Solutions for Essentials of Econometrics, 5th Edition by Damodar N. Gujarati.pdf

SolutionsnManual nfornEssentialsnofnEconometrics,n5enDamodarnGujarati,
n DawnnPortern(All nChapters)
CHAPTERn1
THEnNATURE nANDnSCOPE nOFnECONOMETRICS



QUESTIONS
1.1. (a)nOthern thingsn remainingn then same,nthen highern thentaxn raten is,n then lowernthen
pricen of n an housen willn be.
(b) Assumen thatn thendatan aren cross-
sectional,n involvingn severaln residentialn communitiesn withndifferingntaxn rates
.
(c) Yin=nB1 n+nB2 nXni

wheren Yn =n pricen of n then housen and n Xn =n taxn rate
(d) Yin=nB1 n+nB2 nXnin +nui

(e) Givenn then sample,n onen cann usenOLSn ton estimatenthen parametersn ofnthen mo
del.
(f) Asidenfromn then taxn rate,n othern factorsn thatn affectn housen pricesn aren mo
rtgagen interest n rates,n housen size,n buyers’n familyn income,n then staten ofn then econ
omy,nthenlocalncrimenrate,netc.nSuchnvariablesnmaynbenincludedninnanmorendetail
ed n multiplen regressionn model.
(g) Anpriori,n B2 n <n 0.n Therefore,n onen cann test n H0 n :nB2 n n 0nagainst nH 1 n:nB2 n<n0.

(h) Then estimated n regressionn cann ben used nton predictn then averagen pricen ofn an h
ousen inn an community,n givenn thentaxn raten innthatn community.n Ofn course,n it n isn a
ssumed n that n alln othern factorsn stayn then same.
1.2. Econometriciansn aren now n routinelyn employed n inn government n andn businessn t
on estimaten andn /n ornforecast n (1)n pricen and n cost n elasticities,n (2)n productionn and
n costn functions,n and n (3)ndemand nfunctionsnforn goodsn and n services,n etc.nEcono
metricn forecastingn isn an growthn industry.
1.3. Then economyn willn ben bolsteredn ifn then increasen inn then moneyn supplyn leadsn ton a
n reductionn innthen interestn ratenwhichn willn leadn ton moren investment n activityn an
d,ntherefore,ntonmorenoutput nand nmorenemployment.n If nthenincreaseninnthen mo
neyn supply,n however,n leadsn ton inflation,n then precedingn result n may
1

, not n occur.n Then jobn ofn then econometriciann willn ben tondevelopn an modelnton predi
ct nthen effect n ofn then increasen inn then moneyn supplyn onn inflation,n interest n rate,n e
mployment,n etc.
1.4. Asnanmatternofnfact,nonnOctobern1,n1993nthenFederalnGovernmentndidnincreasen t
hen gasolinen taxn byn 4n cents.n Sincen gasolinen andn carsn aren complementaryn prod
ucts,n economicntheoryn suggestsnthatn ann increasen innthen pricen ofn gasolinen willn
not n onlyn lead nton andeclinen inn thendemandnforn gasolinen but n alson inn thendemand n
forncars,n ceterisn paribus.nThenFord nMotornCompanymaynbenadvisedn ton produ
cen moren fuel-
efficient n carsnton staven off n an seriousn declinen inn thendemandnfornitsncars.nAnnauto
mobilendemand nfunctionnwillnproviden numericaln estimatesn ofn then effectn ofn
gasolinen taxn onn then demandforn automobiles.
1.5.
Theren aren manyn alternativen designsn possible.n However,n ton keepn thingsn simpl
e,n and n discussn just n anbasicn ideanofnthendesign,n wencouldn thinkn ofnusingn annecon
ometricn modeln knownn asn Autoregressiven Distributed n Lagn(ARDL)n ofnthenfor
m:
yn =nn +n y +nn g +nn g +nn  n p n +n +n  n p +nn  ncn +nn  ncn n +nu
t t n−1 0 t 1 t n−1 0 t 1 t n−1 0 t 1 t n−1 t


where
Yt n −nYt n−1 n
yt n = =n realn GDPn growthn raten inn yearn t;
Ytn−1

G −nGt n−1 n
gt n = = t n realn government n infrastructuren investment n growthn raten in
Gt n−1

yearn t;
 nt pn =n personalnincomen taxn raten innyearnt;
 ntcn = corporaten incomentaxnrateninnyearnt;
yt n =n yt n −n yt n−1 n =nchangen inn realn GDPn growthn raten inn yearn t;

gt n =n gt n −ngt n−1 n =n changen inn realn government n infrastructuren investment n growthn r
aten inn yearn t;
 n p n =n n p n −n n p n =n changen inn personaln incomen taxn raten inn yearn t;
t t t n−1
 ncn =n ncn −n ncn n =n changen inn corporaten incomen taxn raten inn yearn t.
t t t n−1



2

,Expected n signsn and n magnitudesn of n then parametersn then regressionn model:




3

, 0 n n n n1;
0,1n n0;
n0,1,0,1n n 0.

Noten that nan moren realisticn modelnwouldn includenanlargern numbern of nlagsn ofnthenreg
ressorsn thann included n inn ourn model,n andnwould n alson includen additionaln regressor
sn knownn asn controln variablesn whichn could n ben determined n based nonneconomicn the
ory.

Now,n based n onn ourn specified n modeln above,n short n runn and n longn runn economic
consequencen of n 1n unit n increasen in g n ,n n pn,n and n  ncn, respectively,n cann be
t t t

determined n byn usingn partialn derivativesn asn follows.

Short n runn economicn consequencesn of n an 1n unit n increasen inn gt aren givenn by:
yt
=n0 n;
gt
yt n+1 n (yt n +n1 g t n )n
=n =n  0 +n1n ;
 




g t g t
yt n+n2 n (yt n+1 n)n
=n =n n( 0 +nn1 );
 




g t g t
yt n+3 n (yt n+n2 n)n (yt n+n2 n)n
=n =n n =n n2 n( 0 +n1n );
  




g t g t g t
and n son on.

Longn runn consequencen isn then sumn of n short n runn consequences
=nn0 +n(n0 +nn1)n+nn(n0+nn )1 n+nn2 n(n +
0 nn )1n+n...

=nn0 +nn0 +nn1 +nn2 n0 +nn1 +nn3 n0 +nn2 1n +n...
=nn0(1n+nn +nn2 n +nn3 n +n...)n+nn1(1n+nn +nn2 n +n...)
0 1
=n n +n n
1n−n 1n−n
0n+n1n
=n .n
1n−n 

Analogously,n short n runn economicn consequencesn of n an 1n unit n increasen inn  n pt are
givenn by:
yt =nn n;
0
 ntp
y (yn +nn  n p n)
t n+1 n
=n t 1 tn n
=n n0 n +n1 ;
 np t  np t



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