Portfolio podcast

I did a Rational Reminder podcast and video, focusing on portfolio theory, but also a tour through asset pricing. My hosts Benjamin Felix and Cameron Passmore were unusually well prepared and asked great questions! Video below, or go here for video, podcast, and transcript for people (like me) who read more than listen.

Weisbach advice

I got a chance to see the page proofs of Michael Weisbach's upcoming book, "The Economists' Craft."  This leapt out at me from the preface: 

A second observation I have made over the years is that, perhaps because of a lack of good advice, many scholars, both doctoral students and faculty members, constantly make the same mistakes. Far too many publicly circulated papers contain incredibly long, mind-numbingly dull literature surveys; introductions that go on and on before they tell the reader what the point of the paper is and why the reader should bother to waste her time on it; data descriptions containing insufficient detail for a third party to replicate the results; tables that are unnecessary, badly labeled, or hard to understand; or overly dry prose written in the passive voice and apparently designed to put the reader to sleep. In addition, many scholars manage their time so badly when giving presentations that they do not get to the main results of their paper until the last five minutes of the talk. Their presentations are often poorly designed, with slides that are incomprehensible or even unreadable owing to their use of fonts so small that participants sitting more than a few rows back cannot read them. Young faculty routinely mismanage their career by not having a coherent research agenda, not getting their papers to journals, or not making connections with people in their field who teach at other universities. Sometimes they do not even bother to show up for seminars in their field at their own university.

 So true. This book's contrary advice will be very useful. 

Virtual finance theory seminar

I'm giving "A fiscal theory of monetary policy with partially-repaid long-term debt" at the virtual finance theory seminar, Wed Oct 28 at 1 PM EDT. Brett Green leads off with "Due Diligence" at 12 PM EDT. If interested, come join. Warning: this is an academic theory paper whose whole point is to look at equations. 

The link has an email address which I don't want to post here, email for a zoom invitation. 

This is an excellent seminar series and one of the first of the new international zooms, which are an exciting development. Thanks to Linda Schilling for organizing.

More on debt

Following my last post on debt I've thought a bit more, and received some very useful emails from colleagues. 

A central clarifying thought emerges. 

The main worry I have about US debt is the possibility of a debt crisis. I outlined that in my last post, and (thanks again to correspondents) I'll try to draw out the scenario later. The event combines difficulty in rolling over debt, the lack of fiscal space to borrow massively in the next crisis. The bedrock and firehouse of the financial system evaporates when it's needed most. 

To the issue of a debt crisis, the whole debate about r<g, dynamic inefficiency, sustainability, transversality conditions and so forth is largely irrelevant. 

We agree that there is some upper limit on the debt to GDP ratio, and that a rollover crisis becomes more likely the larger the debt to GDP ratio.  Given that fact, over the next 20-30 years and more, the size of debt to GDP and the likelihood of a debt crisis is going to be far more influenced by fiscal policy than by r-g dynamics. 

In equations with D = debt, Y = GDP, r = rate of return on government debt, s = primary surplus, we have* \[\frac{d}{dt}\frac{D}{Y} = (r-g)\frac{D}{Y} - \frac{s}{Y}.\] In words, growth in the debt to GDP ratio equals the difference between rate of return and GDP growth rate, less the ratio of primary surplus (or deficit) to GDP. 

Now suppose, the standard number, r>g, say r-g = 1% or so. That means to keep long run average 100% debt/GDP ratio, the government must run a long run average primary surplus of 1% of GDP, or $200 billion dollars. The controversial promise r<g, say r-g = -1%, offers a delicious possibility: the government can keep the debt/GPD ratio at 100% forever, while still running a $200 billion a year primary deficit! 

But this is couch change! Here are current deficits from the CBO September 2 budget update

We were running $1 trillion deficits before the pandemic. Each crisis seems to bring greater stimulus.  

I especially like this view because it doesn't make sense that an interest rate 0.1% above the growth rate vs. an interest rate 0.1% below the growth rate should make a dramatic difference to the economy. Once you recognize some limit on the debt/GDP ratio, and desirability of some long-run stable debt/GDP, there is no big difference between these two values. The surplus required to stabilize debt to GDP smoothly runs from negative couch change to positive couch change. 

I find this a liberating proposition. I find the whole sustainability, long run limits, dynamic inefficiency, transversality condition and so forth a big headache. For the question at hand it doesn't matter! (There are other questions for which it does matter, of course.) 

As we look forward,  debt/GDP dynamics for the next 20 years are going to be dominated by the primary surplus/deficit, not plausible variation in r-g. The CBO's 10 years of 6-8% of GDP overwhelm 1-2% of r-g. If each crisis continues to ratchet up 10% of GDP deficits per year, more so. The Green New Deal, and large federal assumption of student debts, state and local debts, pension obligations, and so forth would add far more to debt/GDP than decades of r vs. g.  

**********

Now that this is clear, I realize I did not emphasize enough that Olivier Blanchard's AEA Presidential Address  acknowledges well the possibility of a debt crisis: 

Fourth, I discuss a number of arguments against high public debt, and in particular the existence of multiple equilibria where investors believe debt to be risky and, by requiring a risk premium, increase the fiscal burden and make debt effectively more risky. This is a very relevant argument, but it does not have straightforward implications for the appropriate level of debt.

See more on p. 1226. Blanchard's concise summary

there can be multiple equilibria: a good equilibrium where investors believe that debt is safe and the interest rate is low and a bad equilibrium where investors believe that debt is risky and the spread they require on debt increases interest payments to the point that debt becomes effectively risky, leading the worries of investors to become self-fulfilling.

Let me put this observation in simpler terms. Let's grow the debt / GDP ratio to 200%, $40 trillion relative to today's GDP. If interest rates are 1%, then debt service is $400 billion. But if investors get worried about the US commitment to repaying its debt without inflation, they might charge 5% interest as a risk premium. That's $2 trillion in debt service, 2/3 of all federal revenue. Borrowing even more to pay the interest on the outstanding debt may not work. So, 1% interest is sustainable, but fear of a crisis produces 5% interest that produces the crisis. 

Brian Riedi at the Manhattan Institute has an excellent exposition of debt fears. On this point, 

... there are reasons rates could rise. ...

market psychology is always a factor. A sudden, Greece-like debt spike—resulting from the normal budget baseline growth combined with a deep recession—could cause investors to see U.S. debt as a less stable asset, leading to a sell-off and an interest-rate spike. Additionally, rising interest rates would cause the national debt to further increase (due to higher interest costs), which could, in turn, push rates even higher.

***********

So how far can we go? When does the crisis come?  There is no firm debt/GDP limit. 

Countries can borrow a huge amount when they have a decent plan for paying it back. Countries have had debt crises at quite low debt/GDP ratios when they did not have a decent plan for paying it back. Debt crises come when bond holders want to get out before the other bond holders get out. If they see default, haircuts, default via taxation, or inflation on the horizon, they get out. r<g contributes a bit, but the size of perpetual surplus/deficit is, for the US, the larger issue. Again, r<g of 1% will not help if s/Y is 6%. Sound long-term financial strategy matters. 

From the CBO's 2019 long term budget outlook (latest available) the outlook is not good. And that's before we add the new habit of massive spending. 

Here though, I admit to a big hole in my understanding, echoed in Blanchard and other's writing on the issue. Just how does a crisis happen? "Multiple equilibria" is not very encouraging. Historical analysis suggests that debt crises are sparked by economic and political crises in the shadow of large debts, not just sunspots.  We all need to understand this better.  

******

Policy. 

As Blanchard points out, small changes do not make much of a difference.  

 a limited decrease in debt—say, from 100 to 90 percent of GDP, a decrease that requires a strong and sustained fiscal consolidation—does not eliminate the bad equilibrium. ...

Now I disagree a bit. Borrowing 10% of GDP wasn't that hard! And the key to this comment is that a temporary consolidation does not help much. Lowering the permanent structural deficit 2% of GDP would make a big difference! But the general point is right. The debt/GDP ratio is only a poor indicator of the fiscal danger. 5% interest rate times 90% debt/GDP ratio is not much less debt service than 5% interest rate times 100% debt/GDP ratio. Confidence in the country's fiscal institutions going forward much more important. 

At this point the discussion usually devolves to "Reform entitlements" "No, you heartless stooge, raise taxes on the rich." I emphasize tax reform, more revenue at lower marginal rates. But let's move on to unusual policy answers. 

Borrow long. Debt crises typically involve trouble rolling over short-term debt. When, in addition to crisis borrowing, the government has to find $10 trillion new dollars just to pay off $10 trillion of maturing debt, the crisis comes to its head faster. 

As blog readers know, I've been pushing the idea for a long time that especially at today's absurdly low rates, the US government should lock in long-term financing. Then if rates go up either for economic reasons or a "risk premium" in a crisis, government finances are much less affected. I'm delighted to see that Blanchard agrees: 

to the extent that the US government can finance itself through inflation-indexed bonds, it can actually lock in a real rate of 1.1 percent over the next 30 years, a rate below even pessimistic forecasts of growth over the same period

It's not a total guarantee. A debt crisis can break out when the country needs to borrow new money, even absent a roll over problem. But avoiding the roll-over aspect would help a lot! Greece got in trouble because it could not roll over debts, not because it could not borrow for one year's spending. 

Contingent plans? Blanchard's concise summary adds another interesting option 

 contingent increases in primary surpluses when interest rates increase. 

I'm not quite sure how that works. Interest rates would increase in a crisis precisely because the government is out of its ability or willingness to tax people to pay off bondholders. Does this mean an explicit contingent spending rule? Social security benefits are cut if interest rates exceed 5%? That's an interesting concept. 

Or it could mean interest rate derivatives. The government can say to Wall Street (and via Wall Street to wealthy investors) "if interest rates exceed 5%, you send us a trillion dollars." That's a whole lot more pleasant than an ex-post wealth tax or default, though it accomplishes the same thing. Alas, Wall Street and wealthy bondholders have lately been bailed out by the Fed at the slightest sign of trouble so it's hard to say if such options would be paid. 

Growth. Really, the best option in my view is to work on the g part of r-g. Policies that raise economic growth over the next decades raise the Y in D/Y, lowering the debt to GDP ratio; they raise tax revenue at the same tax rates; and they lower expenditures. It's a trifecta. In my view, long-term growth comes from the supply side, deregulation, tax reform, etc. Why don't we do it? Because it's painful and upsets entrenched interests. For today's tour of logical possibilities if you think demand side stimulus raises long term growth, or if you think that infrastructure can be constructed without wasting it all on boondoggles, logically, those help to raise g as well. 

********

*Start with \(\frac{dD}{dt} = rD - s.\) Then \( \frac{d}{dt}\frac{D}{Y} =  \frac{1}{Y}\frac{dD}{dt}-\frac{D}{Y^2}\frac{dY}{dt}.\)

*** 

Update: David Andolfatto writes, among other things, 

"Should we be worried about hyperinflation? Evidently not, as John does not mention it"

For these purposes, hyperinflation is equivalent to default. In fact, a large inflation is my main worry, as I think the US will likely choose default via inflation to explicit default. This series of posts is all about inflation. Sorry if that was not clear. 

also 

Is there a danger of "bond vigilantes" sending the yields on USTs skyward? Not if the Fed stands ready to keep yields low.

All the Fed can do is offer overnight interest-paying government debt in exchange for longer-term government debt. If treasury markets don't want to roll over 1 year bonds at less, than, say, 10%, why would they want to hold Fed reserves at less than 10%? If the Fed buys all the treasurys in exchange for reserves that do not pay interest, that is exactly how we get inflation. And mind the size. The US rolls over close to $10 trillion of debt a year. Is the Fed going to buy $10 trillion of debt? Who is going to hold $10 trillion of reserves, who did not want to hold $10 trillion of debt. 

In a crisis, even the Fed loses control of interest rates. 

 

Strategies for Monetary Policy

Strategies for Monetary Policy is a new book from the Hoover Press based on the conference by that name John Taylor and I ran last May. (John Taylor gets most of the credit.) This year's conference is sadly postponed due to Covid-19. We'll have lots to talk about May 2021.

At that link, you can see the table of contents and read Chapter pdfs for free. You can buy the book for $14.95 or get a free ebook.

The conference program and videos are still up.

Much of the conference was about the question, what will the Fed do during the next downturn? Here we are, and I think it is a valuable snapshot. Of course I have some self interest in that view.

As long as I'm shamelessly promoting, I'll put in another plug for my related Homer Jones Lecture at the St. Louis Fed, video here and the article Strategic Review and Beyond: Rethinking Monetary Policy and Independence here. That was written and delivered in early March, about 5 minutes before the lookouts said "Iceberg ahead." John and I don't put a lot of our own work into the conference books, but it sparked a lot of thoughts.  I am grateful to Jim Bullard and the St. Louis Fed for the chance to put those together.

Monetary policy is back to "forget about moral hazard, rules, strategies and the rest, the world is ending." This is a philosophy that happens quite regularly and now has become the rule and strategy. So strategic thinking about monetary policy is more important than ever.  This is a philosophy very much due to John Taylor.

The last part of my Homer Jones paper delves into just what risks the big thinkers of central banking were worried about on the eve of the pandemic. Pandemic was not in any stress test.  BIS, BoE, FSB and IMF  wanted everyone to start stress testing ... climate change and inequality. This is a story that needs more telling.    

Bailout redux

The greatest financial bailout of all time is underway. It’s 2008 on steroids. Yet where is the outrage? The silence is deafening. Remember the Tea Party and occupy Wall Street? “Never again” they said in 2008. Now everyone just wants the Fed to print more money, faster. (Well, there are some free market economists left. But we're a small voice!)

Maybe the Fed is right that if any bondholder loses money, if bond prices fall, if companies reorganize in bankruptcy, the financial system and the economy will implode. I am not here today to criticize that judgement. But if so, we must ask ourselves how we got to this situation, again, so soon. Once is an expedient. Twice is a habit.  It is clear that going forward any serious shock will be met by bailouts, and the Fed printing reserves to buy vast quantities of any fixed-income asset whose price starts to fall.

Why does the Fed feel the need to jump in? Because once again America is loaded up with debt, because bankruptcy is messy, and because the Fed fears that debt holders losing money will stop the financial system from providing, well, more debt.

This crisis is a huge wealth shock. The income lost during shutdown is simply gone. The question is, who is going to take that loss? Borrowing to keep paying bills, the current solution, posits  that future profits will soak up today's losses. We'll see about that. The CARES act puts future taxpayers squarely on the hook to pay today's bills. But where do those bills go? To creditors -- property owners, bond holders, and so forth. If we're looking around for pots of wealth to absorb today's losses, why are bondholders not chipping in? The biggest wealth transfer in history is underway, from tomorrow's taxpayers to today's bondholders, on the theory that if they lose money the economy falls apart?

OK, but why did America load up with debt again, apparently all "systemically important?" Could the expectation of a bailout any time there is an economy wide shock happens have had something to do with it? Will we do anything when this is over to stop companies from once again loading up with debt -- especially short term debt -- and forcing the Fed's hand again?

Meantime, anyone who hoarded some savings in the hope of profiting from fire sales, in the hope of providing liquidity to "distressed markets" has once again been revealed as a chump. Will we do anything to encourage them? Will lots of debt, private gain, taxpayers take the losses,  be the perpetual character of our financial system.

"You can't worry about moral hazard in a crisis," they said, and they didn't. At least last time there was some recognition of moral hazard, and a promise to clean up the moral hazard with reform. Will there be any such effort this time? Is anyone even thinking about the enormous moral hazard we are creating with these precedents? Will  the financial system perpetually a four-year-old on a bicycle, a parent running closely behind with one hand on the seat? Will the "Powell put" on fixed income grow ever larger? Or will we, this time, finally cure the financial system so it can survive the next shock?

A bailout 

Small but symbolic: The federal government just bailed out the airlines -- or more precisely airline stockholders, bondholders, unions, airplane leaseholders and other creditors who would lose in bankruptcy.

 "big airlines will receive 70% of the money as grants—which won’t be paid back—and 30% as loans. The cash comes with strings attached: Airlines must give the government warrants amounting to 10% of a given loan’s value that can be swapped for stocks; they cannot lay off staff until September; and they face restrictions on dividends, buybacks and executive compensation."

Oh, and as the article makes clear, this only gets us maybe through the summer. Anyone want to take a bet that planes are full again by September?

The big banks got bailed out in 2008 — or more precisely, the stockholders, bondholders and creditors of the big banks got bailed out.  Never again, they said. Again.

Now, one can make a case that big banks are “systemic,” that if their bondholders lose money the financial system collapses. Just how are airline bondholders “systemic?” What calamity falls if airline bondholders don’t get paid in full?  Just why is a swift pre-packaged bankruptcy not the right answer for airlines? This seems like a great time to renegotiate airplane and gate leases, union contracts (some require the airlines to keep flying empty planes!) fixed-price fuel contracts and more.

If taxpayers have to give airlines cash grants don't we get some reassurance this doesn't have to happen again? Even I would say, no more debt financing. You can see the instinct in "restrictions on dividends, buybacks and executive compensation." Democrats in Congress wanted "stakeholder" board seats, carbon reporting, and more. Why not go full Dodd-Frank on them? Detailed regulation of their financial affairs, stress tests to make sure they can survive the next time? Like banks, the existing airlines might not end up minding so much a return to the 1970s status as regulated utilities. Or, more likely, like GM, we just forget about it, let them load up on debt again, and pretend there won't be a 2030 bailout?

The Fed's big artillery

The real action is at the Fed. The Fed is buying commercial paper, corporate bonds, municipal bonds. The Fed is explicitly propping up asset prices. The Fed is also lending directly to companies. The current guesstimate is $4 trillion, with $2 trillion already accomplished. More is coming.

It started "small" On March 17, the Fed bailed out money market fund investors, buying the “illiquid” assets of those funds so that the funds could continue to pay out dollar for dollar.  Recall that in 2008, the Fed and Treasury bailed out money market fund investors, buying assets to stop a run on money-market funds' promise that you can always cash out at $1. Never again, they said. Fixed dollar promises must be backed by Treasuries, other funds must let asset values float. Again.

On March 17 the Fed also announced it will buy commercial paper.  “Directly from eligible companies.” Yes, the Fed prints reserves to lend directly to companies that can issue A1/P1 commercial paper.

"By eliminating much of the risk that eligible issuers will not be able to repay investors by rolling over their maturing commercial paper obligations, this facility should encourage investors to once again engage in term lending in the commercial paper market. " 

Why are companies borrowing long term by rolling over commercial paper? Didn't we learn anything about rolling over short term debt in 2008? Are we going to follow up by putting a stop to that? Why don't companies have more equity financing, on which they can just stop paying dividends?

"Investors" you say, it's not all the Fed. Read carefully. "By eliminating much of the risk..." The Fed props up prices, and removes risk. Then private investors will come in. The markets won't ride that bike without the Fed's hand on the saddle, apparently. Why do we bother to have private markets?

On March 17 the Fed started to lend again to primary dealers. These are the traders, much maligned by the Volcker rule.

The PDCF will offer overnight and term funding with maturities up to 90 days...Credit extended to primary dealers under this facility may be collateralized by a broad range of investment grade debt securities, including commercial paper and municipal bonds, and a broad range of equity securities. 

Let's translate. You're the trading desk at, say Goldman Sachs. You want to buy stocks, as you think people are dumping in a hurry. Great, that's what traders are supposed to do: "provide liquidity." But, sadly, you're in the habit of of funding trading activity by borrowing money, short term. And you can't do that right now. So the Fed will now lend you the money to buy stocks, and will take the stocks as collateral! It's almost as if the Fed is buying stocks -- except you get the gains, and if you go under, the Fed gets the stocks! (A friend in the securities industry say nobody is bothering to investigate and price high grade corporates. The Fed is setting the prices.)

Again, the Fed is between a rock and hard place. Yes "balance sheets are constrained." Trading firms don't have enough equity to take on additional risk. The natural buyers at asset fire sales are constrained out of the market. Bail the Fed feels it must. But this is exactly what happened when the Fed first lent to broker/dealers in 2008! Why in the world are we in this position, 12 years after that crisis?

On March 20, the Fed expanded into state and municipal markets. The mechanism is the same: Fed lends to a financial institution, which buys the assets, and then gives the Fed the assets as collateral for the loan. Once again the point is  "enhance the liquidity and functioning of crucial state and municipal money markets."

On March 23, the Fed rolled out real artillery. Ominously, Treasury markets appeared "illiquid," so the Fed has stepped in buying $1.3 trillion in the first month -- more than the Treasury issued.  The Fed is funding Treasury borrowing with newly printed reserves.  The Fed now buys mortgage backed securities.

And now.. corporate bonds. This is well past 2008.

the Primary Market Corporate Credit Facility (PMCCF) for new bond and loan issuance and the Secondary Market Corporate Credit Facility (SMCCF) to provide liquidity for outstanding corporate bonds.

Translation: The Fed will buy new corporate bonds, thus directly lending to corporations. And it will buy  outstanding bonds.

Why would it do that? Well, to "provide liquidity." This is a word that ought to set off BS detectors. Yes, there is such a thing as an "illiquid" market. There is also such a thing as a market whose prices are dropping like a stone. Sell all you want but at 50 cents on the dollar. "I wish I had sold at yesterday's prices" is not illiquidity. You have to pay people a lot to take risk right now. Which is it? Hard to tell. There are ways to tell, of course. For example, illiquid markets have negative price autocorrelation -- a low price today bounces back. I am not aware of the Fed having applied this or any other test. (Research topic suggestion.)

Again, I don't want to criticize, but there sure is a danger of propping up prices under the guise of "illiquidity." The Fed's view that if the Fed takes all risk off the table "liquidity" will reappear is also pretty close to taking risk off the table so prices will rise.

The Fed is already buying new bonds from companies to finance their new expenditures. Propping up prices of existing bonds is a way to let old bondholders cash out at high prices, now before the deluge. Just why can't old bondholders even take mark-to-market losses?

And, if corporate bondholders need to be bailed out in this way, are we going to do anything about it going forward? Do you get to buy junk bonds, high interest municipal debt, and the Fed will let you out if anything bad happens?

Wrap up

OK, I haven't even gotten through March and the Fed is just getting going. Let's wrap up.

The Fed has felt the need to take over essentially all new lending in the economy. The Fed is also propping up most fixed-income prices. The Fed is deliberately removing risk from holding these assets.

Once again, I will be told, "this isn't the time to think about moral hazard." But having done this twice, the first time with huge protest, the second time as if it is perfectly normal, this is the pattern, and the moral hazard is there. The economy will load up on debt, especially short term debt. People will not keep stashes of savings around to provide liquidity or jump on buying opportunities. And the need for bailouts will be larger in the next crisis.

"But the Fed made money in 2008" you may retort. And it has a half chance of making money again. If the recession wraps up in September and these "loans" get paid back, it will do nicely. If the recession goes on a year and all these "loans" go sour, it will not look so pretty.

Yes, in 2008 the Fed and treasury successfully operated the world's largest hedge fund, printing money to buy low-price assets. But is this really the function of the Federal Reserve? Do we want it driving private hedge funds out of the liquidity provision business, by its ability to print rather than borrow money, and by the off-balance-sheet put that the US taxpayer will in the end take losses if this massively leveraged portfolio doesn't work out?

Where is the outrage? Where are the financial economists? Where is the reform plan so we don't do this again? At a minimum, can we say tha  the government could stop subsidizing debt, via tax deduction and regulatory preference for "safe" (ha!) debt as an asset?

Hello out there? In 2008, everyone was writing financial crisis papers. Now everyone is playing amateur epidemiologist.

Finance colleagues, you have a bigger crisis and intervention to study, and a deeper set of regulatory conundrums. Is everyone just too scared of sounding critical of the Fed? Get to work!

The Fed and Treasury's actions are telling us we are on the verge of financial apocalypse. Let's wake up and look at what's coming, especially if it doesn't all get better by September.

Some links 

This post continues from Financial Pandemic.

I had planned a longer post on the details of many of these programs, but this is long enough.


A great explanation by Robert McCauley in FT. Section heads include  1) Acting as a lender of last resort to securities firms, 2) acting as a lender of last resort to investment funds, 3) acting as a securities dealer of last resort, 4) acting as a securities underwriter of last resort and finally 5) acting as a securities buyer of last resort.

A simple tweet storm by Victoria Guida

Via the indefatigable Torsten Slok,

Financial Policy During the COVID-19 Crisis MIT opeds on financial affairs

A great list of policy trackers.

Financing Firms in Hibernation During the COVID-19 Pandemic

The Yale Financial Stability Tracker and especially the Finance Response Tracker are very useful list of what's going on.

Fed Intervention in the To-Be-Announced Market for Mortgage-Backed Securities
by Bruce Mizrach and Christopher J. Neely is a very nice description of what's going on there

The United States as a Global Financial Intermediary and Insurer by Alexander Monge-Naranjo. More contingent liabilities waiting for Uncle Sam bailouts.

A data set of international fiscal responses

New paper: fiscal theory of monetary policy

A second new paper: "A fiscal theory of monetary policy with partially repaid long-term debt."

By "fiscal theory of monetary policy" I mean a model with standard DSGE ingredients, including inertemporal optimization and market clearing, monetary policy described by interest rate targets, price or other frictions, but closed by fiscal theory, "active" fiscal policy rather than "active" monetary policy.

I aim to build a standard simple but somewhat realistic model of this sort, a parallel to the three equation textbook model that has been part of the new-Keynesian tool kit since the 1990s. I keep the model as simple and standard as possible, so the effect of the innovations one the fiscal side are clearer.

Two parts of the specification are central. First, long-term debt allows the model to produce a negative response of inflation to interest rates. Long-term debt also allows a fiscal shock to result in a protracted inflation, which slowly devalues long term bonds, rather than a price level jump.

Second, and most important, the paper writes down a process for fiscal surpluses in which today's deficits are partially repaid by tomorrow's surpluses. Look quickly at the surplus response functions in my last post. When the government runs a deficit, it reliably runs subsequent surpluses that partially repay some of the accumulated debt. The surplus is not an AR(1)! It has an s-shaped response function.

So if you want a realistic fiscal theory model, you need a surplus with an s-shaped response function, but you need to keep "active" fiscal policy. This combination is the central innovation of the paper.

New Paper -- the fiscal roots of inflation

I recently finished drafts of a few academic papers that blog readers might find interesting. Today, "The Fiscal Roots of Inflation."

The government debt valuation equation says that the real value of nominal debt equals the present value of surpluses. So, when there is inflation, the real value of nominal debt declines. Does that decline come about by lower future surpluses, or by a higher discount rate? You can guess the answer -- a higher discount rate.

Though to me this is interesting for how to construct fiscal theory models in which changes in the present value of government debt cause inflation, the valuation equation is every bit as much a part of  standard new-Keynesian models. So the paper does not take a stand on causality.

Here is an example of the sort of puzzle the paper addresses. Think about 2008. There was a big recession. Deficits zoomed, through bailout, stabilizers, and deliberate stimulus. Yet inflation.. declined. So how does the government debt valuation equation work? Well, maybe today's deficits are bad, but they came with news of better future surpluses. That's hard to stomach. And it isn't true in the data. Well, real interest rates declined and sharply. The discount rate for government debt declined, which raises the value of government debt, even if expected future surpluses are unchanged or declined. With a lower discount rate, government debt is more valuable. If the price level does not change, people want to buy less stuff and more government debt. That's lower aggregate demand, which pushes the price level down. Does this story bear out, quantitatively, in the data? Yes.

If you don't like discount rates and forward looking behavior, you can put the same observation in ex-post terms. When there is a big deficit, the value of debt rises. How, on average, does the debt-GDP ratio come back down on average? Well, the government could run big surpluses -- raise taxes, cut spending to pay off the debt. That turns out not to be the case. There could be a surge of economic growth. Maybe the stimuluses and infrastructure spending all pay off. That turns out not to be the case. Or, the real rate of return on government bonds could go down, so that debt grows at a lower rate. That turns out to be, on average and therefore predictably, the answer.

Identities

OK, to work. The paper starts by developing a Cambpell-Shiller type identity for government debt. This works also for arbitrary maturity structures of the debt. Corresponding to the Campbell-Shiller return linearization, $$ \rho v_{t+1}=v_{t}+r_{t+1}^{n}-\pi_{t+1}-g_{t+1}-s_{t+1}. $$ The log debt to GDP ratio at the end of period \(t+1\), \(v_{t+1}\), is equal to its value at the end of period \(t\), \(v_{t}\), increased by the log nominal return on the portfolio of government bonds \(r_{t+1}^{n}\) less inflation \(\pi_{t+1}\), less log GDP growth \(g_{t+1}\), and less the real primary surplus to GDP ratio \(s_{t+1}\). Surpluses, unlike dividends, can be negative, so I don't take the log here. This surplus is scaled to have units of surplus to value, so a 1% change in "surplus" changes the log value of debt by 1%. I use this equation to measure the surplus.

Iterating forward, and imposing the transversality condition, we have a Campbell-Shiller style present value identity, $$ v_{t}=\sum_{j=1}^{\infty}\rho^{j-1}s_{t+j}+\sum_{j=1}^{\infty}\rho^{j-1}g_{t+j} -\sum_{j=1}^{\infty}\rho^{j-1}\left( r_{t+j}^{n}-\pi _{t+j}\right). $$ Take innovations \( \Delta E_{t+1} \equiv E_{t+1}-E_t \) and we have $$ \Delta E_{t+1}\pi_{t+1}-\Delta E_{t+1} r_{t+1}^{n}= -\sum_{j=0}^{\infty} \rho^{j} \Delta E_{t+1}s_{t+1+j} -\sum_{j=0}^{\infty} \rho^{j} \Delta E_{t+1} g_{t+1+j}+\sum_{j=1}^{\infty} \rho^{j} \Delta E_{t+1}\left( r_{t+1+j}^{n}-\pi_{t+1+j}\right) $$ Unexpected inflation devalues bonds. So it must come with a decline in surpluses, a rise in the discount rate, or a decline in bond prices. Notice the value of debt disappeared, which is handy.

The bond return comes from future expected returns or inflation, so it's nice to get rid of that too. With a geometric maturity structure in which the face value of bonds of \(j\) maturity is \(\omega^j\), a high bond return today must come from lower bond returns in the future. $$ \Delta E_{t+1}r_{t+1}^{n} = -\sum_{j=1}^{\infty}\omega^{j}\Delta E_{t+1} r_{t+1+j}^{n} =-\sum_{j=1}^{\infty}\omega^{j}\Delta E_{t+1}\left[ (r_{t+1+j}^{n}-\pi_{t+1+j})+\pi_{t+1+j}\right] $$ Substitute and we have the last and best identity $$ \sum_{j=0}^{\infty}\omega^{j} \Delta E_{t+1}\pi_{t+1+j} = -\sum_{j=0}^{\infty} \rho^{j} \Delta E_{t+1}s_{t+1+j} -\sum_{j=0}^{\infty} \rho^{j} \Delta E_{t+1}g_{t+1+j} +\sum_{j=1}^{\infty} (\rho^{j} -\omega^{j})\Delta E_{t+1}\left( r_{t+1+j}^{n}-\pi_{t+1+j}\right) . $$ With long-term debt a weighted sum of current and future inflation corresponds to changes in expected surpluses and discount rates. A fiscal shock can result in future inflation, thereby falling on today's long term bonds. Equivalently, a surprise deficit today \(s_{t+1}\) must be met by future surpluses, by lower returns, or by devaluing outstanding bonds, so that the debt/GDP ratio is reestablished.

Results

I ran a VAR and computed the responses to various shocks.

Here is the response to an inflation shock - -an unexpected movement \(\Delta E_1 \pi_1\). All other variables may move at the same time as the inflation shock.

Inflation is persistent, so a 1% inflation shock is about a 1.5% cumulative inflation shock, weighted
by the maturity of outstanding debt.

So, where is the 1.5% decline in present value of surpluses? Which terms of the identity matter?
Inflation does come with persistent deficits here. The sample is 1947-2018, so a lot of the inflation shocks come in the 1970s. You might raise three cheers for the fiscal theory, but not so fast. The deficits turn around and become surpluses. The sum of all surpluses term in the identity is a trivial -0.06, effectively zero. These deficits are essentially all paid back by subsequent surpluses.

Growth declines by half a percentage point cumulatively, accounting for 2/3 of the inflation. And the discount rate rises persistently. Two thirds of the devaluation of debt that inflation represents comes from higher real expected returns on government bonds, which in turn means higher interest rates that don't match inflation. (More graphs in the paper.)

Growth here is negatively correlated with inflation, which is true of the overall sample, but not of the story I started out with. What happens in a normal recession, that features lower inflation and lower output? Let's call it an aggregate demand shock. To measure such an event, I simply defined a shock that moves both output and inflation down by 1%. Here are the responses to this "recession shock."

 Inflation and output go down now, by 1%, and by construction. That's how I defined the shock. This is a recession with low growth, low inflation, and deficits. Not shown, interest rates all decline too.

So where does the low inflation come from in the above decomposition. Do today's deficits signal future surpluses? Yes, a bit. But not enough -- the cumulative sum of surpluses is -1.15% On its own, deficits should cause 1% inflation, the fiscal theory puzzle that started me out in this whole business. Growth quickly recovers, but is not positive for a sustained period. Like 2008, we see a basically downward shift in the level of GDP. That contributes another 1% inflationary force. The discount rate falls however,  so strongly as to raise the real value debt by almost 5 percentage points! That overcomes the inflationary forces and accounts for the deflation.

Here is a plot of the interest rates in response to the same shock. i is the three month rate, y is the 10 year rate, and rn is the return on the government bond portfolio. Yes, interest rates at all maturities jump down in this recession. Sharply lower rates mean a one-period windfall for the owners of long term bonds, then expected bond returns fall too.

The point 

Discount rates matter. If you want to understand the fiscal foundations of inflation, you have to understand the government debt valuation equation. Inflation and deflation over the cycle is not driven by changing expected surpluses. If you want to view it "passively," inflation and deflation over the cycle does not result in passive policy accommodation through taxes, as most footnotes presume. The fiscal roots (or consequences) of inflation over the cycle are the strong variation in discount rates -- expected returns.

The fiscal process

Notice that the response of primary surpluses in all these graphs is s-shaped. Primary surpluses do not follow an AR(1) type process. In response to today's deficits, there is eventually a shift to a long string of surpluses that partially repay much though not all of that debt. This seems completely normal, except that so many models specify AR(1) style processes for fiscal surpluses. Surely that is a huge mistake. Stay tuned. The next paper shows how to put an s-shaped surplus process in a model and why it is so important to do so.

Comments on the paper are most welcome.

Online Asset Pricing back again!

My online Asset Pricing course is back again, after one more software/administrative change once again threatened its demise.  It's still on Canvas, but you have to ask to sign on.

The course is here, University of Chicago Canvas course 23303. To log in and use it, you need to email  instructional.design@chicagobooth.edu.  The course is open to anyone, not just University of Chicago students. If that doesn't work, email me john dot cochrane at stanford dot edu, and I'll see what's wrong.

The videos, notes, and other materials are still available ungated on my website, here, under the "Asset Pricing" tab.

If all goes well you see this:

Economic note: It's interesting how software depreciates so rapidly, though its physical being depreciates not at all. Perfectly good software stops working as operating systems and machines get "upgraded," as IT departments seem to latch on to new "solutions" every three years, and so forth. Most of my email from before the mid 2000s is gone due to an "upgrade." My website is in the midst of an "upgrade" crisis, and I can't seem to keep the online class going for more than two or three years. There is an interesting economics paper in this. As son of a historian, I feel for the historians of a few hundred years from now who, looking back on our interesting era, will find a blank void, as all of our records are unreadable.

Everything is f***d

The most hilarious course syllabus I've seen in a while, from Professor Sanjay Srivastava at the University of Oregon.

...

....

The point is serious,  going well beyond the replication problem. Meta-analyses just repeat the same mistakes a hundred times.

"Office hours: Held on Twitter at your convenience." I love it.

Financing innovation

I went to the Financing of Innovation summit at Stanford GSB last Thursday. (Sorry, I can't seem to find a full program online.) Here is a sample of two interesting papers, presented by Amit Seru and Steve Kaplan:

Nobel Symposium on Money and Banking Day 2

Day 2 of the Nobel Symposium on Money and Banking focused on monetary policy. (My last post covered Day 1 on banking.)

Bernanke

Sadly Ben Bernanke's video and slides are not up on the website. Ben showed some very interesting evidence that the crisis was an unpredictable run, rather than the usual story about predictable defaults resulting from too much credit. Things really did get suddenly a lot worse in September and October 2008. Yes, it's easy to say this is defense against the charge that he should have done more ahead of time. But evidence is evidence, and I find it quite plausible that the relatively small losses in subprime need not have caused such a massive crisis and recession absent a run. Ben says the material is part of a paper he will release soon, so look for it. One can understand that Bernanke is careful about releasing less than perfect drafts of papers and videos.

History

Barry Eichengreen gave a scholarly account of why history matters, especially the great depression, and we should pay more attention to it. (Paper, video.) He aimed squarely at typical economists whose knowledge stopped at Friedman and Schwartz, or perhaps Ben Bernanke's famous non-monetary channels paper, in which bank failures propagated the depression. He emphasized the role of the gold standard and international cooperation or non-cooperation, and warned against facile comparisons of the gold standard experience to today's events and the euro in particular.

Randy Kroszner has a great set of slides and an engaging presentation. He also started on parallels with the great depression, and told well the story of the US default on gold clauses. He closed with a warning about fighting the last war -- particularly apt given the exclusive focus of most of this conference on the events of 2008 -- and on how to start a crisis. In his view when Bank of England Gov Mervyn King said: “We will support Northern Rock." People hear "Northern Rock's in trouble? Run!" Likewise, in my view, speeches by President Bush and Treasury Secretary Paulson did a lot to spark the run in the US.

DSGE

A highlight for me, was the session on DSGE models.

Marty Eichenbaum (video, slides, subsequent paper) gave a nice review of the current status of new Keynesian DSGE models, and how they are developing in reaction to the financial crisis and recession, and the zero bound episode.

Harald Uhlig

Critiques, or more precisely lists of outstanding puzzles and challenges, are often more memorable and novel than positive summaries, and Harald Uhlig delivered a clear and memorable one. (Video, Slides)

Asset prices are a longstanding problem in DSGE models. In typical linearized form, the quantity dynamics are governed by intertemporal substitution, and the asset prices by risk aversion, and neither has much influence on the other. (I learned this from Tom Tallarini.) Rather obviously, our recent recession was all about risk aversion -- people stopped consuming and investing, and tried to move from private to government bonds because they were scared to death, not a sudden attack of thriftiness. There is a lot of current work going on to try to repair this deficiency, but it still lives in the land of extensions of the model rather than the mainstream. Harald also points out a frequently ignored implication of Epstein-Zin utility, the utility index reflects all consumption and anything that enters utility

Financial frictions are blossoming in DSGE models, in two forms: First, HANK or "heterogenous agent" models, which add things like borrowing constraints and uninsurable risks so that the distribution of income matters, and in an eternal quest to make the models work more like static ISLM. Second, in response to the financial crisis (see first day!) stylized models of banking and intermediary finance are showing up. I'm still a little puzzled that the more standard time-varying risk aversion part of macro-finance got ignored, (a plea here) but that is indeed what's going on.

The conundrum, here as elsewhere in DSGE, is that the more people play with the models, the further they get from their founding philosophy: macro models that do talk about monetary policy, (now) financial crises, but that obey the Lucas rules: Optimization, budget constraints, markets, or, more deeply, structures that have some hope of being policy invariant and therefore predictions that will survive the Lucas critique. Already, many ingredients such as Calvo pricing are convenient parables, but questionably realistic as policy-invariant.

Harald points out that since most of the frictions are imposed in a rather ad-hoc manner, neither will they be policy-invariant. This is a deeper and more realistic point than commonly realized. Every time market participants hit a "friction," they tend to innovate a way around that friction so it doesn't hurt them next time. Regulation Q on interest rates was once a "friction," and then the money market fund was invented. The result is too often "chicken papers:"

The understandable trouble is, if you try to microfound every single friction from Deep Theory -- just why it is that credit card companies put a limit on how much you can borrow, in terms of asymmetric information, moral hazard, and so forth -- the audience will be asleep long before you get to the data. Also, as we saw in day 1, there is (to put it charitably) a lot of uncertainty in just how contract or banking theory maps to actual frictions. I think we're stuck with ad-hoc frictions, if you want to go that route.

Harald's next point is, I think, his most devastating, as it describes a huge hole in current models that is not (unlike the last two) a point of immense current research effort. The Phillips curve and inflation are the central point of the New Keynesian DSGE model -- and a disaster. 

The Phillips curve is central. The point of the model is for monetary policy to have output effects. Money itself has (rightly) disappeared in the model, so the only channel for monetary policy to work is via the Phillips curve. Interest rates change inflation, and inflation causes output changes. No surprise, it is very hard for that model to produce anything like the last recession out of small changes in inflation. (I have to agree here with the premise of the financial frictions view -- if you want your model to produce the last recession, other than by one huge shock, the model needs something like a financial crisis.)

The Phillips curve in the data is well known

Less well known, but worth lots of attention, is how the now standard DSGE models completely fail to capture inflation. Harald's slide:

The point of the slide, in simpler form: The standard Phillips curve is

inflation today = beta x expected inflation next year + kappa x output gap  + shock

Essentially all inflation is accounted for by the shock. The model is basically silent about the source of inflation. Looking at the model as a whole, not just one equation, Neither monetary policy shocks nor changes in rules accounts for any significant amount of inflation. 

I made a similar graph recently. Use the standard three equation model

Now, use actual data on output y, inflation pi, and interest rate i, to back out the shocks v. Turn off the monetary policy shock vi = 0. Solve the model and plot the data -- what would have happened if the Fed had exactly followed the Taylor rule? 

Answer: Inflation and output would have been virtually the same. The inflation of the 1970s and its conquest in the 1980s had nothing to do with monetary policy mistakes. It is entirely the fault, and then fortunate consequence, of "marginal cost" shocks that come from out of the model. This is a pretty uncomfortable prediction of a model designed to be about monetary policy! Or, as Harald put it

• Data: no Phillips-Curve tradeoff.
• QDSGE: don’t account for inflation with monetary policy shocks.
• The NK / Phillips-Curve-based NK QDSGE models may thus provide a poor guide for monetary policy.

Wait, you ask, what about Marty Eichenbaum's pretty graphs, such as this one, showing the effects of a monetary policy shock?

The answer: After a lot of work, the effects of a monetary policy shock look (at last) about like what Milton Friedman said they should look like in 1968. But monetary policy shocks don't account for any but a tiny part of output and inflation variation, quite contra Friedman (and Taylor, and many others') view.

Last, standard new Keyensian DSGE models have strong "Fisherian" properties. In response to long lasting or expected interest rate rises, inflation goes up. More on this later.

Ellen McGrattan

Ellen stole the show. (Slides.) Take a break, and watch the video. She manages to be hilarious and incisive. And unlike the rest of us, she didn't try to sheohorn a two hour lecture into her 15 minutes.

Her central points. First, like Harald, she points out that the models are driven by large shocks with less and less plausible structural interpretation, and thus further from the Lucas critique solution than once appeared to be the case. The shocks are really "wedges," deviations from equilibrium conditions of the model with unknown sources

What to do? Focus on rules and institutions. This is a deep point. Even DSGE modelers, in the desire to speak to policy makers, often adopt the static ISLM presumption that policy is about actions, about decisions, whether to raise or lower the funds rate. The other big Lucas point is that we should think about policy in terms of rules and institutions, not just actions.

Monetary policy and ELB

Stephanie Schmitt-Grohé (slides, video)  talked about the Fisherian possibility -- that raising interest rates raises inflation. New-Keynesian DSGE models, with rational expectations, have this property, especially for permanent or preannounced interest rate increases, and when at zero interest rates or otherwise in a passive regime where interest rates do not react more than one for one with inflation. She and Martin Uribe have been advocating this possibility as a serious proposal for Europe and Japan that want to raise inflation.

She presented some nice evidence that permanent increases in interest rates do increase inflation -- and right away, not just in the long run.

Mike Woodford. (slides, video)  gave a dense talk (37 slides, 20 minutes) on policy at the lower bound. During the ELB, central banks moved from interest rates to asset purchases and forward guidance. Mike asks,

To what extent does this mean that the entire conceptual framework of monetary stabilization policy needs to be reconsidered, for a world in which ELB might well continue periodically to bind? 

In classic form, Mike sets the question up as a Ramsey problem. Given a DSGE model, what is the optimal policy, given that interest rates are occasionally constrained? He derives from that problem a price level target. The price level target works, intuitively, by committing the central bank to a period of extra inflation after the zero bound ends. It is a popular form of forward guidance. The innovation here is to derive that formally as an optimal policy problem.

Mike's price level target is stochastic, changing optimally over time to respond to shocks. I'm a little skeptical that the central bank can observe and understand such shocks, especially given the above Uhlig-McGrattan discussion about the nature of shocks. Also, as I emphasize in comments, I'm dubious about the great power of promises of what the central bank will do in the far future to stimulate output today. I'm a fan of price level targets, but on both sides, not just as stimulus, but for utterly different reasons.

Mike takes on rather skeptically the common alternative -- quantitative easing, asset purchases during the time of the bound. He points out that to work, people have to believe that the increase in money is permanent, and won't be quickly withdrawn when the zero bound is over. As evidence, he points to Japan:

Similarly, he likes the price level target over forward guidance -- speeches in place of action -- as it is a more credible commitment to do things ex-post that the bank may not wish to do ex-post.

Finally, he addresses the puzzles of new Keynesian models at the zero bound -- forward guidance has stronger effects the further in the future is the promise; effects get larger as prices get less sticky, and so on. He argues that models should replace rational expectations with a complex k-step iterated expectations rule.

Me.

Video, slides from Sweden, slides from my webpage, written version. I covered this in a previous blog post, so won't repeat it all. I put a lot of effort in to it, and it summarizes a lot of what I've been doing in 15 minutes flat, so I recommend it (of course). It also offers more perspective on above points by Mike and Stephanie. My favorite line, referring to Mike's push for irrational expectations is something close to

"I never thought we would come to Sweden, that I would be defending the basic new-Keynesian program, and that Mike Woodford would be trying to tear it down. Yet here we are. Promote the fiscal equation from the footnotes and you can save the rest." 

Emi Nakamura

Poor Emi had to go last in an exhausting conference of jet-lagged participants. She did a great job (video, slides) covering a century of monetary history and monetary ideas clearly and transparently. These are great slides to use for an undergraduate or MBA class on monetary policy, as well. An abbreviated list:

• Gold standard
• Seasonal variation in interest rates under the gold standard; money demand shocks
• Money demand shocks in the 1980s -- how the supposedly "stable" V in MV=PY fell apart when the Fed pushed on M.
  
  
  
• Theoretical instability / indeterminacy of interest rate targets
• The switch to interest rate targets and corridors in operating procedures
• The (near-miraculous) success of inflation targets
  
• Taylor rules and other theory of determinate inflation under interest rate targets
• How is it "monetary economics" without money?
• Why did immense QE not cause inflation? 

The overarching theme is the grand story of a move, intellectual and practical, from money supply targets (of which gold is one) to interest rate targets.

Postlude

Monday featured two panels, Macroeconomic research and the financial crisis: A critical assessment, with Annette Vissing-Jørgensen, Luigi Zingales, Nancy Stokey, and  Robert Barro ; and Banking and finance research and the financial crisis: A critical assessment with Kristin Forbes, Ricardo Reis, Amir Sufi, and Antoinette Schoar.

Perhaps it's in the nature of panels, but I found these a disappointment, especially compared to the stellar presentations in the main conference. Also I think it would have been better to allow more (any, really) audience questions; the whole conference was a bit disappointing for lack of general discussion, especially with such a stellar group.

In particular, Luigi led by excoriating the profession for not paying attention to housing problems and financial crises. I thought this a bit unfair and simultaneously short-sighted. He singled out monetary economics textbooks, including Mike Woodford's, for omitting financial crises. Well, Mike omitted asteroid impacts too. It isn't a book about financial crises. And, after lamabasting all of us, he said not one word about events since 2009. What are we missing now? I had to stand up and ask that rude question, again suggesting that perhaps we are all not listening to Ken Rogoff this time. Annette went on to ask something like "don't you Chicago people believe in any regulation at all," and the respondents were too polite to say what an unproductive question that is and just move on.

Again, I offer apologies to authors and discussants I didn't get to. The whole thing was memorable, but there is only so much I can blog! Do go to the site and look at the other sessions, according to your interests.

Loss Aversion

A frequent email correspondent asked "I’d love to hear your take on “loss aversion.” I just finished listening to Kahneman’s book." My response seems worth sharing with blog readers.

Expected Utility

Let’s review expected utility first. The utility you get from consumption or wealth is a concave function of consumption or wealth. An extra dollar makes you more happy than it makes Bill Gates. So, compare either getting C for sure, or a 50/50 bet of getting C+Delta or C-Delta, i.e. having C or betting 50/50 on a coin flip. The expected utility of C for sure is just U(C). The expected utility of the bet is

EU = prob(loss) * U(consumption if loss) + prob(gain) * U(consumption if gain)

EU = 1/2 * U(C - Delta) + 1/2 * U(C + Delta).

As the graph shows, this is less than the expected utility of C for sure. So, people should decline fair value bets. They are “risk averse”.

Comments. Behavioral fans (New York times has done this often in its economics coverage) criticize “classical economics” by saying it ignores the fact that people fear losses more than they value gains. That’s absolutely false. Look at the utility function. People fear losses more than they value gains. That’s the whole point of expected utility. (You’ll see the confusion in a second).

A common mistake: EU( C) is not the same as U [ E(C )]. You do not find the utility of expected consumption, you find the expected utility of consumption. In my graph, C is equal to the expected value of C-Delta and C+Delta, and the whole point is that the utility of C is bigger than the expected utility of (C-Delta) or (C+Delta). You can take E inside a linear function, but you cannot take E inside a nonlinear function.

Loss aversion

OK, on to loss aversion. In the usual sort of experiments Kahneman found that people seem reluctant to lose money. They have a “reference point” and work  hard to avoid bets that might put them below that reference point. He models that as expected utility with a kink in it, as in the second drawing.

I was careful to draw the reference point as different than C. People do not necessarily place the reference point at the expected value of the bet. In fact, usually they don’t. If betting on stocks, the expected value of the bet is to gain 7% per year. The “don’t lose money” point would be do not go below 0, not do not go below the mean. Here people are especially afraid only of the very left part of the distribution.

Now, really, how are these models different? Expected utility can be any function, and nobody said it doesn’t have a kink in it. The key distinguishing feature of loss aversion – and its Achilles heel – is that the reference point shifts around. If you make some money, and play again, then your kink shifts up to the new amount of money you made. Expected utility is supposed to stay the same function of consumption or wealth. People might change behavior – most likely the utility curve is flatter at high levels of consumption, so rich people are less risk averse. But the curve itself does not shift. The key assumption that distinguishes loss aversion from expected utility is that the kink point shifts around as you gain and lose money.

That’s also the Achilles heel.  The first problem is how do you handle sequential bets. If I go to the casino, and know I will play twice, how do I think about my strategy? With expected utility this is easy, because the expected utility works backwards. Suppose you win the first bet, then figure out what you do in the second bet. For each of win or loss in the first bet, then, you have an expected utility from taking the second bet. The expected utility of the first bet is then the expected vaule of the expected utilities you would have if you won or lost.

Summer School Suggestion

The Asset Pricing online class is back, now hosted on Canvas. This is a first-year PhD level course in asset pricing. Advanced undergraduates and MBAs with some economics and basic calculus can take it too.  I mention it again as it is well suited as a summer school project, and I realized in talking to colleagues that not everyone who knew about the original class knows it's alive again.  Go here to sign up.

Faculty can also assign it or parts of it, and using the canvas system find out if students have taken the quizzes. This makes it a useful summer school prerequisite for fall classses, or you can use it or parts of it in a flipped classrom -- have the students do an online unit, take the quiz, and then show up to class prepared for more advanced discussion.

More information here on my webpage, along with all the videos and notes, and lots of extra material. If you don't want to take the quizzes, you can see the videos and notes without taking the course.

Basecoin

Cryptocurrencies like bitcoin have to solve two and a half important problems if they are to become currencies: 1) Unstable values 2) High transactions costs 2.5) Anonymity.

I recently ran across Basis and its Basecoin, an interesting initiative to avoid unstable values. (White paper here.)

Basecoin's idea is to expand and contract the supply so as to maintain a stable value. If the value of the basecoin starts to rise, more will be issued. If it falls, the number will be reduced.

So far so good. But who gets the seignorage when basecoins are increased? And just what do you get for your basecoins if the algorithm is reducing the numbers? From the white paper:

If Basis is trading for more than $1, the blockchain creates and distributes new Basis. These Basis are given by protocol-determined priority to holders of bond tokens and Base Shares, two separate classes of tokens that we’ll detail later. 

If Basis is trading for less than $1, the blockchain creates and sells bond tokens in an open auction to take coins out of circulation. Bond tokens cost less than 1 Basis, and they have the potential to be redeemed for exactly 1 Basis when Basis is created to expand supply.

Aha, basecoins get traded for ... claims to future basecoins?

You should be able to see instantly how this will unwind. Suppose the algorithm wants to reduce basecoins. It then trades basecoins for "basecoin bonds" which are first-inline promises to receive future basecoin expansions. But those bonds will only have value during temporary drops of demand. If there is a permanent drop in demand, the bonds will never be redeemed and have no value.  They are at best claims to future seignorage. Any peg collapses in a run, and the run threshold is mighty close here.

But it gets worse.

A great EFG

On Friday, I went to the NBER EFG (Economic Fluctuations and Growth) meeting at the SF Fed. Program and papers here.  The papers were great, the discussions were great, the comments were great, even the food was good. (You know you're in California when the conference snack is avocado toast.)

The papers:

Online Asset Pricing is back!

The online Asset Pricing Ph.D. class is back! It died in a Coursera "upgrade," but it is now migrated over to Canvas.

Click here to go to the online class. My Asset Pricing webpage has links to the class, book, and many other useful materials.

It should be open and free to anyone, including all the quizzes, problem sets and exams.

Since it's on the Canvas system, if you are teaching at a University that uses Canvas, you should be able to integrate it with your class, assign all or part of it, and receive grades from quizzes and problem sets. Thus, you can use it as a flipped classroom, assign selected videos and quizzes in advance of a lecture.

It is also ideal for a Ph. D.  program summer school for year 0 or year 1. Again, through Canvas you should be able to assign the class, in whole or in part, and get grades.

It's also well suited to self-study. If you just want to watch the videos and read the notes, they are all here via youtube links on the Asset Pricing webpage.

Huge thanks to Emily Bembeneck and Allison Kallo at the University of Chicago, Mikhail Proshletsov, and above all to Nina Karnaukh now at Ohio State. Nina masterminded all the hard work of moving the class pages and quizzes from the Coursera system to the Canvas system, and fixing innumerable glitches along the way. Thanks also to the Booth School for paying for the transition.

Update: The latest version of the class is here.

Long Run Fed Targets

What should the Fed's long-run interest rate target be? The traditional view is that the glide path should aim at 4% -- 2% real plus 2% inflation.

3%?

One big question being debated right now is whether the "natural'' real rate of interest -- r* or "r-star" in econspeak -- has declined below 2%.

Over the long run, the Fed cannot control the real rate of interest -- that comes from how much people want to save and what opportunities there are for investment, i.e. the marginal product of capital. So, if the real rate of interest is now permanently lower, say 1%, then one might argue that the glide path should aim for 3% long-run interest rate -- 1% real plus 2% inflation target -- not 4%.

Janet Yellen recently came to Stanford and gave a very interesting speech that talked in part about a lower r-star, and seemed to be heading to something like this view. See the picture:

Source: Federal Reserve. 

(She also talked a lot about Taylor Rules, seeming to move much closer to John Taylor's view of how to implement monetary policy. See interesting coverage on John Taylor's blog. On r*, see Measuring the Natural Rate of Interest Redux by Thomas Laubach and John C. Williams for a central paper on r*. Henrike Michaelis and Volker Wieland have an interesting post on r* and Taylor rules, also commenting on Ms. Yellen's speech.)

Of course, cynics will say that it's just the latest excuse not to raise rates. But these are serious arguments which should be considered on their merits.

0%?

Should the glidepath head to 3% interest rates? Maybe not. How about zero?