i)
The estimated coefficients in both the OLS and Logit models represent the relationship between the dependent variable (self-employment) and the independent variables (age, gender, Ed1, Ed2).
In the OLS model:
- The coefficient for age (0.009) suggests that for every year increase in age, the probability of being self-employed increases by 0.009, holding all other variables constant.
- The coefficient for gender (0.065) suggests that males are more likely to be self-employed compared to females, holding all other variables constant.
- The coefficient for Ed1 (0.014) suggests that completing a degree increases the probability of being self-employed, holding all other variables constant.
- The coefficient for Ed2 (-0.006) suggests that having a non-degree higher educational qualification decreases the probability of being self-employed, holding all other variables constant.
In the Logit model:
- The coefficient for age (0.097) suggests that for every year increase in age, the odds of being self-employed increase by a factor of exp(0.097), holding all other variables constant.
- The coefficient for gender (0.619) suggests that males have higher odds of being self-employed compared to females, holding all other variables constant.
- The coefficient for Ed1 (0.111) suggests that completing a degree increases the odds of being self-employed, holding all other variables constant.
- The coefficient for Ed2 (-0.043) suggests that having a non-degree higher educational qualification decreases the odds of being self-employed, holding all other variables constant.
ii)
To calculate the estimated probabilities that a man aged 40 with Ed1=1 is self-employed using the above models, we substitute the values into the equations.
For the OLS model:
OLS = - 0.151 + 0.009(40) + 0.065(1) + 0.014(1) – 0.006(0) = -0.151 + 0.36 + 0.065 + 0.014 = 0.288
The estimated probability that a man aged 40 with Ed1=1 is self-employed using the OLS model is 0.288.
For the Logit model:
Logit = -3.780 + 0.097(40) + 0.619(1) + 0.111(1) – 0.043(0) = -3.780 + 3.88 + 0.619 + 0.111 = 1.83
The estimated odds that a man aged 40 with Ed1=1 is self-employed using the Logit model is 1.83.
The following estimates were made from a sample of 100 individuals. Thedependent variable is 1 if the person is self-employed and 0 otherwise.
OLS = - 0.151 + 0.009age + 0.065gender + 0.014Ed1 – 0.006Ed2 (0.016) (0.003)(0.003)(0.008)(0.005)
Logit = -3.780 + 0.097Age + 0.619gender + 0.111Ed1 – 0.043Ed2 (0.168) (0.033)(0.033)(0.062)(0.047)
Where
Age = age in years; gender = 1 if male, 0 if female; Ed1 = 1 if completed a degree, 0 otherwise; Ed2 = 1 if has a non-degree higher educational qualification, 0 otherwise;. The figures in brackets are conventionally calculated standard errors for the OLS estimates, asymptotic standard errors for the probit estimates.
i) Interpret the estimated coefficients of both OLS and Logit model.
ii) What are the estimated probabilities that a man aged 40 with Ed1=1 is self- employed using the above models?
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