Saturday, March 30, 2013

A timid defense of DSGE models

An economic model (see here)
Image source

This post is for economists and/or econ bloggers and/or people with opinions about this issue of mathematical modeling in macroeconomics. So that might be one or two of my usual readers (I won't mention what that is in percentage terms).

Noah Smith has a good post about some problems with DSGE models, particularly when they are solved using linearization methods (I like Smith's blog; I don't like his comment sections as much). He is not the only person with complaints about the workhorse approach to macroeconomic thinking. Stephen Gordon also has a very nice post, again mainly about linearized DSGE. My post is not about Smith's or Gordon's notes; it's a more general comment on this occasionally popular topic.

I don't want to wade too deeply into this debate for the following reasons:

  • Much of the debate is over my head--not technically speaking, but in terms of knowing how to do science well.
  • The blogosphere is a poor place to have this debate.
  • Many of the people involved (but not Smith or Gordon) probably don't know enough about DSGE models to draw useful conclusions (i.e., if you don't know how to build or solve one, you may be unable to make a highly productive contribution to the debate).
  • Political preferences are involved, which makes it hard to tell whether methodology is really the issue.
  • I don't have a strong enough opinion to justify dragging myself and charitable readers through the weeds, aside from thinking that DSGE models are useful tools.
  • I think linearized models are harder to defend than those with global solutions.

But here's what I will say:

  • Not all DSGE models are solved with linearization. Yes, the New Keynesian ones typically are, and those are the ones informing policy the most--and there aren't a lot of great ways around that. But lots of DSGE models can be solved globally without using Taylor-type approximations, in which case approximation error is far smaller (and is basically determined by Curse of Dimensionality and/or numerical precision issues).
  • I don't like it when people act like we face a big choice between using DSGE or doing empirical work. That's a false dilemma. First, why not do both? Second, that distinction does not always exist. This deserves its own post, but for now: DSGE models are just systems of equations, and they can be estimated; and it's not obvious to me that estimating a DSGE system is any more silly than assuming the world resembles the atheoretic linear functional form we use in purely empirical work. I think we all know that there is no such thing as simply "letting the data speak."
  • In this debate, and in debates about formal modeling in general, some critics tend to make the mistake of thinking that a modeler believes that the assumptions and simplifications of the model are true in the real world. They also like to accuse macroeconomists of thinking they are physicists. Those are straw men. Take your straw man and go home.
  • We must get econ pundits to understand that we're all using models, including non-economist bloggers, even if they're not written down as mathematical expressions. Writing a model down in its entirety so that its assumptions are made explicit and its internal workings can be examined by anyone is an act of intellectual humility. It is baffling to me that people who write down their models formally so we can all argue about them are supposedly worse and more arrogant than those who think they can identify a narrative model's assumptions and keep it internally consistent.
  • There are limits to what the "credibility revolution" techniques from applied micro can do for macro. There is little or no clean identification to be had at the aggregate level, and extrapolating empirical results from small regions to the aggregate level can be misleading. These approaches can definitely shed light on macro topics (the excellent Mian and Sufi papers come to mind), but I think it's a mistake to assume that they are sufficient for all macro questions.
  • In typical empirical work and heuristic/narrative theorizing, it's really difficult to avoid partial equilibrium reasoning. A DSGE model, even a very simple one, has more moving parts than my mind alone can keep track of, and it forces agents to obey resource constraints in a way that is really difficult without formality. You don't have to believe literally in "general equilibrium" to appreciate how GE models allow you to think about feedback mechanisms.
For what it's worth, I have personally learned a lot from using DSGE models. Much of the intuition I use to think about macroeconomics originally came from some DSGE model. When I work with them, I frequently have insights that force me to change the way I think. It's possible that those DSGE critics who have not used them could benefit from spending some time with them to see if they learn anything that was hard to think about before. Maybe there are a lot of longtime DSGE users who have never learned anything from them, but I doubt it.

A recent example: Last week, I was messing with an augmented version of this DSGE model (in my version, there is also a corporate sector and some other stuff). Households choose whether to be workers or entrepreneurs. I was messing with the parameter that governs entrepreneurial productivity (specifically, the scale parameter of the Pareto TFP process). I noticed that sometimes when I increase that parameter and solve the model, the share of households that choose to be entrepreneurs fell. My initial expectation was that increasing how much entrepreneurs can produce with a given level of inputs would make entrepreneurship more enticing (relative to earning a wage) and cause more people to do it. But that's partial equilibrium reasoning. I pushed on the model a little and figured out that it depends on the wealth distribution and capital intensity. Roughly speaking, if entrepreneurs consume most of their new income (rather than saving it), and if production is more capital intensive, entrepreneurship will rise: higher TFP raises capital demand, and people don't save enough to mitigate the upward pressure on the interest rate; and wages and interest rates move in opposite directions when production is Cobb-Douglas-esque, so worker income falls while entrepreneurial income rises. On the other hand, if people save most of their new income and production is less capital intensive, the supply of savings can rise enough to mitigate upward pressure on the interest rate (and downward pressure on the wage). It is possible for wages to rise enough to induce some people to abandon entrepreneurship and become workers.

A lot of people would have seen that coming, and I probably would have if I'd thought it through carefully. But there were other things on my mind. The point is that the model forced me to consider the implications of my ideas and to recognize how conditions in one part of the economy affect things that happen elsewhere. This kind of discipline is important when arguing about the potential effects of this or that policy.

I think most people, including me, are used to thinking in partial equilibrium. DSGE models, at the very least, can force us to think a little more broadly.

I don't see why we can't allow for a wide range of methodological approaches in economics, and even in macroeconomics. I suspect that part of the problem is that recent events have raised everyone's level of interest in macroeconomics. People working in other economics fields, along with a lot of noneconomists, want to get in on the action and be part of the conversation. That's a good thing. But some of them can look a bit like Monday Morning Quarterbacks, making big claims about the failure of the field and recommending all sorts of changes to the standard toolkit as if macro can be approached in the same way as their home field. I think it would be a bad idea to discard the DSGE framework, even as I also think that drill-down empirical work is increasingly important (and possible) in macroeconomics (as should be evident by my other posts).

I also suspect that, for a few people, antipathy towards workhorse macro models is driven by politics. This debate often arises in the context of discussions about fiscal multipliers (ha!) or optimal tax policy, and it sometimes appears that people who don't like the political implications of a paper respond to it by rejecting the entire modeling approach. If that's going on, well, we shouldn't let it affect real economics work.

Update: some related thoughts here.

Monday, March 25, 2013

Implications of a collateral recovery

I wrote about the observed relationship between housing and startups here, where I suggested that "it is likely that housing plays an important collateral role for many entrepreneurs." A paper by Adelino, Schoar, and Severino finds more specific evidence of the notion that housing collateral and entrepreneurship are linked, so maybe I'm not crazy (which is good, since I've been working on a structural model of this stuff for over a year).

This is relevant since house prices appear to have bottomed nationally last year (surprise! Bill McBride nailed it). We'll see if the recovery continues, but it could loosen up collateral constraints for people at the extensive margin of entrepreneurship. Given the importance of startups for net job creation, better collateral might mean more jobs.

Adelino, Schoar, and Severino attempt to estimate the effect of shocks to housing collateral values on entrepreneurial activity. It's pretty difficult to pin down causal estimates of this relationship. They do it using an idea that probably a lot of people have had: Albert Saiz's estimates of housing supply elasticity. These have been used for many purposes; the idea is that they capture constraints on housing supply that are imposed by "exogenous" factors like geography and regulation. If local housing supply is inelastic, shocks to housing demand have large price effects; if local supply is elastic, shocks to housing demand have smaller price effects. If the supply elasticities don't directly drive outcome variables you care about, maybe you can use them to track the consequence of house price movements.

I spent some time thinking about using this instrument some time ago, but I concluded that I would have a hard time convincing myself and others that it is not related to entrepreneurial activity through channels other than house prices. That said, it may be as close as we're going to get to having the kind of exogenous variation we need for this question.

The authors find the following:

We show that leading up to the recession of 2008, areas with rising house prices (and increased leverage) experienced a significantly bigger increase in small business starts and a rise in the number of people who are employed in establishments with fewer than 10 employees compared to areas that did not see an increase in house prices. The same increase in employment cannot be found for large establishments in these same areas. . . . This asymmetric effect on small versus large only holds for instrumented house prices, which suggests that the non-instrumented part of the variation (which is the one that captures endogenous demand) mostly impacts employment at larger firms. This asymmetry points to the interpretation of the collateral lending channel as an important driver of employment creation in small firms.

This result holds within industries (including tradeables), and the effect is particularly strong for industries known to have higher external capital needs. Similar to the popular work by Mian and Sufi (I mentioned their stuff here), the authors estimate the magnitude of this channel's role in aggregate employment and find that "the collateral channel can account for 10-25% of the increase in pre-crisis employment, . . . while the demand channel explains about 40% over the same time period." Note, though, that this approach uses a somewhat unsatisfactory extrapolation from local to national data; as the authors note, general equilibrium effects and other stuff are not accounted for.

The analysis is done on County Business Patterns data, and the authors acknowledge that more can be done with firm-level data. Their house price data come from FHFA and are at the MSA level (as are the Saiz elasticity data). The housing supply instrument relies for its validity on being uncorrelated with entrepreneurial activity except through the collateral channel. I think this is a pretty tough standard to meet, but this may be an unavoidable limitation of research on this topic.

In any case, the results are highly suggestive and are consistent with similar results found elsewhere (that one uses time series identification and gives attention to firm age). I think it's really difficult to not believe that the collapse of housing collateral values is partly to blame for the collapse of startup activity we observe heading into the Great Recession.

If there are a lot of people that are sitting along the extensive margin of entrepreneurship but cannot enter due to collateral constraints, a recovery of house prices could be just what we need (and there may be intensive margin effects as well). Entry creates a lot of jobs; and while this job creation is short lived for many entrants (see here and here), it could get the job market moving again and improve the chances for the next few cohorts of entrants.

Sunday, March 24, 2013

Monetary union with capital controls

Image source

Tim Duy writes:

Is this how the Eurozone experiment will end? Not with a formal "exit," but with a return to banking dominated by national boundaries and enforced by capital controls? No longer a true common currency, but a dozen currencies sharing the same name, each with different value?

This reminded me of, among other multinational currency arrangements, the CFA franc zones. From Barry Eichengreen:

Two special circumstances played a role in the stability of the CFA franc-Frech franc rate. First, all members countries maintained restrictions on payments for capital-account transactions, and several maintained limited restrictions on payments for current-account transactions. Here as elsewhere, capital controls appear to have been associated with the viability of the currency peg. Second, the CFA franc countries received extensive support from the French government. In addition to foreign aid (France being the largest bilateral donor to its former colonies), they received essentially unlimited balance-of-payments financing. 
The contrast with the EMS is worth noting. Where intra-European currency pegs have had to be changed every few years, the link between the French franc and CFA franc remained unchanged for nearly half a century. (first edition, page 185)

From Benjamin Cohen:

Even a minimal sense of community is missing. Mutual trade is small, at a little over 10 percent of the average of exports and imports, while historical antagonisms in some instances remain deep and persistent. (page 175)

The point is not that the franc zones (or other currency unions) are directly comparable with the Eurozone (obviously they are not). Piling on capital controls is unlikely to resolve Europe's banking sector problems, for one. But the notion of a union under a common currency (or hard peg) in which countries use various capital controls to carve out some elements of monetary autonomy is not just academic. The franc zones have done it for decades, and other arrangements like the Sterling Area or even Bretton Woods had these characteristics to some degree.

I have no idea what the Eurozone endgame looks like, but a common currency throughout a series of financially segmented states is at least a possibility. Reversing the globalization of capital, though, isn't likely to be as easy as it once was. The extent to which the proposed Cyprus rules restrict even purely domestic uses of electronic money speaks to the difficulty of preventing cross-border capital flows in the modern climate. 

As a side note, it's always important to remember that the Eurozone was not the first attempt at full currency union. They have existed all over the globe, even just in the last century. The history of currency unions is fascinating for students of economics and geopolitics; a good place to start is Cohen's Geography of Money.

Thursday, March 21, 2013

Put your money on Harvard

A few years ago my friend Tim Layton filled out a March Madness bracket using economics department rankings. He hasn't done it for this year, so I decided to rip off the idea. I follow Tim in using the IDEAS ranking; schools that don't appear in those rankings lose to those that do, and I decide matchups of non-ranked schools using their tournament seed.

Here's the bracket; I did it quickly, so there might be mistakes. Click for a larger image.

I didn't enter this bracket in any pools. Feel free to do so if it's not too late...

UPDATE 3/24: The bracket has 350 points on ESPN, ranking it at 97.8% or #181,205.
UPDATE 3/25: Now the bracket is at 41.7% on ESPN, with 390 points.

Monday, March 18, 2013

We're getting old and fat!

Or, at least, our firms are. Figure 1 plots the share of employment accounted for by "old" firms--6 years or older and 11 years or older (click for larger image). These data are from the BDS, which includes the universe of private, nonfarm establishments (but I look at firm characteristics).

Figure 1
Vertical axis does not start at zero

Note that the 6+ category includes the 11+ category. Observe that old firms account for a large majority of employment. Further, their share has been steadily increasing, with the 11+ category gaining by about 10 percentage points in the last two decades (the decline of young firms has been well documented, e.g., here). I've noted before that startups basically account for all net job creation, but these data are reminders that older firms employ most of us. It's basically a stocks and (net) flows distinction.

Figure 2 plots the share of employment accounted for by what we might call medium or large firms--50 or more employees and 250 or more employees (click for larger image).

Figure 2
Vertical axis does not start at zero

These size categories account for the majority of employment, with just over half of all private nonfarm employment being accounted for by firms with 250 or more employees. This fact seems like an important one to keep in mind when politicians talk about small businesses. Note that, as with old firms, large firms have increased their share of employment in recent decades. Observe also that there is a cyclical element to the size distribution of employment (which is discussed at length by Moscarini and Postel-Vinay; this is a very interesting paper).

Despite this post's title, I don't mean to suggest that the changing age and size distribution of firms is a bad thing. It may or may not be. But it does seem noteworthy. It's also useful to keep the following distinction in mind:

While large and mature businesses account for a very large share of the level of economic activity, the dynamics of entry and exit and the associated dynamics of young and small businesses account for a disproportionate share of the change in activity. (Becker, et al. 2006, 544)

Just for fun, I also diced the size distribution to look at really large firms. Figure 3 plots the share of employment accounted for by firms with 5,000+ and 10,000+ employees.

Figure 3
Vertical axis does not start at zero

About a quarter of all private, nonfarm employees work for a few huge, 10,000-worker firms (about 1,200 firms in 2010, with 640,000 establishments). These size categories show strong cyclical patterns and, perhaps, some elements of the usual upward secular trend.

The relationships between labor markets and the size and age distribution of firms appear to have both secular and cyclical components. Rates of job creation, job destruction, and excess reallocation tend to decline as size and age increase, so the secular trends in employment shares charted here may help explain the secular trends we see in those measures of job market dynamism, somewhat counteracting the movement towards higher-volatility industries.

Monday, March 11, 2013

I don't know what "the fiscal multiplier" is (and related observations)

Image source

I'll borrow a quip from John Rust here. In Lewis Carroll's famous tale. Alice reacts to hearing the poem Jabberwocky:
Somehow it seems to fill my head with ideas--only I don't exactly know what they are.
That's how I feel when I hear people talk about "the fiscal multiplier." The fiscal multiplier isn't a thing. It's not a structural parameter governing economies that we just need to discover. The response of the economy to government spending is likely to depend heavily on the state of the economy and the nature of the spending (definitely read that last link, and read this one too).

This is true of a lot of useful "reduced-form" relationship estimates, of course, but in my mind the fiscal multiplier is the king of reduced-form-ness. The outcome being measured is too far downstream from the treatment causing that outcome--and this is saying nothing of the even more relevant fact that under the usual monetary policy objectives, the "fiscal multiplier" might only be an estimate of the central bank's incompetence.

I know the fiscal multiplier is reasonably well defined in New Keynesian and related models. But it's not easy for me to map that concept onto the real world (while, believe it or not, I can do so with a lot of other NK concepts).

I'm not suggesting that estimating fiscal multipliers is a waste of time or that the estimates we do have are useless. By all means, let's keep researching the range of effects of fiscal policy. I'm just suggesting that the meaning of the multiplier is not always clear, and cherry picking multiplier estimates from the literature to support one's preferences is probably disingenuous. More generally, nobody will ever convince me of the necessity of fiscal stimulus (or of avoiding "austerity") by citing a few multiplier estimates.

Jeffrey Sachs bemoans the prevalence of "crude Keynesianism" in the national policy debate, where crude Keynesians embraces the following:
(1) The belief that multipliers on tax cuts and transfers are stable, predictable and large;
(2) The belief that America's employment and growth problems are overwhelmingly cyclical, not structural, and therefore remediable by short-term aggregate demand management;
(3) The belief that a growing debt burden is a minor nuisance as long as the economy is in recession;
(4) The belief that for practical purposes, the most urgent need is to raise aggregate demand rather than to focus on the quality and type of public spending.
I don't mean to take a stand on the causes of our prolonged employment problems. I had strong views on that back in the days before I realized how confused I am, but not anymore. Even so, I can't think of any reason to believe that good policy can be based on such a temperamental idea as the fiscal multiplier.

I also have no serious position on the related issue of structural vs. cyclical elements of the employment problem. While inflation and inflation expectations stay low, I'm not going to be too concerned about having too much demand stimulus. I know about papers like this one. But I would also say that given some of the secular trends we see in the U.S. economy, it's pretty hard to believe that structural forces are not playing any role in this business cycle. Some data from this post (click for larger images):

And here's one from this post:

...which should be considered along with one from this post:

One more:

There are clearly some big secular trends in the structure of the U.S. economy. Something has been going on for the last 30 years or so. The degree to which this secular stuff affects the business cycle, and the effect that fiscal policy might have on it all, depend on what is causing all these changes. We have a good idea about some of it, but we don't fully understand it all. I think some caution and intellectual humility are appropriate when we make claims about what's going on and what policies we should be applying.

Monday, March 4, 2013

Two economies of young firms, contd.: Tracking cohorts

In  a previous post, I explored some data on job creation and destruction by firm age classes. Those data suggested that after creating lots of jobs in their initial year, cohorts of startups diverge: some continue to grow (fairly rapidly) while others shrink (also fairly rapidly) and disappear. In that post, I was looking at age categories by year rather than tracking individual cohorts of new firms. Tracking cohorts seems like it would be interesting, so Figure 1 displays net job creation for several firm cohorts as they age (click for larger image). I use cohorts born at five-year intervals starting in 1980, then I track them for their first five years (the BDS begins lumping age classes together after that).

Figure 1

The chart basically confirms the conclusions from my last post. For one-year-old firms, we see a mixed bag: some cohorts are still growing while others are already shrinking. Obviously, some of this is driven by broad economic conditions faced by each cohort (for example, the 1980 cohort's first few years were in and out of recessions). By age 2, all cohorts are shrinking in employment terms and will do so through age 5 (with one small exception). Recall, though, that these are net employment numbers; my last post showed that this kind of aggregation is actually hiding the fact that many firms grow rapidly in these age categories.

Figure 2

Figure 2 uses the same data but reports cumulative job creation totals by age (rather than simple annual flows). This allows us to compare cohorts' cumulative effects on labor demand, though it's important to keep in mind that more recent cohorts faced a larger economy than those from previous decades and might therefore be expected to create more jobs.

The 1980 cohort is the only group to have been born around recession. The 2005 cohort saw deep recession as well, basically starting at age 3 but really deepening around age 4 (which is reflected in the chart). Nearly all cohorts see their cumulative net job creation decline over time.

Due perhaps in large part to the "two economies" idea, firm cohorts begin life by adding lots of jobs to the economy; thereafter, they become net job destroyers. Over a 5-year horizon, the cohorts reverse the large positive effect they initially had on job demand, gradually reducing their cumulative contribution to job creation.

Sunday, March 3, 2013

How to think like Nick Rowe

Yes, if the central bank raises or lowers interest rates, this will affect financial markets. But I thought we had gone beyond thinking of monetary policy in terms of raising or lowering interest rates. Or buying or selling bonds in an open market operation. Or raising or lowering the money supply. Or raising or lowering the exchange rate. Those aren't monetary policies.

The quote above is from this post.