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.Chapter 7 Multiple Regression Analysis: Qualitative InformationWooldridge: Introductory 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.Multiple Regression Analysis: Qualitative Information7.1 Describing Qualitative Information7.2 A Single Dummy Independent Variable7.3 Using Dummy Variables for Multiple Categories7.4 Interactions Involving Dummy Variables7.5 A Binary Dependent Variable: The Linear Probability Model7.6 More on Policy Analysis and Program EvaluationAssignments: Promblems 5, 7, 9, Computer Exercises C2, C6, C7, C9 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.Examples: gender, race, industry, region, rating grade, A way to incorporate qualitative information is to use dummy variablesThey may appear as the dependent or as independent variablesThe name in this case indicates the event with the value one.Why do we use the values zero and one to describe qualitative information?Multiple Regression Analysis: Qualitative Information7.1 Describing Qualitative InformationChapter 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.Multiple Regression Analysis: Qualitative Information7.2 A Single Dummy Independent Variable (1/7)ChapterIntercept shiftDefinition of dummy variableInterpret d0Base group or benchmark groupImplication of the same slope for both genders 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.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 intercept:The base category are menThe base category are womenMultiple Regression Analysis: Qualitative Information7.2 A Single Dummy Independent Variable (2/7)ChapterDisadvantages: 1) More difficult to test for diffe-rences between the parameters2) R-squared formula only validif regression contains intercept 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.Estimated wage equation with intercept shift (Example 7.1)Holding education, experience, and tenure fixed, women earn 1.81$ less per hour than menMultiple Regression Analysis: Qualitative Information7.2 A Single Dummy Independent Variable (3/7)Chapter 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.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 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$.Multiple Regression Analysis: Qualitative Information7.2 A Single Dummy Independent Variable (4/7)Chapter 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.Example 7.3: Effects of training grants on 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 Information7.2 A Single Dummy Independent Variable (5/7)Chapter 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.Using dummy explanatory variables in equations for log(y)Dummy indicating whether 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 Information7.2 A Single Dummy Independent Variable (6/7)Chapter 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.Multiple Regression Analysis: Qualitative Information7.2 A Single Dummy Independent Variable (7/7)ChapterExample 7.5 Log Hourly Wage EquationMale is base group: Female is base group: 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.Holding other things fixed, married women earn 19.8% less than single men (= the base category)Define membership in each category by a dummy variableLeave out one category (which becomes the base category)Multiple Regression Analysis: Qualitative Information7.3 Using Dummy Variables for Multiple Categories (1/4)Chapter 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.Multiple Regression Analysis: Qualitative Information7.3 Using Dummy Variables for Multiple Categories (2/4)Chapterwage1.wf1series marrmale=0series marrfem=0series singfem=0smpl if married=1 and female=0marrmale=1smpl if married=1 and female=1marrfem=1smpl if married=0 and female=1singfem=1smpl allls log(wage) c marrmale marrfem singfem educ exper exper2 tenure tenure2 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.Incorporating ordinal information using dummy variablesExample: City credit ratings and municipal bond interest ratesMunicipal bond rateCredit rating from 0-4 (0=worst, 4=best), ) implying a constant partial effect.This specification would probably not be appropriate as the credit rating only contains ordinal information. A better way to incorporate 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 InformationChapter7.3 Using Dummy Variables for Multiple Categories (3/4)Test a constant partial effectThat is, 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.Multiple Regression Analysis: Qualitative InformationChapter7.3 Using Dummy Variables for Multiple Categories (4/4)Example 7.7 Effects of Physical Attractiveness on Wagebeauty.wf1For men:For women: 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.Multiple Regression Analysis: Qualitative Information7.4 Interactions Involving Dummy VariablesChapter7.4.1 Interactions among Dummy Variables7.4.2 Allowing for Different Slopes7.4.3 Testing for Differences across Groups 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.Multiple Regression Analysis: Qualitative InformationChapter7.4.1 Interactions among Dummy Variables (1/2)Section 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.Multiple Regression Analysis: Qualitative Information7.4.1 Interactions among Dummy Variables (2/2)The base group for both models is single men.Model (1) is convenient for testing for wage differentials between any group and the base group.Model (2) allows us to test the hypothesis that gender differential does not depend on marital status (equivalently, that the marriage differential does not depend on gender).Example 7.9 Effects of Computer Usage on WagesChapterSection 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.Allowing for different slopesInteresting hypothesesInteraction termThe return to education is the same for men and womenThe whole wage equation is the same for men and womenMultiple Regression Analysis: Qualitative Information7.4.2 Allowing for Different Slopes (1/3)ChapterSection 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.Estimated wage equation with interaction term (wage1.wf1)ls log(wage) c female educ female*educ exper exper2 tenure tenure2No evidence against hypothesis 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 educ = 12.5 (= average education).Multiple Regression Analysis: Qualitative InformationChapterSection7.4.2 Allowing for Different Slopes (2/3) 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.Multiple Regression Analysis: Qualitative InformationChapterSection7.4.2 Allowing for Different Slopes (3/3)(educ-12.5)0.296 female(0.036) 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.Unrestricted model (contains full set of interactions)Restricted model (same regression for both groups)College grade point averageStandardized aptitude test scoreHigh school rank ercentileTotal hours spentin college coursesMultiple Regression Analysis: Qualitative InformationChapterSection7.4.3 Testing for Differences in Regression Functions across Groups (1/6) 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.Null hypothesisEstimation of the unrestricted modelAll interaction 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 InformationChapterSection7.4.3 Testing for Differences in Regression Functions across Groups (2/6) 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.Joint test with F-statisticgpa3.wf1smpl if ccrsgpanaequation eq_pool.ls cumgpa c sat hsperc tothrsequation eq_dums.ls cumgpa c female sat female*sat hsperc female*hsperc tothrs female*tothrsscalar f_dum=358*(eq_dums.r2-eq_pool.r2)/(1-eq_dum.r2)/4 f_dum=8.18Null hypothesis is rejectedMultiple Regression Analysis: Qualitative InformationChapterSection7.4.3 Testing for Differences in Regression Functions across Groups (3/6) 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.Alternative way to compute F-statistic in the given caseRun separate regressions for men and for women; the unrestricted SSR is given by the sum of 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 groupsMultiple Regression Analysis: Qualitative InformationChapterSection7.4.3 Testing for Differences in Regression Functions across Groups (4/6)SSRur=SSR1+SSR2 ,SSRr=SSRP 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.Multiple Regression Analysis: Qualitative InformationChapterSection7.4.3 Testing for Differences in Regression Functions across Groups (5/6)Chow statistic (gpa3.wf1)smpl if ccrsgpanaequation eq_pool.ls cumgpa c sat hsperc tothrsscalar ssrp=eq_pool.ssr ssrp=85.515smpl if ccrsgpana and female=1equation eq_female.ls cumgpa c sat hsperc tothrsscalar ssr1=eq_female.ssr ssr1=19.603smpl if ccrsgpana and female=0equation eq_male.ls cumgpa c sat hsperc tothrsscalar ssr2=eq_male.ssr ssr2=58.752scalar f=358*(ssrp-ssr1-ssr2)/(ssr1+ssr2)/4f=8.18 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.Multiple Regression Analysis: Qualitative InformationChapterSection7.4.3 Testing for Differences in Regression Functions across Groups (6/6)Two ways to test that there is only a shift in the intercept.test I:smpl if ccrsgpanaequation eq_dumc.ls cumgpa c female sat hsperc tothrsscalar f_c=358*(eq_dumc.ssr-eq_dums.ssr)/(eq_dums.ssr)/3 f_c=1.53test II:scalar f_cc=358*(eq_dumc.ssr-ssr1-ssr2)/(ssr1+ssr2)/3 f_cc=1.53Eq_dums.ssr=ssr1+ssr2 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.Linear 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 Information7.5 A Binary Dependent Variable: The Linear Probability Model (1/5)Chapter 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.Does not look significant (but see below)Example: Labor force participation of married women=1 if in labor force, =0 otherwiseNon-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 Information7.5 A Binary Dependent Variable: The Linear Probability Model (2/5)Chapter 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.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 in the sample has educ =0.5inlf_predict=1smpl if inlf=inlf_predictscalar correct=obssmpl/obsrange correct=0.734smpl allChapter 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.Example: 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-come, 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 Information7.6 More on Policy Analysis and Program Evaluation (1/3)Chapter 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.Self-selection into treatment as a source for endogeneityIn the given and in related examples, the treatment status is probably related to other characteristics 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 regressionThe dummy indicating whether or not there was treatment is unrelated to other factors affecting the outcome. Multiple Regression Analysis: Qualitative InformationChapter7.6 More on Policy Analysis and Program Evaluation (2/3) 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.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 InformationChapter7.6 More on Policy Analysis and Program Evaluation (3/3)