(a) What do you understand by the term ‘autocorrelation’?

(b) An econometrician suspects that the residuals of her model might be autocorrelated. Explain the steps involved in testing this theory using the Durbin–Watson (DW) test.

(c) The econometrician follows your guidance (!!!) in part

(b) and calculates a value for the Durbin–Watson statistic of 0.95. The regression has 60 quarterly observations and three explanatory variables (plus a constant term). Perform the test. What is your conclusion?

(d) In order to allow for autocorrelation, the econometrician decides to use a model in first differences with a constant

yt = β1 + β2x2t + β3x3t + β4x4t + ut (4.76)

By attempting to calculate the long-run solution to this model, explain what might be a problem with estimating models entirely in first differences.

(e) The econometrician finally settles on a model with both first differences and lagged levels terms of the variables

yt = β1 + β2x2t + β3x3t + β4x4t + β5x2t−1

+β6x3t−1 + β7x4t−1 + vt (4.77)

Can the Durbin–Watson test still validly be used in this case?

AppendixLO1