Socio-Econ. Plan. Sci. Vol. 1, pp. 283-295 (1968). Pergamon
Press. Printed in Great Britain
A MODEL FOR ALLOCATING
IN A STATE T. R. LAKSHMANAN CONSAD Research Corporation,
Pa. and the University of Pittsburgh
decades there has been a prodigious and continuing increase in the demand for various public facility investments in urban areas, stemming from the sheer increase in population, higher incomes, greater mobility and expanding leisure. This escalation in demand has placed acute pressures on the current supply of various public facilities and has brought about continuing problems of planning and resource allocations. For many of these public facilities the requirements for long lead-time planning suggests that plans will have to be worked out and reliably implemented so that the urban areas can evolve systematically, consistent with desired human activity patterns and a spectrum of public tastes. This need for long-range developmental planning has been particularly evident in the case of a highly urbanized small state such as Connecticut located in the Megalopolis.* Consequently, there has been an attempt at the State level to anticipate the broad spectrum of public needs and prepare a general development plan for the State. In fact, this attempt to develop a State plan is the vanguard of a general movement among the states to redefine their role as a bridge between local and Federal government when dealing with planning issuesi- Wags have claimed that our three-level federalism leaves “the national government with the money, local governments with the problems and the states with legal powers.” In recent years, Federal money has flowed in response to this situation in various forms, largely directly to the local urban areas. The various functional (e.g. transportation, health, education, etc.) plans developed in urban areas have generally reflected the Federal requirements. This has had the effect, in the view of some states, of the development patterns in their urban areas of being implicitly guided from the Federal level. In highly urbanized states, the development goals are thus largely set, albeit implicitly, by the Federal government with the states being essentially in the role of onlookers. One of the major concerns in the current discussions of “creative Federalism” is the strong desire for the State governments to play a more central role in guiding development patterns within their boundaries. This implies anticipation of future growth and development in the State, setting of development goals, design and evaluation of alternate development plans and the preparation of a “policies” plan for the State. Such a State plan would * The study presented in this paper was carried out for the Connecticut Inter~gional Planning Program whose director has kindly permitted this reporting. The author would Iike to take this opportunity to thank his former colleagues at Alan M. Voorhees and Associates for their help during the course of this study. t See Committee for Economic Development, Modernizing State Government (July 1967). 283
T. R. LAKSHMANAN
provide the framework for regional and urban development plans and various functional programs in the State. A number of states such as New York and Pennsylvania are currently engaged in such an endeavour. Connecticut has been a pioneer in the state planning movement. The Connecticut Interregional Planning Program (CIPP), a joint effort of the Connecticut Development Commission, Department of Agriculture and Natural Resources and Connecticut Highways Department, has addressed itself to the task of developing a comprehensive development plan for the State. CIPP has carried out a fully articulated planning program of identification of goals and objectives of development, deriving therefrom a set of alternative state development plans which will be evaluated in terms of their impacts and a “preferred” State plan selected. The elements of this plan will encompass the economy, land development patterns, transportation facilities, open space and outdoor recreation. This paper is concerned with the description of a model that describes the patterns of land development in the State. This urban growth or land use model is capable of allocating land-using activities-population and non-agricultural employment-in a parent region (e.g. a state) to component sub-areas as stipulated by locational interrelationships built into the model in a policy-sensitive framework. This urban-growth or land-use model is intended to: (a) Provide estimates of the level and structure of the economy of the towns of the State. As such, it provides a tool for measuring the scale and location of demand for transportation, as well as for other services and facilities; and (b) Determine, to the extent feasible, the modifications in these trends by various physical planning policies available to the State of Connecticut. As such, it can help in estimating impacts of policies implied in alternate urban land development plans being prepared by the Connecticut Development Commission.* The model recognizes two geographical levels-the town and transportation zone-for analysis. Allocation of the State’s growth in various activities was achieved in two sequential steps: first from the State to towns, and then from the towns to transportation zones. The model described at length in this paper is the “town model” which describes the share of the state’s growth that each of the component 169 towns attracts. The estimates of economic activities at the town level were used as controls for a simpler allocation model called “the zone model” which distributed the activities to the zones (not described here). This paper begins with a formulation of the town model and a clear statement of the relationships postulated. A description of the statistical work related to the parameter estimation and the town model performance over a historical period follows next. The paper proceeds then to the detailing of the applications of the model to generate projections of employment and population for the future at the town level. The final part of the paper provides a very brief description of the development and use of the zone model.
Economic growth in Connecticut, or for that matter in most parent regions, varies widely among different component sub-areas. Some sub-areas have expanded rapidly over time drawing in persons, materials and capital in great quantities, while others are in various * Such purpose.
are provided by the economic study which developed a state I-O model for this
A Model for Ailocating Urban Activities in a State
stages of relative stagnation and decline. It is to the description of and understanding of the complicated relationships behind this differential growth of subregions that this model is directed. A useful starting point is to describe the measure of economic growth used in this study. The discussion of this measure as an indicator of differential growth of sub-areas will be followed by an enumeration of land-using activities, and a statement of relationships behind the differential growths of sub-areas. Measures of growth The measures of economic growth of relevance in a land-use model are those associated with the volume of economic activities-population growth, employment changes, etc. When attention is focused on volume of activities, different measures of regional economic growth that might be used furnish rather different descriptions. Thus, somewhat different patterns may emerge if growth is measured by absolute increases in population and employment or by relative increases of population and employment. To obtain a reasonable picture of the growth of sub-area, both dimensions-absolute numbers and relative rates-of growth must be observed. These two significant dimensions of growth of population and employment are combined in the analytical framework used in this study, and the measures derivable therefrom. To understand economic growth within the State of Connecticut, or for that matter any parent region, it appears necessary: (I) to relate the sub-area’s development to developments in the parent region as a whole; (2) to “weight” its growth in relative terms, i.e. in terms of departure from the parent region norm; (3) to examine the characteristics of its growth patterns; and (4) to evaluate its changing position with regard to its ability to hold and attract persons and industries. An analytical framework appropriate to an understanding of this nature and providing a useful measure of economic growth of sub-areas is the shif analysis.framework.* A brief development of the shift analysis framework is provided here. The following notation will be used E = Level of activity (e.g. Employment, Population) i = Sector of activity j = Geographical unit (e.g. Town, Transportation zone) 0, t, t -I- 1 = Time periods The net change in population or employment between two points in time (0 and t) in a sub-area (j) in Connecticut can be stated as follows: Net Change (N.C.) = I&t - EQ-,
(1) This net change in a sub-area can be viewed as composed of two components. The first component of net change in any sector is that amount that would result if that sub-area * The detailed articulation of the shift analysis framework is found in: Harvey S. Perloff, E. S. Dunn, E. E. Lampard and R. F. Muth, Regions, Resowces and Economic Growth. The Johns Hopkins University Press, Baltimore (1961), Part II. See also Lowell D. Ashby, ipegionul Change in a ~#tional Setting, St& Working Paper in Economics and Statistics No. 7, U.S. Dept. of Commerce (April 1964). Earlier studies that have used the shift technique in organizing data are: Wilbur Zelinsky, Econ. Geogr. 34,95 (April 1958); and Victor R. Fuchs, J. Reg. Sci., 1 (Spring, 1959).
T. R. LAKSHMANAN
changes (grows or declines) at the same rate as that sector in the State as a whole. component is defined as Proportional Share (P.S.) and is given by
The second component of change is the amount due to the growth rate of the fth subarea in the ith sector being faster or slower than the growth rate in that sector in Connecticut as a whole. It is described as DzJTerentiul Shift (D.S.) or Competitive Shift (C.S.) of the ith sector in the jth sub-area and is written as
03 = &lo
Eijt - &o _~ &t - &u
= Eijt - Eijo
It can be seen algebraically from (l), (2) and (3) that P.S. + D.S. = N.C.
shifts for each sector sums to zero over all geographical
This reflects the fact that the differential shift relates each sub-area (town) to the State’s performance. The towns that grew faster than the parent region have positive values of Du, and those that grew slower than the parent region have negative values of Dv---the latter areas being at a disadvantage with respect to the former. Thus, D~J is the “competitive” element of the town’s growth. When Dsr is summed across all the towns, the State of Connecticut is, in effect, compared to itself. Therefore, no differential shift arises. The measure of economic growth of towns in Connecticut used in this study is the Differential Shift or Competitive Shift in each sector. The land use model will predict the differential shift of each sector in each sub-area, in terms of two sets of variables termed endogenous and exogenous variables. The endogenous variables are those that are to be predicted (i.e. differential shifts) by the model. The exogenous variables are those predetermined, or independent variables. The structure of the model will become clearer in the next section, but it may be briefly pointed out that the differential shift (endogenous variable) of one sector will be predicted in terms of differential shifts (endogenous variables) of other related sectors and several related exogenous variables so as to incorporate interdependencies in economic activities. * Since the differential shifts of towns sum to zero by sector, its use as a dependent or endogenous variable provides good accounting control when used for projection purposes. Further, since differential shift is a relative (competitive) measure of growth in a sector expressed in absolute terms, it is better described in terms of various town characteristics * Also, it will be seen that when an endogenous variable is lagged (expressed for an earlier point in time), it can be also used as an exogenous variable.
A Model for Allocating Urban Activities in a State
(which will be the independent variables in the model) than net change which includes the effect of changes in the sector through state and extra-state factors. By taking the proportional
out of net change in a town deriving
shift, such state
2.0 and extra-state factors are screened out in the description of the town’s growth. In such a context, the town’s characteristics (independent variables) may provide a better explanation of the competitive growth of a town. When the model is used to predict Ds~ to a future point in time say t + 1, it is an easy matter to obtain the net change of the town. Proportional Share for town j in sector i will be given by Edjt(Ett_;; Add to (4) the Dtjt+l predicted The various economic activities will be briefly described first.
to obtain net change (,?&, - &t) whose differential shifts are used as dependent
The activities Six employment sectors and three subgroups of population form the nine activities with which the model is concerned. The employment sectors used in the model are : Manufacturing; Retail and wholesale; Personal services; Business and professional services; Construction; Other. It will be noticed that the goods-producing sectors are aggregated into one sector -manufacturing-while five non-goods producing sectors are recognized. The resident populations in the various towns are disaggregated into three sub-groups using family income as the criterion. There are two ways in which the distribution of income is identifiable. There is the frequency distribution describing the number of households in the State earning different levels of income. Then there is the manner in which this distribution differs among the 169 towns in the State. Both of these distributions were used in the classification of the towns’ households into the three groups in the following manner
6) The cumulative
frequency distribution of family income for the State was prepared for two points in time (1950 and 1960) from Census tapes. Tertile class limits* were then obtained for each time period. (ii) These tertile limits of the State income distribution were then applied to the income distribution in the towns to interpolate and estimate the number of households in each tertile. The population in each tertile in each town was thus obtained for the censal years 1950 and 1960. The computations listed below provide for 1960 and 1950 the three sectors of population: Population in the low income tertile; Population in the middle income tertile; Population in the high income tertile. * The three tertiles will contain the families in the lowest, middle and highest thirds, respectively, the income distribution. The tertile limits used were: 1950 1960 Low income tertile Middle income tertlle Upper income tertile
$2850 $2850-$4499 $4500
$5600 $5600-$8499 $8500
T. R. LAKSHMANAN
From the data on the six employment sectors and the three population groups for two points in time, the differential shifts for all nine sectors were computed by using a specially written computer program. * These nine differential shifts form the dependent variables of the Connecticut Land Use Model. The structure of the model The Connecticut Land Use Model is formulated as a set of simultaneous equations where each equation describes one sector. The characteristics of the simultaneous equation approach will be explained first. The simultaneous equation approach is a generalization of the multiple regression in the following manner. In multiple regression one and only one variable in each equation can be chosen as the dependent variable to be explained by the independent variable. Such a choice can be often arbitrary in view of interdependencies of economic activities. For example, in the fringes of a growing urban area, retail and service activities may follow populations and more population may settle in view of higher level of service amenities. Over a period of time, is service employment the dependent variable or population ? Actually, both are dependent variables and the method of multiple regression equation cannot relate them except in a prespecified sequential manner. The simultaneous equation approach is helpful in such cases where the relation in question is one in a system of relations that hold simultaneously. In our example, the regression coefficient estimates in the population equation will be dependent on the form computed in the retail employment equation. Thus, population and various employment sectors will be described in the model as a system of simultaneous linear equations, which all together provide a more valid description of economic growth in the sub-area than the multiple regression approach. The crucial advantage is that interdependencies in the location of various economic activities can be treated in the simultaneous equations approach. The Connecticut model is (as stated above) a nine equation system; one equation for each of the following activities: Construction employment Retail and wholesale employment Business and professional services employment Personal services employment Manufacturing employment Other Employment Population in Low Income Tertile Population in Middle Income Tertile Population in High Income Tertile
(SIC 15-17)t (SIC 50-59) (SIC 60-62, 89) (SIC 63-88) (SIC 19-39) (SIC-all other)
In each equation of the model the differential shift of that activity between two points in time is the dependent variable. The structure of the model is stated verbally below. For a symbolic version see Table 1. * The computer program for calculating differential shifts was written by the staff of the Connecticut Development Commission and the Connecticut Highways Department. t The codes used here are the classes of industries referred to in the Standard Industrial Classification (SIC) Manual prepared by the U.S. Bureau of the Budget.
A Model for Allocating Urban Activities in a State TABLE 1. THE MODEL
E D A H
= = = =
M = S = B = P = g = k = m = j = 0 = t = a, b=
Level of activity (Number of employees, Population) Differential shift Potential or accessibility of a town to an affecting activity Holding capacity for activities (Maximum level of activities restricted In conjunction with the above symbols, the following subscripts Manufacturing sector Services sector Business and professional service sector Population Tertile of income distribution (g = 1, 2, 3) Industry group in the employment sector Number of industry groups (k = 1, 2, i.e. . .6) Town in the state Beginning of the growth period End of the growth period Parameters
The Model (Manufacturing) Dr = al C 06 + b, Ej + b, X E&, + b, Aj”,-t bp ffy -t b, k
D$ = a, Dy + a, C D~j + b, E&, + b, Ai + b, k
(a) In the goods-producing (manufacturing) sector the differential between two points in time 0 and t) is expressed as a function of
shift in a town (j)
(1) the sum of the differential shifts in all non-goods-producing sectors in that time interval in that town (2) the total employment in goods-producing sectors in that town at the beginning of the time interval (lagged employment) in all non-goods producing sectors at the beginning of the (3) the employment time interval in that town employment in that town at the begin(4) the holding capacity for manufacturing ning of the time interval in Business and (5) the index of accessibility (Aif) of that town to employment Professional Services at the beginning of the time interval
T. R. LAKSHMANAN
This index of accessibility, as follows :
in the highway
Ai5 = C Elk djkCQ
where Eik = The level of an affecting activity (k = j for intrazonal activity)
in the town k
dik = Shortest travel time on highway network between towns j and k; co an empirically derived exponent. In practice, d,,co is supplied as a trip propensity function called F factor usually of the form F = uej”k”. The parameters of this function are obtained from the gravity model run of appropriate trip interchanges. The variable in the manufacturing sector uses the employment in the Business and Professional Services sector for Etk in (5) above. Other accessibility indices may use population or total employment as required. The index of accessibility thus derived is a potential measure and used as a surrogate of average interaction or transport costs. (b) The differential shift in each of the non-commodity-producing sectors-construction, retail, personal services, business and professional services and other-is expressed as a function of: (1) The sum of all the differential shifts in the non-goods-producing sectors in the time interval in that town (2) The differential shifts in the goods-producing sector in that town (3) The employment at the beginning of the growth period in that sector (lagged) in that town (4) The index of accessibility of the town to all population at the beginning of the growth period (c) The differential shift in population in an income tertile is expressed as determined by: (1) The that (2) The (3) The town (4) The (5) The (6) The
differential shift in the population in the next higher income tertile in town (for the high income tertile this variable is not obviously applicable) differential shift in the goods-producing sector in that town sum of differential shifts in all the non-goods-producing sectors in that sum of the differential shifts in all population tertiles in that town index of accessibility to population in that income tertile in that town holding capacity for additional population in the town.
Certain characteristics of the structure of the model may be mentioned. The interdependent nature of the several equations whereby a variable that is dependent in one equation is “independent” in another must be clear. In this framework, the interdependenties in location of economic activities can be simultaneously treated. The notion that activities show spatial associations resulting from the nature of inter-industry linkages is thus built into the model. These spatial linkages are treated in terms of absolute levels of employment and the measures of accessibility to affecting activities.
A Model for Allocating Urban Activities in a State
The effects of internal economies of scale are expressed by the time-lagged levels (at the beginning of the growth period) of sector employment or population. The multiplier effects are treated by the use of differential shifts in other industries as “independent” variables. The accessibility to population is a measure of a town’s attraction as a market and source of labor force. The accessibility to the Business sources is a measure of the “spawning” potential a town offers for small manufacturing plants that utilize external economies of scale by sharing a set of business and professional services. The accessibility to employment is a measure of spatial disposition of residential sub-area to job opportunities in Connecticut. The notion that households display an upward mobility is expressed in using the differential shift in the next higher income group in that town as “independent” variables. Further, since the location of a household group is influenced by the bundle of amenities (defined broadly to include lot size, housetype, land costs and peer group characteristics) required and afforded by it, proximity to their “likes” is important. This tendency for proximity to their economic peers (since these amenities are purchased) is suggested by the use of an index of accessibility to population in their income group as a variable. Finally, both the growth in population and manufacturing employment are related to the respective holding capacities-a policy determined upper bound to population and manufacturing employment in the town. STATISTICAL
The locational notions postulated in the above model were then evaluated by their ability to reproduce a pattern of growth over a historical period. Towards this end, a program of the specification, collection, tabulation and analysis of data on historical growth patterns was initiated. Data collection The Connecticut Interregional Planning Program staff initiated and completed the collection and tabulation of data specified by the model. Specifically, the data collection focused on the delineation of a historical pattern of growth in employment and population by towns in the state. Thus, employment data was collected by two-digit SIC category by town for 1950 and 1962. The major data source was the records of the State Department of Employment Security on Covered Employment. The location and amount of the uncovered employment by SIC category for 1950 was obtained from the Connecticut Labor Department (CLD) estimates. The 1962 uncovered employment estimates were obtained by chasing down specific sources-Government employees, Railroads, Hospitals-and using CLD studies on uncovered employment. The income distribution by towns was obtained from the Census tapes and records. The population change by income tertile was computed by a simple program by the Highways Department. As indicated earlier, the special program was prepared and used to compute Proportional Shift* and Differential Shifts of various employment categories and population tertiles. * Proportional shift was calculated “Industrial Mix”.
in reality as the sum of two other quantities-“State
T. R. LAKSHMANAN
The Connecticut Development Commission developed the holding capacity estimates for population and manufacturing employment. The various accessibility measures were computed on a highway network (specially prepared) for 1950 by the Highways Department. Parameter estimation
The estimation of parameters was accomplished through the use of a (SHARE) Program-IB 9 FES-which provides for the step-wise application of increasingly advanced statistical techniques to mathematical models structured with many dependent variables interrelated and expressed in linear regression-like equations. This program provides options for obtaining parameter estimates by four different methods (in order of increasing complexity): (a) Single equation least squares; (b) Two-stage least squares; (c) Limited information estimation (Maximum likelihood); (d) Full information estimation (Maximum likelihood). The two-stage least square estimates are used in the development of the Connecticut model. These estimates provide what are described as the “structural” set of equations describing the location of economic activities in the towns. These are then converted into the “reduced-form” system, that is, a simultaneous solution of the first set for all dependent variables. The difference between the two sets of equations may be stated differently. While the structural set contains more than one dependent variable in each equation (as defined in Table l), each equation in the reduced-form set contains just one dependent variable, to facilitate prediction purposes. To forecast the future value of a dependent variable (e.g. population differential shift), the computation of the reduced-form equation permits the use of just the independent variables in that equation and their corresponding parameters. The parameter estimates, in general, conformed in relative magnitude and signs to a priori expectations. The multiplier effects of growth in related sectors on the growth of an activity are borne out as posited. The upward mobility of the lower income group and the affinity of the high income population to itself are indicated. So are the effects of the accessibility measures. The negative signs associated with the lagged values of the dependent variable sector levels is interpreted as indicating that older towns with larger levels of activities, and less room to grow, tend to grow slower than the State, resulting in negative differential shifts. This observation is supported by the positive coefficients associated with population and manufacturing holding capacities. It was also noticed that the regression coefficient show a high order of reliability as expressed by the ratios to their standard errors. This is particularly true of the equations using smaller numbers of independent variables where simpler interactions among the variable are possible. Figures l-2 provide a comparison of the observed differential shifts between 1950 and 1962 and the differential shifts obtained from the reduced-form equations. The observed shifts are on the X-Axis and the inferred on the Y-Axis. In some graphs, the plots are pushed to one corner because of one or two extreme values that have to be accommodated. It must be noted that the axes have often d$erent scales. It will be noticed that, generally, the model performance is encouraging though the equations relating to other employment which is a conglomerate residual category of employment shows rather noticeable departures from the observed values. Some large deviations on the graphs were investigated to identify any “unique locators” that cause the wide fluctuations. In the manufacturing employment, for instance, SIC 37,
A Model for Allocating Urban Activities in a State
T. R. LAKSHMANAN
A Model for Allocating Urban Activities in a State
Employment in the Transport Equipment sector including the Groton Pratt-Whitney Aircraft plant and the like was characterized by large So was the Insurance activity of Hartford. Thus it was decided to Insurance as unique locators which will be “hand allocated” outside
Sub-boat plant, the “lumpy” locations. handle SIC 37 and the model.
The land use model described in the previous section was used to develop projections of population and employment for the 169 towns in Connecticut for 1970, 1980, 1990 and 2000. Town projections
Since the land use model is an allocation model, it was used to distribute the growth to the CIPP prepared the projections of the State into towns. The economic consultants forecasts of population and employment by 25 categories for 1970, 1980, 1990 and 2000. * These forecasts have been aggregated into the employment categories relevant to the town model. The Connecticut town land-use model allocated all the employment categories listed in the State to towns except the “unique locators”. The State population growth estimated for the future was split into three equal parts to provide control totals for the population in each of the three income tertiles in conformity with the earlier definition of tertiles. The town projections of employment and population were then carried out under the following assumptions: First is that the land development density policies expressed in the current (1964) zoning and density policies assumed under current trends by the CIPP staff will also be in existence in the projection years, modified to the extent that the staff planners are aware of definite impending changes. Second, the highway network currently in existence will also be in operation in the projection years. In addition, the committed network of highways, as well as the set of additional freeways as specified by the Connecticut Highways Department, are assumed. Such assumptions of the future network were translated during the course of the projection procedures into indices of accessibility for future points in time. A computer program was specified and written for facilitating the projections of nine activities into 169 towns for four points in time. Essentially, this program (a) makes projections of activities through the use of linear models (given the reduced-form equations) and, (b) possesses the additional property of recycling these projections through successive points in time and for various alternative public policies. Though this program was specified and written for land-use projections, it is sufficiently generalized for making projections with linear models for other purposes such as recreation activities and trip generation.
* The employment forecasts were prepared through the use of an input-output model by Dr. Charles Leven and Connecticut Development Commission. See The Connecticut Socio-Economic Growth Model ClPP Staff Paper (1965).