Download Why do we need econometrics? - MA in Development Economics

OLS SHORTCOMINGS
Preview of coming attractions
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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
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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
–
–
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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
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