Discuss the Ramsey’s Test (RESET) for identification of ‘omitted variables’ and ‘incorrect functional form’.

Ramsey's Test (RESET) for Identification of Omitted Variables and Incorrect Functional Form

Ramsey's Test, also known as the RESET test (Regression Specification Error Test), is a diagnostic test used to detect potential misspecification errors in regression models, specifically the presence of omitted variables or incorrect functional forms. The test is based on the idea that if the model is correctly specified, the residuals should not exhibit any systematic patterns when regressed on the fitted values from the original model.

1. Omitted Variables:

• Issue: Omitted variables can bias the estimates of the coefficients in a regression model, leading to incorrect inferences about the relationships between the variables of interest.
• RESET Test for Omitted Variables: In the RESET test, additional terms (such as squared or cubed terms) of the independent variables are added to the original regression model. If the omitted variables are important, these additional terms should capture the omitted effects, and the coefficient estimates should improve.
• Interpretation: A significant improvement in the model's fit after adding the additional terms suggests that the original model may have omitted variables.

2. Incorrect Functional Form:

• Issue: Using an incorrect functional form (e.g., linear instead of quadratic) can lead to biased coefficient estimates and incorrect conclusions about the relationships between variables.
• RESET Test for Incorrect Functional Form: The RESET test can also be used to detect incorrect functional forms by adding transformation terms (e.g., squared or cubed terms) of the independent variables to the original model. If the true relationship is nonlinear, these additional terms should improve the model's fit.
• Interpretation: A significant improvement in the model's fit after adding the transformation terms suggests that the original model may have the incorrect functional form.

3. Implementation:

• To perform the RESET test, the original regression model is estimated, and then additional terms (e.g., squared or cubed terms of the independent variables) are added to the model.
• The model is re-estimated with the additional terms, and the improvement in the model's fit is assessed using a statistical test, such as an F-test.
• If the improvement is significant, it suggests that the original model may have omitted variables or incorrect functional form.

4. Conclusion:

• Ramsey's Test (RESET) is a useful diagnostic tool for identifying omitted variables and incorrect functional form in regression models.
• By detecting these misspecification errors, researchers can improve the accuracy and reliability of their regression analyses and ensure that their conclusions are based on properly specified models.