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«This work is distributed as a Discussion Paper by the STANFORD INSTITUTE FOR ECONOMIC POLICY RESEARCH SIEPR Discussion Paper No. 16-033 Macro-Finance ...»

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This work is distributed as a Discussion Paper by the

STANFORD INSTITUTE FOR ECONOMIC POLICY RESEARCH

SIEPR Discussion Paper No. 16-033

Macro-Finance

By

John Cochrane

Stanford Institute for Economic Policy Research

Stanford University

Stanford, CA 94305

(650) 725-1874

The Stanford Institute for Economic Policy Research at Stanford University supports

research bearing on economic and public policy issues. The SIEPR Discussion Paper

Series reports on research and policy analysis conducted by researchers affiliated with the Institute. Working papers in this series reflect the views of the authors and not necessarily those of the Stanford Institute for Economic Policy Research or Stanford University Macro-Finance John H. Cochrane∗ Hoover Institution, Stanford University, and NBER July 28, 2016 Abstract Macro-finance addresses the link between asset prices and economic fluctuations. Many models reflect the same rough idea: the market’s ability to bear risk varies over time, larger in good times, and less in bad times. Models achieve this similar result by quite different mechanisms, and I contrast their strengths and weaknesses. I outline how macro-finance models may illuminate macroeconomics, by putting time-varying risk aversion, risk-bearing capacity, and precautionary savings at the center of recessions rather than variation in “the” interest rate and intertemporal substitution. I emphasize unsolved questions and profitable avenues for research.

∗ This essay is based on a talk at the University of Melbourne 2016 “Finance Down Under” conference. I am grateful to Carole Comerton-Forde, Vincent Gregoire, Bruce Grundy and Federico Nardari for inviting me. I am grateful to Ivo Welch for thoughtful comments MACRO-FINANCE

1. Introduction Macro-finance studies the relationship between asset prices and economic fluctuations.

These theories are built on some simple facts.

1.1. Facts Asset prices and returns are correlated with business cycles. Stocks rise in good times, and fall in bad times. The great recession of 2008-2009 is only the most recent reminder of this correlation. Real and nominal interest rates rise and fall with the business cycle.

Stock returns and bond yields also help to forecast macroeconomic events such as GDP growth and inflation.1 Stocks have a substantially higher average return than bonds. This number varies a good deal across samples, but typical estimates put the equity premium between 4% and 8%. The consensus is drifting to lower numbers, and the equity premium may be less going forward. Still, even 4% is puzzling. Why do people not hold more stocks, given the power of compound returns to increase wealth dramatically over long horizons? A 4% premium can raise your retirement portfolio value by a factor of 7.4 over 50 years (e0.04×50 = 7.4).

The answer is, of course, that stocks are risky. But people accept many risks in life – in lotteries and at Casinos they even seek out risks. The answer must be that stocks have a special kind of risk, that they fall at particularly inconvenient times or in particularly inconvenient states of nature.

–  –  –

where M denotes the stochastic discount factor, or growth of marginal utility, and Re is an excess return (the difference between the returns on two securities).

In this expression, expected returns are high because stocks fall at particularly inconvenient times – when investors are already hungry (high marginal utility, or high discount factor). Other risks, which investors take more happily, are not correlated with bad times.

So, just what are the bad times or bad states of nature, in which investors are particularly anxious that their stocks do not fall? Well, something about recessions is again an obvious candidate. Losing money in the stock market is especially fearsome if that event tends to happen just as you lose your job, your business is losing money, you may lose your house, and so on.

But just what is it about recessions that causes this fear? How do we measure that event? And what does this large fear that stocks might fall in recessions tell us about the macroeconomics of recessions? These questions are what macro-finance is all about.

–  –  –

where ∆c represents consumption growth and γ is the risk aversion coefficient in the power utility function u(C) = C 1−γ /(1 − γ). This model identifies the precise feature of

recessions that makes people fear especially losses in those times, and not other times:

consumption falls.

MACRO-FINANCE But, as crystallized by the equity premium-riskfree rate puzzle, consumption is just not volatile enough to generate the observed equity premium in this model, without very large risk aversion coefficients. From (1),

–  –  –

With market volatility about 16% on an annual basis, and 4% - 8% average returns, the Sharpe ratio on the left is about 0.25 - 0.5. Aggregate consumption growth only has a 1 standard deviation on an annual basis, 0.01 - 0.02. Reconciling these numbers takes a very high degree of risk aversion γ. Therefore, though the sign is right, this model does not quantitatively answer our motivating question, why are people so afraid of stocks when they do not seem that afraid of other events?





Risk premiums also vary over time, with a clear business-cycle correlation. You can forecast stock, bond, and currency returns by regressions of the form

–  –  –

using as the forecasting variable yt the price/dividend or price/earnings ratio of stocks, yield spreads of bonds, or interest rate spreads across countries. In each case the onemonth or one-year R2 and t statistics are not overwhelming. But measures of economic

importance are quite large. Expected returns vary over time as much as their level:

σ[Et (Rt+1 )] = σ(a + byt ) is large compared to E(Re ). If the equity premium is 4% on e average, it is as likely to be 1% or 7% at any moment in time. Furthermore, this large variation in risk premiums is correlated with business cycles: Expected returns are high, prices are low, and risk premiums are high in the bottoms of recessions. Expected returns are low, prices are high, and risk premiums are low at the tops of booms.

Price volatility is another measure of the economic significance of this phenomenon.

Shiller (1981) (see also Shiller (2014)) famously found that higher or lower stock prices do not signal higher or lower subsequent dividends. It took a long literature to figure MACRO-FINANCE out that this observation is arithmetically equivalent to regressions of the form (2). High prices relative to current dividends must imply higher future dividends or lower future returns. If higher prices do not correspond to higher future dividends, then they mechanically correspond to lower future returns. The “excess” volatility of prices, correlated with business cycles, is exactly the same phenomenon as the predictability of returns and time-variation of the risk premium, also correlated with business cycles.

So, our main question is this: What is there about recessions, or some better measure of economic bad times, that makes people so scared of losing money at those times, and therefore shy away from buying more stocks overall? What is there about economic bad times that makes people even more afraid of subsequent risks, risks that they happily shoulder despite relatively low returns in good times?

These are really two quite separate questions. The first, the equity premium question, addresses what about today’s world makes losing money in the stock market quite so painful, and hence why investors demanded a hefty premium yesterday to hold stocks.

The second, predictability and volatility question, asks what about today’s world makes investors unusually unwilling to hold risk from today until tomorrow, why the market prices of risk vary over time.

1.2. Theories To explain these facts, the macro-finance literature explored a wide range of alternative preferences and market structures. A sampling with a prominent example of each

case:2

1. Habits (Campbell and Cochrane 1999a, 1999b).

2. Recursive utility (Epstein and Zin 1989).

2. Each is a central and prominent citation, an example. In the interest of space, I focus on the ideas through these examples, but I do not attempt a comprehensive literature review, or a history of thought with proper attribution.

MACRO-FINANCE

3. Long run risks ( Bansal and Yaron 2004; Bansal, Kiku, and Yaron 2012).

4. Idiosyncratic risk (Constantinides and Duffie 1996).

–  –  –

6. Rare Disasters (Reitz 1988; Barro 2006).

7. Utility nonseparable across goods (Piazzesi, Schneider, and Tuzel 2007).

8. Leverage; balance-sheet; “institutional finance” (Brunnermeier 2009, Krishnamurthy and He 2013, many others).

9. Ambiguity aversion, min-max preferences, (Hansen and Sargent 2001).

10. Behavioral finance; probability mistakes (Shiller 1981, 2014).

–  –  –

Even the behavioral and probability distortion views are basically of this form. Expressing the expectation as a sum over states s, the basic first order condition is

–  –  –

where X denotes a payoff. Probability and marginal utility always enter together, so distorting marginal utility is the same thing as distorting probabilities. The state variables Y driving probability distortions act then just like state variables driving marginal utility.

–  –  –

enues for improvement? The ideas are in fact quite similar, as I’ll stress in a lot of contexts.

The models all describe a market with a time-varying ability to bear risk. The microeconomic source of that time-varying risk-bearing ability is the primary difference. In the habit model, endogenous time-varying individual risk aversion is at work – people are less willing to take risks in bad times. Nonseparable goods models work in a related way – past decisions such as the size of house you buy affect marginal utility of consumption. In behavioral or ambiguity aversion models, people’s probability assessments vary over time. In long-run risks, rare disasters and idiosyncratic risks models, the risk itself is time-varying. In heterogeneous agent models and institutional finance models, the market has a time-varying risk-bearing capacity, though neither risks, individual risk aversion, or individual probability mis-perceptions need vary over time. In heterogeneous agent models, changes in the wealth distribution that favor more or less risk averse agents induces the shift. In institutional finance models, individuals do not change their attitudes, but they are not active in markets. Instead, the changing fortunes of leveraged intermediaries induce changes in the market’s risk-bearing capacity.

That observation raises the potential of microeconomic observation to tell the models apart. But it also raises the classic question of macroeconomics, when multiple microeconomic stories give the same macroeconomic answer, whether telling apart micro foundations matters. Perhaps to understand economic fluctuations and their link to asset prices, it is enough to study representative consumer preferences, without worrying about their aggregation theory and microfoundations, or at least studying the latter separately and admitting that many micro stories can produce the same representative agent.

Different microeconomic stories for the same aggregate outcomes have different policy implications. For example, internal vs. external habits (habits formed from one’s own experience vs. a neighbor’s experience) have virtually the same asset pricing implications, but quite different welfare implications, since external habits have an externality.

MACRO-FINANCE Misperceptions lead to policy implications that changing risk aversion does not – at least on the questionable assumptions that Federal bureaucracies are less prone to probability misperceptions than investors are, and the deep assumption of welfare analysis that benevolent government respects preferences but not probability assessments. In any case, for welfare and policy analysis, one must take microfoundations more seriously – and one must face the fact that aggregate data are unlikely to tell apart wildly different microeconomic stories.

One might distinguish models by which data for Y turn out to work best. But most of the candidates are highly correlated with each other – most models end up adding a recession state variable, and it is practically a defining feature of recessions that many variables move together – so telling models apart will be hard this way. That fact also means that telling them apart is less important than may seem.

There is some hope in formally testing models – do their moment conditions and crossequation restrictions hold? – and in checking models’ additional assumptions – do conditional moments vary as much and in the way that long-run risk or rare disaster models specify; do cross sectional income and wealth distributions change as much as idiosyncratic risk and heterogeneous agent models specify? But though most models are easily rejected, those rejections correspond to economically uninteresting moments.

And by publication selection bias if nothing else, models are cleverly constructed that there auxiliary assumptions are not easily falsified; the variation in moments they require is small, hard to measure, or depends on rare events.

The models also differ in their tractability, elegance, and the number and fragility of extra assumptions (or “dark matter” in the colorful analogy of Chen, Dou, and Kogan

2015) needed to get from theory to central facts. I think it is a mistake to embrace too quickly a formalistic scientism that ignores these features. In explaining which models become popular throughout economics, tractability, elegance, and parsimony matter more than probability values of test statistics. Economics needs simple tractable models that help to capture the bewildering number of mechanisms people like to talk about.



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