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Path-dependence of measuring real GDP?

Summary:
I normally try to avoid index number theory. Don't trust me on this. It is well understood that real GDP is a very imperfect measure of welfare. We teach that in first year macro. That is not what this post is about. What I'm worried about is whether real GDP is an imperfect measure of itself. Does it have internal validity? If better technology enabled producers of new goods to ramp up production more quickly to meet initial demand, would that cause the measured growth rate to fall? Initially an economy produces 100 kg of apples at per kg. Then bananas get invented. After a long slow adjustment, the economy eventually reaches a new long run equilibrium and produces 50 kg of apples at per kg and 50 kg of bananas at per kg. We know that nominal GDP stays the same at 0. But what happens to real GDP? The answer depends on what happened during the long slow process of adjustment. Was it supply, or demand, or both, that caused the slow adjustment? To keep it simple, assume the price of apples is always per kg (the central bank targets the price of apples). And assume the quantity of bananas produced and consumed increases slowly and continuously from 0 to 50 kg. And assume the statistical agency that measures GDP has access to continuous time data (so we can ignore the difference between Paasche, Laspeyres, and Fisher price indices).

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I normally try to avoid index number theory. Don't trust me on this.

It is well understood that real GDP is a very imperfect measure of welfare. We teach that in first year macro. That is not what this post is about. What I'm worried about is whether real GDP is an imperfect measure of itself. Does it have internal validity?

If better technology enabled producers of new goods to ramp up production more quickly to meet initial demand, would that cause the measured growth rate to fall?

Initially an economy produces 100 kg of apples at $1 per kg. Then bananas get invented. After a long slow adjustment, the economy eventually reaches a new long run equilibrium and produces 50 kg of apples at $1 per kg and 50 kg of bananas at $1 per kg.

We know that nominal GDP stays the same at $100. But what happens to real GDP? The answer depends on what happened during the long slow process of adjustment. Was it supply, or demand, or both, that caused the slow adjustment?

To keep it simple, assume the price of apples is always $1 per kg (the central bank targets the price of apples). And assume the quantity of bananas produced and consumed increases slowly and continuously from 0 to 50 kg. And assume the statistical agency that measures GDP has access to continuous time data (so we can ignore the difference between Paasche, Laspeyres, and Fisher price indices). Remember that Real GDP = Nominal GDP/Price Level. What happens to the price of bananas during the long slow adjustment period?

  1. Assume that supply and demand adjust equally slowly to the invention of bananas. It takes producers time to switch from producing apples to producing bananas, and it takes consumers time to switch from consuming apples to consuming bananas. So the price of bananas is constant at $1 per kg during the adjustment. The weights in the price index slowly change (with a falling number of apples and increasing number of bananas in the basket), but the price index stays constant, because neither price is changing. Real GDP is the same as it was before bananas were invented.
  2. Assume that supply adjusts more slowly than demand. Producers need a high price to give them the incentive to adjust. So the price of bananas starts out above $1, and slowly falls over time to $1. So the price index falls over time. Real GDP ends up higher than it was before bananas were invented.
  3. Assume that demand adjusts more slowly than demand. Consumers need a low price to give them the incentive to adjust. So the price of bananas starts out below $1, and slowly rises over time to $1. So the price index rises over time. Real GDP ends up lower than it was before bananas were invented.

Even if you say that my third case is implausible, and that demand always adjusts more quickly than supply, so the price of new goods (relative to existing goods) always starts out high and falls over time, that does not resolve the problem. The initial price of bananas, when they first appear on the market, depends on how many bananas can be grown in that very first season. Anything that enables producers of new goods to increase production for the initial roll-out will permanently reduce the measured level of real GDP.

The underlying problem is that we do not observe the price of bananas before bananas are invented. Unless you allow a discontinuous jump in real GDP the moment the new good hits the market, even if initial production is negligible, I don't think you can avoid this paradox.

Thanks to commenters (especially louis) on my previous post, and to Brent Moulton via Twitter and David Rosnick via email. Errors and opinions are mine alone.

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