Breaking the Taylor Rule: Why Math Matters

In Part 1, we established that the ECB faces a dilemma. But to prove it, we need to estimate the ECB's Reaction Function. We want to know: If inflation rises by 1%, how much does the ECB raise rates?

The Trap of Simple Regressions

A novice data scientist might simple download data for Interest Rates ($i_t$) and Inflation ($\pi_t$) and run a linear regression (OLS).

This would be a mistake.

Why? Because of Reverse Causality. The Central Bank raises rates to lower inflation. But high inflation causes the Central Bank to raise rates. The arrow points both ways.

$$\text{Inflation} \leftrightarrow \text{Interest Rates}$$

If you run a standard regression, you capture a mix of both effects, resulting in biased and meaningless numbers. This is known as the Simultaneity Bias or Endogeneity.

The Solution: GMM

To solve this, my project uses the Generalized Method of Moments (GMM). Instead of looking at current inflation (which is endogenous), we use 'Instruments'—variables from the past that correlate with inflation but cannot be affected by today's interest rate shock.

By using lagged values of inflation, output gaps, and commodity prices, we can isolate the causal component of the ECB's decision-making.

The Result

When we do this correctly, a shocking picture emerges. The ECB generally follows the Taylor Principle ($$>1$) for the aggregate Eurozone. But when we apply this rule to individual countries, the fit completely falls apart.

In Part 3, we will visualize exactly how big this gap is for countries like Italy vs. Germany.