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Consider a dataset containing the following variables: government expenditure on healthcare (HeathEi ), gross domestic product (GDPi ), population (Popi ), and capital stock (Capitali ) for 153 countries in 2019. Economic theory suggests that government per capita expenditure on Heath Care has a positive effect on per capita GDPi . You estimate the following regression: perGDP \ i = 0.445 (0.022) + 0.443 (0.252) perHeathEi + 0.914 (0.121) perCapitali , where perGDPi = GDPi Popi , perHeathEi = HeathEi Popi , and perCapitali = Capitali Popi , and i denotes a particular country. (a) (10 marks) Discuss whether we can interpret the OLS estimate for \beta 2 causally. In your answer, clearly define what unbiasedness is and the direction of bias. (b) (10 marks) The dataset includes a continuous variable capturing the percentage of the cabinet members in the country i holding a Ph.D. degree, PhDi . A researcher wants to use this variable as an instrumental variable for HeathEi . Explain the intuition behind this approach and the relevant conditions. Do you think this suggestion is sound? Explain. (c) (10 marks) The dataset also contains a dummy variable Democratici which equals 1 if country i is democratic, 0 otherwise. Assuming homoskedasticity, discuss how you could test whether the effect of government expenditure on Heath Care per capita is statistically higher for democratic countries. Clearly indicate the regression you would run and the test you would use.