1. Consider the model given by ln Y = β₁ + β₂ ln X₂ - β₃ ln X₃ + β₄ ln X₄ + u, where Y= per capita consumption of tea, X₂ = real disposable per capita income (measured in dollars), X₃ = price of sugar (measured in dollars per pound), X₄ = price of coffee (measured in dollars per pound). If we want to test the hypothesis that coffee and tea are unrelated products, what is the null going to be?

2. Consider a model where all of the assumptions of the simple regression model hold (i.e. the model is linear in parameters and correctly specified, the disturbance term have independent normal distributions with zero mean and constant variance), but the regressors are stochastic and the values of the disturbance term have independent distributions, and the OLS regression estimator for the slope coefficient (β₂) is given by the following equation.
Would this estimator be a biased or an unbiased estimator?

3. Consider the multiple regression equation:
where for a given time period t, I = actual rate of inflation, U = unemployment rate, and E = expected inflation rate. All variables are measured in percentage terms. Which of the following best describes an interpretation of the regression coefficients?

4. Consider the multiple regression model: EARNINGS = β₁ + β₂ HEIGHT + β₃EDUCATION + β₄EXPERIENCE + u. What test would you perform if you wished to test the following null hypothesis?

5. Suppose the true specification of a model is Y = β₁ + β₂X₂ + β₃X₃ + u, but the model is misspecified and a simple regression model is estimated instead. What is the consequence of omitting one of the explanatory variables?

6. Consider the formula for an F test given by
, where RSS_R and RSS_UR stand for Residual Sum of Squares for the restricted and the unrestricted model respectively, m = number of linear restrictions or the number of regressors omitted from the model, and (n-k) is the degrees of freedom in the unconstrained model. For the model given by: Y_i = β₁ + β₂ X_2i + β₃ X_3i +………+ β_k X_ki + u_i, which of the following nulls can be tested using the above F-test?

7. Which of the following is NOT an advantage of panel data over cross-section data?

8. Suppose we have data for the time period 2000-2010 for real GDP in the US. We calculate a semi-logarithm model given by: ln GDP(t) = 9.5206+ 0.0351t, where GDP = real GDP and t = time per year. How would you interpret the coefficient of t in this model?

9. Consider the model given by ln Y = β₁ + β₂ ln X₂ + β₃ ln X₃ + β₄ ln X₄ + u, where Y = per capita consumption of tea, X₂ = real disposable per capita income (measured in dollars), X₃ = price of sugar (measured in dollars per pound), X₄ = price of coffee (measured in dollars per pound). Suppose that according to economic theory, coffee and tea are competing products. What would be the sign of the coefficient β₄?

10. Suppose an economist postulates that the demand for money at time 't' (Y_t) depends upon the expected rate of interest (X_t^*) at that time: Y_t = β₁ + β₂X_t^* + u_t. Because the expected rate of interest is not directly observable, it is assumed that expectations are formed such that they learn from their previous mistakes. Thus, expectations are revised each period by a fraction δ of the discrepancy between the current value of the interest rate and its previous expected value: X_t^* - X_t-1^* = δ(X_t - X_t-1^*). What would you identify such a model as?

11. Consider the model given by the following equation.
What is the best way to mitigate the problem of interactive terms?

12. Which of the following is likely to occur as a result of multicollinearity?

13. For the following distributed-lag model, what is the interpretation of the sum of the coefficients

14. Which of the following is a possible consequence of the regressors being stochastic, (i.e., the observations of the regressors in the sample are not fixed and given, rather, they are drawn randomly from fixed populations with finite means and finite population variances)?

15. Which of the following is NOT a shortcoming of the linear probability model?

16. Which of the following is used to test hypotheses concerning goodness of fit?

17. Consider the model given by ln Y = β₁ + β₂ ln X₂ + β₃ ln X₃ + β₄ ln X₄ + u, where Y = per capita consumption of tea, X₂ = real disposable per capita income (measured in dollars), X₃ = price of sugar (measured in dollars per pound), X₄ = price of coffee (measured in dollars per pound). Suppose that according to economic theory, sugar and tea are complementary products. What would be the sign of the coefficient β₃?

18. Consider the model given by the following equation.
What is the interpretation of the slope coefficient β₂?

19. Consider the following system of simultaneous equations representing the demand-and-supply model:
Q_s = β₁ + β₂P +u₁ and Q_d =α₁ +α₂P+α₃I +u₂, where Q_s and Q_d are the quantities supplied and demanded respectively, P = price of the commodity, and I = income. Which of these equations are identified, i.e. which of these can be estimated?

20. What is the advantage of the dummy variable technique and running a single regression over the Chow test (i.e. estimating multiple dummy regressions and the 'pooled' regression individually)?

21. What is the rationale behind testing an estimator's consistency even for finite samples?

22. Consider the simple two-variable linear regression model Y_i = β₁ + β₂X_i + e_i, with unknown parameters β₁ and β₂. e is the unobserved random error term. The corresponding OLS regression equation for the above model is:
, where
and
are OLS estimators of β₁ and β₂.respectively, and
is the OLS residual. Given this information, what is the Ordinary Least Squares Estimation Criterion?

23. Consider the model: Y_i = α₁ + α₂G_i +βX_i + u_i, where Y_i = annual salary of a sales manager, X_i = years of experience, and G_i = 1 for males and 0 otherwise. What do the coefficient α₁ + α₂ indicate?

24. A researcher wants to examine if earnings are related to height of individuals in the following way: EARNINGS = β₁ + β₂ HEIGHT + u. With data on 48 individuals, he wants to test if β₂ = 0 against the alternative β₂ ≠ 0. The critical values of t for 5% and 1% levels are given in the table below. What would the researcher's conclusion be if b₂ = 0.30, s.e.(b₂) = 0.12?

25. Assume Y represents the number of slices of bread consumed per person, per day. X represents the price of one pound of bread, measured in dollars. Z represents the income of the consumer. A two variable linear model is computed from the data available, and the result is given as follows:
. The R-square for the model is found to be R^₂ = 0.5972. What is the interpretation of R-square?