"Fixed-weight" problems

RE: Karl Whelan's A Guide to the Use of Chain Aggregated NIPA Data PDF from June, 2000.

The U.S. Department of Commerce in 1996 switched from "fixed weight" calculations to "chain-weight" calculations for converting nominal values to real values. Solved one problem, created another.

I want to understand the problem with the newer method. But I have to start by trying to understand the problem with the older method. Because the problem with the older method, as Whelan describes it, is unbelievable:

While the fixed-weight methodology has the advantage of simplicity and ease of interpretation, it also has a number of undesirable features. Most importantly, the growth rate of a fixed-weight measure real GDP depends on the choice of base year. Take 1998 as an example: The growth rate of fixed-weight real GDP in this year was 4.5 percent if we use 1995 as the base year; using 1990 prices it was 6.5 percent; using 1980 prices it was 18.8 percent; and using 1970 prices, it was a stunning 37.4 percent!

In a footnote, Whelan adds: "These figures actually understate the true pattern."

Yikes. How is this even possible?


I went to ALFRED to see the RGDP data immediately before and immediately after the change:

Graph #1: Last Data Before the Change (blue) and First Data After (red)

Same two series, indexed to the start-date of the red line:

Graph #2: Same Data, Set Equal at Start-of-Red

And as a ratio:

Graph #3: After the Change, relative to Before the Change

Yeah, I don't see anything there. The revision made Real GDP higher, as you would expect. That's our main way of improving the economy these days: revise the data. That's the fallback strategy whenever theorists come to resemble Euclidean geometers in a non-Euclidean world and their deep divergences of opinion destroy the practical influence of economic theory.


Whelan explains:

The reason we get higher growth rates for real GDP when using earlier base years is the well-known problem of "substitution bias" associated with fixed-weight indexes. Categories with declining relative prices tend to have faster growth in quantities; the further back the base year the larger is the weight on these fast-growing categories and so the faster is the growth rate of real output.

He adds:

Similarly, for a given base year, the growth rate of a fixed-weight quantity index tends to increase over time as the output bundle becomes increasingly expensive when measured in terms of the base year's prices. This problem became more severe after the mid-1980s because of BEA's decision to measure computer prices according to the hedonic method...

Yeah, this part I don't get. Why does the growth rate increase as the output bundle becomes increasingly expensive? That doesn't sound right. Giving an example of when it supposedly happened doesn't explain anything.

But the "Categories with declining relative prices tend to have faster growth in quantities" part, that makes sense. If the price of beef goes up more than chicken, people switch to chicken. If beef and chicken prices both go up, people switch to beans.

I'm still troubled by this. I still postpone belief in the truth of Whelan's claim that the "fixed weight" growth rate of real GDP in any given year depends on how distant the base year is from the given year.

I'm still ruminatin'.