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Q1. Obtain a time-series of minimum of 35 observations, for three variables of your own choice of the country from the world development indicators (WDI) data source. However, the choice of variables should be guided by an economic model from Macroeconomics. These variables should be representing an economic model where one variable (Y) is deemed to be dependent on the others (Xs are independent variables). Provide full sources and definitions for those series. (10 marks) Q2. Produce (separate) time-series graphs of these variables in levels and in first differences. Examine these graphs for evidence of drift (trend) or unit roots. (5 marks) Q3. Write down fully an estimating equation that represents your underlying economic model (Hint: it may be easier to use natural logs) in the form: In Y. Bo + B1 In X1 + Ba in X₂+ U (5 marks) Q4. Perform appropriate tests for the presence of a unit root in each of the three series and comment on the findings. (15 marks) where it is the time subscript, and u is the disturbance term. Q5. Estimate your model by OLS and use this to perform a test for cointegration (Do NOT provide a discussion of the standard significance tests for this model) (20 marks) Q6. Compute the first difference for each time series. Perform appropriate tests for the presence of a unit root in each of the three series in the first differences and comment on the findings. Estimate your model in the first differences: A In Y₁ = Bo + B1A In X₁ + B₂ in X₂+ & (20 marks) Q7. Given your answers in Q4-Q6, explain whether Model (1) or Model (2) is more appropriate. Discuss the findings in your preferred equation with respect to the sign, size and statistical significance of the individual coefficients and the overall performance of the model represented by your chosen equation. (25 marks)

Q1. Briefly explain theoretically the association between economic growth with carbon emissions. Also, in the light of theory, briefly discuss the association of other variables listed above with carbon emissions. Obtain data on all variables listed above from WDI for a specific year (choose any one year between 2014-18) and at least 35 countries observations. Produce a histogram of per capita income and analysis and discuss the shape of the histogram. Label it and provide a title for it. (5 marks) 2 Q2. Obtain data required to compute the association between GDP per capita and CO2 emission/capita. Produce scatter plots of CO2 emission per capita (y-axis) against per capita income (x-axis), renewable energy consumption, and trade openness. Based on visual inspection, discuss any patterns and outliers in the data that emerge. Identify the outliers and discuss the impact of outliers on the regression analysis. (10 marks) Q3. Present and discuss the table of summary statistics. This table should contain at least the number of observations, mean, standard deviation, minimum, and maximum values for your chosen variables. (5 marks) Q4. Compute and present a correlation matrix. Discuss correlation between CO2 emission/capita, GDP per capita, Renewable energy consumption (% of total final energy consumption) and trade openness. (5 marks) Q5. (5a) Specify a regression model that explains how C02 emissions/ capita depends on explanatory variables in the light of theoretical association of independent variables with dependent variable and test an appropriate hypotheses. Estimate the model by applying an appropriate econometric method. Interpret your estimated results following theoretical associations between variables/hypotheses testing and by choosing an appropriate level of significance. Reflect your understanding of the overall degree of fit of the model. Present your estimated results in a table and discuss your findings. (10 marks) (5b) Based on the regression results in Q5(a), what are the marginal effects of GDP/ Capita, and renewable energy consumption (% of total final energy consumption). (5 marks) Q6. In the model specified in Q5, you decide to test the possibility that explanatory variable (s) is (are) irrelevant by dropping one or more variables from model and rerunning the equation. Discuss the reason why the variable(s) should and or should not be included in your model. Specify a final regression model which includes all relevant variable(s) that you identified as relevant explanatory variable(s) (Hint: be sure to use our four specification criteria). Present the results in a table and discuss them. (15 marks) Q7. Explain a distinction between an equation that is linear in the coefficients and one that is linear in variables. Examine whether log transformation of dependent and independent variables provides better estimates compared to regression analysis conducted using level-level regression model estimated in Q6. Furthermore, can you compare R-squared estimated results of level-level model with the estimated regression results of the double log regression model? If not, explain the rationale behind it. Present your estimated results using adouble log model in a table and discuss your findings. (15 marks) Q8. (Ba) Specify your final choice of estimated model following analysis conducted at 06 and Q7. What do we mean by heteroskedasticity? Apply alternate methods of testing for heteroskedasticity in your model. Discuss the strengths and weaknesses of those alternate methods for heteroskedasticity. Present your estimated model results in a table

and discuss the heteroskedasticity implications for estimated coefficients in your model. (15 marks) (8b) What are the remedies for heteroskedasticity? Use an alternate test to correct for heteroskedasticity in the estimated model and reproduce the estimated results based on the heteroskedasticity corrected standard errors in a table. Compare this estimated model with your estimated model results obtained in 8(a) and discuss your findings. (15 marks) The End