Suppose you are trying to uncover the relationship between education and wages,

Question

Suppose you are trying to uncover the relationship between education and wages, where education is measured with years of school completed and wage is measured by hourly wage. You know the population model is: 5. wage = 0 + |school + 2ttl-exp wage hourly wage school-years of schooling completed tl_exp total years of work experience a. Using the dataset nlsw_ps2.dta (see instructions at end of problem set for obtaining the dataset and inputting it into Stata) you run the model specified above. To do this in Stata run the following command after the dataset has been opened in the program: regress wage school ttl_exp Report output. What is the interpretation of the estimated B1? b. What if your dataset didn't have a measure for total work experience so instead you ran this model: wage = 0 + |school and obtained estimates Bo and B1. Would you expect B1 to be biased? If so, in what direction would you expect the bias to be? Show your work.

Explanation / Answer

a) b1^ =   0.628457

it means when we increase years of schooling completed , there will be increase in b16 in y

that is wage will increase by 0.628457 units

b)

had total work experience be removed , we expect b1~ to be biased

delta1~ is sample covariance between school and workexperience

E(b1~) = E(b1^ + b2^ delta1~)

= E(b1^) + delta1~* E(b2^)

= b1 + b2* delta1~

bias (b1~) = E(b1~) -b` = b2 delta1~

delta1~ is sample covariance between school and workexperience , which is positive as more years of school completed, more will be work experience

b2 is positive too ,

b2 *delta1~ >0

hence it will be positive bias.

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