Instumental Variables Flashcards
! A good instrument must fulfil the following conditions:
- Relevance: Cov (z, x) ≠ 0. This means that the IV is correlated with the endogenous RHS variable.
- Exogeneity: Cov (z, u) = 0. This means that the IV should not be correlated with the error term. In other words, the IV only affects the dependent variable through the endogenous RHS, not directly.
Consider a simple model to estimate the effect of personal computer (PC) ownership on college grade point average for graduating seniors at a large public university, where PC is a binary variable indicating PC ownership:
GPA = b0 + b1PC + u
i) Why might PC ownership be correlated with u?
a) Measurement error in PC:
If we have a random error when observing PC ownership, then this error would add to the error term and cause a correlation between the measured PC ownership dummy and the residual.
b) Simultaneous relationship:
It is logical to assume that PC ownership may affect grades, but would grades also affect PC ownership? If we have reasons to believe this, then PC and u should be correlated.
c) Omitted variable bias:
If there is another variable that affects performance in school and correlates with PC ownership as well, then we should expect that u is correlated with PC. It has been well established that socioeconomic status affects student performance. The error term u contains, among other things, family income, which has a positive effect on GPA and is also very likely to be correlated with PC ownership.
Endogeneity through Simultaneous relationships is:
If X affect Y but also Y affects X then Corr (X, u) ≠ 0
Endogeneity problem is when…
… the independent variable is correlated with the error term.
What is the econometric problem if X is an endogenous explanatory variable and the model is estimated with Ordinary Least Squares (OLS).
The econometric problem is that if Innovation is, therefore, correlated with the error term E(u|Firmsize, Innovation)≠0, it causes OLS to be a biased or inconsistent estimator.
How are OLS and IV estimates of a coefficient different?
The OLS estimates of a model that requires an IV estimate will be biased, but precise, while the IV estimate will be consistent, but the standard errors incorrect. This is because the IV estimates variance is based only on the variation in the IV.
How are proxy and instrumental variables different in their relationships to x?
A proxy variable uses a direct relationship between z and x, whereas an instrumental variable looks at the indirect relationship between z and x.
If z is correlated with y, can it be a valid instrument?
Yes, as long as it’s not directly correlated.
Write the reduced form equation for X means…
…write down a linear regression model explaining the endogenous explanatory variable by all exogenous variables.
Do x and u need to be uncorrelated in order to use z as a valid instrument for x?
No.
Do z and u need to be uncorrelated to use z as a valid instrument for x?
Yes.
While a proxy variable must be highly correlated/uncorrelated with the omitted variable, a good instrumental variable must not be correlated / uncorrelated with the ommited variable.
A good proxy must be highly correlated with the ommited (through the error term) where as the a good instrumental must not be correlated with the ommited.
Which gets you higher standard errors? OLS or IV?
Standard errors of the estimated parameters with IV are substantially larger than those of OLS
What is the consequence of overidentification
Adding more instumnets than need can cause severe bias in the 2SLS estimators.
The standard errors of the estimated regression parameters will become smaller.
What conclusion can be drawn if H0 (no overidentification) of the (Hensen) Sargan test is rejected?
If we reject the H0 of the Sargan test then Overidentification is a stat. sig. probelm and we cannot trust the IV (2SLS) estimates because they are inconsistent.
They do not solve the bias problems we already knew existed when estimating by OLS.
