Federal Funds Rates & Taylor’s Rule

This read is an add-on to the Online Courses posted on The middle Road. This Section focuses on applied learning of the concepts discussed in the courses. This section is for people who have sufficient knowledge of the concepts underlying the material taught herein. For example, understanding Inflation and Gross Domestic Product is a prerequisite for working on Taylor and Mankiw rule. Taylor’s rule is one of the most significant enablers for policymakers and economists to set policy rates in the US and a key tool for monetary policy. The Taylor Rule is an important framework for arriving at the Nominal Federal Funds Rate.

This is part of the Stabilization Series of online courses covered in Macroeconomics.

Federal Funds Rates are the benchmark rates for driving credit within the US and global economy. These rates influence the prime lending rate and are rates at which depository institutions lend unsecured federal funds overnight. The effective federal funds rate is essentially determined by the market but is influenced by the Federal Reserve through open market operations (policy tool) to reach the federal funds rate target. Open market operations will be discussed separately.

The middle Road was one of the first platforms to suggest the FED must increase the interest rates in 2021 using Mankiw and Taylor’s rule to predict the gap between the prevailing Fed Rate and the estimated Fed Rate.

*The discount rate is the interest rate charged to commercial banks and other depository institutions on loans they receive from their regional Federal Reserve Bank’s lending facility—the discount window. The Federal Reserve Banks offer three types of credit to depository institutions: primary credit, secondary credit, and seasonal credit, each with its interest rate. All discount window loans are fully secured. – FederalReserve.gov

Source: Board of Governors, IMF, fred.stlouisfed.org | Frequency Monthly Fed Funds Rate seasonally adjusted, Discount Rate not seasonally adjusted  

To understand Taylor’s rule, it’s key to have an overview of inflation and inflation measures like the Consumer Price Index and Gross Domestic Price Deflator. Refer to the online course on Macroeconomics to understand Gross Domestic Product- GDP and other concepts in macroeconomics. GDP is the total income generated by an economy and can be calculated through various measures- expenditure, income, and value-based method.  GDP can be nominal or real GDP. Real GDP is adjusted for inflation calculated at a base price. For the US, 2012 is the base year. GDP is discussed in detail in the Macroeconomics course on The middle Road.   

U.S Bureau of Economic Analysis BEA is responsible for producing the National Income and Product Accounts (NIPAs). NIPAs – National Income and Products Accounts present the value and composition of national output and the types of incomes generated in its production in the United States. The GDP of an economy has different components income, production, consumption, investment, and savings, NIPAs capture these measures in the US. The composition of the US economy gives an excellent understanding of various components of GDP. GDP is the total income generated by an economy and can be calculated through various measures- expenditure, income, and value-based method.  GDP can be nominal or real GDP. Real GDP is adjusted for inflation calculated at constant prices usually with reference to a base price. For the US, 2012 is the base year. GDP is discussed in detail in the Macroeconomics course on The middle Road. NIPAs – National Income and Products Accounts present the value and composition of national output and the types of incomes generated in its production in the United States. The GDP of an economy has different components income, production, consumption, investment, and savings, NIPAs capture these measures in the US. The composition of the US economy gives an excellent understanding of various components of GDP.

Consumer Price Index or Cost of Living Index or CPI

Inflation is the increase in an economy’s price levels over a period. Inflation is tracked through price indexes. All countries do not go through inflation. There are periods of deflation, hyperinflation, and disinflation in an economy. For the US, the Consumer Price Index or the Cost of Living Index is the most widely watched price index. Consumer Price Index (CPI), is a measure produced by the Bureau of Labor Statistics (BLS) and calculated monthly. The Consumer Price Index (CPI) is a measure of the average change over time in the prices paid by urban consumers for a constant quality market basket of consumer goods and services. The central bank of Sweden Riksbank defines the cost of living index as the relationship between the monetary amounts required to maintain, the same consumption standard, or the same level of benefit. It compares prices and the consumption level of the population.

Other price indexes in the US explained below. Gross Domestic Purchases Price Index is the broadest measure of inflation within the US economy. GDP Price Index is BEA’s featured measure of the US economy. GDP Price Index like an implicit price deflator measures price changes in goods and services purchased by consumers, businesses, government, and foreigners but not by importers.

The FED closely watches the PCE Price Index and core PCE price index, PCE Price Index is similar to CPI, but the method of calculating and its use are different. Core inflation doesn’t include food, energy, and alcohol prices, therefore less volatile compared to inflation. PCE Price Index only includes purchases by consumers i.e. households and not exports. Both PCE Price Index and core PCE price index are closely watched by the FED. The GDP deflator, another price index is important and is discussed below. CPI is based on a Laspeyres-type index with weights based on a base or historical year, while the Paasche index uses formula weights from the current year. CPI suffers from an upward bias since its basket of goods is constant, an increase in the price of a product might lead the consumer to substitute for another cheaper product which does not reflect in the calculation. PCE is based on the Fisher-Price Index, geometric of Laspeyres and Paasche index. Inflation can be either due to demand-pull or cost-push. Demand-pull is when demand for goods and services exceeds the supply for goods and services or cost-push is when the prices of input goods and services increase due to supply shock, exchange rates, etc. European Central Bank uses Harmonised Index of Consumer Prices (HICP). European Central Bank uses a consumer price index to calculate inflation, harmonised means that all countries in the European Union must follow the same methodology. ECB targets price stability with inflation of 2 percent over medium term, inflation is one of the factors for countries joining the EU. The FED targets price stability, maximum employment and moderate long term interest rates. Central banks will be discussed in depth in the online course on Stabilization. 

Harmonized Index of Consumer Prices composition | Image: The middle Road | Data Source Eurostat 

Types of Inflation 

Headline CPI Inflation Rate

GDP Deflation Inflation rate

Core CPI, consensus percent CPI

Harmonised Index of Consumer Prices

CPIF with a fixed interest rate

Time horizons targeted by various central banks include Point Estimate, Interval within a band, 1-year, Medium Term, Ongoing Core inflation is headline inflation without energy, food, and alcohol

Source: U.S. Bureau of Economic Analysis, Gross Domestic Product: Implicit Price Deflator [GDPDEF], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/GDPDEF, April 15, 2022.  Index 2012=100, Seasonally Adjusted. According to BEA, Seasonal adjustment of a time series removes the average effect of variations that normally occur at about the same time and in about the same magnitude each year—for example, the effect of weather or holidays. After seasonal adjustment, trends, business cycles, and other movements in the time series stand out more clearly. 

Comparison of CPI [CPIAUCSL] Vs Core CPI [CPILFESL] 

Data Source: U.S. Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers: All Items in U.S. City Average [CPIAUCSL], Consumer Price Index for All Urban Consumers: All Items Less Food and Energy in U.S. City Average [CPILFESL] retrieved from FRED, Federal Reserve Bank of St. Louis;https://fred.stlouisfed.org/series/CPIAUCSL. April 16, 2022. Index 1982-1984=100, Seasonally Adjusted. Graph The middle Road

How is the CPI market basket determined in the US ?

According to the U.S. Bureau of Labor Statistics- “CPI market basket is developed from detailed expenditure information provided by families and individuals on what they actually bought. There is a time lag between the expenditure survey and its use in the CPI. For example, CPI data in 2020 and 2021 was based on data collected from the Consumer Expenditure Surveys for 2017 and 2018. In each of those years, about 24,000 consumers from around the country provided information each quarter on their spending habits in the interview survey. To collect information on frequently purchased items, such as food and personal care products, another 12,000 consumers in each of these years kept diaries listing everything they bought during a 2-week period. Over the 2-year period, then, expenditure information came from approximately 24,000 weekly diaries and 48,000 quarterly interviews used to determine the importance, or weight, of the item categories in the CPI index structure.”

First published as part of the Macroeconomic series on Stabilization, the educational video is posted below. John Taylor’s formula calculates the federal funds rate as a function of the output gap and current inflation. For inflation, an implicit price deflator is used. The FED assumes a real interest rate of 2 percent. Below is a comparison of the calculated Federal Funds Rate using Taylor’s rule with the Effective Fed Funds Rate.  

Taylor’s Rule 

Sources: Board of Governors; CBO; BEA; fred.stlouisfed.org

Nominal Fed Funds Rate = Inflation + 2 + 0.5 (Inflation -2) + 0.5 (GDP Gap^)

Nominal Fed Funds Rate = Gross Domestic Product: Implicit Price Deflator + 2 + 0.5 * (Gross Domestic Product: Implicit Price Deflator -2) + 0.5 * (^Real GDP- Real Potential GDP/Real Potential GDP) * 100  

GDP Implicit Price Deflator (IPD) or GDP Deflator: This is another measure that captures inflation in the US, a measure of the increase in the price of goods or services in the US including exports. Imports to the US are not included. GDP Implicit Price Deflator closely mirrors the GDP price index. GDP Implicit Price Deflator (IPD) or GDP Deflator is a “NIPA (National Income and Products Accounts) price measure derived by dividing the current-dollar value of an aggregate or component by its corresponding chained-dollar value and then multiplying by 100. For all periods, the values of the IPD are very close to the values of the corresponding chain-type price index”. (NPA Glossary).

GDP Deflator = Nominal GDP / Real GDP 

Mankiw Rule 

Federal Funds Rate = 8.5 + 1.4 (Core inflation – Unemployment)

Data Source: U.S. Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers: All Items Less Food and Energy in U.S. City Average [CPILFESL], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/CPILFESL, May 22, 2021 | Board of Governors of the Federal Reserve System (US), Effective Federal Funds Rate [FEDFUNDS], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/FEDFUNDS, May 21, 2021. | Calculations & Graph The middle Road