Disasters and Growth

Former student Curt James sent along this link to an article by Frank Hollenbeck about a topic that we’d discussed in class: are disasters good for the economy?

Outside of economics, it’s relatively common to say “oh … boo-hoo about that disaster … but at least it increased growth rates”.

This is known as the broken window fallacy, and goes back to Bastiat.

In contemporary times, people fall for this because of our focus on GDP (a flow variable), and our lack of decent information on national wealth (a stock variable).

The destruction of disasters is a problem because what is wrecked is what is already built. This is part of national wealth, but because we measure that badly, and ignore it most of the time, people are willing to forget about it.

And … it is theoretically true (and empirically confirmed) that disasters increase growth rates. The reason is that all the rebuilding gets counted in GDP.

This all makes sense in the context of a growth model: a disaster takes us further away from the steady state (which is bad), but the further we are from the steady state that faster we move towards it (this is the improved growth rates that people harp on).

Obviously, if you count one part and not the other, you might conclude that disasters are good.

The linked piece reviews some of the literature, but I think it misses an important conclusion. It focuses on the 2002 (not 2007) conclusion of Skidmore and Toya that sometimes disasters do seem to make things better. This result has been cited over 300 times:

… They found a positive relationship between climate disasters (e.g., hurricanes and cyclones), and growth. The authors explain this finding by invoking what might be called Mother Nature’s contribution to what economist Joseph Schumpeter famously called capitalism’s "creative destruction.” By destroying old factories and roads, airports, and bridges, disasters allow new and more efficient infrastructure to be rebuilt, forcing the transition to a sleeker, more productive economy. Disasters perform the economic service of clearing out outdated infrastructure to make way for more efficient replacements.

Hollenbeck argues that this violates Bastiat’s argument.

But I see an argument that he misses. When we calibrate a growth model, we come to the startling conclusion that the lemonade stand story of growth under capitalism (sell some lemonade, and reinvest in the stand to sell even more lemonade) should have played itself out about 2 centuries ago. The story has theoretical support, but that same theoretical support also limits it to explaining a lot less growth than we’ve actually seen. Where does the rest come from?

The answer is labor-enhancing technology, that allows individual workers to control more capital. But then we run into the problem that high tech innovations are relatively easily transmitted across regions, and thus can’t explain regional differences in well-being. So it’s got to be low tech stuff, like culture and institutions, that makes the difference.

How can low tech be growth incompatible? The usual explanation is that it ossifies in place inefficient uses of capital. Typically there’s a political explanation behind this: someone benefits from discouraging more efficient uses, and they use the political system to keep restrictions in place that limit efficiency.

If this is the case, then I see some merit in the results of Skidmore and Toyo that Hollenbeck has missed. Perhaps disasters help out backwards placed because they are most incident on the capital that has passed its useful lifetime. Essentially, corruption preserves capital that stinks, and a disaster can destroy it and create a void that can be filled with more efficient capital.

Why Is Labor Force Participation Declining?

Participation in the labor force (either by being employed or by looking for work) is on the decline in the U.S.

In many ways this issue is a political filter: Republicans think this is all about the lazy people taking over the country, while Democrats think this is about social programs helping people who have better ways to spend their time opt out of the labor market.

Both of these are probably wrong, but you’d need to read and understand some economics to figure that out. Here’s Evan Soltas with some econometric analysis. Do note that these selections are in order within the blog post, but may seem out of order since I’ve removed some context.

… It really is an important question. … The drop in the labor force means that the U.S. has forfeited, perhaps permanently, that labor input and whatever marginal output it would have yielded. A simple calculation¹ suggests that the share of output lost is about three percent; more in-depth calculations from Reifschneider, Wascher, and Wilcox (2013) place it at the center of their estimate of a seven-percent drop in potential output. That's a lot. You don't blow three percent of GDP, let alone seven, every day.

…

I conclude that, of the 2.8-percentage-point decline in the labor force participation rate over that six-year period, more than half (1.7 percentage points) can be explained by underlying changes in demography, though a substantial fraction (1.1 percentage points) cannot.

…

The 95-percent confidence intervals on those figures are that between 1.4 and 1.9 percentage points are explained and between 0.8 and 1.4 percentage points are unexplained.

…

… I've deliberately gone out of my way to include common narratives about why the labor force participation rate has fallen. The aging and retirement of the Baby Boomers. The rise in worker disability. The rise in college enrollment. Furthermore, the unexplained share of this method will identify the specific areas of unexplained changes -- for instance, if women en masse suddenly have decided to stop working (and it turns out they haven't), this method will point at that issue. So one of the huge advantages to this approach is that it allows us to do a bunch of tests of specific theories one-by-one and say whether they hold water or not.

…

What matters to explaining the decline in the labor force participation rate? One thing above all else: aging, which explains 1.3 percentage points of the drop. The next most important: enrollment in school, which explains 0.8 percentage points of the drop. Remember that individual explanations can sum to more than the total, because there are other changes that partially offset. For example, the rise in educational attainment, which comes from this enrollment, explains a 0.6 percent rise in the labor force participation rate, because the well-educated work like crazy.

What matters less? The rise of disability, which explains 0.2 percentage points of the drop. The decline in the birthrate during the recession, which would suggest a 0.1-percentage-point increase, since fewer people are tied down at home with four-year-olds. 

And what just straight up doesn't matter? Changes in the share of people on welfare, disability aside. Changes in health, after accounting for disability and age. Changes in the sex and race composition of the labor force.

The big picture of this is that we just need to stop talking about the primary explanations offered by Republicans and Democrats. They’re both lying.

N.B. I do not see that Soltas included a variable to capture Mulligan’s argument that some of the drop in participation may be due to increased marginal tax rates on the poor.

Via Marginal Revolution.

Spurious Correlations

Here’s a site that plots spurious correlations* between variables. The description indicates that these correlations are found by a data mining program rather than a person.

The above is a true spurious correlation: even though the data is measured across time, it’s hard to see that time is intimately involved in the data generation. Per capita cheese consumption is just not something I can see trending off to infinity.

I do wish there was a section that isolated spurious correlations between trending times series though. In this one, we could reasonably expect both variables to go to infinity if given enough time.

For my part, I think pairs like the second one are more critical to recognize, because there isn’t a sense in which this is ever going to go away if we get more data. In contrast, the correlation in the upper plot will probably go away if we keep plotting it year after year, as eventually per capita cheese consumption levels off or starts to decline.

* A correlation is spurious if it occurs by chance, and has nothing to do with an identifiable cause and effect.

Moving Average and 2014 I Real GDP Growth

The advance (first draft) of real GDP growth for 2014 I came out a few weeks back. It was extremely low: an annualized rate of 0.1%.

The common explanation for that was the rough winter in the eastern half of the country (where about 3/4 of the real GDP is generated. Fair enough.

There were also assertions that the economy would bounce back, as production that was delayed in quarter I was made up for in quarter II.

That’s more or less what MA processes in estimates are meant to catch. AR processes capture the persistence and slow decay of shocks (they can also cover the much rarer case of swings back and forth). MA processes capture shocks that quickly dissipate or which are reversed.

So, whether they know it or not, pundits who argue that real GDP will rebound in 2014 II are implicitly claiming that real GDP has an MA(1) component, and that it’s pretty strong.

We like ARIMA(p,d,q) modeling because it’s flexible and it works well. But, there are typically a large handful of ARIMA processes that will fit a data series relatively well, with combinations of p, d, and q in the 0, 1, or 2 range.

In class, we’re limited by Excel, so we can only do ARI(p,d) or ARIMA(p,d,0) processes. Within that constraint, and ARI(1,1,) or ARIMA(1,1,0) fits real GDP pretty well. But, with better software, most macroeconomists would argue that an ARIMA(1,1,1) fits the log of real GDP well. That part, at least, is consistent with pundits’ positions. But to answer whether that MA(1) component in strong, and works to reverse shocks, requires estimates.

With quarterly data from 1947 I to 2014 I, an ARI(1,1) estimate looks like this:

ΔY_t = 0.008 + 0.374Δy_t-1 + residual_t

Here, y is the natural log of real GDP. This is analogous to the model we estimated in class (and in the handbook) with annual data. The fitted value from this model will have two components from the RHS, while the residual is the difference between the actual and observed values. Like so:

Quarter	ΔY =	Mean +	from AR(1) +	Residual
2013 III	.0101	.0050	.0023	.0029
2013 IV	.0065	.0050	.0038	-.0023
2014 I	.0003	.0050	.0024	-.0071

Do note that this is for quarterly logged data. Because the data is quarterly, we need to multiply it by 4 to annualize it. Because it is logged and in decimal form, we need to move the decimal point two places to the right to convert to percentages.

So, for the second row, we got annualized growth of 2.60% in 2013 IV. Of that, we get 2.00% from the mean, 1.52% from past positive shocks that were embodied in past real GDP and whose persistent effect is captured by the AR(1) term. But, we subtracted off 0.92% because of a negative shock in that quarter.

But things were worse in 2014 I. The mean was the same (the mean always is), but the contribution from last period’s low growth was a weaker 0.96%. Since we expect residuals to equal zero (because this is before we know what they are), we would have forecast growth of 2.96% for 2014 I. But, when it came in much lower, it was from a residual that we can’t explain (other than to tell a story about bad weather).

How bad is that residual? Well, bad, but not horrible: it’s percentile would be in the high teens. We hadn’t gotten a negative shock that bad in 6 quarters, and (befitting the weakness of our economy over the last several years) we haven’t had a positive shock of that magnitude in about 10 years.

The thing is, residuals are unlikely to be repeated (recall that if they have a pattern, we’ve done something wrong). So our expectation now of the residual for 2014 II is still zero.What does the ARI(1,1) forecast for growth in 2014 II. Here goes:

Quarter	ΔY =	Mean +	from AR(1) +	Residual
2013 III	.0101	.0050	.0023	.0029
2013 IV	.0065	.0050	.0038	-.0023
2014 I	.0003	.0050	.0024	-.0071
2014 II	.0051	.0050	.0001	.0000

That forecast for 2014 II works out to just a tad over 2.0%. Anything better than that indicates a positive shock. Anything worse indicates another negative shock. Why is growth forecast to be so weak? Because the AR process looks back at lagged output rather than the lagged residual. There’s no sense in which the AR process gets a bad shock and says “Oh … we’ll claw some of that back the next period.” Instead, the AR process looks back and says that the growth rate was low, and that’s going to persist until we get a positive shock to break us out of our funk.

Now let me show you what an ARIMA(1,1,1) estimate looks like, and how much claw back it says we’re likely to expect. The estimate is:

ΔY_t = 0.008 + 0.501Δy_t-1 + residual_t - 0.146*residual_t-1

This model is a little richer: there’s a little more persistence to approximate growth rates through the larger AR(1) coefficient, but there’s also a tendency for some of the effects of shocks to be reversed. To see this, not the negative coefficient on the last term. This means that a positive shock now will be reversed by 14.6% the next quarter, and vice versa for a negative shock.

Here's how the three fits and forecast work out:

Quarter	ΔY =	Mean +	from AR(1) +	Residual +	MA(1)
2013 III	.0101	.0040	.0031	.0032	-.0001
2013 IV	.0065	.0040	.0051	-.0021	-.0005
2014 I	.0003	.0040	.0032	-.0072	.0003
2014 I	.0051	.0040	.0001	-.0000	.0011

The mean is smaller for this model. That doesn’t mean it’s absent, just that it’s being picked up by other factors. The AR contribution is a bit larger from this model because the AR coefficient is larger. The residuals are very close to what we got with the ARI(1,1) model: this is the sense in which the improvements between one ARIMA model and another are not that large.

The last column is the new one, and it shows the amount of claw back of negative residuals. And, for that last row, it indicates that of the large negative shock in 2014 I, that drew down the growth rate by 2.88%, we will get back about 0.44% in this quarter.

In fact, most of the sense in which this quarter is likely to be weak is the AR component stretching out the weak growth rates of the last couple of quarters. Persistence alone will draw down the growth rate by 1.24% in this quarter: about 3 times the size of the claw back from the MA(1) term.

So, the MA terms are important in modeling real GDP, but not big enough to be the primary part of the story.

And, with either an ARI(1,1) or an ARIMA(1,1,1) we get to roughly the same conclusion: the large negative shock in 2014 I will cause 2014 II to be weak as well, with a forecast of 2.0% growth.

Do keep in mind that one of the messages of this course is that we need to be comfortable with more volatility in macroeconomic outcomes than politicians and pundits are going to tell us. So given that the 95% confidence interval on real GDP growth rates is roughly ± 2%, our forecast for 2014 II is something like 0-4% rather than the more typical 1-5%.

Ignorance of an Economic Miracle

It’s mighty popular to bad mouth the economy, isn’t it?

That goes hand-in-hand with ignoring economic miracles. That’s sensible: if you’re predisposed to saying everything is bad, you’d need to suppress anything that’s good.

This blog has harped a bit on the situation in North Dakota over the last few years. Go ahead: put “North Dakota” in the search bar at the right, and notice the pages of hits it produces.

So, Carpe Diem points out that the final question on Jeopardy the other day was:

Between 2006 and 2013 it went from 39th to 6th in per capita income and its unemployment rate dropped to the nation’s lowest.

The contestants answers were: Texas (a pretty good answer), Arizona (a horrible one, since this was one of the hardest hit states in the Great Recession), and North Dakota.

To me, 1 in 3 speaks volumes about macroeconomic ignorance.

It doesn’t help that Obama hasn’t been to North Dakota since the 2008 campaign, and rarely mentions the state. Very liberal Democratic Senator Byron Dorgan can’t even get him to visit:

I would encourage him to go out. … You've got to see it to believe it.

R.I.P. Gary Becker

Gary Becker, one of the biggest name economists ever, passed away last night.

Becker wasn’t just at the top of the field. He was so good that if you took all the Nobel Prize winners, he was at the top (or pretty damn close to the top) of that group.

We don’t cover Becker much in macroeconomics. But here’s what he’s known for:

• Starting a field on the economics of discrimination. The idea that discrimination Is more common in legally restricted markets (e.g., minimum wages were pushed by unions to keep southern blacks from undercutting northern whites) goes back to Becker’s work in the 1950’s.
• The idea that some capital is in human form, and that education is a form of investment, goes back to Becker’s work in the 1960’s. Becker didn’t invent that idea, but he was involved in the very early research on that. (FWIW: business professors get dissed by non-business professors, supposedly we get paid too much, and they do what they do for the love of teaching. Becker argued that there are people like me, who might have liked to be a cosmologist or a musician, who rationally choose other fields because they like the monetary returns better).
• The idea that families make internal tradeoffs based on economics goes back to Becker’s work in the 1970’s. Adding capital to households (such as washers) reduces the value of time spent doing housework, and should lead to more people leaving homemaking for work outside the home. You think that’s common sense, but it wasn’t before Becker.
• With one of my professors, Isaac Ehrlich, Becker started a field on the economics of crime. Becker gave economic teeth to the seat-of-the-pants argument that criminals are deterred by the probability of getting caught, and the probability of doing time. Again, that might seem like common sense, but it still is not to people who focus on “root causes” explanations of crime (like poverty and discrimination).

Any of those is probably worth a Nobel Prize. Becker did all four, and the Nobel committee’s announcement gave him credit for all of them.