Equity-financed banking

My dream of equity-financed banking may be coming true under our noses. In "the Uberization of banking" Andy Kessler at the WSJ reports on SoFi, a "fintech" company. The article is mostly about the human-interest story of its co-founder Mike Cagney. But the interspersed economics are interesting.

SoFi started by making student loans to Stanford MBAs, after figuring out that the default rate on such loans is basically zero. It

has since expanded to student loans more generally and added mortgages, personal loans and wealth management. Mr. Cagney says SoFi has done 150,000 loans totaling $10 billion and is currently at a $1 billion monthly loan-origination rate. 

Where does the money come from?

SoFi doesn’t take deposits, so it’s FDIC-free. ... Instead, SoFi raises money for its loans, most recently $1 billion from SoftBank and the hedge fund Third Point, in exchange for about a quarter of the company. SoFi uses this expanded balance sheet to make loans and then securitize many of them to sell them off to investors so it can make more loans

Just to bash the point home, consider what this means:

• A "bank" (in the economic, not legal sense) can finance loans, raising money essentially all from equity and no conventional debt. And it can offer competitive borrowing rates -- the supposedly too-high "cost of equity" is illusory.
   
• There is no necessary link between the business of taking and servicing deposits and that of making loans. Banks need not (try to) "transform" maturity or risk.
   
• To the extent that the bank wants to boost up the risk and return of its equity, it can do so by securitizing loans rather than by borrowing. (Securitized loans are not leverage -- there is no promise of your money back when you want it. Investors bear any losses immediately and without recourse.)
   
• Equity-financed banking can emerge without new regulations, or a big new Policy Initiative.  It's enough to have relief from old regulations ("FDIC-free").
   
• Since it makes no fixed-value promises, this structure is essentially run free and can't cause or contribute to a financial crisis. 

More. SoFi does not use the standard methods of evaluating credit risk:

Instead of relying on notoriously inaccurate backward-looking FICO scores, SoFi is “forward-looking.” That means asking basic questions—“Do you make more money than you spend?”—and calibrating where applicants went to college, how long they’ve been employed, how stable their income is likely to be over time.

Why can’t banks do this? Because if you use depositor money for loans, as all banks do, you fall under the jurisdiction of the Federal Deposit Insurance Corp. and the Community Reinvestment Act,...

And Basel and the FSOC and the Fed and so forth. FICO score based mechanical lending standards are also demanded by government-backed securitizers Fannie and Freddie.

Yes, bank "safety" regulations demand that banks purposely lend to people that one can pretty clearly see will not pay it back, and demand that they do not lend money to people that one can pretty clearly see will pay it back.

Now, what will the regulatory response be to this sort of innovation? The right answer, of course, should be hosannas: You have introduced run-free banking, that solves all the financial-crisis worries that 90 years of bank regulation could not solve. Let this spread, and the army of bank regulators, lobbyists, lawyers, and associated politicians can all go, well, drive for Uber.

Somehow I doubt that will be the response from foresaid army. And SoFi might well want to invest in its own lawyers, lobbyists and politicians in today's America.

Rather than by the FDIC, SoFi is monitored by the Consumer Financial Protection Bureau. The overbearing regulator that was Elizabeth Warren’s brainchild thus far hasn’t come down on SoFi—the CFPB is perhaps too preoccupied with using “disparate impact” analysis of old-school auto-loan businesses to focus on a relatively exotic, app-based form of banking. But Mr. Cagney should watch his back.

Indeed he should. In today's rather rule-free environment, the CFPB -- or Department of Justice -- might just discover it doesn't like the demographics of Stanford MBAs as target borrowers.

He’d like to get a national lending license, but that would entail federal-oversight entanglements he’d rather avoid.

If he can.

A little puzzle crops up at the end. For now, I gather SoFi does not issue public equity. The plan for expansion is

insurance companies and sovereign-wealth funds might rent him their balance sheets. 

I'm not sure what "rent a balance sheet" means, but it sounds a lot like private equity or long term debt.  It would be even better for stability and low cost to issue public equity, which is liquid -- investors who need money fast can sell. But public equity comes with its own regulatory scrutiny, and perhaps even that is too much for innovation these days.

MetLife

What does "systemically important" mean? How can an institution, per se, be "systemically important?"  The WSJ coverage of Judge Rosemary Collyer’s decision rescinding MetLife’s designation as a "systemically important financial institution:" gives an interesting clue to how our regulators' thinking is evolving on this issue:

The [Financial Stability Oversight] council argued — bromide alert — that “contagion can result when relatively modest direct, individual losses cause financial institutions with widely dispersed exposures to actively manage their balance sheets in a way that destabilizes markets.”

It's not a bromide. It is a revealing capsule of how the FSOC headed by Treasury thinks about this issue.


"Actively manage balance sheets" is a fancy word for "sell assets." So there you have it. "Systemically important" now just means that an institution might sell assets, because selling assets might lower asset prices. "Contagion" and "systemically important" are no longer about runs; you see one bank in trouble and go take your money out of a different one. "Contagion" and "systemically important"  is no longer the (false, but plausible) domino theory, that if I default and owe you money, you default.

Policy is no longer just about stopping runs. Policy is not just about stopping any large bank from failing, or ever just losing money. Policy is about  stopping asset prices from falling, and stopping even the small marginal additional fall in prices that might accompany one  large institution's sales.  (Except that leverage and capital ratios now force institutions to sell even if they don't want to, a delicious case of contradictory regulatory commands.)

Owen Lamont's classic characterizatiion of policy-maker's attitude toward selling short, now applies to selling at all.

 Policymakers and the general public seem to have an instinctive reaction that short selling is morally wrong. Short selling has been characterized as inhuman, un-American, and against God

The journal nails the basic problem

For eight years, federal regulators have failed to define precisely the “systemic risks” they claim they can identify across the financial landscape.

But no definition makes it easy to endlessly expand the word's meaning.

NBER AP

On Friday I attended the NBER Asset Pricing meeting (program here) in Chicago, organized by Adrien Verdelhan and Debby Lucas. The papers were unusually interesting, even by the high standards of this meeting. Alas the NBER doesn't post slides so I don't have great visuals to show you.


Lars Hansen started with the latest in the Hansen-Sargent ambiguity / robustness work,Sets of Models and Prices of Uncertainty. Stavros Panageas gave a beautiful discussion,  complete with power point animations. He characterized the paper as a major advance, for reducing the range of models over which an ambiguous agent looks for the worst case scenario, and for making that range state-dependent.

In the application, the agent worries that the mean growth rate of consumption and the AR(1) coefficient might be wrong; a more persistent consumption growth process is hurtful, and that pain is more in bad times.

I haven't followed this work closely enough. I still wonder what the testable implcations are -- how different is the asset pricing model from one in which the true consumption growth process is just a bit different from our estimate, in the worst possible way?

Still, it's nice to see a Nobel Prize winner leading off a conference, and with easily the most technical paper at that conference, with another one (Rob Engle) in the audience. That tells you something about the seriousness of this group. Also, this is serious behavioral finance by any metric -- a disciplined model of probability misperceptions, which is nice to see.

Robert Novy-Marx presented  Testing Strategies Based on Multiple Signals, discussed by Moto Yogo. We're all familiar with the phenomenon that if you try 10 characteristics and pick the best few to forecast returns, t statistics are biased and performance falls out of sample.

Robert pointed out that if you put those best 3 in a portfolio, they diversify each other, reducing the in-sample variance of the portfolio, and boosting Sharpe ratios and t-statistics even further.

Many ``smart beta'' funds are doing this, so the fall-off in performance from backtest to real money is relevant beyond academia.

The extent of this bias is impressive. Here is the distribution of t statistics that results when you pick the best three of 20 completely useless signals, and put them in a portfolio. Critical values of 4 and 5 show up routinely in Robert's calculations.

Laura Veldkamp presented her work with Nina Boyarchenko, David Lucca, and Laura Veldkamp,  Taking Orders and Taking Notes: Dealer Information Sharing in Financial Markets. Discussed ably (of course) by Darrell Duffie. Is it a problem that the dealers who are the prime bidders at treasury auctions have been caught talking to each other ahead of the auction?  Surprisingly, no: The Treasury can come out ahead when dealers share information with each other, and investors can potentially come out ahead too.

This warms my contrarian economist heart. We know so little about how markets work, and regulators are so quick to jump on supposedly bad behavor, it's lovely to see a clear and convincing model, that explains the kind of second-order and equilibrium effects that economists are good at.

Brian Weller presented Measuring Tail Risks at High Frequency, discussed nicely by Mike Chernov. Brian's basic idea is to run cross-sectional regressions of bid/ask spreads, normalized by volume and depth, on the cross-section of factor betas. Since spreads are larger when dealers are more worried about big jumps, this produces a measure of time-varying probability x size of such jumps. The measure correlates well with the VIX.

Michael Bauer presented his paper with Jim Hamilton Robust Bond Risk Premia discussed very nicely by Greg Duffee. (My discussion of a previous presentation). This paper is really about whether macro variables help to forecast bond returns. We're used to "Stambaugh bias:'' if you forecast returns with a persistent regressor, and the innovation in the regressor is strongly negatively correlated with the innovation in the return, then the near-unit-root downward bias in the regressor autocorrelation seeps over into upward bias of return predictability. But macro variables forecasting bond returns have innovations nearly uncorrelated with the returns, so that's not much of a problem. Michael and Jim show another problem: with overlappping returns, t statistics can be biased down too.

This led to a pleasant reassessment of bond return forecasts. Some points that came up: econometrics aside, many return forecasters don't do well out of sample. Many of the issues are specification issues orthogonal to this econometric point. For example, evaluating the huge forecastability of bond returns from a combination of level and inflation documented by Anna Cieslak and Pavol Povala, where the forecasters look a lot like a trend, is really about specification and interpretation, not econometrics. I held out the view that the important part of my paper with Monika Piazzesi is the single-factor structure of expected returns, not whether small principal components help to forecast returns. We had a pleasant interchange on whether it's a good or terrible idea to run one-year horizon forecasting regressions. I like them, because they attenuate measurement error. Raising a weekly autoregression to the 52nd power yields junk. Greg likes them, and gave a stirring reminder of Bob Hodrick's point that you can include lags of the forecasting variables instead.

Nick Roussanov presented his paper with Erik Gilje and Robert Ready, Fracking, Drilling, and Asset Pricing: Estimating the Economic Benefits of the Shale Revolution with Wei Xiong discussing. They track the reaction of stock prices to the shale oil boom. In particular, they showed that stocks which rose on a huge shale announcement subsequently rose even more as more good shale news came in. Until, as Wei pointed out, prices collapsed.

Nick also used stock market value to try to get at an estimate of the economics benefits of fracking. It's a worthy effort, but let's remember the difficulties. In a competitive no-adjustment cost world, profits are zero and there are no abnormal stock returns. Stock capitalization may rise, as firms issue stock to invest. But that measures the value of capital invested, not the consumer surplus of shale. Still, the general idea of mixing asset pricing, energy economics, and making economic measurements from stock prices is intriguing.

Jonathan Sokobin, Chief Economist, FINRA presented "An Overview of FINRA Data" which I alas had to miss. I'm delighted anyone from the government wants us to use their data!

The AP meeting has a nice tradition. Usually the most boring part of a conference is the author's response to discussant. The AP meetings do away with this -- or rather, the author can respond if someone in the audience raises his or her hand and says "I'd like to hear your response to x." That actually happened! But by and large the AP meetings preserve time and a tradition of very active participation and discussion, and this one was no different.

Central banks as central planners

Two news items cropped up this week on the general topic of central banks as emergent central planers.: a nice WSJ editorial by James Mackintosh on QE extended to buying corporate debt, and the Fed's proposed rule governing "Macroprudential" countercyclical capital buffers. The ECB also has a new Macroprudential Bulletin with similar ideas that I will not cover because the post is already too long. (Some earlier thoughts on the issue here. As usual, if the quotes aren't showing right, come back to the original of this post here.)

The WSJ editorial:

..as the central banks become more desperate to boost inflation and growth, they are starting to break one of the modern tenets of the profession by funneling that cash directly to what they regard as “good” uses.

The Bank of Japan’s conditions for companies to qualify for central bank funding include

offering an "improving working environment, providing child-care support, or expanding employee-training programs".... increasing capital spending, expanding spending on research and development or boosting what the Bank of Japan calls “human capital.” The latter means pay raises for staff, taking on more people or improving human resources.

The ECB

... plans to pay banks to borrow from it for up to four years so long as they use the money to help the “real” economy, meaning that they don’t simply pump up the housing markets by offering more mortgage finance.

The ECB is also causing a ruckus by stating plans for which private bonds it will buy and which it won't.

What's wrong with this?

“It’s a massive politicization of credit: Here are the legitimate things for lending, and here are the illegitimate things,” said Russell Napier,...“It’s capitalism with Chinese characteristics.”

Indeed. But just "politicization" or "central planning" is not the real danger. Our governments do all sorts of highly politicized credit allocation and subsidization -- energy boondoggles, student loans, export financing, housing housing and more housing, community reinvestment act, and so forth. On that scale, it seems hard to get excited about a little more.

But central banks so far don't, at least in well run countries. Why not? Independence. The deal for central banks has been: The bank gets great independence. In return, it accepts sharply limited powers. It handles money and interest rates, but it does not funnel credit to specific borrowers, nor does it target asset prices.  Branches of government that handle such political decisions are subject to quadrennial electoral wrath.  So, though any expansion of financial meddling is unwelcome, the big danger is the inevitable politicization and loss of independence of the Central bank.

And that will happen sooner than you think. Congressional hearings and bills to contain the Fed are already in Congress.

A bit more under the radar, but needing much more attention, the Fed has unveiled rules for implementing "macro-prudential" policy with "counter-cyclical capital buffers."

The proposed rule makes for fun reading. The

countercyclical capital buffer (CCyB) ...is a macroprudential policy tool that the Board can increase during periods of rising vulnerabilities in the financial system and reduce when vulnerabilities recede.

 [CCyB? OMG, DC alphabet soup is now case-sensitive?]

The CCyB is designed to increase the resilience of large banking organizations when the Board sees an elevated risk of above-normal losses. ... Above-normal losses often follow periods of rapid asset price appreciation or credit growth that are not well supported by underlying economic fundamentals....the Board would most likely use the CCyB ... to address circumstances when potential systemic vulnerabilities are somewhat above normal. By requiring advanced approaches institutions to hold a larger capital buffer during periods of increased systemic risk and removing the buffer requirement when the vulnerabilities have diminished, the CCyB has the potential to moderate fluctuations in the supply of credit over time.

Decoded into English, this is what they're saying: Replay the end of the boom, 2005-2007. This time we really will see the crisis coming. This time we will force banks to issue more stock, hold back on paying dividends and bonuses to conserve capital during the boom when things are going great. This time we will directly tell banks to stop lending even though customers are lining up at the doors for cash-out no-doc refis. Replay the beginning of the bust,  2007-2008. This time we really will demand that banks get even more private capital, and stop paying dividends and bonuses, in the middle of a crisis, even though the same banks may be screaming of its impossibility.

(And... "to hold a larger capital buffer. This entire document uses the incorrect verb "hold" to describe capital, as if capital are reserves. One hopes the ideas are not as confused as the language.)

Hayek's famous criticism of central planning is that planners can't possibly have the information needed to properly supply toilet paper. Which they didn't. So as you read this gobbledy-gook, you should ask just that question -- not whether the Fed is well intentioned or not (it is), but how will Fed officials "assess vulnerabilities,"  "potential systemic vulnerabilities" or tell whether "asset price appreciation or credit growth" are or are not "well supported by underlying economic fundamentals?"

The proposal lays out the answer:

.. by synthesizing information from a comprehensive set of financial-sector and macroeconomic indicators, supervisory information, surveys, and other interactions with market participants. In forming its view about the appropriate size of the U.S. CCyB, the Board will consider a number of financial-system vulnerabilities, including but not limited to, asset valuation pressures and risk appetite, ...

The decision will reflect the implications of the assessment of overall financial-system vulnerabilities as well as any concerns related to one or more classes of vulnerabilities. ...

"valuation pressures" and "risk appetite" are not measurable or even defined quantities. "Classes of vulnerabilities" even less so.

If this sounds pretty wooly, you might be a bit reassured by

The Board intends to monitor a wide range of financial and macroeconomic quantitative indicators including, but not limited to, measures of relative credit and liquidity expansion or contraction, a variety of asset prices, funding spreads, credit condition surveys, indices based on credit default swap spreads, options implied volatility, and measures of systemic risk. In addition, empirical models that translate a manageable set of quantitative indicators of financial and economic performance into potential settings for the CCyB, when used as part of a comprehensive judgmental assessment of all available information, can be a useful input to the Board's deliberations. Such models may include those that rely on small sets of indicators—such as the credit-to-GDP ratio, its growth rate, and combinations of the credit-to-GDP ratio with trends in the prices of residential and commercial real estate... Such models may also include those that consider larger sets of indicators...

Though they might as well say "we will look at every number that comes across the wires." It is painfully obvious though that nobody has any clue how to turn this mass of data into a useful real-time index of "vulnerabilities."

The key is to distinguish a "boom" from a "bubble."  In real time. When all the bankers in your "surveys" and "interactions with market participants" are telling you it's a boom. "We'll look at every vaguely plausible number that comes in" is hardly a reassuring tie to the mast.

But in case even this smorgasbord data-dump seems too limiting; in case some congressional committee member says "you looked at the price of barbecue in setting the first bank of Texas' capital buffer, and that violates the regulation,"

However, no single indictor or fixed set of indicators can adequately capture all the key vulnerabilities in the U.S. economy and financial system. Moreover, adjustments in the CCyB that were tightly linked to a specific model or set of models would be imprecise due to the relatively short period that some indicators are available, the limited number of past crises against which the models can be calibrated, and limited experience with the CCyB as a macroprudential tool. As a result, the types of indicators and models considered in assessments of the appropriate level of the CCyB are likely to change over time based on advances in research and the experience of the Board with this new macroprudential tool.

Translation to English: We will be shooting from the hip, but we will cover up the communique's with a lot of numbers and models and mumbo jumbo to give the illusion of technical competence.

To be clear, I'm all for capital. Lots and lots of capital. Capital issued or retained, not "held," please. I'm for so much capital that the precise amount doesn't really matter.

And that's the point. By pretending that the Fed will set capital ratios down to the second decimal point, and then pretending to be able to adjust that ratio up or down by a few percentage points in response to a Rube-Goldberg model, the Fed pretends there is a very important cost to demanding too much capital, that it knows exactly where the cost-benefit optimum is, not just on average, but with great precision vary it over time. All of this is not just false, it is completely pie-in-the sky.  How can anyone with a straight face claim such an absurd level of competence?

So my objection really is the effort to dress this up with the aura of technocratic competence, or pretend the Fed is putting in rules that it will follow. (The link is, after all, a rule-making proposal.) It would be far more honest to issue one line: "The Federal Reserve will adjust capital requirements as it sees fit." Period.

The result is easy to foresee. "Counter-cyclical capital" and "macro-prudential policy" will become one more completely discretionary and judgmental policy tool for the Fed to command the banks.  It will be subject to intense political forces. The Fed will get it wrong, and feed the flames.  The fallout for the Fed, for good monetary policy, and for the economy will not be good.

While we're on gobbledy-gook language and the revealed confusion by our aspiring technocrats, the  "real economy" language is sad. From WSJ, the ECB

 will cut the interest rate to as low as minus 0.4%—the ECB paying the banks—if the banks lend more to the real economy than a benchmark amount linked to their recent loans.

Here we are in 2016, and our central bankers are peddling the medieval distinction between "real" and "financial" investment. Yes, ordinary Joe can be excused from this fallacy. But people with economics PhDs are supposed to understand that every asset is also a liability. Individually we can "buy paper, not real things." Collectively, we cannot.

“The market would much rather companies take the ECB’s cheap money and use it to buy each other,” said Robert Buckland, an equity strategist at Citigroup Inc.

OK, so even private sector equity strategists can get it wrong. But central bankers are supposed to understand accounting identities. I hope these are journalistic misunderstandings and not an accurate reflection of thinking at the ECB.

Oh, and on negative rates:

German reinsurer Munich Re said it plans to store more than €10 million ($11.3 million) of physical bank notes in vaults to test the feasibility of avoiding negative rates.

The ECB may have to get going on Miles' Kimball's plan to devalue currency relative to bank reserves!

The Habit Habit

The Habit Habit. This is an essay expanding slightly on a talk I gave at the University of Melbourne's excellent "Finance Down Under" conference. The slides

(Note: This post uses mathjax for equations and has embedded graphs. Some places that pick up the post don't show these elements. If you can't see them or links come back to the original. Two shift-refreshes seem to cure Safari showing "math processing error".)

Habit past: I start with a quick review of the habit model. I highlight some successes as well as areas where the model needs improvement, that I think would be productive to address.

Habit present: I survey of many current parallel approaches including long run risks, idiosyncratic risks, heterogenous preferences, rare disasters, probability mistakes -- both behavioral and from ambiguity aversion -- and debt or institutional finance. I stress how all these approaches produce quite similar results and mechanisms. They all introduce a business-cycle state variable into the discount factor, so they all give rise to more risk aversion in bad times. The habit model, though less popular than some alternatives, is at least still a contender, and more parsimonious in many ways,

Habits future: I speculate with some simple models that time-varying risk premiums as captured by the habit model can produce a theory of risk-averse recessions, produced by varying risk aversion and precautionary saving, as an alternative to  Keynesian flow constraints or new Keynesian intertemporal substitution. People stopped consuming and investing in 2008 because they were scared to death, not because they wanted less consumption today in return for more consumption tomorrow.

Throughout, the essay focuses on challenges for future research, in many cases that seem like low hanging fruit. PhD students seeking advice on thesis topics: I'll tell you to read this. It also may be useful to colleagues as a teaching note on macro-asset pricing models. (Note, the parallel sections of my coursera class "Asset Pricing" cover some of the same material.)

I'll tempt you with one little exercise taken from late in the essay.


A representative consumer with a fixed habit \(x\) lives in a permanent income economy, with endowment \(e_0\) at time 0 and random endowment \(e_1\) at time 1. With a discount factor \(\beta=R^f=1\), the problem is

\[ \max\frac{(c_{0}-x)^{1-\gamma}}{1-\gamma}+E\left[ \frac {(c_{1}-x)^{1-\gamma}}{1-\gamma}\right] \] \[ c_{1} = e_{0}-c_{0} +e_{1} \] \[ e_{1} =\left\{ e_{h},e_{l}\right\} \; pr(e_{l})=\pi. \] The solution results from the first order condition \[ \left( c_{0}-x\right) ^{-\gamma}=E\left[ (c_{1}-x)^{-\gamma}\right] \] i.e., \[ \left( c_{0}-x\right) ^{-\gamma}=\pi(e_{0}-c_{0}+e_{l}-x)^{-\gamma}% +(1-\pi)(e_{0}-c_{0}+e_{h}-x)^{-\gamma}% \] I solve this equation numerically for \(c_{0}\).

The first picture shows consumption \(c_0\) as a function of first period endowment \(e_0\) for \(e_{h}=2\), \(e_{l}=0.9\), \(x=1\), \(\gamma=2\) and \(\pi=1/100\).

The case that one state is a rare disaster is not special. In a general case, the consumer starts to focus more and more on the worst-possible state as risk aversion rises. Therefore, the model with any other distribution and the same worst-possible state looks much like this one.

Watch the blue \(c_0\) line first. Starting from the right, when first-period endowment \(e_{0}\) is abundant, the consumer follows standard permanent income advice. The slope of the line connecting initial endowment \(e_{0}\) to consumption \(c_{0}\) is about 1/2, as the consumer splits his large endowment \(e_{0}\) between period 0 and the single additional period 1.

As endowment \(e_{0}\) declines, however, this behavior changes. For very low endowments \(e_{0}\approx 1\) relative to the nearly certain better future \(e_{h}=2\), the permanent income consumer would borrow to finance consumption in period 0. The habit consumer reduces consumption instead. As endowment \(e_{0}\) declines towards \(x=1\), the marginal propensity to consume becomes nearly one. The consumer reduces consumption one for one with income.

The next graph presents marginal utility times probability, \(u^{\prime}(c_{0})=(c_{0}-x)^{-\gamma}\), and \(\pi_{i}u^{\prime}(c_{i})=\pi _{i}(c_{i}-x)^{-\gamma},i=h,l\). By the first order condition, the former is equal to the sum of the latter two. \ But which state of the world is the more important consideration? When consumption is abundant in both periods on the right side of the graph, marginal utility \(u^{\prime}(c_{0})\) is almost entirely equated to marginal utility in the 99 times more likely good state \((1-\pi)u^{\prime}(c_{h})\). So, the consumer basically ignores the bad state and acts like a perfect foresight or permanent-income intertemporal-substitution consumer, considering consumption today vs. consumption in the good state.

In bad times, however, on the left side of the graph, if the consumer thinks about leaving very little for the future, or even borrowing, consumption in the unlikely bad state approaches the habit. Now the marginal utility of the bad state starts to skyrocket compared to that of the good state. The consumer must leave some positive amount saved so that the bad state does not turn disastrous -- even though he has a 99% chance of doubling his income in the next period (\(e_{h}=2\), \(e_{0}=1\)). Marginal utility at time 0, \(u^{\prime }(c_{0})\) now tracks \(\pi_{l}u^{\prime}(c_{l})\) almost perfectly.

In these graphs, then, we see behavior that motivates and is captured by many different kinds of models:

1. Consumption moves more with income in bad times.

This behavior is familiar from buffer-stock models, in which agents wish to smooth intertemporally, but can't borrow when wealth is low....

2. In bad times, consumers start to pay inordinate attention to rare bad states of nature.

This behavior is similar to time-varying rare disaster probability models, behavioral models, or to minimax ambiguity aversion models. At low values of consumption, the consumer's entire behavior \(c_{0}\) is driven by the tradeoff between consumption today \(c_{0}\) and consumption in a state \(c_{l}\) that has a 1/100 probability of occurrence, ignoring the state with 99/100 probability.

This little habit model also gives a natural account of endogenous time-varying attention to rare events.

The point is not to argue that habit models persuasively dominate the others. The point is just that there seems to be a range of behavior that theorists intuit, and that many models capture.

When consumption falls close to habit, risk aversion rises, stock prices fall, so by Q theory investment falls. We nearly have a multiplier-accelerator, due to rising risk aversion in bad times: Consumption falls with mpc approaching one, and investment falls as well. The paper gives some hints about how that might work in a real model.