Question 1 a) A researcher is analyzing the determinants of Covid-19 vaccine uptake. The following model is estimated, using data collected on a sample of over 114,000 individuals in 17 countries. Respondent were asked a series of questions on COVID-19 vaccines. These include whether respondents would take a COVID-19 vaccine if available. The following regression equation is estimated: Vaccine, = B, Children, + B2Easy access, + ByWears mask, tu where: Vaccine, is an indicator variable taking value 1 if individual / agrees to be vaccinated, and 0 otherwise (note: in the table below this variable is reported as "Agrees to be vaccinated"); Children, is the number of children of individual i; Easy access, is an indicator variable that takes the value 1 if individual i perceives that vaccines are easily available in their location and 0 otherwise; Wears mask, is an indicator variable taking the value 1 if individual / usually wears a mask and 0 otherwise. i. Comment on the following table of estimation results. What conclusions can we draw in relation to the determinants of agreeing to be vaccinated? Dept. Var. Agrees to be vaccinated Children -0.015 (0.004) Easy access 0.113 (0.016) Wears masks 0.098 (0.026) Standard errors in parentheses ii. The specification contains only a limited number of regressors. Are there other variables that you think should be included in the specification? Justify your answer. iii. The results presented in the previous table are based on a linear probability model. Discuss your concerns about using the linear probability model. b) A sample of Irish households was taken to investigate how far Irish households tend to travel when they take vacations in Ireland. The following model was estimated: Kilometres, = B1 + ByIncome, + ByAge, + B, Kids, + & Where Kilometres is the distance in kilometres per year, Income is household income, Age is the average age of the adult members of the household, Kids is the number of kids in the household. Assume that E(=) = 0 and var(z) = 92 Income . Discuss in detail how you would estimate this regression equation. c) Consider two nonstationary time series processes, {x,} and {y,) . Assume that they are both integrated of order 1, {x,} ~I(1) and (y,} ~I(1). Explain in detail the meaning of cointegration. How would you test for cointegration between the two series