Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Thursday, April 28, 2016

On the want of U.S. government debt

In a recent article, Narayana Kocherlakota lays out the case for why, under present conditions, the U.S. government should be issuing more debt, using the proceeds to cut taxes, finance infrastructure spending, or both. It's a policy that many economists, including yours truly, have been advocating for some time. And while I generally support the policy, I thought it would be useful, nevertheless, to reflect on some possible counterarguments. It's not a slam dunk case, one way or the other, I think.
Kocherlakota does a good job explaining why a deficit-financed tax cut, or deficit-finance infrastructure spending is a good idea. I want to make it clear that the argument in favor of the policy hinges critically on the presumption that we can rely on Congress to manage the public debt over time in a responsible manner. Let's accept this assumption, provisionally at least, in order to understand the economic argument. I will come back to the political argument later.

While the debt-to-GDP ratio (D/Y) is presently high by historical standards, it's not unmanageable. The key is not the D/Y itself, but its trajectory over time. Clearly, D/Y cannot grow forever. And fortunately, market signals are available to monitor how the public perceives the likely path for D/Y over time. These market signals are: (1) the yields on U.S. treasury debt (at various maturities), and (2) inflation and inflation expectations. So what are these market signals telling us? The yield on U.S. treasuries is presently very low. Both inflation and inflation expectations are presently running below the Fed's 2% target and have done so for years now. So far, so good.

The large increase in D/Y since 2008 together with plummeting yields and low inflation may seem puzzling, but it's not really. Usually, a bad event that triggers a large increase in the public debt also triggers higher bond yields and the prospect of inflation. We can expect this to be the case in any experiment where the supply of debt increases in the face of a stable (or diminished) demand for the debt that is being issued. Think Zimbabwe or Venezuela.

But the U.S. is not Zimbabwe or Venezuela, or the Weimar Republic, for that matter. Rightly or wrongly, the U.S. treasury security is viewed by investors around the world as a safe haven asset. So when the financial crises hit in the U.S. and Europe 2008-10, investors moved en masse into U.S. treasuries (and other sovereign debt instruments viewed to be relatively safe). In short, while the supply of U.S. debt spiked up, the demand for U.S. debt increased by even more. We can infer this from the behavior of bond yields, which went down (the price of debt went up) at the time.

So the economic argument is simple. The U.S. government can presently borrow at essentially zero interest (more or less) even 10 years out and more. This effectively gives the fiscal authority the ability to print money (low-interest debt), so there's no need to rely on the Fed. To the extent that domestic real economic activity is still not firing on all cylinders, why not offer temporary tax cuts to stimulate demand? Why not re-build that crumbling infrastructure, putting people to work, all financed at zero-interest? It sounds like a no-brainer.

Alright, now for a couple of counterarguments, one economic and one political.

An economic argument against temporarily increasing the public debt further (and indeed, taking measures to reduce it) could be made on the basis of the Triffin Dilemma. The economist Robert Triffin noted back in the early 1960s that world reserve currency/debt status is a double-edged sword. On the one hand, it's great that the U.S. can just print paper that is coveted around the globe. If foreigners are willing to export their goods and services to us, expecting only paper in return, then we are extracting wealth from the rest of the world (in exchange for what ever financial service our paper is providing them).

One implication this power, if exercised, is that the world reserve currency issuer is likely to run persistent trade deficits. Triffin worried that the huge amount of U.S. currency held by foreigners exposed the U.S. to foreign risks. What might happen, for example, if foreigners suddenly decided they no longer wanted to hold USD or USTs? This could result in a sudden and dramatic change in the exchange rate, leading to domestic inflation and sharply higher bond yields.

There is also the trade-related argument that persistent trade deficits kill domestic industries and domestic employment. After all, if we can make the rest of the world work for us in exchange for paper, where is the need for us to work at all? The implied boom in domestic leisure consumption sounds good theoretically. But of course, in reality, the gains are not evenly shared. The rich gain by purchasing cheaper foreign goods. The poor are out of their jobs.

A political argument against more government debt could be made by challenging the assumption that it will be managed responsibly. This "we can't trust future politicians to do the right thing" argument is (sadly) not without empirical merit. I am reminded of the following quip by P.J. O'Rourke,
"The Democrats are the party that says government will make you smarter, taller, richer, and remove the crabgrass on your lawn. The Republicans are the party that says government doesn't work and then they get elected and prove it."
I can't help but note a certain irony here. There seems to be a strong presumption among people (Americans in particular) that the government should run its finances in the manner of a household. Economic theory is quite clear that this sentiment, however noble, is just plain wrong. The irony is that to the extent that this sentiment finds its way to being represented in Congress, it proves to be a very valuable "anchoring" device for the fiscal authority.

That is, I sometimes wonder whether US treasury debt is valued around the world the way it is precisely because it is known that Congress is impregnated with a large number of genetic "debt-ceiling" algorithms. It may not be an ideal situation from the perspective of pure economic theory, but then again, it's not hard to think of worse scenarios.

Friday, April 22, 2016

Interest Rates and Aggregate Demand Revisited

Nick Rowe has a nice post (written some time ago) that frames an old macroeconomic issue in a very nice (teachable) way.

In macro policy discussions, one often hears something like "lower interest rates stimulate aggregate demand.'' Many people view such a statement as self-evident. It's only when you think about it for a long time that you realize it's not self-evident at all (few things are when we are left to ponder them long enough, it seems).

The purpose of this post is to add a bit of formalism to Nick's discussion. (Sorry for the wonkish display, but I think it's necessary at this point to make things clear.) To this end, let's begin with an off-the-shelf bare-bones macro model. There is a representative agent (this is not necessary, but makes things easy) with additively-separable log preferences defined over consumption sequences {c(t), t = 0,1,...,∞}, with discount factor 0 < β < 1. Let R(t) denote the gross real rate of interest (risk-free) earned on a bond held from date t to date t+1. Assume that all individuals can borrow/lend freely at the risk-free rate.

Now, consider the cost-benefit calculation associated with the consumption-savings choice. Suppose an individual refrains from consuming one unit of consumption today. The marginal utility cost of this sacrifice is given by 1/c(t). This one extra unit of saving delivers R(t) units of extra consumption tomorrow. The marginal utility benefit of this extra consumption is R(t)β/c(t+1). Individual optimization requires equating marginal cost to marginal benefit:

[1] 1/c(t) = R(t)β/c(t+1) for t = 0,1,...,∞

Condition [1] is sometimes called the consumption-Euler equation, or just the Euler equation, for short. (Noah Smith has a nice post on the Euler equation here.)

One can do a lot with the Euler equation. Here is how it is used to derive "aggregate demand." First, assume that all output is (for simplicity) in the form of nonstorable consumer goods and services. Let N denote population size. Then C(t) = Nc(t) denotes aggregate consumption or GDE (gross domestic expenditure). Now rearrange [1] as follows,

[2] c(t) = [ 1/(R(t)β) ]c(t+1)

Thus, if we hold c(t+1) fixed, then equation [2] traces out a negative relationship between c(t) and R(t). That is, an increase in R(t) results in a decrease in planned present day consumer spending (aggregate demand). This negatively related locus of consumption and interest rate pairs is sometimes called an IS curve (IS = "investment-saving" where investment is fixed at zero in this model). The economic intuition is simple: raising R(t) makes it more attractive to save (lower current consumption). [Never mind for now that any extra saving is likely to boost c(t+1).]

Let me consider an endowment economy where each individual is endowed with a deterministic sequence {y(t), t = 0,1,...,∞}. Usually, y(t) is thought of as an individual's output or income at date t, so that Y(t) = Ny(t) represents GDP (gross domestic product) or GDI (gross domestic income). But more generally (and this is what the General refers to in the General Theory) we can think of y(t) as a maximum production capacity. "Full employment" refers to the special case where Y(t) is the GDP.

The standard neoclassical assumption is that the economy is always at full employment. Maybe calling this property an assumption is not quite accurate. We can derive the property as a result of some deeper assumptions relating to the ability of individuals in an economy to coordinate their activities in an efficient and socially desirable manner (this is the force behind Says' Law, that "supply creates its own demand.") In any case, the upshot is that Y(t) represents the GDP. And since GDE = GDP, we have C(t) = Y(t), or c(t) = y(t), at every date t. Each person consumes his value-added, the economy consumes what it produces.

Suppose that real income grows at rate α, so that, y(t+1) = αy(t). Since c(t) = y(t) for all t, condition [2] can be used to deduce the equilibrium real rate of interest:

[3] R*(t) = α/β

The real interest rate is predicted to be high when growth (α) is high. The real rate of interest is low when growth is low. The intuition here is as follows. An increase in α means that people are expecting higher levels of future income. People will want to bring some of that future income forward in time. They will try to do so by borrowing, or saving less. Either way, the effect is to put upward pressure on the interest rate.

Alright, it's time to do some "textbook" aggregate demand analysis. Actually, I don't like the way textbooks usually do this. The usual assumption is a "sticky wage" that mucks up the labor market (here is my critique on that idea). This idea is certainly not Keynesian:
"There is, therefore, no ground for the belief that a flexible wage policy is capable of maintaining a state of continuous full employment..." [General Theory, 1936 Chp. 19]
Indeed, Keynes (1936) wrote that flexible wages could make things worse, not better (consistent with my Figure 2.12 here.) The best representation of "what Keynes actually meant" is, in my view, expressed formally in the game theoretic notion of multiple Bayes-Nash equilibria (a tool that was not available to Keynes in his lifetime). See Cooper and John (1988), Howitt and McAfee (1990) and Roger Farmer for example.

How to proceed? There are many ways, but I don't want to get bogged down in the details here (although I should stress that the details are critical for other questions). One way to proceed is to embed my static high/low equilibrium model into the model above. In that model, aggregate demand C(t) can be either high or low, and the equilibrium level of output can correspond to the high or low level of demand as a self-fulfilling prophecy.

Here's another way to think about it. Peter Howitt would explain it to me this way. Imagine that the people in our model do not like the smell of their output (any reason to motivate intratemporal trade here will do). So they will want to swap their goods with others. If everything works well here (the neoclassical assumption), then all goods will be traded at par. The real GDP is Y(t).

Now, suppose that trading is costly. Suppose that it is prohibitively costly to sell any output beyond some level k(C), where C is aggregate demand. Assume that k(C) is increasing in C. The idea here is that it is easier to sell larger quantities of output when demand is high. In fact, we could just assume k(C) = C/N. Next, consider an arbitrary 0 < C/N < y. Then the most anyone can expect to sell (and buy) at a given date is c = C/N. In this model, there is a continuum of equilibria, each indexed by an expectation defined over C/N. If everyone expects a thickly traded market, it is individually rational to trade a large volume and, collectively, this is what transpires. "Animal spirits" determine which of these equilibria actually prevail.

Alright, back to Nick's point. Assume that in the "long run," the economy returns to full employment forever. For simplicity, assume that the long-run is expected to occur tomorrow. In this case, c(t+1) = y(t+1) and R(t+1) = α/β for every date t going forward. Now let's take a look at today, t = 0, using condition [2].

[2a] c(0) = [ 1/(R(0)β) ]y(1)

Assume that c(0) is determined by an animal spirit (as described above) such that c(0) < y(0). Then condition [2a] can be used to solve for the equilibrium interest rate,

[4] R(0) = (1/β)y(1)/c(0) > R*(0) = (1/β)y(1)/y(0)

That is, the economy is presently in recession and the interest rate is too high. And if the interest rate is too high, well, then, why not take policy actions designed to lower it? The recession is like diabetes and low interest rate policy is like insulin, as Kocherlokota argues here.

And the argument makes sense IF full employment lives somewhere in the foreseeable future. Lowering the interest rate in this model has the effect of stimulating consumer demand as people try to bring future output closer to the present. But future output here is fixed at full employment. So, to the extent that lowering the real rate of interest increases C(0), the effect is felt entirely in the contemporaneous depressed period in the form of higher real GDP.

But what justifies the assumption that the economy will somehow find its way back to full employment? This is the missing piece in our conventional models.

This leads Nick to ask: what if people do not expect a return to full employment in the near future? Indeed, what if? As it turns out, there are many, many other equilibria in the model above. One such equilibrium path satisfies

[5] C(t+1) = R*βC(t)  where C(t) < Y(t)  for all  t = 0,1,...,∞

That is, the economy can be permanently stuck in a "secular stagnation." Moreover, the equilibrium interest rate is exactly where it should be: it is neither too high  nor too low. Consumption and GDP are growing at rate α. It's just that the level of GDP is permanently below its full employment level.

The real interest rate measures the relative price of output across time. In the equilibrium described by [5], the relative scarcity of output across time is just right. Its the contemporaneous level of output that's off at each date. How is a change in the interest rate supposed to fix this problem?

The short answer is that it can't. In fact, it's easy to construct examples where attempting to lower the interest rate could make things worse (perhaps this is an overdose of insulin, in Kocherlakota's example).

Suppose we're in a situation described by condition [2a], for example. In that exercise, I assumed that y(1) is fixed at full employment and that c(0) is depressed. This is what justified lowering R(0) to stimulate contemporaneous consumer demand. But suppose that animal spirits keep contemporaneous consumer demand fixed, and that the effect of lowering R(0) is to reduce future consumer demand to c(1) < y(1)? There is no a priori reason to expect c(0) to do all the "equilibrating" here. And so, in this manner, the effect of low interest policy could be to cause future recessions, possibly a secular stagnation.


I think most of what I said above can be shown in a conventional 2-period economy (a current and future period). Here are some diagrams.

Consider first the neoclassical general equilibrium (full employment at both dates). Condition [1] states that the slope of the indifference curve is the same as the slope of the intertemporal budget constraint (the real rate of interest). The full employment assumption means that the equilibrium lies on the budget constraint. This is point A in the following diagram.

Suppose now that the economy is expected to be at full employment in the future; i.e., fix c(2) = y(2), but that the economy is presently depressed; i.e., c(1) < y(1). The interest rate is too high, R' > R*. This is point B in the following diagram.

Lowering the interest rate in the diagram above (making the budget line flatter) moves the economy from B back to A. But suppose we instead forecast a future recession, so that c(2) < y(2). Then condition [5] prevails, and the economy moves to point S (secular stagnation) in the diagram below.

And finally, here's how to depict a future recession caused by an artificially low interest rate  policy (point F).

Thursday, April 14, 2016

How old were the inventors of major inventions?

I came across this fun column the other day listing a number of Famous Inventions, like the airplane, the camera, electricity, the car, etc, along with their inventors. A thought crossed my mind: how old were these inventors when they invented these inventions? Were they young like Marconi, who invented the radio in his early 20s? Or were they old like Gutenberg, who invented the printing press in his early 50s? In short, is there an age demographic that is responsible for producing major innovations?

Let's take a look at the data based on 34 major inventions listed in the article I cited above (thanks to Michael Varley for organizing the data).

Here is what the data looks like for the full sample:

I have to admit, I was a little surprised--the median age is 40 (I was expecting younger). In what follows, I report the age distribution for different centuries. I'll save any commentary for another time and let you draw your own conclusions. Feel free to send me links to any literature related to this issue.

Postscript: The demographics of innovation in the United States. Reports that the median age for an innovator is 47 years. It's also interesting to note the disproportionate share of innovation attributable to immigrants and the children of immigrants. 

Postscript April 16, 2016. 
Interesting comment thread here