We haven't had enough RIs recently. I was talking about Blair Fix elsewhere, so I thought I'd this one.

Here is the blog post in question. It was written back in 2020 and the links to the pictures seem to have broken over the past four years.

Generally, Blair Fix argues that everyone else is wrong about economics. Usually, the writing is unnecessarily long-winded. Here we have Fix arguing at length the everybody else is wrong on productivity. In this RI I'll only deal with his ideas on the concept of productivity, I'll set aside the productivity/pay gap which he also discusses.

In this post, I debunk the ‘productivity-pay gap’ by showing that it has nothing to do with productivity. The reason is simple. Although economists claim to measure ‘productivity’, their measure is actually income relabelled.

We'll start by looking at Fix's initial justification for this idea.

Economists define ‘labor productivity’ as the economic output per unit of labor input:

Labor Productivity = Output / Labor Input

To use this equation, we’ll start with a simple example. Suppose we want to measure the productivity of two corn farmers, Alice and Bob. After working for an hour, Alice harvests 1 ton of corn. During the same time, Bob harvests 5 tons of corn. Using the equation above, we find that Bob is 5 times more productive than Alice: [1]

Alice’s productivity: 1 ton of corn per hour

Bob’s productivity: 5 tons of corn per hour

When there’s only one commodity, measuring productivity is simple. But what if we have multiple commodities? In this case, we can’t just count commodities, because they have different ‘natural units’ (apples and oranges, as they say). Instead, we have to ‘aggregate’ our commodities using a common unit of measure.

I will come back to this example later on. Certainly, it is correct.

To aggregate economic output, economists use prices as the common unit. They define ‘output’ as the sum of the quantity of each commodity multiplied by its price:

Output = ∑ Unit Quantity × Unit Price

So if Alice sold 1 ton of corn at $100 per ton, her ‘output’ would be:

Alice’s output: 1 ton of corn × $100 per ton = $100

Likewise, if Bob sold 5 tons of potatoes at $50 per ton, his ‘output’ would be:

Bob’s output: 5 tons of potatoes × $50 per ton = $250

Using prices to aggregate output seems innocent enough. But when we look deeper, we find two big problems:

‘Productivity’ becomes equivalent to average hourly income. ‘Productivity’ becomes ambiguous because its units (prices) are unstable.

I expect that a lot of people here are not very surprised by this. For example, look at this page on the OECD website. It begins with "GDP per hour worked is a measure of labour productivity". This is hardly a secret.

‘Productivity’ is hourly income relabelled

By choosing prices to aggregate output, economists make ‘productivity’ equivalent to average hourly income. Here’s how it happens.

Economists measure ‘output’ as the sum of the quantity of each commodity multiplied by its price. But this is precisely the formula for gross income (i.e. sales). To measure gross income, we multiply the quantity of each commodity sold by its price:

Gross Income = ∑ Unit Quantity × Unit Price

To find ‘productivity’, we then divide ‘output’ (gross income) by the number of labor hours worked:

Productivity = Gross Income / Labor Hours When we do so, we find that ‘productivity’ is equivalent to average hourly income:

Productivity = Average Hourly Income

So far, so good. Fix has told us something that I think everyone knows. Not just everyone here, but everyone who is vaguely familiar with Economics. He hasn't mentioned inflation yet, we'll come to that later.

So economists’ measure of ‘productivity’ is really just income relabelled. The result is that any relation between ‘productivity’ and wages is tautological — it follows from the definition of productivity.

Here is where the real problems start! Fix has just told us that productivity is income relabelled, but what he showed above is that "labour productivity" is a name for income-per-hour. Income is not the same as income-per-hour.

It would be unreasonable to use income as a measure of productivity. Because doing so would not tell us how much effort is required to obtain the income. Income per hour is different. The "per hour" part gives us at least some information about how much effort was needed to obtain the income. Of course, it's not full information, it tells us nothing about other inputs that may be used. That's why there are other more complex productivity statistics.

It's worth going back to Alice and Bob here:

Alice’s productivity: 1 ton of corn per hour

Bob’s productivity: 5 tons of corn per hour

Fix didn't seem to have a problem with this. But is it really all that different to where we are now? Bob makes 5 tons of corn per hour. He then sells that corn. So, his income is also 5 tons of corn per hour. More specifically it is the revenue produced by selling 5 tons of corn per hour.

We should also note that together Alice and Bob produce 6 tons of corn. If that is all that is happening then, in the little economic unit consisting of Alice and Bob the 6 tons of corn are both all production and all income.

There's another problem:

The result is that any relation between ‘productivity’ and wages is tautological — it follows from the definition of productivity.

Income is not the same as "wages". Specifically, wages are the money income of workers. There are other incomes such as rents, interest and profits. Fix will come back to this point and so will I.

Now, I will skip over lots of things that Fix has to say, and come back to some of them later.

To understand the problems with the EPI’s method, we need to backtrack a bit. I’ve already noted that ‘productivity’ is equivalent to average hourly income. But this wasn’t quite correct. ‘Productivity’ is equivalent to real average hourly income:

Productivity = ‘Real’ Average Hourly Income

Unlike ‘nominal’ income, ‘real’ income adjusts for inflation. To get ‘real’ income, we divide ‘nominal’ income by a price index — a measure of average price change:

Real Income = Nominal Income / Price Index

At the start Fix told us that productivity is really income. Then he told us the productivity is really income-per-hour and tried to distract us from the per-hour bit. Now, he tells us that productivity is actually inflation-adjusted income per-hour.

This actually solves some of Fix's other problems. If he'd thought about things in different order perhaps this would have been clear:

In addition to making ‘productivity’ equivalent to average hourly income, using prices to measure ‘output’ also makes ‘productivity’ ambiguous. This seems odd at first. How can ‘productivity’ be ambiguous when income is always well-defined?

The answer has to do with prices.

We expect prices to play an important role in shaping income. Suppose I’m an apple farmer who sells the same number of apples each year. If the price of apples doubles, my income doubles. That’s how prices work.

Now, let's go back to that equation which includes the price index:

Real Income = Nominal Income / Price Index

Ah yes, in the nominator of the equation the income of the apple farmer has risen. However, we need to remember that the price of apples is also included in the denominator of the equation too. It's in the price-index used to adjust for inflation. Fix is wrong here because he has introduced the price-index aspect too late in his thinking.

Let's suppose that the price of apples rises and no other prices change. In that case nominal income will rise because of the extra income to apple farmers. Also, the price index will rise because of the rise in the price of apples.

Ideally, these things should cancel out. That's because the percentage increase in nominal income is the same as the percentage increase in the price index. If the index uses the Laspeyres method then it could cancel out. If it uses another method then it won't cancel out exactly. We also have to remember that in practice the measure of income may be wider than the basket of goods included in the price index. So, in practice there will be inaccuracies.

Notice that here, I'm not saying that price indexes are perfect for measuring price inflation, nor that any specific index is perfect. Reasonable people can have arguments about what to include in the basket, or what statistical aggregation method to use. My point is simply that productivity as a concept accounts for inflation in whatever way the user of it prefers. For example, if you think that price index X is better than price index Y then you can use that to calculate productivity. If you think all price indexes are bad then you can't calculate productivity, but that's also a reasonable viewpoint.

Suppose that Alice grows 1 ton of corn and 5 tons of potatoes. Bob grows 5 tons of corn and 1 ton of potatoes. Whose output is greater? The answer is ambiguous — it depends on prices.

Fix continues to give us an example where the prices of two goods change, one goes up and the other goes down. Does this contain the problem that Fix describes?

Yes and no. Certainly, you can't compare apples to oranges. Nor can you compare corn to potatoes directly.

However, we should remember what productivity measurements are for. To start with consider a small group, or an individual like Bob. Let's say that Bob is working in a modern economy which is dominated by trade. In that case what matters to Bob is how much money his work earns him. So, it is very sensible for his metric of productivity to be dollars per hour (adjusted for inflation by whatever process Bob finds works best for him). Alternatively, let's suppose that Bob is actually Robinson Crusoe on his island. In that case he really does have a problem of comparing the utility he will get out of various different projects. But that problem doesn't apply to the normal case of the modern market economy.

So, small groups may measure productivity, like individuals and companies. Also, larger groups measure productivity, like nations. In this case the situation is rather different. We should remember something that Fix mentions himself more than once. At the high level, production is also income.

It's worth contrasting two of Fix's sentences here. Fix describes critically the things that you "have to believe" to use productivity statistics, he writes:

You have to believe that prices ‘reveal’ utility, and that monetary income is the same as economic ‘output’.

And elsewhere:

The national accounts are based on the principles of double-entry bookkeeping. This means that for every sale there is a corresponding income.

Why should I have a problem believing that income is the same as output when it's the simple consequence of the world we live in? It is impossible to buy something without at the same time giving someone else an corresponding income. It may be that statistical agencies mismeasure these things. But, that doesn't stop them from being actually equal.

It is not that prices "reveal" utility, but that shifts in demand are driven by shifts is preferences. Suppose that people come to prefer corn to potatoes. In that case the price of corn increases and the price of potatoes decreases. Similarly, the volume of corn sold increases and the volume of potatoes sold decreases. Now, of course, the productivity of the corn industry is more important than it was, and the productivity of the potato industry is less important. There is no point in guessing what the productivity of the potato industry could be if people still preferred the same amount of potatoes as they did before, nor is doing that really possible.

Now, I want to be clear about what I'm saying here. My point is simply that labour productivity makes logical sense as a statistic. Also, it's well known what it measures. It is not always a very useful statistic. Other forms of productivity measurement have advantages. But there isn't the mystery or confusion here that Fix claims there is.

I could criticise much more, but this RI is already very long.