The world is a complex place, and the mathematical models used to understand the world are probably even more complex. If you watch the news, political speeches, or even just chat with people on the street, you will see a lot of talk about the macroeconomic variables important to the economy. Here, I want to briefly go through some of the most important headline variables, their values, and what they represent. I want to keep this short and manageable, so I’ll go through these variables one post at a time.

I’ll start with inflation. Inflation, in general, is the percent change in prices year over year in the economy as a whole. Think of this through the following example. Assume an economy only has one good, apples. In the first year, apples cost $1, and in the second year, apples cost $1.25. What is inflation in this economy? The obvious answer is 25%, (1.25-1)/1, but this isn’t the whole story. Let’s look at a more complicated example.

Assume there are two goods, apples and oranges. In year 1, there are two apples produced, and three oranges, apples cost $1, and oranges cost $2. In year 2, there are three apples produced, and two oranges produced, apples cost $3, and oranges cost $5. How would you calculate inflation here? This presents one of the classic problems in calculating inflation: substitution effects. When prices rise for one good relative to another, people consumer more of the cheaper good. To determine what inflation is, we need a brief discussion of what inflation is actually measuring.

From one perspective, inflation measures the change in the price of goods. This would mean the goal is to measure the new price one would have to pay to purchase the old basket. For the previous example, we would fix the basket of goods at year 1, two apples and three oranges. This means to calculate inflation, we would first find the aggregate spending. This is two apples times one dollar, plus three oranges times two dollars. This would result in total spending of eight dollars for the economy. For the next year, we would use the same basket, but new prices. This is two apples times three dollars, plus three oranges times five dollars. This would be an aggregate spending of twenty one dollars. Inflation would then be calculated as (21-8)/8=162.5%. This method of calculating prices is known as the Lasperyes index.

The other way of looking at this is the reverse, or the Paasche index. For that, the year two quantities would be used, so instead of two apples, and three oranges as the basket, three apples and two oranges would be used. This leads to the problem of substitution effects from the opposite direction. These are both valid ways of taking a price index, but still leaves the question of what we are purchasing when we buy goods. For an economist, the answer is utility(loosely thought of as happiness). I won’t go into all of the details here, because this post discusses the idea much more thoroughly than I ever could, but I’ll summarize to say this is approximated by taking the geometric mean of the two, a process known as chaining, which is how the idea of substitution effects are usually dealt with.

Aside from substitution effects, there are two other common problems with measuring inflation. The first is changes in the quality of goods. This is easiest to think of in terms of computers. If you have two computers, across two years, with the same price, and in year two the processing speed increased, did prices change? In the strictest sense, prices remained constant, but you’re getting a better computer for the same cost, thus in real terms, prices for the computer actually decreased. The other very common problem is introduction of new goods. Consider the problem of calculating prices between 1900 and today. In 1900, we did not have many of the technologies we have today, so how accurately can you compare prices and quantities between the two periods? The two prices indexes above would be impossible to calculate, which is usually why calculating the basket more frequently is better.

The next thing I’ll go in to here is the difference between the two most common measures of inflation, CPI, and PCE. CPI has a long history, and is based off of the things that consumers purchased. This usually works through a survey, which consumers are asked to track their spending habits, then other surveyors go out to stores and write down prices. The basket used to be calculated every five years, but now is calculated every two years. The basket for PCE on the other hand, is calculated quarterly, based on the consumption aspect of GDP data, making it a bit easier to deal with quality changes and introduction of new goods. This is also a place where chaining is important. CPI is usually calculated using a fixed basket approach, and while PCE can be calculated with a fixed basket, it is usually chained, which is usually better for dealing with substitution effects. There are some other differences, and a more thorough discussion of the differences can be found here, but these are the main points to remember. It’s also important to note that while many government programs are indexed to CPI, the Fed, and many other people engaged in studying the economy, feel PCE is a better measure.

There is also an important aspect of inflation involving food and energy prices. Inflation measures excluding these are known as core inflation, and are generally better for forecasting. Food and energy prices are very volatile, and tend to react strongly to seasonal aspects, and weather effects. While both aspects are important to consider, if you think there is some short term change in food or energy prices that is artificially holding up or holding town the headline number, it’s usually best to make decisions based off the core number.

This brings me to the last major point I want to make before looking at the numbers. In economics, there is a strong use of the word “real” and “nominal”. This doesn’t always refer to the following explanation, but most often does. Usually, a “real” variable is adjusted for inflation, and a nominal variable is not. It is used to look at the relative quantities of goods, instead of just the headline value, which can be misleading. For a simple example, imagine wages double, and prices double. In nominal terms, prices are twice as high, which seems bad, but in real terms, you can purchase the same quantity of goods, so your well being hasn’t changed.

I’ll conclude this with a summary of the numbers. All of this data comes from the St.Louis Fed.

CPI: 1.05

PCE: .881

Core CPI: 2.23

Core PCE: 1.57