Economics 421/521

Winter 2011

Homework #4

Due in lab next week

1. Perform a Durbin-Watson test at the 5% level of significance for positive first-order autocorrelation using the following regression output (standard errors in parentheses):

Y_{t} = 2.0 + 3.7*X_{1t} - 4.4*X_{2t}, T = 42

(.7) (1.1) (2.8) DW = 1.22

2. Recall the model from homework 1:

Given data on M2, real GDP, and the T-bill rate, estimate the following regression...:

M

_{t}= β_{0}+ β_{1}RGDP_{t}+ β_{2}Tbill_{t}+ e_{t}Don't be surprised if the fit is very good - we'll explain why that may be misleading later in the course.

Does model suffer from serial correlation? Use a Durbin-Watson test to answer the question. Is the fit as good as the R^{2} and t-statistics indicate?

3. Regress the change in the log of real consumption (C) on the change in the log of real disposable income (DI) and test for serial correlation using a Durbin-Watson test. The data are here (the data are quarterly, and span the time period 1947:Q1 - 2007:Q3).

4. Explain why the Durbin Watson statistic is always between 0 and 4. Also explain why the Durbin-Watson statistic is between 0 and 2 when there is positive serial correlation, between 2 and 4 when there is negative serial correlation, and equal to 2 when there is no correlation at all.

5. Continuing with the model we used in problem 2, test for the presence of fourth order serial correlation.

6. Continuing with the model we used in problem 3, use the AR(1) procedure in EViews to correct the model for the presence of first-order serial correlation.

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