According to the US Labor Department, workers productivity in the non-farm sector increased at an annual rate of 1.4% in the fourth quarter of 2019 after declining by 0.2% in the previous quarter. For the year, productivity increased 1.7%, up from 1.3% in both 2017 and 2018. It was the best annual showing since the 3.4% increase in 2010. For most commentators an increase in productivity is considered as 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 whether productivity figures here actually describe the facts of reality.
To calculate productivity, we require the total output produced and the number of workers’ 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 and 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 an average price of these goods.
Can we establish an average goods prices?
There is however a problem with this. 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 $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, $1000/1TV set cannot be added to $40/1shirt, 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.
Fixed weight price index belongs to the world of robots not humans
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 will permit us to ascertain changes in real output.
For instance, in the 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
Observe that hamburgers carry a weight of 0.67 in the total outlays while shirts carry a weight of 0.33.
In period two, hamburgers are exchanged for $2.2, an increase of 10%. Shirts are exchanged in the period two for $21, an increase of 5%. 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
Note that Tom’s monetary expenditure in period two stands at $325 against $300 in period one i.e. an increase of 8.3%. We can then establish that the purchasing power of Tom’s monetary expenditure fell by 8.3%.
10%*0.67 + 5%*0.33 = 8.3%
If we were to assume that Tom’s pattern of consumption represents the average consumer then we could say that the overall purchasing power of the monetary expenditure in the economy fell by 8.3%. Consequently, if it was established that the overall monetary expenditures in period two increased by 8% then we could ascertain that in real terms expenditure declined by 0.3%.
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 labour productivity.
The assumption that weights remain constant over a prolonged period is however, not applicable in the real world. This portrays an individual with frozen preferences i.e. a robot.
Variable weight price index cannot help to ascertain the purchasing power of money
A 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.
For instance, in period two Tom’s pattern of consumption has changed now as he consumes 120 hamburgers rather than 100 hamburgers 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% from period one. We cannot however attribute this increase to the decline in the purchasing power of money whilst ignoring the increase in the quantity of hamburgers bought. The reasons why Tom has increased his expenditure on hamburgers in the period two could be various. One could only infer that changes in the variable weight price index 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 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.
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.
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.
The total purchasing power of money cannot be established conceptually
We suggest that 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 attempts to quantify it is futile.
So what are we to make out of the pronouncement that the labour productivity increased at an annual rate of 1.4% in the fourth quarter of 2019. All that we could say is that this percentage has nothing to do with productivity growth. It is the result of the 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 is going to be. This in turn means that, the rate of growth of what government calls “total real output”, is going to closely mirror rises in money supply.
 Murray N. Rothbard Man Economy, and State p 734
 Ludwig von Mises Human Action p 222
 Murray N. Rothbard, Man Economy and State p740.