Reference no: EM133586600

Econometrics

The following equation describes how the number of Facebook friends depends on your gender and on how long you have been having a Facebook account (measured in weeks):

fbfriends = β₀ + β₁weekold + β₂weekoldsq + δ₀female + u. (1)

The variable fbfriends denotes the number of Facebook friends, weekold is the number of weeks old your Facebook account is, while weekoldsq is weekold squared. Finally, female is equal to one if the account holder is female, zero otherwise. The estimation output from Gretl is the following:

1) What is the interpretation of the coefficient on female? Explain the statistical significance of the coefficient.

2) What is the equation that characterizes the marginal effect of weeks old on the number of Facebook friends?

3) What is the marginal effect of weeks old on Facebook friends for someone who opened her Facebook account 4 weeks ago?

Consider the following linear probability model

married_i = β₀ + β₁age_i + β₂IQ_i + ui. (2)

The variable married is a binary (dummy) variable equal to 1 if individual i is married and 0 if not married. The variable IQ is the intelligence quotient obtained by individual i using standardized tests. The estimation output in Gretl is the following:

 

4) Write down the estimated equation and explain the potential problems with estimating this linear probability model.

The White test for heteroscedasticity in Gretl gives the following results

5) What is heteroscedasticity? Based on the White test, is heteroscedasticity a problem in the estimation of Equation (2)?

6) Explain three potential solutions to the heteroscedasticity problem.

7) Explain the steps in the Weighed Least Squares estimation.

Consider the following alternative model:

marriedi = β₀ + β₁age_i + β₂IQ_i+ β₃exper_i + u_i. (3) where exper is the number of years of working experience.

8) Assume that exper should not be in the model. What happens if you estimate the incorrect Equation (3) instead of the correct model in Equation (2)?

9) Explain the omitted variable problem.

Based on Equation (3), we test the null H₀:β₁=β₃. The test in Gretl yields:

10) What is the interpretation of the linear restriction in the null hypothesis? Do you reject the null hypothesis? Explain.

Because the dependent variable married only takes the values of 1 and 0, we estimate the following probit regression model in Gretl:

11) Why is the probit estimation (Model 3) superior to the OLS estimation (Model 1)? What is the marginal effect of age on the probability of being married based on Model 3? Explain.