QUESTION

# The following model is estimated: Yi = 0.674 + 0.996X1t + 0.136X2t, R2 = 0.341; SER = 0.1993; d = 2.403; T = 60 (0.311) (0.442) (0.

a. The following model is estimated:

Yi = 0.674 + 0.996X1t + 0.136X2t, R2 = 0.341; SER = 0.1993; d = 2.403; T = 60

(0.311)   (0.442)        (0.097)

The estimated residuals, ^ut, are collected from this model and the value preceding the first observation of the sample is set equal to zero. Using this residual series, the following auxiliary regression is estimated over the full sample of 60 observations:

^ut = 0.013+0.034X1t+0.021X2t−0.032 ^ut−1+ηt, R2 = 0.09, SER = 0.0112, d = 1.983, T = 60

(0.062) (0.036)    (0.035)     (0.012)

Use the Breusch-Godfrey test to determine whether there is evidence of statistically significant first-order autocorrelation at the 5% level.

b. The estimated residuals, ^ut, are collected from the model estimated in Question (a) and the two values preceding the first observation of the sample are set equal to zero. Using this residual series, the following auxiliary regression is estimated over the full sample of 60 observations:

^ut = 0.011 + 0.025X1t + 0.017X2t − 0.03 ^ut−1 + 0.004  ^ut−2 + ηt,

(0.062)   (0.036)       (0.035)       (0.035)          (0.01)

R2 =0.096, SER=0.0113, d=1.897, T =60

Use the Breusch-Godfrey test to determine whether there is evidence of statistically

significant second-order autocorrelation at the 5% level.