CPI Formula: How to calculate the Consumer Price Index

The consumer price index (CPI) measures the average level of prices of goods and services in the economy. The CPI formula is used to measure the change in prices by consumers for a representative basket of goods and services during a defined time period. CPI is a widely followed measure of inflation which is used by economists, policy makers, investors to guide economic policy, forecasting and investment decisions.

What is the CPI Formula?

CPI = ( Cost of market basket in a given year / Cost of market basket in base year ) x 100

The CPI formula requires what is called a market basket of goods and services, then the formula utilizes the estimated costs of such a basket to calculate the index value that we know as CPI.

Let’s look at the steps involved in detail:

CPI Formula: The Market Basket

While imperfect, the CPI’s market basket is one attempt to find a quality representation of typical consumer purchases within the economy. It includes things from hundreds of categories and eight major groupings. The groupings are food and beverage, housing, apparel, transportation, medical care, recreation, education and communication and other goods and services.

To determine the specific inclusions of the basket, information is collected from individuals over the course of two years regarding regular expenses and consumption behavior. From the BLS government site: 

For example, CPI data in 2016 and 2017 was based on data collected from the Consumer Expenditure Surveys for 2013 and 2014. In each of those years, about 24,000consumers 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 12,000consumers 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.

The market basket is then built using this information. Note that this not only includes what items to include, but quantities of items. For instance, if a typical consumer is regularly purchasing 5 gallons of milk per month, this quantity is noted. The data is analyzed thoroughly to provide proper weighting and importance of various items based on what data collectors perceive as the typical consumer behavior.

Note that the purchasing behavior is pulled from urban consumers which is estimated to be about 93% of the US population. The buying behaviors of rural consumers are not factored into the CPI.

CPI Formula: Pricing The Market Basket

Once the goods and services that make up the market basket are determined, the next step is to log the prices for such a basket. This includes both current and previous prices of the various goods and services. By pricing the basket both currently and historically, analysts can determine price increases and decreases over time of the identified basket.

To collect the detailed pricing information, BLS data collectors visit thousands of stores, service companies, doctor offices and more both in-person and online. The BLS says that they record the prices of approximately 80,000 items on a monthly basis.

CPI Formula: Computing The Actual Index

To calculate the index value of the CPI, a base year must be identified. The base year serves as a benchmark year against which future years are compared. While the base year can change every so often, it typically doesn’t change for several years in order to provide better comparative data over the course of a few years. 

By dividing the price of the market basket in a given year, say the current year, by the price of the same basket in the base year, then multiplying the value by 100, we are able to get the Consumer Price Index value.

Note that the CPI for the base year will always be 100. This is obvious since we’re dividing the market basket price by the same market basket price (which results in 1), then multiplying by 100. This enables us to easily see increases (or decreases) in the CPI. If the CPI of year 3, for instance, is 125, then we can compare a CPI of 100 to 125 three years later and see a 25% increase in the CPI.

When using the Consumer Price Index, it’s worthwhile to understand how to interpret an actual index value. An index attempts to simplify the movements in a series of data. While one can note the difference in “points” between two index values, it’s more commonly described as a percent change. For instance, you would typically say that the index is up 5% between two time periods rather than referencing a change of, say, 8 points.

What is Core CPI?

A version of the CPI known as “Core CPI” attempts to measure pricing changes of items similarly to the CPI but without food and energy costs. You might see the phrase “All items less food & energy” when describing Core CPI. The reason for this is that some economists perceive food and energy costs as quite volatile and thus it can negatively affect the core or underlying trends of price behavior. Critics of the Core CPI method note how important food and energy is to typical consumers, and as such, believe that excluding the effects of food and energy is silly.

Why is CPI Important?

CPI is commonly used as an economic indicator. Not only is CPI used to interpret the levels of inflation in the economy, but it can be used to estimate the effectiveness of various economic, fiscal and monetary policies. 

Furthermore, CPI can be used on occasion to adjust other economic data to properly measure changes. For instance, you might see measurements described as “inflation-adjusted” in order to see the true rates of growth or change in a dataset. 

Perhaps most importantly, social security payments to millions of retirees are adjusted from time to time with a cost of living adjustment (COLA) which uses the CPI as a major component in determining COLA amounts. In 1973, Congress amended the Social Security Act of 1935 to enable annual cost of living adjustments based on CPI. This adjustment has a direct impact on millions of people. It is estimated that over 60 million people receive social security benefits on a regular basis.

What are the limitations of the CPI and the CPI formula?

There is a common view that the CPI overstates inflation by approximately one percent because there is a bias toward higher prices. The rationale for this is as follows:

First, CPI doesn’t do a good job of factoring in substitution effect when prices of a particular good or service increase. If a price increases, consumers naturally react and substitute this good or service with something else. The CPI formula doesn’t factor this in, but rather assumes consumers are continually buying the same basket of products (until new data is pulled indicating a change in consumer patterns). 

Additionally, major increases in quality of various products are difficult to quantify and to factor into the CPI. While consumers benefit from increased quality, this typically isn’t seen in the CPI until new data indicates a change in consumer behavior. 

Other notable arguments against the CPI

Some economic schools of thought, namely the Austrian school of economics, are quite hesitant to place much value on the Consumer Price Index as well as how the subject of inflation is discussed in general. While inflation is often perceived as the result of rising prices (“rising housing prices are causing a rise in inflation”), the Austrians would disagree with such a statement. As stated at Mises.org:

As economists and others of the Austrian School understand, inflation occurs when the value of money declines relative to the goods and services it can purchase. In other words, inflation is a monetary phenomenon, not a price phenomenon. Prices go up because inflation is happening, not the other way around.

This statement indicates that even the idea of inflation itself isn’t totally agreed upon amongst economists. Austrians are quite critical of Federal Reserve policy that results in increases in the money supply which then leads to more dollars chasing the same amount of goods and services. This then leads to increased prices and what most consider to be “inflation.”

Regardless of your interpretation, the Consumer Price Index is still valuable to understand and know simply because many institutions and economic policies factor it in! The simple fact is that the CPI is widely used, so whether you agree with its calculation, the CPI formula itself or how it is to be interpreted, you can’t dismiss it.