Instrumental Variables in Action: Sometimes You Get What You Need

Anything that happens, happens.

Anything that, in happening, causes something else to happen, causes something else to happen.

Anything that, in happening,

causes itself to happen again, happens again.

It doesn’t necessarily do it in chronological order, though.

Douglas Adams, Mostly Harmless (1995)

Two things distinguish the discipline of Econometrics from our older sister field of Statistics. One is a lack of shyness about causality. Causal inference has always been the name of the game in applied econometrics. Statistician Paul Holland (1986) cautions that there can be “no causation without manipulation,” a maxim that would seem to rule out causal inference from non-experimental data. Less thoughtful observers fall back on the truism that “correlation is not causality.” Like most people who work with data for a living, we believe that correlation can sometimes provide pretty good evidence of a causal relation, even when the variable of interest has not been manipulated by a researcher or experimenter. 

The second thing that distinguishes us from most statisticians—and indeed most other social scientists— is an arsenal of statistical tools that grew out of early econometric research on the problem of how to estimate the parameters in a system of linear simultaneous equations. The most powerful weapon in this arsenal is the method of Instrumental Variables (IV), the subject of this chapter. As it turns out, IV does more than allow us to consistently estimate the parameters in a system of simultaneous equations, though it allows us to do that as well.

Studying agricultural markets in the 1920s, the father and son research team of Phillip and Sewall Wright were interested in a challenging problem of causal inference: how to estimate the slope of supply and demand curves when observed data on prices and quantities are determined by the intersection of these two curves. In other words, equilibrium prices and quantities—the only ones we get to observe—solve these two stochastic equations at the same time. Upon which curve, therefore, does the observed scatterplot of prices and quantities lie? The fact that population regression coefficients do not capture the slope of any one equation in a set of simultaneous equations had been understood by Phillip Wright for some time. The IV method, first laid out in Wright (1928), solves the statistical simultaneous equations problem by using variables that appear in one equation to shift this equation and trace out the other. The variables that do the shifting came to be known as instrumental variables (Reiersol, 1941).

In a separate line of inquiry, IV methods were pioneered to solve the problem of bias from measurement error in regression models. One of the most important results in the statistical theory of linear models is that a regression coefficient is biased towards zero when the regressor of interest is measured with random errors (to see why, imagine the regressor contains only random error; then it will be uncorrelated with the dependent variable, and hence the regression of Y; on this variable will be zero). Instrumental variables methods can be used to eliminate this sort of bias.