# Can we estimate the model some other way to begin

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: t independent. Can we use the Durbin Watson test to detect autocorrelation? What do we do instead? 39 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables The presence of lagged dependent variables makes OLS estimates biased in ﬁnite samples. But they are still consistent. But if there is autocorrelation in the errors then we have inconsistency as well. Yt = β1 + β2 Xt + β3 Yt −1 + ut ut = ρut −1 + εt ε is iid. What is the source of inconsistency? ⇒ Yt −1 and ut are not independent. Can we use the Durbin Watson test to detect autocorrelation? What do we do instead? 40 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables OLS won’t work. Can we estimate the model some other way? To begin with, let’s look at a conventional way of removing autocorrelation with the following simple model without a lagged dependent variable. Yt = β1 + β2 Xt + ρut −1 + εt Yt −1 = β1 + β2 Xt −1 + ut −1 Subtract ρ times the second equation from the ﬁrst and we get after rearranging: Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 Xt −1 + εt 41 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables OLS won’t work. Can we estimate the model some other way? To begin with, let’s look at a conventional way of removing autocorrelation with the following simple model without a lagged dependent variable. Yt = β1 + β2 Xt + ρut −1 + εt Yt −1 = β1 + β2 Xt −1 + ut −1 Subtract ρ times the second equation from the ﬁrst and we get after rearranging: Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 Xt −1 + εt 42 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables OLS won’t work. Can we estimate the model some other way? To begin with, let’s look at a conventional way of removing autocorrelation with the following simple model without a lagged dependent variable. Yt = β1 + β2 Xt + ρut −1 + εt Yt −1 = β1 + β2 Xt −1 + ut −1 Subtract ρ times the second equation from the ﬁrst and we get after rearranging: Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 Xt −1 + εt 43 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables OLS won’t work. Can we estimate the model some other way? To begin with, let’s look at a conventional way of removing autocorrelation with the following simple model without a lagged dependent variable. Yt = β1 + β2 Xt + ρut −1 + εt Yt −1 = β1 + β2 Xt −1 + ut −1 Subtract ρ times the second equation from the ﬁrst and we get after rearranging: Yt = β1 − ρβ1 + ρYt −1 + β2 Xt...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online