Analytical Methods in Economics and Finance

(i) Present the descriptive statistics of the variables Cases and GDP.
Comment on the means and measures of dispersion (standard deviation,
skewness, and kurtosis) of these two variables.
(ii) Estimate the following simple regression model of Cases on GDP:
Cases = β0 + β1GDP + u
Write down the estimated sample regression function and interpret both
estimated coefficients.
(iii) Now estimate the following simple regression model with a log-log
specification:
log(Cases) = β0 + β1 log(GDP ) + u
Report your regression results in a sample regression function. Interpret
the estimated coefficient of log(GDP). Provide an explanation on the sign
of the slope coefficient.
(iv) Estimate an extended model that relates the number of cases to the
countries’ GDP and population:
Cases = β0 + β1GDP + β2 POP + u
Report your results in a sample regression function. Based on your
estimates, how would you interpret the effect of POP on the number of
cases? What can you conclude when you compare the goodness of fit of
this regression model and that of the regression model in part (ii)?
(v) Now re-estimate the equation in (iv) by using the log of each variable.
That is, estimate the model:
log(Cases) = β0 + β1 log(GDP) + β2 log(POP) + u
Report your regressions results in a sample regression function. What is
the estimated elasticity of Cases with respect to GDP? Test whether the
model overall is statistically significant at 1% level.
(vi) Using the estimated model in (v), test whether the coefficient of
logPOP is greater than 1 at 5% level of significance.
(vii) Add the variable Pop65plus to the log-log equation in (v) and
estimate the following model.
log(Cases)= β0 + β1 log(GDP)+β2 log(POP)+ β3Pop65plus+ u
Interpret the coefficient of Pop65plus. Test whether log(POP) and
Pop65plus are jointly significant at 5% level of significance.
(viii) Create a dummy variable indicating whether or not a country is in
Oceania. Add the variable Oceania to the log-log equation in (v) and
estimate the following model.
log(Cases)= β0 + β1 log(GDP)+β2 log(POP)+ β3Oceania+ u
Report your regression results in a sample regression function. Interpret
the meaning of the coefficient for Oceania.
(ix) Create a dummy variable indicating whether or not a country is in
Europe. Add the variable Europe to the log-log equation in (v) and
estimate the following model.
log(Cases)= β0 + β1 log(GDP)+β2 log(POP)+ β3Europe+ u
Test whether Europe has a significant effect at the 1% level of
significance. What doyou infer about the explanatory power of the model
in part (ix) compared to the model that you estimated in part (viii)?
[2 + 3 + 4 + 4 + 4 + 2 + 4 + 3 + 4 = 30 Marks]

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