3. Let us consider more carefully the determinants of wages. As an initial attem
ID: 1149122 • Letter: 3
Question
3. Let us consider more carefully the determinants of wages. As an initial attempt to analyze the effects of education on wages, you estimate the univariate model: However, then someone points out to that some people are just "naturally" better workers than others, regardless of schooling. After giving it some thought, you hypothesize that IQ is a good measure of one's "natural" ability. Thus, you consider an alternative multivariate regression model of the form: (a) what is the interpretation of and . (b) If it is the case that IQ has no effect on wage (in which case the two variables would be said to be independent), how will a1 compare to a1? lated with each other, how will 1 compare to ai? attend school longer on average, will -. How do you think ai will compare to (c) If it is the case that IQ has a positive effect on wage and IQ and education are uncorre- (d) If it is the case that IQ has a positive effect on wage and individuals with high IQ alsoExplanation / Answer
a) a1: An additional year of education increases wages by a1 units.
a'1: Holding all IQ constant, an additional year of education increases wages by a'1 units.
b) If IQ has no effect on wages, then adding this new variable to our previous single regression model should not have any changes to our previous model. We added IQ to our previous model thinking that IQ and wages are positively correlated and that EDUC variable includes the effect of IQ. If this is the case, then adding the IQ variable should lower the coefficient on on EDUC i.e. a1 < a'1. Since IQ has no effects on wages, a1 will be very much equal to a'1.
c) If IQ has a positive effect on wage and IQ and education are uncorrelated, then we would not necessarily see huge differences between a1 and a'1 because the two variables are uncorrelated. There would be some difference of course because our previous model was ignoring the effects of other variables such as IQ that affect wages.
d) If IQ and EDUC are correlated and IQ has an effect on wages, then our previous model was biased and was overestimating the effects of EDUC on wages. In the previous model a1 was also picking up the effect of IQ on wages and thus the value of a1 is overestimated. Adding the IQ variable to the model should lower this overestimated value and therefore, we would have a1 < a'1 .
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