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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