Ares Paper

8/10/2019 Ares Paper

1/27

A GIS Framework to Forecast

Residential Home Prices

Submitted by

Mak Kaboudan & Avijit SarkarSchool of Business, University of Redlands, Redlands, CA !", USA

Corres#ondin$ author% Mak Kaboudan

email% mak'kaboudan(redlands)edu

*el% +- ./00..!1 fa2% +- ""334!31

5ovember !, !6


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A GIS Framework to Forecast

Residential Home Prices

Mak Kaboudan, Avijit Sarkar

School of Business, University of Redlands, Redlands, CA !", USA

Abstract) 7n this #a#er 8e estimate s#atiotem#oral models of average neighborhood

single family home pricesto use in #redictin$ individual property prices) Avera$e home

#rice variations are e2#lained in terms of differences in avera$e nei$hborhood house

attributes, s#atial attributes, and tem#oral economic chan$es) Models ado#tin$ three

different nei$hborhood resolution definitions are estimated usin$ 9uarterly #anel data

over the #eriod !!3 in four cities from four different counties in Southern

California) :ur results su$$est that forecasts obtained usin$ city nei$hborhood avera$e

#rice e9uations have advanta$e over forecasts obtained usin$ e9uations estimated from

city disa$$re$ated data)

Keywords:S#atiotem#oral models1 models 8ith #anel data1 estimatin$ microeconomic

data)

JEL classification% C!41 C!"1 C04

1. Introduction

*his #a#er introduces a ne8 8ay of modelin$ residential home #rices that may hel#

#roduce more accurate and timely forecasts of them) Accurate and timely forecasts of

home #rices clearly hel# home o8ners, develo#ers, financial institutions, and $overnment

a$encies make better decisions) ;or many decades, hedonic #rice models demonstrated

that the #rice of a house is mainly de#endent on its attributes) *hose attributes ty#ically

included house characteristics such as buildin$ s9uare foota$e, number of bedrooms,

!


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number of bathrooms, a$e of the house, lot s9uare foota$e, etc) Ball +4."- #rovides a

revie8 of the early literature) Recent use of $eo$ra#hic information systems +ollako8ski +404- addressed concerns about the functional form to use in their

estimation) *he com#lication is mainly due to s#atial autocorrelation) ?ike tem#oral

autocorrelation, s#atial autocorrelation reduces the efficacy of forecasts obtained 8hen

usin$ standard statistical modelin$ techni9ues) >rior 8ork that addressed s#atial

de#endence either considered $eo$ra#hical coordinates as e2#lanatory variables in the #rice

model +Cla##, !"- or modeled the re$ression residuals s#atially +Basu and *hibodeau,

40-) Most e2istin$ models @ both strictly hedonic or those that address s#atial de#endence

@ focus on #arsimony of estimated e9uations and #roduce outofsam#le #redictions of #rices

for homes sold durin$ the same time #eriod) *he sam#le to forecast and measure model

efficacy ty#ically consists of a 8ithheld #ercent of the sam#le of data available to conduct the

research) *his means that the time dimension is absent in those models and as a result the

forecasts are less useful 8hen makin$ future decisions since #rices of homes chan$e over

time)

*he method of modelin$ residential home #rices #ro#osed in this #a#er aims to move a

ste# closer to #roducin$ #arsimonious home #rice models that take into consideration

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housin$ attributes, s#atial attributes, and tem#oral economic chan$es) *em#oral

economic chan$es +es#ecially chan$es in mort$a$e rates- have had evident si$nificant

effect on real +or inflation adjusted- home #rices) *herefore statistical estimation efforts

should deal 8ith a$$ravated statistical #roblems of s#atial autocorrelation +bet8een

s#atial attributes- and of estimatin$ #anel +or crosssectionaltimeseries- models) 5o

attem#t is made in this #a#er to introduce ne8 methodolo$y to resolve any of the t8o

#roblems) ?o$ical mani#ulations are used to circumvent s#atial correlation1 and e2istin$

methodolo$y is used to resolve #roblems 8ith estimatin$ #anel data) ?o$ical

mani#ulations mainly involve redefinin$ the sco#e of the de#endent variable and

therefore the inde#endent variables) Rather than estimatin$ a model of individual

property prices, a model that estimates average neighborhood home pricesis considered

instead) *his lo$ical mani#ulation is #ossible if it is assumed that homes in a s#ecific

nei$hborhood have similar attributes)

Modelin$ averagenei$hborhood #rices is ne8) Most studies focus on modelin$

individualhome #rices) 7f hedonic models e2#lain variations in #rice levels on avera$e,

#erha#s average home pricesshould be e2#lained instead of individual home price levels)

;urther, s#ecifyin$ and estimatin$ averagerather than individualhome #rice functions is

lo$ical if s#atial de#endency bet8een conti$uous homes e2ists) Basu and *hibodeau

+40- e2#lain that s#atial correlation is a likely #henomenon 8hen dealin$ 8ith

individualhome #rices) *he correlation is because nearby #ro#erties are #robably

constructed about the same time, share location attributes, and ty#ically have similar

structural features) Some studies focus on median#rices as in hou +4.-) Dhile the

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median #rice may be used instead of avera$e #rice, the median#rice may fail to re#resent

homes in its nei$hborhood accurately if that median#riced house ha##ens to be aty#ical)

Modelin$ the averagenei$hborhood #rice calculation may hel# smooth out the effects

of unusual homes) *o estimate the avera$e nei$hborhood #rice model usin$ #anel data,

e2istin$ methodolo$y su$$ests use of a $eneraliEed least s9uare method +


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defined usin$ the county assessorFs #arcel numbers +A>5-) An A>5 is a nine di$it id of

land #arcels assi$ned by the county 8hen a #arcel of land is subdivided +at least in

several 8estern US states-) Conti$uous subdivisions are assi$ned consecutive numbers)

;or e2am#le, if a #arcel of land that is !3 acres lar$e $ets subdivided into 3 #otential

home sites, the 3 ne8 lots $et ne8 #arcel numbers that relate to the ori$inal !3acre lot

number) *o elaborate, assume that before the subdivision, the !3acre #arcel 8as assi$ned

the A>5 "4 at some time in the #ast) After subdivision, the ne8 3 lots are

assi$ned ne8 se9uential numbers that 8ould be somethin$ like% "44, "4

!, etc), 8hich clearly relate to the ori$inal) 7f this is the case, usin$ the A>5Fs first four

di$its of #ro#erties in a city +like ", "4, etc)- #rovides a definition of nei$hborhoods

that contain a fairly lar$e number of conti$uous houses) Selection of the number of di$its

to use is de#endent on the siEe of the city) *he objective 8hen selectin$ such number is

that the number of homes #er nei$hborhood satisfies a minimum level im#osed by

statistical theoretical constraints) +Results #rovided later in this #a#er su$$est choosin$

that number such that nei$hborhoods contain ten to " homes)-

Avera$e nei$hborhood #rice models are different from standard hedonic #rice models and

from models of housin$ submarkets) Avera$e #rice models utiliEe a much smaller number

of observations that ho#efully smooth out of effects of unusual house attributes on

estimated coefficients) Standard hedonic #rice models utiliEe a hu$e number of individual

#ro#erty observations re$ardless of the effects of unusual house attributes) =edonic

models of submarkets estimate a different #rice e9uation for each market se$ment still

usin$ individual home #rices) Gach e9uation thus has a lo8er the number of observations

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than standard hedonic models but re9uires estimatin$ a lar$er number of e9uations1 one

for each submarket)

Ado#tin$ any of the three nei$hborhood definitions to obtain an avera$e #rice of a home

8as never used before) 7t is not #ossible 8ithout a


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follo8s U)S) Census Bureau assi$ned numbers) All houses sold durin$ a $iven 9uarter

8ithin a $iven census tract number belon$ to a nei$hborhood) :nly the leftmost / di$its

of a >5 in cities subject of this study define a nei$hborhood) 7>I4 code +a subset of

7>I/- is the third resolution) 7>I4 is used because usin$ fivedi$it 7> numbers

#roduced only t8o nei$hborhoods for some cities) Addresses of homes sold over the

study #eriod +!!3- in four cities each in a different county in Southern California

8ere $eocoded in Arc5, and 7>I4 nei$hborhoods in Burbank of ?os An$eles

County are in ;i$ure 4+a-, +b-, and +c-, res#ectively) C*, >5, and 7>I4 nei$hborhoods in

Carlsbad of San Jie$o County are in ;i$ure !+a-, +b-, and +c-1 8hile those of Redlands of

San Bernardino County and Riverside of Riverside County are in ;i$ure " and /,

res#ectively) I4 8as desi$ned to satisfy the objective of ma2imiEin$ efficiency

of #ostal service, >5 is e2#ected to 8ork best)

+a- C* 5ei$hborhoods +b- >5 5ei$hborhoods +c- 7>I4 nei$hborhoods

;i$ure 4) Resolutions of nei$hborhoods in Burbank of ?os An$eles County

0


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;i$ure !) Resolutions of nei$hborhoods in Carlsbad of San Jie$o County


;i$ure ") Resolutions of nei$hborhoods in Redlands of San Bernardino County

+a- C* 5ei$hborhoods +b- >5 5ei$hborhoods +c- 7>I4 5ei$hborhoods ;i$ure /) Resolutions of nei$hborhoods in Riverside of Riverside County


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3. The Data

A detailed data set containin$ individual sales and attributes of homes sold in the four

selected counties in Southern California 8as obtained from Jatauick +!3-) 5ot all

cities in the four counties had consistent data and some had incom#lete data) Com#lete

data 8ith consistent variables 8ere identified for four cities Burbank +BB-, Carlsbad

+CB-, Redlands +RJ-, and Riverside +RS-) Si2 years +!!3- of available data for the

four cities are selected) :nly si2 years are used because they cover a #eriod of time 8ith

a##ro2imately consistent lendin$ rules) 7t is a #eriod 8hen banks facilitated borro8in$

8ith ne8 lendin$ conditions such as interest only #ayments and other lendin$ rules that

led to historically relatively lo8 do8n #ayments and lo8 monthly mort$a$e #ayments)

*he #eriod +!!3- is thus selected to minimiEe structural chan$es in lendin$ rules

that may render inconsistent model estimation results) Jata of the first five years +!

!/ inclusive- 8ere used to fit different #rice models for each city) Jata for !3 8ould

then be used to test the efficacy of oneyearahead forecasts the models deliver)

Successful models then #redict the unkno8n #rices for !6)

4. Methodology

Similar to standard hedonic individual#rice models, multi#le re$ression methods a##ly

8hen estimatin$ average#rice models) *he avera$e nei$hborhood #rice is the de#endent

variable and the vector of attributes #rovides the set of inde#endent variables) Because

the data of avera$e nei$hborhood #rices and attributes is a combination of crosssectional

and time series observations or #anel data, standard :?S multi#le re$ression are not

suitable as mentioned earlier) *he method to use for #anel data is the random-effects+or

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errorcom#onents- model) Randomeffects models are estimated as $eneraliEed least

s9uares +


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available by household, A=7 8as a##ro2imated usin$ the #rices of homes and standard

lendin$ rules) Standard lendin$ rules mandate a minimum do8n #ayment of !L of the

amount needed to #urchase a house) Mort$a$e #ayments are ty#ically around "L of a

homebuyin$ householdFs annual income) Usin$ these rules and the avera$e #rice of

homes four 9uarters before a current 9uarter +the time needed to actually com#lete a

#urchase from the time a decision is made to buy a house-, income for a current 9uarter

8as a##ro2imated) *he loan amount la$$ed one year 8as com#uted as% ?At home

#ricet/P )0) ?A 8as then used to a##ro2imate the avera$e monthly mort$a$e #ayment

+>M*-, 8here

k

t / t /

t t k

t /

+MR Q4!-P+4 MR Q4!->M* ?A )

+4 MR Q4!- 4

+= +

+4-

8here k loan duration +"6 months for "year fi2ed loan-) Since the a##ro2imate

annual #ayments +A>t >M*tP4!- are "L of a householdFs annual income +7t-,

t t7 A> Q )"= ) +!-

Dith i 4, N, n houses sold in a nei$hborhood durin$ tth9uarter, the a##ro2imate

avera$e annual nei$hborhood household income +A=7t- is

n

t t

i 4

4A=7 7 )

n =

= +"-

A=7 thus a##ro2imates annual household income for a nei$hborhood i such that #rices of

houses sold a year a$o determine the level of income needed to #urchase a house in the

current 9uarter)


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5. Comarison o! Results

A com#arison bet8een results of estimatin$ avera$e #rices and individual #rices is

#resented here to sho8 8hether avera$in$ #rices does hel# #roduce better estimates of

the e9uations andQor better forecasts) ;irst,


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@ 4)// MRt!@ 4)40 MRt"@ 0)/.3 MRt6I 4)".0 SCJt@ 4)460>At +3-+)- +)- +)- +)- +)-

Usin$ avera$e nei$hborhood #rices%

C*% A>t 4!4)3 I ")63 SS;tI ). CAtI 4)6/ A=7t 4!)!3 MRt" 46)/3 MRt6 +6-

+)- +)- +)- +)- +)- +)->5% A>t 43")0 I /)/ SS;tI )3! CAtI 3)0 ?S;tI )0/3 A=7t

+)- +)- +)"- +)6- +)3-

6)36 MRt" 44). MRt3 4")3" MRt6 +.-

+)!"- +)4- +)-7>% A>t 43 I 0)4. SS;tI 4)3 CAtI 4)/6 A=7t 4)0/ MRt" 46)06 MRt6 +0-

+)- +)- +)- +)- +)- +)-

#arlsbad - #!:

Usin$ individual home #rices for the entire city%

R>t 434)40! I .)34! SS;tI 4)34 CAtI 4")/. 5At +44-

+)- +)- +)6- +)- +)- +)4- +)"-7>% A>t 3)/ I 6!) SS;tI !)." A=7t )4. MRt! )!" MRt" 46)40 >At +4!-

+)- +)- +)- +)3- +)4- +)46-

$edlands - $%:


R>t 0!)/!3 I //)6"/ SS;tI ). CAtI 3)!0 5At +4"-+)- +)- +)- +)-

Usin$ avera$e nei$hborhood #rices%

C*% A>t 44")0 I 3!)4. SS;tI )"3 ?S;tI 4). A=7t .)! MRt!+)- +)- +)6- +)- +)!-

3)3! MRt3 .)0" MRt6 )"0 >=t +4/-

+ +).- +)- +)-

4/


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>5% A>t 6.)4 I /6). SS;tI !)36 A=7t 0)"4 MRt! ")60 MRt" ")0! MRt6 +43-

+)- +)- +)- +)- +)"- +)"-

7>% A>t 3 SS;tI )3/ CAtI !)43 A=7t 44)4! MR! I )!6 >=t +46-

+)- +)- +)- +)- +)"-

$iverside - $&:


R>t 06)!.6 I "")"./ SS;tI )!66 CAtI 4)30! 5% A>t 6). I !4)44 SS;tI ")3! A=7t ")4 MRt! 3)"6 MRt" ")0 MRt6 +!-

+)- +)- +)- +)- +)- +)-

7n e9uations +43- @ +!-, SS; avera$e structure s9uare foota$e1 BJ avera$e number

of bedrooms1 CA avera$e construction a$e1 ?S; avera$e lot s9uare foota$e1 A=7

avera$e minimum household income needed to #urchase a house1 MR mort$a$e rate1

>A #ercent of African American #o#ulation in a nei$hborhood1 >= #ercent of

=is#anic #o#ulation in a nei$hborhood1 SCJ avera$e distance to nearest school in the

nei$hborhood) All estimated coefficients have si$ns consistent 8ith lo$ical e2#ectations

and are si$nificantly different from Eero at the 3L level of si$nificance +e2ce#t for one @

BJ in +4- that is si$nificant at the 6L-) Gstimation +over !!/- and forecast +for

!6- statistics of the above e9uations are in *able 4)

*able 4

Gstimation and forecast com#arative statistics

Gstimation Statistics ;orecast Statistics

:bs) R ! MA>G JD :bs) U >MA>G

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BB

7ndividual >rices% "40 ).0 43)." 4).6 ./ ) 4")/

5ei$hborhoods%

C* !6 )06 0)6 4)3. .6 )3 .).6

>5 4/6 )4 0)"3 4)6" /! )6 0)3"

7> !!4 )03 4)4 4)6! 64 ). 44)/.

CB

7ndividual >rices% 4!" )04 4)4 4)6! !43 )4 4.)"0

5ei$hborhoods%

C* 44. )4 4.)"3 4)06 !3 )4 4/)3

>5 !.6 )00 4")4 4).. 6 )6 4)

7> !6/ )0 4/)/" 4).3 3. ) 4")3"

RJ

7ndividual >rices% """ ).0 4.)0" 4). .00 )4! 43)36

5ei$hborhoods%

C* 433 )0 44).3 4)./ / ) 4!)3"

>5 !/! )4 44)"/ 4)06 6" )0 44)4.

7> !46 )4 ) 4)3 6 ) 4).0

RS

7ndividual >rices% "3.4 ).4 4/)63 4). 4 )44 4.)/3

5ei$hborhoods%

C* 4.0 )06 .)64 4).. "0 ) 4)63

>5 !6 )0. 6)3 4)3/ 3! ). 44)/.

7> "// )0" 0)4 4)6 .. )6 4)".

*he results in *able 4 on estimation statistics #rovide a com#arison bet8een the number

of observations used to obtain each e9uation +obs)-, the R!, MA>G, and the Jurbin

Datson statistic) *he coefficients of determination +R!- for usin$ individual #rice data are

all lo8er than those of the avera$e nei$hborhood #rice e9uations) *he MA>G statistics

also confirm that the avera$e #rice e9uations may have the advanta$e) *he JD statistics

are #ersistently belo8 the critical !) level su$$estin$ sli$ht #ositive autocorrelation

#ersistin$) ;orecast statistics #rovide com#arisons bet8een the number of observations,

the Ustatistic, and the #rediction MA>G +>MA>G-) ;or all four cities, the avera$e

nei$hborhood #rice e9uations sho8 forecast statistics su$$estin$ im#rovements over the

individual home #rice e9uations) 5

resolution models are better than the other t8o)

46


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*o test 8hich e9uation #roduces the better !3 forecasts of individual home pricesfor

each cityFs nei$hborhood resolution, 8e test the null hy#othesis that #redictions of #rices

usin$ the avera$e #rice e9uation #redictions of the same #rices usin$ the individual

#rice e9uation) 7t is assumed here that the avera$e #rice e9uations can be e9ually useful

in #redictin$ individual home #rices) Usin$ the >MA>G statistic, the test can be re8ritten

as%

=o% >MA>G4 >MA>G!

8here >MA>G4 >MA>G obtained 8hen #redictin$ !3 individual #rices usin$ an

avera$e #rice e9uation and >MA>G! >MA>G obtained 8hen #redictin$ the same #rices

usin$ an individual #rice e9uation) *he test statistic to use is%

4 !

! !

4 !

>MA>G >MA>GE

s s

; ;

=

+

+!4-

Dhere s4 variance of >MA>G4, s! variance of >MA>G!, and ; is the sam#le of !3

#redicted e post)

*able !

Com#arison of individual home #rice !3 forecasts

>MA>G4 >MA>G! Escore p-value

4tailed

BB

>5 4/)4/ 4")/ )4 )/6

C* !!).6 4")/ /)3 )

7>I4 !!) 4")/ /).4 )

CB

>5 !)!! 4.)"0 )63 )!6

C* 4.)34 4.)"0 )" )/7>I4 40) 4.)"0 )4. )/"

RJ

>5 46)! 43)36 )3. )!

C* !)/. 43)36 ")! )

7>I4 !)". 43)36 ").4 )

RS

4.


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>5 4)0. 4.)"/ 4)0/ )"

C* 4)60 4.)"/ 4)6. )3

7>I4 40).0 4.)"/ 4)! )43

*he com#arison of the test results are in *able !) Althou$h >MA>G4T >MA>G!in all

situations, the null is not rejected at the 3L level of si$nificance for >5 in three of the

four cities) *his means that it is #ossible to obtain #redictions of individual home #rices

usin$ the avera$e #rice e9uations that are not si$nificantly different from those obtained

usin$ the individual #rice e9uations)

*he better nei$hborhood models may no8 be used to determine the future of housin$

#rices) *hey are used to #redict avera$e nei$hborhood #rices in !6 assumin$ that

houses sold in !3 8ere resold in !6) >redictin$ !6 #rices is #ossible 8ithout

havin$ to #redict any of the e2#lanatory variables1 the income variable is la$$ed one year

and because mort$a$e rates are easily adjusted to account for increases that occurred in

the first half of !6) *he !3 and !6 forecasts 8ere then used to com#ute e2#ected

#rice chan$es bet8een the t8o years) earoveryear e2#ected 9uarterly chan$es in

avera$e nei$hborhood #rice levels usin$ the >5 e9uations is re#orted in *able ") >5 is

selected since it 8as best accordin$ to the statistics in *able !) *he results in *able "

su$$est that home #rices in !6 are e2#ected to rise only in BB and decrease other8ise)

;i$ures 3 +a- @ +d- com#are actual real avera$e nei$hborhood #rices 8ith the e post

forecasts for !3) ;i$ures 6 +a- @ +d- com#are avera$e nei$hborhood e post#rice

forecasts for !3 8ith e ante#rice forecasts for !6)

*able "

!6 over !3 9uarterly e2#ected L #rice chan$es

BB CB RJ RS

4 )! /)!! /).0 ")6

40


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! )0 ")0 4)06 4)/

" )0 6)/. 4)6 3)0

/ !)!! 6).3 !)"0 3).6

4


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;i$ure 3) Actual and #redicted !3 real avera$e nei$hborhood #rices)

!


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;i$ure 6)E post#redicted !3 versus e ante!6 real avera$e nei$hborhood #rices)

!4


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7deally forecast statistics should be com#ared 8ith those re#orted in the literature)

=o8ever, re#orted results found do not use consistent de#endent variables or re#ort the

same statistics) MSG cannot be com#ared since they are de#endent on relative #rices of

homes in different areas and time #eriods analyEed) :nly MA>G can be com#ared) A

com#arison of the statistics found is in *able /) *here is a main difference bet8een the

results in *able " and the results in *able !) *he results in *able ! belon$ to forecasts of

future#rices) *hose in *able / are #redictions of #rices of homes sold in thesame#eriod

as the data used in model estimation)

*able /) Com#arison 8ith literature forecast statistics Sam#le MA>G


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attributes, nei$hborhood attributes, s#atial differences, and mort$a$e rates taken at

different tem#oral la$s)


24/27

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25/27

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26/27

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Schabenber$er :,


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Shiller R +4"- Measurin$ asset value for cash settlement in derivative markets% hedonic

re#eated measures indices and #er#etual futures) Vournal of ;inance /0% 44"4

Dhite = +40- =eteroskedasticityconsistent covariance matri2 estimator and a direct

test for heteroskedasticity) Gconometrica /0% 04.0"0

hou +4.- ;orecastin$ sales and #rice for e2istin$ sin$lefamily homes% a HAR

model 8ith error correction) Vournal of Real Gstate Research 4/%433460

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