World Bank Reprint Series: Number 249 Kyu Sik Lee A Model of Intraurban Employment Location An Application to Bogota, Colombia Reprinted with permission from Journal of Urban Economics, vol. 12 (November 1982), pp. 263-79. Copyrighted by Academic Press. World Bank Reprints No. 215. Michael Cernea, "Modernization and Development Potential of Traditional Grass Roots Peasant Organizations," Directions of Change: Modernization. Theory, Research, anid Realities No. 216. Avishay Braverman and T. N. Srinivasan, "Credit and Sharecropping in Agrarian Societies," Journal of Development Economics No. 217. Carl J. Dahlman and Larry E. Westphal, "The Meaning of Technologi- cal Mastery in Relation to Transfer of Technology," Annals of the American Academty of Political and Social Science No. 218. Marcelo Selowsky, "Nutrition, Health, and Education: The Economic Significance of Complementarities at Early Age," Journal of Develop- menit Economics No. 219. Trent Bertrand and Lyn Squire, "The Relevance of the Dual Economy Model: A Case Study of Thailand," Oxford Economnic Papers No. 220. Gersh-)n Feder and Knud Ross, "Risk Assessments and Risk Premiums in the Eurodollar Market," Journal of Finance No. 221. Bela Balassa, "Policy Responses to External Shocks in Selected Latin American Countries," Quarterly Review of Economics an.d Business No. 222. Choong Yong Ahn, Inderjit Singh, and Lyn Squire, "A Model of an Agricultural Household in a Multi-crop Economy: The Case of Korea," Review of Econiomics and Statistics No. 223. Emmanuel Jimenez, "The Economics of Self-help Housing: Theory and Some Evidence from a Developing Country," Journal of Urban Economirs No. 224. Thawat Watanatada and Clell G. Harral, "Determination of Economi- cally Balanced Highway Expenditure Programs under Budget Con- straints: A Practical Approach," Transport Research for Social and Economic Progress No. 225. George Psacharopoulos, "The Ecoromics of Higher Education in Developing Countries," Comparative Education Review No. 226. Katrine Anderson Saito and Delano P. Villanueva, "Transaction Costs of Credit to the Small-scale Sector in the Philippines," Economic Development and Cultural Chanige No. 227. Johannes F. Linn, "The Costs of Urbanization in Developing Coun- tries," Economic Development and Cultural Change No. 228. Guy P. Pfeffermann, "Latin America and the Caribbean: Economic Performance and Policies," Soluthw-t7estern Review of Management and EconiOmnics No. 229. Avishay Braverman and Joseph E. Stiglitz, "Sharecropping and the Interlinking of Agrarian Markets," American Economic Review No. 230. Abdun Noor, "Managing Adult Literacy Training," Prospects No. 231. Bela Balassa, "Shifting Patterns of World Trade and Competition," Grozjth and Entrepreneurship: Opportunities and Challenges inZ a Changinlg World No. 232. Johannes Bisschop, Wilfred Candler, John H. Duloy, and Gerald T. O'Mara, "The Indus Basin Model: A Special Application of Two-Level Linear Programming," Mathlematical Programnmintg Study JOURNAL OF URBAN ECONOMICS 12, 263-279 (1982) A Model of Intraurban Employment Location: An Application to Bogota, Colombia' KYiU SIK LEE Urban Development Department, The World Bank, 1818 H Street NW, Washington, D,C. 20433 Received March 6, 1981; revised May 18, 1981 A micro model is formulated to study the location behavior of manufacturing firms in urban areas. A bid-rent function is derived from the profit function and captures the firms' locational equilibrium situations. The theoretical model is ex- tended to a multinomial logit specification and estimated using establishment survey results for Bogota, Colombia. The survey included information on (1) attributes of the establishment such as plant space, and (2) attributes of the plant site such as access to markets. The estimated model is capable of predicting the location choices of different types of firms. 1. INTRODUCTION The work reported here is part of a World Bank urban study project. In this paper a theoretical model of employment location is formulated and extended to an empirical specification in the multinomial logit framework. In the descriptive phase of the study, the employment location patterns of Bogota, Colombia, and their changes were extensively analyzed using in- dustrial directory data. The analysis, performed in terms of births, deaths, and relocation of firms, revealed a high degree of employment location dynamics: both the birth and relocation rates were high and evidence of spatial decentralization of manufacturing employment was strong (Lee [9]). Although researchers have drawn attention to the need for modeling employment location behavior, the gap in this area remains unattended in the literature. The analytical work reported in the present paper is an 'Presented at the Econometric Society Annual Meetings, Denver, Colorado, September 5-7, 1980. Support for the work reported in this paper was provided by the City Study research project (RPO 671-47) funded by the World Bank. The views reported here are those of the author and should not be interpreted as reflecting the views of the World Bank or its affiliated organizations. The author thanks Maria Clara de Posada who conducted the survey of establishments and Jose Fernando Pineda who supervised it, M. Wilhelm Wagner and Leslie Kramer for research assistance, and members of the World Bank research staff for comments with particular appreciation for Gregory K. Ingram and Douglas H. Keare. Discussions with Professor Marc Nerlove and comments received from Professor Edwin Mills' seminar at Princeton University were helpful at the early stage of this work. Roger Schmenner provided valuable suggestions for designing the survey instrument. 263 0094-1190/82/060263- 17$02.00/0 Copyright 4 1982 by Academic Press, Inc. All rights of reproduction in any form reserved. 264 KYU SIK LEE attempt to model the location behavior of the firm and to explain observed patterns of employment location. For this purpose, a survey of manufactur- ing establishments was conducted in Bogota, a rapidly growing city com- parable to such United States cities as Phoenix and Houston. This paper presents estimation results based on the survey. The model is presented in the next section, the survey is then briefly described, and finally, the estimated results are reported. 2. A MODEL OF EMPLOYMENT LOCATION Consider T types of manufacturing firms in an urban area. The firm mnaximizes profits as a price taker in both product and factor markets. The firm uses a set of variable and fixed inputs to produce an output. The problem is to determine the optimum combinationi of inputs, including the lot size and the plant location, to attain locational equilibrium profits in an urban area. Consider a production function in the general form Q = f(L, X; Z) () where Q is the output, L the lot size, X a vector of other inputs such as labor, and plant and equipment; Z a vector of site characteristics that are independent of lot size and can be considered as "local public goods"2 such as the quality of public utility services, accessibility to markets, and ameni- ties of the zone of plant location. The profit of the firm is II =pf(L, X; Z)-RL- wX (2) where II is the profit, p the output price, R land rent per unit, w other input prices, such as wage rate, and price of capital input. From the first-order conditions for profit maximization, one obtains the following demand equations for variable inputs: af R (3) aL p af _W (4) ax p( Solving (3) and (4) for the optimal input quantities L* and X*, and substituting them into (2), the "profit function," based on the duality 2Burstein [I] included this variable in the household utility function of her housing demand study. EMPLOYMENT LOCATION MODEL 265 z FIG. 1. The firm's bid-rent function. theorem,3 is obtained as I* =pf(L*, X*; Z) - RL* - wX* = I*(p, R, w; Z). (5) Let t be the unit transport cost for shipment of output; then p - t is the factory price of output. Using p as the numeraire and introducing the location subscript (u), (5) becomes Il*(u)=g[l - (u), K(u), w(u); Z(u)] (6) where II, ti, R, and iw7 are values normalized by p; u refers to the distance to the product market. In locationial equilibrium, for a given u every firm should have the same profit, and there is no incentive for any firm to relocate. An equilibrium rent profile must satisfy fl*(u) =g[ -t T(u), R (u), w~(u); Z(u)] = const.4 (7) As with residential location, a useful interpretation of this formulation of firm location choice is in terms of the bid-rent function of the firm, giving the price for site with characteristics Z that yields profit 17*, Let R*(u) denote the bid rent, then (as in Fig. 1) k"(u)-h[l -T(u), uF(u); Z(u); lI*(u)]. (8) For convenience, suppose the unit transport cost is site invariant within an urban area and include it as an element in the constant term. Also 3For the duality relations between the production function and the profit function, see Diewert [2] and Lau and Yotopoulos [6]. 4Solow [121 shows an equilibrium rent profile of households in an urban area. 266 KYU SIK LEE suppress JI*(u) which is constant. Hence (8) can be written *(u)- h[iw(u); Z(u)] (9) where -= <0; ->0. (10) 3w az For illustration, consider the case of labor input. As the labor-land ratio increases the marginal product of land increases relative to that of labor, and the relative price of land with respect to labor also rises. This argument supports the empirically observed rent gradient in an urban area in the sense that as the distance to the CBD becomes shorter, the intensity of a variable input such as labor increases and the land rent rises.5 In other words, producers respond to input price differentials over space to obtain optimal input combinations including lot size. Also the value of land increases as desirable site characteristics, such as public service provision and accessibility, are improved. Since w;7 is the input price vector normalized by output price, (4) can be rewritten as af (u) = i(U). (11) Substituting (11) into (9), we have the bid-rent function expressed in terms of firm characteristics af/aX and site characteristics Z. For expository reasons, rewrite (9) as K*(u) h[x(u), Z(u)], (12) where x(u)[= (fA/8X)(u)] now represents a vector of firm characteristics, namely input combinations, which in turn depend on technology char- acterized, for example, by type of production process and building struc- ture. As mentioned earlier Z(u) is a vector of site characteristics. Now suppose that there are T types of firms defined by x and S types of sites defined by Z. Let N, be the numiber of type t firms in the market. Then using (12), the bid rent for a site with characteristics Z by the nth firm of type t is given by R*, = h,n(ZZ) n E N, (13) 5A measure of the land price gradient using the survey data used in this study resulted in the following: In land price 8.029 - 0.1126 distance, R2 = 0. 1093, which can be written as land price = 3069e - 0.1126 distance. EMPLOYMENT LOCATION MODEL 267 Note that we have now suppressed the vector x(u) that is used to define the firm type t. For example, all firms of type t are siniilar in terms of output, input combination and technology, that is, they have an identical production function. Following Ellickson's [3, 41 work on residential location, we can interpret this model in terms of predicting the probability of a certain type of firm t to locate at a site with a specified set of characteristics Z. The stochastic version of (13) is R*,= h,,(Z - ) I e,,, ,E N (14) where e,,n is a random disturbance term reflecting unaccounted variations of firm characteristics of type t. Since a given site is occupied by the firm with the highest bid, the relevant variable for determining the probability that a given site is occupied by a firm type t is the maximum bid given by firms of type t. R, = max(K1 ) = h,(Z) + e,, t E- T (15) n where el = max (e,n), n E N,. n If the et are identically and independently distributed Weibull,6 the specification of a logit model follows, namely, the probability that a firm of type t occupies a site with characteristics Z takes the logit specification7 p(t Z) exp[h,(Z)] (16) t'ET The above discussion shows that the basic theoretical approach used in the study of residential location can provide a useful analytical framework for the study of employment location.8 The optimnizing behavior of the firm is postulated as location specific, that is, the choice by the firm of a specific site is part of the production decision; furthermore, the location specific 6For example, the maximum value of an identically and independently distributed normal variate has the Weibull distribution. 7Ellickson [3, 4] derived this variation of the logit model in his residential location study. 8Theoretical and empirical work is rare in this area; Mills [10] and Solow [12] offer basic micro foundations; the work by Hoover and Vernon [5], Struyk and James [13], and Schmenner [11], although descriptive, serves as the empirical bases in the field. 268 KYU SIK LEE equilibrium position of individual firrns is extended to the "locational equilibrium" situation of all firms in an urban area. The theoretical model is easily extended to the stochastic specification of the model in an estimable form. 3. THE DATA i he sample of 126 establishments was drawn for the survey from DANE's 2629 distinct firm records in the industrial directory files covering 1970- 1975,9 stratified by the following four categories: (1) location history, that is, stationary firms, movers, and births'°; (2) the zone system defined by 38 comunas; (3) the type of industry defined by 3-digit SIC codes;, and (4) firm size by employment. To minimize the sampling cost while having sufficient observations for econometric estimation, we chose the textile industry and the fabricated- metal industry as the two main industries to be studied. Both industries had a large share of manufacturing establishments in Bogota. The homogeneity of firms in each industry group makes it possible to test behavioral hypotheses with sufficient degrees of freedom. We added as a third group, however, the "other industries" category with which to do mainly descrip- tive studies about establishments in various other types of industries. The second consideration given in the sampling process was to oversam- ple large firms so that the number of jobs included in the sample could be maximized. Finally, an attempt was made to cover a wide geographic area in such a way that spatial analyses could be possible, including the estima- tion of the rent and wage gradients. Our target sample size was 120 with about equal shares of establishments among the three types of location history. The realized sample of 126 establishments consists of 58 stationary firms, 50 movers (including two firms that moved to Bogota from outside) and 18 births (see Table 1). The newly established firms were mostly small (Table 3). The sample coverage across zones was satisfactory; with 27 comunas covered, the spread was fairly even over the 3 Rings that have high manufacturing employment densities (see Table I and Fig. 2). On the other hand, only a small number of establishments was selected from Ring 1 (CBD) and Ring 6 (3 residential comunas in the north). 9The original DANE (National Statistics Department) files had 3388 records for the 6-year period. To maintain consistency in coverage over the period, however, firms with less than 10 employees or those that appeared in the directory for only one year were not included in our master file. The basic structure of the industrial directory data was documented in Lee [71. 10Stationary firms are defined as those that appeared in all six annual directories with the same address; births are those that appeared for the first time in any year during 1971-1975; movers are those that relocated within Bogota during 1971-1975. An analysis of the employ- ment location patterns by this classification of establishments was done in Lee [9]. EMPLOYMENT LOCATION MODEL 269 TABLE I Sample Composition: Zone by Firm Type Mover Mover within from Zone Stationary Birth Bogota outside Total Ring I 0 2 2 0 4 0.00 50.00 50.00 0.00 100.00 0.00 11.11 4.17 0.00 3.17 Ring 2 7 3 5 0 15 46,67 20.00 33.33 0.00 100.00 12.07 16.67 10.42 0.00 11.90 Ring 3 17 6 13 1 37 45.95 16.22 35.14 2.70 100.00 29.31 33.33 27.08 50.00 29.37 Ring 4 16 3 13 1 33 48.48 9.09 39.39 3.03 100.00 27.59 16.67 27.0& 5000 26.19 Ring 5 16 4 12 0 32 50.00 12.50 37.50 0.00 100,00 27.59 22.22 25.00 0.00 25.40 Ring 6 2 0 3 0 5 40.00 0.00 60.00 0.00 100.00 3.45 0.00 6.25 0.00 3.97 Total 58 18 48 2 126 46.03 14.29 38.10 1.59 100.00 100.00 100.00 100.00 100.00 100.00 Source. The City Study Establishment Survey. In some cases the 4-way stratification severely limited the possibility of drawing sample establishments from a specific population category. For example, not enough textile firms were located in certain comunas. There- fore, sample establishments were also selected from two other industry categories that are closely related to the two main industries; namely, the textile industry was supplemented by the apparel industry, and the fabri- cated-metal industry by the nonelectric machinery industry. As shown in Table 2, the final sample has fairly even shares among the three industry groups: about 35% each for the two main industry groups and 30% for the "other" category. In Table 3, we see that the average size of stationary firms in the sample is almost five times larger than the average size of births, and more than 270 KYU SIK LEE COLOMBIA BOGOTA, RING SYSTEM BASED ON COMUNAS - Comuno Boundaries m '-1 ) 6 Ring Boundories - City Limits I-nternahional Boun,daries 6it r, 5 |fCUADOR _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ FIGURE 2 EMPLOYMENT LOCATION MODEL 271 TABLE 2 Sample Composition: Zone by Industry Fabricated Nonelectric Zone Textiles Apparel metal machinery Other Total Ring I I 1 1 0 1 4 25.00 25.00 25.00 0.00 25.00 100.00 3.03 10.00 2.86 0.00 2.56 3.17 Ring 2 3 1 4 1 6 15 20.00 6.67 26.67 6.67 40.00 100.00 9.09 10.00 11.43 11.11 15.38 11.90 Ring 3 6 6 13 4 8 37 16.22 16.22 35.14 10.81 21.62 100.00 18.18 60.00 37.14 44,44 20.51 29.37 Ring 4 12 1 9 2 9 33 36.36 3.03 27.27 6.06 27.27 100.00 36.36 10.00 25.71 22.22 23.08 26.19 Ring5 10 1 6 2 13 32 31.25 3.13 18.75 6.25 40.63 100.00 30.30 10.00 17.14 22.22 33.33 25.40 Ring6 1 0 2 0 2 5 20.00 0.00 40.00 0.00 40.00 100.00 3.03 0.00 5.71 0.00 5.13 3.97 Total 33 10 35 9 39 126 26.19 7.94 27.78 7.14 30.95 100.00 100.00 100.00 100.00 100.00 100.00 100.00 Source. The City Study Establishment Survey. twice that of movers. This resulted from the oversampling of large firms; the sample average firm size of 135 persons is about twice as large as the average firm size of the establishmnents in the population."' 4. SELECTED ESTIMATION RESULTS We now turn to the estimation of the multinomial logit model (16). Estimation is based on the Bogota establishment survey results and other secondary data sources. Although the survey questionnaire was designed to take no more than 1 hour to complete, it was comprehensive in coverage to include plant characteristics, employment composition, transport access, proximity to markets, local public services, and the respondent's evaluation " According to the industrial directory file of 1975, the average firm size of 1829 establish- ments with 10 or more employees was 65 persons. 272 KYU SIK LEE TABLE 3 Sample Composition: Firm Type by Sizc Firm Employment sizea type (1,4) (5,9) (10,19) (20 49) (50,99) (100 ormore) Total Stationary 0 1 8 13 4 32 58 0.0() 1.72 13.79 22.41 6.90 55.17 100.00 0.00 25.00 38.10 34.21 23.53 72.73 46.03 6.00 16.25 33.54 81.75 324.72 194.66 Birth 1 2 3 9 1 2 18 5.56 11.11 16.67 50.00 5,56 11.11 1(0,00 50.00 50.00 14.29 23.68 5.88 4.55 14.29 3.00 6.00 13.00 26.56 63.00 174.00 39.11 Mover I I 10 16 12 10 50 2.00 2.00 20.00 32.00 24.00 20.00 100.00 50,00 25.00 47.52 42.11 70.59 22.73 39.68 3.00 7.00 13.50 31.94 78.75 335.60 99.14 Total 2 4 21 38 17 44 126 1.59 3,17 16.67 30.16 13.49 34.92 100.00 100.00 100.00 100.00 100,00 100.00 100.00 100.00 3.00 6.25 14.48 31.21 78.53 320.34 134.53 Source. The City Study Establishment Survey. 'The bottom number in each group is the mean employment size of firms in that group. of the plant location. Particular attention was given to the characteristics of movers]2 and the factors that influence location decisions. In (16) specification of the dependent variable requires a stratification of firms by type according to the vector of firm characteristics x; the indepen- dent variables are the site characteristics Z. The survey instrument contains a number of candidate variables for the stratification of firms to define the dependent variable: variables related to output such as product type and annual sales; variables related to technology such as type of production process and building structure; and variables associated with inputs, for instance, plant space, lot size, a-nd the number of production workers. The site characteristics to be used as independent variables include those associ- ated with accessibility to various types of markets (product, material inputs, and labor), and those related with the quality of local public services. Of the 126 firms in the sample, 87 are in the textile and the fabricated metal industries, the two major industries included in the study. We report here estimated results obtained with the specifications shown in Table 4. "2Detailed analv,is of movers appears in Lee [8]. EMPLOYMENT LOCATION MODEL 273 TABLE 4 Stratification of Dependent Variable Number Group Industry Floor space of Observations I SIC 321 and 322 Less than 1000 m2 17 2 SIC 321 and 322 1000 M2 or more 26 3 SIC 381 and 382 Less than 1000 m2 27 4 SIC 381 and 382 1000 m2 or more 17 Total 87 Note, SIC 321, textile; SIC 322, apparel; SIC 381, fabricated metal; and SIC 382, nonelectric machinery. For the dependent variable, the 87 firms in the two major industries are grouped into two plant sizes according to floor space. The independent variables are in the following categories: access to the local markets for output and material inputs measured by the proportion of output sold and inputs bought in Bogota, proximity to residential areas of production and administrative workers, an index of the quality of local public services measured by the frequency of electricity interruption, the extent of ag- glomeration economies measured by the employment-location quotient of individual industries in the zone of location, and the intensity of economic activities and the degree of congestions measured by the population density in the zone of location. The distance to the CBD is included as a measure of accessibility to the city center. Ideally, stratification for the dependent variable should be achieved by more than the 2-way (and 4-cell) classification used here. The small sample size, however, limits such possibilities. Therefore, we include two firm type stratification variables on the right-hand side of the equation, specifically, the year of initial operation at the present location that discriminates old mature establishments against new ones and recent movers, and the owner- ship dummy variable to distinguish renters from owners. All independent variables entered the model as "group-specific" 13 except for the location-quotient variable and the ownership dummy variable; the former being specified as "generic" within the same industiy group, and the latter within the same size group. In the estimation of this multinomial logit formulation, Group 4 was used as the reference group. Therefore, the estimated logit coefficients of group-specific variables should be interpreted as relative differences with respect to the reference group. Hence, the signs of the coefficients do not necessarily mean the direction of causation; they 13This expression is equivalent to "alternative-specific" in the multinomial-logit literature. 274 KYU SIK LEE only reflect the relative orders of magnitudes of individual coefficients with respect to the reference group for a given independent variable. Table 5 reports the estimated logit coefficients and t statistics that are the test of difference between the coefficients of a particular group with respect to those of the reference group. In Table 5, Group 4 (large metal-fabricating firms) was set as the reference group. The I tests indicate that the differences of coefficients are significant between two size groups (large as against small), and are more robust within the same industry (Group 4 vs Group 3). None of the coefficients of Group 2 (large textile firms) was statistically significant. The likelihood ratio index of 0.29 indicates that the overall goodness of fit is good. These patterns held true in the estimation of alternative model specifications with lot size and employment variables in place of the floor space variable. To interpret the estimated logit coefficients the elasticities of probabilities are calculated at sample means and reported in Table 6. This parameter measures the percentage change in the probability of being in the ith group with respect to 1% change in a given independent variable for that group. In Table 6 we first observe that Group 3 (small metal-fabricating firms) has the highest elasticity values for most of the variables; compared with the other two, howvever, this group is least sensitive to the electricity interruption rate ELECINT and the location quotient LOCQT. The most important variable that influences the probability of being in Group 3 is the measure of access to the local input markets INPUTBT, followed by the measure of access to the local product markets PRODSOLD. Local market orientation is very important for this group. For Group I (small textile firms), the measure of access to the local input markets is also the most important variable, followed by proximity to production workers' residential areas WKSOUTH. The weakest variable in this case is distance from the CBD, which implies that small textile firms tend to locate near the CBD compared with the other 2 groups. As distance from the CBD increases, the probability of being in Group 2 is three times higher than that of being in Group 1. However, small metal-fabricating firms tend to locate farther from the CBD than do textile firms of both size groups. In the case of large textile establishments (Group 2), it is interesting to find that the most important variable is the location quotient LOCQT, followed by the electricity interruption rate ELECINT, and the proximity to the residential areas of administrative workers ADMNORTH. For this group of large firms, the measure of access to local markets and the proximity to production workers' residential areas are rather unimportant. Large textile firms tend to be more export-oriented and use capital-intensive production facilities. Also, the fact that large firms have less likelihood of locating in a densely populated area POPDENS is consistent with the finding that they tend to locate farther from the CBD. TABLE 5 Logit Estimation of Firm Location Choice: Dependent Variable, Industry and Floor Space' CONSTANTa PRODSOLD INPUTBT DISTCBD WKSOUTH ADMNORTH ELECINT POPDENS LOCQT YRINOP RENTER Coefficients Group 1 -15.680 0.011 0.019 0.012 0.014 -0.010 0.501 0.0081 0.749 0,159 2.069 Group 2 -2.128 0.008 -0.010 0.032 0.003 -0.016 0.448 0.002) 0.033 - Group 3 -12.880 0.028 0.027 0.151 0.022 -0.020 0.115 0.0121 073 0.095 2.069 Group 4h - - - - - - - - 0.3 - t Statistics Group 1 2.09** 0.74 1.39 0.07 0.80 0.64 1.05 1.11 l 1.69* 1.63* 2.67** Group2 0.57 0.60 0.89 0.21 0.20 1.12 1.11 0.35 J 0.60 Group 3 2.07** 1.83* 2.05** 0.92 1.33 1.40 0.24 1.89*1 1.71 1.20 2.67** Group4 - - - - - -J Percent correctly predicted. 54.02 Number of observations: Group I = 17 Likelihood ratio index: 0.2903 Group 2 = 26 Likelihood ratio statistic: 70.02 Group 3 = 27 Group 4 = 17 Source. The City Study Establishment Survey. 'Definitions of variables are given in the Appendix. bGroup 4 is used as the base. *Significant at the 5% level. **Significant at the 2.5% level. TABLE 6 Elasticities of Probability: Logit Estimation of Location Choice Industry groups by floor space PRODSOLD INPUTBT DISTCBD WKSOUTH ADMNORTH ELECINT POPDENS LOCQT YRINOP RENTER Share Group 1 0.515 1.182 0.052 0.808 -0.496 0.711 0.794 0.544 9.264 1.665 0.1954 Group 2 0.272 -0.293 0.155 0.128 -0.538 0.556 0.124 0.722 1.585 - 0.2989 Group 3 1.367 1.455 0.584 1.120 -0.689 0.123 1.233 0.468 4.630 1.467 0.3103 Group 4 - - - - - - - - - - 0.1954 Source. The City Study Establishment Survey. Notes. For definitions of dependent and independent variables, see the Appendix. The elasticity of probability is defined as ej = (I - p)bijWj, where Pi is the share of ith group, bj the jth logit coefficient of the ith group, and Xij the sample mean of the jth independent variable for the ith group. It should be noted that the logit coefficients reported in Table 5 are the differences with respect to the coefficients of the base group. Therefore, the values of elasticities in this table are the results based on (bij - b*) instead of b,j, where bj* is the coefficient of the base group. EMPLOYMENT LOCATION MODEL 277 With such a small sample and a large number of independent variables, the above results look promising. When the model was specified with lot size and employment size as the stratifying variable (in place of the floor space), the estimation results were quite similar to those reported here. 5. CONCLUDING REMARKS This paper presents an abstract but empirically tractable model of em- ployment location; it shows that the basic theoretical approach used in the housing literature can provide a useful analytical framework for the study of employment location. The results of the establishment survey conducted in Bogota are used to test a multinomial logit specification of bid-rent function following the approach used by Ellickson [4] in his housing study, The estimation of the model was performed with a 2-way stratification of dependent variable by the use of industry type and floor space, each having two categories. Independent variables included were measures of access to the output and input markets, indexes of concentration of econornic activi- ties, and a quality index of public util i services. Even though the sample size was not large, the goodness of fit was satisfactory, and the estimated model was capable of predicting, in probability terms, which types of firms are likely to occupy a site with those characteristics specified by the explanatory variables. The predicted location patterns resulting from the model are consistent with those expected a priori. For small firms the accessibilities to the local input and output markets are most important; the benefits of accessibility to the central area tend to compensate for the high land rent and congestion costs in the high density area. On the other hand, large establishments, which are more export-oriented and require more plant space with modern production technology, tend to locate in outer areas where more space is available at lower cost. The estimated results also show that for large firms, the quality of public utility services is very important, and that the proxim- ity to the residential areas is more important to administrative workers than to production workers. Separate regression results"4 (using the same data set) indicate a strong relationship between the intensity of input (labor and capital) use and land price; given a well shaped (monocentric) rent gradient in Bogota,'" these results support the hypothesis that the firms respond to the substitutability of land with respect to other inputs over space, and this evidence is consistent with the predictions obtained from the logit specification in this paper. The patterns of employment location in Bogota are by no means 14Reported in tht earlier version of this paper presented at the Denver meetings of the Econometric Society. 15See footnote 5, and also Villamizar (141. 278 KYU SIK LEE random; they are quite similar to those observed for large cities in the United States. APPENDIX: DEFINITIONS OF VARIABLES IN TABLE 5 Dependent Variable See Table 4 Independent Variables CONSTANT Group specific constants PRODSOLD Percent of products sold in Bogota INPUTBT Percent of inputs bought in Bogota DISTCBD Airline distance (km) from the CBD (the center of comnuna 31) to the establishment location (the center of the con?una where the establishment is located) WKSOUTH Percent of production workers living in the south ADMNORTH Percent of administrative workers living in the north ELECINT Frequency of electricity interruption; (1, never; 2, once a week; 3, twice a week; 4, more than tw`:' e a week) POPDENS Population per hectare of the comuza where the establishment is located LOCQT Location quotient defined as comnunu j's share of industry i relative to its share of total manufacturing employment (Separate values are used for the two industry groups.) YRINOP Year of initial operation at the present location RENTER Ownership dummy: 1 if renter, 0 if owner. (Assigned to establishments with floor space of less than 1000 m2 in both industry groups.) REFERENCES 1. N. R. Burstein, Voluntary income clustering and the demand for housing and local public goods, J. Urbani Econ. (1980). 2. W. E. Diewert, Applications of duality theory, in "Frontiers of Quantitative Economics" (M. D. Intriligator and D. A. Kendrick, Eds.), Vol. 2, North-Holland, Amsterdam (1974). 3. B. Ellickson, "Economic Analysis of Urban Housing Markets: A New Approach," The Rand Corp., R-2024-NSF (1977). 4. B. Ellickson, An alternative test of the hedonic theory of housing markets, J. Urban Econl., 9, 56-79 (1931). 5. E. M. Hoover and R. Vernon "Anatomy of a Metropolis" Harvard Univ. Press, Cam- bridge, Mass. (1959). 6. L. J. Lau and P. A. Yotopoulos, A test for relative efficiency and application to Indian agriculture, Amer. Econ. Rev. (March 1971). 7. K. S. Lee, "Distribution of Manufacturing Establishments and Employment in Bogota and Cali," City Study Workshop paper (January 16), The World Bank, Washington, D.C. (1978). 8. K. S. Lee, "Determinants of Intra-urban Location of Manufacturing Employment: An Analysis of Survey Results for Bogota, Colombia," Urban and Regional Rep. No. 8 1-3. The World Bank, Washington, D.C. (1981). 9, K. S, Lee, Intra-urban location of manufacturing employment in Colombia, J. Urban Econ., 9, 222-241 (1981). EMPLOYMENT LOCATION MODEL 279 10. E. S. Mills, "Urban Economics," Scott, Foreman, Glenview, III, (1972). 1 1. R. Schmenner, "Making Business Location Decisions," Prentice-Hall, Englewood Cliffs, N.J. (1982). 12. R. Solow, On equilibrium models of urban location, in "Essays in Modern Economics" (Parkin, Ed.), Longmans, Green, New York (1972), 13. R. Struyk and F. James "Intrametropolitan Industrial Location," Lexington Books, Lexington, Mass. (1975). 14. R. Villamizar, "Land Prices in Bogota between 1955 and 1978: A Descriptive Analysis," Urban and Regional Rep. No, 80-2. The World Bank, Washington, D.C. (1980). No. 233. Keith Bradley and Alan Gelb, "Motivation and Control in the Mondragon Experiment," and "The Replication and Sustainability of the Mondragon Experiment," British Journal of Industrial Relations No. 234. Gary P. Kutcher and Roger D. Norton, "Operations Research Methods in Agricultural Policy Analysis," European Journial of Operationaal Research No. 235. Bela Balassa, "Economic Reform in China," Banca Nazionlale del Lavoro Quarterly Review No. 236. S. van Wijnbergen, "Stagflationary Effects of Monetary Stabilization Policies: A Quantitative Analysis of South Korea," Journial of Develop- menlt Econiomics No. 237. Gershon Feder, Richard Just, and Knud Ross, "Projecting Debt Servicing Capacity of Developing Countries," Journal of Financial and Quantitative Analysis No. 238. Richard H. Goldman and Lyn Squire, "Technical Change, Labor Use, and Income Distribution in the Muda Irrigation Project," Economic Development and Cultural Change No. 239. J. Michael Finger, "Trade and the Structure of American Industry," Anntals of the American Academy of Political and Social Science No. 240. David M.G. Newbery and Joseph E. Stiglitz, "Optimal Commodity Stock-piling Rules," Oxford Economic Papers No. 241. Bela Balassa, "Disequilibrium Analysis in Developing Economies: An Overview," World Development No. 242. T.N. Srinivasan, "General Equilibrium Theory, Project Evaluation, and Economic Development," The Theory and Experienice of Economic Development No. 243. Emmanuel Jimenez, "The Value of Squatter Dwellings in Developing Countries," Economic Development and Cultural Change No. 244. Boris Pleskovic and Marjan Dolenc, "Regional Development in a Socialist, Developing, and Multinational Country: The Case of Yutgo- slavia," Internnational Region al Science Review No. 245. Mieko Nishimizu and John M. Page, Jr., "Total Factor Productivity Growth, Technological Progress, and Technical Efficiency Change: Dimensions of Productivity Change in Yugoslavia, 1965-78," The Economic Journzal No. 246. J. M. Finger, "The Political Economy of Administered Protection" (with H. Keith Hall and Douglas R. Nelson), The American Economic Review; and "The Industry-Country Incidence of 'Less than Fair Value' Cases in U.S. Import Trade," Quarterly Review of Economics and Business No. 247. Nancy Birdsall and Susan Hill Cochrane. "Education and Parental Decision Making: A Two-Generation Approach," Education and Devel- opment No. 248. Kemal Dervis, Jaime de Melo, and Sherman Robinson, "A General Equilibrium Analysis of Foreign Exchange Shortages in a Developing Economy," The Economic Journal Issues of the World Bank Reprint Series are available free of charge from the address on the bottom of the back cover. THE WORLD BANK Headquarters: U 1818 H Street, N.W., Washington, D.C. 20433, U,S.A. Telephone: (202) 477-1234 Telex: WUI 64145 WORLDBANK RCA 248423 WORLDBK Cable address: INTBAFRAD WASHINGTONDC Ellropean Office: 66, avenue d'Iena 75116 Paris, France Telephone: (1) 723-54.21 Telex: 842-620628 Tokyo Office: Kokusai Building 1-1, Marunouchi 3-chome Chiyoda-ku, Tokyo 100, Japan Telephone: (03) 214-5001 Telex: 781-26838 The full range of World Bank publications, both free and for sale, is described in the Catalog of Publicationis; the continuing research program is outlined in Abstracts of Current Studies. The most recent edition of each is available without charge from: PUBLICATIONS DISTRIBUTION UNIT THE NORLD BANK 1818 H STREET, N.W. WASHINGCTON, D.C. 20433 U.S.A. ISSN 0253-2131