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## Chain-weighting the base-year problem

from Blair Fix, Jonathan Nitzan and Shimshon Bichler

To reiterate, the base-year problem leads to uncertainty in the calculation of real GDP. But instead of openly reporting this uncertainty, government economists have devised a “fix”. Rather than using a single base year, they “chain” together many adjacent base years. This is a bit like a moving average. They calculate the growth of real GDP between consecutive years, using the first year in each pair as the base, and then “chain” together the resulting growth measures to calculate real GDP levels. This method claims to “fix” or at least lessen the base-year problem. It doesn’t.

The appeal of chain-weighting, according to economists, is that it gets closer to their theoretical ideal. According to this ideal, the weight of each commodity in real GDP is provided by its “true” or “natural” price. When using a single base year, the implicit assumption is that relative prices in that base year are “true” and therefore constitute the “correct” weights (Equation 2). However, if the “correct” weights change over time, and if these changes are mirrored in the movement of relative market prices, we can do better by changing the base year more often (every year) and chain-weight the results.

This argument is superficially convincing, but it falls apart on further inspection. First, chaining together base years is better than using a fixed base year only if the “true” weights indeed change over time, and only if “truth” here is indeed revealed by relative market prices. Unfortunately, there is no way to ascertain either “if”. And as long as these two “ifs” remain hanging – which might be forever – chain-linked measures must be deemed as arbitrary as their fixed-based cousins.

Second, if the “correct” weights of commodities change over time we can no longer be sure that producing more units of a given commodity constitutes “real” growth. For example, the production of 20 per cent more laptops whose “correct” weight falls by 40 per cent reduces the “true” output of laptops by 28 per cent ( ). Moreover, changing weights makes temporal comparisons impossible, since the basic unit of measurement – the “correct” weight – is no longer fixed (more on this issue in the discussion of quality change below).

The only solution to the base-year problem would be if prices were stable. But since we cannot change history, this solution is unattainable.

http://www.paecon.net/PAEReview/issue88/FixNitzanBichler88.pdf