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Instrumental variables are becoming increasingly common in applied economics and statistics. For the uninitiated, can we have some non-technical answers to the following questions:

  1. What is an instrumental variable?
  2. When would one want to employ an instrumental variable?
  3. How does one find or choose an instrumental variable?
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Don't you think that the Wikipedia article about it is enough? – mbq♦ Jul 23 '10 at 17:59
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Questions such as this require a wiki / blog post type of response. I do think questions should not require such long answers. – user28 Jul 23 '10 at 19:50
I'm not sure the right thing to do is to simply ignore this question and refer the asker to the wiki - especially during beta where we are trying to build up the content of the site. Perhaps the question asker should submit each of these questions individually so that they can be better addressed. – Russell S. Pierce Jul 23 '10 at 20:52
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@mbq - the wikipedia example hardly qualifies as nontechnical. It's very reliant on jargon and equations. – rolando2 Aug 4 '11 at 23:39
It HAS become common in economics some time in the 1980s. Some biostaticians have heard of it, too, and apply it in the context of measurement error models, where instruments are narrowly thought of as additional available measurements. They qualify as instruments within the broader econometric context: they are correlated with the variable of interest, and they are uncorrelated with its measurement error. – StasK Aug 23 '11 at 3:08

3 Answers

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As a medical statistician with no previous knowledge of econom(etr)ics, I struggled to get to grips with instrumental variables as I often struggled to follow their examples and didn't understand their rather different terminology (e.g. 'endogeneity', 'reduced form', 'structural equation', 'omitted variables'). Here's a few references I found useful (the first should be freely available, but I'm afraid the others probably require a subscription):

I'd also recommend chapter 4 of:

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up vote 6 down vote

Here are some slides that I prepared for an econometrics course at UC Berkeley. I hope that you find them useful---I believe that they answer your questions and provide some examples.

Charlie

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There are also more advanced treatments on the course pages for PS 236 and PS 239 (graduate-level political science methods courses) at my website: cgibbons.berkeley.edu/teaching.html – Charlie Jul 27 '10 at 19:09
up vote 0 down vote

Non-technical (usually that's all I'm good for anyway): There are times when not only does X cause Y, but Y causes X as well. An instrumental variable is a device that can "clean up" this messy, inconvenient relationship so that the best estimates can be made of X's effect on Y.

The instrumental variable is chosen by virtue of its relationships: it is a cause of X, but, other than acting through X, it has no effect on Y. The instrument (or instruments) is used in Stage One to compute a new "version" of X, one that is in no way a function of Y. This new "predicted" X is then used in a second stage, in a more standard regression, to explain/predict Y. Hence the term Two-Stage Least Squares regression.

One typically finds the IV in processes that are overriding or beyond the control of X OR Y, such as variables that depend on laws, policies, acts of nature, etc.

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