Post on 29-Jan-2016
1 MADE
OLS SHORTCOMINGS
Preview of coming attractions
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QUIZ
• What are the main OLS assumptions?
1. On average right2. Linear3. Predicting variables and error term
uncorrelated4. No serial correlation in error term5. Homoscedasticity+ Normality of error term
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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
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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
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How do we get autocorrelation?
• What we need in the error term is white noise
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How do we get autocorrelation?
• Positive autocorrelation (rare changes of signs)
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How do we get autocorrelation?
• Negative autocorrelation (frequent changes of signs)
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How do we get autocorrelation?
• Model misspecification can give it to you for free
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How do we get heteroscedasticity
• What we need is error terms independent of SIZE of X.
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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
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Omitted variable consequences
• Example – continued– Impact of gender on net wage, controlling for
education
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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?
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Outliers
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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
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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
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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
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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!
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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