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week08-1 - TA session 5 Econ 103 winter 2010 Wed Feb 3 2010...

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TA session 5 Econ. 103, winter 2010 Wed., Feb. 3, 2010, 10:00 a.m. and 1:00 p.m. in PP2400E. 1 Problem 1 First let’s summarize the data and get an idea of what we’re looking at. Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- hispanic | 820 .3646341 .4816212 0 1 citizen | 820 .7121951 .453016 0 1 black | 820 .0890244 .2849528 0 1 exp | 820 12.46949 1.597492 10 15 wage | 820 13.52635 14.96985 1.25 250.6615 -------------+-------------------------------------------------------- female | 820 .4280488 .4950979 0 1 educatio | 820 12.90732 3.141155 0 20 The problem asks you to estimate Y = β 0 + β 1 educ + β 2 exp + β 3 exp 2 + β 4 black + β 5 hispanic + β 6 citizen + in which Y is the log of the wage. 1.1 Do these coefficients give you elasticities? If not, how would you write the model so that β 1 represents an elasticity? Recall that an elasticity is a ratio of two percentage changes. e X,Y = X Y = dX/X dY/Y The coefficient β 1 equals dY/d educ . We know Y is the log wage, so dY = d log wage = dwage wage . So the coefficient does not represent an elasticity, dY 1 = d wage wage d educ but instead a “partial” or “semi” elasticity. It is the ratio of a percentage change in the wage to a unit change in years educated. If you like you can transform a semi-elasticity into a full-fledged elasticity by multiplying by the missing “educ.” e X,Y = d wage/wage d educ/educ = educ · d wage/wage d educ = educ · β 1 Alternatively you can rewrite the model so that the estimator β 1 estimates an elasticity. Let Y = β 0 X β 1 1 X β 2 2 X β 3 3 ... 1
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Taking logs, log Y = log β 0 + β 1 log X 1 + β 2 log X 2 + β 3 log X 3 ... and now, as you know from your course notes (11, page 6), the β 1 estimates an elasticity. 1.2 Now estimate the model Let’s first generate a new variable, which is the logarithm of the wage. gen logwage = log(wage) Let’s first generate a new variable, which is the logarithm of the wage. . gen logwage = log(wage) And while we’re at it, . gen exp2 = exp^2 Now, . regress logwage educ exp exp2 black hispanic citizen Source | SS df MS Number of obs = 820 -------------+------------------------------ F(
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