Pooled OLS

ECON 3209 · Week 17, Lecture 1 · Kerala Agricultural University

Department of Development Economics, KAU

Autumn 2026

Learning Outcomes

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

  1. define panel data and distinguish balanced from unbalanced panels
  2. write the pooled OLS model for repeated observations over units and time
  3. explain the assumptions behind pooled OLS and why they may fail
  4. organise and analyse Kerala district panel data in Python
  5. recognise when ignoring unit heterogeneity becomes problematic

What is Panel Data?

  • Panel data track the same units across time.
  • In this course, units may be households, bank branches, or Kerala districts.
  • A panel combines cross-sectional variation and time variation.
  • Notation: \(i\) indexes units and \(t\) indexes time.

Balanced and Unbalanced Panels

  • A balanced panel has the same number of time observations for every unit.
  • An unbalanced panel has some missing years or periods.
  • Balanced panels are simpler for teaching and computation.
  • Unbalanced panels are common in real research because data collection is imperfect.

The Pooled OLS Model

  • Pooled OLS ignores the panel structure and estimates one regression for all observations:

\[y_{it}=\beta_0 + x_{it}'\beta + u_{it}\]

  • It treats the stacked sample like an ordinary cross-section.
  • This is valid only if unobserved unit-specific factors are uncorrelated with the regressors and error assumptions are otherwise reasonable.

Creating a Kerala Panel in Python

Estimating Pooled OLS

What Can Go Wrong?

  • Districts differ in soil quality, irrigation access, and farmer networks.
  • If these unobserved district characteristics affect both productivity and fertilizer use, pooled OLS becomes biased.
  • Standard errors may also be misleading because panel errors may be serially correlated within districts.

Balanced versus Unbalanced in Practice

Kerala District Example

Suppose we observe crop productivity for 14 Kerala districts over 5 years.

Regressors might include rainfall, fertilizer use, irrigation coverage, and price incentives. Pooled OLS is the first benchmark, but it may ignore persistent district differences such as soil quality.

When Pooled OLS Is Acceptable

  • As a simple benchmark before richer panel methods.
  • When unit-specific unobserved effects are plausibly unimportant.
  • When the goal is descriptive correlation rather than strong causal interpretation.
  • In most panel applications, however, we next consider fixed effects or random effects.

Exercise

Create an unbalanced version of the panel by dropping one year for two districts. Re-estimate pooled OLS and compare the fertilizer coefficient with the balanced-panel estimate.

Summary

  • ✅ Panel data combine observations across units and over time.
  • ✅ Pooled OLS stacks the panel and ignores unit-specific heterogeneity.
  • ✅ Balanced and unbalanced panels differ in data completeness but use the same core logic.
  • ✅ Pooled OLS is a useful benchmark, but omitted unit effects can create bias.

Next Lecture

  • We remove time-invariant district effects using fixed effects.
  • You will learn demeaning and the LSDV approach in statsmodels.
  • This is the main solution when unobserved unit effects correlate with regressors.