9 Instrumental variables

 

This chapter covers

  • Learning different ways to estimate causal effects with instrumental variables
  • Identifying situations where you can apply instrumental variables
  • Learning how to apply instrumental variables with different Python and R packages

Using instrumental variables (IVs) is a technique to estimate causal effects that differ from the adjustment formula. It is applicable only in specific scenarios, particularly when your DAG follows the structure in figure 9.1. Some parts of this DAG are already familiar, such as the typical three-node confounder structure with the decision or treatment variable D, the outcome Y, and the set of confounders C, which we assume is unobserved. Additionally, you may have noticed an extra variable Z, called the instrument, a crucial requirement for applying the IV method.

Figure 9.1 Basic instrumental variables diagram. Confounders are unobserved. Variable Z plays the role of an instrument. This structure lets you overcome the lack of information about confounders in estimating the effect of D into Y.
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Identifying and estimating causal effects with Instrumental Variables
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9.1 Understanding IVs through an example

9.1.1 The example’s DAG

9.1.2 IV assumptions

9.1.3 IVs in RCTs

9.2 Estimating the causal effect with IVs

9.2.1 Applying IVs with linear models

9.2.2 Applying IVs for partially linear models

9.2.3 An alternative formula for the IV method

9.2.4 The lack of a general formula for the general IV graph

9.3 Instrumental variables in practice

9.3.1 Two-stage least squares (2SLS) algorithm

9.3.2 Weak instruments

9.3.3 IVs with DoubleML

9.4 References

9.5 Chapter quiz

Summary