Transcript Mass Appraisal, Hedonic Price Modelling and Urban

Do Peer Effects Shape Residential Values?
Reconciling the Sales Comparison Approach
with Hedonic Price Modelling
François Des Rosiers, Laval University, Canada
Jean Dubé, INRS-UCS, Canada
Marius Thériault, Laval University, Canada
Paper presented at the 17th ERES Annual Conference,
Milan, Italy, June23 -26, 2010
Research partly funded by
Objective and Context of Research
2
Although the hedonic framework can be said to vary
substantially from the traditional sales comparison
approach both are derived from a similar paradigm with
respect to how market values, are determined.
This paper aims at reconciling the two approaches by
integrating peer effects in the hedonic equation, a
concept developed, and mainly used, by labour
economists.
The ensuing model accounts for three types of effects,
namely
endogenous
interactions
effects
(i.e.
comparable sales influences, or peer effects),
exogenous, or neighbourhood, effects and, finally,
spatial autocorrelation effects.
Literature Review and Conceptual Grounds
3
Peer effects, which can be defined as the influence that
members of a group exert on a given individual in the
group, have long been mentioned in the literature
(Leibenstein, 1950; Veblen, 1899).
Game theory: Asch (1956) and by Becker and Becker
(1998) emphasize the role of social interactions with
respect to the individual choice process.
Labour economics: the publication, in 1966, of the
Coleman report (Coleman et al., 1966) on student
performances sparked off this new paradigm.
Manski (1993) seminal contribution: three factors lead
individual behaviour within a group: (i) endogenous
interactions; (ii) exogenous interactions; and (iii) correlated
effects.
Literature Review and Conceptual Grounds
Endogenous interactions: any individual in the group is
affected by the average behaviour of the group.
Exogenous, or contextual, interactions: influence exerted
on individuals by the socio-economic profile of group
members.
Correlated, or latent, effects stem from non-observable
environmental attributes that apply to all group members
and which can be brought forward as an explanation for
the presence of SA in the model residuals.
Impact of peers on:


4
individual productivity at work (Ichino and Maggi, 2000) ;
school performances (Hallinan and Sørensen, 1983; Sacerdote,
2001; Zimmerman, 2003)
Literature Review and Conceptual Grounds
Social interaction models have been applied to the new
social economy (Durlauf and Young, 2001) and for
modelling urban housing markets (Meen and Meen, 2003).
Peer Effect Model:
where: Yig = dependent variable for individual i in group g;
Yg ,
= endogenous variable for the group and parameter;
Xki , β1 = property attributes and parameter;
Xg , β2 = exogenous (or contextual) attributes and parameter
5
Endogeneity problem handled: Yg expressed, for any given
submarket, as the mean sale price of houses for the
previous quarter, with property i sale price being excluded
from the computation.
The Database
Canadian database provided by the former Quebec Urban
Community (CUQ) Assessment Division on some 15,729
single-family detached houses sold between January 1990
and December 1996, with prices ranging from
$50,000 (Can.) to $250,000.
The database contains reliable information on sale prices
and major property attributes (building type and age, living
area and lot size, interior quality descriptors, presence of
specific features); access to local water and sewerage
systems as well as local tax rate are also accounted for.
6
Model also controls for time trend (year dummies), access
to local and regional services as well as socio-economic
and household structure dimensions.
Submarket Delimitation (discriminant analysis)
7
Main regression Findings – OLS Method
A semi-log functional form is used, with liveable area,
building age and lot size also being applied a logarithmic
transformation.
Four different specifications are used (Table 3):




8
The first specification (Base Model,) only includes property
structural and land attributes as well as time dummies;
In the second specification, exogenous, or neighbourhood,
influences are added to the Base Model;
Endogenous effects are substituted to the latter in the third
specification (Peer Effect Model);
Finally, the fourth specification yields the Global Model which
incorporates both exogenous and endogenous effects.
Main regression Findings – OLS Method
Ln_Liveable
Area
(m²)
Ln_Liveable
Area
(m²)
Ln_Lot
Size
(m²)
Ln_Lot Size (m²)
Ln_Building Age (years)
Ln_Building
Age (years)
Access to Water&Sewage
AccessLocal
to Water&Sewage
Tax Rate
Local Tax
Rate
Year 1991
Year 1993
Year 1991
Year1994
Year 1993
Year 1995
Year1994
Year 1996
Regional Accessibility Index
Year 1995
Local Accessibility Index
Year 1996
Nb. of Lone-parent Families
Regional
Accessibility
Index
Median
Household Income
Local Accessibility
Index
% of University Degree
Holders
Nb. of Lone-parent Families
Endogenous Effects
MedianIntercept
Household Income
% of University Degree
Holders
N
R-SquaredEffects
Endogenous
RMSE
Intercept
Moran’s I
N
N.B. : Signif.
R-Squared
RMSE
Moran’s I
9
Peer Effect
Peer Effect
Model
Base Model
Base + NBHD
Attr. Global Model
Base
Model
Base
+
NBHD
Attr.
Model
(All
Var.
(Prop. & Time Attr.)
(Exog. Effects)
(Endog. Effect)
(Prop. & Time Attr.)
(Exog. Effects)
(Endog. Effect)
Included)
Coefficient
Sig.
Coefficient
Sig.
Coefficient
Sig.
Coefficient Coefficient
Sig.
CoefficientSig.
Sig. Coefficient
Sig.
*** 0.4339 *** 0.4339
***
0.4780
***
0.54790.5479
***
0.4780
***
0.4293
***
0.02730.0273
***
0.0752
***
0.0444
***
0.0744
***
***
0.0752 ***
0.0444 ***
-0.0788 ***
-0.1033 ***
-0.0943 ***
-0.1053 ***
-0.0788 ***
-0.1033 ***
-0.0943 ***
0.1661 ***
0.1238 ***
0.1528 ***
0.1216 ***
*** -0.0756 *** 0.1238
***
0.1528
***
-0.21440.1661
***
-0.0490
***
-0.0421
***
-0.2144
*** 0.0232 *** -0.0756
***
-0.0490
***
0.0305
***
-0.0053
0.0101
*
0.04580.0305
***
0.0632
***
0.0036
0.0420
***
***
0.0232 ***
-0.0053
0.0258 ***
0.0604 ***
-0.0038
0.0400 ***
0.0458 *** 0.0430 *** 0.0632
***
0.0036
0.0068
-0.0003
0.0320 ***
***
-0.0038
0.00880.0258 *** 0.0438 *** 0.0604
-0.0176
***
0.0245
***
0.0535 *** 0.0430 ***
0.0455
***
0.0068
-0.0003
0.0335
***
0.0334
***
0.0088
0.0438 ***
-0.0176
***
-0.0060 ***
-0.0088 ***
0.0080 *** 0.0535 ***
0.0103 ***
0.0335 ***
0.0058 *** -0.0060 ***
0.0040 ***
0.5709 ***
0.2478 ***
***
9.0482 ***
8.9648 *** 0.0080
2.4665
***
6.1428 ***
15,729
0.6918
0,1797
9.0482
0.1486 ***
***
Level : * p<0,05; ** p<0,01; *** p<0,00115,729
0.6918
0,1797
0.1486 ***
N.B. : Signif. Level : * p<0,05; ** p<0,01; *** p<0,001
15,729
0.7666
0.1564
0.0919 ***
0.0058
15,729***
0.7414
0.1646
8.9648
***
0.0485 ***
15,729
0.7666
0.1564
0.0919 ***
Global Model
(All Var.
Included)
Coefficient Sig.
0.4293 ***
0.0744 ***
-0.1053 ***
0.1216 ***
-0.0421 ***
0.0101 *
0.0420 ***
0.0400 ***
0.0320 ***
0.0245 ***
0.0455 ***
0.0334 ***
-0.0088 ***
0.0103 ***
***
***
0.0040 ***
0.2478 ***
6.1428 ***
15,729
0.7414
0.1646
0.0485 ***
15,729
0.7720
0.1546
0.0446 ***
15,729
0.7720
0.5709
0.1546
2.4665
0.0446 ***
Main regression Findings – SAR-Err Method
Ln_Liveable
Area
Ln_Liveable
Area(m²)
(m²)
Ln_LotLn_Lot
SizeSize
(m²)
(m²)
Ln_Building
Age
(years)
Ln_Building
Age
(years)
Access to Water&Sewage
Access to Water&Sewage
Local Tax Rate
Local Tax
Rate
Year 1991
Year 1991
Year 1993
Year1994
Year 1993
Year 1995
Year1994
Year 1996
Year 1995
Regional Accessibility Index
Year 1996
Local Accessibility Index
Nb. Accessibility
of Lone-parent Families
Regional
Index
Median HouseholdIndex
Income
Local Accessibility
% of University Degree
Nb. of Holders
Lone-parent Families
MedianEndogenous
Household
Income
Effects
Intercept
% of University
Degree
Holders
N
Endogenous
Effects
R-Squared
Intercept
RMSE
Lambda
Moran’s I
N.B. : Signif.
N
R-Squared
RMSE
Moran’s I
10
Base Model
Base + NBHD
Attr.
Peer Effect
Base
Model
Base + NBHD(Exog.
Attr.
Model
(Property
Attr.)
Effects)
(Prop. & Time Attr.)
(Exog. Effects)
(Endog. Effect)
Coefficient
Sig. Coefficient
Sig.
Coefficient Sig.
Coefficient Sig.
Coefficient Sig.
0,4374 ***0.4339 *** 0,41250.4780
******
0.5479 ***
0,0983 ***0.0752 *** 0,09700.0444
******
0.0273 ***
-0.0788 -0,1173
***
-0.1033 *** -0,1132
-0.0943
***
******
0.1661 ***
0.1238 ***
0.1528 ***
0,1380 ***
0,1184 ***
-0.2144 ***
-0.0756 ***
-0.0490 ***
***0.0232 *** -0,0578
***
0.0305 -0,0618
***
-0.0053
0,0187 ***0.0632 *** 0,02020.0036
***
0.0458 ***
0.0258 ***
-0.0038
0,0594 ***0.0604 *** 0,0626
***
0.0068 0,0580 ***0.0430 *** 0,0631
-0.0003
***
0.0088
0.0438 ***
-0.0176 ***
0,0435 ***0.0535 *** 0,0469 ***
0,0439 ***0.0335 *** 0,0492 ***
-0.0060 *** 0,0139 **
0.0080 *** 0,0288 ***
9.0482 ***
0.0058 *** -0,0049 ***
0,00890.5709
******
8.9648 ***
2.4665 ***
Peer Effect
Global Model
(All Var.
Global Model
Model
(All Var. Effect)
(Endog.
Included)
Included)
Coefficient
Sig. Coefficient Sig.
Coefficient Sig.
0,4239
***
0,4072 ***
0.4293
***
0,0985
***
0,0967 ***
0.0744
***
-0.1053
***
-0,1176
***
-0,1133 ***
0.1216 ***
0,1349 ***
0,1206 ***
-0.0421 ***
-0,0625
***
-0,0572 ***
0.0101
*
0,0049
0,0104 **
0.0420
***
0.0400
***
0,0290
***
0,0412 ***
0.0320
***
0,0244 ***
0,0392 ***
0.0245 ***
0,0228 ***
0,0321 ***
0.0455 ***
0,0100
0,0250 ***
0.0334
***
-0.0088 ***
0,0127 *
0.0103 ***
0,0214 ***
-0,0051 ***
0.0040 ***
0,0102 ***
0.2478 ***
6.1428 ***
0,0043 ***
15,729
0.6918
8,4993
0,1797
0,9953
0.1486 ***
Level : * p<0,05; ** p<0,01; *** p<0,001
15,729
0.7666
***0.1564
***0.0919 ***
15 729
0,7699
0,1551
0,0092 ***
N.B. : Signif. Level : * p<0,05; ** p<0,01; *** p<0,001
15,729
0.7414
8,91060.1646
***
0,98440.0485
******
15 729
0,7824
0,1508
0,0039 ***
15,729
0,3839
0.7720
4,5400
0.1546
0,9882
0.0446
***
***
***
***
15 729
0,7764
0,1529
0,0021 ***
0,0036
0,2623
5,9887
0,9713
***
***
***
***
15 729
0,7852
0,1499
0,0006 *
Main regression Findings – SAR-Err Method
11
A SAR-Spatial Error procedure clearly yields improved
overall performances when compared with the OLS
method – all the more so for the Base Model specification
which generates a 0.77 R-Squared.
As expected, the Lambda parameter (in excess of 0.97) is
highly significant) as the SAR procedure proves most
efficient at solving SA problems, at least to a large extent.
Thus, even with the first specification, the Moran’s I value
drops from 0.1486 (OLS) to a mere 0.0092 (SAR); with the
Global Model, it is down to 0.0006 and only significant at
the 0.05 level.
Main regression Findings – SAR-Err Method
Secondly, controlling for spatial dependence results in
regression parameters displaying a much greater stability
throughout the spectrum of housing characteristics, even
for attributes whose coefficients tend to exhibit pronounced
variability under the OLS procedure.
This is particularly the case with the local tax rate attribute
and with time dummies.
The constant term, finally, is also favourably affected by
adopting a SAR procedure, as reflected in its lessened
fluctuations among model specifications.
12
Main regression Findings – SAR-Err Method
13
Last but not least, regression findings obtained with the
SAR procedure corroborate the usefulness of the
endogenous effect variable in the hedonic price function,
even where spatial dependence is controlled for.
Indeed, under the Peer Effect Model specification, its
parameter reaches 0.3839 (p < 0.001) and remains highly
significant, although with a lower magnitude (0.2623), even
after the inclusion of contextual determinants.
Accounting for peer effects also contributes to lowering SA
in the residuals, as suggested by the sharp drop in the
Moran’s I value, from 0.0039 (Base Model + Exogenous
effects) to 0.0006 (Global Model).
Conclusion and Suggestions
for Further Research
Findings suggest that peer, endogenous, effects do act as
significant determinants of property values and that, when
used in combination with exogenous attributes in the
hedonic price equation, they prove quite effective at
reducing the extent of spatial dependence in the model
residuals.
Furthermore, even where a spatial autoregressive
procedure is applied so as to explicitly account for spatial
autocorrelation influences, the peer effect variable
parameter still emerges as being highly significant and
contributes to lessen SA still further.
14
Conclusion and Suggestions
for Further Research
15
Such findings lead to the conclusion that the comparable
sales approach, as used in traditional appraisal practice, is
a valid one, although its application is typically flawed by
the too small sample size generally used by appraisers.
The peer effect model allows revisiting the conformity
principle which grounds the comparable sales approach,
although within the more structured and rigorous framework
of the hedonic price method.
Further investigation is still needed in order to find out
which submarket delineation should be used to obtain
optimal model performances.