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1、 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Chapter 7 Multiple Regression Analysis with Qualitative Information Wooldridge:Introductory
2、 Econometrics:A Modern Approach,5e 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Qualitative InformationExamples:gender,race,industry,regi
3、on,rating grade,A way to incorporate qualitative information is to use dummy variablesThey may appear as the dependent or as independent variablesA single dummy independent variableDummy variable:=1 if the person is a woman=0 if the person is man=the wage gain/loss if the person is a woman rather th
4、an a man(holding other things fixed)Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Gra
5、phical IllustrationAlternative interpretation of coefficient:i.e.the difference in mean wage between men and women with the same level of education.Intercept shiftMultiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or
6、 posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Dummy variable trapThis model cannot be estimated(perfect collinearity)When using dummy variables,one category always has to be omitted:Alternatively,one could omit the interce
7、pt:The base category are menThe base category are womenDisadvantages:1)More difficult to test for diffe-rences between the parameters2)R-squared formula only validif regression contains interceptMultiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be
8、 scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Estimated wage equation with intercept shiftDoes that mean that women are discriminated against?Not necessarily.Being female may be correlated w
9、ith other produc-tivity characteristics that have not been controlled for.Holding education,experience,and tenure fixed,women earn 1.81$less per hour than menMultiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or post
10、ed to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Comparing means of subpopulations described by dummiesDiscussionIt can easily be tested whether difference in means is significantThe wage difference between men and women is larger
11、 if no other things are controlled for;i.e.part of the difference is due to differ-ences in education,experience and tenure between men and womenNot holding other factors constant,women earn 2.51$per hour less than men,i.e.the difference between the mean wage of men and that of women is 2.51$.Multip
12、le Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Further example:Effects of training grants on
13、 hours of trainingThis is an example of program evaluationTreatment group(=grant receivers)vs.control group(=no grant)Is the effect of treatment on the outcome of interest causal?Hours training per employeeDummy indicating whether firm received training grantMultiple Regression Analysis:Qualitative
14、Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Using dummy explanatory variables in equations for log(y)Dummy indicating whethe
15、r house is of colonial styleAs the dummy for colonial style changes from 0 to 1,the house price increases by 5.4 percentage pointsMultiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible
16、website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Holding other things fixed,married women earn 19.8%less than single men(=the base category)Using dummy variables for multiple categories1)Define membership in each category by a dummy variable2)Leave out one c
17、ategory(which becomes the base category)Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病
18、人Incorporating ordinal information using dummy variablesExample:City credit ratings and municipal bond interest ratesMunicipal bond rateCredit rating from 0-4(0=worst,4=best)This specification would probably not be appropriate as the credit rating only contains ordinal information.A better way to in
19、corporate this information is to define dummies:Dummies indicating whether the particular rating applies,e.g.CR1=1 if CR=1 and CR1=0 otherwise.All effects are measured in comparison to the worst rating(=base category).Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rig
20、hts Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Interactions involving dummy variablesAllowing for different slopesInteresting hypotheses=intercept men=intercept women=s
21、lope men=slope womenInteraction termThe return to education is the same for men and womenThe whole wage equation is the same for men and womenMultiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly
22、 accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Graphical illustrationInteracting both the intercept and the slope with the female dummy enables one to model completely independent wage equations for men and womenMultiple Regression Analysis:Qua
23、litative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Estimated wage equation with interaction term No evidence against hypot
24、hesis that the return to education is the same for men and womenDoes this mean that there is no significant evidence of lower pay for women at the same levels of educ,exper,and tenure?No:this is only the effect for educ=0.To answer the question one has to recenter the interaction term,e.g.around edu
25、c=12.5(=average education).Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Testing for
26、differences in regression functions across groupsUnrestricted model(contains full set of interactions)Restricted model(same regression for both groups)College grade point averageStandardized aptitude test scoreHigh school rank percentileTotal hours spentin college coursesMultiple Regression Analysis
27、:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Null hypothesisEstimation of the unrestricted modelAll interaction
28、effects are zero,i.e.the same regression coefficients apply to men and womenTested individually,the hypothesis that the interaction effects are zero cannot be rejectedMultiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicate
29、d,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Joint test with F-statisticAlternative way to compute F-statistic in the given caseRun separate regressions for men and for women;the unrestricted SSR is given by the sum o
30、f the SSR of these two regressionsRun regression for the restricted model and store SSRIf the test is computed in this way it is called the Chow-TestImportant:Test assumes a constant error variance accross groupsNull hypothesis is rejectedMultiple Regression Analysis:Qualitative Information 2012 Cen
31、gage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人A Binary dependent variable:the linear probability modelLinear regression when the dependent variabl
32、e is binaryLinear probability model(LPM)If the dependent variable only takes on the values 1 and 0In the linear probability model,the coefficients describe the effect of the explanatory variables on the probability that y=1Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.Al
33、l Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Does not look significant(but see below)Example:Labor force participation of married women=1 if in labor force,=0 ot
34、herwiseNon-wife income(in thousand dollars per year)If the number of kids under six years increases by one,the pro-probability that the woman works falls by 26.2%Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or
35、posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Example:Female labor participation of married women(cont.)Graph for nwifeinc=50,exper=5,age=30,kindslt6=1,kidsge6=0Negative predicted probability but no problem because no woman
36、 in the sample has educ 5.The maximum level of education in the sample is educ=17.For the gi-ven case,this leads to a predicted probability to be in the labor force of about 50%.Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied o
37、r duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Disadvantages of the linear probability modelPredicted probabilities may be larger than one or smaller than zeroMarginal probability effects sometimes logically
38、impossibleThe linear probability model is necessarily heteroskedasticHeterosceasticity consistent standard errors need to be computedAdvantanges of the linear probability modelEasy estimation and interpretationEstimated effects and predictions often reasonably good in practiceVariance of Ber-noulli
39、variableMultiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人More on policy analysis and pro
40、gram evaluationExample:Effect of job training grants on worker productivityPercentage of defective items=1 if firm received training grant,=0 otherwiseNo apparent effect of grant on productivityTreatment group:grant reveivers,Control group:firms that received no grantGrants were given on a first-com
41、e,first-served basis.This is not the same as giving them out randomly.It might be the case that firms with less productive workers saw an opportunity to improve productivity and applied first.Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be sc
42、anned,copied or duplicated,or posted to a publicly accessible website,in whole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Self-selection into treatment as a source for endogeneityIn the given and in related examples,the treatment status is probably related to other cha
43、racteristics that also influence the outcomeThe reason is that subjects self-select themselves into treatment depending on their individual characteristics and prospectsExperimental evaluationIn experiments,assignment to treatment is randomIn this case,causal effects can be inferred using a simple r
44、egressionThe dummy indicating whether or not there was treatment is unrelated to other factors affecting the outcome.Multiple Regression Analysis:Qualitative Information 2012 Cengage Learning.All Rights Reserved.May not be scanned,copied or duplicated,or posted to a publicly accessible website,in wh
45、ole or in part.烧伤病人的治疗通常是取烧伤病人的健康皮肤进行自体移植，但对于大面积烧伤病人来讲，健康皮肤很有限，请同学们想一想如何来治疗该病人Further example of an endogenuous dummy regressorAre nonwhite customers discriminated against?It is important to control for other characteristics that may be important for loan approval(e.g.profession,unemployment)Omitting important characteristics that are correlated with the non-white dummy will produce spurious evidence for discriminiationDummy indicating whether loan was approvedRace dummyCredit ratingMultiple Regression Analysis:Qualitative Information