Let’s Talk About the Taylor Rule for Monetary Policy

It has been almost 30 years since the American economist John B. Taylor proposed what has been known as the Taylor rule. The Taylor rule is quoted by news articles especially during the 2020 Corona Virus recession or other periods of economic turmoil. Fund managers and investors want to gauge its guidance on monetary policy. There are also debates by admirable economists concerning how closely the policymakers should follow its predictions., i.e., using it as a prescriptive tool or a benchmarking tool.

Maybe this is the first time you heard the Taylor rule, I will introduce the Taylor rule gently. This post also covers in-depth discussions, hopefully it will be interesting to seasoned economists. I will first explain why the Federal Funds Rate is a powerfully instrument for the Federal Reserve (Fed) to influence the public investment and spending behaviors. I then describe the variation in the CPI source data is not negligible. This variation partly contributes to the debates over whether policymakers should the Taylor rule predictions as a prescriptive tool or as a guiding principle. This article discusses a technical matter: the use of Python Streamlit as an excellent dashboard design instrument. This may interest some data engineers for its elegance as an exhibition tool.

(A) What Is the Federal Funds Rate?

The Fed requires banks to keep a percentage of their customer’s money on reserve, where the banks earn no interest on it. Consequently, banks try to meet the reserve limit every day. If under, banks can pay a little interest to borrow from other banks overnight to meet the minimum requirement. The fed funds rate is the interest rate banks pay for overnight borrowing in the federal funds market. This rate is the primary tool that the Fed uses to conduct monetary policy.

(B) Changes in the Interest Rates Can Change Investments & Spending

Changes in the federal funds rate influence other interest rates such as home mortgage rates or commercial loan rates, as shown in Figure (B). During economic downturns, the Fed can lower the federal funds rate even near zero to stimulate the economy. For example, when home mortgage rates go down, households are more willing to make loans to buy houses; when commercial loan rates go down, businesses are in a better position to borrow money to expand their business, such as property and equipment. Businesses can also hire more workers, influencing employment. And the stronger demand for goods and services may push wages and other costs higher, influencing inflation.

The stock markets are sensitive to the changes in the federal funds rate. A 0.25 percentage point decline in the fed funds rate can cheer the stock markets higher. On the other hand, a 0.25 percentage point increase that trying to curb inflation can result in a decline because it sends a message about slowing growth.

Figure (B): The Federal Funds Rate and Other Interest Rates

(C) The Taylor Rule

The Taylor rule is a formula that can be used to predict or guide the Fed to set the federal funds rate in response to changes in the economy. Taylor’s rule recommends that the Fed should raise interest rates when inflation or GDP growth rates are higher than desired. According to John Taylor’s original paper in 1993, it is:

i = 𝜋 + 0.5y + 0.5(𝜋 — 2) + 2

where

  • i is the federal funds rate,
  • 𝜋 is the expected rate of inflation, and
  • y is the percentage deviation of real GDP from a target, or called the GDP gap. GDP gap (y) = real GDP/potential GDP -1.
  • The 2 in the term (𝜋 — 2) is the inflation target, which is 2 percent.

(C.1) How Does the Formula Work?

Although the Taylor formula is simple, over time some news articles or even study guides have mis-quote the formula, rendering wrong conclusions. Even John Taylor himself has to clarify the mis-information (such as in this post). Here let me give a clear calculation. Suppose:

  • An expected rate of inflation of 1.2%
  • The real GDP or annualized GDP growth rate is 5%, and the potential GDP growth rate is 2%, leaving the GDP gap -3%,

The federal funds rate should be 1.2% + 0.5 * -3% + 0.5 * (1.2%–2%) + 2% = 1.3%.

(C.2) What Does It Mean for Policy?

We have learned when the economy is weak, the Fed can lower the federal funds rate to boost the economy. in the above example the economy under performs the long-term potential GDP by 3%. In order to boost the economy, the federal funds rate is suggested to be as low as 1.3% which is lower than its historical average 2%. In summary, the Taylor rule says the followings:

  • For one percentage point of inflation increase relative to the 2% inflation target, or one percentage point increase in the output relative to its potential, the federal funds rate should go up by 0.5 percentage point.
  • If inflation is at the target 2% and output is at potential (output gap is zero), the real federal funds rate should be at 2%, which is about is historical average (Bernanke 2015).

(D) Key Data Sources for the Inflation Measure

Scholars have found that different data sources for inflation in the Taylor rule can sometimes generate very different values for the federal funds rate (for example, click here or here). This difference to some extent contributes to the debate over whether the Taylor rule is to be followed closely as a prescriptive tool, or loosely as a benchmark tool. Let me guide you to retrieve the data sources.

(D.1) Inflation indexes

Below I summarize four commonly-cited inflation measures in the Taylor rule calculation. From the following indexes, the rate of inflation is calculated as year-over-year percentage.

  • CPI: The “Consumer Price Index for All Urban Consumers: All Items” is a measure of the average monthly change in the price for all goods and services paid by urban consumers. This index is comprehensive that includes roughly 88 percent of the total population, accounting for a wide range of earners such as wage earners, clerical workers, technical workers, self-employed, short-term workers, unemployed, retirees, and those not in the labor force.
  • Core CPI: The “Consumer Price Index for All Urban Consumers: All Items Less Food & Energy” is an aggregate of prices paid by urban consumers for a typical basket of goods, excluding food and energy. This measurement is widely used by economists because food and energy have very volatile prices.
  • GDP Deflator: The “Gross Domestic Product Implicit Price Deflator” is a measure of the level of prices of all new, domestically produced, final goods and services in an economy in a year. Unlike the CPIs, the GDP deflator is not based on a fixed basket of goods and services; the “basket” for the GDP deflator is allowed to change from year to year with people’s consumption and investment patterns.
  • PCE: The “Personal Consumption Expenditure” is the component statistic for “consumption” in gross domestic product (GDP) collected by the United States Bureau of Economic Analysis (BEA). It consists of the actual and imputed expenditures of households and includes data pertaining to durable and non-durable goods and services. It is also called the PCE deflator, PCE price deflator, the Implicit Price Deflator for Personal Consumption Expenditures.

A few articles (like this article) document that different sources of the inflation data contribute more to the variations in the predicted federal funds rate than the GDP data.

(D.2) GDP and Federal Funds Rate Data

  • Real GDP: The “Real Gross Domestic Product” is the inflation adjusted value of the final goods and services produced in the United States.
  • Real Potential GDP: The “Real Potential GDP” is the estimate of the output the economy would produce. The data is adjusted to remove the effects of inflation. The estimates are from the Congressional Budget Office (CBO).
  • Federal Funds Rate: The Federal Open Market Committee (FOMC) meets eight times a year to determine the federal funds target rate.

(E) A Prescriptive or Descriptive Tool?

Dr. Bernanke, the Chair of the Federal Reserve in 2006–2014, pointed out that the predictions of the Taylor rule should be taken as a benchmarking tool rather than a prescriptive tool. Below are two re-prints of Bernanke in 2015. The first graph uses GDP deflator, which is also used by John Taylor’s original 1993 paper to predict the federal funds rate. The second graph uses Core PCE inflation for the federal funds rate. The differences in the two graphs are noticeable.

Credit: Click here
Credit: Click here

(F) On a Technical Matter: Plotting with Python Streamlit

Python Streamlit is a great tool. I like its smart code of Streamlit to make an interactive dashboard. I like its neat interface, as I shared in the article “Building a Stock Market App with Python Streamlit in 20 Minutes”. I made my Python code available via this github. While I talk about dashboard, I recommend you to take a look of the Taylor dashboard by FRED Blog.

My Python code is available for you to download via this link. Open a command prompt and type in streamlit run Taylor_rule.py. You shall see the following message and a new page in the browser.

I want a dropdown menu in the left side bar for users to choose a CPI index and the day range. I also took a video of the dashboard so you know what it looks like.

The Steamlit code is fairly simple. It has a few lines for the sidebar, and a few lines for the main body as below. When you use st.sidebar, it knows to create a sidebar area with the appropriate proportion.

(G) Variation in the Predicted Federal Funds Rate Could be Large

The use of different indexes for the rate of inflation can result in non-negligible variation in the predicted federal funds rate. With the four predicted federal funds rate, I calculate the minimum and maximum differences among them for each month. All my calculation can be found in this Python notebook. The histogram below shows the median difference is about 1.5%. Consider a 0.25 percentage point increase or decrease of the federal funds rate can cause a sensible market reaction, the size of the variation cannot be ignored. This explains why policymakers have their reservations in using the Taylor rule as a prescriptive tool, i.e., following its predictions closely for monetary policy.

Conclusion

Thank you for reading. I hope this has given you a better understanding of the topic. If so, be sure to let me know in the comments.

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