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OLS SHORTCOMINGS

OLS SHORTCOMINGS. Preview of coming attractions. QUIZ. What are the main OLS assumptions? On average right Linear Predicting variables and error term uncorrelated No serial correlation in error term Homoscedasticity + Normality of error term. OLS assumptions consequences.

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OLS SHORTCOMINGS

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  1. OLS SHORTCOMINGS Preview of coming attractions

  2. QUIZ • What are the main OLS assumptions? • On average right • Linear • Predicting variables and error term uncorrelated • No serial correlation in error term • Homoscedasticity + Normality of error term

  3. OLS assumptions consequences • We know that: • We cannot know the error term => we look for estimators • We cannot know the coefficients => we look for estimators • Estimators of coefficients are OK. Even if heteroscedasticity • Estimators of coefficients are OK. Even if autocorrelation • BUT we cannot know if they are different from zero even => if H or A then error terms inappropriately estimated

  4. OLS assumption consequences • If autocorrelation: • Coefficients correctly estimated • Error terms incorrect • If big sample, we do not have to care (estimators are consistent <= asymptotic properties of OLS) • If heteroscedasticity: • Coefficients correctly estimated • Error terms incorrect (estimators are not consisntent <= asymptotic properties of OLS) • What can we do? • Fool-proof estimations: GENERALISED LEAST SQUARES

  5. How do we get autocorrelation? • What we need in the error term is white noise

  6. How do we get autocorrelation? • Positive autocorrelation (rare changes of signs)

  7. How do we get autocorrelation? • Negative autocorrelation (frequent changes of signs)

  8. How do we get autocorrelation? • Model misspecification can give it to you for free 

  9. How do we get heteroscedasticity • What we need is error terms independent of SIZE of X.

  10. Omitted variable consequences • We estimate model of x1 on y • In reality there is not only x1, but also x2 • Estimator of x1 in the first model is BIASED • Example • Impact of gender on net wage

  11. Omitted variable consequences • Example – continued • Impact of gender on net wage, controlling for education

  12. Outliers • What is an outlier? • Atypical observation • It fits the model, but event was „strange” • Wrong observation • It does not fit the model • Really wrong (unemployment rate in Warsaw) • Something unexpected (a structural event, oil shock) • What it does to your model? • Makes your standard error larger/smaller • Makes your estimates sensible/senseless • What can you do with them? • Throw out => need to have a good reason!!! • Inquire, why is it so?

  13. Multicollinearity • What is multicollinearity • Your „exes” correlated among each other • What it does • If perfectly, matrix does not invert => no model • If imperfectly, your estimators are not reliable => why? • You never know if it is xi or xj that drives the result • Your t statistics are inappropriately estimated (you may reject the null hypothesis too often) • What can you do with that? • Nothing really ... => change your model

  14. Endogeneity • What is endogeneity? • Your x and your ε are correlated IN PRINCIPLE (simultaneity) • What it does to your model? • Your estimators are no longer consistent (even if sample veeeery big) • Where does it come from? • Omitted variable problem? (omitted and included variables correlated) • Reverse causality

  15. What about selection bias? • Heckman Nobel Prize 2003 • Say you have three types of answers in a survey • Yes • No • IDK • What if you try to explain Yes/Know, but there is something important in IDK? • Example from yesterday: • employed and Mincer equation versus • employed and unemployed population

  16. How to model? • Testing hypotheses: combined and in a combined way: • These are not equivalent • What to do with insignificant variables • General to specific IS NOT the same as taking only important • How to chose the right specification • Information criteria: Bayesian, Akaike • Adjusted R2 • YOUR APPROACH!

  17. What is OLS model telling you? • Estimated coefficients are nothing but correlations • You know the causality from your theory and not the model! • You cannot test if your relation is really causal • Whatever test you pass, it doesn’t have to make sense • You can have a spurious regression • Think what you are doing! • You can have a problem of outliers • Look at your dots with caution! • Any model is only meaningful, if economics behind it is • Statistical significance is not everything • Look at the size of your estimators and economic significance • Ask yourself reasonable questions • Research for a model sells well, but gives little satisfaction

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