Consider the regression model \(W A G E=\beta_{1}+\beta_{2} E D U C+e\), where \(W A G E\) is hourly wage rate in U.S. 2013 dollars and \(E D U C\) is years of education, or schooling. The regression model is estimated twice using the least squares estimator, once using individuals from an urban area, and again for individuals in a rural area.

a. Using the estimated rural regression, compute the elasticity of wages with respect to education at the "point of the means." The sample mean of WAGE is \(\$ 19.74\).

b. The sample mean of \(E D U C\) in the urban area is 13.68 years. Using the estimated urban regression, compute the standard error of the elasticity of wages with respect to education at the "point of the means." Assume that the mean values are "givens" and not random.

c. What is the predicted wage for an individual with 12 years of education in each area? With 16 years of education?

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Urban Rural = WAGE -10.76 +2.46 EDUC, N = 986 (2.27) (0.16) (se) WAGE = -4.88 +1.80 EDUC, N = 214 (se) (3.29) (0.24)