《计量经济学导论》ppt课件.ppt

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1、Chapter 7,Multiple Regression Analysis with Qualitative Information,Wooldridge: Introductory Econometrics: A Modern Approach, 5e,Qualitative InformationExamples: gender, race, industry, region, rating grade, A way to incorporate qualitative information is to use dummy variablesThey may appear as the

2、 dependent or as independent variablesA single dummy independent variable,Dummy 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 than a man (holding other things fixed),Multiple Regression Analysis: Qualitative Information,Graphical Il

3、lustration,Alternative interpretation of coefficient:i.e. the difference in mean wage between men and women with the same level of education.Intercept shift,Multiple Regression Analysis: Qualitative Information,Dummy variable trap,This model cannot be estimated (perfect collinearity),When using dumm

4、y variables, one category always has to be omitted:,Alternatively, one could omit the intercept:,The base category are men,The base category are women,Disadvantages: 1) More difficult to test for diffe-rences between the parameters2) R-squared formula only validif regression contains intercept,Multi

5、ple Regression Analysis: Qualitative Information,Estimated wage equation with intercept shiftDoes that mean that women are discriminated against?Not necessarily. Being female may be correlated with other produc-tivity characteristics that have not been controlled for.,Holding education, experience,

6、and tenure fixed, women earn 1.81$ less per hour than men,Multiple Regression Analysis: Qualitative Information,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

7、other things are controlled for; i.e. part of the difference is due to differ-ences in education, experience and tenure between men and women,Not 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$.,Mult

8、iple Regression Analysis: Qualitative Information,Further example: 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

9、 employee,Dummy indicating whether firm received training grant,Multiple Regression Analysis: Qualitative Information,Using dummy explanatory variables in equations for log(y),Dummy indicating whether house is of colonial style,As the dummy for colonial style changes from 0 to 1, the house price inc

10、reases by 5.4 percentage points,Multiple Regression Analysis: Qualitative Information,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

11、 category (which becomes the base category),Multiple Regression Analysis: Qualitative Information,Incorporating ordinal information using dummy variablesExample: City credit ratings and municipal bond interest rates,Municipal bond rate,Credit rating from 0-4 (0=worst, 4=best),This specification woul

12、d 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 wor

13、st rating (= base category).,Multiple Regression Analysis: Qualitative Information,Interactions involving dummy variablesAllowing for different slopesInteresting hypotheses,= intercept men,= intercept women,= slope men,= slope women,Interaction term,The return to education is the same for men and wo

14、men,The whole wage equation is the same for men and women,Multiple Regression Analysis: Qualitative Information,Graphical illustration,Interacting both the intercept and the slope with the female dummy enables one to model completely independent wage equations for men and women,Multiple Regression A

15、nalysis: Qualitative Information,Estimated wage equation with interaction term,No evidence against hypothesis that the return to education is the same for men and women,Does this mean that there is no significant evidence of lower pay for women at the same levels of educ, exper, and tenure? No: this

16、 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 Information,Testing for differences in regression functions across groupsUnrestricted model (contains full set o

17、f interactions)Restricted model (same regression for both groups),College grade point average,Standardized aptitude test score,High school rank percentile,Total hours spentin college courses,Multiple Regression Analysis: Qualitative Information,Null hypothesisEstimation of the unrestricted model,All

18、 interaction effects are zero, i.e. the same regression coefficients apply to men and women,Tested individually, the hypothesis that the interaction effects are zero cannot be rejected,Multiple Regression Analysis: Qualitative Information,Joint test with F-statisticAlternative way to compute F-stati

19、stic 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 erro

20、r variance accross groups,Null hypothesis is rejected,Multiple Regression Analysis: Qualitative Information,A Binary dependent variable: the linear probability modelLinear regression when the dependent variable is binary,Linear probability model (LPM),If the dependent variable only takes on the valu

21、es 1 and 0,In the linear probability model, the coefficients describe the effect of the explanatory variables on the probability that y=1,Multiple Regression Analysis: Qualitative Information,Does not look significant (but see below),Example: Labor force participation of married women,=1 if in labor

22、 force, =0 otherwise,Non-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,Example: Female labor participation of married women (cont.),Grap

23、h for nwifeinc=50, exper=5, age=30, kindslt6=1, kidsge6=0,Negative predicted probability but no problem because no woman 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%

24、.,Multiple Regression Analysis: Qualitative Information,Disadvantages of the linear probability modelPredicted probabilities may be larger than one or smaller than zeroMarginal probability effects sometimes logically impossibleThe linear probability model is necessarily heteroskedasticHeterosceastic

25、ity consistent standard errors need to be computedAdvantanges of the linear probability modelEasy estimation and interpretationEstimated effects and predictions often reasonably good in practice,Variance of Ber-noulli variable,Multiple Regression Analysis: Qualitative Information,More on policy anal

26、ysis and program evaluationExample: Effect of job training grants on worker productivity,Percentage of defective items,=1 if firm received training grant, =0 otherwise,No apparent effect of grant on productivity,Treatment group: grant reveivers, Control group: firms that received no grantGrants were

27、 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 Information,Self-selection into treatment

28、 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

29、 evaluationIn experiments, assignment to treatment is randomIn this case, causal effects can be inferred using a simple regression,The dummy indicating whether or not there was treatment is unrelated to other factors affecting the outcome.,Multiple Regression Analysis: Qualitative Information,Furthe

30、r 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 discriminiation,Dummy indicating whether loan was approved,Race dummy,Credit rating,Multiple Regression Analysis: Qualitative Information,