Explain Propensity Score Matching (PSM) and Its Application in Business Analytics

Concept

Propensity Score Matching (PSM) is a statistical method for estimating causal effects from non-experimental or observational data.
It mimics randomization by pairing treated and untreated units that have similar probabilities of receiving treatment, thereby reducing selection bias.

In business analytics, PSM is invaluable when controlled experiments are infeasible — such as evaluating the effect of a marketing campaign, loyalty program, or pricing change applied non-randomly across customers or regions.

1. Core Idea

When treatment assignment is correlated with covariates (e.g., income, age, engagement level), direct comparisons yield biased results.
PSM summarizes all confounding covariates into a single scalar — the propensity score, defined as:

e(x_i) = P(T_i = 1 | X_i)

where:

• T_i = treatment indicator (1 = treated, 0 = control)
• X_i = vector of observed covariates

By matching units with similar e(x_i), analysts balance covariate distributions between groups, approximating a randomized experiment.

2. Implementation Steps

1. Model Propensity Scores:
   Estimate each unit’s probability of treatment using logistic regression, probit models, or machine-learning classifiers (e.g., XGBoost, Random Forest).

2. Match Treated and Control Units:
   Pair treated and control observations with similar propensity scores using:

   • Nearest-neighbor matching
   • Caliper matching (within a tolerance window)
   • Kernel or radius matching

3. Check Covariate Balance:
   Ensure matched samples are comparable using standardized mean differences or “love plots.”

4. Estimate Treatment Effect:
   Compute the Average Treatment Effect on the Treated (ATT):

ATT = E[Y1 - Y0 | T = 1]

using the matched sample.

3. Business Example

A retailer launches a loyalty rewards program in selected stores — usually high-traffic ones.
Comparing sales directly would overstate the effect due to location bias.
By modeling each store’s propensity to adopt the program (based on size, revenue, customer profile) and matching stores with similar scores, analysts isolate the true incremental effect of loyalty participation on sales.

4. Advantages

• Reduces confounding from observed variables.
• Provides a clear causal framework when randomization is not possible.
• Easily combines with other techniques (e.g., DiD + PSM).
• Applicable across domains — marketing, finance, healthcare, HR analytics.

5. Limitations

• Cannot correct for unobserved confounders — only observed ones.
• Needs large overlapping samples (common-support condition).
• Sensitive to propensity-model misspecification.
• Computationally heavy with high-dimensional data.

6. Practical Enhancements

• Inverse-Probability Weighting (IPW): Uses propensity scores as weights.
• Doubly Robust Estimation: Combines outcome modeling and PSM for stronger bias correction.
• Machine-Learning Propensity Models: Improves accuracy under nonlinear or interaction effects.

Tips for Application

• When to apply:

• When analyzing observational data or policy rollouts without randomization.

• To estimate incremental business impact while controlling for observable differences.

• Interview Tip:

• Use this phrasing: “PSM creates a balanced quasi-experiment from messy real-world data.”

• Discuss covariate balance checks, ATT vs. ATE interpretation, and integration with DiD.

• Highlight practical uses — marketing-mix modeling, churn reduction, and regional campaign impact.