The Land Value Gradient in a (Nearly) Collapsed Urban Real Estate Market

Timothy R. Hodge; Gary Sands; Mark Skidmore

doi:10.3368/le.93.4.549

Article Figures & Data

Figures

Tables

Download figure
Open in new tab
Download powerpoint
FIGURE 1
Spatial Distribution of Vacant Land Sales in Detroit
Source: Map © OpenStreetMap contributors; data available under the open Database License, see openstreetmap.org.
Download figure
Open in new tab
Download powerpoint
FIGURE 2
Frequency Distribution of Land Sales Prices
Download figure
Open in new tab
Download powerpoint
FIGURE 3
Detroit Land Value Gradient
Download figure
Open in new tab
Download powerpoint
FIGURE 4
Predicted Land Values in Detroit (dollars)

Tables

Figures

View popup

TABLE 1

Vacant Land Sale Summary Statistics

Variable	Full Sample		Sales Sample
Variable	Mean (Std. Dev.)	Median	Mean (Std. Dev.)	Median
Sale (yes = 1, no = 0)	0.046 (0.210)	—	—	—
Sales price (dollars)	1,744 (63,947)	0.00	37,723 (295,077)	811
Residential (yes = 1, no = 0)	0.427 (0.495)	—	0.688 (0.466)	—
Commercial (yes = 1, no = 0)	0.071 (0.257)	—	0.140 (0.347)	—
Size of lot (square feet)	256,707 (22,100,000)	3,485	54,305 (3,046,622)	3,790
Buildable (yes = 1, no = 0)	0.156 (0.363)	—	0.219 (0.413)	—
Distance to Packard plant (feet)	24,413 (15,210)	21,377	24,413 (15,211)	21,377
Distance to city center (miles)	2.200 (1.323)	2.103	1.842 (1.265)	1.639
Distance to border (miles)	5.561 (2.576)	5.254	6.209 (2.707)	5.944
Sold in 2007 (yes = 1, no = 0)	0.011 (0.102)	—	—	—
Sold in 2008 (yes = 1, no = 0)	0.011 (0.103)	—	—	—
Sold in 2009 (yes = 1, no = 0)	0.007 (0.082)	—	—	—
Sold in 2010 (yes = 1, no = 0)	0.001 (0.029)	—	—	—
Number of observations	81,326		3,788

View popup

TABLE 2

Variable Names and Definitions

Variable	Definition
Sale (yes = 1, no = 0)	Indicator variable equal to 1 if the property sold during the 2006–2010 period, and 0 otherwise
Sales price	Sales price in dollars of land being sold
Residential (yes = 1, no = 0)	Indicator variable equal to 1 if the property sold is zoned residential, and 0 otherwise
Commercial (yes = 1, no = 0)	Indicator variable equal to 1 if the property sold is zoned commercial, and 0 otherwise
Size of lot (square feet)	Size of lot in square feet
Buildable (yes = 1, no = 0)	Indicator variable equal to 1 if the property is large enough (over 5,000 sq ft) to build on, given current zoning policies
Distance from city center (miles)	Linear distance from a given parcel to the city center
Distance from border (miles)	Linear distance from a given parcel to the nearest adjacent city (excludes the Detroit River border)
Distance from Packard plant (feet)	Linear distance from a given parcel to the abandoned and toxic Packard plant
Sold in 2007 (yes = 1, no = 0)	Indicator variable equal to 1 if the parcel was sold in 2007, and 0 otherwise
Sold in 2008 (yes = 1, no = 0)	Indicator variable equal to 1 if the parcel was sold in 2008, and 0 otherwise
Sold in 2009 (yes = 1, no = 0)	Indicator variable equal to 1 if the parcel was sold in 2009, and 0 otherwise
Sold in 2010 (yes = 1, no = 0)	Indicator variable equal to 1 if the parcel was sold in 2010, and 0 otherwise
Effective tax rate	Tax payment divided by state equalized value of the property, which is half of estimated market value

View popup

TABLE 3

OLS and Interval Regression Land Sale Estimates

	(1)	(2)	(3)	(4)	(5)	(6)
Estimation method	OLS	OLS	OLS	Interval regression	Interval regression	Interval regression
Dependent variable	ln(Sales price)	ln(Sales price)	ln(Sales price)	In (Sales price)	ln(Sales price)	ln(Sales price)
Independent variable Residential (yes = 1, no = 0)	0.749^*** (4.70)	0.749^*** (4.72)	0.737^*** (4.65)	1.668^*** (5.44)	1.675^* (5.48)	1.649^*** (5.40)
Commercial (yes = 1, no = 0)	1.578^***(6.59)	1.587^***(6.63)	1.552^*** (6.48)	3.289^*** (7.18)	3.307^*** (7.21)	3.235^*** (7.07)
ln(Size of lot) (square feet)	0.166^* (1.85)	0.169^* (1.88)	0.164^* (1.82)	0.343^** (1.99)	0.350^** (2.02)	0.342^** (1.96)
Buildable (yes = 1, no = 0)	0.302^* (1.79)	0.300^* (1.78)	0.305^* (1.80)	0.634^* (1.93)	0.625^* (1.90)	0.637^* (1.94)
ln(Distance to Packard plant) (feet)	1.434^*** (4.17)	0.731^** (2.14)	1.002^*** (2.88)	3.227^*** (4.38)	1.599^** (2.15)	2.214^*** (2.88)
ln(Distance to city center) (miles)	− 1.330^* (− 1.79)		− 2.446^*** (−2.84)	− 2.813^* (−1.85)		− 5.358^*** (−3.17)
ln(Distance to border) (miles)		− 0.833^***(−2.63)	− 1.243^*** (−3.57)		− 1.919^***(−3.03)	− 2.82^*** (−4.02)
Sold in 2007 (yes = 1, no = 0)	0.181 (1.16)	0.167 (1.07)	0.171 (1.10)	0.597^* (1.95)	0.571^* (1.87)	0.583^* (1.91)
Sold in 2008 (yes = l, no = 0)	− 0.388^** (−2.53)	− 0.392^** (−2.56)	− 0.392^** (−2.56)	− 0.609^** (— 2.05)	− 0.613^** (−2.06)	− 0.611^** (— 2.06)
Sold in 2009 (yes = l, no = 0)	− 0.703^*** (−3.91)	− 0.688^*** (−3.83)	− 0.710^*** (−3.96)	− 1.348^*** (−3.82)	− 1.312^*** (−3.73)	− 1.365^*** (−3.87)
Sold in 2010 (yes = 1, no = 0)	−0.731 (−0.568)	−0.757 (−1.33)	−0.759 (−1.34)	−1.042 (−0.86)	−1.096 (−0.91)	−1.107 (−0.92)
Wald chi²				961.02^***	907.23^***	1,011.23^***
Adjusted R²	0.072	0.073	0.076
Number of observations	3,788	3,788	3,788	3,788	3,788	3,788
Number of left censored observations				963	963	963
Number of right censored observations				944	944	944

Note: z-Statistics in parentheses. All estimates include a set of 53 (of 54) neighborhood indicator variables. OLS, ordinary least squares.
↵* Statistical significance at the 90% confidence interval;
↵** at the 95% confidence interval;
↵*** at the 99% confidence interval.

View popup

TABLE A1

Heckman Vacant Land Sale Selection and Price Estimates

	(1)	(2)	(3)
Estimation method	Heckman	Heckman	Heckman
Dependent variable	Sale (yes/no) ln(Sales price)	Sale (yes/no) ln(Sales price)	Sale (yes/no) ln(Sales price)
Independent variable: first-stage sale (yes/no) estimates
Effective tax rate	0.001^*** (20.46)	0.001^*** (20.46)	0.001^*** (20.46)
Residential (yes = 1, no = 0)	− 0.037^*** (− 7.92)	− 0.037^*** (−7.95)	− 0.037^*** (− 7.95)
Commercial (yes = 1, no = 0)	− 0.019^*** (− 4.69)	− 0.020^*** (−4.76)	− 0.020^*** (− 4.76)
ln(Size of lot) (square feet)	0.002^*** (3.61)	0.002^*** (3.66)	0.002^*** (3.66)
Buildable (yes = 1, no = 0)	0.010^*** (5.86)	0.009^*** (5.80)	0.009^*** (5.79)
ln(Distance to Packard plant) (feet)	0.006^* (1.95)	− 0.012 (0.77)	0.002 (0.79)
ln(Distance to city center) (miles)	0.009 (1.43)		− 0.001 (− 0.18)
ln(Distance to border) (miles)		− 0.012^*** (−3.98)	− 0.012^*** (− 3.71)
Independent variable: second-stage price estimates
Residential classification (yes = 1, no = 0)	0.743^*** (4.76)	0.744^*** (4.79)	0.732^*** (4.71)
Commercial classification (yes = 1, no = 0)	1.542^*** (6.61)	1.557^*** (6.68)	1.519^*** (6.52)
ln(Size of lot) (square feet)	0.160^* (1.81)	0.164^* (1.85)	0.159^* (1.78)
Buildable (yes = 1, no = 0)	0.288^* (1.71)	0.288^* (1.71)	0.291^* (1.73)
ln(Distance from Packard plant) (feet)	1.441^*** (4.24)	0.743^** (2.19)	1.017^*** (2.94)
ln(Distance from city center) (miles)	− 1.366^* (− 1.77)		− 2.458^*** (− 2.88)
ln(Distance from border) (miles)		− 0.807^** (− 2.55)	− 1.218^*** (− 3.51)
Sold in 2007 (yes = 1, no = 0)	0.176 (1.15)	0.163 (1.06)	0.167 (1.09)
Sold in 2008 (yes = 1, no = 0)	− 0.394^*** (− 2.59)	− 0.397^*** (−2.62)	− 0.397^*** (− 2.62)
Sold in 2009 (yes = 1, no = 0)	− 0.713^*** (− 3.99)	− 0.696^*** (−3.90)	− 0.720^*** (− 4.03)
Sold in 2010 (yes = 1, no = 0)	− 0.724 (−1.28)	− 0.751 (− 1.33)	− 0.752 (− 1.33)
Lambda (inverse Mills ratio)	− 0.342	− 0.128	− 0.139
Log pseudo-likelihood	− 23,584	− 23,576	− 23,571
Number of observations	81,376	81,376	81,376
Number of uncensored observations	3,788	3,788	3,788

Note: z-Statistics in parentheses. All estimates include a set of 53 (of 54) neighborhood indicator variables.
↵* Statistical significance at the 90% confidence interval;
↵** at the 95% confidence interval;
↵*** at the 99% confidence interval.

View popup

TABLE B1

Ordinary Least Squares (OLS) and Interval Land Sale Price Regressions with Additional Amenity Distance Variables

	(1)	(2)	(3)	(4)	(5)	(6)
Estimation method	OLS	OLS	OLS	Interval regression	Interval regression	Interval regression
Dependent variable	ln(Sales price)	ln(Sales price)	ln(Sales price)	ln(Sales price)	ln(Sales price)	ln(Sales price)
Independent variable Residential (yes = 1, no = 0)	0.738^*** (4.63)	0.735^*** (4.63)	0.734^*** (4.64)	1.617^*** (5.18)	1.664^*** (5.39)	1.646^*** (5.40)
Commercial (yes = 1, no = 0)	1.564^*** (6.53)	1.575^*** (6.56)	1.555^*** (6.47)	3.269^*** (7.73)	3.282^*** (7.15)	3.238^*** (7.05)
ln(Size of lot) (square feet)	0.168^* (1.88)	0.157^* (1.81)	0.158^* (1.81)	0.325^** (2.32)	0.326^* (1.94)	0.330^* (1.95)
Buildable (yes = 1, no = 0)	0.290 (1.71)	0.303^* (1.79)	0.306^* (1.81)	0.616^** (1.97)	0.646^** (1.97)	0.650^** (1.99)
ln(Distance to Packard plant) (feet)	1.444^*** (4.03)	1.235^*** (3.29)	0.973^** (2.55)	2.641^*** (3.18)	2.864^*** (3.59)	2.234^*** (2.69)
ln(Distance to city center) (miles)		−1.319 (− 1.27)	− 2.23^** (−1.96)		−2.818 (− 1.37)	− 4.971^** (−2.20)
ln(Distance to border) (miles)			− 0.923^** (−2.14)			− 2.142^** (−2.46)
Distance to the city center	− 0.724^** (−2.31)			− 2.315^*** (−2.84)
Distance to the city center²	0.041^* (1.90)			0.155^*** (2.74)
Distance to Cass Tech High School		1.433 (1.39)	1.191 (1.14)	1.665 (0.92)	2.510 (1.23)	1.964 (0.96)
Distance to Communication and Media Arts High School		0.739 (1.50)	0.212 (0.39)	0.820 (0.85)	1.585 (1.67)	0.383 (0.37)
Distance to Marvin Win High School		−0.636 (− 1.16)	−0.788 (− 1.49)	− 1.442 (−1.46)	−0.982 (−0.88)	−1.355 (− 1.25)
Distance to University Prep High School		0.349 (0.69)	0.275 (0.54)	0.742 (0.89)	0.632 (0.65)	0.470 (0.48)
Distance to Eastland Mall		0.775 (0.67)	0.684 (0.60)	0.909 (0.45)	1.634 (0.69)	1.426 (0.61)
Distance to Oakland Mall		−0.425 (−0.17)	0.197 (0.08)	−4.060 (− 0.87)	−1.985 (−0.41)	−0.529 (−0.11)
Distance to Northland Mall		1.150 (0.46)	1.087 (0.44)	−1.467 (−0.33)	1.359 (0.28)	1.240 (0.25)
Distance to Southfield		−2.722 (−0.89)	−2.693 (−0.88)	1.654 (0.28)	−3.727 (−0.61)	−3.722 (−0.61)
Distance to Dearborn		−1.893^** (−2.09)	− 1.389 (− 1.48)	− 6.704^*** (−3.50)	−4.554^** (−2.41)	−3.369^* (−1.72)
Sold in 2007 (yes = l, no = 0)	0.179 (1.15)	0.166 (1.07)	0.158 (1.02)	0.573^* (1.94)	0.571^* (1.88)	0.560^* (1.84)
Sold in 2008 (yes = l, no = 0)	− 0.392^*** (−2.56)	− 0.396^* (−2.59)	− 0.397***(−2.60)	− 0.633^** (−2.14)	− 0.625^** (−2.11)	− 0.624^** (−2.11)
Sold in 2009 (yes = l, no = 0)	− 0.710^***(−3.96)	− 0.687^*** (−3.81)	− 0.697^*** (−3.87)	− 1.370^*** (−3.97)	− 1.331^*** (−3.76)	− 1.354^*** (−3.83)
Sold in 2010 (yes = 1, no = 0)	−0.735 (−1.29)	−0.721 (−1.27)	−0.751 (—1.33)	− 1.039 (− 1.18)	−1.000 (−0.83)	−0.652 (−0.18)
Wald chi²					977.31^***	1,019.80^***
LR chi²				350.74^***
Adjusted R²	0.072	0.077	0.078
Number of observations	3,88	3,788	3,788	3,88	3,788	3,788
Number of left censored observations				963	963	963
Number of right censored observations				944	944	944