Introducing Instrumental-Variables Estimation

{{Summary
 * title=Introducing Instrumental-Variables Estimation
 * authors=Richard j. Murnane, John B. Willett
 * url=http://www.ats.ucla.edu/stat/examples/methods_matter/
 * tags=NatematiasGenerals,statistics,econometrics,instrumental variables
 * summary=Often when we do regression analysis on data that wasn't collected in a study, we're finding relationships between outcomes and predictors that can't include causal claims. While there are some rare moments, like drastic changes, or systems like lotteries that allow us to do natural experiments, they are extremely rare.

Under certain conditions, it is possible to "locate and carve out somehow an exogenous part of the variability" in a predictor... and use only it to estimate the impact on a subsequent outcome, claiming for it an interpretation of causality" (204). In this chapter, Murnane and Willett describe Instrumental-Variables Estimation (IVE), one method for doing so. To do this, we need a third variable, the instrument, which helps us carve out that part of the predictor.

In the chapter, the authors use the example of a study by Dee on the civic returns to education, which was investigating the effect of college attainment on civic engagement (as measured by voter registration). A simple regression of these two cannot support causal claims, "since participants have chosen their own levels of educational attainment, rather than those levels being assigned exogenously." Furthermore, there might be traits like motivation or family support not in the dataset that contribute to both education and civic engagement. In fact, causality may go in the other direction, with civic engagement having an effect on educational attainment.

Instrumental Variables
To build a causal model, Dee relied on a third variable, an instrument that met two critical assumptions:
 * "the instrument must be related to the potentially endogenous question predictor" (college). In practice, this means testing the relationship between the instrument and the question predictor with a χ2 test or regression model.
 * "the instrument cannot be related to the unobserved effects that rendered the question predictor endogenous in the first place" (e.g. the residuals of regressing the outcome on the predictor).

In other words, the effect of the instrument on the outcome must exclusively be through the question predictor; there must not be a "third path" between the instrument and the outcome.

In other studies, instrumental variables have been found in:
 * proximity of educational institutions (used in Dee's study, which might be related to your likelihood to go to college, but not to your likelihood to register to vote)
 * institutional rules and personal characteristics (like age cutoffs for kindergarten, which might influence what class year you're in at school, but not what job you get)
 * deviations from cohort trends (like the difference of class size from the size expected in a model)
 * original random assignment, which is explained in the chapter on Using IVE to Recover the Treatment Effect in a Quasi Experiment

Regression with Instrumental Variables Estimation
When an instrumental variable is found that meets these requirements, it is possible to use a two-stage least squares (2SLS) method to carve out the exogenous part of the hypothesis predictor with help of the instrumental variable, and then use that exogenous part to predict the outcome variable. In this work, the authors show how to create a Path Model to describe the relationship between the instrumental variable, predictor, outcome, and residuals to verify and express that the critical assumptions of IVE are met.

Most of the chapter includes a step-by-step tutorial of how to reason through, carry out, and evaluate IVE analysis. The chapter explains how to add covariates, how to include statistical interactions, and how to fit the right functional form for curved relationships.

Finding and Defending Instruments
The final part of the chapter focuses on the major part of any paper that uses IVE: justifying the suitability of the instrument. They include several examples and walk through three studies to explain how the study was designed and how the instruments were justified. Instruments are often justified through a combination of theory (for example, explaining how rational choice theory might justify the relationship between school proximity and education level but not expect that distance to be related to employment, except through education), sensitivity analyses, and the construction of rival models
 * relevance=This chapter offers a fantastic overview of Instrumental Variables Estimation, walking readers through the reasoning required to carry out this kind of work.

"''I have written up explanation of this method, along with code examples from Python are available here and here. Natematias (talk) 21:29, 19 March 2015 (UTC)"

Notable References
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 * journal=Methods Matter
 * pub_date=2011
 * subject=Education