Monday, April 20, 2015

Consumption-based model and value premium

The consumption based model is not as bad as you think. (This is a problem set for my online PhD class, and I thought the result would be interesting to blog readers.)

I use 4th quarter to 4th quarter nondurable + services consumption, and corresponding annual returns on 10 portfolios sorted on book to market and the three Fama-French factors. (Ken French's website)
The graph is average excess returns plotted against the covariance of excess returns with consumption growth. (The graph is a distillation of Jagannathan and Wang's paper, who get any credit for this observation.  The lines are OLS cross-sectional regressions with and without a free intercept.)

Friday, April 17, 2015

Macro Handbook 2

Last week I attended the first half of the conference on the Handbook of Macroeconomics Volume 2, organized by John Taylor and Harald Uhlig, held at Hoover. The conference program and most of the papers are here.  The second half will be in Chicago April 23-25, program here

Overall, this Handbook is shaping up as a very useful resource.  Really good summary and review papers are a natural way in to long literatures. Bad summary and review papers are long and boring. The conference produced the first kind. Most of the papers are rough first drafts, so make a note to come back when they're finished. A few highlights (with apologies to authors I've left out; I can't review them all here.)

Thursday, April 16, 2015

Banking at the IRS

A while ago in two blog posts here and here I suggested many ways other than currency to get a zero interest rate if the government tries to lower rates below zero. Buy gift cards, subway cards, stamps;  prepay bills, rent, mortgage and especially taxes -- the IRS will happily take your money now and you can credit it against future tax payments; have your bank make out a big certified check in your name, and sit on it, don't cash incoming checks. Start a company that takes money and invests in all these things (as well as currency).

Chris and Miles Kimball have an interesting essay exploring these ideas "However low interest rates might go, the IRS will never act like a bank." Their central point: sure that's how things work now. But with substantial negative interest rates, all of these contracts can change. It's technically possible in each case for people and businesses to charge pre-payment penalties amounting to a negative nominal rate.

Reply: Sure, in principle. Nominal claims can all be dated, and positive or negative interest charged between all dates.

But this did not happen in the US and does not happen in other countries for positive inflation and high nominal rates,  despite symmetric incentives, and at rates much higher than the contemplated 3-5% or so negative rates.  Yes,  with large nominal rates there is pressure to pay faster,  inventory cash-management to reduce people's holdings of depreciating nominal claims, but this pervasive indexation of nominal payments did not break out. The IRS did not offer interest for early payment.

More deeply, what they're describing is a tiny step away from perfect price indexing. If all nominal payments are perfectly indexed to the nominal interest rate, accrued daily, then it's a tiny change to index all prices themselves to the CPI, accrued daily. If "how much you owe me," say to rent a house, is legally, contractually, and mechanically determined as a value times e^rt, and changes day by day, then e^(pi t) is just as easy.

So, price stickiness itself would (should!) disappear under this scenario.

Price stickiness has always been a bit of a puzzle for economists. As the Kimballs speculate how easy it is to index payments to negative interest rates, so economists speculate how easy it is to index payments to inflation. Yet it seems not to happen.

So this point of view strikes me as a bit of a catch-22 for its advocates, who generally are of the frame of mind that prices and nominal contracts are sticky and that’s why negative nominal rates are a good idea to "stimulate demand" in the first place.  If we can have negative nominal rates and change all these legal and contractual zero-rate promises to allow it, then prices won't be sticky any more!   Conversely, I should be cheering, as it amounts to a broad push to unstick prices. That has long seemed to me the natural policy response to the view that sticky prices are the root of all our troubles. It would allow negative rates, but eliminate their need as well.

Alas, the world seems remarkably resistant to time-indexing all payments.

Wednesday, April 15, 2015

Gdefault needs not Grexit

The little grumpy cartoon usually represents me pounding my coffee down in agreement as the WSJ exposes some idiocy. Last week, alas, I spilled my grumpy coffee in disagreement with a little part of its otherwise excellent  "The case for letting Greece go."
Thursday marks another deadline in Greece’s struggle to avoid default, as a €450 million payment to the International Monetary Fund comes due. Athens says it will meet this obligation, but sooner or later Prime Minister Alexis Tsipras and his government will miss a payment to someone if it doesn’t agree with creditors on a new bailout. An exit from the euro would then be a real possibility.
Please can we stop passing along this canard -- that Greece defaulting on some of its bonds means that Greece must must change currencies. Greece no more needs to leave the euro zone than it needs to leave the meter zone and recalibrate all its rulers, or than it needs to leave the UTC+2 zone and reset all its clocks to Athens time. When large companies default, they do not need to leave the dollar zone. When cities and even US states default they do not need to leave the dollar zone. A common currency means that sovereigns default just like large financial companies. (Yes, a bit of humor in the last one.)

Tuesday, April 14, 2015

Blanchard on Countours of Policy

Olivier Blanchard, (IMF research director) has a thoughtful blog post, Contours of Macroeconomic Policy in the Future. In part it's background for the IMF's upcoming conference with the charming title Rethinking Macro Policy III: Progress or Confusion?” (You can guess my choice.)

Olivier cleanly poses some questions which in his view are likely to be the focus of policy-world debate for the next few years.  Looking for policy-oriented thesis topics? It's a one-stop shop.

Whether these should be the questions is another matter. (Mostly no, in my view.)

As a blogger, I can't resist a few pithy answers. But please note, I'm mostly having fun, and the questions and essay are much more serious.

Thursday, April 2, 2015

The sources of stock market fluctuations

How much do dividend-growth vs. discount-rate shocks account for stock price variations?

An under-appreciated point occurred to me while preparing for my Coursera class and to comment on Daniel Greewald, Martin Lettau and Sydney Ludvigsson's nice paper "Origin of Stock Market Fluctuations" at the last NBER EFG meeting

The answer is, it depends the horizon and the measure. 100% of the variance of price dividend ratios corresponds to expected return (discount rate) shocks, and none to dividend growth (cash flow) shocks.  50% of the variance of one-year returns corresponds to cashflow shocks. And 100% of long-run price variation corresponds to from cashflow shocks, not expected return shocks. These facts all coexist

I think there is some confusion on the point. If nothing else, this makes for a good problem set question.

The last point is easiest to see just with a plot. Prices and dividends are cointegrated. Prices correspond to dividends and expected returns. Dividends have a unit root, but expected returns are stationary. Over the long run prices will not deviate far from dividends. So 100% of long-enough run price variation must come from dividend variation, not expected returns.
Ok, a little more carefully, with equations.

A quick review: 

The most basic VAR for asset returns is \[ \Delta d_{t+1} = b_d \times dp_{t}+\varepsilon_{t+1}^{d} \] \[ dp_{t+1} = \phi \times dp_{t} +\varepsilon_{t+1}^{dp} \] Using only dividend yields dp, dividend growth is basically unforecastable \( b_d \approx 0\) and \( \phi\approx0.94 \) and the shocks are conveniently uncorrelated. The behavior of returns follows from the identity, that you need more dividends or a higher price to get a return,  \[ r_{t+1}\approx-\rho dp_{t+1}+dp_{t}+\Delta d_{t+1}% \] (This is the Campbell-Shiller return approximation, with \(\rho \approx 0.96\).) Thus, the implied regression of returns on dividend yields, \[ r_{t+1} = b_r \times dp_{t}+\varepsilon_{t+1}^{r} \] has \(b_r = (1-\rho\phi)+0 = 1-0.96\times0.94 = 0.1\) and a shock negatively correlated with dividend yield shocks and positively correlated with dividend growth shocks.

The impulse response function for this VAR naturally suggests "cashflow" (dividend) and "expected return" shocks, (d/p). (Sorry for recycling old points, but not everyone may know this.)

Three propositions:
  • The variance of p/d is 100% risk premiums, 0% cashflow shocks
Iterate forward the return identity, to get \[ dp_{t} =\sum_{t=1}^{\infty}\rho^{j-1}r_{t+j}-\sum_{t=1}^{\infty}\rho ^{j-1}\Delta d_{t+j} \] multiply by \(dp_t\) and take expectations (all variables are demeaned) \[\sigma^{2}\left( \log\frac{P_{t}}{D_{t}}\right) =\sigma^{2}\left( dp_{t}\right) =\sum_{t=1}^{\infty}\rho^{j-1}cov(dp_{t},r_{t+j})-\sum _{t=1}^{\infty}\rho^{j-1}cov(dp_{t},\Delta d_{t+j}), \] But \(b_d \approx 0 \), so the dividend growth terms are all zero, and 100% of the variance of price-dividend ratios corresponds to time-varying expected returns. (I know this will bore people familiar with it and befuddle those who are not. "Discount rates" has a bit more leisurely review and citations)

  •  The variance of returns is 50% due to risk premiums, 50% due to cashflows. 
\[ r_{t+1}=-\rho dp_{t+1}+dp_{t}+\Delta d_{t+1}% \] \[ \varepsilon_{t+1}^{r} =-\rho\varepsilon_{t+1}^{dp}+\varepsilon_{t+1}^{d} \] \[ \sigma^{2}\left( \varepsilon_{t+1}^{r}\right) =\rho^{2}\sigma^{2}\left( \varepsilon_{t+1}^{dp}\right) +\sigma^{2}\left( \varepsilon_{t+1}^{d}\right) \] The variance of the two shocks comes out very close to a 50/50 decomposition at an annual horizon. It's a lot more expected return at a daily horizon, and less at longer horizons. Here I use the fact that dividend growth and dividend yield shocks are basically uncorrelated.

Why are returns and p/d so different?  Current cash flow shocks affect returns. But a shock to dividends, when prices rise at the same time, does not affect the dividend price ratio. (This is the essence of the Campbell-Ammer return decomposition.)

The third proposition is less familiar:
  • The long-run variance of stock market values (and returns) is 100% due to cash flow shocks and none to expected return or discount rate shocks.
Here's why: \[ \Delta p_{t+1} =-dp_{t+1}+dp_{t}+\Delta d_{t+1} \] \[ p_{t+k}-p_{t} =-dp_{t+k}+dp_{t}+\sum_{j=1}^{k}\Delta d_{t+j} \] so as k gets big, \[ {var} (p_{t+k}-p_{t}) \rightarrow 2 {var}(dp_t) + k {var}(\Delta d_{t}) \] The first term approaches a constant, but the second term keeps growing. As above the central fact is that P and D are cointegrated while expected returns are stationary.

This is related to a point made by Fama and French in their Equity Premium paper. Long run average returns are driven by long run dividend growth  plus the average value of the dividend yield. The difference in valuation -- higher prices for given set of dividends -- can affect returns in a sample, as higher prices for a given set of dividends boost returns. But that mechanism can't last. (Avdis and Wachter have a nice recent paper formalizing this point.)  It's related to a similar point made often by Bob Shiller: Long run investors should buy stocks for the dividends.

A little more generality as this is the new bit.

\[ p_{t+k}-p_t = dp_{t+k}-dp_t + \sum_{j=1}^{k}\Delta d _{t+j} \] \[ p_{t+k}-p_t = (\phi^{k}-1)dp_t + \sum_{j=1}^{k}\phi^{k-j} \varepsilon^{dp}_{t+j} +  \sum_{j=1}^{k} \varepsilon^d _{t+j} \] \[ var(p_{t+k}-p_t) = \frac{(1-\phi^{k})^2}{1-\phi^2} \sigma^2(\varepsilon^{dp}) + \frac{(1-\phi^{2k})}{1-\phi^2}  \sigma^2(\varepsilon^{dp}) +  k\sigma^2(\varepsilon^d) \] \[var(p_{t+k}-p_t) = 2\frac{(1-\phi^{k})}{1-\phi^2} var(\varepsilon^{dp}_{t+1})  + k var(\varepsilon^d_{t+j})\] So you can see the last bit takes over. It doesn't take over as fast as you might think. Here's a graph using sample values,

At a one year horizon, it's just about 50/50. The dividend shocks eventually take over, at rate 1/k. But at 50 years, it's still about 80/20.

Exercise for the interested reader/finance professor looking for problem set questions: Do the same thing for long horizon returns, \( r_{t+1}+r_{t+2}+...+r_{t+k} \) using \(r_{t+1} = -\rho dp_{t+1} + dp_t + \Delta d_ {t+1} \) It's not so pretty, but you can get a closed form expression here too, and again dividend shocks take over in the long run.

Be forewarned, the long run return has all sorts of pathological properties. But nobody holds assets forever, without eating some of the dividends.

Disclaimer: Notice I have tried to say "associated with" or "correspond to" and not "caused by" here! This is just about facts. The facts have just as easy a "behavioral" interpretation about fads and bubbles in prices as they do a "rationalist" interpretation. Exercise 2: Write the "behavioralist" and then "rationalist" introduction / interpretation of these facts. Hint: they reverse cause and effect about prices and expected returns, and whether people in the market have rational expectations about expected returns.

Monday, March 30, 2015

Adam Davidson on Immigration

Illustration by Andrew Rae, source New York Times

Adam Davidson has a very nice New York Times Magazine article, "Debunking the Myth of the Job-Stealing Immigrant", in favor of "radically open borders."

Here's how a top professional journalist and writer puts together the central argument, so much more cleanly than I can do it:
So why don’t we open up?

Thursday, March 26, 2015

A New Structure for U. S. Federal Debt

A new paper by that title, here.

I propose a new structure for U. S. Federal debt. All debt should be perpetual, paying coupons forever with no principal payment. The debt should be composed of the following:
  1. Fixed-value, floating-rate debt: Short-term debt has a fixed value of $1.00, and pays a floating rate. It is electronically transferable, and sold in arbitrary denominations. Such debt looks to an investor like a money-market fund, or reserves at the Fed. 
  2. Nominal perpetuities: This debt pays a coupon of $1 per bond, forever. 
  3. Indexed perpetuities: This debt pays a coupon of $1 times the current consumer price index (CPI).
  4. Tax free: Debt should be sold in a version that is free of all income, estate, capital gains, and other taxes. Ideally, all debt should be tax free. 
  5. Variable coupon: Some if not all long-term debt should allow the government to vary the coupon rate without triggering legal default. 
  6. Swaps: The Treasury should manage the maturity structure of the debt, and the interest rate and inflation exposure of the Federal budget, by transacting in simple swaps among these securities.
Of these, I think the first is the most important. Think of it as Treasury Electronic Money, or reserves for all. Why?

Tuesday, March 24, 2015

Jumps and diffusions

I learned an interesting continuous time trick recently. The context is a note, "The fragile benefits of endowment destruction" that I wrote with John Campbell, about how to extend our habit model to jumps in consumption. The point here is more interesting than that particular context.

Suppose one time series \(x\), which follows a diffusion, drives another \(y\). In the simplest example, \[dx_t = \sigma dz_t \] \[ dy_t = y_t dx_t. \] In our example, the second equation describes how habits \(y\) respond to consumption \(x\). The same kind of structure might describe how invested wealth \(y\) responds to asset prices \(x\), or how option prices \(y\) respond to stock prices \(x\).

Now, suppose we want to extend the model to handle jumps in \(x\), \[dx_t = \sigma dz_t + dJ_t.\] What do we do about the second equation? \(y_t\) now can jump too. On the right hand side of the second equation, should we use the left limit, the right limit, or something in between?

Monday, March 23, 2015

Hospital Supply

In my view, health care supply restrictions are more important than the insurance or demand features that dominate public discussion. If you are spending your own money, yes, you shop for a good deal. But spending your own money in the face of restricted supply is like hailing a cab to LaGuardia at 5 o'clock on a rainy pre-Uber Friday afternoon. We need to free up innovative, disruptive health-care supply. Let the Southwest Airlines, Walmarts, Amazons and Apples in.

But where are the supply restrictions? Alas it's not as simple as the NY taxi commission. Supply restrictions are spread all over Federal, state and local law and regulation, and usually hidden.

So, I was interested to discover an interesting supply restriction in this editorial in the Wall Street Journal last week.
Last year the Daughters of Charity Health System sought to sell its six insolvent hospitals in California to Prime for $843 million including debt and pension liabilities. State law requires the AG [California Attorney General Kamala Harris] to approve nonprofit hospital acquisitions. Ms. Harris attached several poison pills at the urging of the SEIU [Service Employees International Union], which forced Prime last week to withdraw its offer.
State law requires the AG [Attorney General] to approve nonprofit hospital acquisitions. How could this go wrong?

Friday, March 20, 2015

Borio, Erdem, Filardo and Hofmann on the Costs of Deflation

Claudio Borio, Magdalena Erdem, Andrew Filardo and Boris Hofmann have a nice paper, "The costs of deflations: a historical perspective"

Deflation remains the looming zombie apocalypse of international monetary commentary.  Before we argue too much about cause and effect, it's nice to get the correlations straight. And the correlation between deflation and poor growth is much weaker than most people think:

Thursday, March 19, 2015

Levine on the Keynesian Illusion

David Levine has a very nice post on the Keynesian Illusion.

David Levine's analogy for Stimulus
Some big themes: Standard Keynesian economics violates budget constraints. He explains it well, but it is sure to occasion the usual venom from with the "Say's law fallacy" brigade that has a lot of trouble understanding the difference between budget constraints and equilibrium conditions.

David does a lot without equations. That broadens the appeal, but equations can be useful. For example equations clarify that crucial difference between budget constraints and equilibrium conditions. Equations can put to rest silly controversies. We might not still be writing papers, books, and blog posts about what "Keynes really meant," 80 years after the fact, or using "Say's law" as rotten tomatoes, if Keynes had written some equations.  Cynically, maybe the lesson is that lack of equations -- or even an equations appendix or citation -- keeps debate going and your name in the papers.

Wednesday, March 18, 2015

Arezki, Ramey, and Sheng on news shocks

I attended the NBER EFG (economic fluctuations and growth) meeting a few weeks ago, and saw a very nice paper by Rabah Arezki, Valerie Ramey, and Liugang Sheng, "News Shocks in Open Economies: Evidence from Giant Oil Discoveries" (There were a lot of nice papers, but this one is more bloggable.)

They look at what happens to economies that discover they have a lot of oil.

An oil discovery is a well identified "news shock."

Standard productivity shocks are a bit nebulous, and alter two things at once: they give greater productivity and hence incentive to work today and also news about more income in the future.

An oil discovery is well publicized. It incentivizes a small investment in oil drilling, but mostly is pure news of an income flow in the future. It does not affect overall labor productivity or other changes to preferences or technology.
Rabah,Valerie, and Liugang then construct a straightforward macro model of such an event.

Monday, March 16, 2015

Duffie and Stein on Libor

Darrell Duffie and Jeremy Stein have a nice paper, "Reforming LIBOR and Other Financial-Market Benchmarks" I learned some important lessons from the paper and discussion.

Libor is the "London interbank offering rate." If you have a floating rate mortgage, it is likely based on Libor plus a percentage.
In its current form, LIBOR is determined each day (or “fixed”), not based on actual transactions between banks but rather on a poll of a group of panel banks, each of which is asked to make a judgmental estimate of the rate at which it could borrow.
As soon as money changes hands, there is an incentive to, er, shade reports in the direction that benefits the trading desk.
Revelations of widespread manipulation of LIBOR and other benchmarks, including those for foreign exchange rates and some commodity prices, have threatened the integrity of these benchmarks.. 
or report a rate that makes your bank look better (lower rate) than it really is:
During the financial crisis of 2007-2009...Some banks did not wish to appear to be less creditworthy than others... The rates reported by each of the panel of banks polled to produce LIBOR were quickly published, alongside the name of the reporting bank, for all to see. As a result, there arose at some banks a practice of... understating true borrowing costs when submitting to a LIBOR poll. 

Thursday, March 5, 2015

Marginal Revolution on Kleptocracy

I don't often just post links, but sometimes a post is so good, and so complete, it just needs reading without comment.

Marginal Revolution on Kleptocracy

Ok, one comment. The mainstream media are focused on the racial element. This problem is much deeper than race.

Wednesday, March 4, 2015

Mankiw on dynamic scoring

Greg Mankiw has a nice op-ed on dynamic scoring

The issue: When the congressional budget office "scores" legislation, figuring out how much it will raise or lower tax revenue and spending, it has been using "static" scoring. For example, it assumes that a tax cut has no effect on GDP, even if the whole point of the tax cut is to raise GDP.

This is obviously inaccurate. But, as Greg points out, there is a lot of uncertainty in dynamic scoring.

Saturday, February 28, 2015

Doctrines Overturned

(This post is based on a few talks I've given lately. There's not much terribly new. But the effort to revisit, clarify and repackage may be useful even if you're a devoted blog reader, as it is to me.)

The Future of Monetary Policy / Classic Doctrines Overturned

Everyone is hanging on will-she or won't-she raise rates by 25 basis points.

I think this focus misses the more interesting questions for current monetary policy. The last 10 years or so are a remarkable experience, a Michelson-Morleymoment, which overturn long-held monetary policy doctrines. The plan to raise rates via interest on reserves in a large balance sheet completely changes the basic mechanism by which monetary policy is said to affect the economy.

Wednesday, February 25, 2015

On RRP Pro and Con

Thanks to a comment on the last post, I found The Fed working paper explaining Fed's thinking about overnight reverse repurchases, Overnight RRP Operations as a Monetary Policy Tool: Some Design Considerations by Josh Frost, Lorie Logan, Antoine Martin, Patrick McCabe, Fabio Natalucci, and Julie Remache.

(I should have found it on my own, as it's the top paper on the Fed's working paper list.) Cecchetti and Shoenholtz also comment here

My main question was just what "financial stability" concerns the Fed has with RRP, and this paper explains.

Run Free Video

This is a talk I gave at the joint Mercatus/Cato "After Dodd-Frank" conference last spring.  It's based on Toward a Run-Free Financial System.

Friday, February 20, 2015

Liftoff Levers

I read the minutes of the January FOMC meeting. (I was preparing for an interview with WSJ's Mary Kissel) There is a lot more interesting here, and a lot more important, than just when will the Fed raise rates.

Mainstream media missed the interesting debate on "liftoff tools." Maybe the minute the Fed starts talking about "ON RRP" (overnight reverse repurchase agreements) people go to sleep.


Here's the issue.  Can the Fed raise rates? In the old days there were $50 billion of reserves that did not pay interest. The Fed raised rates, so the story goes, by reducing the supply of reserves. Banks needed reserves in proportion to deposits, so they offered higher rates to borrow reserves.

Now, there are about $3 trillion of reserves, far more than banks need, and reserves pay interest. They are investments, equivalent to short-term Treasuries. If the Fed reduce their quantity by anything less than about $2,950 trillion, banks won't start paying or demanding higher interest.  And the Fed is not planning to reduce the supply of reserves at all. It's going to leave them outstanding and pay higher interest on reserves.

But why should that rise transfer to other rates? Suppose you decide that the minimum wage is too low, so you pay your gardener $50 per hour. Your gardener is happy. But that won't raise wages at McDonalds and Walmart to $50. This is what the Fed is worried about -- that it might end up paying interest to banks, but other interest rates don't follow.