# McCallum Rule

## What Is the McCallum Rule?

The McCallum Rule is a monetary policy rule developed by economist Bennett T. McCallum at the end of the 20th century. The McCallum Rule uses a formula to set an operating target level for the monetary base in the next quarter based on the recent average velocity of money, current nominal Gross Domestic Product (GDP), and desired nominal GDP. It is based on a form of the Equation of Exchange from the Quantity Theory of Money. The rule explains how the Federal Reserve should manipulate the supply of money to keep economic growth on a path that is sustainable in the long-run. The McCallum Rule is often contrasted with another monetary policy rule, the Taylor Rule.​​​​​​​

### Key Takeaways

• The McCallum Rule is a monetary policy rule that uses the monetary base as an intermediate target and a desired rate of nominal GDP growth as its ultimate goal.
• The McCallum Rule formula provides a target for the monetary base for the next quarter based on the velocity of money, current nominal GDP, and desired nominal GDP.
• The McCallum Rule can be contrasted to the similar Taylor Rule in monetary policy.

## Understanding the McCallum Rule

The McCallum Rule sets a target for the monetary base in the next quarter equal to a linear combination of the current monetary base, the average change in the velocity of money in recent quarters, the recent growth rate of nominal GDP, and a desired target growth rate for nominal GDP based on the long-run growth trend in real GDP and a specified rate of inflation believed to be consistent with sustaining that long-run growth trend.

Formally the McCallum rule says:

Where:

is the long-run growth rate in real GDP (estimated to be around 3% per year), and

is current growth rate in nominal GDP compared to the previous quarter.

• is the natural log of the monetary base in the current quarter
• is the average change in the velocity of money over the past 16 quarters
• is the desired rate of inflation thought to be consistent with stable long-run growth (estimated around 2% per year)
• is the long-run growth rate in real GDP (estimated to be around 3% per year),
•  is current growth rate in nominal GDP compared to the previous quarter.

This equation tells the Fed how much it should expand or contract the monetary base, through open market operations or other policy tools, in proportion to the difference between actual and desired nominal GDP growth.

Economist Bennett T. McCallum developed the McCallum Rule in a series of papers written between 1987 and 1990. Starting from the Equation of Exchange, he attempted to capture the way the monetary base of a country interacts with the inflation rate and real GDP. Through these indicators, he hoped to predict what would happen in an economy under various conditions and to designate possible corrective measures that could be taken by the Federal Reserve Bank or other central banks.

## The McCallum Rule versus the Taylor Rule

The Taylor Rule is another economic targeting rule designed to help central banks control growth and inflation, created in 1993 by John B. Taylor, as well as Dale W. Henderson and Warwick McKibbin.﻿﻿ It describes an operating target for short-term interest rates in terms of the deviation of inflation and GDP growth from their desired long-term rates.

The McCallum Rule and the Taylor Rule are often considered rival measures to explain economic behavior, but the two rules do not describe or explain the same relationships at all. The Taylor Rule is primarily concerned with the Federal funds rate, while the McCallum Rule describes relationships involving the monetary base.

## How Do You Calculate the Monetary Base?

Monetary base is calculated as the total currency in circulation plus bank reserves.

## Who Controls the Monetary Base?

The monetary base is controlled by the central bank of a given country. They change the monetary base with monetary policies or open market operations.

## What Are the Components of Both the Monetary Base and the Money Supply?

The monetary base, also known as M0, is a measure of monetary supply—it includes the total value of money in circulation, as well as bank reserves. Meanwhile, monetary supply includes all currency in circulation and liquid instruments, such as demand deposits.

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1. Federal Reserve. "Taylor Rules," Page 4.

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