Regression & Causation

Lesson 3: Isolating the Historical Engine

Quantitative Methods for Causal Inference

Statistical Modeling

The Regression Model

In history, we rarely have controlled experiments. Regression is our mathematical way of "holding other things constant" (\(ceteris paribus\)) while testing a specific hypothesis.

\(Y = \beta_0 + \beta_1 X + \epsilon\)

\(Y\) : The Effect

The Dependent Variable. What are we trying to explain? (e.g., Growth, Mortality, Stability)

\(X\) : The Cause

The Independent Variable. What is the hypothesized driver? (e.g., Institutions, Coal, Education)

\(\epsilon\) : The Error

The Residual. Everything else history hasn't told us yet.

Reading the Results

The Coefficient (\(\beta\))

Indicates the direction and magnitude of the relationship.

+ Positive Variables move together

- Negative Variables move in opposition

Statistical Significance

Is the relationship real or just a fluke of the data? Check the P-value.

P < 0.05

The Gold Standard

The Ghost in the Data

Omitted Variable Bias (OVB)

If a historian ignores a key factor that correlates with both the cause and the effect, the regression will "blame" the wrong variable.

"Correlation does not imply causation, but it sure is a hint—unless OVB is lurking."

Example:

Hypothesis: Proximity to the coast (\(X\)) causes high GDP (\(Y\)).

Missing Variable: Institutional quality. Good laws often start in port cities.

Result: Proximity to the coast looks like the cause, but it's actually the institutions!

Challenge

"Did the Industrial Revolution start because of Britain's Coal Deposits (Geology) or its Wages (Economics)? We will use multi-variable regression to pit these two theories against each other."

Resources

VS

Institutions

Regression and Causal Inference

Regression and Causal Inference Slides

Regression Lab Worksheet