The first generation of the California Urban Futures Model (Landis, 1994a, 1994b, 1995) achieved four significant advances in the field of metropolitan growth modeling. It was the first urban growth model which could be used to simulate how realistic regional and/or local development restrictions might impact future development patterns. It was the first operational urban growth model to be truly disaggregate--that is, not to rely on a zones. It was the first operational urban growth model to explore and model the crucially important role of private land developers in determining the future form of metropolitan growth. And, it was the first urban growth model to incorporate--indeed, depend on--GIS.

These advances notwithstanding, the original also suffered from some significant shortcomings. It was limited to residential development. Omitted from the model were methods for projecting and/or allocating future industrial, commercial, and public activities. A second limitation, which was a direct outgrowth of the first, was that the model did not allow different activities to bid against each other for appropriate sites. Unless explicitly prohibited, the "best" sites (that is, those sites which were the most profitable to develop) were always reserved for residential development. Third, and perhaps most critically, the rules used to allocate future development had never been calibrated against historical experience. Instead, residential growth was allocated to sites based on the difference between observed housing prices, and "best-practice" housing development cost functions. Finally, real estate prices, to the extent that they played a role in the CUF Model, were entirely exogenous. New residential development that could not be allocated simply spilled-over into other jurisdictions (subject to user-specified limits on spillover), rather than feeding back into the allocation process through higher prices.

The second generation of the California Urban Futures Model (CUF II) tries to remedy these shortcomings. Unlike the first generation. it:

* Includes multiple sectors;

* Allows different land uses to bid against each other for preferred sites;

* Is calibrated against recent experience; and,

* Incorporates a "pseudo-pricing dynamic" into the development spillover process.

This article explores the development and calibration of the CUF II Model. It begins with a look at recent developments in large-scale urban modeling. Next, it reviews the overall logic of the CUF II Model. Third, it explains the development and calibration of the Land Use Change Model, the newest component of the CUF II Model. It concludes by reviewing the CUF II's advances as well as its remaining deficiencies. A companion article, describes the use of the CUF II Model for simulating county and regional development policies.

RECENT DEVELOPMENTS IN METROPOLITAN ACTIVITY MODELING

As two recent reviews by Wegener (1994, 1995) point out, the state-of-the-art of operational metropolitan activity models is evolving at moderate pace. Two developments of recent years--one theoretical, the other data-oriented--are combining to help metropolitan growth modelers produce ever-more explicit models of urban activity patterns. The first of these is the incorporation of random-utility theory to predict generalized location and travel choices based on observed household, firm, or traveler behaviors. The ability to model metropolitan-scale activities as combinations of individual location and travel choices represents a significant step forward in the theoretical development of urban models.

A second advance is based on the growing availability of longitudinal, micro-scale data, and on the growing power of GIS-based software to analyze such data. Activity data tied to specific locations in space (either through geo-referencing or address-matching) is now available in many locations. This makes it possible to represent the metropolitan area as a collection of individual sites or locations, rather than as zones. It also makes it possible to track and analyze actual patterns of metropolitan land use, demographic, or economic change, instead of relying on changes in zonal aggregates. Building on such newly available data sources first Batty (1992, 1995), and more recently Clarke (1996), have begun to insert processes of spatial change (such as cellular growth and diffusion) into urban activity models.

Despite these advances, a number of significant problems remain. The first is the absence of actual--which is to say, observed-- land or building prices. Site prices are typically determined endogenously in most urban growth models, usually as travel-based shadow prices, or else indirectly through the process of market-clearing. This limits the ability of most metropolitan activity models to simulate the effects of realistic land use policies and regulations, or of non-transportation infrastructure investments. Until urban activity models can be calibrated against the characteristics of observed land use transactions--including location as well as price--their usefulness for real world applications will remain suspect.

A second problem area concerns the modeling of economic activity, particularly jobs. Most existing metropolitan models function adhere to some form of export-base framework. The total demand for regionally exported goods and services is determined exogenously as a model input. Once determined (and converted to jobs), regional economic activity is then sectorally disaggregated into primary and secondary industries, as well as spatially disaggregated by zone. The processes by which actual job changes really occur--through the growth or shrinkage of existing industries, through the birth of new industries, or the decline of older ones, is ignored. Similarly ignored are the non-transportation cost reasons why industries locate where they do.

A third problem area is the continuing (and virtually complete) lack of supply-side information in most urban models. Except for those areas that are absolutely precluded from development (by virtue, for example, of being underwater), the suitability of the built and natural landscape to support new or additional development; or, the capability of the landscape to support development at differing intensities, is completely missing from most all metropolitan activity models. The characteristics of the existing landscape, be it natural and undeveloped, or already developed, are widely presumed to be irrelevant to the amount or location of future activities or land uses. This limitation has meant that urban models can not be reliably used for project-based environmental, social or fiscal impact analysis, or for cumulative impact assessment.

A related problem, first identified by Lee (1973), is the insensitivity of most urban models to many types of policies. Today's generation of urban models are useful for analyzing the travel, congestion, air quality, and perhaps, regional economic implications of new highways and/or transit extensions, but not for much else. Because they typically exclude site-level environmental or regulatory information, today's metropolitan activity models remain incapable of analyzing or simulating local land use and environmental regulations. Indeed, most metropolitan growth models are generally blind to local government boundaries, issues, or policies. The ability to model how local policy changes will affect activity patterns within particular municipal boundaries, let alone model the inter-municipal spill-over effects of policies, is largely missing from today's urban models.

THE LOGIC OF THE CUF II MODEL

The original CUF model was developed to fill some of these gaps. As noted by Wegener and others, it sacrificed comprehensiveness and theoretical elegance in favor of spatial detail and an ability to simulate local policy initiatives. The newest version of the model maintains the same policy-focus and level of spatial detail as the original, while plugging some of its theoretical holes.

Despite its more developed theoretical base, the CUF II Model is conceptually simpler than its predecessor. As shown in Figure 1, the new version consists of three, not four components:

1. Activity Projection: The first component consists of a series of econometric models used to project future households and employment by jurisdiction at ten year intervals. Households are divided into owners and renters. Employment is separated into ten sectors. The development and calibration of the different employment models is detailed in Landis, et.al., 1997.

2. Spatial Database: The second component of the CUF II model consists of a GIS-based database of Developable Land Units (DLUs). As in the prior version, DLUs are potentially developable or redevelopable sites. In the original CUF model, DLUs were generated as the spatial union of multiple GIS layers. The resulting DLU database consisted of thousands of unique polygons, each defined as different along some attribute dimension than its immediate neighbors.

In the current version, DLUs consist of one-hectare (100m x 100m) grid cells, which may or may not be uniquely different from adjacent grid cells. The shift from polygons to grid-cells was made for a number of reasons. First, the analytic power of grid-based GIS procedures has advanced considerably since the first version of the CUF model. Second, data on existing and historical land uses are collected and tabulated at the hectare level by the Association of Bay Area Governments (ABAG). This data is essential to the development and Calibration of the Land Use Change Model, described below. Finally, the hectare grid cell has about the right level of resolution for analyzing pattens of development and land use change. It is sufficiently fine-grained to observe small-scale land use changes, but not too fine-grained so as to obscure those changes with "noise."

The Spatial Database includes ten data layers: i) 1985 and 1995 land uses, by hectare, as identified by the Association of Bay Area Governments; (ii) Percent slope, as estimated from

USGS Digital Elevation Model (DEM) data; (iii) Publicly-owned or controlled lands; (iv) Wetlands, as identified from the National Wetlands Inventory; (v) 1990 City boundaries, obtained from 1992 TIGER files; (vi) 1990 Spheres-of-influence, as digitized from paper maps provided by County LAFCOs; (vii) Urbanization and agricultural land quality, as determined from digital maps provided by the California Farmland Mapping Project; (viii) 1990 General plan designations, as digitized from paper maps provided by Contra Costa, Sonoma, and Solano Counties; (ix) Major highway rights-of-way and interchange locations, as obtained from 1992 TIGER files; and (x) Major rail transit rights-of-way and stations as digitized from paper maps. As noted in Chapter Three, several additional data items are developed from these ten data layers.

3. The Land Use Change Model: The Land Use Change Model is the heart of the CUF II Model. It is a series of equations that relate hectare-scale land use changes (between 1985 and 1995) to more than two-dozen site and community characteristics, including: local population and employment growth; proximity to regional job centers; site slope; whether the site is within or beyond city boundaries or spheres of influence; the uses of surrounding sites; the availability of vacant land; site proximity to freeway interchanges and transit stations; and site proximity to major commercial, industrial, and public land uses.

Because land use change is a discrete rather than continuous phenomenon, the various equations are estimated using a multi-nomial logit procedure. Nine types of site-level land use changes are considered: (i) undeveloped to single-family residential use; (ii) undeveloped to apartment use; (iii) undeveloped to office or retail use; (iv) undeveloped to industrial use; (v) redevelopment from another developed land use to residential use; (vii) redevelopment to commercial use; apartment use; (vii) redevelopment to industrial use; (xiii) remain undeveloped; and (ix) remain in initial developed use. Separate logit models are calibrated for new development and for redevelopment, and for each Bay Area county.

The resulting model parameters can be combined to calculate land use transition probabilities (e.g., the probability that a specific vacant site will be developed in residential use). These probabilities, in turn, may be interpreted as "bids" for development or redevelopment. Projected new development can then be allocated to sites according in order of their bid scores. Bid scores vary by site as well as by potential use. This means that different uses (e.g., single-family residential, apartments, commercial and industrial uses) can effectively bid against each other for specific sites. In this way, the Land Use Change Model incorporates competition between uses and between sites.

This "bidding" framework allows for two types of spillover. If, for example, there are insufficient sites to accommodate projected residential development, but sufficient sites for commercial development, residential growth may be allocated (or spillover) to sites whose "highest-and best-use" (as represented by their bid scores) would otherwise be for commercial development.

Bid scores can also be evaluated across jurisdictions. This facilitates inter-jurisdictional spillover. Activities for which sites are not available in one jurisdiction can spillover into other jurisdictions. This is the most common form of spillover. Alternately, activities may be allocated to sites regardless of jurisdictional boundaries.

Like its predecessor, the CUF II model can be used to simulate future policy scenarios. Unlike the original CUF model, however, which was limited to testing regulatory scenarios, the CUF II Model can also be used to simulate investment scenarios, such as the construction of new freeways or transit systems. The results of these simulations show the locations and patterns of development, in addition to the total amount and density.

MODELING URBAN LAND USE CONVERSION: A DISCRETE CHANGE APPROACH Viewed from an airplane or a satellite, processes and forms of metropolitan land use change often appear to follow regular and explainable patterns. Lower-density residential development extends outward as farm or resource lands at the urban edge are gradually developed. Industrial areas develop around major inter-urban transhipment facilities such as seaports, airports, railroads, or highways. Commercial and office development occurs around key intra-metropolitan transportation nodes. Apartment complexes are developed near central city and suburban central business districts.

What appears be regular and explainable--perhaps even inevitable--at the metropolitan scale, is not quite so regular when viewed at the level of the individual parcel or site. There are many reasons why and when individual sites change land use. Some reasons are well-known and consistent with established theories of metropolitan growth: A new highway makes a low-priced agricultural site accessible to regional job centers. New residential development exceeds the market size threshold required to make a nearby retail center economically viable. Restrictive land use controls enacted by higher-income municipalities force new development to be displaced outward.

Other reasons are more idiosyncratic. A farmer who prefers to continue farming refuses to sell his land to a subdivider despite being offered a terrific price. Excessive exactions or uncompromising neighborhood opposition prompt a developer to skip over a preferred site in favor of a one which is just easier to develop. A retail developer misjudges the market and builds a shopping center before there is sufficient residential demand. One land speculator in need of ready cash sells to another who has deeper pockets. A pro-growth majority planning commission gives way to a slow-growth majority.

Over the long-run, perhaps 20 or 30 years, many of these idiosyncratic reasons give way to the logic of the market. The heirs of the reluctant farmer finally decide to sell to a developer. Rising land and property values allow developers to pay for required infrastructure or environmental mitigation, negating previous fiscal or environmental constraints. Commercial areas establish themselves, generating real agglomeration economies. Looked at from above, or better yet, in retrospect, the pattern of metropolitan growth seems inevitable.

Far from being inevitable, the pattern of metropolitan growth is actually path-dependent. Which particular sites were developed (or not developed) in the 1960s determine which sites will be available for development or redevelopment in the 1980s. If the truculent farmer had sold his land in the 1970s, the metropolitan area might have looked different in the 1990s.

Because metropolitan growth actually occurs as a cumulative, path-dependent process of individual parcel changes, it has proven to be extremely difficult to model statistically. Conventional--which is to say, regression-based--statistical approaches are not particularly appropriate to the task of modeling site-level land use change, or for incorporating site-level spatial effects such as proximity. Instead, urban modelers have chosen to focus on aggregate patterns of urban growth, usually by studying land use change (or, more specifically changes in level of activities which use land) at the zonal level. The characteristics of individual sties, as well as the factors which shape the motivations of the buyers and sellers of those sites, then conveniently disappear.

The Logit Framework

Choices or changes between categories, for example, the change that occurs when a vacant parcel is developed to a residential use, are more appropriately modeled using a non-linear logistic, or logit model. Logit models typically come in two forms: binomial, meaning there are only two choice or change possibilities; and multi-nomial, meaning that there are three or more choice or change possibilities. Multi-nomial logit models are typically much harder to calibrate and interpret than binomial models. Because we are modeling changes into multiple land use categories (e.g., single-family residential vs. multi-family-residential vs. commercial, vs. industrial.), all of the models presented below are multi-nomial in form.

They are also non-ordinal. This means that the categories which make up the dependent variables can not be ordered or ranked. As applied to processes of land use change, this means that no one type of land use change can be presumed, a priori, to be universally superior to another. The extent to which commercial uses, for example, are judged superior to residential uses, is determined exclusively by the data and the resulting model coefficient estimates. The fact that the models are non-ordinal means that various land uses can effectively "bid" against each other on a site-by-site basis.

Regardless of whether it is ordinal or non-ordinal, the multi-nomial logit model takes the following general form:

Prob[i|l] = {exp (b₀ ^l + b₁^l x_i1 + b₂^l x_i2 + ...... + b_m^l x_im)

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S_l=1,L exp (b₀ ^l + b₁^l x_i1 + b₂^l x_i2 + ...... + b_m^l x_im)}

where: Prob[i|l] is the probability that each grid-cell site i is developed or redeveloped to use l;

x_im are explanatory, or independent variables for each site i;

b_m are the logit coefficients (to be estimated) associated with land use l and variable x_m;

and L is the full set of land use changes.

Multi-nomial logit models have primarily been used to analyze the behavior of individual decision units at a single point in time. As explained by McFadden and Domenich (1975), the use of a the logit estimator to model individual choices is based on three assumptions. The first is that when faced with complete information, individuals will rationally choose the alternative that maximizes their own utility. A second assumption is that the commodity space which describes the alternative set must be differentiable and convex (Fisher and Nijkamp 1985). A third assumption--one which is usually treated as implicit--is that individual choices are independent. What this means is that the decisions made by one individual neither do nor can affect the decisions made by other individuals. This last assumption rules out the possibility of strategic behavior.

Adapting the multi-nomial logit model to the task of explaining land use change requires some additional assumptions. We begin by assuming that the decision to develop a previously vacant site (or to redevelop a previously developed site) will be based on a rational evaluation of the prospective profit or rent associated with different potential forms of development.. For a given site (denoted by the subscript i), let R(y/i) denote the profit potential associated with a particular land use change, y. An alternative land use change, y* will occur if and only if :

That is, the site will be developed into the land use that generates the highest potential profit. The profit potential associated with each choice, R(y/i), is determined by a set of site attributes. Some attributes are observable. Others are indeterminate or unobservable. Because some attributes are unobserved, the land use change function is assumed to be probabilistic. Let Pr(y/i) denote the probability that choice y is made for site i. Under assumptions of profit-maximization:

Under the simplest assumption that the unobserved attributes are independent and identically distributed according to a Gumbel Type I extreme value distribution, this probability takes the form of a multi-nomial logit function. (See McFadden 1974, for the mathematical proof of this derivation). Much as random utility theory underlies the use of the logit function to model consumer choice, we use the idea of a "random" profit function to develop models of land use change.

Transforming consumer-based random utility theory into developer-based random profit theory requires overcoming two problems. The first is theoretical. It involves the assumption that land developers act independently of each other--that is, that each developer or landowner independently appraises the profit potential for every site, and bids accordingly. As noted above, this assumption rules out the possibility of oligopolistic (whereas groups of landowners or developers act in concert) or strategic behavior (whereas one developer acts primarily to pre-empt or manipulate another). The problem is that landowners and developers do engage in oligopolistic and strategic behavior. And so, for that matter, do many land sellers.

Perhaps the more appropriate question is not whether land sellers, landowners, and developers engage in strategic behavior (we assume they do); it is whether that behavior is likely to succeed. To the extent that land development has been shown to be no more profitable over the long-run than other businesses, the answer to this second question is probably no. Competition, we assume, levels the playing field and makes the expected return (or profitability) associated with strategic behavior close to zero.

A second problem stems from the nature of the observations used to calibrate the models, below. It revolves around the question of agents. In the case of conventional discrete choice analysis, the agent is the individual or household. Consider the case of commuters comparing alternative work trip modes, or of households trying to decide where to live. In the commuter case, each traveler faces a series of mode choices (e.g., driving, walking, or taking the bus), all of which can be decomposed into a comparable set of attributes (e.g., travel time, wait time, travel cost). In the household location case, each household faces a series of residential choices, all of which can also be decomposed into comparable attributes (house size, neighborhood, distance to work, school quality, etc.). Each traveler chooses the work mode, which, based on its attributes, maximizes his or her utility. Similarly, each household chooses a house and location, which, based on their joint attributes, maximizes its utility. In both examples, an identifiable agent confronts and makes real choices.

Now consider the case of site level land use change. The agent in this case should be the site owners (or developers with site control). Each owner is confronted with the decision of whether or not to initiate a land use change. The factors influencing that decision, will include, among others, the attributes of the site. Following the logic identified above, each owner should make the land use change decision (including the possibility of no change) which maximizes their profits.

Yet as we note below, the unit of analysis (or observation) in this research is the site, not the developer or landowner. And while we have reasonably complete information on the characteristics of sites, we lack information regarding the characteristics or motivations of land owners and developers. Put another way, we lack agents. To overcome this problem, we again invoke the idea of competition. We argue first, that given a highly competitive market and few barriers to entry, the agent doesn't matter. Whether a particular developer is well-capitalized or poorly-capitalized, whether they specialize in residential development or retail development, whether their experience is local or national; in a competitive market, these factors are likely to be of far, far less importance than the demand for urban development and the availability of appropriate sites.

Unit of Analysis

The parcel is the near-ideal unit of analysis for studying land use change. Parcels have area, location, single uses, and best of all, are the basis of all land transactions. Regrettably, complete (digital) parcel maps are not yet available for any Bay Area county for any year.

What is available, is a region-wide database of dominant land uses by organized by hectare. As compiled by the Association of Bay Area Governments (ABAG), this database is organized according to the Anderson (197-) land cover classification system. To make the modeling process more manageable, we collapsed the 100-plus land use categories contained in the ABAG land use database into seven: (i) undeveloped; (ii) single-family residential; (iii) multi-family residential; (iv) commercial; (v) industrial; (vi) transportation; and (vii) public.

Hectare grid-cells have both advantages and disadvantages as units of analysis. They are small enough to capture the detailed fabric of urban land used but large enough to avoid problems of data "noise." And, since they are fixed, changes and trends across time can be easily identified. On the negative side, they lack physical or legal reality. Unlike parcels, they are not transacted. Nor are they directly regulated. Thus, they are not themselves the subject of development or redevelopment decisions.

The nine-county database includes nearly 1.8 million grid-cells. Even when stratified into smaller county subsets, the database is too large to analyze within a multi-nomial logit framework. To make the analysis more manageable, we eliminated those grid-cells which we believed were extremely unlikely to have changed land use between 1985 and 1995. These included grid-cells which were known to be wetlands, grid-cells more than 50 kilometers from a highway, and grid cells more than 30 kilometers from a highway with a slope exceeding 20%. The effect of this screening was to reduce the quantity of land use changes to be modeled to a computationally manageable level.

MODEL SPECIFICATION AND CALIBRATION

Two sets of logit models of land use change are calibrated below. The first examines the determinants of land use change among undeveloped sites between 1985 and 1995. The second looks at the determinants of land use change among previously developed sites. Both types of models follow the same general form:

Pr[Land use change_ijkl] = f { initial site use_i, site characteristics_i, site accessibility_i,

community characteristics_j, policy factors_ij,

relationships to neighboring sites_i }

where: Pr[Land use change_ijkl] indicates the probability that site i in community j changed from land use k to land use l between 1985 and 1995;

i ndicates each hectare grid cell;

k, the initial (1985) land use of site i, is either undeveloped or developed;

And l, the terminal (1995) land use of site i is either single-family residential, multi-family residential, commercial, industrial, or else is unchanged from the initial use.

The two sets of models were calibrated for every Bay Area county except San Francisco. As noted above, the calibration datasets includes all developed sites in the Bay Area as of 1985, and a 50% superset of 1985 vacant sites most likely to be developed. Table 1 presents a frequency of the calibration datasets organized by county and by initial and terminal land use.

Table 1

The Dependent Variable: Categories and Levels of Land Use Change

Most of the sites that were vacant in 1985 were still vacant in 1995. The percentage of undeveloped sites in 1985 which were also undeveloped in 1995 ranged from a low of 94.3% in Contra Costa County, to a high of 98.9% in Marin County. Of the initially vacant sites that did change land use between 1985 and 1995, the largest share changed to single-family housing. The share of 1985 vacant sites converted to single-family use by 1995 ranged from a low of .9% in Marin County, to a high of 5.2% in Contra Costa County. Commercial and industrial development accounted for much less vacant land conversion than did new residential development. The share of 1985 vacant sites converted to commercial uses by 1995 ranged from a low of .17% in Napa County, to a high of 1.2% in Alameda County. The share of 1985 vacant sites converted to industrial uses also varied widely by county--from a low of .04% in San Mateo County, to a high of .54% in Alameda County. New apartment construction throughout the Bay Area was relatively meager between 1985 and 1995. The share of 1985 vacant sites converted into apartment use ranged from a low of .01% in Napa and Solano counties, to a high of .1% in Alameda County.

Redevelopment rates varied even more widely among counties than rates of new development. Redevelopment rates --that is, the area of sites which were redeveloped between 1985 and 1995 as a share of all developed sites in 1985--varied from a high of 5.2% in Alameda County, to a low of less than .1% in Marin County. As might be expected, redevelopment rates between 1985 and 1995 were higher in the Bay Area's urbanized counties (e.g., Alameda, Contra Costa, San Mateo, and Santa Clara), and lower in the its rural and suburban counties (Napa, Solano, and Sonoma). Marin County, was exception to this. Despite the county's older, more established status, only 14 hectares (about 35 acres) of redevelopment occurred in Marin County between 1985 and 1995.

Most redevelopment activity, regardless of county, took the form of residential redevelopment; that is, redevelopment from some other urban use, to housing. The share of developed sites in 1985 which were redeveloped to residential use by 1995 varied from a high of 4.8% in Alameda County, to a low of .1% in Marin County. Measured in absolute terms instead of percentages, the greatest amounts of residential redevelopment occurred in Santa Clara (2,340 hectares) and Alameda (1,096) counties. Santa Clara County also led the Bay Area in hectares of commercial and industrial redevelopment. Five hundred hectares (about 1,250 acres) of urban uses in Santa County were redeveloped to office, retail, and business park uses between 1985 and 1995. Another 71 hectares were redeveloped to industrial uses. Commercial redevelopment activity between 1985 and 1995 also exceeded 100 hectares in Alameda, Contra Costa, and Sonoma Counties. Other than Santa Clara, Sonoma County was the only Bay Area county in which there were significant amounts of industrial redevelopment 1985 and 1995.

Independent Variables: The Many Determinants of Land Use Change:

The general logit model specified above includes six sets of independent variables. They are:

1. The initial site use.

2. The demand for particular types of land uses in the general area.

3. The generalized accessibility of the site to other activities.

4. The nature and extent of any physical constraints, and/or the cost of overcoming those constraints.

5. The nature and extent of local policy constraints (such as zoning controls) which limit or restrict development, and/or the difficult of changing those constraints.

6. The existence of any positive and/or negative influences exerted by neighboring sites.

Not all of these factors can be conveniently or comprehensively measured. Site-level demand is particularly difficult to measure, as are certain types of policy constraints. Current and reliable data describing specific factors such as zoning, impact fees, traffic congestion, and infrastructure availability are hard to acquire and expensive to encode in a form convenient for use with statistical models. In a region with as many people (almost six million) and local governments (over 100) as the Bay Area, data collection and common encoding is particularly difficult.

The spatial scale of analysis also differs for different factors. Population and job demand are commonly measured and projected at county or jurisdiction level. Accessibility, by contrast, is commonly measured at the level of the traffic analysis zone (TAZ). Neighborhood effects, development constraints, and externality effects are more disaggregate still; if they are measured, it is usually at the site or parcel level. Modern relational databases and GIS packages enable analysts to overcome some but not all of these variations in spatial scale.

The following sections describe each of the independent variable sets:

1. Initial Site Use: The models that follow differentiate between land use change that occurs to previously vacant sites, and land use change that occurs to previously developed sites. The initial land use in the former set of models is all the same. In the latter set of models, sites may be initially developed in residential use (single-family or multi-family), commercial use (retail or office), or industrial use.

Conventional urban economics holds that commercial and industrial uses are generally of a "higher order" than residential uses. That is, they are capable of generating higher land rents. To the extent that this generalization holds true, previously-developed residential sites should, all else being equal, be more likely to be redeveloped into commercial or industrial uses. Conversely, previously-developed commercial or industrial sites should be less likely to be redeveloped into residential use.

2. Demand Factors: The probability that a vacant sites will be developed, or that previously-developed sites will be redeveloped, should depend in large measure on the strength of the demand for space. All else being equal, we would expect land use change to be more frequent in growing cities, and less frequent in declining cities. We measured demand in two ways: (i) as the rate of household growth or change during the previous five years (1980-85); and, (ii) as the rate of job growth or job change during the previous five years. Both variables were measured at the city level; all sites within a city were presumed to be subject to comparable demand pressures. Assuming that population and employment growth causes land conversion (and not vice-versa), we expected the estimate coefficients of both variables to be positive.

Too other general demand measures were also included: (iii) the initial number of households in the city (as of 1985); and (iv) the initial number of jobs in the city, also as of 1985. For reasons that are not exactly clear, population growth in the Bay Area during the 1980s favored newer smaller cities over older, larger cities. All else being equal, we would thus expect sites in larger cities to be less likely to either change land use or be developed than sites in smaller cities. This suggests that the estimated coefficient associated with the number of households in each city should be negative.

The size-effect of a city's employment base may be either positive or negative. On the positive-effect side, there may be agglomeration economies associated with larger employment centers. This would tend to make nearby undeveloped sites more attractive, thereby increasing their probability of being development. Moreover, recent employment growth in the Bay Area, unlike recent population growth, has been focused in a few large job centers. This would also suggests that the relationship between the size of a particular city's employment base, and the probability of a site within that city being developed or changing use is likely to be a positive.

On the negative effect side, land and commercial space prices are likely to be higher in cities with larger economies than in cities with smaller economies. To the extent that employers are drawn to less expensive land, the effect of employment size on land use change may be negative.

We included one final variable in the various models to test the hypothesis that the relationship between the number of jobs and households in a community somehow affects the likelihood of land use change. Depending on the terminal use, theory indicates that this variable could cut both ways: To the extent that cities prefer to attract a balance of jobs and housing, higher jobs-housing ratios might be negatively affect the likelihood that a site be developed in residential use. Conversely, because of agglomeration economies, new jobs might be attracted to already job-rich communities, thereby boosting the likelihood that a particular site be developed in commercial use.

3. Accessibility and Distance Effects: Starting with von Thunen, urban economists have argued that the demand for sites (as measured by land prices and densities) should be greatest near major city centers, primarily for reasons of minimized worktrip transportation costs. The San Francisco Bay Area has three regional employment centers (San Francisco, Oakland, and San Jose) and many more subcenters (e.g., Walnut Creek, San Ramon, Pleasanton, Fremont, Santa Clara/Sunnyvale, Palo Alto, San Mateo, Hayward, Berkeley, Richmond, Fairfield, Vallejo, and Santa Rosa). To capture any potential regional accessibility affect, we used GIS to measure the euclidean distance from every developable and redevelopable site to downtown San Francisco and downtown San Jose. To the extent development really does favor closer-in locations, we would expect the estimated coefficients of these two measures to be consistently negative.

Accessibility can be also be measured more generally. Regardless of trip destination or purpose, activities located near major freeway interchanges or transit stations have a higher level of generalized accessibility than activities located farther away. Because of this, we would expect such sites to be in greater demand, and thus, to face greater development and redevelopment pressures. To test this hypothesis, we measured the aerial distance from every site to the closest freeway interchange and/or BART stations. To the extent that proximity to regional transportation facilities encourages land use change, we would expect the coefficients of these two measures to be negative.

4. Physical and Cost Constraints: The physical characteristics of a site may present absolute or relative constraints to its development. Sites which include permanent wetlands are absolutely constrained from development. Sloped sites face relative constraints: they can be developed or redeveloped but typically at a higher cost than flat sites. To develop sites far from existing urban services (e.g., roads, sewer and water service, and electrical and telephone service) requires either that those services be newly provided, or that they be extend from existing service areas. Either way, the necessity of providing services substantially raises the increases the cost of developing vacant land at the urban fringe.

Sites identified as permanent wetlands under the National Wetlands Inventory are excluded entirely from this analysis.

Site slope is identified through the use of five dummy variables, corresponding to five slope classifications: (i) 0-2% slope; (ii) 3-5% slope; (iii) 6-9% slope; (iv) 10-15% slope; and (v) 16% or greater slope. Site slopes were originally estimated from U.S.G.S. DEM (Digital Elevation Model) data files. Because of the higher costs associated with hillside development, we generally expect to observe a negative relationship between the dummy variables denoting steeper slopes and the probability of site development. The dummy variable indicating a 0% slope was purposely omitted in order to guarantee a unique solution.

Developers who propose projects in existing urban areas (sometimes called "infill") are sometimes able to take advantage of existing road and transit capacity as well as hook-up to existing water and sewer lines, and to electrical and telecommunications grids. All else being equal, this reduces total development costs. Developers who propose projects at the urban edge may also be able to take advantage of existing infrastructure capacity; although in practice, significant and costly additions are often required as a condition of development approval. Developers who pioneer entirely new areas, or propose projects beyond the urban fringe either have to provide their own infrastructure capacity, or else pay to extend existing services to their projects. Either way, the costs of providing services to far-flung projects tend to be very high.

To try to capture this effect, we used GIS to measure the linear distance (in 200 meter increments) from each site to the nearest sphere-of-influence boundary. The greater this distance, we assume, the higher the cost of providing required infrastructure and urban services. Thus, we would expect to observe a negative relationship between the measured distance between a particular site and the closest sphere-of-influence boundary, and the probability that the site is developed.

The costs of providing infrastructure and essential urban services varies by use and jurisdiction as well as with distance. Some jurisdiction impose more costly and extensive infrastructure standards than others. Similarly, some jurisdictions impose more onerous standards on certain types of development. Finally, most Bay Area jurisdiction assess impact fees on new development. Because state law governing the setting of impact fees requires only that there be a "rational nexus" between the fee amount and the impact, fee amounts can vary widely between jurisdictions, between different uses, and even according to the location within a particular jurisdictions. Because we were unable to assemble a complete and reliable schedule of impact fees for different uses in all Bay Area communities, we did not include impact fees (or exactions) in the model.

5. Policy Constraints: Most constraints to development are political, not physical. Just about every local governments in California utilizes zoning to stipulate which uses and densities are permitted where. Similarly, California municipalities are supposed to designate their ultimate "build-out" boundaries as "spheres-of-influence." New development is supposed to be channeled to sites within sphere-of-influence boundaries, and steered away from unincorporated areas outside sphere boundaries. And increasing number of California jurisdictions are moving to limit the development of farmlands, primarily as a means of preserving open space.

Policy constraints are rarely absolute. Zoning can be, and is frequently changed. Indeed, experienced developers typically look for under-zoned properties in the hope of changing their zoning to a higher, and thus more profitable use. Likewise, sphere-of-influence boundaries can be easily extended. And incentive programs such as Williamson Act contracts intended to protect farmland have so far failed to catch on.

Because of the cost and difficulty of obtaining, digitizing, and coding accurate, up-to-the minute zoning maps for every jurisdiction, we did not include zoning categories in the model. We did, however, determine whether each site was within a current sphere-of-influence boundary. All else being equal, and despite the laxness with which current sphere-of-influence requirements are being implemented, we expect that vacant sites outside sphere boundaries would be less likely to be developed and thus change use.

Using digital maps of farmland quality published by the California Farmland Mapping Project, we determined whether undeveloped sites were located on land classified as: (i) prime farmland; (ii) farmland of state or local importance; (iii) farmland being cultivated with a unique crop; and (iv) livestock grazing land. Only the prime farmland classification was included in the model as a variable.

6a. Adjacent Use Effects: All else being equal, we would expect site land uses to be strongly affected by the pattern of neighboring or adjacent uses. We would expect, for example, that a vacant site surrounded by residential uses would be more likely to be developed into residential or retail use than into office or industrial use. Likewise, we would expect that a vacant site surrounded by commercial uses would more likely be developed into commercial use than into single-family residential use.

Five variables denoting the share of neighboring sites in each major land use (single-family, multi-family, commercial, industrial, and transportation) were included in each model. We computed these variables in two steps. First, for every site, we used GIS to identify the (initial) land uses of each adjacent site. (As noted above, sites are represented by 100m by 100m grid-cells. Thus, every grid-cell is surrounded by eight other grid cells.) Next, we computed the initial percentage of surrounding sites (or grid cells) in residential use, commercial use, industrial use, public use, or being used for transportation facilities. The resulting percentages vary between 1 and 0: a value of 1 indicates that a site is completely surrounded by a particular use; a value of 0 indicates no level of adjacency.

Except for transportation uses, we would expect the estimated coefficients for each of these variables to be positive. That is, we would expect that the probability of a vacant site being developed would be higher if it were entirely surrounded by residential uses than if it were surrounded by a mixture of residential, commercial, industrial, and public uses. The same logic would also apply for other developed land uses.

It would not necessarily apply to for surrounding vacant sites. To the extent that vacant sites function as competition for other vacant sites, the higher the percentage of surrounding vacant sites, the higher the level of competition, and thus the lower the likelihood that a particular vacant site might be developed.

The opposite interpretation is also possible. To the extent that there are minimum size thresholds for particular types of development, developers would tend to favor vacant sites surrounded by other vacant sites. To determine which effect dominates, we used GIS to count the number of vacant hectare grid-cells within 200 meters of each site. A negative coefficient would indicate that the competitive-supply effect dominates the size-threshold effect; a positive coefficient would indicate the opposite.

6b. Inter-Use Externalities and Proximity Effects: Different land uses generate both positive and negative externalities. Indeed, the desire to mitigate negative externalities has long been the classic argument behind zoning. Industrial uses are typically separated from residential uses to minimize aesthetic, safety, and property value spillovers. Likewise, high-density residential development is often separated from lower-density single-family development to minimize the potential for noise, traffic, and other potential spillovers.

Externalities need not be positive. The shopping center located near a large subdivision or apartment building is the beneficiary of a positive spillover--in this case, a large potential market. Similarly, the current emphasis being given mixed-use development is based on the presumption that for certain mixtures of uses, positive externalities exceed negative externalities.

To test for the existence and importance of inter-use externalities, we used GIS to measure the euclidean distance from each site to the nearest commercial site, industrial site, and public use site. To the extent that the negative externalities associated with a combination of uses exceed the positive externalities, we would expect the estimated coefficients of these variables to be negative. Conversely, a positive coefficient would indicate that the positive externalities associated with proximity between uses exceed the negative externalities. Finally, to the extent that proximity effects and inter-use externalities don't matter, we would expect the variable coefficients not to be statistically significant.

Table 2 summarizes the various independent variables and their expected signs.

Table 2

Measuring Goodness-of-Fit

We begin by looking at how well the various models explain what actually happened--that is, by looking at the "goodness-of-fit" between the model predictions and actual land use changes. Unlike the r-square measure generated by linear regression, multi-nomial logit procedures do not generate a single goodness-of-fit measure. Instead, determinations of logit model quality are made according to whether the estimated models correctly classify the observations by category when compared with the observed category distribution. This idea of correct classification is often expressed in terms of the ratio of concordant predictions (those in which the predicted choice or change matches the observed choice or change) to the total number of observations. The number of concordant predictions can be determined using two different methods:

1. Maximum-Probability: The maximum-probability method is based on the assumption that the predicted choice or change is the one which has the highest probability of occurring regardless of the total number of observed choices or changes.

To illustrate the maximum-probability method and its problems, consider the case of an initially vacant site developed into residential use. (In terms of model calibration, the observed change in site status is vacant-to-residential.) The predicted change is estimated based on the results of the multi-nomial logit model. The predicted probabilities of land use change according to the model are .4 for conversion to residential use, .2 for conversion to commercial use, .1 for conversion to industrial use, and .3 that the site remains vacant. (Note that estimated probabilities sum to one.) Assuming the prediction process is unconstrained, the predicted change in site status will be from vacant-to-residential, corresponding to the highest change or choice probability. Note that the highest change/choice probability in this example is only .4.

Note that this method of case-by-case classification according to maximum probability is independent of the total number of observed choices. Suppose, for example, that the maximum-probability procedure described above were to generate 50 predictions of vacant-to-residential land use change, but that the actual number of observed vacant-to-residential land use changes was only 25. Depending on the individual model, the maximum probability method can significantly over- or underestimate the total number of observed category choices or changes.

2. Case-constrained: The case-constrained method imposes the additional assumption that the total number of predicted choices or changes can not exceed the observed number. In the example described above, only the first 25 vacant-to-residential land use changes would be counted as concordant.

The case-constrained method uses the maximum-probability measure to classify observations subject to the total case constraint. Once this constraint is met, an observation could potentially be classified into a lower-probability category. If for example, the total vacant-to-residential case constraint had already been met, the observation described above would be classified according to the next-highest probability--in which case it would remain vacant. The case-constrained method typically results in fewer total mis-predictions than the maximum-probability method, but is more likely to over-predict or under-predict in one or two categories.

Table 3 presents both types of goodness-of-fit measures for all 16 multi-nomial land use change models, including eight vacant land models (one for each Bay Area County, except San Francisco) and eight redevelopment models.

Overall, the vacant land use change models fit the data reasonably well. Using the more reliable case-constrained good ness-of-fit-measure, overall model fits very from a high of 99.0% for Napa County (meaning that the model correctly predicted 99% of all observed 1985-95 grid-cell land use changes) to a low of 92.2% for Contra Costa County. Model fits using the maximum-probability method are comparable.

As a group, the models also do quite well at predicting which vacant sites are most likely to remain vacant. Case-constrained concordancy measures for "vacant-to-vacant" land use changes vary from a high of 99.5% for Napa County (meaning that the model correctly predicts that 99.5% of vacant sites in Napa County in 1985 would also be vacant in 1995) to a low of 96.0% in Contra Costa County. Given that most vacant sites in 1985 remained vacant through 1995 (see Table 1), the very high level of concordancy for the vacant-to-vacant category is not surprising.

The various goodness-of-fit measures are much lower for vacant-to-single-family residential land use changes. They vary from a high of 48.3% in Solano (meaning that the model correctly predict only about half of vacant-to-residential land use changes) to a low of 21.6% in Sonoma

Table 3

County. Note that the maximum-probability goodness-of-fit measures are even lower than the case-constrained measures.

In the case of vacant-to-commercial land use changes, the two goodness-of-fit measures vary widely by county. In Napa County, the model correctly predicts 78.8% of vacant-to-commercial land use changes according to the case-constrained method, and 74.2% according to the maximum-probability method. In neighboring Contra Costa County, the same model specification correctly predicts only 12.4% of vacant-to-commercial land use changes using the case-constrained measure, and 0% using the maximum-probability measure.

There is also considerable goodness-of-fit variation between counties for vacant-to-industrial land use changes. The case-constrained measure ranges from a high of 47.9% in Napa County, to a low of only 6.1% in nearby Contra Costa County. Except for Marin, the other seven counties fall between these extremes.

Vacant-to-apartment land use changes were the least common form of major land use change in the Bay Area between 1985 and 1995 (see Table 1). Because there were so few vacant-to-apartment observations upon which the various logit models could be calibrated, their ability to correctly predict such changes is limited. Prediction concordancy varies from a high of 31.3% in Solano County (using the case-constrained goodness-of-fit measure) to a low of only 10.4% in Contra Costa County. As with the other developed categories, note the generally poor quality of the maximum-probability goodness-of-fit measures.

The eight redevelopment models also explain overall rates and patterns of redevelopment--or more precisely, the lack of redevelopment--reasonably well. Using the more reliable case-constrained good ness-of-fit-measure, overall model fits very from a high of 95.8% for Solano and Sonoma counties, to a low of 91.4% in Santa Clara County. These high levels of model fit are, for the most part, based on how well the models explain the lack of redevelopment that occurred in the Bay Area between 1985 and 1995 (See Table 1). Case-constrained concordancy measures for "no change" in developed use vary from a high of 97.9% in Sonoma County, to a low of 95.5% in Santa Clara County.

The redevelopment models have much less ability to predict actual redevelopment. For residential redevelopment (that is, for sites that changed from a non-residential use in 1985 to a residential use in 1995), the case-constrained measure of concordancy varies from a high of 24.7% in Alameda County, to a low of 14.7% % in Santa Clara County. The ability of the models to explain commercial redevelopment (sites which changed from a non-commercial use in 1985 to a commercial use in 1995) is no better: case-constrained concordancy measures vary from a high of 49.7% in Alameda County, to a low of 2.6% in Napa County. The redevelopment models do a somewhat better job explaining industrial redevelopment (sites which changed from a non-industrial use in 1985 to an industrial use in 1995). Model fits for industrial redevelopment range from 66.7% in San Mateo County (meaning that the models correctly predict 66.7% of industrial redevelopment cases), to a low of 14.1% in Santa Clara County.

Models of Vacant Land Change: Parameter Estimates and Significance

Multinomial logit models generate much more and much richer output than conventional regression models. Indeed, for complicated models such as these, the amount of output can sometimes seem overwhelming. Rather than present the various model results by land use within county (the form in which they were originally calibrated), we present them by county within use. This makes it possible to compare the role and importance of different explanatory factors between counties.

Conversion of Undeveloped Sites to Single-family Land Uses: Residential development accounted for almost three-quarters of Bay Area vacant land development between 1985 and 1995, so the robust reliability of the logit models which capture those changes is not surprising (Table 4). As expected, and regardless of the county, demand factors played a consistent role in explaining vacant-to-single-family land conversion.

The effects of individual demand factors, however, were not always as predicted. Contrary to expectations, the higher the rate of job growth in a city between 1980 and 1985, the lower the

Table 4

probability that an undeveloped site within that city would be developed in single-family use. Household growth rates (between 1980 and 1985) were positively correlated with 1985-95 vacant-to-single-family land use conversion in San Mateo, Santa Clara, Solano, and Sonoma counties--as expected--but not in Alameda, Contra Costa, Marin, and Napa counties.

The effect of city size on residential land conversion also varied by county. Vacant sites in cities with larger populations in Alameda, Santa Clara, and Solano Counties were slightly more likely to be developed in residential use; while residential development favored sites in smaller cities in Contra Costa and San Mateo counties. Vacant sites were more likely to be developed into single-family residential use in cities which were job centers in 1980 in Alameda, Contra Costa, San Mateo, and Santa Clara Counties, but less likely to be developed into residential use in employment-rich cities in Napa and Solano counties. The general preference of residential development for job-rich cities is also evident from the positive coefficients associated with local jobs-housing ratios (although again, the sign, magnitude, and significance of this relationship can be seen to vary widely by county).

The rise of the edge cities and the forces of decentralization notwithstanding, vacant sites closer to San Francisco and/or San Jose were generally more likely to be converted into single-family residential use than more distance sites (as indicated by the negative coefficient estimates.) The importance of regional accessibility varied also widely by county. In Alameda County, for example, vacant sites closer to San Francisco or San Jose were neither more nor less likely to be developed into single-family use. Vacant sites in Contra Costa, Napa, and Solano counties, by contrast, were more likely to be developed in single-family use the closer they were to San Jose, and the farther they were from San Francisco.

The role of freeway proximity as a determinant of vacant-to-single-family land conversion also varied by county. Undeveloped sites close to freeways in Alameda, Contra Costa, Marin, Solano, and Sonoma counties were more likely to be developed into single-family use, while similar sites in Napa, San Mateo, and Santa Clara counties were less likely to be developed into single-family use. Likewise, proximity to a BART station served to discourage single-family residential development in both Alameda and Contra Costa counties.

Except in Alameda County, steeply sloped sites were far less likely to be developed into single-family use than flatter sites. The higher probability of residential development associated with moderately steep sites in Alameda County was probably due to the fact that those sites commanded bay and valley views.

All else being equal, prime farm sites were far less likely to be converted to single-family uses than other under undeveloped sites. this was especially true in Contra Costa and Solano counties. (Whether this disassociation between residential development and prime farm status is the result of local land use controls, or the ability of farmland to remain a viable economic use, or both, can not be determined from the model coefficients.)

The ability of sphere-of-influence boundaries to function as defacto urban limit lines between 1985 and 1995 was virtually nonexistent. In every county except for Contra Costa, vacant sites located inside existing spheres of influence were far less likely to be developed than comparable site outside sphere boundaries.

The extent to which distance from the urban edge served to discourage so-called "leapfrog" residential development also varied by county. All else being equal, the further an Alameda, Napa, or Solano site was outside an existing sphere-of-influence boundary, the more likely it was to be developed in residential use. By contrast, sites in Contra Costa, San Mateo, and Sonoma counties far beyond sphere-of-influence boundaries were less likely to be developed in single-family use than closer-in sites.

Vacant sites surrounded by residential uses were no more nor less likely to be converted to residential use that sites surrounded by other uses, or by a mixture of uses. Vacant sites surrounded by commercial or industrial uses, however, were generally less likely to be converted to single-family residential use. (In Contra Costa and Marin counties, by contrast, the higher the percentage of adjacent sites in commercial use, the greater the probability that a vacant site would be converted to residential use.)

Also inconsistent was the effect of vacant land supplies on undeveloped-to-residential land conversion. Vacant sites in Contra Costa, Marin, San Mateo, and Solano counties which were surrounded by other vacant sites were more likely to be converted to single-family use--suggesting that residential developers in these counties typically require larger sites. The opposite was true in Santa Clara County, were vacant sites were more likely to be developed into residential use if they were not surrounded by other vacant sites.

To the extent that there are any spillover-effects from commercial uses to residential uses, they are mostly positive. Regardless of county, the closer a vacant site was to a commercial use, the more likely it was to be developed in single-family residential use. As expected, the opposite was true for industrial uses: all else being equal, vacant sites near industrial uses were less likely to be developed in single-family use than other vacant sites. sites. (The two exceptions to this were in San Mateo and Solano counties, where vacant sites near industrial uses were actually more lily to be developed in residential use.)

The extent to which public uses generated positive or negative externalities varied by county as well. In Alameda, Napa, Santa Clara, Solano, and Sonoma counties, vacant sites near existing public uses (typically schools and parks) were more likely to be developed in single-family residential use. In Contra Costa County, by contrast, vacant sites located near existing public uses were actually less likely to be developed in residential use.

Conversion of Undeveloped Sites to Multi-family Residential Uses: We begin our discussion of the results of the vacant-to-multifamily land use model (Table 5) with a caveat. Whether in terms of overall fit or coefficient reliability, the vacant-to-multi-family land use change model is less robust than the vacant-to-single-family model discussed above. This is partly because there were relatively few instances of vacant to-multi-family land use change between 1985 and 1995. It also follows from the fact that we estimated rather than directly observed the locations of sites in multi-family use in 1995. Altogether, we estimate that 263 hectares of undeveloped land were converted to multi-family use between 1985 and 1995. Vacant-to-multifamily land conversion accounted for a little more than one percent of Bay Area land use change between 1985 and 1995.

The effects of individual demand factors upon vacant-to-multi-family land use change varied sharply between counties. In Alameda County, for example, vacant sites located in larger cities and cities that had experienced recent (1980-85) household growth were more likely to be developed into multi-family residential use. In Contra Costa County, by contrast, where vacant-to-multi-family land conversion was concentrated in cities which were job-rich, but not necessarily large in terms of population. In Santa Clara County, vacant sites were more likely to be developed in residential use if they were located in cities that had experienced significant prior household growth, but not job growth. In Solano County, multi-family development was

Table 5

concentrated in larger cities, while in Sonoma County, it was focused in smaller cities.

The effect of regional accessibility on vacant-to-multi-family land conversion was far more consistent. Except for San Mateo and Solano counties, the closer a vacant site was to San Francisco, the more likely it was to be developed in multi-family use. Except for the North Bay counties, proximity to San Jose was also strongly correlated with multi-family land conversion.

The role of freeway proximity as a determinant of vacant-to-multi-family land conversion was much less consistent. Undeveloped sites close to freeways in Marin, Santa Clara and Solano counties were more likely to be developed into multi-family use, while similar sites in Contra Costa and San Mateo counties were less likely to be developed into multi-family use. Proximity to a BART station also served to discourage vacant-to-multi-family conversion in Contra Costa County; in Alameda County, proximity to a BART station had no significant effect--positive or negative--on vacant-to-multi-family land conversion.

Except in Marin County, steeply sloped sites were far less likely to be developed into multifamily use than flatter sites. Indeed, in most counties, the minimal number of vacant-to-multi-family land use conversions on anything other than flat sites made it difficult for the model to converge on a unique coefficient estimate. The same was also true for undeveloped prime farmland sites, and for vacant sites located inside city spheres-of-influence. Somewhat curiously, vacant sites in Contra Costa, Napa, San Mateo, Solano, and Sonoma counties were somewhat more likely to be developed in multi-family use the farther they were outside a sphere-of-influence boundary.

No discernable association is evident in any Bay Area County between the probability that a vacant sites would be developed in multi-family use, and the type and/or mixture of surrounding land uses. Proximity to an existing commercial use, by contrast, was associated with a higher probability of multi-family residential land development in every Bay Area county except Napa and Sonoma In a somewhat surprising finding, vacant sites near existing industrial uses were more likely to be converted multi-family use in Contra Costa, Marin, Napa, Solano, and Sonoma counties. Vacant sites near schools, parks, and other public uses were more likely to be developed into multi-family use in Alameda, Santa Clara, and Solano counties, but less likely to be developed into multi-family use in Contra Costa, Napa, and Sonoma counties.

Conversion of Undeveloped Sites to Commercial Uses: The commercial land use category subsumes all measure of retail, service, and office land uses. The 1980s was a period of tremendous commercial construction throughout the Bay Area, and new commercial development accounted for 14.7% percent of region wide vacant conversion between 1985 and 1995.

All else being equal, one might expect commercial development to be more commonplace in job-rich communities, or in fast-growing job centers. As Table 6 shows, this was indeed the case for vacant sites in Alameda and Contra Costa counties. In San Mateo, Santa Clara and Solano counties, however, commercial development favored sites in cities with slower-growing economies, and/or in cities with fewer jobs. (There were too few cases of vacant-to-commercial development in Martin and Napa counties upon which to calibrate a logit model.)

The commercial land use category includes retail centers. Accordingly, one might expect to find some-what higher rates of vacant-to-commercial land use change among sites in cities with larger and/or fast-growing populations. This was indeed the case in San Mateo, Santa Clara, Solano counties, and to a much lesser extent, in Sonoma County. It was not the case in either Alameda or Contra Costa Counties, were vacant-to-commercial land use change seems to have favored sites in smaller and/or slower-growing cities.

New commercial development in the Bay Area remains very much oriented toward San Francisco. All else being equal, vacant sites closer to San Francisco were more likely to be converted to developed in commercial use than more distant sites. (Napa County sites were an exception to this.) Accessibility to San Jose--the Bay Area's other major job center--was less consistently associated with the probability that a vacant site would be commercially developed.

Freeway accessibility is often thought to be the single-most important factor influencing commercial development. Surprisingly, the role of freeway proximity as a determinant of vacant-to-commercial land conversion varied widely. In Alameda, Contra Costa, Marin, and Solano counties, undeveloped sites near freeway interchanges were far more likely to be developed in commercial use than mor distant sites. In San Mateo, Santa Clara, and Sonoma counties, by contrast, proximity to a freeway interchange did not seem to play a significant role in encouraging new commercial development. Napa County was again an outlier, as the likelihood that vacant sites would be developed in commercial use actually increased with

Table 6

distance from a freeway interchange.

As was also the case for residential development, steeply sloped sites were far less likely to be commercial developed than flatter sites. Vacant sites in Alameda, Contra Costa, and Santa Clara counties were also much likely to be developed in commercial use if they were located on prime farmland. In Marin, Napa, San Mateo, Solano, and Sonoma counties, by contrast, a particular site's farmland status did not seem to affect its commercial development potential. affect

Regardless of county, the ability of sphere-of-influence boundaries to contain new commercial development appears to have negligible. All else being equal, vacant sites outside existing sphere-of-influence boundaries were more likely to have been developed in commercial use than vacant sites inside sphere-of-influence boundaries.

The extent to which distance from the urban edge served to discourage commercial "leapfrogging" also varied widely by county. All else being equal, the further a site in Alameda, Marin, Santa Clara, or Solano counties was outside an existing sphere-of-influence boundary, the higher its probability of development. The opposite was true in Contra Costa, Napa, San Mateo, and Sonoma counties, where sites closer to sphere-of-influence boundaries were more likely to be commercially developed.

In general, vacant sites surrounded by residential uses were less likely to be developed into commercial use than sites surrounded by other uses, or by a mixture of uses. (Here again, Napa county sites proved an exception to this generalization) . Vacant sites surrounded by other vacant sites were more likely to be developed into commercial use, suggesting the importance of large-scale land assembly to commercial development. As above, the significance of this effect varied widely by county.

Commercial land uses are subject to both centripetal (clustering) and centrifugal (dispersing) forces. In general, the clustering forces are stronger. Vacant sites in Alameda, Contra Costa, San Mateo, Solano, and Sonoma counties were much more likely to be developed in commercial use the closer they were to other existing commercial land uses. (In Marin and Napa counties, by contrast, the probability that a vacant site would be developed in commercial use decreased with proximity to existing commercial land uses.. New commercial developments , like new residential developments, were more likely to be repelled by than attracted to existing industrial land uses. (Once again, commercial development in Napa County proved to be a consistent exception to this generalization.)

Conversion of Undeveloped Sites to Industrial Uses: The industrial land use category subsumes all manufacturing and production facilities as well as warehouse, distribution, and construction uses. Altogether, new industrial development accounted for 6.3% of Bay Area vacant land change between 1985 and 1995.

The factors which explain industrial development patterns in the Bay Area differ widely by county (Table 7). In Alameda County, for example, a vacant site was more likely to be developed into industrial use if was flat, near a freeway interchange, or near an existing commercial or industrial land use, or outside an existing sphere-of-influence boundary. Vacant Alameda sites surrounded by residential or commercial uses were less likely to be developed in industrial use. Vacant sites in job-rich cities, or cities that experienced recent job growth were also less likely to be industrially developed. A similar set of factors accounted for industrial development patterns in Santa Clara County. Additionally, Santa Clara sites were less likely to be converted to industrial uses if they were on prime agricultural land.

Two other counties, Solano and Sonoma, experienced significant amounts of new industrial development between 1985 and 1995. New industrial development in Solano County was attracted to existing industrial sites, but repelled from commercial sites. Sloped sites, sites located far beyond sphere of influence boundaries, and prime agricultural land sites were also less likely to be developed in industrial use. Curiously, Solano County sites located near freeway interchanges were less, not more likely to be developed in industrial use. As in Alameda and Santa Clara counties, new industrial development favored sites in or near cities with growing populations, but not expanding economies. In Sonoma County, new industrial development followed still a different pattern, favoring flat sites in the southern part of county, sites near existing industrial uses, and sites beyond city and sphere-of-influence boundaries.

Table 7

Parameter Estimates and Significance: Redevelopment Models

Redevelopment is typically a much more complicated and idiosyncratic process than new development. Whereas new development creates (or at least helps create) the urban fabric, redevelopment typically occurs within the context of an existing urban fabric. This drastically increases the number of interests or stakeholders involved in the redevelopment process. It also increases the uncertainty associated with a particular redevelopment project. Getting the politics right is often more important to successful redevelopment projects then getting the economics right. Because local politics are notoriously difficult to model, the statistics (including both coefficient estimates and measures of goodness-of-fit) associated with the various redevelopment models tend to be much more uneven that the statistics associated with the new development models, above.

Redevelopment to Residential Use: The usual image of urban redevelopment is that it is a process whereby older residential or industrial sites are recycled into newer commercial and business uses. In fact, redevelopment to residential use dominated all other forms of redevelopment in the Bay Area between 1985 and 1995. According to the Association of Bay Area Governments, more than 7,800 hectares of land were redeveloped into single-family or apartment use between 1985 and 1995.

Despite its apparent popularity, the factors behind residential redevelopment in the Bay Area are far from systematic. In fact, as Table 8 shows, the factors which explain residential development differ widely and erratically between counties. Indeed, the only factor which consistently explains recent patterns of residential redevelopment in more than one county was distance to a sphere-of-influence line. Except in Alameda County, the closer a particular site was to a sphere-of-influence line, the more likely it was to be redeveloped into residential use. Contrary to the new development case, above, sites near freeway interchanges were less likely, not more likely, to be redeveloped into residential use

All else being equal, residential redevelopment in Alameda County favored sites in the southern part of the county, as well as sites in larger cities. Sites near freeway interchanges or BART stations, or in job-rich cities were less likely to be redeveloped into residential use. In Contra Costa County, residential redevelopment favored sites close to San Francisco, as well sites near existing commercial land uses. The same two factors contributed to residential

Table 8

redevelopment in Santa Clara County, as did local rates of household growth, and nearby vacant land.

Santa Clara County sites less likely to be redeveloped into residential use were those located near freeway interchanges, those with any type of slope, and those located in job-rich cities. In Marin County, residential redevelopment was (and is) so rare that none of the factors included as independent variables could explain it. In Napa County, residential redevelopment between 1985 and 1995 favored sites far away from freeways as well as sites near existing commercial and industrial uses. Proximity to industrial uses also served to encourage residential redevelopment in San Mateo County, although curiously, proximity to commercial uses had the opposite effect. In Solano County, sites near industrial uses were more likely to be redeveloped in residential use, although sites surrounded by industrial land uses were not. Sites in Sonoma County were more likely to be residentially redeveloped the closer they were to freeways and industrial uses, but the further they were from residential uses.

In almost no Bay Area County did a particular site's initial land use, its proximity to public land uses such as parks or schools, or the mix of adjacent land uses affect the likelihood that it would be residentially redeveloped.

Redevelopment to Commercial Use: Four Bay Area counties--Alameda, Contra Costa, Santa Clara, and Sonoma--experienced significant amounts of commercial redevelopment (i.e., land use change from a developed non-commercial use to a commercial use) between 1985 and 1995. Commercial redevelopment was an extremely infrequent form of land use change in the region's other counties.

Commercial redevelopment is as idiosyncratic and difficult to model as residential redevelopment. Of the many explanatory factors listed in Table 9 only two were consistently associated with higher rates of commercial redevelopment between 1985 and 1995: initial proximity to a commercial use, and municipal household growth.

The effects of other explanatory factors varied by county. All else being equal, commercial redevelopment in Alameda County favored flat sites closer to San Francisco, or near freeway interchanges, or surrounded--at least initially--by residential uses. In neighboring Contra Costa County, commercial redevelopment favored flat sites far from public uses, and/or sites located in

Table 9

cites with declining economies such as Richmond. In Santa Clara County, the sites most likely to be commercially redeveloped between 1985 and 1995 were those located in existing commercial areas, or those close to downtown San Jose, or those initially in industrial or transportation use. Santa Clara County was the only Bay Area county in which a site's initial use played any role in shaping whether it was likely to be commercially redeveloped. In Sonoma County, commercial redevelopment favored sites close to freeway interchanges, sites closer to San Francisco, and sites within or close to sphere-of-influence boundary lines.

Redevelopment to Industrial Uses: Industrial redevelopment--that is, redevelopment from a residential, commercial, or public use to an industrial use--is an infrequent occurrence in the San Francisco Bay Area. (Most industrial development occurs on previously undeveloped land.) Region wide, just over 200 hectares of urban land were redeveloped to industrial use between 1985 and 1995.

The majority of the region's industrial redevelopment occurred in just two counties: Santa Clara and Sonoma (Table 10). In Santa Clara, the sites most likely to be industrially redeveloped between 1985 and 1995 were those which were close to freeway interchanges, those which were close to existing commercial or industrial uses, those which were inside sphere-of-influence boundaries, and those in large but not necessarily job rich cities. Proximity to San Francisco, but not necessarily San Jose also contributed to the likelihood that a site would be redeveloped into industrial use.

The pattern of industrial redevelopment in Sonoma County was somewhat different. Sonoma County sites most likely to be industrially redeveloped included those near freeways, those near existing commercial uses, and those outside city or sphere-of-influence boundaries. Industrial redevelopment in Sonoma County was concentrated in sites in cities with expanding economies but not necessarily expanding populations.

The counties with the next largest totals of industrial redevelopment between 1985 and 1995 were Alameda and Napa. Industrial redevelopment in Alameda County favored flat sites, sites in larger cities, sites close to BART stations and sites close to commercial uses. Proximity to freeway interchanges and other industrial sites, two factors which were extremely important in Santa Clara, were not important in Alameda County. In Napa County, industrial redevelopment was concentrated in sites near or adjacent to industrial land.

Table 10

SUMMARY AND CONCLUSIONS

The CUF II Model is a significant improvement over its predecessor and step forward in the continuing evolution of urban growth models. The foremost feature of the CUF II Model is that it allows competing land uses to bid against each other on a site-by-site basis, without any a priori assumption regarding which uses are superior or inferior. This is achieved by using a multi-nomial logit estimator for model calibration. The fact that the model is actually calibrated against observed site-level land use changes, as opposed to zone-based changes in activity levels, is also significant. To our knowledge, the CUF II Model is the first urban growth model to realistically incorporate the potential for urban redevelopment--that is, that a site might be redeveloped from one urban use to another.

Through its links to GIS, the CUF II Model makes it possible to identify the determinants of land use change at different spatial scales. The land use change model, for example, incorporates site-level measures such as slope and proximity to major transportation infrastructure; neighborhood effects such as the role of adjoining land uses in encouraging or discouraging development; city-scale effects such as population and employment growth; and regional effects such a accessibility to major employment centers. The land use change model also includes key policy variables such as site distance to the nearest sphere-of-influence boundary, and distance to the nearest rail transit station. The presence of all of these variables makes it possible for the CUF II Model to test the spatial impacts of an unprecedented set of realistic policy variables, including, for the first time, new freeway and transit facilities.

The CUF Model is not just more advanced that its predecessor, it is also different. Whereas the previous version of the CUF Model approximated sites as spatially homogeneous collections of development attributes (termed Developable Land Units, or DLUs), the CUF II Model represents potential development sites as hectare grid-cells. The shift to grid cells (made possible by advances in GIS technology) make it possible for CUF II Model to incorporate multiple adjacency and nearest neighbor effects, as well as better measure distances.

Like its predecessor, the CUF II Model is modular. Alternative regional and/or local household and employment projections can be inserted into the model. The model can also be updated as new information becomes available. Perhaps most important, the CUF II Model is capable of simulating and summarizing processes of urban growth at the site level, just like its predecessor.

The Things that Matter

The CUF II Model shines a spotlight on the mechanisms and processes of urban land use change. In doing so, it brings to the forefront those factors which most matter. It also makes clear the interactions between the determinants of land use change and land use policy.

What causes a particular vacant site to be developed, or an already-developed site to be redeveloped? The answers to this question vary by place and land use. The factors most consistently associated with recent vacant-to-single-family residential land use change in the Bay Area have been: (i) proximity to a freeway interchange; (ii) low rates of community job growth, and; (iii) proximity to nearby retail activities. The availability of flat sites was found to important in every Bay Area county but Contra Costa. All else being equal vacant sites atop prime agricultural land were less attractive to residential developers than lower-quality agricultural sites. Infill sites (e.g., vacant sites within existing city spheres-of-influence) were generally less attractive than more far-flung sites. Sites near existing industrial uses, were, not surprisingly, less attractive to single-family home developers than other sites. Conversely, vacant sites near public uses, especially schools and parks, were more likely to be residentially developed. The closer a site was to downtown San Jose, the more likely it was to be developed to single-family use. Except in Sonoma and San Mateo counties, the same was not true for sites near downtown San Francisco. New housing development was slightly more likely to occur in cities with large numbers of jobs.

The same factors that explain single-family housing development patterns--freeway proximity, site slope, distance to downtown San Jose, and proximity to commercial uses--also explain apartment development patterns. New apartments, like new single-family homes, were not particularly attracted to infill sites. Nor were they consistently attracted to sites near public uses such as schools and parks. In Alameda County, proximity to BART had no effect on apartment development; in Contra Costa County, vacant sites near BART stations were less likely to be developed in apartment use.

Patterns of vacant-to-commercial and vacant-to industrial land use change also varied widely by county. New retail uses in Alameda and Contra Costa Counties, for example, favored cities with large numbers of jobs, sites closer to downtown San Francisco and San Jose, sites near freeway interchanges, and sites near other commercial uses. New retail uses in Santa Clara County, by contrast, favored sites in communities with fewer jobs and more houses, site closer to San Francisco but not downtown San Jose, and sites near existing industrial areas; they did not favor sites near freeways or other retail uses. In Marin County, new retail users preferred sites with direct freeway access and sites close to downtown, but were "repelled" by existing commercial land uses. Industrial users generally favored vacant sites in growing communities, sites with freeway access, and most of all, sites near other industrial users.

Redevelopment is typically a much more complicated and idiosyncratic process than new development. Accordingly, Bay Area patterns of redevelopment varied widely by terminal use and by county. Still, a few generalizations regarding redevelopment do apply. Redevelopment occurs only on flat or near-flat sites. Contrary to the new development case, freeway proximity was not a consistent determinant of redevelopment activity. Nor was proximity to a BART station. Except for industrial redevelopment, a site's initial use had little impact on its terminal use. Sites were more likely to be redeveloped to commercial and industrial uses the closer they were to other commercial and industrial uses (respectively). All else being equal, redevelopment activity in the Bay Area favored larger (but not necessarily job-rich) cities with growing populations but not necessarily growing economies.

All of these results are subject to four caveats. The first is that they are based on observed land use changes which occurred between 1985 and 1995. Their applicability to earlier periods, or for that matter, to the current one, is unclear. Second, these results are based on analyses of changes in dominant land use at the hectare, not parcel, level. To illustrate the limitations of this type of analysis, consider the case of a hectare grid-cell that, as of 1985, was 40 percent undeveloped, 30 percent residentially-developed, and 30 percent commercially-developed. Next, suppose that a single new home was built in 1987 on a vacant parcel within the same grid-cell. According to our (and ABAG's) definitions, the dominant land use of this grid-cell would have changed from 'undeveloped' in 1985, to 'residential' in 1995. These types of threshold-changes, while uncommon throughout the entire data set, were not unknown either. Third, while the various models do a good job predicting which sites will not change land use (e.g., remain vacant, or not be redeveloped), they are generally less capable of predicting which specific sites will shift land use. Clearly, there are many other factors that shape land use change which should be included in the various models. Fourth, the extent to which the model results reflect underlying public policy regimes, particularly local zoning, is unclear. The fact that new commercial development favored sites near freeways may simply reflect the fact that so many parcels near freeways are zoned for commercial development. Similarly, the observation that new residential development did not favor "prime" agricultural sites may be more indicative of the success of agricultural preservation policies than of underlying developer preferences.

An Agenda for CUF II.1 and for CUF III

Like all urban growth models, the CUF II Model still has plenty of room for improvement. The model is horrifically data hungry--although recent advances in GIS technology make that hunger easier than ever to satisfy. Despite its relatively simple structure, the model is not easy to understand or explain. Its bid-based approach to allocating competing land uses, while intuitively appealing, sometimes leads to unrealistic results.

Judging from their middling goodness-of-fit results, the current multi-nomial logit land use change models are still incomplete. Factors like local zoning designations and codes need to be tested and added to the models, as do local public service quality and availability, and better measures or sub-regional accessibility. The extent of bias due to spatial autocorrelation also needs to be carefully investigated. The fact that the estimated logit equations are based on all sites rather than a random sample also introduces potential bias.

The biggest remaining gap in the CUF II Model is that it doesn't incorporate actual or imputed real estate prices. Prices serve three essential functions in urban real estate markets. The first is to provide independent signals to both buyers and producers regarding appropriate land uses and land use intensities. Second, and of greater importance, prices function to "clear" real estate markets. Market clearing is the process whereby individual transactions between willing buyers and sellers lead to marketwide outcomes that are fully reflective of supplier costs, and of demander preferences and incomes. Third, prices are the mechanisms through which markets adjust to short-term imbalances between supply and demand.

The CUF II Models's lack of prices is especially problematic when simulating spillovers. As currently structured, activities which can not be accommodated in one location (usually for reasons of insufficient land or because of policy constraints) costlessly spillover to the next best location. Within a particular radius (as determined by the user), there is no particular penalty associated with spillover. Real life doesn't work that way. Confronted with the possibility that their preferred sites may be unavailable, many activities will not consider alternative sites. They will instead raise their bid prices for their preferred sites. The result will be an increase in site prices (in the form of economic rents) together with some degree of spillover (by those activities which will consider alternative sites). Because the CUF II Model does not include explicit prices, it can not deal with different price elasticities of demand, or, for that matter, of supply. Its sole response to unaccommodated demand is through the spillover mechanism.

A second and related limitation of the CUF II Model is that it lacks agents. The multi-nomial logit models that form the heart of the CUF II Model are all reduced-form models. That is, they focus on the characteristics of transactions (land use change in this case) but give short shrift to the characteristics and motivations buyers (e.g., households and businesses) or sellers (e.g., land owners and developers). To the extent that the timing and nature of actual land use changes reflect the economic characteristics and personal motivations of real people and real businesses, and not just the locational characteristics of sites, the CUF II model may be regarded is seriously incomplete, or potentially biased, or both.

In the absence of agents, one must assume that all site demanders (households and businesses), and all site providers (developers and land owners) are functionally the same--which is to say that they value particular sites in the same ways. This assumption is neither true nor defensible. Households come in many different sizes, configurations, and lifecycles, and with sharply varying preferences for location, housing, travel, and public services. Businesses likewise are extremely diverse, even within a single industry. On the supply side, landowners often sell to developers for lifecycle rather than purely economic reasons. Likewise, the actual projects developers build often have more to do with what the entitlements process will allow than what the market will reward. Adding information on agents to the CUF Model should improve both its reliability and robustness.

How might such information be added? Perhaps the simplest approach would be to include the demographic and/or economic characteristics of local households and/or businesses as independent variables in the logit specifications. The simplicity of this approach notwithstanding, it would likely exacerbate problems of ecological fallacy. A better long-term approach would be to employ techniques of micro-simulation; that is to observe and then try to model the bid and acceptance functions associated with a representative sample of households, business, landowners, and developers.

Ultimately, of course, the logit equations used to explain land use change must be linked back to the regressions equations used to predict population and job growth. While is convenient to model land use change and activity allocation (or land use change) as separate phenomena, it is certainly not correct. Where new development of different types goes (and where it does not go); the price structure of new development; the extent to which development is imported or exported from different communities; the importance of infrastructure investments and inter-use externalities--all of these outcomes ultimately become the inputs to yet a new round of metropolitan-scale growth and change.

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