Some Problems with Worker Productivity Stats

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Frank Shostak
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According to the US Labor Department, worker productivity in the non-farm sector increased at an annual rate of 1.4 percent in the fourth quarter of 2019 after declining by 0.2 percent in the previous quarter. For the year, productivity increased 1.7 percent, up from 1.3 percent in both 2017 and 2018. It was the best annual showing since the 3.4 percent increase in 2010. For most commentators, an increase in productivity is considered an indication that the US economy is becoming healthier and wealthier.

After all, the increase in productivity means that workers are now generating a greater amount of goods per hour. Notwithstanding, there are serious doubts as to whether productivity figures here actually describe the facts of reality.

To calculate productivity, we require the total output and the number of worker hours that went into the production of this output. Productivity then is:

Productivity = Total output/number of hours

Total Real Output Cannot Be Established

To calculate a total, several things must be added together. To add things together, they must have some unit in common. The fact that there are a great variety of products produced in the non-farm business sector means that it is not possible to add them up to get a total. It is not possible to add refrigerators to cars and shirts to obtain total output. Since the total real output cannot be meaningfully defined, obviously it cannot be quantified.

To solve the problem of measuring total real output, statisticians divide total monetary expenditure on goods by the average price of these goods.

Can We Establish an Average Price of Goods?

There is, however, a problem with this method. What exactly is a price? The price, or the rate of exchange of one good in terms of another, is the amount of the other good divided by the amount of the first good. In the money economy, price will be the amount of money divided by the amount of the first good.

Suppose two transactions were conducted. In the first transaction, one TV set is exchanged for $1,000. In the second transaction, one shirt is exchanged for $40. The price or the rate of exchange in the first transaction is $1000/1 TV set. The price in the second transaction is $40/1 shirt.

In order to calculate the average price we must add these two ratios and divide them by 2. However, $1000/1 TV set cannot be added to $40/1 shirt, implying that it is not possible to establish an average price. On this Rothbard wrote:

Thus, any concept of average price level involves adding or multiplying quantities of completely different units of goods, such as butter, hats, sugar, etc., and is therefore meaningless and illegitimate. Even pounds of sugar and pounds of butter cannot be added together, because they are two different goods and their valuation is completely different.1

A Fixed-Weight Price Index Doesn’t Work on Constantly Changing Human Beings

The use of a fixed-weight price index seems to offer a solution to the calculation of an average price. By means of this index, it is held, we could establish changes in the overall purchasing power of money, which in turn would permit us to ascertain changes in real output.

For instance, in period one Tom bought 100 hamburgers for $2 each. He also bought five shirts at $20 each. His total outlay in the period one stood at

$2(100) + $20(5) = $300

Hamburgers carry a weight of 0.67 in the total outlays while shirts carry a weight of 0.33.

In period two, hamburgers exchange for $2.2, an increase of 10 percent, and shirts are exchanged for $21, an increase of 5 percent. By applying unchanged weights, i.e., an unchanged pattern of consumption, we can establish that Tom’s monetary expenditure stood at

$2.2(100) + $21(5) = $325

Tom’s monetary expenditure in period two stands at $325 against $300 in period one, i.e., an increase of 8.3 percent. We can then establish that the purchasing power of Tom’s monetary expenditure fell by 8.3 percent:

10%(0.67) + 5%(0.33) = 8.3%

If we were to assume that Tom’s pattern of consumption represents that of the average consumer, then we could say that the overall purchasing power of the monetary expenditure in the economy fell by 8.3 percent. Consequently, if it was established that the overall monetary expenditures in period two increased by 8 percent then we could ascertain that in real terms expenditure declined by 0.3 percent.

Every ten years government statisticians conduct extensive surveys to establish a pattern of spending of a “typical” or an “average” consumer. The obtained weights in turn serve to establish changes in the average price and hence in the purchasing power of money. Once changes in the purchasing power of money are established, one could make an estimate of changes in the total real output and of labor productivity.

The assumption that weights remain constant over a prolonged period is, however, not applicable in the real world. This is a portrait of an individual with frozen preferences (i.e., a robot).

A Variable-Weight Price Index Cannot Help Ascertain the Purchasing Power of Money

The view that a variable-weight price index could bring more realism to the picture and hence permit the estimation of the purchasing power of money also misses the point.

In the world of a fixed-weight price index, the change in prices is entirely attributed to changes in the purchasing power of money. This is not so with respect to the variable-weight index.

For instance, in period two Tom’s pattern of consumption has changed now, as he consumes 120 hamburgers rather than 100 and still buys five shirts. His overall monetary expenditure in the period two is:

$2.2(120) +$21(5) = $369

This means that Tom’s expenditure has increased by 23 percent from period one. We cannot, however, attribute this increase to the decline in the purchasing power of money while ignoring the increase in the quantity of hamburgers bought. The reasons why Tom has increased his expenditure on hamburgers in period two could be various. One can only infer that changes in the variable-weight price index are driven by monetary and nonmonetary factors. The influence of these factors on prices is, however, intertwined and cannot be separated.

Consequently, it is not possible to isolate changes in the purchasing power of money from changes in this price index. Without this information, it is not possible to calculate changes in real spending.

According to Rothbard,

All sorts of index numbers have been spawned in a vain attempt to surmount these difficulties: quantity weights have been chosen that vary for each year covered; arithmetical, geometrical, and harmonic averages have been taken at variable and fixed weights; “ideal” formulas have been explored—all with no realization of the futility of these endeavors. No such index number, no attempt to separate and measure prices and quantities, can be valid.2

Also, according to Mises,

In the field of praxeology and economics no sense can be given to the notion of measurement. In the hypothetical state of rigid conditions there are no changes to be measured. In the actual world of change there are no fixed points, dimensions, or relations which could serve as a standard.3

Moreover according to Rothbard,

There are only individual buyers, and each buyer has bought a different proportion and type of goods. If one person purchases a TV set, and another goes to the movies, each activity is the result of different value scales, and each has different effects on the various commodities. There is no “average person” who goes partly to the movies and buys part of a TV set. There is therefore no “average housewife” buying some given proportion of a totality of goods. Goods are not bought in their totality against money, but only by individuals in individual transactions, and therefore there can be no scientific method of combining them.4

The Total Purchasing Power of Money Cannot Be Established Conceptually

In the real world, the total purchasing power of money cannot be established, even conceptually. Thus when $1 is exchanged for one loaf of bread all we can say that the purchasing power of $1 is one loaf of bread. If $1 is exchanged for two tomatoes then this also means that the purchasing power of $1 is two tomatoes.

It is not possible however to establish the total purchasing power of money since we cannot add up two tomatoes to one loaf of bread. We can only establish the purchasing power of money with respect to a particular good in a transaction at a given point in time and at a given place. Hence, if something cannot be established conceptually it is obvious that any attempt to quantify it is futile.

• 1. Murray N. Rothbard, Man, Economy, and State with Power and Market, 2d scholar’s ed. (Auburn, AL: Mises Institute, 2009), p. 734.
• 2. Ibid.
• 3. Ludwig von Mises, Human Action, scholar’s ed. (Auburn, AL: Mises Institute, 1998), p. 222.
• 4. Rothbard, Man, Economy, and State, p. 740.