OLS SHORTCOMINGS Preview of coming attractions

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

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

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

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

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

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

How do we get autocorrelation? Model misspecification can give it to you for free

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

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

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

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?

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

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

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

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!

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