Chapters3and4

1. Wooldridge Textbook, Chapter 3, Computer Question C6.[Small Note/Point of clarification:log(wage)isequivalenttoln(wage)forWooldridge, despitethesetwothings technically being different mathematical objects.Therefore, when you see log(wage), just use ln(wage).]

2. UsetheWAGE2dataagain.

a. Regressln(wage)oneducandIQ. Reportandinterpretboththecoefficienton

educandthecoefficientonIQ.

b. Nowdothefollowing:

1. RegresseduconIQand save the residuals from this regression (hint:use the 'predict'commandaftertheregressionwiththeappropriateoptionafterthe comma,justlikewedidinclass).Let'slabeltheresidualse^ducr.[Remember: ifyouestimate themodeleduci=0+1IQi+iandobtainfitted values (ormodelpredictions)ase^duci=0+1IQi,thenthe estimated residual ise^ducr=educie^duci=educi01IQi.]

2. Regress ln(wage) one^ducr.Report and interpret the coefficient one^ducr.How doesitcomparetothecoefficientoneducfrompart(a)?Giventherelationship betweenthecoefficienthereandthatinpart(a),whatcanyousayabout how to interpret the estimated coefficients in a multiple regression? (Hint: we talked about the 'partialling out' interpretation in class.There is also a great discussion in Chapter 3.)

c. Nowregressln(wage)onIQonlyandsavetheresiduals fromthisregression.Let's call these residualsln(^wage)r.Now regressln(^wage)rone^ducr(from above) and reportthecoefficient.Howdoesitcomparetotheestimated coefficientfrompart (a)andestimated coefficientfrompart(b)?

ln(^wage)risthepartofln(wage)that isindependentofIQande^ducris the part ofeducthat is independent ofIQ.Given this knowledge, expand here on your explanation in part (b) about how to interpret estimated coefficients in a multiple regression.

3. LoadtheStatadatasetCRIME1.dtafromtheAssignment3folderonourclasswebsite.

a. Regressnarr86onpcnv,ptime86,andqemp86.Howdoesemploymentin1986affectarrests?Is it statistically significant at the 5% level on a two-sided test.

b. Is the estimated coefficient onqemp86statistically different from 0.1 at the 5% level using a two-sided test?

c. The data contains information on demographic characteristics.Add to the model thevariablesblack,hispan,born60, whichareindicatorvariablesforBlack and Hispanic ethnicity, and being born after 1960.Interpret the estimated coefficients for each of these variables.Are they individually significant?

d. TheR2increases from the first to the second specification, which is not surprising. Doesthisindicatethatthedemographicvariablesarejointly statisticallysignificant? Conduct a formal statistical test of this hypothesis by estimating both the restricted and unrestricted models and using the relevant information to calculate the test statistic and then conduct the test.Verify that you get the same answer using Stata'stestcommand.

4. ComputerquestionC9inChapter4ofWooldridgeTextbook.