A behavioral model of intra-urban employment location : an application to Bogota, Colombia

Uo Urban and Regional Report No. 80-8 A BEHAVIORAL MODEL OF INTRA-URBAN EMPLOYMENT LOCATION: AN APPLICATION TO BOGOTA, COLOMBIA Kyu Sik Lee October, 1980 This report was prepared under the auspices of the City Study Research Project (RPO 671-47) as City Study Project Paper No. 13. The views reported here are those of the author, and they should not be interpreted as reflecting the views of the World Bank or its affiliated organizations. This report is being circulated to stimulate discussion and comment. Urban and Regional Economics Division Development Economics Department Development Policy Staff The World Bank Washington, D.C. 20433 TABLE OF CONTENTS Page 1. Ititroduction .................................................. 1 2. A Model of,Employment Location ................................ 2 3. The Data ...................................................... 9 4. Selected Estimation Results ..................................* 16 5. Concluding Remarks ............................................ 24 References 1. Introduction The work reported in this paper is part of the continuing research effort in an urban study project in the World Bank. In this paper a theoretical model of employment location is formulated, and extended to an empirical specification in the multi-nominal logit framework. In the descriptive phase of the study, Bogota's employment location patterns and their changes were extensively analyzed using the industrial 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.rate and the relocation rate were high and the evidence of the spatial decentralization of manufacturing employment was strong (Lee, 1979). Although researchers have drawn a good deal of attention to the need for modelling employment location behavior, the gap in this area still remains unattended in the literature. The analytical work reported in the present paper is an attempt to model the individual firm's location behavior and explain the observed patterns of employment loca- tion. For this purpose, a survey of manufacturing establishments was con- ducted in Bogota, Colombia, which is a rapidly growing city comparable to such U.S. cities as Phoenix or Houston. This paper presents the estimation results based on the survey results. The model is presented in the next section; then the nature of the survey is briefly described, and finally the estimation results are reported. 2. A Model of Employment Location Consider T types of manufacturing firms in an urban area. The firm maximizes 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 to be solved is to determine the optimum combination of inputs, including the lot size and the plant location, to attain the locational equilibrium level of profits in an urban area. Consider a production function in the following general form: (1) Q = f (L, X; Z), where Q = output, L = lot size, X a vector of other inputs such as labor, and plant and equipment; Z = a vector of site characteristics which are independent of lot size and can be considered as "local public goods"1/ such as the quality of public utility services, accessibility to markets, and amenities of the zone of plant location. The firm's profit is defined as: (2) H = p f (L, X; Z) - RL - w X where R = profit, p = price of output, R = land rent per unit, w-= other input prices such as wage rate, and price of capital input. 1/ Burstein (1980) included this variable in the household utility function in her housing demand study. -3- From the first order conditions for the maximization of profit, one obtains the following demand equations for variable inputs: (3) Df = R 9L p (4) 3f = w UX 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 theorem -, is obtained as (5) TI =.p f (L, X; Z) - RL -wX = H (p, R, w; Z) Let t = unit transport cost for shipment of output; then p-t is the factory price of output. Using the price of output (p) as the numeraire and introducing the location subscript (u), (5) becomes (6) I (u) = g [1 - t (u), R (u), w (u); Z (u) ] where T, t, R, and w are values normalized by p; u refers to the distance to the product market. 2/ For the duality relations between the production function and the profit function, see Diewert (1974), and Lau and Yotopoulos (1971). -4- In the locational equilibrium situation, for a given distance (u) every firm should have the same pro it, and there will be no incentive for any firm to relocate. An equilibrium rent profile must satisfy -* 3/ (7) .H (u) = g [1-t(u), R(u), w(u) ; Z(u) ] constant.- As in the case of the residential location in the literature, a useful interpretation of this formulation of firm location choice is in terms of the firm's "bid-rent" function, a function giving the price for site with characteristics Z, that will yield profit level TI Let R (u) denote the bid rent, then (8) R (u) = h [1-t(u), W(u); Z(u); T (u) ]. h z 3/ Solow (1972) shows an equilibrium rent profile of households in an urban area. -5- For convenience, let us suppose the unit transport cost is site- invariant within an -rban area and include it as an element in the constant term. Also suppress T (u) which is constant. Hence (8) can be written as (9) R (u) = h (w (u) ; Z(u) ), where (10) 3R < 0 ;3R > 0. For illustration, consider the case of labor input. As the labor- land ratio increases, the marginal product of land will increase relative to that of labor, and the relative price of land with respect to labor will also rise. 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 , abor icrea 4/ intensity of variable input such as labor increases and the land rent rises.- In other words, the producers respond to input price differentials over space to obtain optimal input combinations including lot size. Also the value of land will increase as the desirable site characteristics, such as public service provision and accessbility, are improved. Since w is input price vector normalized by output price, 4/ A measure of the land price gradient using the survey data used in this study resulted in the following: In Land price = 3.029 -'0.1126 Distance, R2 = 0.1093, (3.17) which can be written as Land price = 3069 e -0.1126 Distance -6- equation (4) can be rewritten as (11) af (u) = w (u) ax Substituting (11) into (9), we have the bid-rent function expressed in terms of firm characteristics Df and site characteristics Z. X For expository reasons, rewrite (9) as (12) R (u) = h (x (u), Z(u) ), where x(u) ( = @f (u) ) now represents a vector of firm DX characteristics, namely input combination, which in turn depends on technology characterized,for example, by type of production process and building structure. 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 site defined by Z. Let Nt be the number of type t firms in the market. Then using equation (12), the bid-rent for a site with charac- teristics Z by the nth firm of type t is given by (13) R = h (Z ), ne N tn tn n t Note that we have now suppressed the vector x(u), which is used to define the firm type t. For example, all firms of type t are similar in terms of output, input combination and technology, i.e., they have -7- an identical production function. Following Ellickson's (1977, 1980) 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 specified as (14) R =h (Z ) + e ,n EN, tn tn n tn t where etn is a random disturbance term reflecting unaccounted variations of firm characteristics of type t. Since a given site will be occupied by the firm with the highest bid, the relevant variable for determining the probability that a given site will be occupied by a firm type t is the maximum bid given by firms of type t. (15) Ktmax = max(Rt) = h t(Z) + e ,te T, where et = max(e tn), ne Nt. If the e are identically and independently distributed Weibull5 t the specification of a logit model follows, namely, the probability that a firm of type t will occupy a site with characteristics Z will take the / For example, the maximum value of an identically and independently distributed normal variate has the Weibull distribution. -8- following form of logit specification.- (16) p (tIZ) = exp (ht (Z) E exp (h t (Z) ), where t t. teT 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.-/ The firm's optimizing behavior is postulated as location specific, i.e., the firm's choice of a specific site is part of the production decision; furthermore, the loca- tion specific equilibrium position of individual firms 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. 6/ Ellickson (1977, 1980) derived this variation of the logit model in his residential location study. 7/ Theoretical and empirical work is rare in this area; Mills (1972) and Solow (1972) offer basic micro foundations; the work by Hoover and Vernon (1959), Struyk and James (1975), and Schmenner (1979), although descriptive, serves as the empirical bases in the field. -9- 3. The Data A sample of 126 establishments interviewed in the survey was drawn from DANE's 2,629 distinct firm records in the industrial directory files covering 1970-1975, 81stratified by the following four categories: (1) location history, i.e., stationary firms, movers, and births,9- (2) the zone system defined by 38 comunas; (3) the type of industry defined by three digit SIC codes; and (4) firm size by employment. In order to minimize the cost af sampling while having- a sufficient number of observations for econometric estimation, we chose the textile industry and the fabricated metal industry as two main industries to be studied. Both industries had a large share of establishments in Bogota's manufacturing. The homogeneity qf firms in each industry group will make it possible to test behavioral hypotheses with sufficient degrees of freedom. However, we added as a third group the "other industries" category to do mainly descriptive studies about establishments in various other types of industries. The second consideration given in the sampling process was to over-sample large size firms so that the number of workers included in the sample could be maximized. Finally, an attempt was made to cover a wide 8/ The original DANE (National Statistics Department) files had 3,388 - records for the six-year period. In order to maintain consistency in coverage over the period, however, firms with less than 10 employees or those which appeared only for one year in the directory were not included in our master file. The basic structure of the industrial directory data was documented in Lee (1978). 9/ Stationary 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 employment location patterns by this classification-of establishments was done in Lee (1979). - 10 - geographic area in such a way that spatial analyses could be possible including the estimation 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 ones (Table 3). The sample coverage across zones was quite satisfactory; with 27 comunas covered, the spread was fairly even over the three Rings which have high manufacturing employment densities (see Table 1 and the attached map of Bogota).. On the other hand, only a small number of establishments was selected from Ring 1 (CBD) and Ring 6 (three residential comunas in the north). In some cases the four-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. Therefore, sample establishments were also selected from two other industry categories that are closely related with the two main industries, namely, the textile industry was supplemented by the apparel industry, and the fabricated metal industry by the non-electric 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. - 11 - Ta.bl 1; SAMPLE COMPOSITION: ZONE BY FIRM TYPE NUMBER OF FIRMS BY ZONE AND TYPE ROWS.......CATEGORIES OF COMUNA COLUMNS.... CATEGORIES OF FTYPE : MOVER : MOVER :STATIONA: : WITHIN FROM :RY BIRTH BOGOTA :OUTSIDE TOTAL 0 : 2: 2: 0: 4 RING 1 : 0.00': 50.00 50.00 : 0.00 : 100.00 0.00 : 11.11 : 4.17 : 0.00 : 3.17 7 : 3 : 5 : 0 15 RING 2 : 46.67 : 20.00 33.33 0.00 : 100.00 12.07 16.67 10.42 : 0.00 11.90 17 6 13 1 37 RING 3 45.95 : 16.22 : 35.14 : 2.70 : 100.00 29.31 : 33..3.3 : 27.08 : 50-00 29.37 16 : 3 : 13 : 1 : 33 RING 4 : 48.48 : 9.09 : 39.39 : 3.03 : 100.00 :27.59 : 16.67 : 27.08 : 50.00 : 26.19 16 : 4 : 12 : 0 : 32 RING 5 : 50.00 : 12.50 : 37.50 : 0.00 : 100.00 27.59 22.22 : 25.00 : 0.00 : 25.40 2: 0: 3: 0 : 5, RING 6 : 40.00 0.00 : 60.00 : 0.00 : 100.00 3.45 : 0.00 : 6.25 : 0.00 : 3.97 TOTAL : 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 -12- BOGOTA: Ring System Based on Comunas 6 35 - 13 - ТаЪI� 2: SAMPLE COMPOSIT20N: ZONE ВУ INDUSTRY г • . NUMBER OF FIRMS 8У ZONE AND TNOUSTRY ` ROwS.......OдтEGORIES OF COMUNA . COLUMNS....CATEGORIES OF INDUSTRY , , . :NON EI.EC: • , , :FABRICAT:7RIC МаС: . :7EКTILES:APPAREL :ED METAL:HINERY : QTHE1� . TOTAL, --°----------------------------------------------------------- , 1, 1, 1. 0. 1. 4 FING 1: 25.00 : 25.00 : 25.00 : 0.00 : 25.00 : 100.00 . 3.03 : 10.00 : 2.86 : 0.00 : 2.56 : Э.97 -------------------°--------------------------_°-------------- . 3: 1: 4: 1: 6: 15 F'ING 2: 20.00 : б.бг : 26.67 : б.бг : 40.00 : 100.00 � . 9.09 : 10.00 : 11.43 : 11.11 : 15.38 : 11.90 ----------------------------°--------------------------------- . 6: 6: 13 : 4: 8: 37 RING Э: 7с3.22 : 16.22 : 35.14 : 10.81 : 21.62 : 100.00 . 18.18 : 60.00 : 37.14 : 44.44 : 20.51 : 29.37 � ---°---------------------------------------------------------- . 12 . 1. 9. 2. 9. 33 RING 4: 3б.3б : З.ОЗ : 27.27 : 6.06 : 27.27 : 100.00 . 36.36 : 10.00 : 25.71 : 22.22 : 23.0£ : 25.19 ------------------------�------------------------------------- � . 10 . 1. 6. 2. 13 . Э2 RING 5: 31.25 : 3.13 : 15.75 : б.2°5 : 40.63 : 100.00 . ЗО.ЗО : 10:00 : 17.14 : 22.22 : 33.33 : 25.40 ----------------°-----------------------°--------------------- . 1. 0. 2. 0. 2. 5 ' RING 6: 20.00 : 0.00 : 45�.00 : б.00 : 40.00 : 100.00 . З.ОЗ : 0.00 : 5.7i : 0.00 : 5.13 : 3.9Т -------------------------------------------------------------- 33 : i0 : Э5 : 9: 39 : 126 , 70ТА� . 25.i9 : 7.94 : 7. 8: 7.14 : 30 95 . 100.00 ' : 100.00 : 00.00 : 10 . . .00 : 1� 00 : 100.00 �SOUrce:� The City 5tudy EstaЪlishmeпt 5urvey 14 In Table'3, we.can see that the average size of stationary firms in the sample is about four times larger than the average size of births, and more than twice that of movers. This resulted from the design of over- sampling large size firms; the sample average firm size of 135 persons turned out to be about twice as large as the average firm size of the establishments in the population. 10/ 10/ According to the industrial directory file of 1975, the average firm size of 1,829 establishments with 10 or more employees was 65 persons. - 15 - 'Table 3; SAMPLE COMPOSITION: FIRM TYPE DY SIZE TYPE OF FIRM AND NUMBER OF FULLTIME EMPLOYEES--TOTAL ROWS.......CATEGORIES OF ESTBTYPE COLUMNS... .CA.EGORIES OF EMPFULTL (100, (1,4) : (5,9) :(10,19) :(20.49) :(50.99) 9999) : TOTAL : 0 : 1 : a 13 4 : 32 : E8 STATIONA: 0.00 1.72 13.79 :. 22.41 6.90.: 55.17 100.00 py 0.00 25.00 38.10 : 34.21 : 23.53 : 72.73 46.03 : : 6.000 16.250 : 33.538 81.750 :324.719 :1 655 1: 2 : 3 : 9 : 1: 2: 18 BIRTH : 5.56 11.11 : 16.67 : 50.00 : 5.56 : 11.11 100.00 : 50.00 : 50.00 14.29 : 23.68 : 5.88 4.55 : 14.29 : 3.000 : 6.000 13.000 ':-26.556 : 3.000 :174.000 1 : 10 : 16 : 12 : 10 : 50 MOVER : 2.00 : 2.00 : 20.00 : 221 : 4.00 : 20.00 : 100.00 50.00 : 25.00 : 47.62 : 42.11 : 70.59 : 22.73 : 39.68 3.000 : 7.000 : 13.500 : 31.938 : 78.750 :335.600 140 2 : 4 : 21 : 38 : 17 : 44 : 126 TOTAL 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 : 10.00 3.000 : 6.250 : 14.476 : 31-211 : 78.529 :320.341 :34.532 1/ The circled numbers are mean values. Source: The City Study Establishment Survey - 16 - 4. Selected Estimation Results We now turn to the estimation of the multinomial logit model which is specified as equation (16) on page 8. The 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 one hour to complete, it was quite comprehensive in coverage including plant characteristics, employment composition, transport access, proximity to markets, local public services, and the respondent's evaluation of the plant location. Particular attention was given to the'characteristics of movers-1/ and the factors that influence location decisions. In eqpation (16), the specification of dependent variable requires a stratification of firms by type according to the vector of firm characteristics x; the independent.variables are the site characteristics Z. The survey instrument contains a number cf candidate variables for the stratification of firms to define the dependent variable: variables related with output such as product type and annual sales; variables related with technology such as type of production process and building structure; and variables associated with inputs, for instance, plant space, lot size, and the number 11/ Detailed analysis of movers was done in a separate paper. - 17 - of production workers. The site characteristics to be used as independent variables include those associated 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 firms are in the textile and the fabricated metal industries, the two major industries included in the study. We report here estimation results obtained with the following specification. For the dependent variable, the 87 firms in the two major industries are grouped into two plant sizes according to the floor space. Stratification of Dependent Variable Industry Floor Space No. of Observation Group 1 SIC 321 and 322 less than 1,000 m2 17 Group 2 SIC 321 and 322 1000 M2 or more 26 Group 3 SIC 381 and 382 less than 1,0002 27 Group 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 = non-electric machinery.) - 18 - The indeperient 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 agglomeration economies measured by the employment location quotient of individual industries in the zone of location, the intensity of economic activities and the degree of congestions measured by the population density in the zone of location, and the distance to the CBD as a general accessibility measure. Ideally, the stratification for the dependent variable should be achieved by m.re than the two-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, namely, the year of initial operation at the present location which 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" 12/ except for the location quotient variable and the ownership dummy variable; the former being specified as "generic" within the same industry 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 12/ This expression is equivalent to "alternative-specific" in the multinomial logit literature, - 19 - 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 only reflect the relative orders of magnitudes of individual coefficients with respect to the reference group for a given independent variable. Table 4 reports the estimated logit coefficients and t statistics which are the test of difference between the coefficients of a particular group with resepct to those of the reference group. In Table 4, Group 4 (large metal fabricating firms) was set as the reference group. The t tests indicate that the differences of coefficients are significant between two size groups (large as against small), and it is 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 on the strong side. These patterns held true in the estimation of alternative model specifications with lot size and employment variables in place of the floor space variable. In order to interpret the estimated logit coefficients, the elasticities of probabilities are calculated at sample means and reported in Table 5. This parameter measures the percentage change in the probability of being in the ith group with respect to one percent change in a given independent variable for that group. In Table 5, first we observe that Group 3 (small metal fabricating firms) has the highest elasticity values for most of the variables; this group, compared with the other two, is however least sensitive to the electricity interruption rate (ELECINT) and the*location quotient (LOCQT). The most important variable that influences Table 4: LOGIT ESTIMATION OF FIRM LOCATION CHOICE DEPENDENT VARIABLE: INDUSTRY AND FLOOR SPACE 1 CONSTANTV! 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 0.008 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 0.012 0.738 0.095 2.069 Gru 2/ Group 4- - - - - - ------ 3/ t -Statistics - Group 1 2.09 0.74 1.39 0.07 0.80 0.64 1.05 1.11 1.69* 1.63* 2.67 Group 2 0.57 0.60 0.89 0.21 0.20 1.12 1.11 0.35 60.60 C Group 3 2.07 1.83* 2.05 0.92 1.33 1.40 0.24 1.89 1.71 1.20 2.67 Group4 - - - - - - Percent correctly predicted: 54.02 Number of observations: Group 1 = 17 Likelihood ratio index: 0.2903 Group 2 = 26 Likelihood ratio statistic: 70.02 Group 3 = 27 Group 4 = 17 1/ Definitions of variables are on the next page. 2/ Group 4 is used as the base. 3/ The coefficients with a single asterisk are significant at the 5% level and those with a double asterisk are si-nificant at the 2.5% level. Data Source: The,City Study Establishment Survey. - 21 - Definitions of Variables in Table 4 Dependent Variable: 4 groups defined as Group 1 = SIC 321 and 322; floor space less than 1,000 m2 Group 2 = SIC 321 and 322; floor space of 1$000 m2 or more. 2 Group 3 = SIC 381 and 382; floor space less than 1,000 m2 Group 4 = SIC 381 and 382; floor space of 1,000 m2 or more. (SIC 321 = textile, SIC 322 = apparel, SIC 381 = fabricated metal, and SIC 382 = non electric machinery). Independent Variables: CONSTANT = Group specific constants; PRODSOLD = Percent of product sold in Bogota; INPUTBT - Percent of inputs bought in Bogota; DISTCBD = The airline distance in km from the CBD (the center of comuna 31) to the establishment location (the center of the comuna 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 twice a week) POPDENS = Population per hectare of the comuna where the establishment is located; LOCQT = Location quotient defined as comuna 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 t1 if renter, 0 if owner. (Assigned to establishments with floor space of.less than 1,000 M2 in both industry groups.) Table 5: ELASTICITIES OF PROBABILITY: LOGIT ESTIM4ATION OF LOCATION CUOICE 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 Note: For definitions of dependent and independent variables, see page 21. The -lasticity of probability is defined as e = (1 ) b where p= the share of ith group, ij - jX bij = jth logit coefficient of the ich group, and Xij = sample mean of the jth independent variable for the ith group. It should be noted that the logit coefficients reported in Table 4 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 (b - b ) instead of bij, where b is the coefficient of the base group. Data Source: City Study Establishment Survey. - 23 - the probability of being in Group 3 is the measure of access to the local inputTmarkets (INPUTBT), followed by the measure of access to the local product markets (PRODSOLD). Local market orientation is very important for this group. For Grot;p 1 (small textile firms), the measure of access to the local input markets is also the most important variable, followed by the proximity to the production workers' residential areas (WKSOUTH). The weakest variable in this case is the distance from the CBD, which implies that small textile firms tend to locate near the CBD compared with other two groups. As the distance from the CBD increases, the probability of being in Group 2 will. be in fact three times higher than that of being in Group 1. However, small metal fabricating firms tend to locate farther away from the CBD than is the case with the 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 away from the CBD. -24- With such a small sample size and a fairly large number of independent variables, the above results look promising. When the above 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 presented an abstract but empirically tractable model of employment location. Using the results of the establishment survey conducted in Bogota, the multinomial logit specification of "bid-rent" function was tested. The estimation of the model was performed with a two-way strati- fication 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 economic activities, and a quality index of public utility 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 included explanatory variables. The predicted location patterns resulting from the model are consistent with those expected a priori. For instance, for small firms the accessibility to the local input and output markets are 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, tend to locate - 25 - in outer areas where more space is available at lower cost. Separate 13 / regression results-- (using the same data set) show a strong relationship between the intensity of labor and capital input use and land price: given a well-shaped (monocentric) rent gradient in Bogota,14-/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. We may conclude that Bogota's pattern of employment location are by no means random; they are actually quite similar to those observed for large cities in North America and Europe. 13/ Reported in the earlier version of this paper presented at the Denver meetings of the Econometric Society. 14/ See footnote 4, and also Villamizar (1980). REFERENCES Burstein, N.R. (1980), "Voluntary Income Clustering and the Demand for Housing and Local Public Goods," Journal of Urban Economics, March. Diewert, W.E. 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