Questions -

Question 1. Explain the importance of the error term in econometrics.

Question 2. The 'market model' of asset returns states that

R_t = α + βR_mt + u_t

where Rt and Rmt denote the excess return of a stock and the excess return of the market index for the London Stock Exchange. The above model was then estimated using time series data with 50 periods (with standard errors in parentheses).

R^{^}_t = 0.567 + 1.045R_mt, T = 50

SE (0.33) (0.06)

a) Interpret the coefficients (including the constant) in the above model.

b) Using a t-test and a 5% level of statistical significance, are the individual estimated coefficients, including the constant term, each statistically significantly different from zero.

c) Using a t-test, does the coefficient β equal 0.5?

d) Compute a 99% confidence interval for the slope coefficient β and interpret the result.

Question 3. The following model of stock prices is to be estimated:

log s_t = α₀ + α₁ log m_t + α₂ log y_t + α₃ log p_t + u_t

Where: s_t is the stock price index, m_t is the money supply, y_t is output and p_t is the price level and u_t is an error term. We expect the above model to have the following signs on the coefficients:

α₁ > 0, α₂ > 0, α₃ < 0

The model was estimated using monthly data from January 1990 to December 2003 and generated the following results (standard errors in parentheses):

log s^{^}_t = 0.65 + 0.72 log m_t - 064 log y_t - 0.35 logp_t

(0.92) (0.12) (0.32) (0.21)

R^-2 =0.54, F(3, 164) = 64.17

a) Interpret the coefficients on the variables (ignore the constant).

b) Using a t-test and a 5% level of statistical significance, are the individual estimated effects, other than the constant term, each statistically significant from zero?

c) Is the explanatory power of the regression model significant at the 5% level of statistical significance?

d) Based on the above answers, do you consider the above model fits the data reasonably well? (Assume the diagnostic tests were all passed).

Question 4. You decide to investigate the relationship given in the null hypothesis of:

H₀: β₃ + β₄ = 1 and β₅ = 1

What would estimate the restricted regression? The regressions are carried out on a sample of 96 quarterly observations, and the residual sums of squares for the restricted and unrestricted regressions are 102.87 and 91.41, respectively. Perform the test. What is your conclusion?