The Other Side of That TFP Coin (and something unrelated)

Yesterday I took a quote from a conversation at ResearchGate. I won't give you the link again, because every time I go there ResearchGate pops up a window asking me to "join for free". I close the window and it doesn't bother me again, and it doesn't seem to damage my computer, far as I can see. But still.

However, I do want to look at some of the stuff from that conversation. John Ryding, whom I quoted yesterday, links to the download page for a paper by Charles R. Hulten, who writes:

Economists have long recognized that total factor productivity is an important factor in the process of economic growth. However, just how important it is has been a matter of ongoing controversy. Part of this controversy is about methods and assumptions. Total factor productivity growth is estimated as a residual, using index number techniques. It is thus a measure of our ignorance ...

Ignorance, yeah. What I said yesterday:

Total Factor Productivity is the contribution to economic growth that's left over, after we subtract the contributions to growth that we understand ... It is the contribution to growth that we do not understand.

At ResearchGate, Hak Choi agreed with John Ryding, saying "For me, TFP is merely residue."

Residue. Something left over. Yeah. That's how it is calculated, according to several sources (including the Bank of England). Total Factor Productivity is a statistical discrepancy with a fancy name.

And then, at ResearchGate, Fabrizio Pompei offered a "contradictory" view:

Actually, TFP as mere residual is only one way to observe total factor productivity. Generally, TFP is a productivity measure involving all factors of production.

Yeah, I don't need to read a sweeping generality to know that the part of economic growth which is not explained by capital, and not explained by labor, must be explained by everything else.

I think economic growth is important, and restoring economic growth is important, and I think we need to know more than that "everything" is responsible for growth.

Fabrizio's contradictory view included the mention of the book An Introduction to Efficiency and Productivity Analysis, a 331-page PDF by Timothy J. Coelli and three other writers.

I knew I shouldn't look at it, but I did, and sure enough, it shut down my tirade against Total Factor Productivity.

Dominating, isn't it?

Now... It's over 300 pages long, so I don't expect to read it. But I was looking it over this morning before work, and it did look interesting. Of course, my options were to keep reading, or to go to work.

I want to say one last thing about TFP. I only read a few pages out of the book, so I don't know. But it looks like the book is an investigation of four different ways to measure efficiency and productivity, with "total factor productivity" among them. What it does not appear to be is an investigation of the relation between TFP and efficiency. That relation seems to be assumed. But like I said, I read very little.


In the introduction of the Efficiency and Productivity Analysis book I got severely distracted. They present a graph to show the difference between efficiency and productivity. The graph shows a hypothetical firm's inputs on the X axis, and its outputs on the Y axis:

To illustrate the distinction between technical efficiency and productivity we utilise Figure 1.2. In this figure, we use a ray through the origin to measure productivity at a particular data point. The slope of this ray is y/x and hence provides a measure of productivity. If the firm operating at point A were to move to the technically efficient point B, the slope of the ray would be greater, implying higher productivity at point B. However, by moving to the point C, the ray from the origin is at a tangent to the production frontier and hence defines the point of maximum possible productivity. This latter movement is an example of exploiting scale economies. The point C is the point of (technically) optimal scale. Operation at any other point on the production frontier results in lower productivity.

From this discussion, we conclude that a firm may be technically efficient but may still be able to improve its productivity by exploiting scale economies.

If they move from Point A to Point B they produce more. But if they move from Point B to Point C they get maximum output per unit of input.

As I see it, the optimum size of that hypothetical firm is at Point C.

I talk about the "Laffer limit" sometimes: Doing more of something gives better and better results for a while. But after the Laffer limit is reached, it gives worsening results.

This first occurred to me back in maybe the early 1980s when I used to get the Kiplinger letter -- a B-size sheet of paper, 11"x17", folded in half to make a four-page A-size paper, 8½"x11", with four pages of Kiplinger info, for far too much money, even back then.

Anyway I was reading the Kiplinger letter one day, they were talking about agribusiness as I remember, and they said that agribusiness was growing "beyond its economies of scale". That floored me. It was so big that it was losing money. Its growth was driving its rate of profit down.

Why would anybody do that? My answer is: the tax code. The business income tax gives you a tax break for growing your company. So you grow, to get the tax break. And even if you grow beyond your economies of scale, the government gives you a tax break that more than makes up the difference.

So businesses grow, and big ones buy up little ones, and we lose competition that way, but the growing businesses get a tax break, so to them it's worth it. And at some point they find their profit rate is not as high as it was when they were smaller, but hey, they get those luscious tax breaks. So the government gets less revenue, and businesses merge and consolidate, and the economy is distorted by growth beyond economies of scale, and you can't keep this up or your economy will turn to shit.

And then policymakers strengthen the incentives, thinking that merger and consolidation is the same as growth.


There was a little more in Chapter 2:

In summary, the production function depicted in Figure 2.1 violates the concavity property in the region OD and violates the monotonicity property in the region GR. However, it is consistent with all properties along the curved segment between points D and G - we refer to this as the economically-feasible region of production. Within this region, the point E is the point at which the average product is maximised. We refer to this point as the point of optimal scale (of operations).

The figure 2.1 is similar to 1.1, but annotated differently. And the authors are explicit, defining a "point of optimal scale", meaning scale of operations specifically. And their graph shows plenty of room for a company to grow beyond its economies of scale.

So, we're not talking Total Factor Productivity anymore. I'll come back to that eventually. But I couldn't let this go.