Week 3 Flashcards
Which three mechanisms can break the OLS2?
- Omitted variables
- Mismeasured regressors
- Simultaneous equations (equilibrium)
Instrumental variable (IV) regression
An alternative estimation strategy that operates under different exogeneity assumption than OLS.
Endogeneity
If the exogeneity assumption for OLS (OLS-2) is not satisfied we say that the regressors are endogenous.
Omitted variable problem
Incorporating relevant variables into the error term (instead of modeling them as regressors) can cause the exogeneity assumption to fail.
Omitted variable bias in short vs. long regression:
If we drop a variable with k=2, the short model k=1 might not estimate the true coefficient consistently. It will be shifted by a bias term. This bias term arises due to the correlation between the omitted x2 with the remaining x1… So if the correlation is zero OR if the effect of the dropped variable B2 is zero, there is no bias.
Simultaneous equations
Ex equilibrium conditions. This might cause endogeneity if the regressors are only observable in equilibrium (as with price in the market). Therefore, we can learn about the unobserved component (U) by observing the regressors… Exo does not hold.
Measurement error (regressor)
Sometimes we are not able to perfectly observe a regressor (X1) that we want to include in a regression. Instead, we observe an imperfect measurement (X1*+W), where W is the measurement error.
Classical measurement error assumption:
The set of assumptions that we use when using another observable variable instead of X1 when it’s unobservable:
- E[W]=0
- Var(W)>0
- W is independent of everything, incl. X1 and U.
These assumptions are restrictive and allows only nice behaviour of W. It turns out that it is still not enough…
Attenuation bias
Bias resulting from mismeasurement of a regressor (when using omitted variables in the case of measurement error, W). We estimate a scaled down version of the true parameter, biased toward zero.
Proxy variable
A variable that gives an approximation of an unobserved variable and replaces that one in the regression.. The proxy variables suffer from measurement error.
Structural equation
Describes a model for how an outcome is generated. The term is used in the context of instrumental variable regression.
Instrumental variable (IV) regression
An alternative procedure to estimate the parameters in a structural equation. IV regression has different assumptions than OLS and therefore it may be applicable even though OLS assumptions are not met.
Instrumental variable/instrument
A special observed variable that can be used to generate an exogenous version of an endogenous variable. So if X1 is endogenous, we solve it by observing Z1 which is exogenous to the regression but related to X1.
Instrumental relevance condition
The instrument (Z) is correlated with the endogenous regressor (X1) even after we take out the co-movement between the endo and the exo. cov(Z1,X1)!=0
Instrument exogeneity assumption
The Z cannot predict the level of U.
E[U | Z1] = 0
