Durbin-Watson test is not powerful when lagged dependent variable is in regressors (design matrix)

Question

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Question restatement: The statement given is 'Durbin-Watson test is not powerful when lagged dependent variable is in regressors (design matrix)'.

Option 1: True
- The Durbin-Watson (DW) statistic is a classic test for first-order autocorrelation in the residuals of a regression. When you include a lagged dependent variable as an regressor, the residuals become highly influenced by that predictor because y_{t-1} is by construction highly correlated with y_t through the underlying dynamics. This strong relationship reduces the part of the residual structure that the DW statistic can detect as new autocorrelation beyond what is already captured by the lagged dependent variable, leading to reduced power to detect additional autocorrelation. In short, including a lagged dependent variable often makes DW less effective at identifying remaining serial correlation, so the claim that its power is diminished is correct.

Option 2: False
- If one argued that the DW test remains perfectly powerful or that including a lagged dependent variable has no impact on its ability to detect autocorrelation, this would contradict the standard econometric understanding. The inclusion of y_{t-1} changes the residual structure and the distributional properties underpinning the DW test under typical OLS assumptions, and practitioners often turn to alternative tests (like Breusch-Godfrey) when a lagged dependent variable is present. Therefore, claiming that the DW test is still highly powerful in this setting would be misleading.

Summary:
- The common teaching is that the DW test loses power when a lagged dependent variable is included, making the statement in the question true. The False option contradicts established reasoning and is therefore incorrect.

AS.440.617.80.SP25 Quiz 4. Time Series regression

Durbin-Watson test is not powerful when lagged dependent variable is in regressors (design matrix)

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