Measuring Output of the GDP Factory

Martin Feldstein writes,

More generally, as Triplett and Bosworth (2004) note, the official data imply that productivity in the health industry, as measured by the ratio of output to the number of employee hours involved in production, declined year after year between 1987 and 2001. They conclude (p. 265) that such a decline in true productivity is unlikely, but that officially measured productivity declines because “the traditional price index procedures for handling product and service improvements do not work for most medical improvements.” More recent data show that health sector productivity has continued to decline since 2001.

When you think of a factory producing, say, slate shingles, measurement of output is pretty straightforward. That makes measurement of productivity pretty straightforward.

Now introduce a second good, iron nails. These are produced in a different factory, but the idea of aggregation is to treat the economy as if it were a single GDP factory producing shingles plus nails. Of course, if you measure output as shingles plus nails, you will get strange results. If the economy produces 1 less shingle and 101 more nails, the total goes up by 100. But you do not know if the value of what was produced went up at all.

To obtain a more reasonable measure of total output, the statisticians take a weighted average of nail production and shingle production, where the weights are based on relative prices. If one shingle sells for $1.01 and one nail costs $.01, then producing 1 less shingle and 101 more nails results in no change to total output.

But using relative prices this does not completely solve the problem. Relative prices can change. Then you have to decide whether to base the weights on last year’s prices, this year’s prices, or some combination of the two.

But choosing a relative-price base year does not completely solve the problem, either. Relative prices can change because of quality change. Suppose that this year the shingle maker produces shingles that are more durable than the shingles produced last year, but charges the same price. Because quality has gone up, the relative price has gone down. Will the statisticians capture this?

Think of what you are trying to accomplish with these sorts of measurements. You might start by asking for any particular product how many hours a low-skilled worker would have to work in order to obtain that product. Brad DeLong once calculated that five hundred years ago it would take someone about three days in order to obtain the equivalent of one bag of flour. For today’s low-skilled workers in the U.S., this would take only a matter of minutes.

But then, how do you take a weighted average over many products? What do you do about quality change? How do you value new products?

Next, you have to note that people with more skills have higher wages, which reduces the number of hours that they must work to obtain the same goods. As the skill mix of the population changes, how do we want that to affect our measure of the productivity of the GDP factory?

In my view, the attempt to treat the economy as a GDP factory is bound to be very far from precise. It always amazes me when economists take seriously a concept like “the change in the trend rate of productivity.” The level of productivity is a very imprecise measure, for the reasons sketched above. When you measure the growth rate of productivity, you necessarily boost the noise to signal ratio. Then, when you measure the change in the rate of productivity growth rate of productivity, you once again boost that noise to signal ratio, to the point where you are pretty close to talking nonsense.

6 thoughts on “Measuring Output of the GDP Factory

  1. In general numbers and stats tell a story but it is important to understand what they are actually saying. AEI did a chart saying one person for coal equals 2 workers on natural gas versus 79 workers on solar with obvious implication that coal is really great. Of course, they did not the labor of captial expeditures, nor the long range ability of solar. (In Socal desert with high SCE, our solar paid for itself after 6 years.)

    • “In Socal desert with high SCE”

      But Solar is a persuasion play. You should be telling people NOT to buy solar so that the solar is cheaper and more available to people with good insolation…

      • We have people putting in expensive residential solar based on virtue signalling and green persuasion in places that should be some of the last places to get solar coverage. People aren’t usually making rational calculated decisions. And half a rational calculated decision is often worse than no calculations at all.

        If you want to argue that we need massive investment in research, I’m with you. But massive spending on roll-out I’m skeptical of.

  2. Assuming nails, shingles and lumber are used in construction, we would expect the inventory variance of nails, shingles and lumber to be equal. If not, either the nail guy, or the shingle guy is late to arrive, and that is unproductive.

  3. Maybe PSST is good or maybe not.

    But your critique seems to go deeper. Forget practical issues of measurement in the real world. There is a vast and old literature on price indexes and aggregation theory. You seem to have rejected that entire literature as irredeemably useless and irrelevant.

    The way I see it, business cycle theory is one thing, and measurement is something else. I recommend you don’t confuse them.

    Maybe GDP measurement is just fine, and measures of business cycles are accurate, and PSST is true also.

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