Calculating

If inflation is a little more than we say, real output must be a lot less than we think.


I set up a little example in a spreadsheet, a ten-year test run to answer the question, What happens to "real GDP" if inflation is a little more than we say it is?

Here's the thing: NGDP is actual GDP, valued at actual prices. But then they take NGDP and split it into two parts¹ -- RGDP, the real stuff that was produced, and P, the change in the price of all that stuff.

So, NGDP being what it is, if they underestimate the real stuff, they must overstate the price change to make the numbers work. If they overestimate the real stuff, they have to understate the price change to make the numbers work.

It works out great if they overestimate the real stuff, if that's the way it works out, because it makes output look bigger, and prices more stable. Whether that is actually what is going on, is another question -- one that I do not ask.

The important thing to notice is that the real output number and the price level number move in opposite directions. Again: NGDP being what it is, if we assume a bigger RGDP then we must assume a smaller P. If we assume a smaller RGDP then we must assume a bigger P.

But how much bigger? How much smaller? These are the questions I want to ask.


Lately, the Fed has been using a 2% inflation target.²  Some people say 2% is too low and we ought to have 4% inflation.^{3 4}  Meanwhile, other people have been talking about 5% NGDP growth.⁵

I set up my example with ten years of 5% NGDP growth and 2% inflation, to see what happens after ten years. And for comparison, I set up another example using the same 5% NGDP growth, with 4% inflation.

The numbers on yellow background are the constant growth rates for NGDP and the two inflation rate tests.

All values start at 100 in year 1. Year 2 and later values for NGDP and the PRICE columns are calculated from the constant growth rates. Values for RGDP are calculated by dividing the NGDP number by the price index.

Base year for the RGDP columns is Year 1.

After ten years of 2% inflation, prices have gone up 19.5%. After ten years of 4% inflation, prices have gone up 42.3%.

After ten years of lower inflation, RGDP has increased 29.8%. For the higher inflation, RGDP has increased by 9%.

In this example:
• After 10 years of 2% inflation, prices are up about 20% and output about 30%.
• After 10 years of 4% inflation, prices are up over 40%, and output less than 10%.

So if inflation is a little more than we say, real output must be a lot less than we think.


1. Statistics Canada, Chain Fisher volume index - Methodology:

Growth in the gross domestic product (GDP) or any other nominal value aggregate can be decomposed into two elements: a "price effect", or the part of the growth linked to inflation, and a "volume effect", which covers the change in quantities, quality and composition of the aggregate. The volume effect is presented in the National Accounts by what is referred to as the "real" series (such as the real GDP).

Note that StatCan refers to "GDP" and "real GDP". The former is actual GDP, valued at actual prices; this is commonly called "nominal GDP" or "NGDP". However, standard usage equates GDP with NGDP, because both refer to actual GDP.

The latter -- "real GDP" -- is often abbreviated RGDP. This is the value of NGDP that remains after stripping away the changes in value due to changing prices.

2. James Bullard, Inflation Targeting in the USA (PDF), 6 Feb 2012:

At the January meeting, the Federal Open Market Committee (FOMC) took an important step forward by naming an explicit, numerical inflation target for the U.S. of 2 percent, as measured by the personal consumption expenditures (PCE) price index.

3. Char Weise at Creative Destruction, in comments:

I'm not ashamed to call for more inflation... An inflation rate of 3-4% would not have significant harmful economic effects relative to the current 2%.

4. Tim Duy, The Disingenuous James Bullard:

If Bullard wants to take a hard line against higher inflation, so be it. In reality, that hard line has been adopted by the vast majority of Fed officials. They aren't inclined to touch the inflation option for fear, I think, that it would work.

5. At The Money Illusion: George Soros endorses a 5% NGDP target, quoting Soros:

...and aiming at nominal GDP growth of up to 5%, so that Europe could grow its way out of excessive indebtedness.