1. Consider the following estimated regressions log(wage) 1 +0.05union wage 30 1
ID: 2946681 • Letter: 1
Question
1. Consider the following estimated regressions log(wage) 1 +0.05union wage 30 10uniorn union 0.2 + 0.0510 union-0.20.05log(IQ) log(wage) 10.93 log(educ) + 0.04exper 0.0006exper2 0.17female -0.011femaleexper where, wage is in dollars per hour, union is a dummy variable that takes 1 when the worker is unionized, IQ is in points, education and experience are in years and female is another binary variables that takes the 1 when the worker is female (a) Provide an interpretation for the coefficient on union in equations (1) and (2). How are they different? (b) Provide an interpretation for the coefficient on IQ in equations (3) and (4). How are they different? In the following, you need to be explicit about the ceteris paribus assumption. (c) Provide an interpretation for the coefficient on educ in equation (5) (d) What is the marginal contribution of experience to log(wage) in equation (5)? Is this contribution constant or it depend on other factors? (e) What is the marginal contribution of female to log(wage) in equation (5)? Is this contribution constant or it depend on other factors? (f) Provide an interpretation for the coefficient on experience in equation (5) (g) Provide an interpretation for the coefficient on experience in equation (5) (h) Provide an interpretation for the coefficient on female in equation (5). (i) Provide an interpretation for the coefficient on the interaction between female and experience in equation (5).Explanation / Answer
(a) The coefficient of union in equation (1) indicates that if we change union by 1 unit we would expect our dependent variable variable i.e. wage to change by 100*(0.05) = 5%. The coefficient of union in equation (2) indicates that If you change independent variable i.e. union by one, we would expect dependent variable i.e. wage to change by 10.
(b) The coefficient of IQ in equation (3) indicates that If you change independent variable i.e. IQ by one, we would expect dependent variable i.e. union to change by 0.05. The coefficient of IQ in equation (4) indicates that If we increase independent variable i.e. IQ by one percent, we expect union to increase by (0.05/100)=0.0005 units of union.
(c) The coefficient of educ in equation (5) indicates that if we change educ by one percent, we would expect wage to change by 0.93 percent.
(d) The marginal contribution of variable educ on log(wage) is if we change educ by one percent, we would expect wage to change by 0.93 percent. This contribution is not constant, it depends on other variables.
(e) The marginal contribution of variable female on log(wage) is if we change female by 1 (unit), we would expect our wage variable to change by 100*0.17 = 17 percent. This contribution is not constant, it depends on other variables.
(f) The coefficent if experiance in equation 5 indicates that if we change experiance by 1 (unit), we would expect our wage variable to change by 100*0.04=4 percent.
(g) The coefficent if experiance2 in equation 5 indicates that if we change experiance by 1 (unit), we would expect our wage variable to change by 100*0.04=4 percent.
(h) The coefficient of female in equation (5) indicates that the sign of coefficent is negative so the relationship is concave.
(i) The coefficient of the interaction between female and experiance in equation (5) indicates that the sign of coefficent is negative so the relationship is concave.
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