Taylor Rule

What is the Taylor Rule?

The Taylor Rule is a mathematical formula that suggests how central banks (like the Federal Reserve in the United States) should adjust their nominal interest rates in response to changes in inflation and economic growth.

Proposed by economist John Taylor in 1993, the rule balances the dual mandate of price stability and maximum sustainable employment. It provides a benchmark to judge whether interest rates are too high (which might trigger a recession) or too low (which might fuel high inflation).

The Taylor Rule Formula

The standard equation is expressed as:

$$i = r^* + \pi + a_\pi(\pi - \pi^*) + a_y(y - y^*)$$

Where:

• $i$ is the target nominal policy interest rate (the target federal funds rate).
• $r^*$ is the equilibrium real interest rate (historically assumed to be 2%).
• $\pi$ is the current inflation rate.
• $\pi^*$ is the target inflation rate (usually set at 2%).
• $y - y^*$ is the output gap (the percentage deviation of real GDP from potential GDP).
• $a_\pi$ is the weight given to the inflation deviation (standard value is 0.5).
• $a_y$ is the weight given to the output gap (standard value is 0.5).

Taylor Rule Variants: 1993 vs. 1999

Over the years, different variants of the Taylor Rule have emerged to reflect changing economic conditions:

• Standard Taylor Rule (1993): Uses a weight of $0.5$ for both inflation ($a_\pi$) and the output gap ($a_y$). This is the original formulation that closely modeled the Federal Reserve's behavior during the late 1980s and early 1990s.
• Balanced Taylor Rule (1999): Maintains the $0.5$ inflation weight but increases the output gap weight to $1.0$. This modification suggests a more aggressive response to output instability and output gaps.

Understanding the Output Gap

The output gap represents the difference between actual economic output (real GDP) and the economy's maximum potential output when operating at full capacity (potential GDP).

$$\text{Output Gap} = \frac{\text{Real GDP} - \text{Potential GDP}}{\text{Potential GDP}} \times 100$$

A positive output gap suggests the economy is operating above capacity, creating inflationary pressures. A negative output gap indicates slack in the economy, suggesting potential recessionary conditions where rate cuts might be needed to stimulate demand.