No. 9213
MEASURING THE VALUE OF SCHOOL QUALITY by
Lori Taylor September 1992
Research Paper Federal Reserve Bank of Dallas
This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (
[email protected])
H e a s u r i n gt h e V a l u eo f S c h o o lQ u a l i t y .
Lori L. Taylor FederalReserveBankof Dallas
A u g u s2t 8 , 1 9 9 2
P r e l i m i n a r yD r a f t - - P l e a s eD o N o t Q u o t e
*
T h e a u t h o r i s g r a t e f u l t o t h e D a l l a s I n d e p e n d e nStc h o o lD i s t r i c t f o r B. Fomby,JamesK. allowing accessto its iata, to StephenP.A. Brown,Thomas t sn d t h e i r commena f o r l i h e a l a n D e n n i s H . S u l l i v a n a n d K e l l y A . Hjghtower, assistance. her research to Rueffer for suggestions,and Linda
M o s t r e a l e s t a t e a g e n t sw i l l t e l l y o u t h a t h o u s e ss e l l f o r h i g h e r p r i c e s in areas that have good schools. Economistsappearto have confirmedthis common wisdomin their analysesof property values (see, for example,Jud and Watts, 1981, or l,lalden,1990). However,economistsstudying property values (and possibly.$any-home.buyers) .quality as a function of have-meas ured..school the achievenentsof a school's graduatesrather than as a function of the v a l u e a d d e dt o t h o s e g r a d u a t e sb y t h e s c h o o.l T h i s d e f i n i t i o n i s a t o d d sw i t h t h e l i t e r a t u r e o n s c h o o lq u a l i t y n e a s u r e m e nwt ,h i c hh a s g e n e r a l l y c o n c l u d e d that the prefemed measureof school quality is the school's marginal effect o n s t u d e n t s( s e e , f o r e x a m p l eH a n u s h eakn d T a y l o r , 1 9 9 0 ) . I f ' s p e c . i f i c a t i o ne r r o r i n t h e e s t i m a t e so f s c h o o lq u a li t y c a p i t a l i z a t i o n i s s i g n i f i c a n t , t h e n p o li c y r e c o m m e n d a t i ot hn as t a r e b a s e do n t h e p r e v i o u s e s t i m a t e sc o u l d b e m i s l e a d i n g . F o r e x a m p l e i,f p r e v i o u se s t i m a t e so v e r s t a t e t h e e x t e n t t o w h i c h s c h o o lq u a l i t y d i f f e r e n c e sa r e c a p i t a l i z e d i n t o p r o p e r t y values, then analysts trying to judge voter support for a school bondelection c o u l d s u b s t a n t i a l l y o v e r - e s t i n a t es u p p o r ta m o n g h o m e o w n e r sI .n t h j s p a p e r , the author demonstrates that the specification emor can be substantial and t h a t p r e v i o u se s t i m a t e so f s c h o o lq u a li t y c a p i t a li z a t i o n c o u l d e a s i l y r e f l e c t differences in student and Darent characteristics rather than differences in school effects.
The ]'lodel To answeq r u e s t i o n sa b o u tt h e d e g r e et o w h i c hr n i s s p e c i f i c a t i o nh a s m a r r e de s t i m a t e so f t h e c a p i t a li z e d v a l u e o f s c h o o lq u a li t y , o n e m u s t f i r s t c o n s t r u c tm e a s u r eosf t h e m a r g i n a li m p a c to f s c h o osl .
F o l l o w i n gt h e
n e t h o d o l o g oy u t l i n e d i n H a n u s h eakn d T a y l o r ( 1 9 9 0 ) , t h e a u t h o rm o d e l ss t u d e n t
a c h i e v e m e ni nt p e r i o d T a s a f u n c t i o n o f t h e s t u d e n t ' s c o m p l e t eh i s t o r y o f school(S) andfamily (F) characteristics T-1
Air = dr + yrsrr + prsit * Eo.
T-1
+ |
T-1
yrsit + !
T
gtFrt
* E tr. '
(l)
whereAiT is the achievement of student i in period T, S,. represents characteristics of the schoo'lattendedby student i in period t, and F,. r e p r e s e n t sf a m i l y c h a r a c t e r i s t j c si n p e r i o d t . B e c a u s e q u a t i o nI i s r e c u r s i v e , o n e c a n e x t r a c t t h e t o t a l m a r g i n a l inpact of the current school by est'imating Ait
= dr * lAir_,
* FrFi,
*
E q*"r* *
€ir.
(2)
k=1
wherethe sik are dummy variables that e q u a l o n e i f t h e i t h student attends school k and equal zero otherwjse. In t h i s f o r m u l a t i o n ,q k representsthe margina1effect of (or value addedby) s c h o o lk , a n d Ar,n =,d, * lAi,r-, + FrFi,t
(3)
representsthe level of student achjevement that could be expectedregardless of the school attended, I n t r o d u c i n gt h e s en e a s u r e so f t h e val ue addedby schools and the expectedachjevement of students into a hedonicmodelof property values d e c o m p o s tehse c a p i t a l i z a t j o n o f s t u d e n tachievement into tv'roDarts, The f i r s t i s t h e p a r t o f s t u d e n ta c h i e v e m e nthat t can be attributed to schools and i s s u b j e c t t o m a n i p u l a t i o nb y t h e m ;t h e secondis the Dart of student
achjevement that can be attributed to the characteristics of the student body and is not directly affected by changesin school pol icy.
To the extent that
these two components of student achievement are capitalized differently, analysesusing the capitalized value of student achievement to proxy for the c a p j t a l i z e d . y a l . u e - osfc h o o l sw j l l b e m j s l e a d j . n q .
The Data F o c u s i n go n a s i n g l e s c h o o lt a x a t i o n d i s t r i c t a v o i d sc o m p l i c a t i o n st h a t jurisdictions. m i g h t a r i s e f r o m d i f f e r e n c e si n t a x r a t e s a n d t a x b a s e sa m o n g [ ^ l i t hf e w e x c e p t i o n s ,p r o p e r t i e sw j t h i n t h e j u r i s d i c t i o n o f t h e D a l l a s I n d e p e n d e nStc h o o lD i s t r i c t ( D I S D )a r e a l s o i n t h e c i t y a n d c o u n t yo f D a l l a s . B e c a u s teh e s e j u r i s d i c t i o n s t a x u n i f o r m l yv l i t h j n t h e j r b o u n d a r i e st,h e p r o p e r t i e sf a c e t h e s a m ec i t y , c o u n t ya n d s c h o o ld j s t r i c t t a x r a t e s . T h e r e f o r e ,d i f f e r e n c e si n p r o p e r t yv a l u e sw i t h i n t h e s a m p l es t u d i e dd o n o t r e p r e s e n tc a p i t a i i z e d d i f f e r e n c e si n t a x r a t e s , DISDprovided data on student body characterjstjcs and student a c h j e v e m e ns tc o r e sf o r 8 7 p r i m a r ys c h o o l si n i t s j u r i s d i c t i o n f o r t h e y e a r s 1 9 8 5 ,1 9 8 6 ,a n d 1 9 8 7 . T h e s t u d e n tb o d yc h a r a c t e r i s t i c su s e d i n t h e a n a l y s i s were the percentageof studentswhowere N0NIIHITE and the best-available proxy f o r s o c i o - e c o n o msi ct a t u s ( t h e p e r c e n t a g o e f s t u d e n t sr e c e i v i n g f r e e o r reduced-pricelunches, P_LUNCH). data used in the The student achievement analysis were averagescores for fourth-grade students on the Iowa Test of B a s j c S k i l l s ( I T B S )i n m a t h e m a t i casn d r e a d i n gi n 1 9 8 6a n d 1 9 8 7a n d t h e previous year's averagescores for the samecohort (third-grade scores in 1985 and 1985, respectively). The variables P0STTEST represent the and PRETEST averagecombinedmathematics and reading scores in the fourth and third
g r a d e s ,r e s p e c tvi e l y , D a t a o n 3 1 0 D a l l a s s i n g l e - f a m i l yh o m e st h a t s o l d i n J u l y 1 9 8 7c a m ef r o m the SREAllarket Data Center's annualpublication of residential property t r a n s a c t i o n s . T h e h o u s i n gd a t a u s e di n t h i s a n a l y s i s i n c l u d e t h e s a l e p r i c e of the property-in thousands..(SALEPR), the the. number. of batirooms(NUI.IBATHS), y e a r j n w h i c ht h e h o m ew a s b u i l t ( Y R B U I L Tt)h, e n u m b eor f s q u a r ef e e t i n t h e structure (SQFEET), and dummy variables that take on the value of one if the h o u s eh a s a f i r e p l a c e o r a s w i m m i npgo o l ( F I R E P L A a CnEd P 0 0 1 ,r e s p e c t i v e l y ) . Fromthe SREA data on addresses,the author also constructedvariables on d i s t a n c et o t h e c e n t r a l b u s i n e s sd i s t r i c t ( D I S T A N CaEn)d a d u m mvya r i a b l e f o r +lhetheror not the property is located south of downtown Dallas (S0UTH_DAL). T a b l e I r e p o r t s s u m m a rsyt a t j s t i c s f o r t h e v a r j a b l e s u s e di n t h i s a n a l y s i s .
The Estinati on To provide a frame of reference, the author estimates the relationship betweenhousingcharacterjstics, averagestudent test scores in 1987and the v a l u e o f p r o p e r t i e ss o l d i n J u l y o f t h a t y e a r u s i n g l i n e a r , l o g - l i n e a r , a n d l o g - 1 o gs p e c i f i c a t . i o n s( s e e T a b l e2 ) .
Not surprisingly, the estinations
i n d i c a t e t h a t p r o p e r t yv a l u e s i n D a l l a s a r e a n i n c r e a s i n gf u n c t i o n o f t h e s i z e of a homeand the numberof bathroomsand a decreasingfunction of the d i s t a n c ef r o m t h e c e n t r a l b u s i n e s sd i s t r i c t .
Housew s i t h s w i m m i npgo o l s a r e
r o u g h l y 2 0 p e r c e n tm o r ee x p e n s j v et h a n h o u s e sw i t h o u t s w i m m i npgo o l s , a n d h o m e si n s o u t h e r nD a l l a s a r e c e t e r i s p a r i b u ss u b s t a n t i a l l y l e s s e x p e n s i v et h a n h o n e si n t h e n o r t h e r np a r t s o f t h e c i t y .
T h e e s t i m a t i o na l s o i n d i c a t e s t h a t
s t u d e n ta c h i e v e m e nd ti f f e r e n c e sa r e s i g n i f i c a n t l y c a p i t a li z e d i n t o p r o p e r t y v a l u e s . E v a l u a t e da t t h e m e a n ,a l - o e r c e n t i n c r e a s ei n s t u d e n ta c h i e v e m e ni nt
the fourth grade increasesproperty va1ues by between1.0 and 1.4 percent, dependingon the functional form. H o w e v e ri,t i s n o t c l e a r i f t h e r e l a t i o n s h i p b e t w e e ns t u d e n ta c h i e v e m e n t and property values found in the benchmark regressionsrepresentscapital ized school qu.alitJL--Answering.this.question-.r€quires.estimates of value addedand averageexpectedachievement for each primary school in DISD. However, p r i v a c y c o n c e r n sm a k es t u d e n t - s p e c i f i cd a t a u n a v a i l a b l ea n d f o r c e e q u a t i o n2 to be estimated in residual form. POSTESTk=d+IPRETEST"+pr1 + p*,
(4)
where P0STTESTk is the average,combinedtest score for fourth graders in school k, PRETESTk is the average,combinedtest score for the samecohort in the third grade, F is a vector of student body characterjstics (N0NWHITE and P_LUNCH), and lt1 = epSl + e".
(5)
U n f o r t u n a t e l y ,e s t j m a t i n gs c h o o le f f e c t s a s e q u a t i o nr e s i d u a l s i n t r o d u c e ss e r i o u s p r o b l e m sf o r t h e s e c o n ds t a g eo f t h e a n a l y s i s . B e c a u s teh e v a l u e - a d d erde s i d u a l sm e a s u r e s c h o o le f f e c t s w ' i t h s u b s t a n t i a le r r o r , h y p o t h e s i st e s t s b a s e do n t h e e s t j m a t e dc o v a r i a n c em a t r i x o f t h e h e d o n i c e q u a t i o nw o u l db e b i a s e d ( M u r p h ya n d T o p e,l l 9 e 5 ) . T h e a u t h o r d e a l s w i t h t h e s e p r o b l e m sb y u s i n g a d d j t i o n a l i n f o r m a t i o ni n t h e d a t a s e t t o e n h a n c e the e s t i m a t i o no f t h e s t a g e o n e e q u a t i o n s ,a n d b y a p p l y i n gt h e e r r o r c o r r e c t j o n techniquessuggestedby Murphyand Topel to the secondstage hypothesis testing. F o r t u n a t e l y ,t h e d a t a s e t c o n t a i n ss u f f j c i e n t a d d i t i o n a l i n f o r m a t i o nt o
e s t i m a t ee q u a t i o n( 4 ) f o r 1 9 8 6a s w e l l a s 1 9 8 7 .B e c a u s teh e r e s i d u a l s a r e a functjon of school effects, and one would expect school effects to be highly correlated over tine, the two years of data permit one to estimate a systemof two equations, POST|ESTk,8T = ds., i Lj?RETESTk,B6 * PFli * V*,", = POSTTESTk,8E oeo + LJ?RETESTk,B5 * pF'ft-; + Fr,ee ,
(6)
u s i n g s e e m i n g l yu n r e l a t e dr e g r e s s i o n( S U R t) e c h n i q u e s . r B e c a u s teh e s y s t e m of two equations incorporatesmore information than would an estimation of the f i r s t e q u a t i o na 1 o n e ,t h i s a p p r o a c h s h o u l dr e d u c et h e p o r t i o n o f t h e g . s t h a t r e p r e s e n t sm e a s u r e m eenftf o r .
T a b l e3 r e p o r t s t h e r e s u l t s o f t h i s f i r s t - s t a g e
e s t i m a t i o nf o r b o t h a l i n e a r a n d a l o g a n i t h m i cs p e c i f i c a t i o n . I n t h e s e c o n ds t a g e o f t h e e s t i m a t i o n ,t h e a u t h o r s u b s t i t u t e st h e p r e d i c t e dv a l u e s a n d r e s i d u a l s f r o m t h e f i r s t - s t a g e e q u a t i o n sf o r 1 9 8 7f o r t h e observedstudent achievenentjn the benchmark hedonicequationsand uses the techniquessuggestedby Murphyand Topel to comect the standarderrors for h y p o t h e s i st e s t i n g . T h e a u t h o r u s e st h e f i r s t - s t a g e e s t i m a t e sf r o m t h e l i n e a r s p e c i f i c a t i o n f o r t h e l i n e a r a n d 1 o g - l i n e a rs p e c i f i c a t i o n so f t h e h e d o n i c m o d e i ,a n d t h e f i r s t - s t a g e e s t i m a t e sf r o m t h e l o g a r i t h m i cs p e c i f i c a t i o n f o r t h e 1 o g - 1 o gs p e c i f i c a t i o n o f t h e h e d o n i cm o d e. l U s i n ga l o g a r i t h m i c s p e c i f i c a t i o n i n t h e f i r s t s t a g e t o d e r i v e l o g a r i t h m i ce s t i m a t e so f v a l u e addedand predicted achievement rather than transformingthe estimates from ' F o r s j m p l i c i t y , t h e a u t h o rr e s t r i c t t h e c o e f f j c i e n t s o n X a n d t h e p v e c t o r t o b e t h e s a m ea c r o s se a c hp a i r o f e q u a t i o n s .F - t e s t s o f t h e l e g i t i m a c y o f t h i s r e s t r j c t i o n d o n o t r e j e c t t h e h y p o t h e s i st h a t t h e s e c o e f f i c i e n t s a r e the samefor 1986and 1987. F-tests do reject the hypothesisthat the intercept terms are also equal.
t h e l i n e a r f i r s t - s t a g e s p e c i f i c a t i o ng r e a t l y s i m p l i f i e s e x t r a c t i o n o f t h e appropriate vari ance- covariancenatrix for the lilurphy-Topel correction and does not appearto influence the results.
The Pearsoncorrelations between
the values for VALUE ADDED and PREDICTED ACHIEVEMENT from the logarithmic specification*and.log t E n s f o r m a t i o n sf o r L h e s a m ev a r i a b l e s f r o m t h e l i n e a r s p e c i f i c a t io n a r e . 9 8 2 3a n d . 9 9 1 9 ,r e s p e c t i v e l y . The l4urphy-Topel error coruection involves using the vari ance-covariance matrix of the first-stage estination to inflate the standarderrors that are u s e di n h y p o t h e s i st e s t i n g i n t h e s e c o n ds t a g e . P a r a m e t eers t i m a t e sa r e u n a f f e c t e db y t h e c o r u e c t i o n . S p e c i f i c a l l y , o n e t e s t s h y p o t h e s euss i n g t h e var'iance-covariancematrix A
A
E . o r r " " . " o - E . n c o r r e c r e d(iz t z l - ' z l
,TA
F. i/'(e) FJ z(zt
zJ-1,
(7)
w h e r eZ i s t h e m a t r i x o f s e c o n d - s t a gree g r e s s o r s ,F - i s a m a t r i x o f f i r s t stage regressorsthat is weightedby the squareof the difference betweenthe coefficients on the generatedregressors (VALUE-ADDED and PREDICTED ACHIEVEHENT) from the secondstage, and t(6) js the variance-covariance matrix from the first-stage regress'ion. In these examples,the error correction is s n a l l a n d h a s n o i m p a c to n t h e i m p l i c a t i o n so f t h e h y p o t h e s i st e s t s . T h e e s t j m a t i o n sr e p o r t e di n T a b l e 4 c l e a r l y i n d i c a t e t h a t t h e v a l u e addedby schools and the predicted achievements of students can be capital ized d i f f e r e n t l y a n dt h e r e f o r et h a t s p e c i f i c a t j o ni s i m p o r t a n t . I n t h i s e x a m p l e , which is robust to a nunberof common functional forms, property values are a function of the expectedachievement of students and not of the marginal e f f e c t s o f s c h o osl .
Gonclusi ons P r e v i o u ss t u d i e s o f t h e c a p i t a li z e d v a l u e o f s c h o o lq u a li t y h a v eb e e n m i s s p e c i f i e d . E s t i m a t e su s i n g i n f o r m a t j o no n f o u r t h - g r a d e r sj n t h e D a l l a s I n d e p e n d e nStc h o o lD i s t r i c t s u g g e s t h a t t h e m i s s p e c i f i c a t i o ni s i m p o r t a n t . In parti cuJ.ar'.. -in-t.e.rpreti ng the.relationship be-tween student achievement and property values as evidencethat school quality differences are capitalized maybe very wrong. Althoughdifferences in student achievementin the fourth grade appearto have beencapitalized into property values, the estimation i n d i c a t e s t h a t t h e v a l u e a d d e db y D a l l a s s c h o o l si n t h e f o u r t h g r a d e i s r o t r e f l e c t e d i n l o c a l p r o p e r t yv a l u e s . Evidencethat estimatesof capital ized school quality nay be wrongcan h a v es e r i o u s i m p l i c a t i o n sf o r e d u c a t i o n a pl o 1i c y .
F o r e x a m p l e i,n s t j t u t i n g a
p o li c y o f s c h o o lc h o i c e ( w h i c hw o u l di m p l y t h a t r e s i d e n c ei n t h e n e i g h b o r h o o d i s n o l o n g e r a r e q u i r e m e nfto r a t t e n d i n ga p a r t i c u l a r s c h o o l )w o u l dr e d u c e property va1ues by the amountof the capital ized school quality unless t r a n s p o r t a t i o nc o s t s w e r e s u b s t a n t i a.l T h e r e f o r e ,t h e d e g r e eo f o p p o s i t i o nt o s u c h a r e f o r mw o u l dd e p e n do n t h e d e g r e eo f s c h o o lq u a l i t y c a p i t a li z a t i o n . U s i n gm i s s p e c i f i e de s t i m a t e so f s c h o o lq u a li t y c a p i t a li z a t j o n c o u l d c a u s e a n a l y s t st o e r r s u b s t a n t i a l l yw h e ne s t i n a t j n g v o t e r s u p p o r tf o r s c h o o lc h o i c e o r v a r i o u s o t h e r r e f o r mp r o p o s a l s .
REF ERENCES H a n u s h e kE, r i c A . , a n d L o r i L . T a y l o r , " A l t e r n a t i v eA s s e s s m e not sf t h e P e r f o r m a n coef S c h o o 1 s , "T h eJ o u r n a lo f H u m a R n e s o u r c e s2, 5 : 2 , 1 9 9 0 , 179-201. J u d , G . D o n a ' l da, n d J a m e sM . t l a t t s , " s c h o o l sa n d H o u s i n gV a l u e s , "L a n d E c o n o m i c s5,7 : 3 , 1 9 8 1 ,4 5 9 - 4 7 0 , Itlurphy,Kevjn M., and RobertH. Topel, "Estirnationand Inference in Two-Step E c o n o m e t r iHc o d e l s , "J o u r n a lo f B u s i n e s sa n d E c o n o m iSct a t i s t j c s , 3 : 4 , I985,370-379. SREA litarketCenter Data Inc,, North TexasAnnual 1987, DamarCorp, Atlanta, G e o r gai , 1 9 8 7 . l,Ja1den, Michael 1., "MagnetSchoolsand the Differential Impactof School Q u ailt y o n R e s i d e n t i a lP r o p e r t yV a l u e s , "T h e J o u r n a l o f R e a l E s t a t e R e s e a r c h5, : 2 , 1 9 9 0 ,2 2 1 - 2 3 0 .
TABLE1 Summary Statistics Variable
Mean
SALEPR
1 5 6. 1 2
148.62
YRBU I LT
5 7. 7 0
1 6 .7 3
SQFEET
1997.87
10t3.79
NU14BATHS
2.08
0.94
FIREPLACE
0 .6 5
0. 4 8
POOL
u.lb
u.5/
DISTANCE
2.46
0. 8 3
SOUTHDAL
0 .2 5
0.43
P0STTESTsT
4 6. 9 1
4.26
PRETESTs6
4 0. 9 0
4.27
NoNt.lH ITEsT
7 7. 3 3
21.51
P_LUNCH87
59.18
21.06
P0STTESTs6
49.22
3.81
PRETEST85
4t.45
J.YU
N0Nt.lH ITEs6
7 5. 8 4
2l.45
P_LUNCH86
5 7. 9 7
zL.ta
10
Std. Deviati on
TABLE 2 Benchmark Reqressions Li near INTERCEPT
-172.28* (s8.18)
Log-Linear
Log-Log
2.90* (0.26)
- 6 .2 5 * (r.20)
YRBU I LT
-1.06* (0 . 4 1 )
0.001 ( 0. 0 0 2 )
- 0 .0 3 ( 0 .0 e )
SQFEET
0 .0 7 * ( 0 .0 1 )
0 .0003* ( 0. 0 0 0 0 4 )
0.98* ( 0 .0 e )
NUMBATHS
4 9 .I 6 * ( 1 0 .0 5 )
0 .22* ( 0. 0 5 )
0,27* ( 0 .l 0 )
POOL
3 0 .2 4 * (1s.14)
0.17* (0.07)
0.20* (0.07)
( r 2. 3 7)
I4.83
0.14* (0.06)
0.02 ( 0 . 0 6)
DISTANCE
-26.94*
-0.20*
(o.03)
-0.37* (0.07)
SOUTH_DAL
-14.24
{r2.76)
-0.30* (0.06)
-0.25* ( 0 . 0 6)
4.26* (1.30)
0. 0 2 * (0.01)
1.00* (0.2e)
FI REPLAC E
(7.ss)
POSTTEST R-SQUARED
.6665
.7504
* , S i g n i f i c a n t l y di fferent from zero a t t h e 5 - p e r c e n tl e v e l Standardemors a r e i n p a r e n t h e s e s .
I1
.7577
TABLE 3 Fi r s t - S t a g eR e g r e s s i o n s
Li near INTERCEPT 1987
Logarithmic
(3.10)
2.93 (0.24)
INTERCEPT 1986
37.93 (3.12)
2.97 ( 0 .2 4 )
NONl.lHITE
-0.04 (0 . 0 1 )
-0.05 ( 0 . 0 2)
P-LUNCH
-0.06
(0 . 0 r)
-0.05 (0.01)
PRETEST
0 .4 2 (0.06)
(0.0s)
SYSTEM R-SQUARED OBSERVAT IONS
5J. YJ
.5580 87
0.38
.5491 87
A l 1 r e g r e s s o r sa r e s i g n i f i c a n t l y d i f f e r e n t f r o m z e r o a t t h e 5 - p e r c e n t1 e v e ,1 Standardemors are in oarentheses.
.tL
TABLE 4 Second-Stage Regressions Li near INTERCEPT
YRBU I LT
SQFEET
NUMBATHS
Log-Linear
-387.91* ((8e.43)) (80.l2)
2.49t ( ( o . 3 8 )) ( 0 . 3 7)
Log-Log -7.57*
((1.4e)) (1.47)
-0.96* ( ( 0 .4 0 )) (0.40)
( (o.oo2) )
-0.02 ( ( 0 .0 e )) ( 0 . 0 e)
0 .0 7 * ( ( 0 .0 1 )) ( 0 .0 1)
0 .0003* ( ( 0 . 0 0 0 4)) ( 0. 0 0 0 0 4 )
( (0.oe)) (0.0e)
0.001
(0.002)
0 .9 7 *
( ( 0. 0 s ) (0.0s)
0.20*
0.?4* ( ( 0 .l o ) ) ( 0 .l 0 )
3 9 .0 7 * ((15.00))
0.19* ( ( 0 . 0 7 )) ( 0 . 0 7)
0.27t ( ( 0 . 0 7 )) (0.07)
((1?.2?)) (t2.20)
-8.85
0.15* ((0.06)) ( o .0 6 )
0.04 ( ( 0 . 0 6 )) (0.06)
-32.57* ((7.64)) (7.s7)
-0.21* ((0.04)) (0 . 0 4 )
- 0. 3 9 * ((0.07)) ( 0 . 0 7)
((12.74)) (12.61)
-0.29* ((0.06)) (0.06)
- 0. 2 3 * ( ( o. 0 6 )) ( 0. 0 6 )
VALUEADDED
-2.79 ((?.24) (2.24)
((o.ol)) (o. 0 1 )
PREDICTED ACHIEVEMENT
9.10* ((l.ee)) (1.7e)
41.92* ((10.01))
( r 0 .0 1 )
POOL
( I 4 .e e )
FIREPLACE
DISTANCE
SOUTHDAL
-7 ?E
R-SQUARE
.6820
0.01
0.03*
((o.01)) ( 0 .0 1 ) .75?.4
* S i g n i f i c a n t l y d i f f e r e n t f r o m z e r o a t t h e 5 - p e r c e n tl e v e l . Correctedstandarderrors are in doubie oarentheses. O r i g i n a l s t a n d a r de m o r s a r e i n p a r e n t h e s e s . 13
0. 4 0
( ( 0 . 4 e)) (0.4e) I .35*
((0.38)) ( 0 . 3 i) .7596
RESEARCHPAPERSOF THE RESEARCHDEPARTI,IENT IEDERAL RESERVEBANK OF DALI.AS Awallable, at no charge, fron the Research Department Federal Reserve Bank of Dallas, Station K Dallas, Texas 75222
9L01,
: Outliers Large Shocks.,-Jrnall Shocks., ..,and.Xconornic -Eluctuations Macroeconomic Time Series (Nathan S. Balke and Thomas B. Fonby)
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Evaluating Monetary Base Targeting and Scott E. Hein)
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llhat Motlvates Oll Producers?: DahI and Mine Yucel)
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Hyperinflation, and Internal Debt Repudiation ln Atgentina and Brazil: Plans (John From Expectations Management to the "Bonex" and "Collor" H. Welch)
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Learning From One Another: The U.S. and European Banklng Experience (Robert T. Clair and Gerald P. O'Driscoll)
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Detecting Lewel Shifts ln Time series: Proposed Solution (Nathan S. Balke)
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Underdevel-oprnenLand the Enfotcernent of Lalts and Contracts Freeman)
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An Econometric Analysis of Borrowing Constraints (John V. Duca and Stuart S. Rosenthal)
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credit cards and Money Demand: A cross-Sectional and l,Ii1lian C. l,/hitesell)
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and Real Internal Ratlonal Inflation (John BYazi-I? H. llelch)
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Ttre Optinality TabeIlini)
91L5
North Amettcan Free Trade and the Peso: The Case for Currency Area (Darryl Mcleod and John H. I{elch)
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Public
Purchases
in
for U.S.
and ReaI Wages (Mark Wynne)
in Texas School Quality
L. Taylor
and Beverly
ln Mexico:
J.
Fox)
H)rPotheses (Carol
Tescing Alternative
Misspecification
and a
(Scott
and Household Debt
Study (John V. Duca
Debt Bubbles ln Argentina
of Nominal ConLracts (Scott
Debts and Deficits
Joseph H. Haslag
and
Freenan and Guido
a North American
A conrnent (John H. Welch)
The Algebra
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Allocatlve Inefficlency !n Education Lori. Taylor, I,Iill iarn l.Ieber)
9LL9
A to Pay for Public Schools: Student Enigration and the Willingness ( L o r i L. Test of the Publicness of Publlc Hieh Schools in the U.S. ravlor I
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Are..De€p Recessions Nathan S. Balke)
92OZ
The Case of the "Misslng
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Links to the Home country: Innlgrant and Factor Rewards (David M. Gould)
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Does Aggregate Output Have a Unit
9205
Inflation
'9206 '
of Price
and lts
Stability
(Nathan s. Balke and Kenneth M. Enery)
9LL7
( SharanaGrosskopf,
FolJ-owed-$y St'rong Recoveries?
Kathy Hayes,
(Mark A. W)mne and
M2" (John V. Duca)
variability:
Implications
Root?
for
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A Note (Kenneth M. Enery)
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and Tax Nonbank conpetitlon, The Effects of Credit Availability, (John Garrett) V. and Bonnie on Bank Consumer Lending Duca Reforrn
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0n the Future Erosion of the North American Free Trade Agreement (william c. cruben)
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Threshold
92lO
in cointegration and Tests of a Cl-assical Model of Inflation (Raril Feliz Antbal and Peru Argentina, Boliwia, RrazLI, Mexico, John H. Llelch)
Cointegration
(Nathan S, Balke and Thonas B. Fonby)
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Nomlnal Feedback Rules for Monetary Policy: Koenlg)
gZLz
The Analysis
92L3
Measuring the value
of Fiscal
Pollcy
in Neoclasslcal
of School Quality
(I-ori
and
Some Couments (Evan F.
Modelsl Taylor)
(Mark i'Iynne)
