Correcting Autocorrletation in a Model with Dummies

[coraUK]

How can I get SPSS output that corrects for first-level autocorrelation in the dependent variable and gives me appropriate beta estimates and significance levels? I used dummy variables for time and state effects in a model, I have 22 YEAR dummies and 51 STATE dummies. The method I want to copy is explained in an older paper:



Eij = pEij-1 + Sij



"Where ρ is the autocorrelation between the εijth and εij-1th errors and δij is a normally and independently distributed error with a constant variance across time and counties. The residuals from the weighted least squares fit were used to estimate rho. The dependent variable Yij was then transformed into Yij - ρ Yij-1. The regression analysis was rerun with these transformed independent and dependent variables." Can anyone explain what was done in this example and how I can do the same?

 

[EnumaElish]

It is standard autocorr. correction, except for the panel structure of the data. SPSS needs to be somehow "told" that the dataset is panel (has a cross-section dimension in addition to a time series dimension).

 

[tacman]

In this example, the researcher is using dummy variables for time and state effects in their model. However, they have found that there is first-level autocorrelation in the dependent variable, meaning that the errors in the model are correlated with each other over time. This can lead to biased and inaccurate beta estimates and significance levels.

To correct for this autocorrelation, the researcher has followed a method explained in an older paper. This method involves transforming the dependent variable by subtracting the product of the autocorrelation coefficient (ρ) and the lagged dependent variable (Yij-1) from the original dependent variable (Yij). This transformed dependent variable, Yij - ρ Yij-1, is then used in the regression analysis along with the original independent variables.

By using this method, the researcher is able to remove the autocorrelation from the dependent variable and obtain unbiased beta estimates and significance levels. To replicate this method in SPSS, you can follow these steps:

1. Run the initial regression analysis with the original dependent and independent variables.

2. Save the residuals from this regression analysis by clicking on "Save" under the "Statistics" tab and selecting "Save Unstandardized Predicted Values."

3. Compute the autocorrelation coefficient (ρ) using the saved residuals. This can be done by going to "Analyze" > "Regression" > "Autocorrelation" and selecting "Durbin-Watson" under "Method."

4. Create a new variable by subtracting the product of ρ and the lagged dependent variable (Yij-1) from the original dependent variable (Yij). This can be done using the "Compute" function under the "Transform" tab.

5. Run the regression analysis again, this time using the transformed dependent variable and the original independent variables.

By following these steps, you will be able to replicate the method used in the example and correct for first-level autocorrelation in your model.