1) Lets suppose that we want to study how education and unemployment status have impact on happiness. We have two binary variables indicating happy (=1) or otherwise (=0), and unemployed (=1) or employed (=0), and years of schooling (edu) variable as a (nearly) continuous variable. Our logit estimates for a constant (that is, value of 1), edu, and unemployment are -1.32, 0.05 and -0.53, respectively. The sample means for years of schooling and unemployment variables are 12 and 0.32, respectively.

(a) Write down a latent variable model for happiness liking to the observed dependent variable.

(b) State the assumption that allows us to set up the probability of being happy to be a cumulative distribution function of logistic distribution.

(c) Calculate the chance (probability) of being happy for those who are unemployed with 12 years of schooling and the chance (probability) of being happy for those who are employed with 12 years of schooling. What is the effect of unemployment on being happy for those who have 12 years of schooling?

(d) Calculate the marginal effect of education (that we assume to be a continuous variable) on being happy for those who are unemployed with 12 years of schooling.

(e) Calculate PEA, the partial effect of education at the average of explanatory variables