Solution Manual - Introductory Econometrics: A Modern Approach 8th Edition - Wooldridge (Chapter 1 - 19)

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IntroductoryEconometrics
JeffreynM. nWooldridge


Chapter n1 The nNature nof nEconometrics nand nEconomic nData ........................................ 1
Part n1 Regression nAnalysis nwith nCross-Sectional nData.............................................. 1
Chapter n2 The nSimple nRegression nModel ....................................................................... 1
Chapter n3 Multiple nRegression nAnalysis: nEstimation..................................................... 2
Chapter n4 Multiple nRegression nAnalysis: nInference .................................................. 4
Chapter n5 Multiple nRegression nAnalysis: nOLS nAsymptotics ......................................... 5
Chapter n6 Multiple nRegression nAnalysis: nFurther nIssues ............................................... 6
Chapter n7 MultipleRegression nAnalysis nwithQualitative nInformation:Binaryvariables
n8 nChapter n8
Heteroskedasticity ........................................................................................... 9
Chapter n9 More non nSpecification nand nData nproblems ................................................. 12
Part n2 Regression nAnalysis nwith nTime nSeries nData .................................................. 14
Chapter n10 Basic nRegression nanalysis nwith nTime nSeries nData ................................. 14
Chapter n11 Further nIssues nin nUsing nOLS nwith nTime nSeries nData ............................. 16
Chapter n12 Serial nCorrelation nand nHeteroskedasticity nin nTime nSeries nRegression ... 19
Part n3 Advanced nTopics ............................................................................................. 23
Chapter n13 Pooling nCross nSections nacross nTime. nSimple nPanel nData nMethods ....... 23
Chapter n14 Advanced nPanel nData nMethods ................................................................ 25
Chapter n15 Instrumental nVariables nEstimation nand nTwo nStage nLeast nSquares ........ 27
Chapter n16 Simultaneous nEquations nModels .............................................................. 30
Chapter n17 Limited nDependent nVariable nModels nand nSample nSelection nCorrections
n 31 nChapter n18
Advanced nTime nSeries nTopics ................................................................. 35
Chapter n19 Carrying nOut nan nEmpirical nProject .......................................................... 39
Appendix: nSome nfundamentals nof nprobability ................................................................ 42

,Introductory Study nNotes nby nZhipeng
Econometrics Yan
Chapter1 The nNature nof nEconometrics nand nEconomic nData
I. The ngoal nof nany neconometric nanalysis nis nto nestimate nthe nparameters nin nthe
nmodel nand nto ntest nhypotheses nabout nthese nparameters; nthe nvalues nand
nsigns nof nthe nparameters ndetermine nthe nvalidity nof nan neconomic
ntheoryand nthe neffects nof ncertain npolicies.
II. Panel ndata n- nadvantages:
1. Having nmultiple nobservations non nthe nsame nunits nallows nus nto ncontrol
ncertain nunobserved ncharacteristics nof nindividuals, nfirms, nand nso non. nThe nuse
nof nmore nthan none nobservation ncan nfacilitate ncausal ninference nin
nsituations nwhere ninferring ncausality nwould nbe nvery nhard nif nonly na nsingle
ncross nsection nwere navailable.
2. They noften nallow nus nto nstudy nthe nimportance nof nlags nin nbehavior nor nthe
nresult nof ndecision nmaking.




Part n1 Regression nAnalysis nwith nCross-Sectional

nData nChapter n2 The nSimple nRegression nModel

I. Model: nY n= nb0 n+ nb1x n+ nu
1. Population nregression nfunction n(PRF): nE(y|x) n= nb0 n+ nb1x
2. systematic npart nof ny: n b0 n+ nb1x
3. unsystematic npart: nu

II. Sample nregression nfunction n(SRF): nyhat n= nb0hat n+ nb1hat*x
1. PRF nis nsomething nfixed, nbut nunknown, nin nthe npopulation. nSince nthe nSRF
nis nobtained nfor na ngiven nsample nof ndata, na nnew nsample nwill ngenerate na
ndifferent nslope nand nintercept.


III. Correlation: nit nis npossible nfor nu nto nbe nuncorrelated nwith nx nwhile
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nbeing ncorrelated nwith nfunctions nof nx, nsuch nas nx .
E(u|x) n= nE(u) n nCov(u, nx) n= n0. nnot nvice nversa.

IV. Algebraic nproperties nof nOLS nstatistics
1. The nsum nof nthe nOLS nresiduals nis nzero.
2. The nsample ncovariance nbetween nthe n(each) nregressors nand nthe nresiduals nis
nzero. nConsequently, nthe nsample ncovariance nbetween nthe nfitted nvalues nand nthe
nresiduals nis nzero.

3. The npoint n(x, ny) nis non nthe nOLS nregression nline.
4. the ngoodness-of-fit nof nthe nmodel nis ninvariant nto nchanges nin nthe nunits nof ny nor nx.
5. The nhomoskedasticitynassumption nplays nno nrole nin nshowing nOLS nestimators
nare nunbiased.


V. Variance
1. Var(b1) n= nvar(u)/SSTx
a. more nvariation nin nthe nunobservables n(u) naffecting ny nmakes nit nmore
ndifficult nto nprecisely nestimate nb1.




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,Introductory Study nNotes nby nZhipeng
Econometrics Yan
b. More nvariability nin nx nis npreferred, nsince nthe nmore nspread nout nis nthe
nsample nof nindependent nvariables, nthe neasier nit nis nto ntrace nout nthe
nrelationship nbetween nE(y|x) nand nx. nThat nis, nthe neasier nit nis nto nestimate
nb1.
2. standard nerror nof nthe nregression, nstandard nerror nof nthe nestimate nand
1
nthe nroot nmean nsquared nerror 
2
n= u
(n
2)

Chapter3 Multiple nRegression nAnalysis: nEstimation
I. The npower nof nmultiple nregression nanalysis nis nthat nis nallows nus nto
ndo nin nnonexperimental nenvironments nwhat nnatural nscientists nare
nable nto ndo nin na ncontrolled nlaboratory nsetting: nkeep nother nfactors
nfixed.


II. Model: nY n= nb0 n+ nb1x1 n+ nb2x2 n+ nu
b n ( v n y n)/( v2), nwhere nv nis nthe nOLS nresiduals nfrom na nsimple nregression nof nx1
n n n n
m



1 i1 n i i1
n i1
i1
on nx2.
1. n v nis nthe npart nof nx1 nthat nis nuncorrelated nwith nx2, nor nv nis nx1 nafter nthe neffects nof
nx2 nhave nbeen npartialled nout, nor nnetted nout. nThus, nb1 nmeasures nthe nsample
nrelationship nbetween ny nand nx1 nafter nx2 nhas nbeen npartialled nout.


III. Goodness-of-fit
1. R2 n= nthe nsquared ncorrelation ncoefficient nbetween nthe nactual ny nand nthe
nfitted nvalues nyhat.
2. R2 nnever ndecreases nbecause nthe nsumof nsquared nresiduals nnever nincreases
m




nwhen nadditional nregressors nare nadded nto nthe nmodel.


IV. Regression nthrough nthe norigin:
1. OLS nresiduals nno nlonger nhave na nzero nsample naverage.
2. R2 ncan nbe nnegative. nThis nmeans nthat nthe nsample naverage n“explains” nmore
nof nthe nvariation nin nthe ny nthan nthe nexplanatory nvariables.


V. MLR nAssumptions:
A1:linearin parameters. n A2:
m




random nsampling.
A3: nZero nconditional nmean: nE(u|x1, nx2, n…, nxk) n= n0
When nA3 nholds, nwe nsay nthat nwe nhave nExogenous nexplanatory nvariables. nIf nxj
nis ncorrelated nwith nu nfor nany nreason, nthen nxj nis nsaid nto nbe nan nendogenous
nexplanatory nvariables.
A4: nNo nperfect ncollinearity.
A1 n– nA4 n nunbiasedness nof nOLS

VI. Overspecifying nthe nmodel:
1. Including none nor nmore nirrelevant nvariables, ndoes nnot naffect nthe nunbiasedness

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, Introductory Study nNotes nby nZhipeng
Econometrics Yan
nof nthe nOLS nestimators.




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