Introduction to Causal Inference and Instrumental Variables

In many practical business scenarios it is impossible to design a perfect randomized experiment, so we need to infer causal relationships and estimate causal effects from observational data.

The article first distinguishes two families of causal‑effect estimation methods:

Methods that require all confounders to be observed (e.g., Propensity Score Matching (PSM), Coarsened Exact Matching (CEM), Inverse Probability of Treatment Weighting (IPTW), Difference‑in‑Differences (DID), Synthetic Control Methods (SCM), Uplift models, Regression Discontinuity Design (RDD)).

Methods that can handle unobserved confounders, the most representative being Instrumental Variables (IV).

Instrumental variables must satisfy three core conditions:

Relevance: the instrument Z is correlated with the treatment A.

Exclusion: Z affects the outcome Y only through A.

Independence: Z shares no common cause with Y.

Because the three conditions are often unverifiable, a fourth condition is required for identification. Two common choices are:

Homogeneity – the causal effect of A on Y is constant across individuals (or within strata of Z).

Monotonicity – there are no “defiers”; the instrument never makes a unit less likely to receive the treatment.

The article illustrates the IV estimator with a binary instrument Z (e.g., high cigarette price) and a binary treatment A (smoking cessation). The Wald estimator is expressed as:

ATE = (E[Y|Z=1] - E[Y|Z=0]) / (E[A|Z=1] - E[A|Z=0])

When the instrument is weak (small denominator), confidence intervals widen and bias can be amplified. The discussion also covers how to verify relevance empirically, the dangers of violating exclusion or independence, and the impact of multiple instruments.

Finally, the article compares IV with other causal methods, noting that IV still requires model assumptions, is highly sensitive to assumption violations, and is applicable only in relatively rare settings where a strong, valid instrument exists.

The piece concludes with a summary of the covered methods and a call for careful application of causal inference techniques in practice.