Tuesday, September 30, 2014

A Statistical Discrepancy


If you go to FRED for the default graph of GDP, the title reads Gross Domestic Product and the left border reads (Billions of Dollars).

If you then change the "Units" for the graph to "Percent Change from Year Ago" the left border changes to read (Percent Change from Year Ago). But the title still says Gross Domestic Product.

It's a pretty minor point. But it makes sense: GDP is GDP, whether you look at it in billions of dollars or as percent change values. That's probably obvious. I just want to make sure it's obvious.


At Vox last May, Yglesias pondered differences between Gross Domestic Product and Gross Domestic Income:
This morning we learned that GDP shrank at a 1 percent annual rate and GDI shrank at a 2.3 percent annual rate. Disturbing. And you may be even more disturbed when you learn that GDP and GDI are the exact same thing.

Check out any economics textbook and they will tell you that GDI = GDP. And it does. By definition. And yet when the government sets about to measure GDP and GDI they are never equal.

In theory, these two series should add up to the same thing. In practice, data sources are always imperfect and they don't add up to the same thing. The difference is known as the statistical discrepancy.

That's it: The difference is known as the statistical discrepancy.


But today's topic is TFP, not GDP.

Back in June I wrote:

I don't know how they figure Total Factor Productivity. Maybe it's an error term. Maybe there's a discrepancy in the calculation and they use TFP to reduce or eliminate the discrepancy.

Back in June I got the idea that TFP is "an error term". I quoted Simplicitus:

Total factor productivity is the otherwise unexplained productivity left over after all the individual factors (labor, capital, etc.) are taken out.

and I said

See? That's why I say TFP seems like an error term, a correction value, an adjustment to make the answer come out right.

I quoted Diego Comin:

Total Factor Productivity (TFP) is the portion of output not explained by the amount of inputs used in production.

and I said

This is starting to get familiar... the growth of labor and capital do not fully account for the growth of output. The difference ... is called TFP, Total Factor Productivity.

So that's pretty much how I came to think of Total Factor Productivity as an error term. It is the measure of a discrepancy.


There is a statistical discrepancy between GDP and Gross Domestic Income. They call it a statistical discrepancy.

There is a statistical discrepancy between GDP growth and aggregate production functions like the Solow Growth Model. They call it "Total Factor Productivity".

With GDP and GDI they don't take the statistical discrepancy and make up a name for it like Total Income Productivity and make it not seem like a discrepancy. They just call it a discrepancy.

But with GDP growth it's different. They take labor and capital and fit them to an equation, and compare the result to GDP growth. And when it comes out on the low side, they say there must be something else involved, and they give it the name "Total Factor Productivity".

They explain it by saying Oh, well, that's the increase in labor efficiency. And yes, it makes good sense. But it's just a story. It's not empirical. It's not based on anything. And it doesn't account for the effects of things like the growing accumulation of private debt.

TFP cannot be measured directly. Instead it is a residual ... a mismatch in the calculation ... a statistical discrepancy ... a big one.


This is what fascinates me about TFP: It's a black box.

I want to open up the box and see what's in there.

6 comments:

jim said...

Art wrote: " TFP cannot be measured directly. Instead it is a residual ... a mismatch in the calculation ... a statistical discrepancy ... a big one."

Every business is required to report to the IRS wages/salaries that it pays, Capital costs and the total output of the business. If we disregard the illegal economy all that data provides everything needed to calculate TFP (neglecting the black market part of the economy). TFP is simply a ratio of total output to labor and capital combined.
There is no statistical discrepancy. The only question is whether making that calculation tells you anything useful.

The story that goes with making that calculation is that if you see a higher portion of the fruits of production going to labor and capital and less to other costs that indicates production is getting more efficient.

If you believe that story, then it looks like Germany has been growing steadily less efficient for the last 35 years.

http://research.stlouisfed.org/fred2/graph/?g=LTO

The Arthurian said...

Jim wrote: "The story that goes with making that calculation is that if you see a higher portion of the fruits of production going to labor and capital and less to other costs that indicates production is getting more efficient."

There are no "other costs". The factors of production (labor and capital, say) receive all the income that is generated by the production of output.

There are no other costs: GDI equals GDP.

This is all new to me, but when they figure TFP it seems they don't look at the cost of labor. They look at the hours of labor. And they look in particular at the growth of hours worked in comparison to the growth of output. And they do something similar with capital.

If in a period of N years labor and capital grow by 20%, then you might expect output to grow by 20% also. If output grows more than 20%, this is when they make their claims about improved efficiency: A given amount of input produces more output.

Here is the problem I have: You can't just claim "it must be efficiency" but that is what they seem to do.

I want to know the details of what makes the economy more "efficient". I think a lot of it must arise from the the quantity, velocity, and distribution of money and debt.

jim said...

If somebody claims they are calculating TFP for a particular segment of the economy (durable goods for instance) it seems obvious to me that there are "other costs" that are not income to that segment.

The Arthurian said...

Microfoundations?

jim said...


My point is you haven't made a good case that TFP has anything to do with the discrepancy between GDI and GDP. For one thing the GDI to GDP discrepancy tend to balance out if you look at a long enough period. The graphs I've seen show periods when one was higher and other periods when the other is higher.

The story that goes with the TFP calculation may well be bogus but I don't think the formula is intended to be an accounting of the difference found in measuring production and income.

The Arthurian said...

(after a long delay)

In the post I wrote --
This is what fascinates me about TFP: It's a black box.

Just the other day Roger Farmer wrote --
... It is a black box we call technological progress.

Farmer also says --
"There has, of course, been a great deal of work on theories of endogenous growth. Paul Romer and Robert Lucas have both produced seminal pieces on that topic that led to reams of economic research papers that try to understand Solow’s black box."

He adds --
"To a macroeconomist who is interested in secular stagnation, these theories are a big disappointment."