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Econometrics 101

Causal Inference & Regression Foundations
ImpactMojo Workshop Series • Statistical Methods for Development Economics
75-90 Minutes

Workshop 1: Understanding Causation vs Correlation

Target Audience: Development economists, policy analysts, impact evaluators, researchers, and data scientists working on causal questions

Prerequisites: Multivariate Analysis 101 or equivalent regression knowledge, basic statistics

Materials Needed: Statistical software (R/Stata/Python), sample datasets, calculators

Learning Objectives

By the end of this workshop, participants will be able to:

Part 1: The Fundamental Problem of Causal Inference

20 minutes

The Classic Question: Does Education Cause Higher Income?

Observed Correlation: People with more education earn more money (r = 0.6 in Indian NSS data)

But is it causal? Consider these alternative explanations:

  • Ability bias: Smarter people get more education AND earn more
  • Family background: Wealthy families provide both education and job connections
  • Motivation: More motivated people stay in school longer AND work harder
  • Signaling: Education doesn't increase productivity, just signals ability
  • Selection bias: Only certain types of people choose higher education

The Policy Question: If we expand access to education, will incomes actually rise?

Holland's Fundamental Problem

"No causation without manipulation" - To establish causation, we need to compare what happens to the same unit when it receives treatment versus when it doesn't. But we can never observe both states for the same person at the same time.

The Counterfactual: What would have happened to the treated units if they had not been treated?

The Potential Outcomes Framework

Rubin Causal Model

For each individual i:

  • Y₁ᵢ = Potential outcome if treated (educated)
  • Y₀ᵢ = Potential outcome if untreated (no education)
  • Tᵢ = Treatment indicator (1 if educated, 0 if not)
  • Yᵢ = Observed outcome = TᵢY₁ᵢ + (1-Tᵢ)Y₀ᵢ

Individual Treatment Effect: δᵢ = Y₁ᵢ - Y₀ᵢ

The Problem: We only observe one potential outcome per person!

Average Treatment Effect (ATE): δ = E[Y₁ᵢ - Y₀ᵢ] = E[Y₁ᵢ] - E[Y₀ᵢ]

Naive Comparison: E[Y|T=1] - E[Y|T=0] = ATE + Selection Bias

Part 2: Threats to Causal Inference

25 minutes

Major Sources of Bias

Confounding Variables

Problem: Third variables affect both treatment and outcome

Example: Family wealth affects both education access and income opportunities

Solution: Control for confounders in regression

Reverse Causality

Problem: Outcome affects treatment, not just vice versa

Example: Health affects income, but income also affects health

Solution: Instrumental variables, panel data

Selection Bias

Problem: Treatment groups differ systematically

Example: Motivated students choose higher education

Solution: Random assignment, natural experiments

Measurement Error

Problem: Imperfect measurement of variables

Example: Self-reported income vs actual income

Solution: Better data, instrumental variables

Bias Identification Exercise (10 minutes)

Scenario: A study finds that microfinance borrowers have higher business profits than non-borrowers.

Your Task: Identify potential sources of bias in concluding that microfinance causes higher profits:

Confounding

What variables might affect both microfinance access and profits?

  • Entrepreneurial ability
  • Business experience
  • Social networks
  • Location/market access
Selection Bias

How might microfinance borrowers differ systematically?

  • More motivated entrepreneurs
  • Better business ideas
  • Higher risk tolerance
  • Credit-worthy characteristics
Reverse Causality

Could higher profits lead to microfinance access?

  • Successful businesses seek expansion capital
  • Profitable enterprises qualify for loans
  • Visible success attracts lenders
Measurement Issues

What measurement problems might exist?

  • Self-reported profit data
  • Survival bias (failed businesses exit)
  • Seasonal profit variations
  • Definition of "profit"

Part 3: Multiple Regression for Causal Inference

20 minutes

The Conditional Independence Assumption

When Can Regression Identify Causal Effects?

Key Assumption: Conditional on observed covariates X, treatment assignment is "as good as random"

Y = β₀ + β₁T + β₂X₁ + β₃X₂ + ... + βₖXₖ + ε

Causal Interpretation: β₁ is the average treatment effect IF we control for all confounders

The Big IF: This requires controlling for ALL variables that affect both treatment and outcome

Building a Causal Regression Model

Step-by-Step Approach

1. Theory First: Draw a causal diagram (DAG) showing relationships

  • What causes the treatment?
  • What causes the outcome?
  • What causes both? (These are confounders)

2. Include Confounders: Control for variables that affect both T and Y

  • Background characteristics
  • Pre-treatment variables
  • Time-invariant factors

3. Avoid Bad Controls: Don't control for post-treatment variables

  • Mediators (part of the causal pathway)
  • Colliders (create spurious associations)
  • Outcomes affected by treatment

4. Check Robustness: See if results change with different specifications

  • Different control variables
  • Different functional forms
  • Different samples

Regression Design Exercise (10 minutes)

Research Question: Does participating in an employment training program increase wages?

Available Data:

  • Post-training wages (outcome)
  • Training participation (treatment)
  • Age, gender, education (demographics)
  • Previous work experience
  • Motivation score (from pre-training survey)
  • Post-training job search behavior
  • Regional unemployment rate
Variable Include as Control? Justification
Age Yes Affects both training participation and wages
Education Yes Confounder - affects participation and outcomes
Previous experience Yes Pre-treatment variable affecting both
Motivation score Yes Affects who joins training and wage outcomes
Job search behavior No Post-treatment - might be mediator
Regional unemployment Yes Affects labor market opportunities

Part 4: Interpreting Regression Results

15 minutes

From Coefficients to Causal Claims

Example Regression Output:

Dependent Variable: Log Monthly Income (Rs.) Variables: Coefficient Std Error p-value Education (years) 0.078 0.012 < 0.001 Age 0.045 0.008 < 0.001 Age² -0.0004 0.0001 < 0.001 Female -0.234 0.045 < 0.001 Rural -0.156 0.038 < 0.001 Experience (years) 0.032 0.009 < 0.001 N = 8,543 R² = 0.42 F-statistic = 524.3

Interpretation:

  • Education coefficient (0.078): One additional year of education is associated with a 7.8% increase in income, holding other variables constant
  • Causal interpretation: IF all confounders are controlled, this represents the causal effect of education
  • Magnitude: Moving from 8 to 12 years of education (4 years) predicts 31% higher income
  • Significance: Result is statistically significant, but is it economically meaningful?
Common Interpretation Mistakes
  • "Correlation implies causation": Statistical significance ≠ causal effect
  • "Controlling for everything": Including bad controls can bias results
  • "R² = validity": High R² doesn't guarantee causal interpretation
  • "Precision = accuracy": Small standard errors don't eliminate bias

Assessing Causal Validity

Internal Validity Checks
  • Placebo tests on unaffected outcomes
  • Robustness to different specifications
  • Sensitivity analysis for unobserved confounders
  • Pre-treatment covariate balance
External Validity Considerations
  • Representativeness of sample
  • Generalizability across contexts
  • Heterogeneous treatment effects
  • Policy relevance of estimates

Part 5: When You Need Advanced Methods

10 minutes

Beyond OLS: Advanced Causal Inference Methods

When regression isn't enough, consider these approaches:

Method When to Use Key Assumption Example
Instrumental Variables Endogenous treatment, unobserved confounders Valid instruments exist Distance to school as IV for education
Difference-in-Differences Policy changes, panel data Parallel trends Minimum wage policy impact
Regression Discontinuity Arbitrary assignment thresholds No manipulation of running variable Scholarship eligibility based on test scores
Fixed Effects Unobserved time-invariant factors No time-varying confounders Individual or location fixed effects
Matching Observational data, selection on observables Conditional independence Propensity score matching

Choosing the Right Method

Method choice depends on:

  • Data structure: Cross-section, panel, or experimental?
  • Assignment mechanism: How do people get treated?
  • Assumptions credibility: Which assumptions are most plausible?
  • Policy question: What parameter do we want to estimate?

There's no universally best method - the right choice depends on context and credible identification strategy.

Essential Resources for Causal Inference

Foundational Texts:

Applied Development Economics:

Software and Tools:

Data Sources for Practice:

Next Steps in ImpactMojo: