Regression model diagnostics and complications

Econometrics: Multicollinearity, Heteroscedasticity, and Autocorrelation

• Multicollinearity, a problem in regression analysis, can lead to incorrect parameter estimates and signs.
• Detection of multicollinearity includes high R2 with few significant t-ratios and high pairwise correlations among explanatory variables.
• Options to address multicollinearity include doing nothing, redefining the model, or using principal components analysis.
• An example of multicollinearity is given using long-term demand drivers for housing prices based on panel data for 50 U.S. metropolitan areas.
• Heteroscedasticity, where the variance of the error term is not constant, has various causes such as clustered volatility and spatial autocorrelation.
• Consequences of heteroscedasticity include less efficient estimators, making statistical inference less reliable.
• Detection of heteroscedasticity can be done through graphical methods, Breusch-Pagan and White’s tests, among others.
• Remedial measures for heteroscedasticity include using weighted least squares, dividing each observation by the heteroscedasticity, and using heteroscedasticity-consistent standard errors.
• Heteroscedasticity in time series econometrics can be addressed through visual checks, various tests, and estimation of GARCH models.
• Autocorrelation, a violation of the classical linear regression model, occurs when error terms are correlated over time.
• Consequences of autocorrelation include inefficient estimators and unreliable statistical inferences.
• Detection of autocorrelation can be done through visual checks and various tests, and remedial measures include using Cochrane-Orcutt or Hildreth-Lu methods.

Econometrics: Autocorrelation, Model Specification, and Omitted Variable Bias

• Autocorrelation violates the classical linear regression model (CLRM) assumption of zero covariance between error terms of different observations.
• Consequences of autocorrelation: OLS estimators remain unbiased and consistent, but they are no longer efficient; standard errors are underestimated, impacting hypothesis testing.
• Detection of autocorrelation includes graphical methods, Durbin-Watson test, and Breusch-Godfrey test.
• Remedial measures for autocorrelation include first-difference transformation, generalized transformation, and the Newey-West method.
• Autocorrelation is common in time series data and affects the estimation of univariate models with lagged variables.
• Model specification errors include exclusion of "core" variables, inclusion of superfluous variables, and incorrect functional form.
• Omission of relevant variables leads to biased coefficients, inconsistent estimation, and unreliable hypothesis testing and forecasts.
• Omitted variable bias occurs when an omitted variable is correlated with included variables and is a determinant of the dependent variable.
• An F-test can compare the restricted and unrestricted models, indicating if omitted variables belong in the model.

Test your knowledge of econometrics with these quizzes covering topics such as multicollinearity, heteroscedasticity, autocorrelation, model specification, and omitted variable bias. Identify the consequences, detection methods, and remedial measures for these common issues in regression analysis and time series econometrics.