Preliminary draft Comments welcome EMPLOYMENT SUBCENTERS AND THE DISTRIBUTION OF ECONOMIC ACTIVITY by Steven G. Craig and Janet E. Kohlhase * Department of Economics University of Houston Houston, TX 77204-5882 May 2010 Acknowledgments: We would like to thank Ronald Elul and Dan McMillen for helpful comments. We also benefited from comments from seminar and meeting participants at Tulane, the Regional Science Association International meetings and the American Real Estate and Urban Economics Association meetings. * corresponding author. Contact at 713-743-3799 (phone), 713-743-3798 (FAX), or via e-mail at jkohlhase@uh.edu. 1
EMPLOYMENT SUBCENTERS AND THE DISTRIBUTION OF ECONOMIC ACTIVITY ABSTRACT The paper explores the nature and influence of employment subcenters on the distribution of economic activity in Houston. First, indirect measures of economic linkages between each of the subcenters and the central business district (CBD) are examined. We find that most subcenters are linked to the CBD because of complementary relations in output or input markets. Second, we estimate polycentric employment and population density functions that allow for the economic links and test various spatial definitions of the subcenters. We find the best characterization of one of Houston s subcenters centered along the Houston port to be an entire corridor rather than a few discrete points. However, we find no support for specifying subcenters as rings along circumferential highways. Keywords: employment subcenters, polycentric city, employment density, population density 2
I. Introduction The goals of this paper are to empirically examine employment centers 1 and to show how their existence impacts the distribution of economic activity in a polycentric city. Our empirical research is motivated by the variety of theories that attempt to predict the number and characteristics of employment centers outside of the traditional downtown central business district (CBD). The lack of accepted theories has not prevented the empirical urban literature from discussing how to recognize employment subcenters (McDonald, 1987; Small and Song, 1994; McMillen and McDonald, 1997; McMillen, 2001, and Craig and Ng, 2001). The approach here deviates from this literature, however, by attempting to target some of the aspects that might affect the number and types of employment subcenters. Our approach will nonetheless hopefully assist in defining employment subcenters, by focusing on their economic attributes. Three elements of the urban economic landscape have been found in theory to be important, although the existing theories are nonetheless incomplete in some important aspects. 2 One, employment subcenters may exist because there are limits to the agglomeration economies in the CBD, and thus they partially substitute for the CBD (White, 1999, and Anas, Arnott, and Small (1998), hereafter AAS). Two, subcenters may instead be tied to various elements of the local economy, for example various output markets, or specific input markets (White, 1999). And three, economic subcenters may represent specialized parts of the economy that are in general independent of the CBD (Heikkila, et. al, 1989). To the extent our empirical exploration is successful, we hope to develop one of the first in-depth studies of the interrelations between the traditional CBD and subcenters as viewed by both consumers and 3
firms. As such our work will contribute toward sorting out the various theories that predict urban polycentricity. We hope to shed some light on the economic roles that subcenters play in the context of an entire urban area, a topic deserving of more research according to AAS (1998, p. 1443). We use the metropolitan area of Houston, Texas as the example. 3 Our research strategy is to examine the elements that might affect economic motivations surrounding subcenter formation by first looking at details of the type of economic activity within employment subcenters and developing some measure of the economic relationship between the subcenters and the CBD. Then using results about the linkages between the subcenters and the CBD, we will attempt to more fully characterize the physical shape of subcenters and measure how they impact the distribution of economic activity in an urban area, as measured by employment and population densities. If subcenters simply mirror the CBD in both industrial and occupational groups, one role of theory might be to explore the limits to agglomeration economies for a single CBD, and then to explain how, when limits are reached, alternatives to the CBD might arise. Alternatively, it is also possible to imagine that subcenters arise to exploit agglomeration economies for particular industries or occupations that are independent of each other, or even compete with each other. In this case, theory might instead explore how subcenters could arise when firms attempt to avoid the competitive aspects of alternative industries. These types of concern are related to the geographic form of a subcenter. If subcenters do not have the characteristic circular shape used to characterize CBDs (for example if they are a corridor), they may have a different function than the single employment centers that typify monocentric models. 4
In the rest of our paper we discuss issues surrounding the specification of polycentric density functions for population as well as employment. Part II gives an overview of the geography of the study area, the Houston region, and Part III describes the data. Part IV examines whether, and to what extent, Houston s subcenters are linked with the CBD. Ideally we would like to be able to examine the links directly by analyzing intra-urban area trade flows between the CBD and each of the subcenters. However such data does not exist for Houston. So we are forced to look for indirect evidence of economic linkages. One approach is to think about how differential economic linkages could be reflected in land use differences, in our case as measured by density data on population and employment. Our results, based on estimating single-node population and employment density functions, indicate that there is market demand for simultaneous access to more than one (sub)center by both firms and residents. 4 This leads us to specify in Part V, polycentric density functions reflecting complementarity amongst the centers. We attempt to classify the subcenter s relative links to the CBD and to each other. We also explore the intra-subcenter economic geography. That is, we examine whether various subcenters are best characterized by a single point, or instead whether subcenters can better be characterized by an entire corridor (in our case seagoing port access), or a ring (in our case circumferential highways) 5. We conclude by speculating whether the three aspects of our empirical exploration are related, that is, whether the shape of the subcenters, or their concentration, appears to affect their relation to the CBD. II Houston s Employment Centers 5
Our empirical work starts with exogenously defining the set of employment centers as the CBD and the seven subcenters identified in Craig and Ng (2001) and shown in Figure 1. The Craig and Ng method uses a non-parametric specification to evaluate the upper tail of employment densities. In their method, areas with employment densities at the 95 th percentile or above, conditional on the distance from the CBD, that also appear to influence neighboring areas are essentially identified as employment subcenters. The subcenters so identified include wellknown areas within Houston such as the Galleria, Clear Lake, Carillon, Greenspoint, Baytown, Pasadena, and LaPorte (see Figure 1). The geography of the eight employment centers defined by Craig and Ng are small areas, defined by the boundary of an appropriate census tract. We abstract from the areal definition, and refer to these as point centers hereafter. The seven subcenters lie on three concentric rings around the CBD. Houston's largest employment subcenter is the Galleria area, called "Uptown" by some real estate professionals. This is a retail and office area bordering on the innermost circumferential freeway (I 610) and the main southwest freeway (US 59), and is the only subcenter identified on a ring about six miles from the CBD. On the next ring, about 13 miles from the CBD, are Carillon, Greenspoint, and Pasadena. Carillon essentially lies west on a line from the CBD through the Galleria. This area is thus in some sense a sub-subcenter, in that it might be expected to have a more direct relationship to the Galleria than the CBD. 7 Greenspoint is near the airport at the confluence of two major highways north of the CBD. Pasadena is one of the three administrative centers around the Houston Ship Channel. The third ring, at about 21 miles from the CBD, contains Clear Lake, Baytown, and LaPorte. Baytown, and LaPorte are, besides Pasadena, the other two administrative centers around the Houston Ship Channel. The final point subcenter, Clear Lake, 6
is relatively far from the CBD on the third ring, and in some senses seems least related to the CBD. It contains NASA, a government installation not necessarily related to industries located in the CBD, and is also close to the recreation areas associated with the Gulf of Mexico. The methodology of Craig and Ng (2001) only allows identifying as potential subcenters those areas on concentric circles at various distances from the CBD. The methodology may be limiting if in fact the geography of a subcenter does not follow a concentric ring, but in fact cuts across several rings. Our main area of concern is the concentrated employment along Houston s Ship Channel, of which Craig and Ng found three discrete areas to be separate subcenters. We explore below whether the three point subcenters (hereafter referred to as Ship Channel Points ) merit attention as separate subcenters, or instead whether the entire Ship Channel region which includes the 26 Census tracts adjacent to the Ship Channel should be considered the subcenter (hereafter referred to as Ship Channel Corridor ). Moreover, we investigate whether the highway rings themselves, defined as all census tracts which border a particular loop highway, can be considered subcenters, rather than a few discrete areas along the rings. Because we find that the ring specification is not robust, we will report statistics only for the point subcenters along the ring Similar considerations may apply for the Los Angeles area. For example, Gulliano and Small (1991) identify five point subcenters in Los Angeles essentially along Wilshire Boulevard. An alternative formulation, however, would be that the entire roadway is an employment subcenter, so that the series of discrete subcenters would be a single continuous subcenter corridor. Such a specification is consistent, for example, with a low marginal cost of additional transport along a piece of transportation infrastructure, but where access to that infrastructure 7
may be valuable. 8 Characterization of subcenters as either individual areas, or as having a different shape, is important for understanding some of the issues underlying what procedures to use to identify the location of employment subcenters (McDonald, 1987; Small and Song, 1994; McMillen and McDonald, 1997, McMillen, 2001). Given the unsettled nature of not only empirical work but of theoretical work in this area, it may be that alternative geographic shapes for employment subcenters might affect our understanding of the relationship between the subcenters and a CBD. 9 A point (or equivalently a single census tract) may be too limiting as a specification for some of the economic roles that subcenters might be expected to fulfill. A highway, or a river/port, may fulfill the economic role of a subcenter along an entire line, rather than at one location. 10 That is, the typical CBD area of a modern city is rarely at an export transportation node as is often assumed in the basic monocentric models of Alonso/Mills/Muth (O Sullivan, 1996). 11 This makes economic sense, because human capital is the primary input for most of the offices located in the CBD, and management is the primary output. Conversely, however, for the production of physical goods as is typical of manufacturing (or chemicals such as in Houston), land is a needed input into production. Further, the marginal cost of an additional mile along a route may be small relative to shipping goods across the nation, or the world. In cases such as these, an employment subcenter may consume a great deal of space, and attempting to locate the center at a single point may be impossible. We explore whether the Ship Channel in Houston is a subcenter that is best characterized by a corridor, rather than by specific points. The Ship Channel, also known as the Port of Houston, is the world s eighth largest port. 12 The port ranks second in the US in total tonnage 8
shipped. It is a 25 mile corridor built by widening and dredging a local river, and it is lined with public and private wharves and docks, as well as extensive manufacturing and refining facilities, along its entire length. 13 Extensive rail and highway links exist to transport products to and from the docks. Physically, the Ship Channel begins at the Turning Basin, about four miles from the CBD and stretches to Galveston Bay. The geographic characteristics of the corridor inspired us to test whether or not the presence of that entire line--the Ship Channel-- is an important determinant of Houston s spatial structure. We will thus test how defining the Ship Channel as a subcenter corridor compares to using the three individual subcenter points identified by Craig and Ng (2001): Baytown, Pasadena and LaPorte. 14 An alternative specification we explore is a circular subcenter (hereafter termed ring ), which is consistent with the concentric circle subcenters identified in several theoretical models of population density functions (see White (1976) and Ross and Yinger (1995)). We explore two such rings in Houston. The inside loop, I-610, is about six miles from downtown. The second loop, called the Beltway, is about thirteen miles from downtown. Both freeways represent important highway access to the rest of the area, as well as to the rest of the country. The Galleria area is located on I-610, while Carillon, Greenspoint, and Pasadena are on the Beltway (see Figure 1). To the extent researchers look for employment centers by examining employment density functions centered on a CBD, it might be expected that the entire ring of a concentric circle, rather than one or two points along it, would serve as the employment center. We thus test whether the entire ring of the two loop highways can be considered as subcenters, consistent in form with our test as to whether a corridor can serve as a subcenter, and as opposed to the individual points along the circumferential highways. 9
III. Data Description We estimate population and employment density functions for Houston based on 1990 Census data for Harris County, the county containing Houston. 15 The unit of observation is a census tract, of which there are 569 in Harris County containing at least ten people and 576 containing at least ten jobs. Employment is measured as the location of work using the Journey to Work survey from the 1990 Census. Similarly, we use the Census definitions in the Journey to Work survey to describe the industry and occupations within each employment center. Population is measured using the actual Census count. 16 Densities are measured per square mile, and distance in miles. Distance from each census tract to the CBD and other employment centers is measured in miles between the tract centroids using a Geographic Information Systems (GIS) program. 17 While land use data are available for the city of Houston, we follow McDonald (1987) and others and estimate the gross, rather than net, employment and population density function s. 18 Tables 1 and 2 report characteristics of Houston employment by center and for Harris County, the county that contains most of the city. Houston is considered a dispersed urban economy as illustrated by the fact that only 10% of Harris County s total employment occurs in the CBD, and only 14% occurs in the combination of the CBD and the 7 subcenters identified by Craig and Ng (2001). The number increases to 17% if the Ship Channel Corridor is included. The CBD is nonetheless still the dominant place of work in the metropolitan area (see Table 1), as more than 127,000 people work in the CBD, or 83,532 per square mile. The Galleria has employment densities less than half of downtown. The remaining subcenter points have much less total employment and lower employment densities. 19 The corridor and ring subcenters have 10
more total employment but lower employment densities than do the point subcenters. There are about 59,000 employees in census tracts adjacent to the Ship Channel, the corridor subcenter, implying an employment density of about 1100 employees per square mile. Compared to the Ship Channel corridor, there are many more employees in the tracts contiguous with the two loop freeways (the ring subcenters), about 237,000 near the Loop 610 and 171,000 near the Beltway, with slightly higher employment densities of 1,400-3,600 per square mile Table 2 details the extent of the dispersion of types of employment in each of the subcenters. For each subcenter, shares of employment, presented in percentage form, show the sectoral breakdowns of industry and occupation. All subcenters show quite diverse employment patterns. Herfindahl indexes, 20 a measure of concentration where a value of one indicates complete concentration, are small for all centers. For the industry breakdown, the indexes range from.14 for the CBD to.21 for Clear Lake. For occupation, the indexes are all about.30 for all geographies. It is interesting to note that in comparing all geographies, the CBD is the most diverse in terms of industrial structure as evidenced by the smallest index, but the most concentrated in terms of occupation as evidenced by the greatest index. IV. Economic Links between Subcenters and the CBD: Substitutes or Not? While the best fit for density functions has been found with quite flexible functional forms, 21 an alternative approach is to examine how the various subcenters interact explicitly with the CBD and each other. Conceptually, the subcenters may act as substitutes with the CBD or other subcenters or be complementary to them. The advantage of investigating explicit 11
interaction is that we hope to add some perspective on the search for an empirical definition of employment subcenters, given that this search has to date been atheoretic. Specifically, the relationship between subcenters, and between subcenters and the CBD, should be important to understanding their existence and to cataloguing how many there are. In the investigation of polycentric cities, a logical starting point for estimating density functions is to generalize the monocentric model s negative exponential form. Three generalizations, summarized in AAS and first proposed by Heikkila et. al. (1989), have been proposed: the envelope approach, the additive form, and the multiplicative form, respectively. An important issue is that the various specifications of the polycentric density function presuppose the type of interrelationship between the employment centers; that is each specification imposes a different assumption on how the occupant of a given location values access to each of the centers. The assumptions range from viewing each employment center as a perfect substitute, or as a perfect complement, or some hybrid. In what follows, we will examine each case in detail We next consider how examining properties of density functions can provide indirect evidence of the type of potential economic linkages between the CBD and each of the subcenters 22. Consider the land surrounding the CBD and one of the subcenters. If agents, firms or consumers, locating on a particular parcel have demand for access to both the subcenter and the CBD, we could label the centers as complements. For example consumers may view both the CBD and subcenter as dual employment locations or dual shopping destinations. Firms may view the CBD and subcenter as sources of intermediate inputs or dual markets for its outputs. If the CBD and subcenter had complementary economic links, we would expect a higher land use 12
density between the CBD and the subcenter, than on the side of the subcenter away from the CBD. If, on the other hand, there is no difference in the densities on either side of a given subcenter, then the economic agents likely view the CBD and the subcenter as substitutes, in that access to only one of the centers is valued. If the CBD and subcenter are substitutes, we can conclude that the CBD and the subcenter are economically independent of each other. The envelope approach reported in AAS defines the polycentric density function as the upper envelope of the individual density functions associated with each subcenter. The density at any given location can be expressed as: (2) DEN = i idsti α γ i e max[ ] where DEN is the density of population or employment at a given location, DST is the distance from that location to employment center i, i = 1,2,...,C, C is the number of centers, α i and the γ i are parameters to be determined. The envelope approach assumes that each center is a substitute for all others. Urban theory predicts a series of declining bid-rent functions exist around each of the centers. Then the land rent and density at any given point is determined by the center having the largest influence at that point, and that center need not be the closest center. Land use would be segregated into distinct zones, each supported by a single employment center accessed by the local population or firms; no cross-access would occur. There are problems with the envelope approach from both theoretical and econometric perspectives. Theoretically, the envelope approach seems improbable in an urban setting for at least two reasons. The primary problem is that if agents only have demand for access to one 13
center, there would be no reason to compete with other agents who have demand for alternative centers. There would be economic pressures for employment agglomerations characteristic of perfect substitute subcenters to arise outside the urban area, that is in a greenfield development because of the cheaper land. Second, it seems improbable to assume that people will never shop at more than one subcenter, or change jobs to another subcenter, or have business contacts at another subcenter. Moreover, empirical testing of the envelope approach is quite tricky and to the best of the authors knowledge has never been directly tested in a polycentric model. 23 Given the difficulty of implementation, we propose a different procedure to test one of the underlying hypotheses behind the envelope approach, that centers are substitutes for each other. The envelope approach implies that land use densities at a given distance from a subcenter would be equal in any direction from a subcenter if there was no advantage to having access to both the CBD and subcenter locations. If a subcenter and the CBD are considered substitutes by the agents that would be willing to access either, then the density gradient anchored on the subcenter should have equal gradients between the CBD and the subcenter and away from the subcenter. If the subcenter and the CBD are considered complements by the agents that access each, we would expect to see a difference in the density functions by direction. The density gradient toward the CBD would be flatter than the density gradient on the far side (away from) of the subcenter. Therefore an indirect test of the hypothesized economic links between each subcenter is to empirically test whether or not density gradients are constant in different directions around each subcenter. 14
To operationalize our test we estimate single-node negative exponential density functions centered on each of the subcenters. We allow population and employment density functions to have different slopes in the direction toward the CBD compared to otherwise as shown in Equation (2) below. N A (2) DEN = α e o e ( γ NEAR DST γ AWAY DST) u where DEN is population or employment density around a particular subcenter, DST is distance in miles to the subcenter, NEAR is a dummy variable indicating if a parcel lies in an area toward the CBD (1=yes), and AWAY is a dummy variable indicating if a parcel lies in an area away from the CBD (1=yes), and u is an error term. Multiplying the two dummy variables by DST creates the two slope dummy variables, NEAR DST and AWAY DST. To test hypotheses about economic links between the CBD and each subcenter, we examine whether a density gradient is of equal magnitude on each side of a given subcenter, that is whether γ N equals γ A. 24 In the estimation, we spatially restrict the zones of influence around each subcenter by limiting the data in each regression. In general, we define the zone as that area in a concentric circle of radius, r, around a subcenter, where r is equal to the distance between that subcenter and the CBD. Therefore we define as NEAR all census tracts in the zone falling within an arc of radius r from the CBD. AWAY is defined as those census tracks in the zone that are not NEAR. 25 The results of our examination of the economic links between each subcenter and the CBD are presented in Tables 3 and 4. Table 3 presents estimates for population density and for employment densities disaggregated by ten industrial sectors. Table 4 examines population and 15
employment densities broken down by four broad occupational groups. By looking at both population and employment densities we can examine the relative roles (if any) of inputs and outputs in linking the CBD to each subcenter. Further, we use the industrial linkages to speculate about whether each subcenter serves the CBD, or instead whether each subcenter services its own set of markets, in which case the complementarities with the CBD may be more varied than if a subcenter simply serviced the CBD industries. The empirical results support the perception that four out of the five subcenters in the Houston area are economically linked as complements to the CBD. First, looking at the employment densities based on total jobs, all five subcenters have negative and significant coefficients on the directional distance variable AWAY DST, while the coefficients on NEAR DST are negative and statistically different than the away direction, or are positive and insignificantly different from zero (Table 5). Tests that the coefficients are equal show that all subcenters except for Clear Lake are strongly tied to the CBD, since the near CBD coefficients are smaller in absolute value, or even positive, compared to the away coefficients. 26 That Clear Lake appears unconnected to the CBD, at least relative to the other subcenters, is demonstrated more thoroughly when total employment is disaggregated by industry and occupational groups. Hypothesis tests show that Clear Lake is independent of the CBD for all ten industrial sectors as well as the four occupational groups, in that no statistically significant difference in the distance slopes toward or away from the CBD is found. Clear Lake is the area close to NASA, initially created by government funding decisions. There seem to be two possibilities, although ones we cannot test, for why Clear Lake is not linked to the CBD. One is that the industries in the NASA area have no relationship to the industries downtown in either the 16
input markets or output markets. 27 Alternatively, the recreation possibilities in Clear Lake are such to cause the subcenter to be independent from the CBD since residents value nearness to Galveston Bay and the Gulf of Mexico rather than access to the CBD. If it is true the amenity values of Clear Lake motivate location without linkages to the CBD, the amenity values must be sufficient to compete with demand for closeness to the CBD. The considerable distance of Clear Lake from the CBD would help in this case, since there are many alternative areas equally close to the CBD for those who have no demand for the Clear Lake attributes. 28 That the Galleria area lies on a line between Carillon and the CBD may affect the results for both subcenters, and areas considered near to the CBD for Carillon may be on either side of the Galleria. 29 Nonetheless, for no industrial sectors nor occupational groups are there equal coefficients on the two directional distance variables for Carillon. 30 Thus this subcenter appears very strongly linked toward the CBD, as well perhaps as the Galleria. The remaining three subcenters, the Galleria, Greenspoint and the Ship Channel, also show significant differences between the near and far coefficients for most, but not all, industrial and occupational groups. For the Galleria, seven of the ten industrial sectors show statistically significant links to the CBD, the exceptions are in mining, construction, and FIRE. Thus the linkages appear to be in industries that represent exports potentially to the rest of the world, such as manufacturing, as well as in support areas such as firm services and public administration. That there is no linkage in mining is on the surface surprising, since both the CBD and the Galleria have significant employment shares. On the other hand, the mining industry (Houston s most important relative to other cities in the nation) appears to be highly diversified across the city, for example all the subcenters show considerable employment shares. 31 Thus it may be that 17
the mining industry is large enough that there are no specific locational advantages to any one area within the city that outweigh potential congestion, or other forces that limit agglomeration economics. Greenspoint shows significant linkages to the CBD in all industries, again with the exception of mining. The Ship Channel Corridor, on the other hand, shows only four statistically significant industrial sectors linked to the CBD, firm services, consumer services, mining, and wholesale trade. Five other industries including manufacturing, transportation, utilities, FIRE, and public administration, however, nonetheless have large differences in the distance coefficient estimates (they are of opposite signs) despite that they are estimated with large standard errors (especially the near coefficients). Thus there is some suggestion in our results of a slight tendency to specialize, in that there is a major industry group omitted from the statistically significant linkages in all of the subcenters excepting Carillon; mining is omitted from the Galleria, manufacturing (weakly) is omitted from the Ship Channel, and mining is omitted from Greenspoint. Nonetheless, the industrial sectors with statistically significant linkages between each of the subcenters and the CBD are broad, suggesting at most a very mild degree of specialization. Looking at population density allows us to glimpse how consumers view the economic links between the CBD and each subcenter. The story becomes a bit more complicated, however, since a consumer s choice of location is dependent on many factors besides accessibility to employment, including amenities, school quality and other public services, tax considerations and neighborhood characteristics. Moreover, accessibility may have multidimensional attributes as consumers may value access to centers for entertainment and 18
shopping as well as employment. Nevertheless, looking at the single-node population density functions around each center is instructive. It appears that consumers view the Ship Channel Line and Clear Lake as being independent of the CBD. That is consumers do not differentially value access to the CBD over access to either the Ship Channel or Clear Lake. On the other hand, it appears that consumers view the other subcenters as complements to the CBD, in that they differentially value access to both the CBD and relevant subcenter over access to just the subcenter itself for the Galleria, Carillon and Greenspoint. V. Polycentric Density Functions and Intra-subcenter Geography Given the above discussion, a reasonable specification of a polycentric density function must allow for potential complementary interactions between employment centers. To do so, a specification must have the characteristic that multiple centers affect the density at a given location. Two specifications that possess this characteristic are the additive form and multiplicative form generalizations of the negative exponential (AAS 1998, Heikala 1989). The additive form allows all centers to influence the density at a given location via specifying the sum of several negative exponentials: DST (3) DEN e i i = α γ + u C i= 1 i where DEN is the population or employment density at a given location, DST is the distance to employment center i, C is the number of centers (including the CBD and the subcenters), α i and the γ i are parameters to be estimated, and u is an error term. While theoretically appealing in that 19
subcenters are related as complements with the effects diminishing with distance, econometric considerations call this form into question. Even though Small and Song (1994) successfully estimated the additive form for Los Angeles, AAS (1998, p.1442) report that convergence problems are often encountered in the nonlinear techniques required to estimate the additive form. Convergence difficulties were experienced by McMillen and McDonald (1998a, p. 171) and ourselves with attempts to estimate the polycentric additive form. To overcome the difficulties with the additive form, we instead estimate the multiplicative polycentric density function as below: (4) DEN = αo e C i= 1 γ DST i i e u where as before DEN is the density of population or employment, DST is the distance to employment subcenter i, C is the number of centers, α 0 and the γ i are parameters to be estimated, and u is the error term. The multiplicative form allows the subcenters to be linked in a complementary manner because the density at each location depends on distances to all centers, albeit in a more complicated manner than that in the additive form. The multiplicative form offers both advantages and disadvantages compared to the additive specification. First, the estimation of the multiplicative form is easier: by taking the natural log of both sides, it can be estimated with standard linear models. However, the specification has a disadvantage in that the density at a particular location could potentially be driven to zero if it was extremely far from even one subcenter 32. Any estimation of the multiplicative form, must overcome such a potential mathematical problem. One approach would be to limit the spatial extent of the influence of certain subcenters by expressing distance 20
in an inverse form as has been used by McMillen and McDonald (1998a, b). Another approach, which we adopt, is to spatially limit the zones of influence of a subset of centers. If in fact the spatial influence of a subcenter is limited, a specification that tests for the influence of a subcenter beyond its true influence will result in biased estimates, because the farthest out areas will be influenced by other subcenters or by the CBD. Conversely, if the market influence of a subcenter is specified to be overly narrow, the point estimate on the density function will be inefficient, but not biased. 33 For example, when we estimate Equation (4) and allow each subcenter is to influence the entire metropolitan area, we find distance to the CBD to be statistically insignificant as an explanation for density, and that many of the distance to subcenter coefficients are positive. In general we restrict the zones of influence (market areas) of each subcenter to be circles of about 24 miles in radius. Three exceptions exist in our treatment of market areas. First, the CBD is allowed to influence all tracts. Second, we restrict the Ship Channel Corridor to affect only the East side of Houston, defined roughly as those census tracts lying in the 90 degree angle bisected by the Ship Channel with the CBD as vertex (about 1/3 of the Census tracts). And third, the Galleria is allowed to affect only the West side (defined as not East ). While the market areas are substantial, the approach implies that no subcenter is allowed to influence more than about one-half the city (with the exception of the Galleria that affects about 2/3 of the tracts). Experimentation shows defining the market area too narrowly obscures any influence of the subcenters. 34 We use the results of estimating Equation (4) to explore two important aspects of the economic geography of a city that allows full complementarity between centers. First we explore how to best define the shape of a subcenter. That is, we examine whether each subcenter 21
can best be characterized as a point (area), corridor, or ring in the context of the multiplicative form. Second (and presented in the next part of the paper), we explore the relative complementarity between the subcenters and the CBD, and between the subcenters themselves. The results of estimating Equation (4) for population and employment densities are presented in Tables 5 and 6 for four separate specifications. The first two columns examine how different geographical definitions of the Ship Channel affect density, and the last two columns examine how different geographical definitions along the circumferential highways affects density. Our preferred specification, labeled Model B, is in column two of both tables. To summarize, we find the corridor specification of an employment subcenter works well for the Ship Channel corridor, although not so for our the ring specification of the loop highways. Turning to the details of Table 5, our preferred model, Model B, shows that while the CBD is the most important factor determining population density, two of the point subcenters, the Galleria and Clear Lake, are important as well. Only Greenspoint (the north subcenter) and Carillon (the far west subcenter) are found to have no significant effect on population density. The interesting finding, however, is the Ship Channel as a corridor appears to have a more pervasive impact on population density than do the three separate Ship Channel area subcenters, Baytown, Pasadena and LaPorte. 35 The first column, Model A, shows the estimation results when the three Ship Channelarea points are added to the density function which includes the Ship Channel corridor. Only the LaPorte area has the expected negative sign on distance, while the Baytown area is found to be a population nadir as it has a positive sign. The third area, Pasadena, is found to have no significant effect on population. Further, when all three separate areas are included in the 22
regression, we find that the coefficient on distance to the Ship Channel corridor is not significantly different from when the three areas are excluded (Model B), and remains significantly different from zero. Our conclusion is that the entire corridor is a better description of the Ship Chanel subcenter than is any particular point near the Ship Channel. And because the entire 25-mile Ship Channel grants ocean access, it would be surprising if the reverse were found, as there is a negligible difference in ocean-bound transportation costs along the line. Further, the industrial plants located along the Ship Channel require land as an input, which results in a more spatially dispersed concentration than is the case, for example, with office workers in the CBD. The third and fourth columns in Table 5 test whether a similar result can be found for the circumferential highways. In contrast to our Ship Channel corridor results, we find the individual employment subcenters are much better at explaining population density than are the ring highways. Comparing Model C to Model B, we find the influence of the Galleria is not reduced by inclusion of Loop 610, and that there is not a significant influence of Loop 610 on population density. Similarly, the influences of Carillon and Greenspoint areas are not impacted by the introduction of Beltway 8 into the regression, and neither the points along the Beltway (Carillon and Greenspoint) nor the Beltway significantly influences population density. Model D shows that even removing the point subcenters along the circumferential highways (the Galleria, Carillon and Greenspoint) does not draw the ring highways coefficients to significance. Again we are led to prefer Model B, which allows the entire Ship Channel corridor to affect population density, but which only allows the three separate points along the loop highways to affect population density. 23
As an additional test of the influence of the alternative employment subcenters, we present estimation results for employment density in Table 6. First, we find the well known result that employment gradients are steeper than population gradients (O'Sullivan, 2003). More important, however, these results confirm the earlier finding that specifying the Ship Channel as a corridor (Model B) is preferred to using the three separate employment subcenter points in addition to the line, or instead of the line. Further, we find support for specifying the areas around the loop highways as subcenter points, rather than specifying each highway loop as a subcenter. While coefficients on Loop 610 are significantly different from zero in Models C and D, the coefficients are positive instead of the theoretically expected negative sign, and thus are not supportive evidence of designating the entire Loop 610 as a subcenter. The coefficients on Beltway 8 remain statistically insignificant regardless of whether or not the points on the Beltway (Carillon and Greenspoint) are included. 36 And this is despite that, for employment density, only the influence of Carillon is significant while Greenspoint is not. Our conclusions from these results are that the Ship Channel Corridor is a subcenter, but that the ring freeway lines are not. Our suspicion is that access to the Ship Channel is valuable all along its path. The circumferential freeways, however, do not appear valuable enough by themselves to cause employment concentrations. That is, it appears other factors are needed to entice firms to agglomerate along their entire length. For example, the Galleria subcenter is the second most important in Houston after the CBD, and it is not only on a ring freeway (I 610), but also on a major arterial freeway (US 59). Similarly, Greenspoint is on the farther out ring (the Beltway), but also on another major arterial freeway (I-45). 24
VI Relative Complementarities between Centers The polycentric specification (4) allows us to interpret the complicated polycentric density function for Houston is detail. An important issue is the relative degree of complementary link between each subcenter and the CBD and amongst each of the subcenters. The issues are explored by examining the generalized density gradients associated with each subcenter based on geographically correct assumptions. The polycentric generalization of the density gradient, or proportional change in density, must be based on a total derivative, rather than a partial derivative because of the mathematical nature of the two dimensional structure of the city on a plain. If an agent moves away from subcenter one, then the distance to the CBD and to the other subcenters most likely will not stay constant but will also change. As a consequence, the generalized density gradient associated with center one depends on the weighted sum of all the γ coefficients, where the weights are how distance to individual centers change when the distance to center one changes by DST 1. That is (5) dden ddst 1 Den ddst2 ddst3 ddstc = γ1 γ2 γ3... γc ddst ddst ddst 1 1 1, where C =last center. The specification allows a rich description of the density gradient function and allows for different values in different directions from any given center. We first investigate the relative complementaries between each subcenter and the CBD by calculating Equation (5) for a move toward the CBD. A flatter density gradient implies a 25
stronger tie to the CBD, and hence a greater degree of complementarity. Because the gradients are not constant as in a monocentric model, we calculate the density gradients for each of the subcenters at two logical alternate locations. First we start at each subcenter, and move toward the CBD (this allows different distances from the CBD, but the same distance from each subcenter). Second we hold constant the distance from the CBD and then move toward the CBD (this allows different distances from each subcenter, but the same distance from the CBD). Table 7 reports the polycentric density gradients for the two experiments described above for both population and employment totals. Given that the absolute value of the density gradients are less for the Galleria, we conclude that the complementary link between the CBD and the Galleria is stronger than that of between the CBD and the other subcenters. Table 8 reports the polycentric density gradients examining the links between the Galleria and the other subcenters to see to which other subcenter it most closely tied economically. We follow the same approach as for the CBD-subcenter links by calculating the resulting gradient at a constant distance from each subcenter along a ray toward the Galleria, and at a constant distance from the Galleria along rays between each subcenter and the Galleria. We could do similar calculations anchoring on each subcenter, but in the interest of space, do not report results here V. Summary and Conclusions This paper examines the nature of, and impetus for, multiple employment subcenters in Houston, an urban landscape that fits as closely as any area of which we are aware the flat- featureless-plain assumption of the classic urban model. We thus hope the empirical features we 26
uncover are of assistance at building a theoretical model of the formation of employment subcenters. A contribution of our work is an analysis of how subcenters are economically linked to the CBD, research that has heretofore been scant (AAS, 1998). What is unusual about our research is that we analyze economic links by looking at characteristics of employment and population density functions, in particular examining whether or not directional gradients of the density functions show linkages to the CBD by industry and occupation. If economic links are important between the CBD and the subcenters, then the economic growth or decline of the CBD would be expected to have important repercussions on the economic health of the other subcenters (Voith, 1998). We have found strong evidence for complementary economic linkages between the CBD and all but one of the subcenters, Clear Lake. Further, population density shows linkages for all subcenters except the Ship Channel and Clear Lake. Based on the different employment mix evident for the Ship Channel corridor, it appears to serve an industrial role and thus might be expected to have a different economic role than the other subcenters. The Clear Lake area, on the other hand, exhibits several traits that make it appear to be independent in many ways of the CBD, both because of differences in its industrial employment mix and because there is no evidence of even population linkage to the CBD. We find that employment subcenters that are more specialized in industries not well represented by the CBD, especially Clear Lake, are found to have weaker links to the CBD than those that seem to mirror the CBD. 37 What is interesting, however, is it is difficult to categorize the other four subcenters by industrial or occupational concentration, and combined with the evident value firms and residents appear to place on joint these areas seem to closely mirror the CBD. Thus it would 27
appear that theories that explore the limits to agglomeration economies may be the most fruitful avenue for explaining the continued rise across the country of employment subcenters, but that care should be given to alternative forms and motivations as well. Another contribution of our work concerns our exploration of the polycentric nature of the Houston area. We explore the various specifications of polycentric density functions found in the literature and find a preference for the multiplicative form. We then used the multiplicative form to search for the best way to represent the geography of employment subcenters. Our examination of subcenters reveals that the search in the literature for particular areas of employment concentration seems well founded, but needs to be expanded to include corridors as well as points. Specifically, we find the entire corridor along the Ship Channel functions as a subcenter, and better fits the polycentric density function than do individual point subcenters at discrete locations near the Ship Channel. The finding of the corridor as a subcenter rather than rings as subcenters may be applicable to other urban areas. As mentioned earlier, the corridor along Wilshire Boulevard in Los Angles from Gulliano and Small (1991) could be considered as one large subcenter rather than identifying several individual points. Depending on the nature of the industries along a corridor such as a port, a corridor as a subcenter is theoretically attractive because the marginal transport cost to the rest of the world may be low, while the industries along it may be land intensive. Subcenter rings would also appear to fit such a criteria; however, we do not find empirical evidence that the entire perimeter of the circumferential highways in Houston work well as subcenters. Instead certain points along the rings, usually at intersections of major transport thoroughfares, are empirically better fits for subcenters. 28