Are American workers becoming more productive? It would be nice to know, but it is a difficult question to answer. Notwithstanding pretensions to scientific accuracy, the data used to measure productivity are unreliable.

According to a recent announcement by the US Labor Department, workers productivity in the non-farm sector increased at an annual rate of 5.3% in the second quarter after rising by 1.9% in the previous quarter. Year-on-year productivity increased by 5.1%, the highest such gain since the third quarter of 1983 when productivity was up 5.3%.

After the release of these data, the Dow Jones Industrial Average jumped by 1%. Players in the stock market interpreted the surge in productivity as another indication that the US economy is becoming healthier and wealthier.

There is nothing inherently wrong with this conclusion. After all, a rise in productivity would indicate that workers are churning out a greater amount of goods and services per hour. The trouble is that there are serious doubts as to whether productivity figures describe the facts of reality.

To calculate productivity, statisticians look at total output produced and the number of workers' hours that went into production of this output. In short: Productivity = Total output / number of hours

To calculate a total, several data sets must be added together. To be added, analytical rigor requires that they have some unit in common. But the "non-farm business sector" includes a huge diversity of products and services; it is not possible to simply add these up and arrive at a total. There is not unit of measurement common to refrigerators, cars, and shirts that make it possible to derive total output. Since the total real output cannot be meaningfully defined obviously it cannot be quantified.

The statisticians' technique of employing total monetary expenditure adjusted for prices simply won't do. What is a price? It is the rate of exchange between goods established in a transaction between two individuals at a particular place and at a particular point in time.

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 $1000. In the second transaction one shirt is exchanged for $40. The price or the rate of exchange in the first transaction is $1000/1TV 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, it is conceptually meaningless to add $1000/1TV set to $40/1shirt.

It is interesting to note that in the commodity markets prices are quoted as Dollars/barrel of oil, Dollars/ounce of gold, Dollars/tonne of copper, etc. Obviously it wouldn't make much sense to establish an average of these prices. Likewise it doesn't make much sense to establish an average of the exchange rates Dollar/Sterling, Dollar/Yen, etc.

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. (*Man, Economy, and State*, p. 734).

The use of a fixed weight price index seems to offer a solution that bypasses the problem of a direct 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 will permit us to ascertain changes in real output. Thus if total money outlay increased by 10% and the purchasing power of money fell by 5% one could say that real outlay grew by 5%. The following example illustrates the essence of a fixed weight price index.

In period 1, Tom bought 100 hamburgers for $2 each. He also bought 5 shirts at $20 each. His total outlay in period 1 is $2*100 + $20*5 = $300. Observe that hamburgers carry a weight of 0.67 in the total outlay while shirts carry a weight of 0.33.

In period 2, hamburgers are exchanged for $3, an increase of 50%, shirts are exchanged for $25 an increase of 25%. By applying unchanged weights, i.e. an unchanged pattern of consumption, we will find that the purchasing power of Tom's money fell by 41.7%. (50%*0.67 + 25%*0.33 = 41.7%)

Now, if we were to assume that Tom's pattern of consumption represents an average consumer then we could say that the overall purchasing power of money fell by 41.7%.

It was observed that people's spending increased from $100 million in period 1 to $140 million in period 2 i.e. a 40% increase. By applying the information that the purchasing power of money fell by 41.7% we can establish that in real terms spending stood at $98.8 million in period 2 a fall of 1.2% from period 1.

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 total real output and of labor productivity.

The assumption that weights remain constant over a prolonged period of time is, however, not applicable in the real world. This assumption implies an individual with frozen preferences i.e. a robot. According to Mises in the world of frozen preferences the idea that money's purchasing power could change is contradictory. (*Human Action*, p. 222).

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. (*Man, Economy, and State*, p. 740)

Since the fixed weight price index has nothing to do with reality it means that the overall purchasing power of money cannot be established. Indeed it cannot be established, even conceptually. Thus when $1 is exchanged for 1 loaf of bread we can say that the purchasing power of $1 is 1 loaf of bread. If $1 is exchanged for 2 tomatoes then this also means that the purchasing power of $1 is 2 tomatoes.

However, it is not possible to establish total purchasing power of money since we cannot add up 2 tomatoes to 1 loaf of bread. In short, 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.

The view that a variable weight price index could bring more realism 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. Changes in the variable weight index imply that prices are driven by monetary and non-monetary 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 knowledge 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." (*Man, Economy, and State*, p. 744).

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." (*Human Action*, p. 222)

We can thus conclude that the various price deflators that government statisticians compute are arbitrary numbers. If the so-called deflators are meaningless, so is the real output statistic, which is employed in the calculation of workers productivity.

Furthermore, the entire concept of total labour productivity is dubious. Let us assume that in period 1 it was observed that the electronic sector produced 10 TV sets per hour of labour. It was also observed that the clothing industry produced 100 shirts per hour of labor. In period 2 it was found that one-hour of labor in the electronic sector produced 8 TV sets while in the clothing sector 120 shirts.

Based on this information it is not possible to say anything about total labor productivity. All that we can say is that productivity fell in the electronic sector and increased in the clothing sector. Even if in both sectors productivity were to increase it is not possible to establish the numerical increase of total labor productivity.

So what are we to make out of the pronouncement that labor productivity increased by 5.1% in the second quarter? All that we could say is that this percentage has nothing to do with productivity growth. It is the result of monetary spending adjusted by a meaningless deflator.

As a rule the more money created by the central bank and the banking sector, the larger the monetary spending will be. This in turn means that, the rate of growth of what government calls "total real output," will closely mirror rises in money supply. Essentially, the more money pumped, the greater the "total output" will be. But this is not real production but only a statistical illusion.

The "strong" second quarter "labor productivity" is most likely the result of last year's aggressive monetary pumping by the Fed. Year-on-year in December, the money base grew by 15.3%. Since early this year the pace of monetary pumping has fallen quite sharply, by July it stood at 6.8%. This raises the likelihood that "labor productivity" will weaken sharply in the months ahead.

The fallacy is in thinking that these ups and downs in official data have anything at all to do with discerning real economic activity.