Abstract
This article uses data on 3,788 vacant land sales to explore the pattern of land values in the city of Detroit, Michigan. The analysis provides evidence of a U-shaped land value gradient. Land values are relatively high in and near the central business district (CBD), but the land value gradient is very steep; estimated land values drop precipitously to less than $1,000 for typical sized lot in a vast “donut” area surrounding the CBD. However, land values begin to rise near the city’s border. (JEL R14)
I. INTRODUCTION
Its recent declaration of bankruptcy has brought the city of Detroit, Michigan, to the forefront in the media as well as among policy makers and researchers. Years of business and population exodus have resulted in thousands of parcels of vacant land, some of which are offered for sale every year. These vacant property sales provide an opportunity to explore the pattern of land values across the city. The stylized monocentric city model generates a land value gradient that declines the farther the parcel is from the city center. While there are numerous examples of exceptions to this general framework in the real world, the model has been a very useful tool for urban economists.
Does a city in significant decline, such as Detroit, exhibit the land value gradient predicted by the monocentric city model? In this paper, we use data on 3,788 vacant land sales that occurred over the 2006–2010 period to explore the spatial pattern of land values in the city of Detroit. As a prelude to our full analysis, we find that property values are relatively high near the central business district (CBD), but the land value gradient is very steep; land values in the “donut” area around the city center are extremely low. Our analysis also shows that land values increase near the adjacent suburbs along the city’s borders but remain much lower than the land values at the city center. Specifically, land values at the border are up to 20 times larger than those in the city’s “donut” area, and land values at the center are approximately 30 times greater than those at the border.
II. REAL ESTATE/VACANT LAND ENVIRONMENT IN DETROIT
As Detroit’s population declined from 1.85 million in 1950 to 714,000 in 2010, there was a corresponding decline in the demand for housing in the city. The net loss in housing units during this period totaled almost 200,000. According to a 2009 survey by Data Driven Detroit (2010), there were over 90,000 vacant residential parcels in Detroit, 27% of all residential parcels.
Each year about 1% of the more than 90,000 vacant parcels are sold. Figure 1 shows the geographic distribution of vacant land sales in Detroit over the 2006–2010 period. Nearly all areas of the city have numerous vacant land sales. We have confidence that we can effectively estimate land value patterns for the entire city because of the broad distribution of land sales.
Spatial Distribution of Vacant Land Sales in Detroit
Source: Map © OpenStreetMap contributors; data available under the open Database License, see openstreetmap.org.
III. LITERATURE REVIEW
The monocentric city model developed by Muth (1969) and Mills (1972) provides a baseline for understanding urban spatial structure. The model has been used extensively and has frequently been subject to empirical testing. Duranton and Puga (2014) provide a comprehensive review of this literature. While many researchers no longer consider the monocentric city model to be an accurate depiction of modern urban spatial structure, McMillen (2006) notes that the central city still dominates urban spatial patterns in many cities: “Although the model is oversimplified, it remains a useful analytical tool, requiring only modest modifications to be remarkably accurate” (p. 129).
In our empirical analysis, we use a modified monocentric city framework to guide our analysis of Detroit land values. The modifications are informed by our knowledge of the city, as well as the work of several researchers. The first consideration is the acknowledgment that although the city center dominates many urban places, other spatial forces influence property value. For example, Dubin and Sung (1987) consider rent gradients in nonmonocentric cities where households value access to CBD and non-CBD locations alike. Similarly, Brueckner, Thisse, and Zenou (1999), Cheshire and Sheppard (1995), Waldfogel (2008), Ahlfeldt (2010), and Combes, Duranton, and Gobillon (2012) show accessibility to amenities, employment, landmarks, and scenic views, which are not always located in the CBD, is an important determinant of property values. Finally, Albouy and Ehrlich (2013) and Colwell and Sirmans (1978) find that land prices are affected by lot size, and Colwell and Munneke (1997) demonstrate how property value gradient estimations can be biased if one does not control for parcel size, since parcels tend to be larger the farther they are from the CBD.
The second consideration extends the basic model of spatial variation and recognizes the role of neighborhood factors to improve model fit. Rosenthal and Ross (2015) provide a comprehensive review of this literature. This research has identified a number of relevant factors, including public transportation (Glaeser, Kahn, and Rappaport 2008), age of the housing stock (Rosenthal 2008; Bruecker and Rosenthal 2009), the quality of public services, particularly education and public safety (Epple and Ferreyra 2008), and tax prices to explain the location decisions of higher-income households, the creation of new municipalities, and higher land values (De-Bartolomé and Ross 2008).
The final consideration and perhaps most useful conceptualization is based on historic patterns of development and redevelopment. As a city accommodates growth by expanding its footprint, the newest and highest-valued housing will typically be found on its periphery (Brueckner and Rosenthal 2009). When redevelopment occurs it begins closest to the city center, moving outward to create bands of newer housing, with higher-income occupants.
In the case of Detroit each of these issues must be considered. Spatially, shopping and employment opportunities are found primarily in Detroit’s suburbs, and proximity to the suburbs, or to major roadways providing easy access to these areas, may play a key role in land values within the city. There also exist a number of disamenities that may affect land values, such as abandoned and/or toxic sites. In addition, our empirical specification is informed by Colwell and Munneke (1997) in that we include parcel size as an explanatory variable.1 Regarding neighborhood factors, the quality of public services has been found to vary across the city of Detroit, although taxes are levied at the same rate (Detroit Office of the Emergency Manager 2013). We control for these, and other, neighborhood differences by including a vector of neighborhood indicator variables. Finally, historical patterns of redevelopment in Detroit have been minimal, at least until recently (Vojnovic et al. 2016), as the city has experienced decades of population decline. Thus, the neighborhoods at Detroit’s periphery continue to be among the highest valued. With this review, we now turn our attention to estimating the determinants of land values in Detroit using detailed data on recent land sales.
IV. EMPIRICAL ANALYSIS
The framework we use to evaluate land values in Detroit is a Cobb-Douglas land price function similar to that outlined by Colwell and Munneke (1997):
[1]
where for parcel i, γ is the area (A) elasticity of price, δ is the rate at which price changes with distance to the city center (c), and β is the price of the first square foot of a parcel at the city center. We expect a steep land value gradient in the area immediately surrounding the city center. However, we also hypothesize that land values will begin to rise near the city borders, as shopping and other amenities are available in the adjacent suburban communities. We therefore empirically test the following augmented land price function:
[2]
where ρ is the rate at which the price changes with the distance to the nearest city border (b). We define distance from the city border as distance from the border of the nearest adjacent community, rather than to the river. Note that because of the irregular shape of the city, the distance to the center (c) and distance to the border (b) are not complementary.2
From equation [2], the basic empirical specification is
[3]
where Pit is the sales price of vacant lot i in period t, with key variables A, b, and c as previously defined for parcel i; N is a vector of j (53 of 54) neighborhood indicator variables; T is a vector of t time indicator variables for the years in which the parcels was sold; and e is the error term. In addition, our regressions include the following control variables to estimate price differentials: indicator variables for whether or not the parcel is zoned Residential or Commercial,3 an indicator variable for whether the parcel is large enough to be Buildable according to current zoning regulations,4 and Distance to Packard plant, which is perhaps Detroit’s most notorious toxic abandoned manufacturing site.5 Note that with this specification the distance from the CBD and city border are identified using the within-neighborhood variation land values. Also, with the logarithmic specification, most of the variation in distances is close to the target from which the distance is being measured. Thus, the interpretation of the coefficients is such that land values will vary by distance within neighborhoods from various target locations. For example, looking within a single neighborhood near the CBD, the coefficient on distance from the CBD will capture land value differences attributable to distance from the CBD within a neighborhood; land values are expected to be higher in the portion of the neighborhood located closer to the CBD.
Data
The city of Detroit’s Assessment Division provided parcel-level data for this research.6 The raw data include information for 444,183 real and personal property parcels, of which we focus on vacant land parcels. In total, there were 93,786 vacant parcels. We excluded 10,225 vacant parcels that were sold as part of a “bundle”—that is, a single sale price of the given parcel was recorded with one or more additional properties—because it is not possible to determine the value of a particular parcel within the bundle. We also omitted all 2,235 industrial parcels from the analysis, yielding a total of 81,326 taxable and nontaxable residential and commercial parcels in our sample. Of these, 3,788 parcels, 4.6%, sold during the 2006–2010 period.7
We focus on recently sold properties for two reasons. First, the sales prices of recently sold properties represent the city’s most recent market values. It is particularly important to capture the effects of the 2008–2010 real estate crisis, as we do with our set of time indicator variables in equation [3].8 Second, given that there is a continual process of tearing down dilapidated housing stock, the further back one goes in time the more likely it is that the last sales price is for an improved property. That is, most parcels in the city were improved at one point in time. While we know the current status of each parcel (vacant or developed), we do not have data about when demolitions occurred. Therefore, we limit our sales data to reduce the risk of mistakenly classifying a currently vacant parcel as a vacant sale when it may have actually been developed at the sale date.
Summary statistics for all of the variables we consider are provided in Table 1, and more detailed definitions for all variables are provided in Table 2. Consider first the full sample of all 81,326 vacant parcels. About 43% of these are classified as residential and 7% are classified as commercial. The remaining properties are in nontaxable status, with most of these held by the city or some other public entity. The average lot size is very large at 256,707 square feet, but the median is just 3,485. Further, only 16% of the lots are larger than 5,000 square feet, which is the threshold for being “buildable” under Detroit’s current zoning ordinance. The average property is 2.2 miles from the city center and 5.6 miles from the nearest adjacent community. Finally, note that in 2010, relatively few properties sold. This is primarily due to the fact that our 2010 data include information for only part of the year.
Vacant Land Sale Summary Statistics
Variable Names and Definitions
Turning to the sample of parcels that actually sold during the 2006–2010 period, the mean price is high ($37,723), but the median sales price is just $811. About a third of all sales were for less than $10. In addition, the vacant parcels that sold are, on average, closer to the city center and farther from the city border than the full sample. With this summary of the data, we now present estimation issues we must address before discussing the results of our empirical analysis.
Econometric Issues
We begin our analysis using an ordinary least squares (OLS) method with a correction to obtain robust standard errors. However, there are three complicating issues that we consider and address: (1) truncation of land values on the left-hand side, (2) overdispersion of land values on the right-hand side, and (3) potential sample selection bias due to the fact that not all parcels are equally likely to be offered for sale. Consider first the issues of truncation and overdispersion.
Truncation and Skewness
Figure 2 provides a frequency distribution of all land sale prices in our data. As shown in Figure 2, there is truncation at the low side of the price distribution, with just over a third of land sale observations recorded at a price of $10 or less. This might reflect dire market conditions that exist in some Detroit neighborhoods, or it may result from county government policy to set the price of a tax delinquent parcel to include back taxes owed in addition to the documented sale price.9 Unfortunately, information on recently sold parcels does not include the amount of back taxes due at the time of purchase, and we may not observe the full price for some of the land sales. Regardless, truncation bias may result, as observations with positive error terms are disproportionately sampled.10 In addition to truncation on the left side of the distribution, Figure 2 shows a number of highly priced vacant land sales that may affect the coefficient estimates generated from OLS analysis, though the high-side skewness is minor when price data are expressed in natural logarithms. Exceptionally large values can substantially affect coefficient estimates, even if they represent only a small percentage of the total sample.
Frequency Distribution of Land Sales Prices
We address the truncation and skewness problems simultaneously by implementing an interval regression procedure.11 Treating lowvalued observations as censored (as the interval regression procedure does) allows these observations to potentially take more negative (or higher positive) values, which mitigates potential truncation bias. Treating high-valued observations as censored allows us to include them in the sample by mitigating the disproportionate impact due to their exceptionally large values. In our analysis, we treat any sales price observation outside the interquartile range as censored: properties with sales prices of $200 or less, and $9,000 or more, are censored at the respective threshold values.12 While somewhat ad hoc, an interval regression procedure is arguably an improvement over the standard OLS estimation that ignores these issues. We present OLS regression and interval regression estimates in our analysis, with robust standard errors, and note that both produce qualitatively consistent coefficient estimates. Before we present our estimates, we must discuss the third econometric challenge.
Sample Selection Bias
While researchers such as McMillen (1991) and Colwell and Munneke (1997) have addressed sample selection in the context of zoning regulations, to our knowledge the existing literature has not addressed the idea that all parcels are not necessarily equally likely to be sold.13 For example, nearly half of Detroit’s vacant parcels are owned by a public entity; it may be that publicly owned parcels are less likely to be sold than privately owned parcels. Similarly, a large number of parcels are too small to be developed according to current zoning guidelines and may therefore be less likely to be purchased. Failure to account for these sample selection issues could generate biased estimates. Our full sample data set includes all vacant land (sold and unsold) in Detroit as of 2010, allowing us to test for sample selection bias and, if present, address it with appropriate econometric techniques. Specifically, we estimate the determinants of the probability that a parcel is sold during the 2006–2010 period, and then, conditional on the parcel selling, the determinants of the sales price. This joint process is estimated simultaneously using a procedure proposed by Heckman (1979).14 In the first step, we estimate the selection equation, represented by
[4]
where Si indicates whether property i is sold (yes = 1, no = 0); PCi is a vector of property characteristics that includes the Effective tax rate, indicator variables for whether a lot is zoned Residential or Commercial, Size of lot, and whether the lot is Buildable (yes = 1, no = 0); and Di is a vector of “distance” variable(s) that includes the distance from the parcel to the city center (Distance to city center), the distance the parcel is from the city’s border (Distance to border), as well as Distance to Packard plant.15
In the second stage of the Heckman procedure, we estimate factors that determine the sales price, conditional on the property being sold. The Heckman second-stage outcome equation is represented by equation [5]:
[5]
where Sales price (P) for parcel i is equal to price at which the parcel sold during the 2006–2010 period, Xi is a vector of property characteristics that includes all of the variables in the selection equation except for Effective tax rate. Effective tax rate is included in the selection equation, but not the second-stage price equation to identify the system of equations. While each vacant parcel is subject to the same statutory millage rate, effective tax rates differ considerably across properties at the time of sale as a result of Michigan’s taxable value cap policy (Proposal A, enacted in 1994). Specifically, the tax cap restricts the year-over-year increase of a property’s taxable value to the lesser of 5% or the rate of inflation. Only once a property sells does the taxable value reset to the full rate. Of particular relevance to this paper, property owners with a lower effective tax rate have a lower cost of holding a property, resulting in a lower likelihood of selling their property. This is known as the “lock-in” effect and influences the decision to sell, but not the sales price, because all sold properties have the same effective tax rate, equal to the statutory rate (Hodge, Sands, and Skidmore 2015).16 We estimate the selection and outcome equations jointly by maximum likelihood.
Nonparametric Methods: Locally Weighted Regression
Following Meese and Wallace (1991) and McMillen (1996), we also use nonparametric methods to evaluate Detroit land values. Specifically, we used the locally weighted regression (LWR) technique in which more weight is given to “nearby” observations when estimating the land value regression. The local fitting approach developed by Cleveland and Devlin (1988) defines “local” by actual distance.17
As described by McMillen and Redfearn (2010), minimizing equation [6] with respect to α and β yields the LWR estimator:
[6]
The weight that observation i receives in estimating the value of P at the target point X is determined by the kernel function K(ψ).18 There are a number of choices for the kernel weighting function, where an increase in ψ signifies declining weights. Our results are not sensitive to the choice of kernel weight function. However, the choice of bandwidth, h, is very important since it determines the proportion of observations that receive a positive weight and how quickly weight declines with distance. We follow Cleveland and Devlin (1988) and McMillen (1996) and estimate regressions using 30% of the observations as our bandwidth.
LWR analysis requires that a separate regression be estimated for each observation in the data set.19 The locally weighted estimator generates coefficient estimates for each value of X and allows us to generate predicted values of P, as described in detail by McMillen (1996). We have an added layer in our analysis as we wish to generate predicted land values for more than 300,000 parcels in the city (improved and vacant), but we have only 3,788 actual vacant land sales. Once we generate predicted land values for all the observations in our data set, we create a map that illustrates the pattern of predicted land values for the entire city.
Empirical Results
Parametric Estimates
The OLS and interval regression estimates are presented in Table 3, and the Heckman sample selection estimates are found in Appendix A. Consider Table 3, where columns 1–3 contain the OLS estimates and columns 4–6 contain the interval regression estimates. In columns 1 and 4, we include the control variables and ci (distance from the city center). In columns 2 and 5, we include the control variables and bi (distance to the border). Finally, in columns 3 and 6 we include both ci and bi. These different specifications allow us to evaluate the respective roles of ci and bi on land values. Note that the OLS and interval regression analyses yield qualitatively similar coefficients, though the coefficients are much larger in the interval regressions.
OLS and Interval Regression Land Sale Estimates
Before discussing the key distance variables, consider the control variables. Relative to the omitted category (nontaxable parcels), residential and commercial parcels sold for higher prices. Larger and buildable lots also sold for more, highlighting the importance of property rights in the determination of land values. Detroit’s zoning regulations now require a larger minimum lot size for construction, which restricts the right to build on thousands of existing small lots that predate the current standard. In principle, a property owner may receive approval to build on a small lot, but the process requires time and money, and the outcome is uncertain. Lots that sold before the real estate crash in 2008 sold for more; the time indicator variables show that average land sales prices in 2010 were more than 70% lower than 2006. Finally, our estimates indicate that properties immediately surrounding the abandoned Packard plant sold for less.
Turning to the key variables of interest, we see that distance to the CBD is a significant determinant of price; vacant properties sold for a higher price near the CBD, as is typical in the monocentric city model and stems from the significant reinvestment in Detroit’s CBD in recent years (Hudson-Weber Foundation 2013). However, the coefficient on the distance from the border is negative and statistically significant; that is, property values decline the farther the parcel is from the border. These two specifications seem to offer conflicting information on the form of the land value gradient. To reconcile these findings, consider the estimates in column 3 and 6, where we include both the distance from the city center and the distance to the border in a single regression. We see that both distance variables are larger in absolute magnitude, and their statistical significance also increases. Properties close to the city center are valued more highly, as are properties near the border. A primary finding in these regressions is that we observe a U-shaped land value gradient, where property values are highest near the CBD and near the city’s border.20 We also present estimates from the first-stage sale selection equation and then the second-stage sales price equation in Appendix A. Though we find evidence of sample selection bias, the estimates are very similar to the OLS and interval regression estimates, and so we do not discuss them in detail here.
To illustrate further the dual effects of the two distance variables, consider Figure 3, which provides a stylized land value gradient generated from coefficients on distance from the CBD and distance from the border using the estimates presented in column 3 of Table 3. Figure 3 shows that property values are relatively high near the city center, but they dissipate rapidly as distance from the center increases. Land values drop to about $5,000 per parcel 2 miles from the CBD. McMillen (2006) notes that high-income cities tend to flatten the land-value gradient. In the case of Detroit, incomes are now very low; thus, it is not surprising the land value gradient is so steep. Property values in the ring 4 to 6 miles from the city center are extremely low, less than a $1,000, but land values begin to rise about 1 mile from the border. Although rising land values near the border are consistent with the notion that accessibility of amenities and employment in suburbs serves to buoy land values in the city, we test this theory by estimating a series of regressions including specific amenities within the city (best schools) and in the nearby suburbs (shopping and employment centers for Detroit residents). These estimates, which are provided Appendix B, show that proximities to specific amenities in the suburbs are not a driving factor in land values. When we include the amenity variables along with the distance from the border variable, the coefficient on the distance from the border remains statistically significant. This additional analysis suggests that land values may rise near the border because these properties are farther from the disamenities (dilapidated housing, vacant lots, crime, etc.) in the “donut” area around the city center.21
Detroit Land Value Gradient
We note the negative impact of the Packard plant on land values. We also included distance to other toxic sites in some specifications, but these variables were not significant determinants of sale price. The distances from major roadways were also not statistically significant determinants of sales price. Nevertheless, the Packard plant result suggests that removal of this toxic site would improve land values of nearby properties.
Nonparametric Estimates: LWR
The estimates generated from the LWR approach are not easily summarized in a table, given that this approach generates a regression for each of the 3,788 properties in our data set. Instead we calculate predicted land values for the entire city, including parcels with structures, and create a map of predicted land values (Figure 4). Researchers such as McMillen (1996) and Sunding and Swoboda (2010) have also used maps to illustrate findings from LWR analyses. The LWRs include distances from the Packard plant as well as an array of distance measures from each parcel to major roadways leading in and out of the city. The predicted land value map clearly illustrates Detroit’s very steep land value gradient. As before, land values are very high in the CBD, depicted by the striped area, which represent the highest 0.1% of land values on the map. Values plunge rapidly as distance from the CBD increases, but generally begin to rise near the city’s border. While there are several areas within the donut area around the CBD that have retained some value, generally the analysis shows that land values are extremely low in the donut area around the CBD. Predicted land values in the lightest gray areas are less than $1,000 for the average sized lot.
Predicted Land Values in Detroit (dollars)
Figure 4, which shows projected land values for all parcels, offers a nuanced presentation of predicted land values. In addition to the broad “donut” of low land values, Figure 4 reveals within-neighborhood variations in land values along the city border that are consistent with both theoretical and empirical research. For example, predicted land values for industrial properties generally fall into the lowest-value quintile, wherever these parcels are located; residential parcels in close proximity to industrial land also have lower values. Finally, the variations in land values illustrated in Figure 4 are similar to property value maps generated from LWR analyses by McMillen (1996) for Chicago and Sunding and Swoboda (2010) for Southern California; LWR can generate substantial changes in predicted land values across space.
V. CONCLUSIONS AND IMPLICATIONS
This article provides several insights, the first of which is the documentation of a U-shaped land value gradient. Land values are relatively high in Detroit’s central city and drop precipitously to about $5,000 just 2 miles from the CBD. Examining our results at a more detailed level, property values fall to less than $1,000 for a typical-sized lot in certain areas surrounding the CBD (lightest gray locations in Figure 4). Generally, land values begin to rise near the city’s border. Our results are more consistent with the notion that higher land values on the periphery can be attributed to the distance from disamenities, rather than access to suburban amenities, such as shopping and employment. While these findings are not surprising to those familiar with the Detroit real estate market, they may be used to inform city strategies for investing in and maintaining neighborhoods. In particular, our estimates show that property along the periphery has retained more value than in other parts of the city; if the goal is to preserve and enhance property values and thus preserve property tax base, city officials may want to consider explicit strategies for maintaining the stability of the peripheral neighborhoods and not focus attention solely on the substantial investments currently being infused into the city center.
The work of Rosenthal (2008) may also inform longer-run strategies. According to Rosenthal’s evaluation, neighborhoods cycle from high income to low income over time, and then back again. Further, this cycle is heavily influenced by the aging of the housing stock. Higher-income households gravitate to neighborhoods where the housing stock is newer and of higher quality, whereas older neighborhoods with aging housing stock attract lower-income households. The rise and decline of neighborhoods is to a large extent determined by the age and quality of the housing stock. In Detroit, much of the oldest and most dilapidated housing stock has been torn down; these areas are now available for the development of new housing.
In contrast, the housing stock in the first ring suburbs in the Detroit region is aging. This suggests that we may see a reversal of migration patterns in the coming years. That is, higher-income households may seek new high-quality housing either in the outer suburbs or potentially back in the city where large tracts of land are available for redevelopment. Similarly, the aging housing stock in the firstring suburbs, which is now quite reasonably priced, may attract lower-income households. There may be at least some potential for suburbanites to cycle back into the city neighborhoods. However, a necessary condition is that Detroit officials will have to provide a tax and public service environment that is conducive to redevelopment. Offering a competitive tax rate and quality core public services will be important if the city is to be positioned for the long-run dynamics described by Rosenthal (2008). Improvement to the tax-service package in Detroit is also essential for ameliorating the ongoing tax delinquency problem (Alm et al. 2014), thus reducing the flood of properties moving into public hands. While there is evidence to suggest resurgence in the central city,22 prospects for the reemergence of Detroit for higher-income redevelopment seem limited.
The Detroit Future City (2010) report offers a strategic framework for developing a vision for Detroit’s future, and one component of this framework includes a discussion of vacant land management. As highlighted by Detroit Future City (2010), public lands are held by many public entities, including city, county, and state agencies, as well as autonomous or quasi-governmental entities such as the Detroit Public Schools, the Detroit Housing Commission, and the Detroit Economic Growth Corporation. Few other cities have such fragmented holding of their public land inventory. There is no consistency of policy, procedure, or mission among these agencies, while many are hamstrung by burdensome legal requirements and complex procedures. The Department of Planning and Development controls the largest number of properties, yet its ability to do strategic disposition is constrained by procedural obstacles, including the need to obtain City Council approval for all transactions, however small and insignificant from a citywide perspective.
Regardless of whether the potential long-run decline/renewal dynamics documented by Rosenthal (2008) will be manifested in Detroit in the coming years, an essential element in preparing for any future development is for the city and other public entities to develop a unified mission and framework for managing a vast amount of potentially very valuable land.
In addition to the policy relevance of our analysis, we offer contributions to the literature on urban land values and redevelopment. First is the evaluation of land values in the context of a declining city in the wake of the real estate crisis. Second, we use a unique data set that includes both actual vacant land sales data and data on unsold vacant land in the city of Detroit to estimate a land value gradient. We also provide evidence for a U-shaped land value gradient in Detroit and that the values of small lots are suppressed by minimum lot size requirements.
Acknowledgments
We thank the Lincoln Institute of Land Policy for financial support. We also thank Fred Morgan of the City of Detroit Assessment Division for providing detailed parcel-level data and former Councilman Kenneth Cockrel for inviting us to work on this issue. We also thank the editors and anonymous referees for valuable comments and suggestions.
Appendix A: SAMPLE SELECTION ESTIMATES
Just as with the OLS and interval regression estimates, we present in column 1 of Table A1 the estimates with control variables and the distance to the CBD, in column 2 control variables and distance to the border, and in column 3 both the distance to the city center and the border. The selection equation coefficients clearly demonstrate potential for selection bias; parcels with higher effective tax rates, that are of larger size, are buildable under current zoning regulations, and are closer to the border are more likely to have been sold during the 2006–2010 period.23 We also see that parcels that are zoned Residential and Commercial are less likely to have been sold than properties in nontaxable status. Further, the estimated effect of the independent variables is large enough to be meaningful. A 50% increase in square feet of area increases the probability that the parcel will be sold by 1%. The probability that a lot will be sold increases by 0.5% if it meets the threshold size for being Buildable under current zoning regulations, and according to the estimates in column 3, a 10% increase in the distance from the city border reduces the probability that the parcel will sell by 1%.
While the selection estimates are of interest and value, our primary focus is on the determinants of sales price, which are also present in Table A1. After correcting for sample selection, we see that these estimates are very similar to the OLS regressions. Overall, the Heckman estimation results suggest that, while there is clearly nonrandom selection of parcels into the “sold” status, nonrandom selection appears not to be generating significant bias in the coefficient estimates.
Heckman Vacant Land Sale Selection and Price Estimates
APPENDIX B: LAND PRICE ESTIMATES WITH ADDITIONAL AMENITY DISTANCE VARIABLES
Ordinary Least Squares (OLS) and Interval Land Sale Price Regressions with Additional Amenity Distance Variables
Footnotes
The authors are, respectively, assistant professor, Department of Economics, Oakland University, Rochester, Michigan; professor emeritus, Urban Planning Program, Wayne State University, Plymouth, Michigan; and professor, Department of Agricultural, Food, and Resource Economics and Department of Economics, Michigan State University, East Lansing.
↵1 To address the concern about possible endogeneity of parcel size, we also estimate the model without parcel size; results are similar to those presented.
↵2 The correlation between the two measures is 0.605.
↵3 The omitted category is nontaxable parcels, which are properties sold by the city, other public entity, charitable groups, or other not-for-profit entities.
↵4 Under current zoning law, a parcel must be at least 5,000 square feet in order to build on the lot. However buildable lots could be smaller in prior years; these now-vacant lots cannot be built upon under the current zoning regulations without special approval from city officials.
↵5 Detroit has many toxic sites, but not all are well known and thus they may not affect sales prices. See Thomason (2013) for a discussion of Detroit’s toxic legacy. In addition to the Packard plant, we considered distances to the following toxic/dilapidated sites: Michigan Central train depot, Carter Industrials, Federal Mogul, ChemServ Corp., Detroit Coke, Revere Copper and Brass, Marathon Oil refinery, Koch Carbon, and Bellevue (Uniroyal). However, these sites were generally not significant determinants of land values in analyses using parametric approaches. We also included an array of distance measures from a parcel to major roadways leading in and out of the city. Again, these were generally not significant predictors of land values and are therefore not included in parametric estimates presented in the paper.
↵6 The contact person for the assessor data at the city of Detroit is Joel Howrani Heeres. Public access to parcel data is available at https://data.detroitmi.gov/Property-Parcels/Parcel-Map/fxkw-udwf.
↵7 Because of abandonment and foreclosures, the Detroit Land Bank Authority currently owns about 20% of the parcels in Detroit. The Land Bank has focused on the sale of developed properties; but their extensive inventory of vacant parcels is not being actively marketed. Nevertheless, there are nontaxable vacant land sales in our sample.
↵8 The omitted base year indicator is for 2006. The included time indicator variables are for 2007, 2008, 2009, and 2010.
↵9 About 30% of all privately owned vacant lots are tax delinquent.
↵10 It is often the case that the coefficient estimates are smaller with OLS because of truncation at the lower bound, which reduces the correlations between the dependent and independent variables. This is a common difference between coefficient estimates generated from OLS and methods that address truncation in the data.
↵11 We also estimated a Tobit model to address zero and very low valued properties; the results are similar to those presented.
↵12 We also estimated a series of interval regressions in which the left- and right-side observations are treated as censored, but the cut-off points are incrementally moved from the interquartile to the interquintile and interdecile ranges. The coefficients generated from these regressions are similar to those presented, and the magnitudes of the coefficients get closer to the OLS estimates as the range is widened.
↵13 We thank Daniel McMillen for bringing this issue to our attention.
↵14 See Achen (1986) and Sigelman and Zeng (1999) for theoretical and intuitive discussions on the Heckman procedure.
↵15 Distance to the Packard plant is measured in feet to better capture scale effects in the logarithmic specification. We expect any negative effects of the plant to dissipate quickly. Also, note that year indicator variables are omitted from the first-stage regression due to multicollinearity, but are included in the second-stage regression to control for citywide change in price over time. It is somewhat unusual to exclude some variables from the first-stage regression, and this could potentially affect the estimates (Wooldridge 2003). However, omitting the time indicator variables from both the first- and second-stage regressions yields results that are very similar to the Heckman estimates reported in Appendix A.
↵16 Against this claim, Bradley (2017) found evidence of small increases in residential sale prices in Ann Arbor, Michigan, resulting from Michigan’s taxable value cap. Hodge and Komarek (2016) support this claim, as they informally test this effect in Detroit and find that property owners in Detroit do not capitalize the previous owner’s accumulated benefit.
↵17 See also McMillen (2010), McMillen and Redfearn (2010), Sunding and Swoboda (2010), and Swoboda, Nega, and Timm (2015) for property value applications in urban economics.
↵18 In equation [6], for ease of exposition, both property characteristics and distance variables are included in X.We used the tri-cube kernel function, which is (70/81) (1 − |z|3)3*I |Z| < 1).
↵19 We estimated the locally weighted regression using the R “McSpatial” package, as described by McMillen (2015).
↵20 When distance to the border is replaced by the square of the distance to the city center, the results are similar with the same nonlinearities identified; however, the explanatory power is lower than that of the original specification. These estimates are provided in Appendix B
↵21 These findings are also generally consistent with those of Brueckner, Thisse, and Zenou (1999), who suggest that proximity to higher-income households may be seen as an amenity that contributes to higher land values.
↵22 See for example recent articles on redevelopment led by Daniel Gilbert (Detroit Free Press 2014), on rising housing costs in downtown Detroit (Christie 2014), and the potential for foreign investors, particularly Chinese investors, to acquire property in Detroit (National Public Radio 2014).
↵23 The coefficients presented for the first-stage selection equation are the marginal effects generated for mean values of the independent variables.
