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.