised area employment density while increasing central city employment density, when controlling for population size. It is sensible that transit services might centralise employment within urbanised areas; that is, employment density might get higher within central cities, but might also get lower elsewhere. This supposition is borne out when running models without central city employment density and population density (models not shown). In that case, urbanised area employment density is positive in the OLS models, and insignificant in the IV models, with t-statistics below 1.

With bus + rail seats per capita as the transit measure, we found a coefficient of −35.96, implying a reduction in urbanised area employment density of about 132 employees per square mile (14 per cent) for a median-value increase of 3.66 bus + rail seats per 1000 capita (Table 2, column 4). There were also some diagnostically acceptable results for rail service mile density (Table 2, column 5), with a coefficient of −0.166, implying that a mean-value increase in rail service miles per area reduces urbanised area employment density by 52 employees per square mile, a reduction of about 6 per cent.

Metropolitan area population

For the last of our three agglomeration measures, metropolitan area population, we included a lagged measure of population from 1970 as an independent control. Again, only a few population models came close to having proper diagnostics. In this case results were sensitive to the choice of instruments and not all relationships were statistically significant. A model of bus seats had proper diagnostics but found no significant relationship with population (Table 2, column 6). We found mixed results when the transit measure was bus + rail service miles. When three instruments were used—population in 1900, a climate index and the percentage of the metro area covered in water—the model of bus + rail service miles barely missed the underidentification cutoff, had strong instruments and was not clearly overidentified, and showed a strong positive relationship, implying a 48,000 person increase in population for a median-value increase on this measure with population (Table 2, column 7). Yet when 1898 rail length and an index of climate were used as instruments, there was no significant relationship, while the diagnostic tests were more robust (Table 2, column 8). We found a similar pattern for bus service miles (Table 2, columns 9 and 10).

Our measures of transit reflect investments made long before 1970 in many cities with heavy rail and commuter rail. The dataset does not include dates of transit capacity additions over such a long time-period. We separately estimated the same models with light rail track mileage separated from the other rail types, since the majority of light rail was built after 1970. We found that light rail was positively associated with population growth, and commuter rail and heavy rail negatively associated, but the models suffered from weak instruments and we do not display the results here.

5.2 Agglomeration–Productivity Models

We next regressed wages per worker and GMP per capita in 2008 upon the same three measures of agglomeration, lagged by four years. For the instrumental variable models, the first stage was to model the agglomeration measures as a function of a set of exogenous and endogenous instruments, including the presence of rail as well as other measures of transit; followed by a model of per worker wages or per capita GMP as a function of the instrumented agglomeration measures and controls. Because diagnostics on the models with three simultaneously instrumented agglomeration measures were sometimes poor, we also tried instrumenting two at a time and estimated a series of staged models (not shown here) in which each of the agglomeration measures was instrumented separately in turn while controlling for the other two un-instrumented agglomeration measures. The results, discussed later, were robust to these variations.

Note that transit service is not instrumented in the productivity models. It is treated as a control variable here to help isolate the independent effects of agglomeration from the capitalisation of travel time savings that could also influence wages or GMP, as discussed previously.

We start with per capita wages. Population and central city employment density were positively associated with average wages in the OLS model, with elasticities of 0.02 and 0.03 respectively, while urbanised area employment density was small and insignificant (Table 3, column 1). Because we could not find successfully instrumented models with all three agglomeration measures, urbanised area employment density was omitted in the second wage model (column 2) which retains similar-sized coefficients for both population and central city employment density. In the final wage model (column 3), we simultaneously instrumented central city employment density and population, finding larger elasticities for both than in the OLS model, increasing to 0.03 and 0.07 respectively.

Table 3.

Per worker wages and per capita gross metropolitan product (2008) as a function of lagged, instrumented agglomeration measures (2004)

	1	2	3	4	5	6
	Per worker wages (logged)			Per capita GMP (logged)
	OLS	OLS	IV^a	OLS	IV^b	IV^c
Metro area population (logged)	0.0215*	0.0216*	0.0312*	0.00416	−0.018	0.0116
Metro area population (logged)	(2.33)	(2.35)	(2.13)	(0.24)	(−0.76)	(0.55)
Central city employment density (logged)	0.0325*	0.0317*	0.0716*	−0.00799	0.0957	0.0336
Central city employment density (logged)	(2.18)	(2.41)	(2.38)	(−0.28)	(1.18)	(0.70)
UZA employment density (logged)	−0.00249			0.130**	−0.409*
UZA employment density (logged)	(−0.11)			(3.17)	(−1.97)
College-educated share (human capital) (logged)	0.0706**	0.0701**	0.0542*	0.336***	0.468***	0.356***
College-educated share (human capital) (logged)	(2.62)	(2.64)	(1.97)	(7.50)	(5.89)	(7.57)
Freeways/arterials per capita (logged)	7.69	7.611	12.05	17.99	34.15	24.83*
Freeways/arterials per capita (logged)	(1.22)	(1.22)	(1.85)	(1.51)	(1.88)	(2.19)
Rail transit in metro area	0.0508*	0.0507*	0.00325	0.0891*	0.141**	0.0858*
Rail transit in metro area	(2.29)	(2.29)	(0.13)	(2.13)	(2.84)	(2.20)
Bus + rail seats (logged)	−0.00309	−0.00312	−0.0112**	−0.0141**	−0.00372	−0.0142*
Bus + rail seats (logged)	(−1.10)	(−1.12)	(−2.91)	(−2.66)	(−0.42)	(−2.24)
Constant	10.33***	10.32***	9.866***	−3.043***	0.436	−2.490***
Constant	(53.35)	(65.54)	(28.45)	(−8.06)	(0.32)	(−5.69)
R ²	0.714	0.714	0.73	0.728	0.569	0.715
N	322	322	348	322	319	319
Kleibergen–Paap test of weak identification			11.17		4.745	24.27
Stock–Yogo probability			<10%		<10%	<10%
Hansen’s J			6.194		4.331	3.151
Hansen’s J probability			0.185		0.363	0.0759

p<0.05, ** p<0.01, *** p<0.001; t statistics in parentheses. OLS: ordinary least squares. IV: instrumental variables (two-stage least squares). “L4” refers to a four-year lag (measured for the year 2004).

Included but not shown in wage models (1-3): Metropolitan area employment shares in mining, wholesale, retail, transportation/utilities, information, professional services, arts and entertainment, food and accommodation. Included but not shown in GDP models (4-6): Metropolitan area employment shares in mining, wholesale, retail, transportation/utilities, finance/insurance, real estate, other services.

Notes: ^aPopulation & central city density instrumented. ^bUrbanised area and central city employment density instrumented; metropolitan area population uninstrumented. Six instruments: Population of metro area in 1900, passenger and freight rail track mileage in 1898, in state allowing township form of government, climate index, has metropolitan government structure, percent of metropolitan area covered by water. ^cPopulation and central city employment density instrumented; urbanised area employment density omitted. Three instruments: Population of metro area in 1900, passenger and freight rail track mileage in 1898, in state allowing township form of government.

Next we turn to gross metropolitan product (GMP) per capita. Urbanised area employment density was positively correlated when using OLS, while the other two measures did not achieve statistical significance (column 4). The sign flips when urbanised area employment density and central city employment density are instrumented (column 5), and the magnitude becomes larger, increasing to −0.41. Even when urbanised area employment density is omitted altogether, neither population nor central city employment density is correlated with GMP per capita (column 6). In models not shown here, when population and central city employment density were omitted, urbanised area employment density was no longer significantly associated with GMP per capita, although the sign remained negative and the magnitude remained relatively large, at −0.3. We also carried out other robustness tests on the GMP per capita model, such as omitting various other variables, and in each case we found a negative coefficient for urbanised area employment density, usually with statistical significance. An intuitive explanation is that centralisation of employment within the central-city portion of the urbanised area could be associated with higher firm productivity. The result could also be partly due to an underspecified GMP model, which would ideally include a more complete measure of capital inputs. We included state-level fixed effects in the initial models, as a proxy for capital availability (following Abel et al., 2011), but those models failed the overidentification test, so were omitted in subsequent models.

Human capital—as measured by the share of population of working age with a college degree—was insignificant in some of the wage models while staying significant and large in the GMP models. This could be partly because of collinearity of population and central city employment density with wages and human capital.

Finally, transit seat capacity in the instrumented wage models shows a negative coefficient. This conforms to firm theory, which would predict lower offering wages for workers facing reduced transport costs. Yet it is also negatively correlated with GMP, when theory would predict some positive capitalisation of travel time savings in firm revenues. We tested multiple other measures of transit service in the wage and GMP models, and only total transit seat capacity was statistically significant.

5.3 Linking Transit Service with Productivity via Agglomeration

We estimated how transit services are associated with wages and GMP by calculating elasticities for the successfully instrumented regressions in both sets of models with statistically significant estimates. We show six such combinations—three for central city employment density, two for urbanised area employment density and one for metropolitan area population (Table 4). These effects are net of each other, because both stages of our models control for all three agglomeration measures simultaneously.

Table 4.

Net transit-productivity elasticities via three agglomeration channels

Transit service measure	Agglomeration measure^a	Transit–agglomeration coefficient	Mean transit–agglomeration elasticity^b	Agglomeration–wage elasticity^c	Net transit–wage elasticity	Agglomeration–GMP elasticity^d	Net transit–GMP elasticity
Bus + rail seats per 1000 capita	CCED	87.63	0.33	0.0716	0.0234	—	—
Bus + rail seat density (per UZA square miles)	CCED	30.99	0.34	0.0716	0.0244	—	—
Rail service miles per 1000 capita	CCED	1.314	0.36	0.0716	0.0255	—	—
Bus + rail seats per 1000 capita	UZED	−35.96	−0.24	—	—	−0.409	0.097
Rail service miles density (per UZA square miles)	UZED	−0.166	−0.45	—	—	−0.409	0.185
Bus + rail service miles (100,000s)	Pop	0.0615	0.34	0.0312	0.0107	—	—

CCED - central city employment density; UZED- urbanised area employment density; Pop - metropolitan area population.

Average point elasticities calculated by multiplying linear coefficients by the transit measure for each metropolitan area with transit service, and taking the average percentage change in the agglomeration measure.

From Table 3, column 3.

From Table 3, column 5.

Using coefficients from Table 2, we calculated point elasticities with respect to the three agglomeration measures for each metro area having non-zero values for transit service, and averaged them (Table 4, column 3). Following equations (12) to (14), net elasticities were calculated simply by multiplying these average point elasticities by the agglomeration productivity elasticities from Table 3. For central city employment density, a ten per cent increase in bus + rail seats, bus + rail seat density, or rail service miles per capita is associated with between a 0.23 and 0.26 per cent net increase in average wages (Table 4, rows 1–3). The negative coefficient for transit with respect to urbanised area employment density outside the central cities, combined with a negative influence of urbanised area density on GMP when controlling for central city employment density and population, means that 10 per cent increases in bus + rail seats per capita or rail service mile density are associated with increases in GMP per capita ranging from 1 to 1.9 per cent via the urbanised area employment density pathway (Table 4, rows 4–5). Finally, a 10 per cent increase in bus + rail service miles is associated with a population-based wage increase of 0.1 per cent (Table 6, row 6).

For illustrative purposes, we can calculate dollar value estimates using 2008 data on average wages and the size of the worker pool by metropolitan area in the US. We do so just for central city employment density, which are the most statistically robust results. The marginal dollar value of increasing transit service by 10 per cent, with subsequent increases in central city employment density, varies between $53 and $194 in wages per worker yearly depending on metropolitan area variation in the average wage. Across metropolitan areas, the net productivity benefit averages around $45 million per year and ranges from $1.5 million to $1.8 billion depending on the size of the metropolitan area.

5.4 Tests of Robustness

We also tested for non-linearity, including threshold effects of density levels and interactions. One might expect that agglomeration economies would exist only with high-enough levels of population or employment density. In the agglomeration–productivity models, we tested dummy variables for above-median population and above-median employment density as well as tritiles and splines for the same divisions. The coefficients on different ranges were within 10 per cent of each other and the differences were not statistically significant, implying that the log–log model form is accurate. We also tested for non-linearity in the transit–agglomeration models, expecting that only sufficiently large transit systems might have significant effects on employment density or population. While doing so was hindered by the relatively small number of metropolitan areas with rail service, we found no strong evidence of non-linearity here either.

6. Conclusions

These results suggest that the per capita productivity benefits of increasing transit service are smaller for larger metropolitan areas in percentage terms, but the net effects are larger because of the larger pool of workers. Benefits are even higher on a percentage basis for areas with existing transit systems, since percentage changes to larger systems result in substantially larger absolute changes. For example, a 10 per cent increase in transit service has a much larger overall productivity benefit in the Chicago area, which has a large labour force and an extensive transit system, than it does in the Tampa–St Petersburg metro, which has a smaller labour force and a less developed transit system.

Of the three measures of agglomeration, the most reliable and intuitive results were for the effects of transit service on wages via the central city employment density agglomeration channel. Previous research on physical agglomeration and productivity has often used metropolitan area-wide agglomeration measures, but finer measures such as this one are potentially influential. Central cities are particularly important because they include concentrations of employment that are most likely to be served by transit. Interestingly, we find that total transit services—including buses, which are more commonly used outside the core CBD—are about as highly associated with central city employment density as rail service. The results for the total transit measures also help to validate the rail-only results, because they include many more cities with non-zero values for transit service.

There are several caveats to mention. The relationship between transit and physical agglomeration is possibly very long term, in marked contrast to travel-time-based agglomeration economies, which can occur quickly. Our analysis used metropolitan-level measures, thus investigating only urbanisation economies and neglecting industry-specific agglomeration mechanisms. Despite correcting for endogeneity and using lags, our data were essentially cross-sectional and so there are the usual reasons for caution in applying these estimates to future increases in transit service. Given the varying transit service measures used in our analysis, and the difficulty of estimating models with suitable diagnostic results, the estimates should be interpreted mostly by sign, statistical significance and overall magnitude. While we additionally control for the effects of highways, this variable is not instrumented; likewise, we do not control for access to ports or airports, which might also have agglomeration and productivity impacts.

Impediments to improving this work are significant, but at least partly surmountable as data become more readily available. It would be particularly informative to have sufficient panels to estimate long-run effects. More finely created measures of agglomeration, such as measures of firm clustering near transit stops, would also be useful.

These results have significant policy implications if they hold up under the scrutiny of further research. They imply that there is a fairly large external productivity benefit from transit investment and that current benefit–cost frameworks in the US undervalue the benefits of transit service improvements, particularly in large cities with existing transit systems. Integrating the agglomeration benefits of transit service improvements within a comprehensive benefit–cost framework is an important challenge for future research and practice.

Footnotes

Acknowledgements

The work presented here builds on a chapter from the final report for Transit Cooperative Research Program Project H-39 (see below). Niels Voorhoeve, Bryan Grady, Nicholas Tulach, Dan Tischler and Nicholas Klein provided research assistance with data assembly, data cleaning, construction of agglomeration measures and running initial statistical scripts. Jaison Abel graciously provided human capital and climate data for metropolitan areas and Matthew Turner made his 1898 rail map available to us. Dan Graham and Mike Manville made helpful comments and suggestions. Many thanks also to two anonymous referees for Urban Studies for their helpful suggestions and critiques.

Funding

Funding was provided by the Transit Cooperative Research Program Project H-39, “Methodology for Determining the Economic Development Impacts of Transit Projects”. The authors thank the project panel and contract manager Larry Goldstein.

Notes

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