Instrumental Variables Regression (1) Flashcards
goal of instrumental variables
- to know the causal relationship between the response variable Y and X
consistency
an estimator is consistent if it get closer to the true parameter values with higher probability as the sample size increases
potential sources of endogeneity
- Omited varaible bias from a variable that is correlated with X but is unobserved ( so cannot be included in the regression) and for which there are inequate control variables
- simultaneous causality bias ( X causes Y, Y causes X)
- Errors-in-variables bias ( X is measured with error)
if you have omitted variables
what type problem you have?
possible solution
- endogeneity problem
- solution: instrumental variables (IV)
Symbol for instrumental variable
variable Z
IV regression require Z
conditions for a valid instrument
- Relevanve
- Exogeneity
how to use IV Z?
Two-stage Least Square Estimation
Stage 1: Run OLS regression of the suspected variable X on z and constant. (then use X^)
Stage 2: Run OLS regression of Y on X^ and a constant
The idea of IV estimator
IV regression breaks X into two parts:
- a part that might be correlated with u
- a part that is not
Endogenous variable
Is one that is CORRELATED with u
Exogenous variable
Is one that is UNCORRELATED with u
Terminology of Endogenous
- Literally means “determined within the system”
but the definition is too narrow cuz it may fall on IV bias errors in variables bias
Large sample inference
- In large sample, the sampling distribution of the TSLS estimator is normal
- The idea behind the large-sample normal distribution of the TSLS estimator is that it involves an average of mean zero i.i.d random variables