The evolution of land values in the context of rapid urban growth : a case study of Bogota and Cali

World Bank Reprint Series: Number 293 Rakesh Mohan and Rodrigo Villamizar The Evolution of LandValues in the Context of Rapid Urban Growth A Case Study of Bogota and Cali, Colombia Repr~ntedw ~ t hpermlsslon from Matthew Cullen and Sharon Woolery, eds., W l d Congress on land Pol~cy,1980(Lexmgton, Mass D C Heath and Company, LexingtonBooks, 1982),chap. 14,  World Bank Reprints No. 253. Lany E. Westphal, "Fostering Technological Mastery by Means of Selective Infant- Industry Protection," Trade, Stability, Techrrolugy, and Equity in Latin America No. 254. Gershon Feder, "On Exports and Economic Growth,"Jorirnul of Development Economics No. 255. Mohan Munasinghe, "Third World Energy Policies: Demand Management and Conservation," Energy Policy No. 256. Keith Marsden and Alan Roe, "The Political Economy of Foreign Aid: A World Bank Perspective," Labour and Society No. 257. Jarnes A. Hanson, "Contractionary Devaluation, Substitution in Production and Consumption, and the Role of the Labor Market," Jourtlnl of Interriational Economics No. 258. Christiaan Grootaert, "The Conceptual Basis of Measures of Household Welfare and Their Implied Survey Data Requirements," The Review of lncorne arld Wealtlz No. 259. Guy Pfeffermannand Richard Webb, "Poverty and Income Distribution in Brazil," The Review of Incowle nrld Wealtll No. 260. Pradeep K. Mitra, "A Theory of Interlinked Rural Transactions," lournal of Public Economics No. 261. David L. Lindauer and Richard H. Sabot, "The Public/Private Wage Differential in a Poor Urban Economy," jourrrul 17fDevelopment Ecorzonlics No. 262. J. B. Knight and R. H. Sabot, "Labor Market Discrimination in a Poor Urban Economy," Journl7l of Developnlerit Studies No. 263. Car1 Dahlman and Larry Westphal, "Technical Effort in Industrial Development: An Interpretative Survey of Recent Research," The Economics of New Techrzology in Developing Countries No. 264. Michael Bamberger, "The Role of Self-HelpHousing in Low-Cost Shelter Programs for the Third World," Built Erlvirotlwlerlt No. 265. Bela Balassa, "The Adjustment Experience of Developing Economies after 1973," IMF Condifionulity No. 266. Bela Balassa, "Outward Orientation and Exchange Rate Policy in Developing Countries: The Turkish Experience," The Middle East lourrzal ? No. 267. Dipak Mazumdar, "Segmented Labor Markets in LDCs," Arrzericnt~Econi~rnicReview No. 268. Stephen P. Heyneman and William A. Loxley, "The Effect of Primary-School Quality on Academic Achievement across Twenty-nine High- and Low-Income Countries," The Anlerica~llillirnul of Soric~lqyy No. 269. James R. Follain, Jr., Gill-Chin Lim, and Bertrand Renaud, "Housing Crowding in Developing Countries and Willingness to Pay for Additional Space: The Case of Korea," ]ournu/ L IDeoelopnler~kErotlavnics ~ No. 270. Bela Balassa, "Policy Responses to External Shocks in SLI~-SaharanAfrican Countries," ]ournal of Pc~licyMi~delitr~y No. 271. Jaime de Melo and Sherman Robinson, "Trade Adjustment Policies and Income Distribution in Three Archetype Developing Economies," ]or4rnul ($ Deaeloptrlenf Ecor~o~nics No. 272. J . B. Knight and R. H. Sabot, "'The Role of the Firm in Wage Determination: An African Case Study," 0st;lrri Ecoirottiir Pr~pers No. 271 William G. 'Tyler, "Thc Anti-Export Bias in Commercial Policies and Export Perfor- mance: Some Evidence from Recent Brazilian Experience," IVe~tzi~irtsc~~r~ftfic/zes Archio  14 The Evolution of Land Values in the Context of Rapid Urban Growth: A Case Study of Bogota and Cali, Colombia Rakesh Mohan and Rodrigo Villamizar A Simple Model of Urban Land Values That land policy is an important component in the process of public policymaking is evident. One of the key ideas resulting from the United Nations Conference on Human Settlements when it met in Vancouver in 1976 was embodied in the preamble to the recommendations for national action on land: "Land, because of its unique nature and the crucial role it plays in human settlements, cannot be treated as an ordinary asset controlled by individuals and subject to the pressures and inefficiences of the market" (Lichfield 1980). It is ironic, then, that our knowledge of the actual operation of urban land markets and of the resulting land values is highly limited. Pronouncements on the desirability of, and on the contents of, urban land policy are easy to find; facts on which these policies are based are, however, distinguished by their absence. Our objective in this paper is to present a somewhat detailed case study of what has happened to land values in two ~olombiancities during a period of extremely rapid growth when both the cities have roughly doubled their size. We believe that only when we can understand the role of land values in the urban economy and of their relationship with, and effect on, the evolving urban structure of cities during periods of rapid growth, can we begin to enunciate policies that ultimately enhance public welfare. Much of the concern with the operation of land markets arises from the observation of rising land values that are seen as unwarranted or undesirable. Second, when land values do rise rapidly, certain lucky individuals who own land are seen to reap large windfall gains, which they have done little to earn. Such anxiety is understandable since land is a major component of the production of housing-which everyone needs-and of The views reported here are those of the authors. They should not be interpreted as reflecting the views of the World Bank or its affiliated organizations or of Corporaci6n Centro Regional de Poblaci6n.  World Congress on Land Policy, 1980 urban production facilities-on which everyone depends for their live- lihood. Windfall gains or large gains are usually associated with aspects of monopoly power, and thus there is a general suspicion that urban land markets are characterized by monopolistic arrangements. An understanding of the operation of urban land markets and their relationship with urban growth would, however, reveal that these land-value increments must necessarily occur along with urban growth and more in certain parts of the city than in others. Thus, even when there is no monopoly in landowner- ship, windfall gains would accrue to individuals who happen to own land in those parts. The latter is more an income-distribution issue than a land- policy issue. Before presenting the empirical information on land values in Bogotd and Cali, we develop a highly simplified but useful model of land values, which will serve to put in perspective the patterns observed. Gregory Ingram has already presented a paper in this conference that places land in the con- text of conventional economic theory. We continue in a similar vein but pay more attention to the role of land values in ordering the internal structure of a city. The model we developed is highly simplified and might appear to belabor the obvious. Its results, however, are surprisingly powerful and help us understand the patterns we then observe. Urban land is demanded as an asset in two ways. It is, first, a factor of production in the production of housing, factories, or public services (such as roads and parks), when returns to it come in the form of housing services or income from the produced goods. It is also demanded as what might be termed a pure asset in people's portfolios. Developed land is used as both: it usually forms the major portion of a family's assets, as well as a factor of production in housing. Undeveloped land, however, is mainly used as a pure asset. "The function of land prices is to allocate land to valuable uses" (Mills and Song 1979, p. 99). Thus, high land prices indicate scarcity, and the use of land is economized. This can also be stated conversely: when land is scarce, its price is high and its use is consequently economized. As with the prices of other goods, the price of land is important as a signal for the rational allocation of its use. From what does land derive its value? In agricultural uses it is easy to understand that an acre of more-fertile land produces more food and is therefore more valuable as compared with an acre of less-fertile land. In the urban context it is clearly not fertility that gives land its value, but we can stretch the agricultural analogy to obtain an understanding of the value of urban land. If we consider a city surrounded by agricultural land of equal that produces the food consumed in the city, will the land be valuable regardless of the distance from the city? Probably not. We can expect the price of food in the city to be the same regardless of its If all the land is equally fertile we can expect all other inputs  Case Study of Bogoti and Cali 219 to cost the same per acre regardless of the distance from the city. The farmers farther from the city, however, have to spend more on transporta- tion per ton of food than those nearer the city. All farmers will therefore want to locate nearer the city and will consequently bid up the value of land near the city. We will observe what might be called a land-value gradient, with land values declining with distance from the city. We can now drop our unrealistic assumption of equal fertility. More-fertile land will be more valuable than less-fertile land at the same distance; land nearer other amenities such as water sources will be more valuable as well. We now have a simple model of the value of agricultural land: V, = (distance, fertility, other amenities) where V, is the value of land per unit area. By employing minor changes in terminology, we have a model of urban land values. If we regard distance as a measure of access characteristics, fertility as merely use of site-specific characteristics, and rewrite amenities as neighborhood qualities, we can now write, V, = (access characteristics, neighborhood qualities, site-specific characteristics), and we have a plausible model of urban land values. To revert to agricultural land once more, when the city expands, land near the city is converted to urban use, and distance from the edge of the city decreases for all the remaining land. We can therefore expect the value of each plot to rise. The access of each plot improves, and therefore its value rises as well. Much the same thing happens within the city as the city grows and access of plots improves. People congregate in a city in order to take advantage of improved employment opportunities provided as a result of the concentration of a variety of activities that arise because of a concentration of people. The argument is somewhat circular but does capture the essence of cities. In general, economic activities are concentrated in or near the center of a city (we can even define the center of a city as that part of the city that has a con- centration of activities). Measures of the concentration of activities include density of employment and density of residential population. Character- istically, employment densities are highest in the center of cities and decline with distance from the city center. Thus, access characteristics of land also decline with distance from the city center. If all employment in a city is in the center, access characteristics will obviously decline with distance from the city center. This is not an unrealistic representation of small cities, where almost all of the commercial economic activity is located in the city center.  World Congress on Land Policy, 1980 As a city grows, the access characteristics of its center decline on account of increasing average distances from the city center of the residential population. Thus, commercial economic activity springs up in all parts of the city, and ac- cess characteristics of neighborhoods distant from the city center improve. Consequently we can expect residential densities, as well as land values, to in- crease in all parts of the city. This phenomenon is not very different from the effects of an expanding city in agricultural land values. From this simple, plausible model of land values we therefore have a number of strong results: First, land values, population densities, and employment densities can be expected to decline with distance from the city center. Indeed, more-rigorous economic models suggest an exponential decline of these quantities from the city center. Second, an expanding or growing city will result in the rise of land values and densities all over the city, with perhaps a proportionally smaller increase in the center because of its hypothesized relative loss in access cha.racteristics. If the pattern of decline from the city center is exponential, we would then ex- pect the curve to rotate somewhat, as shown in figure 14-1. If V,is the value of Land at the center of the city, VoArepresents the land-value pattern at an initial time period and VoBwhen the city has expanded outward to B later. We are assuming here that V, has remained constant. The slope of such a curve, or the percentage decline in land values or densities per unit distance, is a convenient summary measure describing the structure of the city. The smaller the slope of a density gradient, the smaller the proportion of people residing within a given distance of the city center. The decrease in this slope is often referred to as a measure of decentralization. Third, with a declining slope and nondecreasing V# we can therefore ex- pect a growing city to have secularly rising average land values. Distance Figure 14-1. Pattern of Land Values in a Growing City (1)  Case Study of ~ o g o tand Cali i Fourth, we have suggested that as a city grows, we can expect the con- centration of economic activity to decrease in the center and that subcenters would develop in other parts of the city. Where these subcenters develop, because of their relatively better access characteristics (as compared with other land at the same distance from the city center), we would expect relatively higher land values. A land-value surface in a growing city therefore can be expected to change from a smooth, conical-type surface to one with ridges, valleys, and small hills. Fifth, until now we have concentrated on the access characteristics while ignoring the other determinants of land values: neighborhood qualities and intrinsic quality of the land. In the intrinsic quality of land or site-specific characteristics, we include the level and quality of infrastructure provision and the geography of the site (for example, whether it is level, sloping, or uneven). At similar access levels, we would expect land with higher intrinsic quality to be more valuable. Neighborhood qualities are essentially exter- nalities-positive or negative. Examples of positive externalities are the availability of good views, good neighbors, and good roads. Negative exter- nalities include noise and air pollution. A simple view of urban structure and land has yielded a relatively sophisticated model of the determination of urban land values. Note that I have spoken only of urban land values, not prices. Our observations so far are therefore system free. We may choose to adopt whatever price system we like in conformance with a society's preferences, but to the extent that we regard value as the opportunity cost of using a commodity, the conjec- tures or hypotheses of land-value patterns are general. Consequently if price is determined in a market system, we can use conformance to these patterns as one indication of the efficient functioning of the market. In a market system the price of land at time t is the discounted sum of expected returns from holding it in the future. Specifically: where POis the price of land at time o, R, is the return from it at time t, and r is the discount rate. Thus, the price of land today depends on the return we expect from it tomorrow. This gives another clue as to why land prices can be expected to rise with rapid urban growth. Land values, or opportunity costs, tend to rise in a growing city. In addition, as people come to expect these increases, they will tend to capitalize them today with the expectation of higher returns tomorrow. Thus, we get our sixth result: land prices can be expected to lead urban growth; that is, prices increase before the opportun- ity cost of the land increases.  222 World Congress on Land Policy, 1980 Until now we have mainly talked about the price or value of specific parcels of land. What do we mean when we say that the price of land has in- creased in general? Such a statement is difficult to interpret. The observed price of any commodity is essentially a distribution around some mean, and it is, in general, not too difficult to find the mean. If a market does not con- tain significant distortions, the variance in observed prices is small. Thus, a statement concerning the trend of apple prices, for example, is relatively unambiguous. The key idea is that the good is homogeneous, and we can then talk about its price. As we have seen, urban land derives its value largely from its location (access characteristics and neighborhood qualities), and the value of one parcel can be different from another by an order of magnitude. An extreme view would be that each plot of land is unique and land is therefore not a homogeneous commodity whose average price we can easily discuss. Nonetheless, it is clear that if a growing city causes the land-value pattern to change from ?,A to y,B in figure 14-1, we can say unambiguously that land values have increased in the city. If, however, the change is as in figure 14-2, V,A changes to V2Bas the city expands, land values in the city center have declined and increased near the periphery. Now we cannot make an unambiguous statement about increasing land values in the city. Even the aggregate land values for the whole city are not very informative since the land area has also changed. Thus we need to be careful in making statements about changes in average land value in the context of rapidly expanding cities. Changing Structure of Urban Land Values and Population Densities Both Bogota and Cali have grown at remarkable rates of growth for an ex- tended length of time. Bogota has expanded more than eightyfold over the D~stance Figure 14-2. Pattern of Land Values in a Growing City ( 2 )  Case Study of Bogota.and Cali 223 last hundred years and Cali fiftyfold to sixtyfold during the same period. More importantly, they have both grown five to six times in the post-World War I1 period alone. Table 14-1 summarizes the growth of these cities since 1800. In comparison, in another fast-urbanizing country, South Korea, its two largest cities, Seoul and Busan, have also grown by similar magnitudes. Growth in Colombian cities was most rapid in the 1950s and 1960s and has since slowed. Like land values, overall population densities depend crucially on the definition of a city's boundaries. According to available sources, it appears that the area of BogotA City has been successfully redefined along with its growth, with the surprising result that overall density has remained roughly constant at 100 to 110 persons per hectare. Furthermore, according to cur- rent definition of the boundaries of Cali, the population density of Cali is also very similar. In comparison, the central cities of New York (covering the boroughs of Manhattan, Bronx, Brooklyn, and Queens) and Tokyo (each about 8 million to 9 million people) have densities of about 110and 150 persons per hectare (Mills and Ohta 1976, p. 685); Chicago and Philadelphia about 60; central Buenos Aires 150 and central Mexico City 210 (central areas covering about 3 million people in each city); and Calcutta and Bom- bay about l20 to 140(Mohan 1979).Except for Bombay and Calcutta, these comparisons are for central cities. Probably Bogota is more densely populated than comparable Latin American cities if similar definitions are used but less so in the central city. It is of interest that its density is not very different from New York City (excluding Staten Island). The structure of the two cities has changed with this rapid growth. Table 14-2presents information on changing population densities by ring in the two cities from 1964 to 1978. (See figures 14-3 and 14-4). Ring 1 is the central business district (CBD). Both cities are semicircular in shape, with mountains constraining growth in the other half of the circle. Thus each Table 14-1 Growth of Bogota and Cali, 1800-1978 Bogoro Cali Area Growrh Rare Densirv Growth Rare Year (hectares) Population (% per year! (persons per hecrare) Populatron fmo per year) 1800 n.a. 22,000 6,000 1900 909 100,000 1.5 l l0 24,000 1.4 1938 2,514 330,000 3.2 131 88.000 3.5 1951 n.a. 660,000 5.5 n.a. 284,000 9.0 1964 14,615 1,730,000 7.4 118 638,000 6.3 1973 30,423 2,877,000 5.8 95 930,000 4.2 1978 30,886 3,500,000 4.0 113 1,100,000 3.4 Source: Mohan (1979);Tabares (1979).  224 World Congress on Land Policy, 1980 Table 14-2 Evolution of Population Density by Rings, Bogota and Cali, 1964-1978 (persons per hectare) -p Bogota Cali Area A rea (100 hectares) 1964 1973 1978 (100 hectares) 1964 1973 1978 Ring I (CBD) 5 220 180 205 1.4 210 150 I60 Ring 2 15 210 210 220 15 140 125 l35 Ring 3 25 100 140 140 30 95 135 160 Ring 4 60 90 I50 155 30 25 70 100 Ring 5 140 25 80 110 15 25 50 70 Ring 6 60 I 17 32 Total 305 506 95 115 91 706 103 l21 Source: Mohan (1979); Pach6n (1980); Tabares (1979). Note: All figures rounded. 'City area has been kept constant for all these calculations. In fact both cities grew during the period In question, and many peripheral areas included here were outside the city boundar~esin 1964. ring is semicircular. The maximum distance from the city center is about 15 kilometers (to ring 6) in Bogota and about 10 kilometers (to ring 5) in Cali. Various features of these patterns are worth noting. First is the remarkable similarity in structure of the two cities. Growth has clearly occurred by ac- cretion in the outer rings. The density in the CBD has tended to decline somewhat from about 200 persons per hectare. The growth has occurred on the fringes of the existing cities, along with densification of the inner rings. This process is somewhat different from the growth pattern observed in most U.S. cities as they grew in the early 1900s. "Quantum changes in the technology of urban transit imply not only a layering of incrementally lower density rings in the industrial metropolis, but also sharply lower aggregate densities in entire urban areas, the main growth of which came after 1920-in the auto age" (Norton 1979, p. 69). Thus while Bogota and Cali have also decentralized with growth in the sense that a smaller proportion of the total population lives in any area of constant radius, they have not decentralized like many U.S. cities, where central cities have actually lost populations in absolute terms. This pattern of accretion has been very much in accordance with our hypothetical conjectures. What has happened to land values during the same period? Good land- value data are notoriously difficult to obtain. One of the problems is that it is difficult to separate the value of land from the structure built on it. Most transactions observed in built-up cities are, however, of plots with buildings on them. We have been fortunate in obtaining a unique data set of about six thousand transactions in Bogota covering the period 1955 to 1978 from the files of the long-established real estate firm of Wiesner and Cia Ltd. Guil- lermo Wiesner has kept meticulous records for almost forty years because  Case Study of ~ o g o tand Cali i 225 l Figure 14-3. Bogota Ring System l  World Congress on Land Policy, 1980 North Figure 14-4. Cali Ring System  Case Study of ~ o g o t and Cali 6 227 of his own interest in land valuation. We were able to choose the vacant-land- only transactions and therefore did not have to separate land values from built-up property values. This data set contains more transactions near the city center in earlier years and fewer in later years; the converse is the case for the outer rings. We have confidence in the overall quality of the data except that the land values in the CBD might be on the low side in the later Years. There is little vacant land left in the center of the city; it may be that the last vacant plots being transacted have other quality problems and are therefore not representative of the CBD land values. The data set for Cali, obtained from the Cali Municipal Planning Office, is probably of less-consistent quality since the methods of collection were dif- ferent. The office has kept files on land value averages for each barrio or neighborhood. In 1964 there were 84 such observations and in 1978-1979 about 170. These neighborhood averages were based on direct observation, as well as interviews with local real estate agents. The compilation has been done by different individuals over this time period. We do not know the averaging procedure used within the barrio. Nonetheless, the overall patterns are clear, and we now turn to table 14-3, which gives a summary of the evolving land price surfaces for Bogota and Cali from 1964 to 1978. The prices are given in constant 1978 Colombian pesos; earlier nominal values have been converted to 1978 prices by using the consumer price index. The overall pattern is that there is relative stagnation of land prices near the center and higher rates of price increases near the periphery. This is quite consistent with the evolution of density patterns. There are, however, some surprises. The Bogota data in- dicate an actual decline of land prices in and near the CBD in real terms. This may be because of data problems. Nonetheless, it is clear that land prices have not risen appreciably in real terms in the center of Bogota. The trends are better seen in figure 14-5, which shows a land price index for each ring from 1955 to 1977 in comparison with the consumer price index. Land prices have essentially risen along with the consumer price index in rings 1 to 3 and ahead of it in rings 4, 5, and 6. The picture for Cali is broadly similar but with some differences. First, the magnitude of Cali land prices is similar to that in Bogota. Indeed, the CBD prices seem somewhat higher in Cali than in Bogota. Accounting for data problems, we can at least conjecture that they are unlikely to be less than in Bogota. Their growth rates do seem to be somewhat higher.' That their magnitudes are now somewhat similar is consistent with their densities being similar. Mills and Song (1979) also found for South Korea that the growth in land values in the three largest cities was less than in the next nine largest. Thus, it is safe to conclude that the growth of land values is not higher in larger cities. At this point, we need to recall the hypotheses suggested by our simple land-value model. (1) Land values and population densities do decline from  Table 14-3 Evolution of Land Values by Rings, Bogoth ahd Cali, 1964-1978 (1978 Colombia pesos per square meter) Bog016 Cali A verage A veroge Distonce Growth Rote Disronce Growth Rote from CBD 1964-1978 from CBD 1963-1979 (km.) 1963-1965 1972-1974 1975-1977 (9% per yeor) (km.) 1963 1974 1979 (% per year) Ring I 0 4.250 3,900 3.100 -2.3 0 5,900 4,600 6.400 0.6 Ring 2 2.2 1.850 1,660 1,550 - 1.3 1.8 1.100 1.100 2.400 5.6 Ring 3 3.8 1,350 1,350 1,320 - 0.2 3.4 520 480 1,030 4.9 Ring 4 6.5 870 1,080 1.130 1.9 5.4 380 410 960 6.6 Ring 5 9.8 570 800 850 2.9 6.9 I 50 370 810 12.0 Ring 6 15.4 370 700 730 4.9 Sources: Villamizar (1980);Velasco and Mier (1980).,l978 exchange rate USSl = 38.00.  Case Study of ~ o g o tand Cali i 229 ---- Consumer price index 1956 1960 1962 1964 1966 1968 1970 1972 1974 1976 Years 6,500 6,500 I I I I 1 6,000 6,000 5,500 5,500 5,000 ---- Consumer price index 5,000 4,500 4,500 4,000 4,000 m p - 3,500 3,500 3,000 3,000 li 2,500 2,500 2,000 2,000 1,500 , 1,500 y3 1,000 ..T; F/ 1,000 /H/ 500 500 .---W- I 1 I I 1956 1960 1964 1966 1972 1976 Years Source: Villarnizar (1980). p. 16. Figure 14-5. Land Price Indexes in Bogoti  230 World Congress on Land Policy, 1980 the city center in Bogota an Cali. (2) Land values and densities increase all over the two cities along wlth urban growth, but proportionately less so in the center. (3) Bogota and Cali do have rising average land values; in Bogota they have growth at about 3 to 4 percent per year in real terms since 1955. Recall, however, the caution with which average land values should be interpreted. To reemphasize this point, we can say with confidence that land prices have increased in real terms on the periphery, but at best, they have remained constant in the center. We now measure the changes in land-value and density patterns more systematically by measuring the changes in density and land-value gra- dients. We can express the two patterns by simple exponential equations: and where D, is the population density at Xkilometers from the center, V, is the land value X kilometers, and Do, Vo, g and h are the parameters to be estimated from the data. In fact Do and V. estimate the density and land value at the center (when X =o, D, = Do e-O = Do);and g and h estimate the two gradients that can be interpreted as the percentage decrease in den- sity and land values, respectively, per kilometer. Tables 14-4 and 14-5 pre- sent the results of these calculations. First consider table 14-4, which gives the density gradients for Bogota and Cali for 1964, 1973, and 1978. The unit of observation is the barrio or neighborhood. The table shows that g declines over time as expected for both the cities and is higher'for Cali than for Bogota. For purposes of com- parison, in 1970 g was -0.08 for New York, about -0.13 for Atlanta, -0.22 for Seoul, -0.17 for Mexico City, -0.12 for Buenos Aires, and -0.08 for Tokyo (Ingram and Carroll 1981; Mills and Tan 1978). Thus Bogota has a gradient similar to other large cities. Among smaller cities like Cali we have information for Montcrrey, -0.27, and Guadalajara -0.41 (Mexico); Belo Horizonte, -0.27, and Recife, -0.17 (Brazil); Sapporo, -0.23 (Japan); and Busan, -0.13 (South Korea). We may conclude that Cali is not atypical. In general we can expect that the larger the city, the higher the income, and the lower the transportation costs (Mills and Tan 1978),the lower is g. This also implies that g depends on the age of the city (Harrison and Kain 1974). Older cities were built when intracity transporta- tion costs were high and therefore the central cities were very dense. Conse- cluentl~they had very high land values in the center. This pattern tended to persist over time. We can therefore expect that the fast-growing cities in Latin America would have relatively flatter density gradients.  5 Table 14-4 V, C+ Population-Density Patterns in Bogota and Cali, 1964-1978 C a Y D,: Density at CBD ~opu~otion 0, (thousands) N" Actualb Estimate g' I C Estimote g R2 (thousands/sq.km.) (0 0 -- e-. Call 1964 540 131 21 39 (17) -0.51 0.21 1973 930 195 16 24 (11) -0.44 0.09 1978 1,100 193 16 29 (11) - 0.25 0.11 Sources: Bogota barrio population data from City Study files. Cali barrio population data from Tabares (1979). Note: Equation estimated was D* = Dn e-gX where DVis population density in people per square kilometer at distanceXin kilometers and D, is estimated population dens6y at ~ B D . 'Number of data points in regressions. b~esidentialpopulation density for central business district (CBD). 'Estimate of D, from equation in note. *~stimateof D, from D , = D,e(81~ ~2,". Other results not reported here. + 'All estimates significant at the 0.01 level.  Table 14-5 Land-Vdue Patterns in BogotP and Cali (Pricesin 1978 Col.pesos per m2 and distances in kilometers) V,-' Price or CBD Populorion ffhourcrndsl W Actuolb Esrimore IC Esrimore 2d he RZ Bogor4 1959 38 6,300 2,400 -0.18 0.56 1965 1.730 38 5,600 2,500 (2,470) -0.15 0.55 1973 2,878 38 5.500 1,9o(J (2.290) -0.08 0.39 1977 3,500 38 4,300 1.760 (2,240) p -0.07 0.35 a Coli 0 1959 5,000 2.240 -0.55 0.44 2 1%3 640 84 ~ , m O 2.030 (4,700) -0.51 0.41 % 1974 WO 155 3.700 1,030 (2.130) -0.25 0.30 a, 1979 1,100 171 5,300 2.070 (4,950) -0.23 0.27 g Sources: Mohan (1979); Tabares (1979); Villamizar (1980); Velasco and Mier (1980). 0 3 Note: Equation run was Vx = V, e where Vxis price at distanceXand P, is estimated price at CBD. r P, 'Number of data points in regressions. 3 a b~pproxirnateaverage for CBD. Highest observed values are about three times these values. T1 'Estimate of V, from equation in note. d~stimateof V, from vx= V. c fhV ~$1. Other results not reported here. + 'All estimates significant at the 0.01 level.  Case Study of Bogotiand Cali Now we observe the estimates for Do:the hypothetical density at the center of the city. Column 4 gives the estimated densities in thousands per square kilometer. Column 3 gives actual observed densities. Note that cen- tral densities have remained relatively constant with a small observed decline, a phenomenon at least consistent with the behavior of land values in Bogota. The estimated values are consistently higher. The CBD contains a large proportion of commercial economic activity and a relatively small residential population. It is therefore to be expected that estimated Do would be higher than the actual. Now consider table 14-5, which gives comparable land-value patterns for Bogota and Cali. Once again, the estimates for land-value gradients decline with time in both the cities, as expected, and those for Cali are steeper than those for Bogota. The comparability with the density gradients is remarkable (table 14-6). The estimated patterns are brought together and graphed in figure 14-6,where their comparability is evident. Recalling our simple model, we would expect land-value gradients to be similar to density gradients. Fur- thermore, they are consistently lower than the density gradients, as has been theorized (Mills and Song 1979, p. 109). A comparison of estimated V. (land value at the center of the city) with actual V. reveals that our estimates are con- sistentlylower than the actual values. This implies that the gradient of the curve should be much steeper at the center of the city than we have estimated. Be- cause of the high concentration of economic activity at the center, we can ex- pect the land values to be determined much more by the employment density than by the residential density. Employment density falls rapidly from the cen- ter, and it is therefore quite plausible that land values will exhibit a similar de- cline. Estimated V. therefore is quite likely to be lower than this central peak. This brings us to a minor revision of the land-value and population- density functions. We have observed that the estimated densities were con- sistently higher for the CBD than the actual densities while land values are consistently lower. Indeed what we would expect is for residential densities to increase somewhat from the CBD and then decline, while land values should decline rapidly from the city center and then slow down. We have therefore attempted to fit quadratic exponential functions to the data: Table 14-6 Changes in Density and Land Value for Bogota and Cali Bogora Cali Land Value Densir v Land Value Densit v  234 World Congress on Land Policy, 1980 Populat~on.DensityGradient. ~ o g o t i Populallon.Denrlty Oradlent, Call D~stancefrom CBD ~nk~lometers D~stancrfrom CBD in kilometers Land.Value Gradient, Call D~stancefrom CBD in kilometers D~stancefrom CBD in kilometers Source: Tables 14-4 and 14-5. Figure 14-6. Changing Urban Structure of Bogotfi and Cali, 1964-1978 and With g, positive and g, negative, the shape of the curve is as suggested above for the density (figure 14-7), while for land values h, is negative and h, is positive, which gives a rapidly declining curve, illustrated in figure 14-8).  Case Study of Bogoti and Cali 30,000 0 0 2 4 6 8 10 Distance from CBD in Kilometers Source: Tables 14-4 and 14-5. Figure 14-7. 1978 Population-Density Gradient, Cali The signs of the estimated coefficients are consistent with these conditions. The quality of statistical fit improves in all cases, implying that the quadratic functions are better approximations to the actual patterm2 In particular, note column 5 in tables 14-4 and 14-5. The estimates of Do and V, from the quadratic functions are somewhat closer to the actuals. Therefore the land-value surfaces of Bogota and Cali have evolved about as we would expect within the context of a very simple urban model. Land values have been highest at the CBD but have remained at a constant level in real terms over at least the past fifteen years. They have increased faster as one moves out from the city center and very much in accordance with the accretion of population that has occurred in successive outer layers of the city. The increases in real terms have been modest. Bogota and Cali do not display a chaotic land market in this sense. If anything, the behavior of the land-price surface and of population densities is a bit too regular. Both density gradients and land-value gradients have flattened, but we must not be too hasty to conclude that these cities have decentralized in the sense of central cities losing population. It is important to note that among large European cities, this process of decentralization is of long standing. The population of central London reached its peak in 1930-1940, Paris in 1920,  236 World Congress on Land Policy, 1980 Distance from CBDin Kilometers Source: Tables 14-4 and 14-5. Figure 14-8. 1979 Land Value Gradient, Cali Vienna in 1910, and Rotterdam, Ziirich, Hamburg, Glasgow, and Amster- dam in 1950-1960(Mitchell 1978, p. 12). All have declined since those dates, but with increasing suburban populations. To the extent that people con- gregate to improve economic opportunities for themselves and thereby im- part higher values to iand, we need to understand these processes better. With low transportation costs (despite the energy crisis) and changing manufacturing technology, there is reason to believe that manufacturing jobs are indeed increasingly moving to peripheral locations (Lee 1979), although the volume of these jobs has not yet been large enough to reduce the importance of the city center as a commercial center. We can expect greater movement of commerce and service jobs with manufacturing in the future with the obvious consequences on access characteristics of peripheral locations. The Smoothly Evolving Land-Value Surface: Some Wrinkles So far we have treated the city in a relatively simple manner. The measure- ment of land-value and population-density gradients assumes that the city is symmetrical around the city center. In the cases of Bogota and Cali, each  city is constrained by mountains on one side, and the cities are therefore semicircular, with the city center roughly at the center of the semicircle. The cities are not, however, symmetrical otherwise. If we divide each city into approximate pie slices or radial sectors, as shown in figures 14-9and 14-10, we observe distinct differences among the sectors (see Mohan 1979and Ter- re11 1980). In Bogota in particular, the north (sectors 7 and 8) can be characterized as rich and the south (sectors 2 and 3) as poor. Sectors 4 and 5 comprise the industrial zone or corridor. In Cali the picture is more mixed, but, broadly, the western part of the city (sectors 2, 6, and 7) is richer than the eastern part (sectors 3, 4, and 5). In general, jobs exceed the number of resident workers in the rich sectors, and the converse is true in the poorer sectors. As we might expect, the density of population is higher in the poor as opposed to the rich sectors. The question now is how these differences in land use in different sectors of the city affect population-density patterns and land values. Do density patterns and land-value gradients hold up if calculated for different sectors of the two cities? In order to illustrate the patterns, we include computer maps of land value and population density in Bogota, which show at a glance where population densities and land values are high: the darker the shading, the higher the density or land value. Contrary to our expectations the two maps do not appear to be too similar. (See figures 14-11 and 14-12). It is true in general, though, that in any direction from the CBD, the darker shading is nearer the center, with lighter and lighter shades as we move toward the edge of the city. Within the same ring (or same distance from the CBD) it is clear that both densities and land values are quite heterogeneous. Indeed, the denser areas appear to have lower land values than the less-dense areas within the same ring. How is the paradox to be resolved? Until now we have concentrated on the access characteristics of land as determinants of land value and have been using distance from the CBD and residential densities as proxies for access characteristics. Now we must enrich our notions of access characteristics. In addition we have to consider the other determinants of land value mentioned in our simple model: neighborhood quality and intrinsic quality of land. By access characteristics we mean the proximity of land parcels to economic opportunities. We had hypothesized that large or dense agglomerations of people were instrumen- tal in increasing these economic opportunities and that this was the reason for the clustering of population near the city center. Thus a concentration of economic activity in the center produced relatively high population den- sities and consequently high land values, both of which then declined uith distance. The observation that the rich live in some parts of the city and the poor in others leads us to revise some of these ideas. That more jobs are located in rich sectors means that those sectors are economically more attractive  World Congress on Land Policy, 1980 Figure 14-9. Bogota Sector System  Case Study of 8ogotA and Cali 239 Figure 14-10. Cali Sector System and firms have a greater tendency to locate there. Thus the lower densities of those areas are being more than enhanced by purchasing power. As a proxy for access characteristics, we have to employ the notion of purchasing power. The product of population and mean income is probably not a good measure of these access characteristics since the requirements of a large number of poor people do not aggregate; each household has meager demands so poor sectors can support only a limited number of economic ac- tivities. Consequently the rich neighborhoods have an excess of jobs over the resident labor force, and the access characteristics of these neigh- borhoods are not adequately measured by population densities. In ad- dition we can expect the infrastructure provisions (such as roads, lighting, water supply, and sewerage) to be better in high-income neighborhoods, and therefore both neighborhood quality and intrinsic site characteristics are more desirable. All of these factors combine to produce somewhat higher land values than the population densities would lead us to expect in relatively rich neighborhoods. We estimated the population-density and land-value gradients for each sector in Bogoth and Cali and emerged with striking results. Table 14-7 gives the estimates of these gradients along with the R2for each estimated regression. 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