Consider the following OLS results for a wage model in which education, tenure, tenure squared, experience, experience squared and a dummy variable equal to 1 if the individual is a female and zero otherwise are the explanatory variables:
Number of jobs = 526
F (6, 519) = 68.18
Prob > F = 0.000
R squared = 0.440
Adjusted R squared = 0.4343
lwage Coefficient / standard error = t p-value
Female -0.2926511 / 0.0358055 = -8.28 0.000
Education 0.0801967 / 0.00675773 = 11.87 0.000
Experience 0.0294324 / 0.0049752 = 5.92 0.000
Tenure2 0.0317139 / 0.0068452 = 4.63 0.000
Experience2 -0.0005287 / 0.0001073 = -5.43 0.000
Constant 0.4166691 / 0.0989279 = 4.21 0.000
a) Write the mathematical model.
lwage = + B1 Female + B2 Education + B3 Experience + B4 Tenure + B5 Experience + error t
b) What might be the theoretical reasons for including the squared terms in tenure and experience?
The squared terms are to make them have two curves, for example a curved graph line with wage of the Y axis and experience on the X axis, that represents the diminishing marginal return to scale. Where the non-linear impact on wage has a negative coefficient. The data can tell us that the more experience someone gains can have an negative impact on wage after a certain point, sometimes it can be insignificant.
c) Carefully interpret the estimated coefficient on the female dummy. Do you reject the null hypothesis that the true parameter on female is equal to zero?
The female coefficient is a qualitative variable, meaning it is relative – binary. First, the significance level is 1%, second the sign is negative and third female earn less than 29% less, reject as of P-value.
d) How strong is the evidence that experience has nonlinear effects on log wage? Show a graph of the implied relationship between experience and log wage.
Experience is squared to capture the non-linear effects on log wage. The graph would have log wage on the Y axis and Experience on the X axis, showing a convex curve.
e) Consider a young individual entering the labour market for the first time in the beginning of year 1. By the end of year 1, how much will the expected wage have grown? Carefully explain your calculations.
The year experience would be plus the corresponding coefficient number: 0.0294324 or 29% to the wage.
f) Interpret F-test results.
The F-test represents the overall validity of the model.
H0: B1 = B2 = B3 = B4 = B5 = 0
H1: At least one coefficient is unequal to zero.
As we reject the null hypothesis of f-test, at least one of the variables (coefficients) is statistically significant, so the model has statistical validity.