Before zoning chicago by karolina Moretti

Regional Science and Urban Economics 29 (1999) 473–489

Land use before zoning: The case of 1920’s Chicago Daniel P. McMillen a , *, John F. McDonald b ,c a

Department of Economics, Tulane University, New Orleans LA 70118, USA Department of Economics, University of Illinois at Chicago, Chicago, USA c Department of Finance, University of Illinois at Chicago, Chicago, USA

Received 15 September 1997; received in revised form 9 December 1998; accepted 7 January 1999

Abstract Attempting to mitigate the negative externalities associated with mixed land use, most major US cities passed comprehensive zoning ordinances in the 1920’s. Modern analysts suggest that more exclusionary motives account for zoning’s widespread popularity. We document the extent to which land use was mixed before Chicago adopted its first zoning ordinance. We find numerous instances where manufacturing and commercial lots were present on residential blocks. Mixed land use was most prevalent in older areas of the city and in areas where it caused little harm—along major streets and near public transportation.  1999 Elsevier Science B.V. All rights reserved. Keywords: Zoning; Land use; Nonparametric JEL classification: R14; R52; C14; N42

1. Introduction The number of American cities with zoning ordinances rose from 35 to nearly 500 during the 1920’s (Mills, 1979). What accounts for zoning’s popularity surge? Much credit goes to concerns over negative externalities associated with having commercial and manufacturing establishments in residential areas. The first Chicago zoning ordinance of 1923 is exemplary. The Chicago Zoning Commission *Corresponding author. Tel.: 11-504-862-8344; fax: 11-504-865-5869. E-mail address: dmcmill@mailhost.tcs.tulane.edu (D.P. McMillen) 0166-0462 / 99 / $ – see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S0166-0462( 99 )00004-6

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

474

was established in 1919, three years after New York’s prototype was passed. Approval for the zoning ordinance came on April 16, 1923. The Final Report of the Library, City Planning and Zoning Committee of the Chicago Real Estate Board on Zoning in Chicago (1923, p. 5) argues that the externalities were sufficiently severe to have caused land values to have declined by as much as $1 billion, and cites (p. 12) ‘‘innumerable instances of the invasion of residential property by objectionable buildings and uses [which shows] the importance of prompt action in the prevention of such nuisances in the future.’’ Zoning ameliorates the effects of negative externalities by separating land uses, but it is not the only means by which land uses can be segregated. If the presence of manufacturing and commercial establishments lowers residential land values by more than the gain in non-residential values, then the Coase Theorem (Coase, 1960) suggests that landowners in the affected area have an incentive to collectively ensure that the land be residential. Indeed, Siegan (1972) argues that land use patterns in Houston, which is the only major city in the United States left without a zoning ordinance, are not much different from those in other large cities. Houston has big companies that develop large tracts of land, and substitutes private covenants for public zoning. If instead development occurs through the uncoordinated efforts of individual land owners, the Coase Theorem may fail to hold because cooperation is costly. Externalities of mixed land use may prove serious if non-residential enterprises are attracted to residential areas. Externalities are unlikely to be serious if non-residential firms find it profitable to locate near similar establishments. Mayer and Wade (1969) (p. 234) suggest that manufacturing clustering was the rule in Chicago: Chicagoans introduced the organized industrial district idea to the United States. Under this scheme, the district acted like the residential developer, assembling land, laying out streets, and installing utilities. It often provided architectural engineering and financial services to the industrial clients; occasionally the district even furnished dining facilities and executive clubs. But most of all it brought together comparable business enterprises and created an attractive environment that most single companies could not readily provide themselves. Similarly, agglomeration economies for shops and offices are likely to provide commercial firms with incentives to locate away from residential districts. If land use segregation is the norm, why was it necessary to zone every square foot of the City of Chicago for either single-family residential, multiple-family residential, commercial, or manufacturing use? First, it is important to recognize that norms are not ironclad. Offending land uses can occur occasionally, causing financial hardships on those whose property values fall. In principle, land values could be improved through selective zoning, forcing the relatively small number of

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

475

offensive manufacturing and commercial firms out of residential areas. But the courts in the 1920’s did not look favorably on selective zoning: comprehensive zoning ordinances covered the entire city to pass court review, despite the likelihood that mistakes would be made. Second, the purpose of zoning may be less benign than the externality argument presumes, instead being used as a means of excluding undesirable groups, whether or not ‘undesirability’ is justified on economic or other grounds. As Mills ((1979) p. 537–538) argues, ‘‘The history and analysis of land-use controls can hardly be said to be one of the happier aspects of American life. They constitute an extraordinarily broad and powerful grant of authority to local governments to use for ill-defined purposes... [T]he combination of real-estate taxes as the main source of local government revenues and a laissez-faire attitude on the part of the courts toward local-government land-use controls guarantees that controls will be excessively exclusionary.’’ Little is known about land use before zoning because nearly all American cities were zoned in the 1920’s, before extensive data sets were collected. Although several studies have analyzed land use patterns in cities without zoning (Cappel, 1991; Siegan, 1972; Warner, 1978), the only detailed quantitative analysis is presented in McDonald and McMillen (1998). McDonald and McMillen’s results are consistent with those of the other authors, suggesting that land use was predictable and orderly in Chicago in 1921. Land was most likely to be residential farther from the central business district (CBD) and nearer Lake Michigan. Commercial land use was most common along major streets and near elevated train stations. Nearly all land near navigable waterways was used for manufacturing. McMillen and McDonald’s (1993) analysis of land values implies that these land use patterns were sufficiently similar to those produced by a Coasian market that zoning was not capable of raising land values in 1920’s Chicago. Our previous studies focus on overall land use patterns, but do not explicitly consider the exceptions where manufacturing or commercial firms located in residential areas. In this paper, we begin by documenting the frequency and patterns of mixed land use. We find that medium or heavy manufacturing establishments are far more likely to locate in isolated sites than to be mixed with other uses. Light manufacturing and commercial firms often locate near one another. All uses—including residential—are commonly found on blocks with mixed land use. We next present multinomial logit estimates of the probability that a city block contains one of the following five land use combinations: all residential, all commercial, all manufacturing, commercial and residential, and manufacturing combined with some other land use. The categories are chosen to mimic the structure of the Chicago zoning ordinance, and reflect the actual data frequencies (potential categories with few observations are omitted). The multinomial logit model predicts all categories well. Commercial and manufacturing establishments are drawn to major streets and to areas near elevated and commuter train lines. Manufacturing establishments are attracted to sites served by navigable waterways

476

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

and freight rail lines. Mixed land use occurs primarily in older areas of the city at sites that are attractive to all uses, most importantly along major streets and near public transportation. Urban areas are more complex than assumed in the monocentric city model. Some areas have wetlands, others have forested hills; some streets are large and uncongested, while others have troublesome bottlenecks. Functional forms may be far more complex and nonlinear than implied by convenient econometric models. Nonparametric estimation procedures can be very useful in such situations. We extend previous work by proposing a nonparametric logit model that is suited for spatial modeling. The nonparametric model identifies exclusive commercial and mixed manufacturing blocks better than multinomial logit. Our most important results survive the scrutiny of the more complicated estimator: major streets in older areas of the city are more likely than other locations to have mixed land use. The results support our previous work by suggesting that externalities were not severe enough in 1920’s Chicago to warrant a city-wide zoning ordinance. Small shops might exist at some street intersections, but such cases were hardly sufficient to warrant restricting land use in every block of the city. Grandfather clauses were included in the zoning ordinance to allow existing non-residential firms to continue in residential areas even when segregating land uses could have raised land values. The long-run effect of the 1923 Chicago zoning ordinance was to create monopoly power for existing non-conforming uses, while delaying or preventing the market’s ability to adapt to changing economic conditions.

2. Data Prior to adopting the zoning ordinance, Chicago’s Zoning Commission arranged to have a map drawn showing the use of every building in the city. The detailed map shows current (1921) building heights, setbacks, and lot widths. Primary categories for land uses include housing, commercial, storage wholesale, five categories of manufacturing, and special uses. Each category is divided further. Housing includes single-family dwellings, two-flats, apartments, boarding or lodging houses, and vacant residential buildings. Commercial includes retail stores or offices; garages and public liveries; gas stations; hotels with retail stores on the ground floor; automobile show rooms; theaters; undertaking; and ‘‘small manufacturing where not more than 5 skilled workmen are employed and where there is no noise, smoke, odor, fumes, gases, danger, or yard storage.’’ Externalities are used to distinguish the five manufacturing categories. Manufacturing A includes ‘‘general manufacturing which is carried on in [a] building without yard storage and without noise, smoke, odors, danger, excessive fire risk, or other nuisance features.’’ Category D has the most harmful externalities: ‘‘manufactures and storage of explosives and high pressure gases.’’ Our data set is a sample of 1116 blocks drawn at approximately four-block

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

477

intervals from an area bounded by Devon Ave. on the north side (6400 North), 67th St. on the south, Central Ave. on the west (5600 West), and Lake Michigan on the east. The data points form a lattice. All blocks were zoned for multiplefamily residential, commercial, or manufacturing use. Our objective is to determine the extent of land use mixing within an area. One complication is choosing the appropriate area to analyze. Boundaries between neighborhoods are sometimes quite sharp in a city. Homeowners may not be concerned about the effects of a ‘nuisance’ activity which is outside of their neighborhood, even if the nuisance is only a block or two away. Obvious measures of the appropriate area include the full block, the block plus those surrounding it, the block face plus the block face across the street, or simply the block face. We chose the last option for three reasons. First, zoning maps published in 1923 clearly show that the block faces were zoned uniformly for one use, while opposing block faces or surrounding areas often were zoned for other uses. This observation suggests that zoning officials thought the block face was the appropriate unit of analysis. Second, most urban nuisances dissipate quickly with distance, but any nuisance on the block face is likely to affect a homeowner. In contrast, nuisance activities across the street or in the street behind one’s home may be viewed as a minor hassle of urban life. Third, using the block face as the unit of observation simplifies a daunting data collection task. Our measure runs the risk that we overestimate the number of blocks with exclusive land use, but reduces the risk that a nuisance activity is indicated in an area that homeowners view as exclusive. The land use map is so detailed that many categories are unobserved or few in number. We employ six basic categories to assure a sufficient number of observations in each—vacant, residential, commercial, light manufacturing, medium or heavy manufacturing, and ‘other’. The last category includes government buildings and, most commonly, churches. For our logit models, we supplement the land use data with standard explanatory variables. Measures of access include distance from Chicago’s CBD, Lake Michigan, the nearest elevated train (‘el’) station, and the nearest commuter train station. We distinguish between el and commuter train stations because the el is used for intra-city travel, whereas commuter trains bring passengers from the suburbs. Although commercial firms may find access to both types of stations valuable, city residents will presumably pay a premium only to be near the el. We also include distance from a navigable river or canal as an explanatory variable because manufacturing firms are concentrated at sites near waterways. We include a dummy variable for location along a major street because these sites are highly valuable for all land uses. Chicago’s grid street system has major streets every mile (1600 north, 2400 north, etc.).1 In previous work (McDonald and McMillen, 1998; McMillen and McDonald, 1

We do not include diagonal streets because our sampling procedure excludes them.

478

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 â&#x20AC;&#x201C; 489

1993), we also included dummy variables for proximity to a freight rail line, waterway, and el line, where proximity is defined as within one-eighth of a mile (a distance of one block). We continue to use the freight rail line dummy: sites near rail lines are expected to attract manufacturers, while creating nuisances that repel residences. However, we are forced to exclude the other two explanatory variables because they predict at least one land use category perfectly in the estimated logit models.

3. Block-face land use patterns We begin our data analysis by determining the frequency of mixed land use in our sample. Table 1 shows that 452 of the 1116 blocks contain only one use or are entirely vacant, and another 224 blocks combine vacant land with a single use. Fewer than 40% (the remaining 440 of 1116) of the blocks have mixed land use. The third column of figures in Table 1 shows the number of blocks in which the indicated land use is combined with one or more other uses. The column includes significant double counting. For example, a block with residential, commercial, and light manufacturing lots is counted in each of the first three rows. Residential lots are mixed with other uses in 57.08% of the blocks that contain residential lots. Commercial lots are the most likely to be mixed with other uses: over 80% of the blocks containing commercial also include other uses. Although medium and heavy manufacturing lots are combined with other uses in only 25.49% of the

Table 1 Frequencies of mixed vs. exclusive land use

Residential Commercial Light manufacturing Medium or heavy manufacturing Other land use Vacant Column total

One use only (% of row)

One use plus vacant (% of row)

Two or more uses (% of row)

122 (17.45) 55 (11.78) 24 (19.20) 71 (69.61) 30 (27.52) 150 (27.93) 452 (22.17)

178 (25.46) 33 (7.07) 4 (3.20) 5 (4.90) 4 (3.67) â&#x20AC;&#x201C;

399 (57.08) 379 (81.16) 97 (77.60) 26 (25.49) 75 (68.81) 387 (72.07) 1363 (66.85)

224 (10.99)

Row total 699 467 125 102 109 537 2039

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

479

blocks, light manufacturing lots are frequently mixed with other uses. Table 1 demonstrates that mixed land use was quite common in 1920’s Chicago. Table 2 analyzes the extent of land use mixing within multiple-lot blocks. A block with a store on the corner followed by six houses is more segregated than a block with three houses on each end and a store in the middle. To construct Table 2, we begin at the edge of each block and count the number of times one use is followed by another as we move to the block’s end. To understand how this table is constructed, consider a hypothetical block with a store followed by three houses. The first row of Table 1 would indicate that residential lot j is next to residential lot j 1 1 twice on this block, but no residential lot is followed by another use. The second row would indicate that commercial lot j is followed once by residential lot j 1 1, but not by other uses. Our convention of starting on one side of the block means that the matrix defined by Table 2 is not symmetric. We treat Table 2 as a Table 2 Land use patterns in multiple-lot blocks Land use, lot j

Res.

Com.

Light mfg.

Medium or heavy mfg.

Other land use

Vacant

Column total

Land use, lot j 11 Res.

Com.

Light mfg.

2736 2337.84 (25.66) [3204] 348 654.73 (223.40) [167] 34 87.16 (210.13) [16] 8 25.68 (26.15) [6] 37 40.54 (20.98) [40] 262 279.05 (21.87) [280] 3425

360 677.12 (224.12) [180] 497 189.63 (27.67) [519] 38 25.24 (2.87) [6] 2 7.44 (22.23) [2] 12 11.74 (0.08) [10] 83 80.82 (0.28) [71] 992

39 94.20 (210.24) [15] 43 26.38 (3.65) [9] 37 3.51 (18.35) [25] 6 1.04 (4.97) [5] 3 1.63 (1.09) [2] 10 11.24 (20.39) [4] 138

Medium or heavy mfg.

Other land use

5 27.99 (27.74) [4] 5 7.84 (21.13) [2] 6 1.04 (4.94) [4] 18 0.31 (32.16) [18] 1 0.48 (0.75) [1] 6 3.34 (1.52) [6] 41

36 40.27 (21.20) [39] 10 11.28 (20.43) [9] 3 1.50 (1.25) [1] 0 0.44 (20.67) [0] 3 0.70 (2.79) [3] 7 4.81 (1.05) [7] 59

Vacant

Row total

284 282.59 (0.16) [295] 66 79.14 (21.71) [62] 11 10.54 (0.15) [4] 4 3.10 (0.53) [4] 4 4.90 (20.43) [4] 45 33.73 (2.11) [45] 414

3460

969

129

413

5069

The first number in each cell is the actual frequency. The second number is the expected frequency. T2values are in parentheses. Expected values under zoning are in brackets.

480

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

contingency table (Agresti, 1996) to construct the expected frequencies and t-values.2 The diagonal elements of Table 2 indicate that houses tend to locate next to houses, stores next to stores, and so forth. The off-diagonal elements contain the more interesting results. The first row of Table 2 indicates that commercial, light manufacturing, and medium or heavy manufacturing lots follow residences far less frequently than if land use were assigned randomly. The second row indicates that commercial lots are apt to be followed by light manufacturing, but not by medium or heavy manufacturing. However, the third and fourth rows indicate that all types of manufacturing are prone to locate together. ‘Other’ land use and vacant lots are mixed with other uses fairly randomly. The numbers in brackets in Table 2 show expected land use patterns under Chicago’s 1923 zoning ordinance. Zoning was hierarchical in the 1920’s. Residential zoning excluded commercial and manufacturing establishments. Residences were permitted in areas zoned commercial, but manufactures were prohibited. All uses were permitted in areas zoned for manufacturing. Grandfather clauses, which were included for legal reasons in the zoning ordinance, permitted existing non-conforming land uses to continue indefinitely. We ignore the grandfather clauses to generate the expected land use patterns because the zoning maps indicate the long-run plans of the Zoning Commission. If a block is zoned residential, we assume any manufacturing or commercial establishments are converted to residential use. When a block is zoned commercial, we assume residential lots remain residential, but any manufacturing lots are converted to commercial use. Land use is not altered on blocks that are zoned for manufacturing. We assume that ‘other’ land uses and vacant lots are unaltered by zoning. The bracketed numbers in Table 2 show that zoning was expected to alter existing land use patterns. Instances where residences were next to commercial establishments would be reduced by about a half. Light manufacturing firms also were likely to be zoned out of areas that formerly had mixed land uses. Heavy manufacturing was hardly affected by the zoning ordinance because it already was highly segregated. Most blocks were not altered by zoning even in the absence of grandfather clauses. Blocks with mixed land use were often zoned for one of the more restrictive uses. Together, Tables 1 and 2 suggest that mixed land use was common in 1920’s Chicago, but integration was still limited. Commercial lots were often mixed into residential areas, but far less likely than by chance. Manufacturing firms were far 2

To illustrate, consider the first entry in Table 2. Residential lots are followed in one direction by other residential lots 3460 times, and are followed in the other direction by residential lots 3425 times. With 5069 total joins between lots, these numbers indicate that sheer randomness would produce residential-residential joins (3460 / 5069)3(3425 / 5069)3506952337.84 times. The variance is 2337.843(123460 / 5069)3(123425 / 5069), leading to a standard error of 15.514. The t-value is (273622337.84) / 15.514525.66.

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

481

more likely to locate near commercial establishments or other manufacturers than to be near houses. However, both tables demonstrate that the Zoning Commission’s worries were not entirely unfounded in that residential and manufacturing uses were occasionally mixed together on the same block.

4. Logit estimation procedures Our results so far do not distinguish between locations within the city. Controlling for location is important because mixed land use is less of a problem in some areas of a city than in others. For instance, mixed land use may be desirable in older areas near the CBD that comprise people who place a high value on access, whereas residents of more distant locations may prefer exclusive developments. This section presents logit models explaining block-level land use. Our objective is to determine whether mixed land use is most common in areas where it is more desirable, that is, along major streets, near the CBD, and near public transportation. Our dependent variable indicates which of six land-use categories is represented on a block—exclusively residential, exclusively commercial, exclusively manufacturing, residential and commercial, or manufacturing combined with one or more other uses.3 Descriptive statistics are presented in Table 3. Exclusively residential blocks are more likely to be far from the CBD, el stops, and navigable waterways, and are unlikely to be near freight rail lines or along major streets. Blocks are more likely to be exclusively commercial along major streets. Proximity to rail lines and navigable waterways greatly increases the chance of having manufacturing firms on a block. In fact, the dummy variable representing proximity to a river or canal cannot be included in the logit models because it perfectly predicts the absence of residential land. Mixed land use is most common along major streets and close to el stops. Unlike simple descriptive statistics, logit models control for the effects of other variables. We present both nonparametric and standard multinomial logit estimates. Nonparametric procedures offer important advantages in analyzing spatial data, as recent research demonstrates (Brundson et al., 1996; Fotheringham et al., 1997; McMillen, 1996; McMillen and McDonald, 1997; Meese and Wallace, 1991). The homogenous plain of theoretical urban models is a useful assumption, but real cities are far more complex. Terrain variations, parks, traffic bottlenecks, and the 3

The 150 completely vacant blocks are excluded from the analysis, leading to 966 observations for the logit models. Small numbers force us to combine some land uses. We treat ‘other’ land use as commercial because churches and government buildings seem most like commercial establishments. Light, medium and heavy manufacturing are combined, and we do not distinguish between manufacturing–commercial and manufacturing–residential blocks. The resulting categories are consistent with the hierarchical structure of Chicago’s first zoning ordinance.

482

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

Table 3 Descriptive statistics Explanatory variable

All res.

All com.

All mfg.

Res. and com.

Mixed, with mfg.

Distance to CBD

6.281 1.693 1.305 9.461 3.609 2.276 0.000 9.250 1.037 0.900 0.125 4.142 0.871 0.540 0.000 2.675 9.00 9.00 2.448 1.333 0.125 6.482 0.000 300

5.889 2.463 0.177 10.229 3.544 2.069 0.000 8.750 0.941 0.937 0.000 3.893 0.816 0.472 0.000 2.226 17.19 58.59 1.891 1.376 0.000 6.250 3.12 128

4.257 1.634 0.673 7.385 3.408 1.704 0.125 6.875 0.803 0.547 0.000 2.501 1.042 0.493 0.062 2.129 91.67 13.89 0.907 1.111 0.000 4.056 37.96 108

5.007 1.904 0.884 9.376 3.095 1.876 0.125 9.000 0.735 0.670 0.000 3.925 0.872 0.493 0.062 2.388 8.92 22.46 1.622 1.104 0.125 5.923 0.00 325

3.524 1.907 0.177 8.203 2.620 1.805 0.062 7.125 0.477 0.398 0.000 1.973 0.857 0.523 0.000 2.253 40.95 33.33 1.310 1.122 0.000 5.101 4.76 105

Distance to Lake Michigan

Distance to ‘el’ stop

Distance to commuter train stop

Near freight rail line (%) Along a major street (%) Distance to river or canal

Near a river or canal (%) Number of observations

The mean is presented first in cells with four entries, followed by the standard deviation, minimum and maximum.

like cause local peaks and valleys in bid rents that are difficult to capture with standard measures of accessibility. The standard alternative of using quadratic or cubic terms for distance variables is useful for modeling broad spatial trends, but cannot account for local effects such as an increase in commercial bid rents around a neighborhood shopping area. Nonparametric procedures capture local effects by putting more weight on nearby observations when constructing an estimate for a point. Spatial nonparametric procedures currently have been used only for models with continuous dependent variables. A straightforward extension of Cleveland and Devlin’s (1988) locally weighted regression procedure is useful for models with discrete dependent variables.4 4

The following extension of locally weighted regression to logit models generalizes the model proposed by Tibshirani and Hastie (1987). Their model is a special case in which w ij 51 for the q observations closest to observation i, and w ij 50 otherwise. The parameter q is the ‘window width’, which must be specified before estimating the model.

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 â&#x20AC;&#x201C; 489

483

For continuous dependent variable models, locally weighted regression involves repeated applications (one per data point) of weighted least squares. The weights decline with distance from the target observation. A similar procedure is useful for logit models. Let w ij be the weight given to observation j when constructing the estimate for observation i. For a multinomial logit model with K 1 1 alternatives, locally weighted estimates are obtained by maximizing the following pseudo log-likelihood function for each observation (i 5 1,...,n):

O w (I n

ln Li 5

log(P0i ) 1 ? ? ? 1 IKi log(PKi ))

(1)

j 51

where Ik is a dummy variable indicating that alternative k was chosen, and Pk is the probability of choosing alternative k. Normalizing on the base alternative such that b0 50, the probabilities are given by exp( b 9k x i ) Pki 5 ]]]]] K 11 exp( b 9m x i )

(2)

m 51

Locally weighted logit estimates are obtained by maximizing Eq. (1) separately for each observation, which produces n distinct estimates of the coefficient vectors ( b1 , . . . , bK ). The model differs from standard multinomial logit in the weights: multinomial logit has w ij 51 for all values of i and j. The nonparametric logit model allows for spatial variation by giving more weight to nearby observations when estimating the coefficients for observation i. Various specifications can be used, but we have found that a standard normal density kernel works well:

S D

d ij w ij 5 f ] hs i

(3)

where w ij is the distance between observations i and j, s i is the standard deviation of d i , and h is the bandwidth. Larger bandwidths put more weight on observations farther the target point. We use crossvalidation to choose the bandwidth, leading to a value of 0.5 for h in our empirical models.5 With one estimated set of coefficients for each observation, nonparametric estimation procedures generally are better suited for prediction than for hypothesis testing. One possibility is to use the bootstrap to test whether average values of the 5 We vary h from 0.3 to 1.0 in increments of 0.1, and calculate separate coefficient vectors bki for each observation i after omitting the ith observation. Observation i is omitted to eliminate the tendency to choose excessively small bandwidths when the target is included in estimation. We then use Eq. (2) to calculate Pki , using bki and x i to construct the estimate for each observation i. We choose the value of h that provides the highest value of

O OI n

i 51 m 50

log Pmi .

484

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

coefficients are different from zero. Although McMillen and McDonald (1997) demonstrate the feasibility of this procedure in a regression model, bootstrap repetitions are prohibitively costly for logit models. Another possibility is to focus on one observation—perhaps the median—as in Meese and Wallace (1991). White (1982) robust covariance matrix can then be used to construct standard errors based on the first and second derivatives of the pseudo log-likelihood function. In this paper, we focus our attention on the improvement in forecasting performance provided by nonparametric logit. We find significant improvements in the ability to forecast mixed land use. Nonparametric logit coefficient and marginal effect estimates vary greatly over the city of Chicago, indicating local effects that are smoothed over by standard multinomial logit.

5. Estimation results Standard multinomial logit results are presented in Table 4. All variables add significant explanatory power to the model. To aid in the interpretation of the results, Table 5 presents estimated marginal effects. The marginal effects are averages across all 966 observations. For continuous variables, the average marginal effect of explanatory variable k on the probability of alternative m is simply

Table 4 Multinomial logit results Explanatory variable

All com.

All mfg.

Res. and com.

Mixed, with mfg.

21.212 (2.439) Distance to CBD 0.042 (0.471) Distance to Lake Michigan 0.121 (1.543) Distance to ‘el’ stop 20.367 (1.796) Distance to commuter train stop 20.146 (0.590) Near freight rail line 1.135 (3.259) Along a major street 2.764 (9.876) Distance to river or canal 20.376 (3.403)

21.076 (1.752) 20.316 (2.328) 0.335 (2.630) 20.709 (2.491) 0.015 (0.051) 4.779 (10.905) 1.093 (2.551) 20.864 (4.873)

1.825 (5.449) 20.193 (3.028) 0.095 (1.652) 20.313 (2.025) 20.202 (1.112) 0.177 (0.580) 1.131 (4.472) 20.353 (4.265)

2.068 (4.588) 20.755 (6.352) 0.277 (2.926) 20.831 (2.568) 20.583 (2.089) 2.334 (6.791) 2.041 (6.157) 20.106 (0.665)

Constant

The base block is all residential. Absolute asymptotic t2values are in parentheses. The log2likelihood value is 21079.35 and the average probability is 40.03%.

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

485

Table 5 Multinomial logit marginal effects Explanatory variable

All res.

All com.

All mfg.

Res. and com.

Mixed, with mfg.

Distance to CBD

3.420 (1.695) [16.716] 22.176 (0.900) [20.494] 6.520 (2.682) [22.589] 3.500 (1.738) [22.677] 219.590 (7.752) [11.810] 225.051 (12.766) [24.646] 5.969 (2.771) [24.559]

2.509 (2.323) [12.814] 0.122 (0.746) [1.920] 20.544 (1.791) [3.322] 0.174 (0.971) [1.937] 20.053 (6.302) [0.042] 25.412 (10.547) [15.443] 21.222 (1.502) [8.009]

0.026 (1.678) [0.169] 1.063 (1.546) [11.087] 21.471 (2.310) [7.577] 1.736 (3.161) [13.450] 35.599 (17.819) [7.111] 23.531 (6.447) [9.864] 23.735 (5.761) [15.205]

20.940 (3.105) [3.808] 20.155 (1.413) [1.432] 20.578 (3.861) [2.039] 21.422 (2.164) [7.851] 226.232 (13.714) [15.571] 24.492 (6.292) [3.978] 23.557 (3.289) [17.103]

25.014 (4.271) [13.480] 1.147 (1.171) [10.381] 23.927 (3.351) [12.044] 23.988 (3.624) [14.109] 10.276 (6.758) [5.019] 7.662 (6.184) [11.061] 2.545 (3.576) [13.084]

Distance to Lake Michigan

Distance to ‘el’ stop

Distance to commuter train stop Near freight rail line

Along a major street

Distance to river or canal

Average estimated marginal effects are followed in parentheses by sample standard deviations. Estimated standard errors are used to calculated the bracketed absolute t2values.

100 n ] ≠P / ≠x ki n i 51 mi For dummy variables, we calculate discrete changes:

100 n ] (P (x 5 1) 2 Pmi (x ki 5 0)). n i 51 mi ki Variances are calculated by the delta method (Greene, 1997). Table 5 indicates that greater distance from the CBD increases the probability that a block is exclusively residential or commercial, and decreases the probability of mixed land use. Blocks closer to Lake Michigan are more likely to be exclusively residential, and are significantly less likely to have any manufacturing land. Sites near el stops are more likely to have commercial or manufacturing lots, and less likely to be all residential. Mixed land use is common near commuter

486

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

train stations. Blocks closer to navigable waterways are less likely to be exclusively residential or to have mixed land use with manufacturing, and are more likely to be exclusively commercial, exclusively manufacturing, or a combination of residential and commercial. The discrete variables have a pronounced effect on land use. Sites next to freight rail lines are far more likely to be used exclusively for manufacturing or to have mixed land use with manufacturing, and are far less likely to be exclusively residential or to combine residential and commercial uses. Sites along major streets are more likely to be exclusively commercial and are far less likely to be exclusively residential. They also are much more likely to combine residential and commercial use than to be exclusively residential. The log-likelihood value for standard multinomial logit is 21079.35. A similar n K expression is obtained for nonparametric logit by calculating o o Imi log Pmi , i 51 m 50 which leads to a pseudo log-likelihood value of 2995.93. Most estimated marginal effects are similar across Tables 5 and 6. The primary effect of nonparametric estimation is to increase the variation in the marginal effects by allowing for local effects and for variations across different areas of the city. The predominance of statistically significant coefficient and marginal effect estimates in the multinomial logit model suggests that all dependent variable categories follow predictable spatial patterns, including the two representing mixed land use. Table 7 provides more direct evidence of the model’s predictive

Table 6 Nonparametric logit marginal effects Explanatory variable Distance to CBD

All res.

3.946 (4.150) Distance to Lake Michigan 22.790 (2.184) Distance to ‘el’ stop 5.902 (7.431) Distance to commuter train stop 1.213 (2.932) Near freight rail line 218.659 (9.252) Along a major street 227.102 (16.183) Distance to river or canal 7.761 (4.555)

All com.

All mfg.

Res. and com.

Mixed, with mfg.

20.615 (3.403) 3.127 (3.053) 22.519 (7.504) 1.741 (2.940) 1.710 (8.130) 32.831 (11.952) 22.419 (6.853)

20.243 (4.195) 1.413 (3.359) 1.620 (8.469) 0.602 (2.537) 31.597 (21.445) 25.173 (14.480) 24.047 (6.634)

2.024 (6.079) 22.363 (2.946) 22.005 (4.955) 20.654 (4.802) 225.890 (17.267) 29.159 (14.063) 24.639 (7.561)

25.112 (5.366) 0.612 (2.540) 22.998 (6.265) 22.902 (3.658) 11.242 (8.484) 8.602 (7.813) 3.344 (5.343)

Average estimated marginal effects are followed in parentheses by sample standard deviations. The log2likelihood value for the nonparametric logit model is 2995.93, with an average probability of 43.16%.

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 â&#x20AC;&#x201C; 489

487

Table 7 Predictions Actual land use

Total

Predicted land use 0

Total

179 189 (93.17) 32 29 (39.75) 5 3 (33.54) 79 78 (100.93) 8 8 (32.61) 303 307 (300)

12 11 (39.75) 35 62 (16.96) 5 3 (14.31) 38 42 (43.06) 5 15 (13.91) 95 133 (128)

9 12 (33.54) 13 8 (14.31) 82 84 (12.07) 16 9 (36.34) 28 19 (11.74) 148 132 (108)

99 85 (100.93) 44 19 (43.06) 7 8 (36.34) 187 188 (109.34) 46 32 (35.33) 383 332 (325)

1 3 (32.61) 4 10 (13.91) 9 10 (11.74) 5 8 (35.33) 18 31 (11.41) 37 62 (105)

300

128

108

325

105

966

Multinomial logit predictions are followed by nonparametric predictions in each cell. Expectations based on random land use are in parentheses. The land use categories are (0) all residential, (1) all commercial, (2) all manufacturing, (3) residential and commercial, and (4) mixed land use with some manufacturing.

performance.6 All dependent variable categories are identified fairly accurately. Nonparametric estimates are more accurate at identifying exclusively commercial blocks and blocks that combine manufacturing with other land uses. The estimated logit models confirm our speculations from the beginning of Section 4: mixed land use is most common near the CBD, near el stops, and near commuter train stations. The probability of mixed residential and commercial uses is much higher than exclusively residential use along major streets. The probability of mixed land use that includes manufacturing rises near freight rail lines and along major streets. Mixed land use is uncommon in newer areas at the edge of the city. Land markets follow eminently predictable patterns in land use assignments even when zoning does not exist.

The expectations presented in parentheses in Table 7 are constructed under the assumption of random land use. For example, 128 of 966 blocks (13.25%) are exclusively commercial, so randomness generates incorrect predictions of exclusive commercial use for 0.13253300539.75 of the 300 of the exclusively residential blocks.

488

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

If land use was highly segregated in 1920s Chicago, why did the city adopt a comprehensive zoning ordinance? Modern analysts sometimes suggest that exclusionary motives explain zoning’s popularity, but a hierarchical zoning ordinance is hardly exclusionary. Moreover, only 30 of the 1146 blocks included in our first pass through the data set were zoned for single-family housing.7 It seems far more likely that the stated objectives of the zoning ordinance were overstated but not mendacious. Externalities caused problems in some areas, and despite the grandfather clauses zoning could potentially reduce some future land use conflicts. But zoning mainly followed the current market, which was nearly inevitable because the market had already separated land uses to a considerable degree. By providing insurance against future land use changes, zoning may still be valuable when it largely follows the market. However, that very resistance to change may cause future land use conflicts.

6. Conclusion Chicago joined the groundswell of support for zoning in the 1920s. The Zoning Commission was explicit in its concern for the negative externalities caused by mixed land use. Urban economists are more skeptical of zoning’s ability to improve on a competitive market’s allocation of land. Mixed land use reduces commutes and shopping trip distance in a city that relies primarily on walking and public transportation. Zoning retards or eliminates the market’s ability to adjust to changing economic conditions and creates local monopoly power for non-conforming land uses permitted through grandfather clauses. In this paper, we present empirical results that could be used to support either side of the zoning debate. We find that mixed land use was quite common in 1920’s Chicago. Residences, stores, and manufacturing firms sometimes were present on the same block. Apartments sometimes were on the same block as a firm engaged in heavy manufacturing. But we also find that the patterns of mixed land use are quite predictable, and are consistent with a city of people who once valued access to employment sites but who were beginning to prefer to live in exclusively residential enclaves. Mixed land use was common on major streets, near public transportation, and in older parts of the city near the CBD. Newer residential areas rarely combined land uses.

References Agresti, A., 1996. An Introduction to Categorical Data Analysis, John Wiley, New York. Brundson, C., Fotheringham, A.S., Charlton, M.E., 1996. Geographically weighted regression: A method for exploring spatial nonstationarity. Geographical Analysis 28, 281–298. 7

We omitted the 30 single-family residential blocks from subsequent analysis.

D.P. McMillen, J.F. McDonald / Reg. Sci. Urban Econ. 29 (1999) 473 – 489

489

Cappel, A.J., 1991. A walk along willow: Patterns of land use coordination in pre-zoning New Haven (1870–1926). Yale Law Journal 101, 617–642. Cleveland, W.S., Devlin, S.J., 1988. Locally weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Association 83, 596–610. Coase, R.H., 1960. The problem of social cost. Journal of Law and Economics 3, 1–44. Fotheringham, A.S., Brundson, C., Charlton, M., 1997. Geographically weighted regression: A natural evolution of the expansion method applied to spatial data, Manuscript, University of Newcastle. Greene, W.H., 1997. Econometric Analysis, Prentice Hall, Upper Saddle River, NJ. Mayer, H.M., Wade, R.C., 1969. Growth of a Metropolis, University of Chicago Press, Chicago. McDonald, J.F., McMillen, D.P., 1998. Land values, land use, and the first Chicago zoning ordinance. Journal of Real Estate Finance and Economics 16, 135–150. McMillen, D.P., 1996. One hundred fifty years of land values in Chicago: A non-parametric approach. Journal of Urban Economics 40, 100–124. McMillen, D.P., McDonald, J.F., 1993. Could zoning have increased land values in Chicago? Journal of Urban Economics 33, 167–188. McMillen, D.P., McDonald, J.F., 1997. A nonparametric analysis of employment density in a polycentric city. Journal of Regional Science 37, 591–612. Meese, R., Wallace, N., 1991. Nonparametric estimation of dynamic hedonic price models and the construction of residential housing price indices. Journal of the American Real Estate and Urban Economics Association 19, 308–332. Mills, E.S., 1979. Economic analysis of urban land-use controls. In: Mieszkowski, P., Straszheim, M. (Eds.), Current Issues in Urban Economics, Johns Hopkins University Press, Baltimore, pp. 511–541. Siegan, B. 1972. Land Use without Zoning, D.C. Heath and Co., Lexington, MA. Tibshirani, R., Hastie, T., 1987. Local likelihood estimation. Journal of the American Statistical Association 82, 559–567. Warner, Jr., Sam, Bass, 1978. Streetcar Suburbs: The Process of Growth in Boston (1870–1900), Harvard University Press, Cambridge, MA. White, H., 1982. Maximum likelihood estimation of misspecified models. Econometrica 53, 1–16.