# RECORD a2a7539a9c4a1cf05650ab56eedb83ae824bb636
# TITLE: Nonlinear Effects of School Quality on House Prices
# YEAR: 2003.0  VENUE: nan  DOI: 10.20955/r.92.185-204
# AUTHORS: Abbigail J. Chiodo; Rubén Hernández-Murillo; Michael T. Owyang
# PAGES: 29  CANDIDATE TABLE PAGES (1-based): [25, 27, 28]
# ABSTRACT: We reexamine the relationship between quality of public schools and house prices and find it to be nonlinear. Unlike most studies in the literature, we find that the price premium parents must pay to buy a house in an area associated with a better school increases as school quality increases. This is true even after controlling for neighborhood characteristics, such as the racial composition of neighborhoods, which is also capitalized into house prices. In contrast to previous studies that use the boundary discontinuity approach, we find that the price premium from school quality remains substantially large, particularly for neighborhoods associated with high-quality schools.


===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) =====

Nonlinear Effects of School Quality on House Prices
ECONOMIC RESEARCH
FEDERAL RESERVE BANK OF ST. LOUIS
WORKING PAPER SERIES
Authors
Abbigail J. Chiodo, Rubén Hernández-Murillo, and Michael T. Owyang
Working Paper Number
2003-039E
Revision Date
September 2009
Citable Link
https://doi.org/10.20955/wp.2003.039
Suggested Citation
Chiodo, A.J., Hernandez-Murillo, R., Owyang, M.T., 2009; Nonlinear Effects of School
Quality on House Prices, Federal Reserve Bank of St. Louis Working Paper 2003-
039. URL https://doi.org/10.20955/wp.2003.039
Published In
Federal Reserve Bank of St. Louis Review
Publisher Link
https://doi.org/10.20955/r.92.185-204
Federal Reserve Bank of St. Louis, Research Division, P.O. Box 442, St. Louis, MO 63166
The views expressed in this paper are those of the author(s) and do not necessarily reflect the views of the Federal Reserve
System, the Board of Governors, or the regional Federal Reserve Banks. Federal Reserve Bank of St. Louis Working Papers
are preliminary materials circulated to stimulate discussion and critical comment.


===== PAGE 25 (score 92, numeric-paren 61, table-words 6, var-words 9) =====

Table 3: Education Regressions: Full Sample.
(1)
(2)
(3)
log adj price
log adj price
log adj price
test math
0.21734***
0.22192***
0.31693***
(7.79)
(7.13)
(7.70)
test math sq
0.03002
0.01555
(1.48)
(0.76)
test math cb
-0.03606**
(-2.60)
house bedrooms
0.01062
0.01502
0.01575
(1.09)
(1.52)
(1.62)
house bathrooms
0.14086***
0.14413***
0.13458***
(4.75)
(4.93)
(4.44)
house baths sq
-0.00612
-0.00740
-0.00501
(-1.14)
(-1.37)
(-0.89)
house age
0.00065
0.00057
0.00123
(0.37)
(0.31)
(0.67)
house age sq
0.00002
0.00002
0.00002
(1.35)
(1.31)
(1.03)
house lotarea
0.00123***
0.00120***
0.00119***
(4.21)
(4.27)
(4.17)
house livingarea
0.45365***
0.44475***
0.43526***
(20.02)
(17.35)
(19.05)
house stories
0.39693***
0.38775***
0.37835***
(11.29)
(10.58)
(10.87)
house rooms
0.07484***
0.07421***
0.07245***
(10.10)
(10.21)
(10.11)
cenbl fem
-0.00061
-0.00050
-0.00053
(-0.88)
(-0.73)
(-0.79)
cenbl nonwhite
-0.00221***
-0.00277***
-0.00257***
(-3.62)
(-5.06)
(-4.57)
cenbl p5 14
-0.00017
-0.00033
-0.00021
(-0.19)
(-0.38)
(-0.24)
tax
-0.04636
-0.04457
-0.03562
(-1.65)
(-1.51)
(-1.28)
cons
10.00143***
9.99065***
9.96337***
(59.89)
(57.55)
(58.13)
N
38,656
38,656
38,656
R2
0.697
0.699
0.702
Adjusted R2
0.697
0.698
0.702
t-Statistics in parentheses.
* Significant at 10%; ** significant at 5%; *** significant at 1%.
24


===== PAGE 26 (score 7, numeric-paren 5, table-words 1, var-words 0) =====

Table 4: Specification Tests: Full Sample
Premium Model f(Y ) = ψ1Y + ψ2Y 2 + ψ3Y 3
Linear
Quadratic
Cubic
With Neighborhood Controls
Null hypothesis
ψ1 = 0
ψ1 = ψ2 = 0
ψ1 = ψ2 = ψ3 = 0
Wald F-Statistic
60.757***
27.686***
30.665***
Null hypothesis
ψ2 = 0
ψ2 = ψ3 = 0
Wald F-Statistic
2.192
7.446***
Null hypothesis
ψ3 = 0
Wald F-Statistic
6.754**
* Significant at 10%; ** significant at 5%; *** significant at 1%
25


===== PAGE 27 (score 184, numeric-paren 139, table-words 9, var-words 9) =====

Table 5: Education Regressions: Boundary Sample
(1)
(2)
(3)
(4)
(5)
(6)
log adj price
log adj price
log adj price
log adj price
log adj price
log adj price
test math
0.06437**
0.06274***
0.04659
0.03227*
0.03579*
0.03172
(2.58)
(2.90)
(1.64)
(1.78)
(1.93)
(1.20)
test math sq
0.02656**
0.02909**
0.02209**
0.02284**
(2.47)
(2.47)
(2.48)
(2.40)
test math cb
0.00514
0.00137
(0.73)
(0.21)
house bedrooms
0.03726***
0.03730***
0.03749***
0.03816***
0.03805***
0.03809***
(3.88)
(3.89)
(3.90)
(4.02)
(4.01)
(4.00)
house bathrooms
0.10834***
0.10785***
0.10792***
0.10349***
0.10318***
0.10320***
(5.78)
(5.80)
(5.82)
(5.81)
(5.82)
(5.83)
house baths sq
-0.00529*
-0.00533*
-0.00535*
-0.00488
-0.00491
-0.00491
(-1.68)
(-1.70)
(-1.71)
(-1.58)
(-1.60)
(-1.60)
house age
-0.00408***
-0.00411***
-0.00412***
-0.00453***
-0.00454***
-0.00454***
(-2.73)
(-2.75)
(-2.76)
(-3.11)
(-3.13)
(-3.14)
house age sq
0.00004***
0.00004***
0.00004***
0.00004***
0.00004***
0.00004***
(2.89)
(2.91)
(2.92)
(3.15)
(3.16)
(3.17)
house lotarea
0.00089**
0.00089**
0.00089**
0.00088**
0.00088**
0.00088**
(2.41)
(2.41)
(2.41)
(2.39)
(2.40)
(2.39)
house livingarea
0.35315***
0.35228***
0.35236***
0.34332***
0.34297***
0.34301***
(15.43)
(15.29)
(15.29)
(15.52)
(15.49)
(15.49)
house stories
0.27574***
0.27559***
0.27558***
0.26621***
0.26625***
0.26626***
(9.30)
(9.30)
(9.31)
(9.55)
(9.57)
(9.57)
house rooms
0.05974***
0.05952***
0.05945***
0.05902***
0.05893***
0.05891***
(7.38)
(7.33)
(7.31)
(7.43)
(7.40)
(7.39)
cenbl fem
-0.00044
-0.00039
-0.00039
(-0.66)
(-0.59)
(-0.59)
cenbl nonwhite
-0.00219***
-0.00223***
-0.00222***
(-3.50)
(-3.56)
(-3.55)
cenbl p5 14
0.00154**
0.00153**
0.00154**
(2.25)
(2.24)
(2.25)
tax
-0.06787***
-0.05526***
-0.05465***
(-3.21)
(-2.88)
(-2.73)
cons
11.13260***
11.12998***
11.13935***
8.86314***
8.72871***
8.72454***
(32.85)
(32.96)
(32.97)
(59.31)
(62.61)
(60.54)
N
10190
10190
10190
10182
10182
10182
R2
0.769
0.770
0.770
0.772
0.772
0.772
Adjusted R2
0.763
0.763
0.763
0.766
0.766
0.766
Boundary fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
t-Statistics in parentheses.
* Significant at 10%; ** significant at 5%; *** significant at 1%.
26


===== PAGE 28 (score 14, numeric-paren 11, table-words 1, var-words 0) =====

Table 6: Specification Tests: Boundary Sample
Premium Model f(Y ) = ψ1Y + ψ2Y 2 + ψ3Y 3
Linear
Quadratic
Cubic
Without Neighborhood Controls
Null hypothesis
ψ1 = 0
ψ1 = ψ2 = 0
ψ1 = ψ2 = ψ3 = 0
Wald F-Statistic
6.632**
4.658**
3.130**
Null hypothesis
ψ2 = 0
ψ2 = ψ3 = 0
Wald F-Statistic
6.115**
3.114**
Null hypothesis
ψ3 = 0
Wald F-Statistic
0.527
With Neighborhood Controls
Null hypothesis
ψ1 = 0
ψ1 = ψ2 = 0
ψ1 = ψ2 = ψ3 = 0
Wald F-Statistic
3.178*
3.581**
2.381*
Null hypothesis
ψ2 = 0
ψ2 = ψ3 = 0
Wald F-Statistic
6.166**
3.102**
Null hypothesis
ψ3 = 0
Wald F-Statistic
0.043
* Significant at 10%; ** significant at 5%; *** significant at 1%
27


===== PAGE 29 (score 9, numeric-paren 0, table-words 2, var-words 1) =====

Table 7: Implied House Premia from Math Test Scores
Change in Math score (SD)
0.5
Equivalent percentage of mean
4.6%
Regression model
Full sample with
Boundary sample with
Boundary sample with
neighborhood controls
no neighborhood controls
neighborhood controls
Linear coefficient
0.21734
0.22192
0.31693
0.06437
0.06274
0.04659
0.03227
0.03579
0.03172
Quadratic coefficient
–
0.03002
0.01555
–
0.02656
0.02909
–
0.02209
0.02284
Cubic coefficient
–
–
-0.03606
–
–
0.00514
–
–
0.00137
Case 1 (Mean score - 1 SD)
Percent increase in house price
10.87
8.84
11.53
3.22
1.15
0.60
1.61
0.13
-0.01
Dollar value at mean (full sample)
16,092
13,097
17,066
4,766
1,696
885
2,389
197
-11
Dollar value at mean (boundary sample)
15,435
12,562
16,369
4,571
1,626
849
2,292
189
-10
Case 2 (Mean score)
Percent increase in house price
10.87
11.85
15.78
3.22
3.80
3.12
1.61
2.34
2.17
Dollar value at mean (full sample)
16,092
17,542
23,374
4,766
5,629
4,622
2,389
3,468
3,219
Dollar value at mean (boundary sample)
15,435
16,826
22,419
4,571
5,399
4,433
2,292
3,326
3,088
Case 2 (Mean score + 1 SD)
Percent increase in house price
10.87
14.85
9.23
3.22
6.46
7.19
1.61
4.55
4.77
Dollar value at mean (full sample)
16,092
21,988
13,662
4,766
9,562
10,642
2,389
6,739
7,058
Dollar value at mean (boundary sample)
15,435
21,090
13,104
4,571
9,171
10,207
2,292
6,464
6,770
The premium is computed from the logarithm specification ∆p/p = ∆ln(p) = ∆f(µ), so the percent change
in house prices is given by ∆f(µ) = f(µ1) −f(µ0) and the premium at the mean price is ∆f(µ) × ¯p.
28