Regression model diagnostics and complications
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Questions and Answers

In applied econometric analysis, which assumption of the classical linear regression (CLRM) is violated if there is a perfect linear relationship among the regressors?

  • No multicollinearity (correct)
  • Independence of errors
  • Homoscedasticity
  • Normality of residuals

    • What are the consequences of high multicollinearity in regression analysis?

  • T ratios of regression coefficients increase
  • Standard errors of regression coefficients decrease
  • OLS estimators are still BLUE, but one or more regression coefficients have large standard errors (correct)
  • OLS estimators become biased

    • What is the term used to describe a situation where the regressors are highly (but not perfectly) collinear in a regression model?

  • Heteroscedasticity
  • Perfect collinearity
  • Serial correlation
  • Imperfect collinearity (correct)

    • What does the RESET test involve?

    <p>Re-estimating the original model with additional regressors and using an F-test to determine model appropriateness</p> Signup and view all the answers

    What can overfitting a model by adding irrelevant variables lead to?

    <p>Inefficient coefficient estimates</p> Signup and view all the answers

    When does misspecification of the functional form of a regression model occur?

    <p>When researchers fail to account for the nonlinear nature of variables</p> Signup and view all the answers

    What are the consequences of errors of measurement in the regressand?

    <p>Lead to larger estimated variances and standard errors in OLS estimation</p> Signup and view all the answers

    What is required when errors of measurement occur in the regressors?

    <p>The use of instrumental or proxy variables</p> Signup and view all the answers

    What problems can outliers, leverage, and influence points create in OLS estimation?

    <p>Giving equal weight to atypical observations</p> Signup and view all the answers

    What are leverage points in the data?

    <p>Disproportionately distant from the bulk of the sample</p> Signup and view all the answers

    How do errors and data issues impact coefficient estimates in econometric models?

    <p>Lead to biased or inefficient coefficient estimates</p> Signup and view all the answers

    Why is careful data collection and model specification necessary in econometric analysis?

    <p>To mitigate errors and ensure the validity of the econometric analysis</p> Signup and view all the answers

    What is crucial for econometric practitioners to make informed decisions in model building and analysis?

    <p>Understanding the consequences of errors</p> Signup and view all the answers

    What does the Jarque-Bera (JB) test of normality assess?

    <p>Normality assumption of the error term in the regression model</p> Signup and view all the answers

    What distribution does the JB statistic follow?

    <p>Chi-square distribution with 2 degrees of freedom</p> Signup and view all the answers

    How is non-normality of residuals addressed?

    <p>By adding omitted variables or using natural log transformations</p> Signup and view all the answers

    What problem arises when there is a feedback relationship between the Y and X variables?

    <p>Simultaneity problem</p> Signup and view all the answers

    What do simultaneous equation regression models consider?

    <p>Feedback relationships among variables and distinguish between endogenous and exogenous variables</p> Signup and view all the answers

    What does the Hedonic housing price function aim to capture?

    <p>The effect of various factors on housing prices</p> Signup and view all the answers

    What is the aim of the Jarque-Bera (JB) test?

    <p>To test the normality assumption of the error term in the regression model</p> Signup and view all the answers

    Which of the following is a consequence of heteroscedasticity?

    <p>Less efficient estimators</p> Signup and view all the answers

    What are the options to address multicollinearity?

    <p>Doing nothing, redefining the model, or using principal components analysis</p> Signup and view all the answers

    How can heteroscedasticity in time series econometrics be addressed?

    <p>Through visual checks, various tests, and estimation of GARCH models</p> Signup and view all the answers

    What is an example of multicollinearity provided in the text?

    <p>Long-term demand drivers for housing prices based on panel data for 50 U.S. metropolitan areas</p> Signup and view all the answers

    What are the consequences of autocorrelation?

    <p>Inefficient estimators and unreliable statistical inferences</p> Signup and view all the answers

    How can detection of multicollinearity be done?

    <p>High R2 with few significant t-ratios and high pairwise correlations among explanatory variables</p> Signup and view all the answers

    What are the detection methods for heteroscedasticity?

    <p>Graphical methods, Breusch-Pagan and White’s tests, among others</p> Signup and view all the answers

    What are the remedial measures for heteroscedasticity?

    <p>Using weighted least squares, dividing each observation by the heteroscedasticity, and using heteroscedasticity-consistent standard errors</p> Signup and view all the answers

    What is autocorrelation in the context of regression analysis?

    <p>Correlation between error terms over time</p> Signup and view all the answers

    What can be a cause of heteroscedasticity?

    <p>Clustered volatility and spatial autocorrelation</p> Signup and view all the answers

    How can detection of autocorrelation be done?

    <p>Through visual checks and various tests</p> Signup and view all the answers

    What are the consequences of autocorrelation in the context of regression analysis?

    <p>OLS estimators remain unbiased and consistent, but they are no longer efficient; standard errors are underestimated, impacting hypothesis testing.</p> Signup and view all the answers

    What is omitted variable bias in the context of regression analysis?

    <p>It occurs when an omitted variable is correlated with included variables and is a determinant of the dependent variable, leading to biased coefficients and unreliable hypothesis testing.</p> Signup and view all the answers

    How is autocorrelation commonly detected in regression analysis?

    <p>Graphical methods, Durbin-Watson test, and Breusch-Godfrey test.</p> Signup and view all the answers

    What are the remedial measures for autocorrelation in regression analysis?

    <p>First-difference transformation, generalized transformation, and the Newey-West method.</p> Signup and view all the answers

    What are model specification errors in regression analysis?

    <p>Exclusion of 'core' variables, inclusion of superfluous variables, and incorrect functional form.</p> Signup and view all the answers

    What does omitted variable bias lead to in regression analysis?

    <p>Biased coefficients, inconsistent estimation, and unreliable hypothesis testing and forecasts.</p> Signup and view all the answers

    What can an F-test compare in regression analysis?

    <p>The restricted and unrestricted models, indicating if omitted variables belong in the model.</p> Signup and view all the answers

    What is the consequence of model specification errors in regression analysis?

    <p>Biased coefficients, inconsistent estimation, and unreliable hypothesis testing and forecasts.</p> Signup and view all the answers

    What is the consequence of autocorrelation on OLS estimators in regression analysis?

    <p>They remain unbiased and consistent, but they are no longer efficient; standard errors are underestimated, impacting hypothesis testing.</p> Signup and view all the answers

    What are the detection methods for autocorrelation in regression analysis?

    <p>Graphical methods, Durbin-Watson test, and Breusch-Godfrey test.</p> Signup and view all the answers

    Study Notes

    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.

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    Applied Econometrics Regression Diagnostics & Complications PDF

    Description

    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.

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