Economics 421/521

Winter 2008

Homework #4

1. What are the consequences of estimating an autoregressive model using OLS?

2. 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

3. 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?

4. Regress real consumption (C) on 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).

5. 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.

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