How do I calculate and predict the real U.S. Federal Reserve interest rate?

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Increase of the U.S. Federal Reserve's interest rate The markets have been waiting for more than a year. The deadline for this event was set far away, but even they have not been fulfilled under the power of external circumstances. The world economy is shaking, the dollar is actively growing, and the Central Bank of America is in no hurry to act.

In this environment, we would like to approach this question from a mathematical point of view and see if the markets are expecting the Fed to tighten monetary policy for a reason. Are there any real prerequisites for this?

Janet Yellen has repeatedly stated that the U.S. Federal Reserve is not guided by some "mechanical rule" when deciding on the key interest rate. As we know, the central bank can influence mainly short-term interest rates, because the longer the term of a deposit or loan, the stronger the market influence. Thus, rates on 30-year government bonds are determined solely by the market (i.e., by numerous macro factors), while rates on 10-year bonds are determined with little intervention by the authorities.

QE programs and the US real interest rate

Since 2008, thanks to asset purchase program (QE1-QE3)The U.S. Federal Reserve's balance sheet, which has become the main instrument of monetary policy, rose roughly from $0.8 trillion to $4.4 trillion, and the yield on 10-year U.S. bonds fell from 4% to 2%.

Figure 1. The U.S. 10-year bond rate and the U.S. Federal Reserve's balance sheet.

According to a number of estimates quantitative easing programs in the U.S. are equivalent to a significant - perhaps by 5 percentage points - reduction in the federal funds rate at its current zero level (0-0.25%). It is because of the enormous injection of liquidity into the U.S. banking system (as part of QE programs) and the use of linear forecasting models in a highly volatile market there is a significant discrepancy between the actual federal funds rate and its theoretical value.

The formula for calculating the interest rate for the central banks of the world

Since 1993, the world's major central banks have used, to varying degrees, the Taylor rule, which is a response function whereby the interest rate is adjusted by the national central bank in response to changes in inflation (Consumer Price Index - CPI) and real economic activity (real GDP):

where

- the nominal short-term interest rate set by the Central Bank at the time t,
- the target level of the nominal interest rate,
- long-term equilibrium real interest rate (assumed to be 2%),
- current inflation in annual terms,
- annual inflation target (taken as 2%),
- some coefficients, which we estimate using the method of least squares (MSN).

The positive GDP gap (GDP hep) is called the inflation gap, which indicates that the growth of aggregate demand outstrips the growth of aggregate supply, reinforcing inflationary expectations.

What should the U.S. Federal Reserve interest rate be today!

When we calculate the GDP hep, instead of the data on GDP used similar data on industrial production. This was done in order to avoid a lag in the US Federal Reserve's decision on the key interest rate (since GDP estimates are published quarterly, while estimates of industrial production and the key interest rate are published once a month in the US). A linear trend approximation was used to calculate the potential level of industrial production.

The Taylor rule of thumb for the U.S. Federal Reserve interest rate for the July 1954-July 2015 sample is as follows:

(1)

Figure 2. Actual and theoretical U.S. federal funds rate, July 1954-July 2015.

In addition, we analyzed the Taylor equation, in which the GDP gap, is considered as the deviation of the natural rate of unemployment - NAIRUequal to 5%, from its current value - UR.

(2)

Figure 3. Actual and Theoretical U.S. Federal Funds Rate #2, July 1954-July 2015.

The average absolute forecast error for equation (1) was 1.83%, while equation (2) was about 1.72%. Thus, equation (2) more accurately predicts the future value of the federal funds rate. According to these models, the current federal funds rate should be in the 1.84-2.01% range, not in the 0-0.25% range.

This means that at the moment the Fed's interest rate is significantly low, so market expectations for a rapid tightening of monetary policy are quite logical. Time will tell if this will happen in the fall or if we will have to wait for the winter meetings.

This article is featured in the 97th issue of ForTrader.org magazine

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