Monday, February 13, 2012

Chucking the Solow growth model, cont.

A few posts back, I wrestled with Jim Bullard's hypothesis that a fall in asset prices caused a permanent negative shock to GDP. Since then, a whole bunch of people have weighed in with interesting comments.

Scott Sumner and Paul Krugman raise the first of the two issues I had raised: It is tough to interpret housing price changes as destruction of the capital stock. I can actually think of a few ways that housing price changes might affect productivity, and so can Brad DeLong, but I think we both agree that the change would be second-order.

David Andolfatto conjectures that regime-switching models of productivity growth - a sort of modified RBC model - could produce the kind of effects Bullard is talking about. But I don't think that's quite right, at least not the models that Andolfatto is talking about. In those models, asset prices fall because productivity falls; asset price changes are not the cause of changes in output, as Bullard hypothesizes.

What I find more interesting is this older Andolfatto post, which David kindly linked me to in the comments. It points to a model by Robert Shimer in which real wages are sticky. In that model, destruction of part of the capital stock does, in fact, lead to a permanent fall in GDP. (It does represent a chucking of the Solow growth model, because in the Solow model, real wages are not sticky. Shimer's model will not exhibit the conditional convergence that is the Solow model's main result.). This is very interesting. I'll have to take a closer look at the model, to see exactly how it works. If this model matches reality, then my second problem with Bullard's hypothesis is no longer a problem.

Right off the bat, I have some doubts about Shimer's model. Rapid growth after wars and natural disasters is a common phenomenon. And the evidence for conditional convergence is pretty strong. But the later part of Shimer's paper replaces the "real wages can never change" model with a model of search frictions in which real wages eventually move, slowly enough to cause jobless recoveries but presumably quickly enough to allow conditional convergence in per capita GDP across countries. That seems a lot more believable, though it still doesn't explain the "bounce back" from wars and disasters. Anyway, like I said, I'll have to take a closer look at the paper to see if the model makes sense.

So, assuming Bullard has in mind a model like Shimer's, we still have the question of why a fall in housing prices represents destruction of the capital stock.

Update: Jim Bullard responds. It appears what he had in mind is something like this:

1. The "trend" rate of growth had slowed in the 2000s, for whatever reason (technology slowdown, etc.).

2. However, self-fulfilling (but unrealistic) expectations about asset prices temporarily pushed GDP growth above its new, lower trend.

3. The end of that expectations-fueled boom sent the economy back to its new, lower trend growth path.

Not sure if I've got it entirely correct, but that seems to be the gist. It does not rely on destruction of the capital stock to explain the recession, rendering the rest of this post largely irrelevant (though interesting nonetheless).

Readers of this blog will know that I am very sympathetic to the idea of self-fulfilling expectations, sunspot equilibria, etc. I do still have one problem with this story, though. For this kind of story to produce a one-time permanent drop in GDP followed by resumed growth at the old trend rate, it would have to be that the 2000s housing boom masked a productivity slowdown that is now over. That could happen, sure, but I'd like to see some evidence before I believe it. Also, it would leave a puzzle as to why inflation was low during the bubble...


  1. Abstracter and abstracter.

    Right now I'm wondering if our accumulating trade deficit is reducing our capital stock? As a reducto absurdum, why couldn't we let China make everything we use until all our factories had rusted from disuse and we had no capital left?

    I hear China has built way too many ships. Why won't that ruin the shipbuilding industry around the world? They did the same thing with solar panels.

    I realize these are unsophisticated arguments.

  2. I suspect that after a war, wage stickiness pretty much goes out the window. I saw a program about the history of Daimler Benz that said that after WW II the workers came back and worked for a mere pittance to get the bombed out factories cleaned up and back in production.

    What is the ratio of total capital to the annual output of the economy? If you consider plant and equipment it is probably less than one. If you include roads, bridges, housing and commercial buildings you might get up to three. Include education and you might get up to four.

    Any country willing to have a net savings rate of 10% of gdp can build or rebuild pretty quickly. Western Germany and Japan had rebuilt by the mid 1960s after being basically bombed flat in 1945.

    That is the problem I have with Bullard. We know from historical experience that massive destruction of physical wealth can be made up in a twenty year period. The United States has primarily lost paper wealth so the bounce back time should be much smaller (ie less than five years).

  3. Anonymous10:03 AM

    I've heard it claimed that rebuilding after a natural disaster adds to GDP. If so, could they not be used as a natural experiment to analyze effects of reduction in capital stock, local stimulus spending etc.

  4. Asset shocks can definitely affect economies. The recession of 2000-2002 in the States was at least partially due to the popping of the tech bubble. However, at least the tech bubble left behind lots of useful infrastructure. The worst recessions, like what we had, are ultimately about severe malinvestment and debt overhangs.

  5. "What is the ratio of total capital to the annual output of the economy?"

    A rule of thumb used to be that it takes three dollars of investment to generate one dollar of income, in what used to be called underdeveloped countries anyway. This was from Barbara Ward's "The Rich Nations and the Poor Nations." It's still worth a read, if only for the way people of good will thought about these issues fifty years ago. She is a good writer.

  6. I thought that Solow's growth model was that total factor productivity grows not because of capital deepening but because of technological improvement. Obviously you all are talking about something else.

    As for housing as capital, it is not a productive asset the way machinery is. It is a consumer durable. It's only when you start thinking abstractly that the distinction becomes blurred. What stickiness of wages has to do with it I don't know.

    Obviously I don't speak Pig Latin.

  7. Bullard's Point 2:

    However, self-fulfilling (but unrealistic) expectations about asset prices temporarily pushed GDP growth above its new, lower trend.

    Geeze, you'd think a guy who actually works at the fed could have a look at Fed data.

    I'd like to see any evidence for above trend GDP growth in the bubble years.

    Seriously. WTF?!?


  8. Minds think alike. I prposed Bullard's correction of his earlier claim in a comment on DeLong on Krugman on Bullard

    His new claim is that output was above potential in 2006. That is possible with imperfect information and very possible with nutso crazy irrationaliy given the definition of the phrase.

  9. Noah,to add to your skepticism, none of the relevant technology measures (patenting or R&D) have experienced a decline like the did in the 1970s.