Monday, September 22, 2014

Total Fudge-Factor Productivity

Noah links to an old Beckworth where Beckworth ponders Tyler Cowen's Great Stagnation. Here's Beckworth:
To see just how marked this TFP decline was after 1973 and whether the recent TFP gains make up for any of the loss, I went to the data.  Below is a figure constructed using the quarterly TFP series of John Fernald at the San Francisco Fed. (Click on figure to enlarge.)

I want to go to the data, too. Because when I first laid eyes on Beckworth's graph, I didn't think it showed Total Factor Productivity. I thought it was another one of those slowdown-of-income-growth graphs that I was looking at recently. Total Factor Productivity graphs have two changes in the trend-line, not one:

Graph #2: Total Factor Productivity (FRED)
The FRED graph shows Total Factor Productivity in red, and shows "natural log" values like Beckworth did in his graph.

On the FRED graph, the trend changes once around 1966, and again around 1982. On Beckworth's graph, the trend changes once around 1973, and that's it. I think that's odd. But I was not the first to notice. In comments on Beckworth's post, João Marcus wrote:
Leonard Nakamura of the Philly Fed has done work in that area. Here´s an article from 1997.
His Figure 1 more or less replicates the figure in the post. I remember that in 1999 I saw a revision of Figure 1. It changes significantly. TFP (MFP) flattens between 1965-81 and then takes off again.

João Marcus sees the same mismatch that I see in the two TFP graphs.

Numbers aside, I do like Beckworth's graph. I like it because it shows a great stagnation that began long ago and continues pretty much to the current moment. I've seen that stagnation in the "slowdown of income growth" graphs. I've seen it in inflation-adjusted GDP. So I think Beckworth's graph shows a slowdown that really happened -- whether or not it really happened in TFP.

But I do have a couple problems with his graph. For one, I don't like his trend lines. Here's my problem: If you start at the 1947 end of the graph, the blue line and the trend line follow the same path pretty well. However, if you start at the 2007 end and work backwards, you want to put the change-in-trend kink at 1966, not 1973 where Beckworth has it. This happens a lot when you're eyeballing trend lines: Starting from different ends of the graph, you end up seeing different trends.

So I can agree with Beckworth that there was a "great stagnation" but I don't necessarily agree with him on the start-date of it. And that's kind of a big deal. Putting Beckworth's turning point in question just might raise doubt about Tyler Cowen's "low-hanging fruit" story.

There's another thing that bothers me about Beckworth's graph. Here are his thoughts on Cowen's stagnation, after pondering his graph:
Okay, I am impressed and far less skeptical of the Great Stagnation theory. In my previous post I argued that Cowen failed to appreciate how dramatically our lives have changed since the advent of the internet and faster computing.  Now I am thinking these gains are but a faint shadow of what they could have been had TFP continued to grow at its 1947-1973 trend.  The "good old days" really were better in terms of TFP growth.

Oh -- I certainly agree that our economy performed better before 1973 than after. But Beckworth is at a turning point -- deciding whether to accept the view that our economy performed better before 1973 than after, based on a graph of Total Factor Productivity. And the TFP numbers are in doubt.

Set the numbers aside, and TFP is still not a good basis on which to base a decision like Beckworth's -- because Total Factor Productivity is a fudge factor.

TFP is an adjustment to make the answer come out right ... because the growth of labor and capital do not fully account for the growth of output.

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

Jazzbumpa quotes Wikipedia: "TFP cannot be measured directly. Instead it is a residual, often called the Solow residual, which accounts for effects in total output not caused by inputs."

Total Factor Productivity is "a residual". We use it to explain the part of growth that we can't explain. TFP is like the ether or Einstein's cosmological constant.

TFP is not an explanation. It is a fudge factor. Total Factor Productivity is not a sound basis upon which to make the kind of judgement that Beckworth is making. He'd be better off looking at slowing income growth or inflation-adjusted GDP.

I took Beckworth's JPG, saved it as a PNG, and used PAINT.NET to erase the background. Then I overlaid it on the FRED graph of Total Factor Productivity:

bottom image
top image

Graph #3: Beckworth's TFP (blue) Overlaid on FRED TFP (red)

For the overlay, I matched up the early years, and let the rest of it blow in the wind. You can see the the red FRED numbers are obviously lower that Beckworth's blue during the 1970s. But after about 1982 the red version rises sooner and more quickly than the blue. FRED's red line even comes pretty near to getting back to Beckworth's 1947-1973 trend line.

Which numbers are less iffy, I really can't say.


The Arthurian said...

The Arthurian said...

Roger Farmer: "Growth, in the Solow model, is caused by an exogenous increase in an unexplained factor called technological progress."

That sums it up pretty well. We don't know where it comes from, and we can't explain it.

The Arthurian said...

Jared Bernstein says Total Factor Productivity is a "fudge factor".

See? I was right.