Model comparison is very important in econometric analysis. Mr Homoscedasticity Mbewe, a Senior Researcher at the Ministry of Finance was conducting an analysis into factors that influence consumer loan default in Zambia. He obtained the following restricted model (model 1): Variable P-value Coefficient Model Values Age 0.08 0.03 R-squared=0.66 Income 0.05 0.08 ESS=3973 Marital status 0.01 0.10 Model 2: The unrestricted model has additional variables of 'Employment status' with 0.31 P-value and - 0.08 coefficient value; and 'Financial literacy' with 0.23 p-value and 0.013 coefficient value. The sample size (n) of his study was 542 and he used 5% level of significance in his estimation. The RSS value of the unrestricted model is 2023.61 i) Using the F-test, demonstrate how Mr. Homoscedasticity can conduct his model comparison (between restricted and the unrestricted models). [10 Marks] ii) Given the information below, comment on the model fit and compare your conclusions to those under the F-test conducted in (i) [7 Marks]

Criteria Model 1 Model 2 AIC 4020.12 4068.53 BIC 4055.08 4157.82

Adjusted R-squared 0.68 0.64

iii) Instrumental variables are important in some sections of econometric analysis. As a student of econometrics, explain the concept of instrumental variables and situations in which they are useful. [5 Marks]

iv) Explain one possible variable state of the employment variable given individuals were asked whether they were employed or not. [3 Marks]

v) In the second model, explain how you can interpret the employment variable assuming it is significant, and in the 'level-level' model specification. Note that the coefficient of employment is negative.