Zero intolerance

In an earlier post, I summarized the main arguments people have used for and against a September lift-off.  There are, of course, other arguments one can make and bond guru Bill Gross isn't shy about offering his view on the matter in his September 23 2015 investment outlook.

According to Gross, the Fed's low interest rate policy constitutes a form of "financial repression." His argument, as far as I can tell, goes as follows. Long-term prosperity depends on the stock of productive capital. The stock of productive capital is augmented by investment (the flow of newly produced capital goods). Investment is financed out of saving. Low interest rates discourage saving. Therefore, low interest rates are ultimately a prescription for secular stagnation.

Gross claims that "no model will lead to this conclusion." I'm not exactly sure what he means by that. I think what he means "forget about theory, let's just look at the facts." Unfortunately, facts do not always speak for themselves.

So what sort of evidence does he select to support his conclusion? He begins by noting that inflation-adjusted interest rates (on high-grade bond instruments, I presume) were on average negative over the period 1930-1979 and on average positive since then (thanks to Volcker) until recently. Here's what the data looks like since the end of the Korean war (FRED only gives me the interest rate series since then).

The blue line plots the nominal yield on a one-year treasury, the red line plots the one-year CPI inflation rate. Blue minus red gives us a measure of the realized inflation-adjusted return on a nominally risk-free security. Returns were relatively high in the 1960s, 1980s, 1990s, and relatively low in the 1970s, 2000s, and 2010s (so far).

In relation to this observation, Gross writes approvingly of Fed policy decisions in the early 1980s:

But then Paul Volcker turned the bond market upside down and ever since (until 2009), financial markets enjoyed positive real yields and a kick in the pants boost to other asset prices, as those yields gradually came down and increased the present value of bonds, stocks and real estate.

This is a bizarre statement in some respects. First, as the data above makes clear, it was nominal yields that gradually came down--real yields remained elevated for two decades after the event. Second, he evidently does have a model of how a policy-induced increase in the nominal interest rate leads to prosperity: as yields march downward from an elevated level, capital gains are realized in a broad range of asset classes. This is a bizarre argument both in its own right and because it ignores the initial capital losses realized on wealth portfolios when the policy rate is suddenly increased.

So, no, I don't think that model makes much sense. But if so, then how do we make sense of the data? The fact is that the U.S. economy generally did prosper after the 1981-82 recession. Most economists attribute this subsequent era of prosperity in part to the fact that Volcker's policies ushered in an era of low and stable inflation. Jacking up the interest rate was just a temporary measure to bring inflation down. And once inflation began to drift down, nominal yields declined because of the Fisher effect. The fact that real yields remained elevated was just the by-product of an accelerated growth in productivity (after the 1970s productivity slowdown) that likely had little to do with monetary policy.

But maybe this conventional interpretation is incorrect. Could Gross be on to something? Maybe there is a model that justifies his conclusion. I've been thinking about this lately, wondering just what such a model would look like. Here is what I came up with.

Consider a textbook macro model. Let S(r,y) denote the supply of saving, assumed to be increasing in real income y (GDP) and the real interest rate r. Let I(r,x) denote the demand for investment, assumed to decreasing in the real interest rate r and increasing in the expected productivity of capital investment, x.

In a closed economy, domestic saving must equal domestic investment, so S(r,y) = I(r,x). This equation gives us the famous IS curve: the locus of (y,r) combinations consistent with S=I. This relation exists, in one form or another, in virtually every macro model I'm aware of.

The neoclassical view is that the market, left to its own devices, will determine a "full employment" level of income, y*. With y* so determined, the equilibrium rate of interest r* is determined by market-clearing in the loanable fund market, S(r*,y*) = I(r*,x).

Business cycles are generated by fluctuations in the x. High x is associated with optimism, low x with pessimism (over the expected return to capital spending). The diagram below demonstrates what happens when the economy switches from an optimistic outlook to a pessimistic outlook. Let point A denote the initial equilibrium position. A decline in x to x' shifts the investment demand schedule downward. Lower investment demand puts downward pressure on the interest rate--the economy moves along the saving schedule from point A to B. If depressed expectations persist, then the lower level of investment leads to a lower stock of productive capital. This has the effect of depressing GDP. As income declines from y* to y', the saving schedule shifts down and the economy moves from point B to C.

Point C is characterized by lower income, lower investment, lower saving and a lower real interest rate. This is the neoclassical explanation for why periods of why real interest rates are procyclical. Low interest rates are not the product of "financial repression." They are symptomatic of a depressed economic outlook. And any attempt to artificially increase the real interest rate is going to make things worse, not better. One cannot legislate prosperity by increasing the interest rate.

Now, if I understand Gross correctly, he seems to be saying that present circumstances are not the byproduct of depressed expectations. The problem is that the Fed is keeping the real interest rate artificially low. Let's try to interpret this view in terms of the following diagram. The economy naturally wants to be at point A, where the interest rate is higher, along with saving, investment and income. But the Fed is keeping the interest rate artificially low--at zero, in the diagram below.

The effect of the zero interest rate policy is to discourage saving. While the demand for investment is high (point D), there's not enough saving to finance it (point B). As such, the level of investment falls from A to B. The lower investment eventually translates into lower GDP. As income declines, the saving schedule shifts down and the economy eventually settles at point C. This is secular stagnation brought about by the Fed's financial repression.

So is this a sensible argument? There is a problem with it that Gross touches on in his piece when explaining how low interest rates are harmful:

How so? Because zero bound interest rates destroy the savings function of capitalism, which is a necessary and in fact synchronous component of investment. Why that is true is not immediately apparent. If companies can borrow close to zero, why wouldn’t they invest the proceeds in the real economy? The evidence of recent years is that they have not.

Indeed, the logic of the argument is not apparent at all. With interest rates so low, the business sector should be screaming for funds to finance huge new capital expenditures (point D in the diagram above). But they are not. Why not? At this stage, he simply abandons the logic and refers to the evidence. As if the evidence alone somehow supports his illogical argument.

There are, in fact, some logical arguments that one can use to interpret the facts. One is given by the neoclassical interpretation in the first diagram above. Expectations are depressed because the investment climate is poor (feel free to make a list of reasons for why this is the case). The demand for investment is low. Low investment demand is keeping the real interest rate low. The Fed is just delivering what the market "wants" in present circumstances. Raising the interest rate in the present climate would be counterproductive.

There is another argument one could make. Suppose that the investment climate is not depressed. There are loads of positive NPV projects out there just waiting to be financed. Unfortunately, financial conditions are such that many firms find it difficult to find low-cost financing to fund potentially profitable investment projects. In the wake of the financial crisis, creditors still do not fully trust debtors to make good on their promises. As well, regulatory reforms like the Dodd-Frank Act may make it more difficult to supply credit to worthy ventures. In the lingo used by macroeconomists, firms may be debt-constrained. The situation here is depicted in the following diagram.

The debt-constraints that afflict the business sector's investment plans caps the total amount of investment that will be financed by creditors--the investment demand schedule effectively becomes flat at this capped amount. The financial crisis moved the economy from point A to B. As before, lower investment ultimately reduces the productive capacity of the economy, so that income declines. The decline in income shifts the saving schedule down--the economy moves from B to C. The equilibrium interest rate is low--not because of Fed policy, but because investment is constrained. Savers would love to extend more credit if investors could be trusted and if regulatory hurdles were removed. But alas, present circumstances do not permit this saving flow to be released (except, potentially, to finance government expenditures or tax cuts). The effect of a policy-induced increase in the interest rate in this case would be to lower income even further. (The saving schedule would have to shift down even further to ensure that S=I.)

If the analysis above is correct, then the recommendation to increase interest rates in the present climate is off base. Low interest rates are not the cause of our ills--they are symptomatic of deeper problems. The way to get interest rates higher is to adopt policies that would stimulate investment demand (the neoclassical view) and/or adopt measures that would remove financial market frictions (the debt-constraint view). A deficit-financed tax cut (or subsidy) on investment spending would constitute one such measure.

There are, of course, other models that one could use to justify a policy-induced increase in the interest rate in present circumstances. Some members of the FOMC, for example, view the economy as having largely recovered and are now worried about the effect of very low interest rates on the prospect of future inflation. These types of arguments, however, are quite a bit different from the Gross hypothesis. But if he wants higher interest rates, maybe he should use them! A bit of a warning though: I don't think his bond portfolio is going to like the consequences.

The costs of interest rate liftoff for homeowners

The results of some interesting experiments to report here from the work of my colleague Carlos Garriga and his coauthors, Roman Sustek and Finn Kydland. DA

The statement from the July meeting of the Federal Open Market Committee reveals a support for starting to increase interest rates this Fall, provided some further improvement in the labor market. Such monetary policy stance is currently held also by policy makers in the U.K., as hinted by some members of the Monetary Policy Committee, the rate-setting body of the Bank of England.

An important channel through which interest rates affect the typical household is the cost of servicing mortgage debt. Standard mortgage loans require homeowners to make nominal installments—regular interest and amortization payments—calculated so that the loan is fully repaid by the end of its term. Changes in the interest rate set by the central bank affect the size of these payments, but differently for different types of mortgage loans. In addition, the real value of these payments depends on inflation.

Mortgage contracts and debt servicing costs

Fixed-rate mortgages (FRM), characteristic for the U.S., have a fixed nominal interest rate and thus constant nominal installments for the entire term of the loan, typically 15 or 30 years. The FRM interest rate is determined at origination on the basis of the mortgage lenders’ expectations of the future path of the central bank interest rate. In contrast, the interest rate of adjustable-rate mortgages (ARM), a standard contract in the U.K., changes every time the central bank interest rate changes. The nominal installments of ARM loans are thus recalculated on every such occasion, to ensure the full repayment of the loan by the end of its term.[2]

While mortgage contracts specify nominal installments, either fixed of adjustable, the real cost of servicing mortgage debt depends on inflation. The effects of the liftoff on homeowners will therefore depend not only on the mortgage type and the future path of interest rates but also on what happens to inflation during the liftoff.

It is instructive to illustrate the effects of the liftoff on homeowners in terms of changes in mortgage debt servicing costs (DSC)—nominal mortgage payments deflated by inflation as a fraction of household real income. This variable provides a metric of the burden of mortgage debt to homeowners as it measures the fraction of real income homeowners have to give up to meet the mortgage payment obligations of their contract. The numerical examples below illustrate these points.[3]

Liftoff scenarios

Figure 1 considers two alternative paths of the central bank interest rate, a slow liftoff and a fast liftoff from the current nearly zero lower bound (ZLB). In both cases, the interest rate is assumed to revert to 4 percent, the pre-2007 crisis average. In the fast liftoff case, it reaches the half-way mark of 2 percent in two years’ time, whereas in the slow liftoff case this mark is not reached until about eight years from the start of the liftoff. 

Figure 2 plots DSC in the case of liftoff that is not accompanied by an increase in inflation. In this case the path of the nominal interest rate in Figure 1 coincides with the path of the real interest rate. Figure 3 contrasts this case with a situation where the increase in the central bank interest rate is accompanied by a one-for-one increase in the inflation rate. In this case, the real rate is left unchanged at zero percent and the path of the nominal interest rate in Figure 1 is equivalent to a path of the inflation rate. While both assumptions are extreme, they demonstrate how the effects of the liftoff depend on the inflation rate.

In both figures, the DSC under the various liftoff scenarios are compared with a baseline case, in which both the central bank interest rate and the inflation rate stay unchanged at zero percent (blue dotted line), approximately the current situation. In this case, DSC are about 20 percent due to the assumed lenders’ markup of three percentage points.

A liftoff without inflation

When inflation stays at zero percent during the liftoff (Figure 2) the real mortgage payments of existing homeowners with FRM loans are unaffected. This is because the FRM interest rate has been fixed at origination before the liftoff and inflation stays at zero percent. However, new FRM loans will be priced according to the expected path of the central bank interest rate in Figure 1 and will therefore carry a higher interest rate. The new FRM interest rate is higher the faster is the liftoff. In the case of the fast liftoff, the higher interest rate implies DSC of almost 30 percent; under the slow liftoff, DSC will be 25 percent (the solid red lines in Figure 2).

When mortgages are ARM, the liftoff affects both, existing and new homeowners. The dashed green lines plot DSC for new ARM homeowners and essentially track the paths of the central bank interest rate—DSC gradually increase from 20 percent to 32 percent under the fast liftoff and to 27.5 percent under the slow liftoff. For existing homeowners with ARM the effects depend on when the loan was originated. The more recently originated was the loan the more will the path of DSC resemble that for new loans. DSC of loans that are almost repaid will be almost immune to the liftoff. This is not only because the debt outstanding gets smaller over the life of the loan, but also because mortgage payments in later periods of the life of the loan are mostly amortization payments, rather than interest payments.

A liftoff accompanied by inflation

When the liftoff is accompanied by equivalent increase in inflation, and no change in the real rate, the impact of the liftoff on DSC is greatly attenuated (Figure 3). First, existing FRM homeowners gain from the higher inflation and these gains grow over time as persistent inflation deflates the real value of the nominal payments, which under FRM are constant. Those with the more recently originated mortgages gain the most over their homeownership tenure (the dash-dotted red lines in the figure show the case of a mortgage with 119 quarters remaining; that is 29 years and 3 quarters). New FRM borrowers, however, will face a higher mortgage rate and, as a result, initial DSC of almost 30 percent in the fast liftoff case (solid red line). But the real value of those payments will also gradually decline over time.  

For ARM homeowners, both the existing and new homeowners, there are two opposing forces in place. On one hand, higher nominal interest rates increase nominal mortgage payments. On the other hand, higher inflation reduces their real value. The first effect is stronger initially but the second effect dominates over time. Furthermore, the point where the second effect starts to bite depends on the speed of the liftoff. While in the fast liftoff case the first effect dominates for the first eight years (32 quarters), in the slow liftoff case it hardly bites at all (dashed green lines).

Policy implications

To sum up, the effects of the liftoff on homeowners depend on three factors: (i) the prevalent mortgage type in an economy (FRM vs ARM), (ii) the speed of the liftoff, and (iii) what happens to inflation during the course of the liftoff.

If inflation stays constant at near zero then in the U.S., where FRM loans dominate, the liftoff will affect only new homeowners. In the U.K., where ARM loans dominate, the negative effects will in contrast be felt strongly by both new and existing homeowners.

However, if the liftoff is accompanied by sufficiently high inflation as in our examples, the negative effects will be much weaker in both countries. In the U.S., the initial negative effect on new homeowners will be compensated by positive effects on existing homeowners. And in the U.K., provided the liftoff is sufficiently gradual, neither existing nor new homeowners may face significantly higher real costs of servicing their mortgage debt.

Therefore, if the purpose of the liftoff is to “normalize” nominal interest rates without derailing the recovery, central bankers in both countries should wait until the economies convincingly show signs of inflation taking off. Furthermore, the liftoff should be gradual and in line with inflation.

Buzz words: “If the purpose of the liftoff is to “normalize” nominal interest rates without derailing the recovery, the Federal Reserve Bank and the Bank of England should wait until the economies show convincingly signs of inflation taking off.”

Carlos Garriga

Research Officer

Federal Reserve Bank of St. Louis

(314) 444-7412

carlos.garriga@stls.frb.org

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[2] In the U.K., the typical mortgage is the so-called standard-variable rate mortgage, which has an interest rate fixed for the first year or two. After this initial period, the interest rate can vary at the discretion of the lender, but usually the resets coincide with changes in the Bank Rate, the Bank of England policy interest rate. A “tracker” mortgage is explicitly linked to the Bank Rate. Here we abstract from these details.

[3] The examples assume that a homeowner’s real income does not change throughout the life of the loan, the loan at origination is four times the homeowner’s income, and mortgage lenders’ mark-up over market interest rates is three percentage points.r market interest rates is three percentage points.

On the Chinese fiscal stimulus memory hole

As evidence of China's growth slowdown mounts, Tyler Cowen asks why people no longer seem to be talking about that country's much-heralded fiscal stimulus of 2008-2009. I put the question to China expert Yi Wen, my colleague here in the research division of the St. Louis Fed. I thought it would be of some interest to share what he had to say. DA

There are several issues involved here regarding China’s economic performance and the effects of its stimulus packages.

1) As the following graph shows, 5 years after the financial crisis, U.S. industrial production remained 1.3 percent below its peak level; Industrial output in the EU remains at 12.2 percent below its level five years ago; Japan’s industrial production remains at 19.2 percent, below its level; China’s industrial output is 76.1 percent above the level five years previously. Recall that these regions were and are still china’s largest trading partners and China’s total exports have declined permanently by more than 40% since the crisis and still not recovered.

China’s industrial production therefore increased by over three quarters during a period when U.S. industrial production stagnated and EU and Japanese industrial production significantly declined. That is a conclusive success for China in this competitive struggle.

2) China’s stimulus package was designed to spend mainly on infrastructure buildup during a period when the costs of investment financing (borrowing) were the lowest. Since the operation of China’s first high-speed railroad merely six years ago, 28 Chinese provinces are now already covered by the world largest and longest high-speed rail network (more than ten thousand miles, greater than 50% of existing world capacity). If China had waited instead for 10 more years to do this, the costs would be many, many times higher.

3) Those being said, China today indeed faces the problem of excess industrial capacity, similar to US and European nations and Japan before WWI. China’s strategy to solve this excess capacity problem is to build a global infrastructure system (through so called “one belt, one road” program) that integrates the entire Eurasia continent and the Indian and Atlantic oceans transports, e.g., a full-fledged speed-train network stretching all the way south to Singapore and north to Russia and east to Europe is already under construction. This program is now backed by the newly established Asian Infrastructure Investment Bank (AIIB). This may look foolish to economists (remember China build the Great Wall for nothing J, not even shown up in GDP) but at least it will benefit global trade with significance no smaller than the Great Voyage. The age of maritime global trade (kick started by the Great Voyage) is perhaps going to be replaced or enhanced by cross continent land trade (a revision to the ancient Eurasian trade through the Silk Road).

To sum up, the Chinese appear to be more optimistic than the westerners, especially the well-trained economists, after 300 years of rejecting Capitalism (see my Working paper and forthcoming book: https://research.stlouisfed.org/wp/more/2015-006.  History will tell if they are right or not.

Arguments for and against lift off

Should the Fed raise its policy rate this September or not? Seems like a lot of people want to know. For those not following the discussion closely, let me try to summarize what I think are the main arguments for and against a September rate increase.

The main argument for postponing "lift off" goes as follows. The Fed has a mandate to stabilize inflation and unemployment around a set of targets: 2% for inflation and (say) 5% for unemployment. We are presently a bit below the inflation target and a bit above the unemployment rate target. IF one believes that raising the policy rate will move inflation downward and unemployment upward, why would one want to do so right now? How can it make sense to undertake an action that is likely to move both inflation and unemployment further away from their targets? Better hold off for now and await incoming data. There is absolutely no sign of inflation either right now or in the future. If anything, market-based measures of expected inflation are falling.

The main argument for lift off goes as follows. While inflation and unemployment are presently away from their targets (and not by much), this does not mean that ZIRP is consistent with keeping these variables near their targets in the near and medium term. ZIRP has been helpful in bringing unemployment down, but its trajectory is such that it may very well fall below its "natural" rate. IF one believes in the Phillips curve, then undershooting the unemployment rate target will manifest itself as inflationary pressure. And while inflation is presently low, there are reasons to believe this to be transitory. If it is, and if unemployment continues to fall, the Fed may find itself with inflation running above target. At that point the Fed would have to  raise its policy rate much more aggressively than it is contemplating now. Better to raise a modest 25 bp in September (at press conference) rather than wait for December or later (there is no press conference scheduled for the October FOMC meeting). The Fed can keep its policy rate low, or even reverse course as economic conditions dictate. This is still a very easy monetary policy. And it is not unreasonable for the Fed to act in a manner that prevents it from falling "behind the curve" (as it has arguably done in the past).

Of course, both of these views are predicated on essentially the same theoretical (essentially New Keynesian) framework. If you don't buy into this framework (for what it's worth, I do not), you're likely to have a different set of policy recommendations. Feel free to propose yours below!

Is Germany's Trade Surplus a Problem?

Ben Bernanke's recent post "Germany's Trade Surplus is a Problem" got me thinking about "global imbalances" again. I'm still not sure what to make of the issue. May as well think out loud.

The word "global imbalance" sounds ominous. What does it refer to? Let's start by thinking "locally," as in an economy consisting of you and me. Suppose we both work producing a good that each of us desire. From my perspective, any goods you ship to me are "imports." From your perspective, the goods shipped to me constitute "exports." If you export more than you import--so that your net exports are positive--you are running a trade surplus and I am running a corresponding trade deficit. This is the definition of "imbalanced" trade.

There is the question of how goods are paid for and how any imbalance is financed. Suppose we live in a common currency area. One possibility is that is that we pay for our shipments fully with money. At the end of the day, your trade surplus implies that you acquired more money from me than I acquired from you. Putting things this way leads us to question the notion of "imbalanced" trade. Sure, I acquired more goods from you--but you acquired more money from me in exchange. It all balances out, doesn't it?

Yes, it does. But it's still true that you exported more goods than you imported. And that extra money you acquired...what do you plan to do with it? Sit on it forever? (Actually, I explore this possibility here.) More likely than not, you are planning to spend it one day. When that day comes, I will be induced to sell you more goods than I buy from you. It will then be my turn to run a trade surplus--an act that renders trade "balanced" in the long-run.

Nothing fundamental changes in the story above if my trade deficit is instead financed by me paying you with a private or government debt instrument, or by me issuing you a personal IOU.

But what if the pattern of trade just described persists? What if you just keep sending me more goods than I send you? Then you are running a persistent trade surplus and I am running a persistent trade deficit. You are acquiring more money and securities, while I am depleting my money and possibly issuing debt.

Well, that's right...but so what? Maybe I am young and you are middle-aged: my growth prospects look great and yours appear diminished. I am a vibrant emerging economy and you are an advanced mature economy. Maybe it makes sense for the mature slow-growing economy to lend goods (especially capital goods) to the fast-growing economy. Indeed, Kollman et. al. (2015, pg. 53) estimate that strong growth from emerging economies contributed significantly to the German trade surplus, especially in the 2001-08 period. (Labor market reforms and an increased private saving rate are estimated to have had a larger impact since 2008.)

If we abstract from credit risk--the possibility that I or some other emerging economy may falter in some manner and fail to repay, then a persistent trade imbalance looks like an all-around good thing--something to be welcomed, not discouraged. And even if debtors do fail to repay, so what? Creditors presumably enter into lending arrangements knowing there is a risk of default. (Things become more complicated when we add elements like governments prone to bail out creditors, and creditors that become overzealous in their desire to make collections. But I'll leave this story for another day.)

So what is the problem with Germany's trade surplus? Let's say you're Germany and I'm a country in the periphery--e.g., one of the so-called PIGS. Both you and I are wobbled by the 2008 financial crisis, but me (a debtor) relatively more so than you (a creditor). Suppose, for example, my growth prospects are suddenly diminished--I'm looking more like the mature slower-growth you lately.

Since our growth prospects are now more aligned, there's not much of a rationale for you to run trade surpluses and for me to run trade deficits--at least, not with each other. What this means is that you should no longer work so hard to make goods for my market. And because I now borrow fewer goods from you, I'll have to work a little harder myself to make up the difference. Except that you go and spoil everything by wanting to remain super busy. So you continue to work hard to export goods to me. And because my market is flooded with your goods, there is no real opportunity (or maybe even desire) for me to work harder--it's tough to compete with you. Your trade surplus translates into a lack of demand in the periphery. Why don't you use your surplus to build yourself a bridge, or something? That'll be good for you and it'll be good for me.

That's the Bernanke point of view in a nutshell. I don't think it's entirely wrong, but I do have a problem with the story. Recall where I wrote "there's not much of a rationale for you to run trade surpluses and for me to run trade deficits, at least not with each other?" Well, that's pretty much what happened--with some delay and to an approximation--between  Germany and the rest of the EMU. That is, while Germany continued to run trade surpluses in the post 2008 period, these surpluses were not made at the "expense" of other EMU countries--see the following figure.

Germany's trade surplus is presently around 200B EUR. But its trade surplus with the rest of the EMU is only 30B EUR, which is only about 1% of German GDP. This is down from a peak of about 100B EUR in 2007. Here's another way of looking at it:

So given that Germany's trade surplus with the rest of the EMU is greatly diminished, maybe it's not the problem Bernanke thinks it is. (Whether the earlier surpluses are presently a problem is a different matter of course.)

I'm more inclined these days not to view trade imbalances as intrinsically desirable or undesirable in of themselves. If they are associated with a problem, I think they're more likely symptomatic than causal. To me, it makes sense that a mature economy like Germany should help finance growth in emerging economies. And should economic weakness in the periphery lead to trade becoming more balanced, this is no reason to cheer. After all, balanced trade is also an outcome associated with financial autarky.

Adopting this view does not preclude recommending some of the policies that Bernanke advocates. If the present low yields on safe assets like U.S. treasury debt and the German bund are the byproduct of malfunctioning financial markets leading to a "safe-asset shortage," then a wide class of theories suggest the potential benefits of a debt-financed expansionary fiscal policy (e.g., see here) and not necessarily because such policies stimulate "aggregate demand" (e.g., see here).

Whether additions to the public debt are used to finance public infrastructure spending, purchases of private securities, tax cuts, or something else, is something policymakers must weigh. But these decisions are likely not as important as just "getting the debt out there." The added supply is needed to prevent the seemingly insatiable private demand for the product from driving yields to zero (and lower). As the evidence suggests, in very low yield environments, excess demand for government debt is deflationary. And unexpectedly low inflation is not the tonic that economic theory prescribes for indebted countries struggling to recover from a severe recession.

***

PS. Bernanke also suggests Germany's trade surplus would have been lower if Germany had its own currency, which would presumably now be stronger than the euro against other currencies. But take a look at Switzerland, where the trade balance has grown in the face of a first stable, then strengthening, Swiss franc.

Competitive Innovation

In my previous post I took a crack at understanding Paul Romer's mathiness critique. As far as the post related to Romer (most of it was devoted to Brad DeLong's careless embellishment of the idea), my assessment was that Romer is basically just frustrated that his ideas have not swept away the competition in the field of growth theory. I do not believe that the academics Romer called out are defending indefensible positions for the sake of academic politics. To me, the present situation looks more like a healthy competition between theories of growth emphasizing different mechanisms. This is just what one would expect in a field where the forces at work are complicated and the answers to important questions are hard to come by.
 
Judging by his reply to my post here, it seems that Romer has a rather low opinion of me. Evidently, I am an "Euler-theorem denier." Admittedly, this is not the worst thing I've ever been called. But in addition to this, I am apparently motivated to deny the truth of this mathematical proposition because doing so signals my commitment to an academic club of serpents that includes the likes of Nobel prize-winning economists Bob Lucas and Ed Prescott. Paul, you flatter me.

I want to take some time here to address the specific charge leveled against me by Romer:

Andolfatto’s brazen mathiness involves a verbal statement about a mathematical model that flies in the face of an impossibility theorem. No model can do what he claims his does. No model can have a competitive equilibrium with price-taking behavior and partially excludable nonrival goods.

Romer's proposition is stated clearly enough. Now all we have to do is check whether it's valid or not. If I can produce a counterexample, then I will have shown Romer's proposition to be invalid. Let me now produce the counterexample.

Consider an economy where people combine raw labor (n) with skill (x) to produce labor services (e) according to the formula e = xn. Interpret n as hours worked over given period of time and assume, for simplicity, that everyone has the same n. On the other hand, people generally differ in their skill level, x. People with greater skills (or skill sets) are represented by larger values of x.

What makes people operating in the same environment more or less skilled than one other? Well, it could be several things. Consider two laborers, one of which is endowed with a physical tool that doubles labor productivity. Then we can write x = 1 for the one laborer and x = 2 for the other. Now consider two entrepreneurs, one of which is possessed with a "mental tool" (an idea, or some general know-how) that doubles labor productivity. Then we could similarly write x = 1 for the one entrepreneur and x = 2 for the other.

Physical and mental tools can differ along an important dimension called "rivalry." Economists call physical objects "rival"(or "subtractable") goods because a physical tool can be in the possession of only one laborer at any given time. The same need not be true for a mental good like an idea. Suppose that "knowing how to perform a task at level x" requires knowledge of a certain recipe. Unlike a physical good, an idea is not subtracted from your mind if you share it with someone else. If I teach you my calculus tool, this in no way diminishes my capacity to use the same calculus tool (or what amounts to the same thing, a perfect replica of my calculus tool). Economists call goods with this property "non-rival" or "non-subtractable" goods.

Alright then, let's proceed to the next step. Assume that the aggregate production function takes the form Y = aE, where a > 0 is a scalar and E represents the aggregate labor input measured in "efficiency units." That is, E equals the sum of e = xn over a population of size N. Let me normalize n = 1 and define X as the sum of x over population N. In this case, E = XN.

Notice that the aggregate production function exhibits constant returns to scale in E. The function is also linear in N. Of course, the function displays increasing returns in X and N together. That is, if we double both X and N, output Y is more than doubled.

The question Romer might ask at this point is "where are the books in this economy?" What he means by this is why can't the smartest person in this economy (the one with the largest x) not publish his knowledge in a recipe book and sell it to the others for a huge gain? This is an excellent question. The answer to it is that knowledge is not always very easily communicated and absorbed by all members of society in this manner. To the extent that knowledge transfer is difficult, the smartest guy in the room has a temporary monopoly over the idea that generates the highest x. Personally, I am surprised that Romer is so offended by this assumption of a missing market. Any university professor knows that distributing the course text book does not, by itself (re: Lucas quote 2009), lead to a growth of his/her students' knowledge base. Some types of knowledge can be sold, but other types of knowledge must be absorbed through effort, not through simple purchase. It is an empirical question as to which type of knowledge transfer mechanism is more or less important.

Next, I want to impose perfect competition. I do this not because I am wedded to the idea that this is how one must model the economy. I do it because Romer claims that it cannot be done.

But wait a minute...how can I assume perfect competition when the smartest person has a monopoly over his/her x? The answer is simple. The people in this economy are competing over the supply of efficiency units of labor e. There is no monopoly over the supply of labor services, e. Under perfect competition, the equilibrium price of an efficiency unit of labor is given by w* = a.  Of course, the measured wage per unit of raw labor (w*x) differs across people according to their skill x. The person with the highest x commands the highest price per unit of raw labor.

I should like Paul to note that Euler's theorem does indeed hold in my economy. The entire output is exhausted as payments for labor services (measured in efficiency units). Would people ever devote costly effort to learn something that would give them a higher x in this competitive economy? Sure, why not? Suppose that some raw labor time can be moved away from work and into a learning activity (l). The opportunity cost of this time is the person's foregone wage w*xl. The benefit is the expected value of learning something new (a higher x).

Anyone with an elementary training in economics can plainly see that the model described above has a competitive equilibrium with price-taking behavior and partially excludable non-rival goods. Ergo, Romer is wrong.

I am led to speculate how Romer might object to my counterexample. I suspect he might claim that the x in my model is not really a non-rival good. I get the feeling he might be defining a non-rival good as an idea that can be costlessly disseminated and instantaneously absorbed throughout the population (unless the use of the idea is protected by patent, etc.). If this is the case, then the argument would seem to be one of semantics.

In any case, I have made my point. Romer's proposition above is invalid. One can model a competitive equilibrium with price-taking and partially excludable non-rival goods. This should not be taken as a criticism against Romer's preferred modeling strategy. I'm actually a fan of his research program. My complaint with Romer's mathiness critique is that it ascribes unseen and unknown ulterior motives to a class of economists that find it fruitful to view growth through the lens of competitive equilibrium.

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PS. I see that Nick Rowe has offered a thoughtful response to Romer's "whack-a-mole" comment.

In the after-mathiness of discontent

If you're like me, you're probably still trying to wrap your mind around the debate on "mathiness" in the economics profession. I haven't put an inordinate amount of time into the project, but I have made an honest effort trying to understand the nature of Paul Romer's lamentations.

Just what is mathiness, anyway? I'm not sure that a precise and commonly-accepted definition exists. It's not surprising that such a catchy word was soon interpreted in myriad of conflicting ways. This is what happens with words.

To his credit, Romer soon recognized that the word he invented was being interpreted in ways he did not mean. He offers a sort of mea culpa here: Mathiness and Academic Identity. It is definitely a clarification (and I think, a softening) of his initial position. Here are what I take to be its two main points:

So my objection to mathiness is not a critique of the assumptions or structure of the models that others propose. It is a critique of a style that lets economists draw invalid inferences from the assumptions and structure of a model; a style that authors can use to persuade the reader (and themselves) to adopt conclusions that do not follow by the rules of logic; a style that tolerates wishful thinking instead of precise, clearly articulated reasoning. The mathiness that I point to in the Lucas (2009) paper...involves hand-waving and verbal evasion that is the exact opposite of the precision in reasoning and communication exemplified by Debreu/Bourbaki, and I’m for precision and clarity.

I wrote that the economists I criticize for using mathiness are engaged in a campaign of ACADEMIC politics, not one of national politics. Whatever was true in the past, the now fight is over ACADEMIC group identity. For example, one of the things that the people I criticize are campaigning for is a methodological restriction to models with price-taking. For them, price-taking is dogma. To make the case for this restriction, they are not presenting scientific arguments grounded in logic and evidence.

Hmm. He's critical of a style that lets economists draw incorrect inferences from the assumptions of a model. This is in contrast, I suppose, to all the other styles that permit people to draw incorrect inferences from the assumptions of their pet theories. He gives the example of Lucas (2009), to which I will return in a moment. The other charge is that some economists (them, not us of course) are "dogmatic." They campaign for and adopt methodological restrictions, like price-taking behavior, even when the logic and evidence does not permit it.

The two points above are linked to the same phenomenon: the apparent unwillingness of Romer's competitors in the field of growth theory to see the error of their ways and the superiority of his preferred approach. Mathiness is impeding scientific progress in the field of growth theory (and possibly throughout the economics profession as well).

What is the basis for these charges? As an outsider in the field of growth theory, it's hard for me to say (though I do have a paper in the area, which I'll talk about below). I think that Deitz Vollrath has a reasonable take on the issue here: More on Mathiness. Thankfully, we have Brad DeLong (Putting Economic Models in Their Place) doing his best to embellish the critique and apply it more broadly to macroeconomic theory--a subject more familiar to me.

Let's start with DeLong, who states:

He (Romer) seems, to me at least, to be very worried principally about two aspects of modern economic discourse. The first is to take what is true about one restricted class of theories and generalize it, claiming it is true of all theories and of the world as well.

Is there really any economist who behaves in this manner? Do we all not already know that our assumptions are provisional? That we may make one set of assumptions to address some questions and another set of assumptions to address other questions--that we have no grand unifying theory? So who, pray tell do these folks have in mind? Well, Paul Romer's thesis adviser, for one. Here, they quote Lucas (2009) who writes:

Some knowledge can be ‘embodied’ in books, blueprints, machines, and other kinds of physical capital, and we know how to introduce capital into a growth model, but we also know that doing so does not by itself [my italics] provide an engine of sustained growth. 

Now which parts of the quote above constitute a violation of scientific inquiry in your mind? Probably none. But I think it was the last part that got Romer's goat because he might have interpreted it to mean that "we know that Romer's models do not embody a mechanism that can provide an engine of sustained growth." I don't know--that's not the way I interpret the passage. Let's suppose Lucas had instead written "...but we also know that doing so does not necessarily provide an engine of sustained growth." Would that have been better? Can we all just be friends now?

I think it may be instructive to read the section from which the quote was lifted:

Is this really something to get so riled up over? Romer pg. 91 charges Lucas with making "untethered verbal claims"--an opinion he is of course free to hold. But I contend that it is just an opinion. Moreover, it's an opinion over the use of English, not math. It would have been far more useful and compelling, I think, if Romer had instead critiqued the model's internal logic and its ability to interpret the data. Isn't this the way science is supposed to progress? (Romer might reply that he's tried, but that his supervisor just won't listen because he's so dogmatic. I'll return to this possibility below.)

In any case, nowhere do I see evidence of DeLong's outlandish claim that Lucas is peddling an hypothesis he asserts to be true of all theories and of the world as well. But DeLong continues as follows:

Thus what Lucas claims must be true about the world as a matter of correct theory--that the big secret to successful economic growth cannot lie in creating and acquiring the kind of knowledge that gets "'embodied' in books, blueprints, machines..."--rests on the barely-examined decision to restrict attention to only a few kinds of models.

My goodness...this Lucas character...who does he think he is? You know, I have an idea. Why don't we actually go read the offending article and see what he's really up to? To whet your appetite, here's the introductory paragraph:

You know, call me crazy, but that opening passage does not sound like a call to arms to me. Lucas starts off with an interesting question. He bows respectfully to existing growth theory (including Romer's brand). He notes that they are based on important features of reality and that they are interesting theories. It's just that to him...[now, I want you to brace yourself and to please forgive the man...he is, after all, just an academic trying to explore alternative interpretations of the way the world works]...you see, to him, the existing theories of growth are not central (i.e., they are missing something that Lucas thinks is more important).

Lucas then proceeds in this highly provocative way: "In this paper I introduce and partially develop a new model of technical change..." From the way DeLong is writing, you'd think that Lucas had instead written "In this paper, I introduce and develop the grand unifying theory of economic growth and development. I await my second Nobel prize."

You can see how much fun I am having with this. Let me continue, along with DeLong, who writes:

The problem comes with the second principal aspect of "mathiness": to claim that one and only one mode of interaction and one and only one mode of individual decision-making is admissible at the foundation level of economic models. Here Romer attacks the assumption that the only allowable interaction is one of price-taking behavior: selling (or buying) as much as one wants at whatever the single fixed price currently offered by the market is. And here I would attack the assumption that individual decision-making is always characterized by rational expectations.

While there are certainly economists who make liberal use of the price-taking assumption in their research, there are equally many who do not. And I am not aware of any economist who would make the claim that the only allowable interaction is one of price-taking behavior. Many economists do feel more strongly about the desirability of imposing "rational expectations." But there is, of course, a vibrant community of those who feel otherwise. And it's not as if people who employ non-rational expectations models are ostracized from the community--unless you call being appointed a central bank president a form ostracism (see, for example, this piece by Jim Bullard).

Why do people have such a bee in their bonnet when it comes to the assumption of price-taking behavior? It's just a pricing protocol (a mechanism that determines prices). Many macro models, especially in the search and matching literature, use bilateral bargaining protocols to determine prices. Monopolistic competition is an assumed market structure together with an assumed pricing protocol. The pricing protocol there is usually quite restrictive: a monopolistic competitor is only permitted to charge a single price for his product. That is, nonlinear pricing schedules (which would increase both profit and social welfare) are assumed away--despite the overwhelming evidence of their use (e.g., retail and wholesale establishments often apply price discounts on large quantities purchased.)

[Aside: Many people are under the impression that monopoly is necessarily inefficient. This is not a valid conclusion. The conclusion follows from an auxiliary assumption that rules out an optimal nonlinear pricing protocol. Walter Oi makes this point in what is surely one of the best titles ever for an economics article: A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly.]

For Romer, the issue has to do with (I think) of how to reconcile the costly acquisition of nonrivalous (nonexcludable) ideas with perfect competition. DeLong hints at this when he writes:

Thus Paul Romer sees, in growth theory, the current generation of neoclassical economists grind out paper after paper imposing on the world "the restriction of 0 percent excludability of ideas required for [the] Marshallian external increasing returns" necessary for there to even be a price-taking equilibrium.

But DeLong (and Romer) are (I think) wrong on this dimension, at least, on a technical level. It is in fact possible to write down a growth a model where nonrivalous ideas are partially excludable (subject to costly acquisition) in a competitive equilibrium with price-taking behavior. My paper here (with Glenn MacDonald) constitutes one such example.

[Aside: In an extension of my model with Glenn, entrepreneurs are motivated to discover a technological advancement that, conditional on discovery, is assumed to diffuse rapidly among a small but measurable set of firms. This "small" group of firms on the technological frontier is "large" enough to assume price-taking behavior. The technology leaders earn profits (return on their knowledge capital) while laggards attempt to imitate the leaders--an effort that collectively generates the classic S-shaped diffusion dynamic--a phenomenon ignored by most growth models--including Romer's. An alternative and possibly more appealing set up would have been to permit one firm to have a short-lived monopoly right over a technological discovery. I think it's doubtful that any of our main results would have changed under this alternative specification. It's definitely an interesting question to explore and the alternative specification may have implications for questions that we were not interested in pursuing. The point I want to stress is that we did not assume price-taking behavior out of respect for a dogma. It just turned out to be a convenient way to approach things. And I think the approach is still fine, depending on the set of questions the researcher wants to focus on. Telling me that I must behave otherwise in the interest of science seems rather...what's the word I'm looking for here...I think it starts with a D...].

To many people, the assumption of price-taking behavior and rational expectations is thought to imply no useful role for government policy. In fact, nothing could be further from the truth. It is well-known that the equilibria of noncooperative games are generically suboptimal (so that well-designed interventions can be welfare-improving). For that matter, the equilibrium of a monopolistically competitive model can be efficient (and therefore warrant no government intervention). Adopting any one of these assumptions a priori is not, by itself, going to lead to a predetermined policy recommendation. And yet, DeLong seems to suggest that this is indeed the case when he writes:

And I see, in macroeconomics, paper after paper and banker after banker and industrialist after industrialist and technocrat after technocrat and politician after politician claiming that everything that governments might to to speed recovery must be counterproductive, or at least too risky--because that is what is in the case in a very restricted class of rational-expectations models.  

DeLong claims to see (without providing examples), in macroeconomics, "paper after paper" claiming that everything governments do is worse than useless. As evidence for this this, he cites two economists writing in the 1930s. Why not take a look at what people are publishing in high-level journals today? Here is just one example, drawn from the "freshwater" based Journal of Monetary Economics for March 2015. Among the papers published in this issue, I see:

1. Optimal Taxation with Home Production
2. Macroeconomic Regimes
3. Managing Markets with Toxic Assets
4. Financial Stress and Economic Dynamics: The Transmission of Crises
5. Liquidity, Assets and Business Cycles

I'll let this evidence speak for itself. What of his suggestion that the "austerity" forces are motivated by what is true in a restricted class of rational-expectations models? I'm afraid it's just another preposterous statement on his part. As he notes, recommendations of "austerity" were being made even in the 1930s. But that was well before rational-expectations models even existed. I might add that economists today frequently recommend government interventions that rely on rational expectations (e.g., Michael Woodford's "forward guidance" policy proposal).

Let me conclude now by returning to Romer. I'm still not absolutely sure what the mathiness critique is really all about. I think that Romer might just be frustrated (possibly with some justification) that his ideas haven't swept away his competition. Because his ideas are so firmly rooted in logic and evidence, the only thing that can evidently explain the continued resistance is academic politics shrouded in a cloak of mathiness.

Well, that's one interpretation and, who knows, maybe there's an element of truth to it. But my preferred interpretation is that what we seem to have here is simply a healthy clash of ideas competing in the marketplace for ideas. Let's not get too frustrated when our preferred (and obviously superior) theory does not sweep away the competition.

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Steve Williamson has his own interesting take on the issue here.