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.