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OLS SHORTCOMINGS Preview of coming attractions 1 MADE QUIZ • What are the main OLS assumptions? 1. On average right 2. Linear 3. Predicting variables and error term uncorrelated 4. No serial correlation in error term 5. Homoscedasticity + Normality of error term 2 MADE 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 – – – 3 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 MADE 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 4 MADE How do we get autocorrelation? • What we need in the error term is white noise 5 MADE How do we get autocorrelation? • Positive autocorrelation (rare changes of signs) 6 MADE How do we get autocorrelation? • Negative autocorrelation (frequent changes of signs) 7 MADE How do we get autocorrelation? • Model misspecification can give it to you for free 8 MADE How do we get heteroscedasticity • What we need is error terms independent of SIZE of X. 9 MADE 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 10 MADE Omitted variable consequences • Example – continued – Impact of gender on net wage, controlling for education 11 MADE 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? 12 MADE Outliers 13 MADE Multicollinearity • What is multicollinearity – Your „Xs” 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 MADE 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 MADE 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 MADE 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 MADE 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 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 18 MADE