Over the years I’ve argued that economists are horribly confused about the concept of “income.” They use income for tax incidence discussions and also economic inequality, whereas on theoretical grounds consumption is clearly the appropriate variable. And yet until a few minutes ago I never realized just how confused we were (which I guess means I was equally confused).

I did a post over at MoneyIllusion on real wages, and commenter Foosion directed me to a Paul Krugman post on the topic. Krugman tries to show that real wages have done poorly, but is only able to do so by deflating the wage series by the CPI. I used the PCE, which is preferred by most experts, and found a significant rise in real wages since the 1990s. But it was this comment by Krugman that left me scratching my head:

My second chart shows real GDP per household — nominal GDP, deflated by the consumer price index, divided by the total number of households; and compares it with median household income, both expressed as indexes with 1979=100. We’ve had substantial income growth since then, but very little for the median household, because so much of it has gone to the top.

Now it’s a free country, and Krugman can define “real GDP” any way he likes. But the term ‘real GDP’ has a pretty well accepted meaning among economists, and it’s definitely not NGDP/CPI. Instead, real GDP is NGDP divided by the price index of the goods that make up NGDP, i.e. the GDP deflator.

At this point I realized that I was being too hard on Krugman. After all, GDP is just another term for gross national income. And economists have been using the CPI to deflate income data of all sorts for decades. But the fact that we’ve been doing it doesn’t make it any less insane. Let’s look at some basic definitions (sorry David).

GDP = C + I = C + S = GDI

So in a simple model with no trade or government, national income has two parts, consumer goods and investment goods. Obviously if we want to calculate the real value of consumption, we ought to use the price level of consumer goods (the CPI or the PCE). And if we want to calculate real income/output, we’d deflate using the price level of all goods, consumer and investment. And yet how often do you see economists calculate real income by using the CPI or the PCE? Indeed I made this mistake in my MoneyIllusion post, using the PCE. The correct deflator is the GDP deflator. (Yes, it gets more complicated with government and trade, but that doesn’t excuse this fundamental error.)

Perhaps economists are interested in the purchasing power of income under the assumption that all income was consumed. But in that case GDP would equal C, and investment would be zero. So the two price indices would be identical. As long as GDP does not equal C, it makes no sense to deflate income with the CPI or the PCE.

If you are still reluctant to give up on the notion that the “cost of living” should be measured in terms of consumption price indices, I think I know why you are confused. Yes, in a sense the CPI or PCE is the deflator that is appropriate for living standards comparisons, but that means our bigger mistake is that we are using income as a measure of economic wellbeing, whereas all our economic models tell us that consumption is the appropriate variable.

Unless I’m mistaken this is embarrassing. First the economics profession ignores the implications of their models by using income where consumption is appropriate. That’s already pretty bad. Then to make matters worse we don’t deflate income with the appropriate price index, the one for all of income, not just consumption. Instead we deflate income (i.e. C+I) with a consumption price index. We use the wrong indicator of well being, and then pick the price index that would be appropriate if we’d chosen the right indicator of well-being!

Does this matter? Not before 1970. But since then it matters a lot. Commenter E. Harding sent me a graph showing that since 1970 the CPI has risen far faster than the PCE, and even the PCE has risen more than the GDP deflator. This mistake explains much of the phony claim that “real income” has stagnated since the 1970s. (Although many articles also make other mistakes, ignoring fringe benefits like health insurance, or government transfers.) PS. Unfortunately I had to shrink this graph to fit the 400 pixel max at Econlog. The fast rising red line is the CPI, the green is the PCE and the blue is the GDP deflator.

Update: I misinterpreted the graph sent to me by E. Harding. The blue line was the price index for the business sector. In this new graph the GDP deflator is added, and is very slightly above the PCE. So the problem is less worrisome than I assumed. 