Tuesday, April 15, 2014

Interest, to Deficit, to Debt

What drives the federal government's near-term fiscal outlook is, to a surprising extent, interest payments rather than Medicare and Medicaid. They are set to grow faster than mandatory or discretionary spending over the next decade, from 1.3 percent of GDP to 2.6 percent of GDP.



The difference between rising debt over the next decade and keeping debt stable as a percentage of GDP is just one percentage point in the average interest rate on the U.S. public debt.

Paul Krugman has argued recently that the Congressional Budget Office's forecast for interest rates is too high -- and inconsistent with the odds that the economy remains somewhat depressed for some time to come. I figured it would be useful to do some math and test some of the assumptions in the latest CBO forecast.

First, I backed out its forecast for the average interest rate on U.S. public debt -- you can do this by dividing interest payments as a percentage of GDP by debt as a percentage of GDP. What you find is that the CBO expects this rate to reach 4.2 percent by 2024.


Is that reasonable? Well, it's hard to know without having a good sense of how the average interest rate on U.S. public debt behaves. It turns out that you can proxy for it very closely with the 10-year Treasury. I added the forecast line in green. The public debt interest rate in blue is estimated by taking the annual federal expenditure on interest payments and dividing it by the stock of total public debt.


That doesn't seem to be an impossible path for the average interest rate on public debt. In fact, we can use the 20-year Treasury and the 10-year Treasury to back out the 10-year, 10-year-forward rate -- the expected interest rate on the 10-year Treasury note in 2024. Given a current 10-year rate of 2.63 percent and a current 20-year rate of 3.35 percent, the 10, 10 forward rate is 4.08 percent.

But what if you assume that the interest rate will be 3 percent rather than 4.2 percent? How does the debt outlook change? Well, at that rate, debt stays constant for the next decade as a share of GDP, given the CBO's forecast for primary balance (the deficit ex-interest). Here's the graph comparing the two assumptions for the interest rate:


And here's the graph showing how this change in interest rates has a big impact on the near-term outlook for the federal debt:


I'm not making any claim that three percent is the correct assumption for the interest rate. In fact, I've presented some evidence as to why four percent is closer to market expectations. But it's always interesting to see how sensitive debt forecasts are to small changes in parameters like the interest rate. I guess this does illustrate Carmen Reinhart's view that highly-indebted governments almost always turn to financial repression.

Thursday, April 10, 2014

How Big Is the Gender Pay Gap?

“It’s not a myth; its math,” President Barack Obama said of the pay gap between men and women in the workplace. “You can look at the numbers. You can look at the pay stubs.”

It's true that the average woman working full-time earns 23 percent less than the average man who works full-time does. Yet this tells us a lot less than it might seem at first glance.

Men and women differ in occupations, work experience, education, hours and so many other qualities that “average” doesn’t get you close to the real concern about pay equity: That women earn less simply because they are women, and that a woman would be paid less than a man who is otherwise exactly alike her.

In this post, I'm going to do a cursory analysis of data from the March Current Population Survey from 1990 to 2013. You should check out the classic study on gender pay gaps here, from Francine Blau and Lawrence Kahn; these two essays by Claudia Goldin are also a terrific grounder on what and how economists think about the issue.

There's no doubt that, in raw average terms, women earn less than men on an hourly basis. Here's a kernel-density plot of the distribution of the natural logarithm of the hourly wage in 2013, divided according to gender. The black vertical line denotes the federal minimum wage. You can see the wage gap for yourself: the men's wage distribution, in red, is further to the right than the women's wage distribution, in blue.



But perhaps one might think the right question to ask with respect to gender equity isn't this raw average, but rather the counterfactual story about two people who are identical but for their gender. Econometric analysis can get us a good deal of the way there, and that's what this post is about.

Let's think about the factors that tend to be associated with higher or lower hourly wages. People with more work experience and more education seem likely to earn more, as are people who enter into occupations that are generally well-paid, like law or medicine, or unionized, like manufacturing. And it's well known that there are substantial racial differences in pay. We might also expect that pay varies according to whether you work in an urban area or a rural one and your geographic region of the country. We also know that hourly wages have generally risen over time as a result of inflation and productivity growth. And we might imagine that marriage and the number of children, especially young ones, has some effect on pay.

When we control for all of these influences -- which, let's suppose for the moment, are all independent of the gender pay gap -- how much of the gap persists? Whatever goes away is explained by these factors rather than purely gender.

The technical specification of the regression is that we're constructing a Mincer earnings function with controls for NAICS occupation, age, race, SMSA urban status, US Census region, marital status, union membership, number of children, number of children under age five, the logarithm of reported usual weekly hours, and time fixed effects by gender.

Using Stata to run the regression on my CPS survey data, which includes a sample of 209,000 people, I get the following table. From left to right, the columns are year, my point estimate for the gender pay gap in that year, the standard error, the t-statistic, the p-value, and then the 95-percent confidence interval around my point estimate.



My estimate of the gender pay gap is that women were paid about 7.7 percent per hour less than men on average in 2013, holding everything else equal. The gap was 14.3 percent in 1990. Depending on my regression specification, I was able to push the gender pay gap coefficients around only somewhat -- I think the range of reasonable estimates of the 2013 adjusted gender pay gap is probably 4 percent to 10 percent.

We're talking about a hypothetical woman working in the same occupation, in the same region of the country, of the same work experience, education, and race, and with the same family and working hours -- that woman is paid significantly less than a man to whom she is alike in all these respects, though the pay gap is smaller than the raw version.

It's not clear, though, that we really should be controlling for all these things. It's fair enough that people with more experience earn more. But it's reasonable to think that things like occupational choice and working hours are all influenced by the same gender discrimination we're seeking to detect. The pay gaps that result from women ending up in lower-paying fields are part of the pay gap insofar as that's true -- they're not something to explain away. More on this soon.

Note: This post is a re-do of an earlier one, which had a technical issue in the regression specification. Hat tip to Justin Wolfers, who spotted the problem, and to John Schmitt for some helpful further comments. You can download the .do file here, and the data from IPUMS here

Thursday, March 20, 2014

Slacking Off

Update (3/20): Alan Krueger has a highly relevant paper for the Brookings Papers on Economic Activity that concludes the long-term unemployed likely exert minimal influence on labor markets, including wage determination.

We're at the stage of the conversation about labor-market slack, it seems, where everybody is looking for the takeaways and points of meaningful agreement.

Cardiff Garcia has an excellent overview of how the debate on the labor-market slack issue has evolved. For people looking to dive in, Jérémie Cohen-Setton has a shorter look at the evidence and the arguments. Tim Duy says it was crazy that people ever thought that "overshooting" was ever in the cards. And Ryan Avent says no, it wasn't crazy -- and the case for a modest overshooting remains airtight.

Just a few odds and ends to share from me. I looked at the extent to which quits lead wages -- and found the lead time to be something on the order of a year, as you can see in this graph:



Regressing wages on 12-month lagged quits yielded a forecast for year-over-year increases in wages of about 3 percent. That was broadly in line with monthly and quarterly VAR estimates, including and excluding unemployment and consumption in the model. So something on the order of three-percent wage growth next year, and three-to-four-percent the year after that, both seems about right qualitatively and is what some simple modeling would predict.

That's not much to fear. What's been missed, though, is that the U.S. is not at the beginning of a normal tightening cycle. The federal funds rate is not one or two percent as it was in the 1990s and 2000s bottoms. It is zero. And there is billions in further easing beyond that.



When I look at the data and historical Fed behavior, it's hard for me to see a monetary policy that does not involve the beginning of an exit now and rate hikes in 2015. Even that incorporates some degree of overshoot -- if not in terms of inflation, as Avent wants, than certainly in terms of the unemployment rate.

It seems that, too, is the conclusion of the FOMC. The downward revision of the unemployment rate forecast now pegs full employment at the end of 2016. And the assessments of appropriate monetary policy suggest the FOMC is attached to the idea of rate hikes in 2015 and proceeding slowly from there.

Thursday, March 13, 2014

Tuesday, March 11, 2014

Trading in Your Feathers

There are two main dovish arguments. The first is that we're "nowhere close" to full employment or meaningful capacity constraints, as the Economic Policy Institute's Josh Bivens argues. The second is that, even if we are close, it's worth chancing it with inflation because the benefits of a robust recovery greatly exceed its risks of taking it a bit too far, as The Economist's Ryan Avent and The Financial Times' Cardiff Garcia both have said.

Bivens argues that the U.S. economy hasn't recovered in a significant way. He suggests the output gap has shrank by less than half, or perhaps even less than a third. It's the thoroughest update I've seen on the dovish case. What it boils down to is that the output gap looks big and employment is still depressed, and there's no evidence of price inflation or fiscal crowding-out.

Where do Bivens and I diverge? We definitely do. The key part about most definitions of full employment is the behavior of wages. You know you're at full employment when you see wages increasing in a big way. You know you're not when wage growth is quiet. This is why I am watching the wage determination process and at quits. There's really no way to get to that definition of full employment from estimates of the output or unemployment gaps, as that assumes the level of potential, the essence of what you're trying to prove. Inflation comes closer, but it will likely lag wages.

What I'd love to hear him answer: The U.S. is seeing 8 million too many quits a year for there to have been no reduction in slack in labor markets. That's 6 percent of total employment. In fact, quits suggest the unemployment rate is accurately measuring labor-market slack.

Avent's and Garcia's arguments are more interesting, and we agree much more than we disagree. Both are willing to accept that the output gap isn't quite as large as Bivens suggests. Yet Avent and Garcia both say it's worth pressing onward because we might be able to recoup lost capacity, give wages a boost after a long period of stagnation, and because a macroeconomic equilibrium with slightly higher inflation and higher nominal interest rates is in itself desirable. The last point is that when inflation and interest rates are too low, it renders monetary policy impotent as a tool to fight future recessions.

Right. There's no doubt that the costs and benefits of an "overshoot" of full employment are asymmetric. Stay too loose for too long, and you get a temporary bit of inflation. Exit too early, and you leave the work of fixing the recession unfinished forever. Who wouldn't take the first one?

The problem with this cost-benefit logic is that the consensus policy track already agrees with it, as do I, to the extent to which the logic works. Futures markets anticipate the first rate hike in the fall of 2015. Rate are then set to rise about one percentage point per year. This locks in a solid amount of "overshoot" already.

How do I figure that? The unemployment rate is 6.7 percent. It has fallen roughly 0.8 percentage points per year. Extrapolate forward to the fall of 2015, and you get that the first rate hike will happen with an unemployment rate of about 5.5 percent. The Fed's estimate of the natural rate of unemployment is 5.2 percent to 5.8 percent, and the middle of that range is 5.5 percent.

Markets therefore expect the Fed to cross its own estimate of full employment with its policy rate at zero. That's extraordinary. See the graph below. By the time the hikes actually kick in -- 2016 and 2017 -- unemployment could be the four-percent range. It's hard to see how that exit wouldn't produce an overshoot and a jump in wages, and how that wouldn't be sufficient to get interest rates way off the zero lower bound.



Jared Bernstein and Dean Baker, who also wrote in response to my piece in Bloomberg, say that quits aren't that high, and that 6.7 percent unemployment is still way above full employment. What the graph above shows is that this is really a matter of degree. 6.7 percent is above full employment, yes, but full employment is two years away.

So here's what I don't get: What more do Avent, Garcia, Bernstein, and Baker -- and more generally, the doves who say they disagree with me -- want? I owe Ryan L. Cooper a shout-out here, too.

Their implication is that a yet larger overshoot is desirable. Much of their arguments are abstract, but the specifics make it almost unbelievable: Should the first rate hike really come when unemployment has a four in the first digit? I'm all with them until that point.

I think the expected path for monetary policy is already dovish, and wisely so. It was an awful recession. But there really is such a thing as "too much." This is already quite a lot. And to say that the current policy path is broadly appropriate, as I've done, really does imply that it's time to start talking about how tight the labor market is, about how much slack the U.S. economy has left, and about tightening.

The reason the Fed is tapering now and talking ever more frankly about rate hikes is ultimately because yes, it's about time.

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Updates (3/13 wrote post, 3/14 added chart)



This post received further responses from Ryan Avent and Dean Baker, both of whom say that a linear projection for unemployment is overly optimistic. Alright. I didn't want to overcomplicate it.

Baker suggests that unemployment will fall 0.3 percent a year for the next three years, given GDP growth and productivity forecasts. I think that's unrealistically low. It's quite likely that labor-force dropouts continue to elevate that rate above what we might expect from GDP and productivity. In the case that he's right, though, and we wake up in mid-2015 with the unemployment rate still in the mid-6-percent range, I wouldn't object to his policy prescription. Nor would, I think, the Fed. No need for tightening then.

As Avent points out, the Fed's forecast is that progress on unemployment will slow down, though not to 0.3 percent per year. Last December, they saw unemployment between 5.8 percent and 6.1 percent by the end of 2015. I think it's likely this forecast is revised lower next week; the unemployment rate has dropped 0.3 percentage points since then.

But even if you don't, my basic point wasn't super sensitive to small differences in the unemployment rate. 5.8-percent unemployment still means the first rate hike comes as the Fed hits its own threshold for full employment. Hikes that proceed at one percentage point per year still mean that, at the end of 2016, the Fed will have its policy rate at one percent while unemployment is in the low-5-percent range.

When you compare that to Fed exits from the 1990 and 2001 recessions, it is clear that this is already a departure from the norm, and to the dovish side. And rightly so. This is not 1990 or 2001. Yet waiting until 2016 or 2017, as Brad DeLong suggested in his excellent overview of the debate, would also seem imprudent, as I've argued above.

Avent argues that none of this is overshooting unless inflation rises, and markets don't expect higher inflation, judging from breakevens. I think this is the right argument. Perhaps it is that markets think the Fed can get away with the moderate overshoot it has planned -- overshoot in terms of real potential -- without much of a rise in inflation.

Friday, March 7, 2014

Exit Easing, Enter NGDP

Let's say you're a policymaker. You worry about a variety of risks. Risks on the upside of your forecast -- like "what if wage growth gets to 3.5 percent?" -- and risks on the downside of your forecast -- like "what if GDP growth slows back down to the 2-percent range, and inflation stays near 1 percent?"

And you have yet more tough problems at the moment. Long-term unemployment is terrible, but it's not clear how much it affects wage determination. (More on that on Monday, by the way.) The risks of overshooting and undershooting full employment are asymmetric -- undershooting is far worse than overshooting -- and what constitutes "full employment" is especially unclear. If you do allow some overshoot, or you realize after the fact you've allowed it, how do you contain expectations of inflation and the monetary-policy response?

These problems, these questions, and this moment all seem particularly suited to nominal GDP level targeting. Why?

1. Because it allows for an overshoot without disordering expectations beyond it. 

This is where the "level" part comes in handy. By setting an unambiguous exit path, you circumvent the fear that a temporary overheating in 2015 would be something the Fed has to spend the next few years undoing with tighter policy in 2016, 2017, and 2018.

To the extent to which you can maintain outcomes near an NGDP path, in fact, the degree of temporary overshoot becomes a policy choice. It's determined by the starting level for the NGDP target. My view -- and, for that matter, the apparent view of the Fed's top monetary economist, William English -- is that NGDP level targeting would vastly outperform any alternative policy in terms of closing the output gap quickly without excess inflation, but that trying to return back to the pre-recession NGDP growth path probably implies too much overshoot in the medium run. Check out page 68 of the paper, which graphs a hawkish and a dovish starting point.

2. Because it neutralizes the supply-side issue.

I really don't know how close the U.S. is to its supply constraints. The level of confidence anyone can have has got to be low, though I would assign a higher probably to the "close" view today than I would have before this post. So what you really want is a policy that is robust to that uncertainty -- i.e. that would perform well whether or not supply was an issue.

This is not a particularly good trait of the current policy regime, under which the policy response to changes in inflation after unemployment drops below 6.5 percent has yet to be defined. It is one of NGDP targeting, which abstracts away from the issue of supply by allowing the Fed to just think about the path of nominal demand. The tradition of thinking about NGDP as unaffected by supply goes all the way back to Robert Lucas in 1973.

3. Because NGDP is better than unemployment. 

The last few years have shown the unemployment rate to be, at best, a questionable barometer of labor-market conditions and real economic growth. It's not likely those problems -- the shrunken labor force, long-term unemployment, demographic change -- resolve themselves anytime soon. And, if you're not watching unemployment, then what real variable are you watching? It seems to me that one runs out of comprehensive economic summary statistics rather quickly.