Structural Breaks in Python

ECON 3209 · Week 13, Lecture 3 · Kerala Agricultural University

Department of Development Economics, KAU

Autumn 2026

Learning Outcomes

By the end of this lecture, you will be able to:

1. explain the idea of a structural break and regime change
2. estimate before-after dummy and interaction models
3. understand the logic of the Chow test
4. compare restricted and unrestricted models in Python
5. interpret policy shifts using a cooperative credit scheme example

What Is a Structural Break?

A structural break occurs when the relationship between \(Y\) and \(X\) changes across regimes.

Examples: - before vs after a new cooperative credit scheme - pre- and post-flood periods - different pricing regimes

Break in Intercept or Slope?

A regime dummy can capture a change in the intercept.

An interaction with the regime dummy can capture a change in the slope.

\[Y_i = \beta_0 + \beta_1 X_i + \beta_2 Post_i + \beta_3(Post_i\cdot X_i) + \varepsilon_i\]

Chow Test Logic

The Chow test compares: - a restricted model with one common relationship - an unrestricted model with separate relationships across regimes

If allowing separate regimes reduces the residual sum of squares a lot, that is evidence of a break.

Cooperative Credit Scheme Example

Suppose Kerala introduced a new credit support scheme in year 6.

We ask: - Did the average repayment rate change? - Did the relationship between borrower income and repayment change?

This is exactly a structural-break question.

Python Demo: Simulate Pre/Post Scheme Data

Python Demo: Restricted vs Unrestricted Models

Python Demo: Compute a Chow-Style F Statistic

Python Demo: Plot the Two Regimes

Policy Interpretation

• A positive post coefficient means the average repayment score shifted upward.
• A positive interaction means income became more predictive after the scheme.
• Together, these coefficients describe both level and slope changes.

Practical Notes

• Structural breaks may come from policy, climate, institutional change, or data revisions.
• Dummy-based break models are simple and transparent.
• Formal break testing becomes especially important in longer time series.

A structural break says the same model no longer fits all observations equally well.

🏋️ Exercise

1. Simulate data for borrower repayment before and after a scheme change.
2. Estimate a restricted model and a full break model with an interaction.
3. Compare model fit and compute a Chow-style F statistic.
4. Plot fitted lines for the pre- and post-scheme periods.

Summary

✅ Structural breaks occur when regression relationships change across regimes or periods.

✅ Regime dummies can capture shifts in intercepts, and interactions can capture shifts in slopes.

✅ The Chow-test idea compares restricted and unrestricted residual sums of squares.

✅ Dummy-based break models are useful for evaluating policy changes such as credit scheme reforms.

✅ Plots and model comparisons make structural changes easy to communicate.

Next Lecture

Week 14 — Nonlinear Regression

We will cover: - log transformations - polynomial models - splines and piecewise fits - curve fitting and model comparison