Linear IV

One concern about using standard Ordinary Least Squares regression is that the policy variables of interest may be "confounded." That is, there may be a causal arrow from the unobserved characteristic to the policy variable of interest. A "solution" to this problem is to use instrumental variables.

Instrumental variables estimation implements the picture below by estimating two relationships. The first is the relationship between Z and X. The second is the relationship between Z and Y. Both of these relationships are observed and the instrument is (assumed to be) exogenously determined in each. The hope is that by estimating these relationships it is possible to infer the relationship of interest, the effect of X on Y.