"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'.

"the hedonic method"

I'm reading Karl Whelan's A Guide to the Use of Chain Aggregated NIPA Data PDF. Menzie Chinn linked to it, and Justin Fox, regarding errors in the use of "chain-weighted" inflation-adjusted data.

I need some background on "hedonics":

Source: OECD

Source: Abstract, The Hedonic Method by Laura O. Taylor at Springer Link

In economics, hedonic regression or hedonic demand theory is a revealed preference method of estimating demand or value. It breaks down the item being researched into its constituent characteristics, and obtains estimates of the contributory value of each characteristic....
Hedonic models are commonly used in real estate appraisal, real estate economics, and consumer price index (CPI) calculations. In CPI calculations, hedonic regression is used to control the effect of changes in product quality. Price changes that are due to substitution effects are subject to hedonic quality adjustments.

Source: Wikipedia, Hedonic regression

Whelan describes the problem with the old "fixed-weight" method, the problem which led to the adoption of the "chain-weight" method:

... 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 pioneered by Zvi Griliches (1961). This approach revealed enormous declines in the quality-adjusted price of computing power and the introduction of these prices accentuated the tendency of fixed-weight GDP to accelerate over time.

"The quality-adjusted price of computing power". That's the "hedonics" thing.

OECD describes quality adjustment:

The process - or the result of the process - of estimating what the market price of a replacement product would be if it had the characteristics of the product it replaces and with whose price its price is to be compared.

BLS explains it less objectively:

The CPI is calculated using prices for a fixed basket of goods and services through time. While the basket is periodically revised to reflect changing consumer expenditures, some items being priced in the sample come and go from the marketplace, making collection of these prices from month to month difficult. When an item is no longer available in the marketplace, a similar replacement item is selected. Often there are no similar items from which to choose, and as a result, a less comparable item is selected, potentially introducing quality change and an associated price differential into the index. The hedonic quality adjustment method removes any price differential attributed to a change in quality by adding or subtracting the estimated value of that change from the price of the old item.

consumerpriceillusion has a different take:

Ostensibly, the CPI is a linear combination of the “prices” of things/stuff consumers could actually purchase weighted by a percentage that the “ideal consumer” spends on any particular stuff/thing in his “ideal” basket. The main problem here is that the “prices” used are not the prices a consumer would actually pay; instead the real price for an item is scaled by what the BLS calls a “Hedonic Quality Adjustment (HQA)”. The HQA was designed to solve a real world problem economists face: the market keeps pumping out new and better devices. In practice the HQA is used to artificially depress the prices used in the calculation of the CPI.

For me... Well, let me tell you about my experience with computers. When I bought my first modem it cost me $150. It was a 300 baud modem. Several years later I bought a 56K modem. It cost me $150. For me, $150 was an acceptable price for a modem.

My first hard drive cost me $400. It was a 40-meg drive. Several years later I bought another hard drive: 400 gig. It cost me $400. For me, $400 was an acceptable price for a hard drive.

In my experience, the price of modems and hard drives didn't go up at all. But if you used hedonics to "adjust" those prices for quality, the prices would have fallen. A lot.

But the prices didn't fall. The technology got better, but the prices didn't fall.

"In practice the HQA is used to artificially depress the prices used in the calculation of the CPI."

Yup.


Oh. The reason this comes up. There is a lot of noise these days about low productivity, and how productivity "really" isn't low. It's just not counted right, they say. Or it's not countable. Or some other story. It's all noise.

It is noise that will eventually lead to a revision in the way productivity is calculated. A revision that makes productivity look better than it is today. A bullshit revision, another one, like not counting people who are unemployed and like using hedonic adjustment to "reduce" inflation.

I object.

The whole is not equal to the sum of its parts? Really?

Menzie Chinn, in Assessing Trends in Real Shares at Econbrowser brings up a problem: "Chain-weighted" real numbers don't add up. Chinn links to Justin Fox's Friends Don't Let Friends Calculate Shares of Real GDP. Both of them link to Karl Whelan's A Guide to the Use of Chain Aggregated NIPA Data (PDF).

Chinn quotes Fox: "the different components of real GDP can no longer be added together. That is, they can be added together but, except in the base year, they don't add up to real GDP." Pretty clear.

Fox also says:

The BEA's remedy to the problem is to put up warnings against doing share-of-real-GDP calculations all over its website.

That's pretty funny. Also true, as even I have noticed those warnings.

But I'm having an awful lot of trouble understanding the problem. To use the example both Chinn and Fox use, consider manufacturing as a share of GDP. If you figure Nominal Value Added (for manufacturing only ) relative to Nominal Value Added (for all of GDP) you are okay. But maybe you think your result is unsatisfactory because prices have gone up more slowly for manufacturing than for all of GDP ("think health care", Justin Fox says). The nominals don't give you a good picture of manufacturing's share of real output over time. But that's not the error.

The error comes in when you switch to inflation-adjusted data. Since the mid-1990s, inflation-adjusted values have been figured by the "chain-weighted" method. Because they use this new method, when you take the inflation-adjusted components of GDP and add them up, the total doesn't come out equal to inflation-adjusted GDP. Here's Whelan:

A crucial feature of this chain aggregation methodology is that the real aggregate of X and Y will generally not equal the arithmetic sum of the real series for X and Y.

For chain-weighted values, the whole is not equal to the sum of its parts. That's the problem. That much I get, but that's where I lose it.

It just doesn't make any sense to me. Y=C+I+G+NX, but only if they're nominal values? I have to ruminate on this for a while.