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Instrumental Variables

Instrumental Variables (IV) approaches are the most common only after ordinary least squares (OLS).  But the field has become more critical of their usage (Deaton (2009), Heckman and Urzua (2009)). In large part, improper use of IV has generated skepticism. Still, instruments remain a powerful tool to estimate causal relationships when randomization is not feasible.

Imagine you, promising young economist, are trying to estimate the effect television watching on autism. It's a controversial topic, so you cannot get funding from government or private foundations who are trying to maintain good public relations. Even if you had the money, You cannot randomize TV watching for many subjects and, since the effects are likely modest, you won't be able to detect an effect.

The estimation problem here is that TV-watching is an endogenous variable. Autistic children may prefer TV to other activities, or factors (such as mother IQ) may be correlated with TV and autism. An instrument is any variable that is correlated with TV-watching but uncorrelated with other factors of autism.

Maybe you've recalled that when it was rainy outside, you spent more time indoors watching TV. In fact, that's true for many families. One analyst used unusually rainy periods as an instrument on how much TV children watched. He found that in areas with more unexpected rain, children watched more TV and children had increased rates of autism (1, 2).

The finding was controversial. And by no means definitive. But here's the value: IV can be used to approximate large-scale, human-subjects experiments without much expense.  And these sorts of experiments would be completely infeasible otherwise. Because of Waldman's paper, psychology is taking another look and conducting further tests.  

Some helpful hints on using instruments:
  • Instruments are usually best when exogenous (not decided by) the subject. Policy changes are typically considered exogenous.
  • Being exogenous is not sufficient--the variable must also be uncorrelated with other factors. While policy changes are exogenous, they may not be unrelated to other factors; for instance, policy changes could be triggered by other variables or the same subjects could be influenced by several concurrent policy changes.
  • Once you have a good instrument, you can interact the instrument with other covariates to generate other good instruments. This can be helpful for identifying non-linear effects.

This last point is a subtle one. If an instrument is valid, then any function of the instrument is also a valid instrument (Loken et al., 2012).

Often an instrument is protected by the fact that we have no conception for how it may be endogenous which is necessary but not sufficient for IV suitability.

It's also helpful to see how instruments have gone wrong in the past.  The two classic examples of instrumental variables are 
  1. Angrist's Vietnam draft lottery paper (here); Heckman provides critiques here.
  2. Angrist and Krueger's quarter-of-birth paper (here); Jaeger et al. provide critiques here.
Keywords: Instruments, instrumental variables, IV, internal validity, external validity, local average treatment effect, LATE, unbiased estimator, omitted variables, Andrew Johnston, Andrew, Johnston, economics, applied economics, economist, microeconomics, empirics, empirical economics, Wharton