Calculating the Real Interest Rate from a Money Market Rate and CPI

Summary

The document explains how to derive a real interest rate from a money market rate and consumer price inflation, in the context of a study modeling the probability of stock market crises. The question arises because a cited paper describes its control variable as a money market rate adjusted using the Consumer Price Index, without spelling out the transformation.

The answer gives two approaches. A common approximation subtracts CPI inflation from the money market rate. For a more exact relationship, it states that one plus the real rate equals one plus the nominal money market rate divided by one plus CPI inflation. The distinction is between a simple rate difference and a multiplicative adjustment that accounts for compounding. The document does not specify data frequency, whether CPI is recorded as a rate or index level, or how to align observations across countries; those choices must be settled before applying the formula to a dataset.

Key ideas

• A simple approximation to the real rate subtracts CPI inflation from the money market rate.
• An exact relationship divides one plus the nominal rate by one plus the inflation rate, then subtracts one.
• The distinction matters when rates and inflation are not negligible.
• Data units and timing conventions are not specified and need to be handled separately.

Tags

# How to measure the real interest rate using the consumer price index


# How to measure the real interest rate using the consumer price index












I am examining how investor sentiment affects the probability of stock market crises. I am using methodology similar to this paper https://ideas.repec.org/p/dij/wpfarg/1110304.html.

One of the control variables in the model is the real interest rate. The authors calculate their measure of the real interest rate as "the money market rate, using the Consumer Price Index" (Table on page 25 of their paper).

I have CPI data for the countries that I am using in my study. However, I am not clear on how to transform Money Market Rate and CPI data into a measure of the real interest rate.

Thanks.

## Answer by Owe Jessen (score 3, accepted)

https://quant.stackexchange.com/a/27761

Real rate = Money Market Rate - CPI

Approximately.

As I do want to be exact (thanks, @noob2): $(1+real)=\frac{1+MMR}{1+CPI}$

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