Steven Engelhardt

I keep seeing statements such as the following pop up in the news:

And taking general inflation into account, it is slightly cheaper than what motorists paid in March 1981 in the aftermath of the Iran hostage crisis. Then, gas cost $1.41 a gallon, or $3.12 in 2005 dollars.

Hebert, H. Josef. “Q&A: Less oil, costly ethanol; that’s trouble” The Modesto Bee. 26 April 2006.

My immediate observation was that gas prices themselves are a part of the inflation calculation, and this may influence the comparison. I set about to explore this in more detail, and my findings are below.

Let’s consider, for the sake of argument, if the CPI were calculated using a basket of two goods: 50% gasoline and 50% food. Assume that in one year, the nominal price of gasoline jumps 10%, and the nominal price of food stays flat. We can represent this situation as the following table:

Note that real price in year Y + 1 is calculated by rescaling the Total price back to $2. This is equivalent to calculating CPI by taking the weighted changes in nominal prices for the basket of goods, and then deflating the nominal price of the product in year Y + 1 by the calculated CPI rate (5%).

Although the price of gas was the only thing that changed, the CPI-deflated real increase in the price of gas is only 1.0476/1 = 4.76%. Had gasoline not been part of the CPI calculation (i.e. only food were used to calculate CPI), the CPI rate would have been 0%, and the real increase in the price of gas would have been equal to the nominal increase: 10%.

In other words, because a good which experienced a relatively high rate of inflation was included in the calculation of CPI, it led to a lower reported real rate of inflation of the good than would have occured had it not been included in the calculation of CPI.

There’s another side to this observation as well. Using the original calculation of CPI, you can note that while the nominal price of food didn’t get any cheaper, the real price did, solely because of the increase in the price of gas. Similarly, had gas not been used to calculate CPI, the real price of gas would have increased by 10%, but food would not have gotten any cheaper. So, in effect, you trade reported inflation rates among products when you change how you calculate CPI. However, if you purchase exactly 50% gas and 50% food, the net effect is the same.

In other words, how your consumption compares to that of the CPI basket is crucial. For example, using the initial assumptions, if you purchase more gasoline than the CPI statistic used in its calculation, then your personal “inflation rate” is higher than the CPI; purchase less gasoline, then your personal “inflation rate” is lower. This is simply a restatement of the fact that the CPI represents some kind of “average” basket of goods, which your personal consumption patterns are unlikely to exactly match, and thus your personal inflation rate is almost certainly never the same as the CPI.

What I personally find interesting is that if you assume your real income stays constant and you purchase the same distribution of goods as the CPI, your consumption level stays exactly even, but your spending distribution among products may vary drastically. For example, look how in the inital CPI example there was a movement of 2.4% of spending from one product to another. What are the implications of such movement?

I would be very interested in seeing a breakdown of how the spending distribution of consumers, as a percentage of income basis, varies across incomes and across time. I can think of many goods where the percentage of income on spending generally decreases with time (appliances, computers, food, etc.) and I wonder where the “new-found” income goes.