ECON6034: Econometrics and Business Statistics - Economics Assignment Help

Assignment Task:

Question 1 

Suppose we wish to estimate the relationship between food expenditure and some of its determinants. The file Foodexp.xlsx contains 200 observations from a cross-section of households for the following variables. 

Foodexpi: Weekly expenditure on food (excluding restaurants) in dollars.

Income: Weekly household income in dollars.

Children: Number of dependent children living in the household.

Retired: A binary (0/1) indicator of whether the head of the household is retired {ret.=1}. 

(a) Consider a regression model 

Foodexp = β₀ + β₁ log(Income )+β₂ Children + β₃ Retired_i + ε 

Estimate the model using Eviews and provide the summary results (A summary results should include fitted equation with coefficients, standard error, t-statistic, p-value, sample size, F-statistic and R-squared). 

(b) Interpret the coefficient estimates and their significance at the 5% significance level. [4 marks] 

(c) Does the sign of the coefficients agree with your expectations? Comment. 

(d) Based on the regression output, if Income increases by 10% what is the estimated change in Foodexp, holding Children and Retired constant. [4 marks] 

(e) Test the overall validity of the regression model at the 5% significance level. State the hypotheses, restricted and unrestricted model, test statistics and its distribution when null hypothesis is true, critical value, and your conclusion. 

(f) Construct 95% confidence interval for β , the slope of the log(Income) variable and interpret your results. 

(g) Based on your answer in part (f), without performing a hypothesis test, would you reject the hypothesis H:β = 100, H:β ≠ 100. Explain? [4 marks] 

(h) Plot the least squares residuals against log(Income) and comment on the pattern. Is there any evidence of heteroscedasticity? [4 marks] 

(i) Test for the existence of heteroscedasticity at the 5% significance level. Use the Breusch-Pagan-Godfrey test and attach your Eviews results. Clearly states all steps in your test; null and alternative hypotheses, the auxiliary regression and the test statistic, critical value, your decision and the conclusion. [6 marks] 

(j) Re-estimate your model with robust standard errors and attach your Eviews output. Compare your results with the output in part (a). Comment. [4 marks] 

(k) Now run the following regression model: 

Foodexp = α + α log(Income) + e 

(l) Compare your model that with part (a). Which model would you choose? And Why? 

Question 2 

A researcher wants to analyse the relationship between the three-month T-bill rate, tb3, the annual inflation rate, inf based on the consumer price index, and the federal budget deficit, def as a percentage of GDP and develops the following model. The data is stored under the file name is intdef_A.xlsx 

tb3 = α + α inf + α def + ε 

(a) Use Eviews to obtain a line plot among these three variables (one graph) and comment on the plot. (Hint: to make the graph in Eviews: Quick → Graph → tb3 inf def →Ok →Line & Symbol → OK.) 

(b) Obtain sample correlation coefficient between these variables and comment on the strength of the relationships? (Hint: to obtain correlation in Eviews: Quick → Group Statistics → Correlations → tb3 inf def → Ok.) 

(c) Estimate the above regression model and provide the Eviews output. 

(d) Interpret the coefficients α and α . Does the sign of the coefficients agree with your expectations? Explain. 

(e) Provide and interpret the coefficient of determination, R . 

(f) Plot the residuals of the model and comment on any pattern.

(g) Add a one lag of inf and def to the equation in part (a) and re-estimate your model. and report the result. Are the coefficients for the two lag variables individually significant at the 5% level? To add lag variables in Eviews type inf(-1) def(-1)

(h) Conduct the second order autocorrelation test for the model in part (c) at the 5% significance level. Attach your Eviews results. Clearly states all steps in your test; Null and alternative hypotheses, the auxiliary regression and the test statistic, critical value, your decision and the conclusion. 

(i) Re-estimate your model with Newey-West standard errors and provide your output. Compare your results with the output in part (c). Comment.

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