I did an interview with Cloud Yip at Econreporter, Part I and Part II, on various things macro, money, and fiscal theory of the price level. It's part of an interesting series on macroeconomics. Being a transcript of an interview, it's not as clean as a written essay, but not as incoherent as I usually am when talking.
On the same topics, I will be giving a talk at the European Financial Association, on Friday, titled "Michelson-Morley, Occam and Fisher: The radical implications of stable inflation at the zero bound," slides here. (Yes, it's an evolution of earlier talks, and hopefully it will be a paper in the fall.)
And, also on the same topic, you might find useful a set of slides for a 1.5 hour MBA class covering all of monetary economics from Friedman to Sargent-Wallace to Taylor to Woodford to FTPL. That too should get written down at some point.
The talk incorporates something I just figured out last week, namely how Sims' "stepping on a rake" model produces a temporary decline in inflation after an interest rate rise. Details here. The key is simple fiscal theory of the price level, long-term debt, and a Treasury that stubbornly keeps real surpluses in place even when the Fed devalues long-term debt via inflation.
Here is really simple example.
Showing posts with label Thesis topics. Show all posts
Showing posts with label Thesis topics. Show all posts
Tuesday, August 16, 2016
Thursday, July 28, 2016
Macro-Finance
A new essay "Macro-Finance," based on a talk I gave at the University of Melbourne this Spring. I survey many current frameworks including habits, long run risks, idiosyncratic risks, heterogenous preferences, rare disasters, probability mistakes, and debt or institutional finance. I show how all these approaches produce quite similar results and mechanisms: the market's ability to bear risk varies over time, with business cycles. I speculate with some simple models that time-varying risk premiums can produce a theory of risk-averse recessions, produced by varying risk aversion and precautionary saving, rather than Keynesian flow constraints or new-Keynesian intertemporal substitution.
Update 11/30/2020. The link now works and points to the published article
Friday, June 17, 2016
Syverson on the productivity slowdown
Chad Syverson has an interesting new paper on the sources of the productivity slowdown.
Background to wake you up: Long-term US growth is slowing down. This is a (the!) big important issue in economics (one previous post). And productivity -- how much each person can produce per hour -- is the only source of long-term growth. We are not vastly better off than our grandparents because we negotiated better wages for hacking at coal with pickaxes.
Why is productivity slowing down? Perhaps we've run out of ideas (Gordon). Perhaps a savings glut and the zero bound drive secular stagnation lack of demand (Summers). Perhaps the out of control regulatory leviathan is killing growth with a thousand cuts (Cochrane).
Or maybe productivity isn't declining at all, we're just measuring new products badly (Varian; Silicon Valley). Google maps is free! If so, we are living with undiagnosed but healthy deflation, and real GDP growth is actually doing well.
Chad:
Background to wake you up: Long-term US growth is slowing down. This is a (the!) big important issue in economics (one previous post). And productivity -- how much each person can produce per hour -- is the only source of long-term growth. We are not vastly better off than our grandparents because we negotiated better wages for hacking at coal with pickaxes.
Why is productivity slowing down? Perhaps we've run out of ideas (Gordon). Perhaps a savings glut and the zero bound drive secular stagnation lack of demand (Summers). Perhaps the out of control regulatory leviathan is killing growth with a thousand cuts (Cochrane).
Or maybe productivity isn't declining at all, we're just measuring new products badly (Varian; Silicon Valley). Google maps is free! If so, we are living with undiagnosed but healthy deflation, and real GDP growth is actually doing well.
Chad:
First, the productivity slowdown has occurred in dozens of countries, and its size is unrelated to measures of the countries’ consumption or production intensities of information and communication technologies ... Second, estimates... of the surplus created by internet-linked digital technologies fall far short of the $2.7 trillion or more of “missing output” resulting from the productivity growth slowdown...Third, if measurement problems were to account for even a modest share of this missing output, the properly measured output and productivity growth rates of industries that produce and service ICTs [internet] would have to have been multiples of their measured growth in the data. Fourth, while measured gross domestic income has been on average higher than measured gross domestic product since 2004—perhaps indicating workers are being paid to make products that are given away for free or at highly discounted prices—this trend actually began before the productivity slowdown and moreover reflects unusually high capital income rather than labor income (i.e., profits are unusually high). In combination, these complementary facets of evidence suggest that the reasonable prima facie case for the mismeasurement hypothesis faces real hurdles when confronted with the data.
An interesting read throughout.
[Except for that last sentence, a near parody of academic caution!]
Monday, June 13, 2016
Lottery Winners Don't Get Healthier
Alex Tabarrok at Marginal Revolution had a great post last week, Lottery Winners Don't get Healthier (also enjoy the url.)
Alex does not emphasize the most important point, I think, of this study. The natural inference is, The same things that make you wealthy make you healthy. The correlation between health and wealth across the population reflect two outcomes of the same underlying causes.
Wealthier people are healthier and live longer. Why? One popular explanation is summarized in the documentary Unnatural Causes: Is Inequality Making us Sick?
The lives of a CEO, a lab supervisor, a janitor, and an unemployed mother illustrate how class shapes opportunities for good health. Those on the top have the most access to power, resources and opportunity – and thus the best health. Those on the bottom are faced with more stressors – unpaid bills, jobs that don’t pay enough, unsafe living conditions, exposure to environmental hazards, lack of control over work and schedule, worries over children – and the fewest resources available to help them cope.
(My emphasis above)The net effect is a health-wealth gradient, in which every descending rung of the socioeconomic ladder corresponds to worse health.If this were true, then increasing the wealth of a poor person would increase their health. That does not appear to be the case. In important new research David Cesarini, Erik Lindqvist, Robert Ostling and Bjorn Wallace look at the health of lottery winners in Sweden (75% of winnings within the range of approximately $20,000 to $800,000) and, importantly, on their children. Most effects on adults are reliably close to zero and in no case can wealth explain a large share of the wealth-health gradient:
In adults, we find no evidence that wealth impacts mortality or health care utilization.... Our estimates allow us to rule out effects on 10-year mortality one sixth as large as the crosssectional wealth-mortality gradient.The authors also look at the health effects on the children of lottery winners. There is more uncertainty in the health estimates on children but most estimates cluster around zero and developmental effects on things like IQ can be rejected (“In all eight subsamples, we can rule out wealth effects on GPA smaller than 0.01 standard deviations”).
Alex does not emphasize the most important point, I think, of this study. The natural inference is, The same things that make you wealthy make you healthy. The correlation between health and wealth across the population reflect two outcomes of the same underlying causes.
Saturday, April 23, 2016
Lessons Learned I
I spent last week traveling and giving talks. I always learn a lot from this. One insight I got: Real interest rates are really important in making sense of fiscal policy and inflation.
Harald Uhlig got me thinking again about fiscal policy and inflation, in his skeptical comments on the fiscal theory discussion, available here. At left, two of his graphs, asking pointedly one of the standard questions about the fiscal theory: Ok, then, what about Japan? (And Europe and the US, too, in similar situations. If you don't see the graphs or equations, come to the original.) This question came up several times and I had the benefit of several creative seminar participants views.
The fiscal theory says
\[ \frac{B_{t-1}}{P_t} = E_t \sum_{j=0}^{\infty} \frac{1}{R_{t,t+j}} s_{t+j} \]
where \(B\) is nominal debt, \(P\) is the price level, \(R_{t,t+j}\) is the discount rate or real return on government bonds between \( t\) and \(t+j\) and \(s\) are real primary (excluding interest payments) government surpluses. Nominal debt \(B_{t-1}\) is exploding. Surpluses \(s_{t+j}\) are nonexistent -- all our governments are running eternal deficits, and forecasts for long-term fiscal policy are equally dire, with aging populations, slow growth, and exploding social welfare promises. So, asks Harald, where is the huge inflation?
I've sputtered on this one before. Of course the equation holds in any model; it's an identity with \(R\) equal to the real return on government debt; fiscal theory is about the mechanism rather than the equation itself. Sure, markets seem to have faith that rather than a grand global sovereign default via inflation, bondholders seem to have faith that eventually governments will wake up and do the right thing about primary surpluses \(s\). And so forth. But that's not very convincing.
This all leaves out the remaining letter: \(R\). We live in a time of extraordinarily low real interest rates. Lower real rates raise the real value surpluses s. So in the fiscal theory, other things the same, lower real rates are a deflationary force.
Harald Uhlig got me thinking again about fiscal policy and inflation, in his skeptical comments on the fiscal theory discussion, available here. At left, two of his graphs, asking pointedly one of the standard questions about the fiscal theory: Ok, then, what about Japan? (And Europe and the US, too, in similar situations. If you don't see the graphs or equations, come to the original.) This question came up several times and I had the benefit of several creative seminar participants views.
The fiscal theory says
\[ \frac{B_{t-1}}{P_t} = E_t \sum_{j=0}^{\infty} \frac{1}{R_{t,t+j}} s_{t+j} \]
where \(B\) is nominal debt, \(P\) is the price level, \(R_{t,t+j}\) is the discount rate or real return on government bonds between \( t\) and \(t+j\) and \(s\) are real primary (excluding interest payments) government surpluses. Nominal debt \(B_{t-1}\) is exploding. Surpluses \(s_{t+j}\) are nonexistent -- all our governments are running eternal deficits, and forecasts for long-term fiscal policy are equally dire, with aging populations, slow growth, and exploding social welfare promises. So, asks Harald, where is the huge inflation?
I've sputtered on this one before. Of course the equation holds in any model; it's an identity with \(R\) equal to the real return on government debt; fiscal theory is about the mechanism rather than the equation itself. Sure, markets seem to have faith that rather than a grand global sovereign default via inflation, bondholders seem to have faith that eventually governments will wake up and do the right thing about primary surpluses \(s\). And so forth. But that's not very convincing.
This all leaves out the remaining letter: \(R\). We live in a time of extraordinarily low real interest rates. Lower real rates raise the real value surpluses s. So in the fiscal theory, other things the same, lower real rates are a deflationary force.
Tuesday, March 29, 2016
A very simple neo-Fisherian model
A sharp colleague recently pushed me to write down a really simple model that
can clarify the intuition of how raising interest rates might raise, rather than lower, inflation.
Here is an answer.
(This follows the last post on the question, which links to a paper. Warning: this post uses mathjax and has graphs. If you don't see them, come back to the original. I have to hit shift-reload twice to see math in Safari. )
I'll use the standard intertemporal-substitution relation, that higher real interest rates induce you to postpone consumption, \[ c_t = E_t c_{t+1} - \sigma(i_t - E_t \pi_{t+1}) \] I'll pair it here with the simplest possible Phillips curve, that inflation is higher when output is higher. \[ \pi_t = \kappa c_t \] I'll also assume that people know about the interest rate rise ahead of time, so \(\pi_{t+1}=E_t\pi_{t+1}\).
Now substitute \(\pi_t\) for \(c_t\), \[ \pi_t = \pi_{t+1} - \sigma \kappa(i_t - \pi_{t+1})\] So the solution is \[ E_t \pi_{t+1} = \frac{1}{1+\sigma\kappa} \pi_t + \frac{\sigma \kappa}{1+\sigma\kappa}i_t \]
Inflation is stable. You can solve this backwards to \[ \pi_{t} = \frac{\sigma \kappa}{1+\sigma\kappa} \sum_{j=0}^\infty \left( \frac{1}{1+\sigma\kappa}\right)^j i_{t-j} \]
Here is a plot of what happens when the Fed raises nominal interest rates, using \(\sigma=1, \kappa=1\):
When interest rates rise, inflation rises steadily.
Now, intuition. (In economics intuition describes equations. If you have intuition but can't quite come up with the equations, you have a hunch not a result.) During the time of high real interest rates -- when the nominal rate has risen, but inflation has not yet caught up -- consumption must grow faster.
People consume less ahead of the time of high real interest rates, so they have more savings, and earn more interest on those savings. Afterwards, they can consume more. Since more consumption pushes up prices, giving more inflation, inflation must also rise during the period of high consumption growth.
One way to look at this is that consumption and inflation was depressed before the rise, because people knew the rise was going to happen. In that sense, higher interest rates do lower consumption, but rational expectations reverses the arrow of time: higher future interest rates lower consumption and inflation today.
(The case of a surprise rise in interest rates is a bit more subtle. It's possible in that case that \(\pi_t\) and \(c_t\) jump down unexpectedly at time \(t\) when \(i_t\) jumps up. Analyzing that case, like all the other complications, takes a paper not a blog post. The point here was to show a simple model that illustrates the possibility of a neo-Fisherian result, not to argue that the result is general. My skeptical colleauge wanted to see how it's even possible.)
I really like that the Phillips curve here is so completely old fashioned. This is Phillips' Phillips curve, with a permanent inflation-output tradeoff. That fact shows squarely where the neo-Fisherian result comes from. The forward-looking intertemporal-substitution IS equation is the central ingredient.
Model 2:
You might object that with this static Phillips curve, there is a permanent inflation-output tradeoff. Maybe we're getting the permanent rise in inflation from the permanent rise in output? No, but let's see it. Here's the same model with an accelerationist Phillips curve, with slowly adaptive expectations. Change the Phillips curve to \[ c_{t} = \kappa(\pi_{t}-\pi_{t-1}^{e}) \] \[ \pi_{t}^{e} = \lambda\pi_{t-1}^{e}+(1-\lambda)\pi_{t} \] or, equivalently, \[ \pi_{t}^{e}=(1-\lambda)\sum_{j=0}^{\infty}\lambda^{j}\pi_{t-j}. \]
Substituting out consumption again, \[ (\pi_{t}-\pi_{t-1}^{e})=(\pi_{t+1}-\pi_{t}^{e})-\sigma\kappa(i_{t}-\pi_{t+1}) \] \[ (1+\sigma\kappa)\pi_{t+1}=\pi_{t}+\pi_{t}^{e}-\pi_{t-1}^{e}+\sigma\kappa i_{t} \] \[ \pi_{t+1}=\frac{1}{1+\sigma\kappa}\left( \pi_{t}+\pi_{t}^{e}-\pi_{t-1} ^{e}\right) +\frac{\sigma\kappa}{1+\sigma\kappa}i_{t}. \] Explicitly, \[ (1+\sigma\kappa)\pi_{t+1}=\pi_{t}+\gamma(1-\lambda)\left[ \sum_{j=0}^{\infty }\lambda^{j}\Delta\pi_{t-j}\right] +\sigma\kappa i_{t} \]
Simulating this model, with \(\lambda=0.9\).
As you can see, we still have a completely positive response. Inflation ends up moving one for one with the rate change. Consumption booms and then slowly reverts to zero. The words are really about the same.
The positive consumption response does not survive with more realistic or better grounded Phillips curves. With the standard forward looking new Keynesian Phillips curve inflation looks about the same, but output goes down throughout the episode: you get stagflation.
The absolutely simplest model is, of course, just \[i_t = r + E_t \pi_{t+1}\]. Then if the Fed raises
the nominal interest rate, inflation must follow. But my challenge was to spell out the market forces
that push inflation up. I'm less able to tell the corresponding story in very simple terms.
(This follows the last post on the question, which links to a paper. Warning: this post uses mathjax and has graphs. If you don't see them, come back to the original. I have to hit shift-reload twice to see math in Safari. )
I'll use the standard intertemporal-substitution relation, that higher real interest rates induce you to postpone consumption, \[ c_t = E_t c_{t+1} - \sigma(i_t - E_t \pi_{t+1}) \] I'll pair it here with the simplest possible Phillips curve, that inflation is higher when output is higher. \[ \pi_t = \kappa c_t \] I'll also assume that people know about the interest rate rise ahead of time, so \(\pi_{t+1}=E_t\pi_{t+1}\).
Now substitute \(\pi_t\) for \(c_t\), \[ \pi_t = \pi_{t+1} - \sigma \kappa(i_t - \pi_{t+1})\] So the solution is \[ E_t \pi_{t+1} = \frac{1}{1+\sigma\kappa} \pi_t + \frac{\sigma \kappa}{1+\sigma\kappa}i_t \]
Inflation is stable. You can solve this backwards to \[ \pi_{t} = \frac{\sigma \kappa}{1+\sigma\kappa} \sum_{j=0}^\infty \left( \frac{1}{1+\sigma\kappa}\right)^j i_{t-j} \]
Here is a plot of what happens when the Fed raises nominal interest rates, using \(\sigma=1, \kappa=1\):
When interest rates rise, inflation rises steadily.
Now, intuition. (In economics intuition describes equations. If you have intuition but can't quite come up with the equations, you have a hunch not a result.) During the time of high real interest rates -- when the nominal rate has risen, but inflation has not yet caught up -- consumption must grow faster.
People consume less ahead of the time of high real interest rates, so they have more savings, and earn more interest on those savings. Afterwards, they can consume more. Since more consumption pushes up prices, giving more inflation, inflation must also rise during the period of high consumption growth.
One way to look at this is that consumption and inflation was depressed before the rise, because people knew the rise was going to happen. In that sense, higher interest rates do lower consumption, but rational expectations reverses the arrow of time: higher future interest rates lower consumption and inflation today.
(The case of a surprise rise in interest rates is a bit more subtle. It's possible in that case that \(\pi_t\) and \(c_t\) jump down unexpectedly at time \(t\) when \(i_t\) jumps up. Analyzing that case, like all the other complications, takes a paper not a blog post. The point here was to show a simple model that illustrates the possibility of a neo-Fisherian result, not to argue that the result is general. My skeptical colleauge wanted to see how it's even possible.)
I really like that the Phillips curve here is so completely old fashioned. This is Phillips' Phillips curve, with a permanent inflation-output tradeoff. That fact shows squarely where the neo-Fisherian result comes from. The forward-looking intertemporal-substitution IS equation is the central ingredient.
Model 2:
You might object that with this static Phillips curve, there is a permanent inflation-output tradeoff. Maybe we're getting the permanent rise in inflation from the permanent rise in output? No, but let's see it. Here's the same model with an accelerationist Phillips curve, with slowly adaptive expectations. Change the Phillips curve to \[ c_{t} = \kappa(\pi_{t}-\pi_{t-1}^{e}) \] \[ \pi_{t}^{e} = \lambda\pi_{t-1}^{e}+(1-\lambda)\pi_{t} \] or, equivalently, \[ \pi_{t}^{e}=(1-\lambda)\sum_{j=0}^{\infty}\lambda^{j}\pi_{t-j}. \]
Substituting out consumption again, \[ (\pi_{t}-\pi_{t-1}^{e})=(\pi_{t+1}-\pi_{t}^{e})-\sigma\kappa(i_{t}-\pi_{t+1}) \] \[ (1+\sigma\kappa)\pi_{t+1}=\pi_{t}+\pi_{t}^{e}-\pi_{t-1}^{e}+\sigma\kappa i_{t} \] \[ \pi_{t+1}=\frac{1}{1+\sigma\kappa}\left( \pi_{t}+\pi_{t}^{e}-\pi_{t-1} ^{e}\right) +\frac{\sigma\kappa}{1+\sigma\kappa}i_{t}. \] Explicitly, \[ (1+\sigma\kappa)\pi_{t+1}=\pi_{t}+\gamma(1-\lambda)\left[ \sum_{j=0}^{\infty }\lambda^{j}\Delta\pi_{t-j}\right] +\sigma\kappa i_{t} \]
Simulating this model, with \(\lambda=0.9\).
As you can see, we still have a completely positive response. Inflation ends up moving one for one with the rate change. Consumption booms and then slowly reverts to zero. The words are really about the same.
The positive consumption response does not survive with more realistic or better grounded Phillips curves. With the standard forward looking new Keynesian Phillips curve inflation looks about the same, but output goes down throughout the episode: you get stagflation.
The absolutely simplest model is, of course, just \[i_t = r + E_t \pi_{t+1}\]. Then if the Fed raises
the nominal interest rate, inflation must follow. But my challenge was to spell out the market forces
that push inflation up. I'm less able to tell the corresponding story in very simple terms.
Monday, March 21, 2016
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.
(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.
Sunday, November 8, 2015
The 13 Trillion Dollar Question
On Tuesday Nov 10 there will be a conference in Chicago on "The $13 Trillion Question: Managing the U.S. Government’s Debt" hosted by the Initiative on Global Markets at Chicago Booth, and the Hutchins Center on Fiscal and Monetary Policy at Brookings. (The Brookings announcement here.)
Robin Greenwood will present "The Optimal Maturity of Government Debt and Debt Management Conflicts between the U.S. Treasury and the Federal Reserve" arguing that the Fed and Treasury are working to cross-purposes -- the Fed buys what the Treasury sells -- and that the government should go after low rates on long term bonds rather than the budget insurance of issuing long term bonds.
(The government faces the same decision a homeowner does: borrow at near-zero floating rates, but maybe rates shoot up and so do your payments, or borrow long at 2% rates, and pay more if rates don't go up. Robin and Larry favor the former. I'm more risk averse. Maybe living in California has sensitized me that just because you haven't seen an earthquake recently doesn't mean you shouldn't buy earthquake insurance. But it's a good argument to have qualitatively -- what's the risk, and what's the reward.)
I will present "A new structure for Federal Debt," arguing for an overhaul of which instruments the Treasury issues, to make them more useful for financial markets and financial stability as well as for government borrowing and risk management. (Earlier blog post about this paper here.)
There will be extensive discussion and broader issues, and (the big draw) a panel of Seth Carpenter, Charles Evans, and Sara Sprung, moderated by David Wessel.
The conference is by invitation, but you can still sign up here until they run out of room, or email Jennifer (dot) Williams at chicagobooth (dot) edu. It will also be viewable by live webcast, link here, starting 1:30 central.
Update: Video of the event here.
Robin Greenwood will present "The Optimal Maturity of Government Debt and Debt Management Conflicts between the U.S. Treasury and the Federal Reserve" arguing that the Fed and Treasury are working to cross-purposes -- the Fed buys what the Treasury sells -- and that the government should go after low rates on long term bonds rather than the budget insurance of issuing long term bonds.
(The government faces the same decision a homeowner does: borrow at near-zero floating rates, but maybe rates shoot up and so do your payments, or borrow long at 2% rates, and pay more if rates don't go up. Robin and Larry favor the former. I'm more risk averse. Maybe living in California has sensitized me that just because you haven't seen an earthquake recently doesn't mean you shouldn't buy earthquake insurance. But it's a good argument to have qualitatively -- what's the risk, and what's the reward.)
I will present "A new structure for Federal Debt," arguing for an overhaul of which instruments the Treasury issues, to make them more useful for financial markets and financial stability as well as for government borrowing and risk management. (Earlier blog post about this paper here.)
There will be extensive discussion and broader issues, and (the big draw) a panel of Seth Carpenter, Charles Evans, and Sara Sprung, moderated by David Wessel.
The conference is by invitation, but you can still sign up here until they run out of room, or email Jennifer (dot) Williams at chicagobooth (dot) edu. It will also be viewable by live webcast, link here, starting 1:30 central.
Update: Video of the event here.
Thursday, October 22, 2015
Open-Mouth Operations
(Note: This post uses mathjax and has embedded pictures. When posts are reposted elsewhere these often get mangled. If it's not displaying well, come to the original at johnhcochrane.blogspot.com)
Our central banks have done nothing but talk for several years now. Interest rates are stuck at zero, and even QE has stopped in its tracks. Yet, people still ascribe big powers to these statements. Ms. Yellen sneezes, someone thinks they hear "December" and markets move.
Buried deep in the paper I posted earlier this week is a potential model of "open mouth" operations, that might of interest to blog readers.
Use the standard "new-Keynesian" model \[ x_{t} = E_{t}x_{t+1}-\sigma(i_{t}-E_{t}\pi_{t+1}) \] \[ \pi_{t} = \beta E_{t}\pi_{t+1}+\kappa x_{t} \] Add a Taylor rule, and suppose the Fed follows an inflation-target shock with no interest rate change \[ i_t = i^\ast_t + \phi_\pi ( \pi_t - \pi^\ast_t). \] \[ i^\ast_t = 0 \] \[ \pi^\ast_t = \delta_0 \lambda_1^{-t} \] Equivalently express the Taylor rule with a ``Wicksellian'' shock, \[ i_t = \hat{i}_t + \phi_\pi \pi_t \] \[ \hat{i}_t = - \delta_0 \phi_\pi \lambda_1^{-t}. \] In both cases, \[ \lambda_{1} =\frac{\left( 1+\beta+\kappa\sigma\right) +\sqrt{\left( 1+\beta+\kappa\sigma\right) ^{2}-4\beta}}{2} \gt 1 \] Yes, this is a special case. The persistence of the shocks is just equal to one of the roots of the model. Here \(\delta_0\) is just a parameter describing how big the monetary policy shock is.
Now, solve the model by any standard method for the unique locally bounded solution. The answer is \[ \pi_{t} = \delta_0 \lambda_1^{-t}, \] \[ \kappa x_{t} = \delta_0 (1-\beta \lambda_1^{-1}) \lambda_1^{-t} \] \[ i_t = 0 \]
Here is the equilibrium path of inflation and interest rates (flat red line at zero).
Our central banks have done nothing but talk for several years now. Interest rates are stuck at zero, and even QE has stopped in its tracks. Yet, people still ascribe big powers to these statements. Ms. Yellen sneezes, someone thinks they hear "December" and markets move.
Buried deep in the paper I posted earlier this week is a potential model of "open mouth" operations, that might of interest to blog readers.
Use the standard "new-Keynesian" model \[ x_{t} = E_{t}x_{t+1}-\sigma(i_{t}-E_{t}\pi_{t+1}) \] \[ \pi_{t} = \beta E_{t}\pi_{t+1}+\kappa x_{t} \] Add a Taylor rule, and suppose the Fed follows an inflation-target shock with no interest rate change \[ i_t = i^\ast_t + \phi_\pi ( \pi_t - \pi^\ast_t). \] \[ i^\ast_t = 0 \] \[ \pi^\ast_t = \delta_0 \lambda_1^{-t} \] Equivalently express the Taylor rule with a ``Wicksellian'' shock, \[ i_t = \hat{i}_t + \phi_\pi \pi_t \] \[ \hat{i}_t = - \delta_0 \phi_\pi \lambda_1^{-t}. \] In both cases, \[ \lambda_{1} =\frac{\left( 1+\beta+\kappa\sigma\right) +\sqrt{\left( 1+\beta+\kappa\sigma\right) ^{2}-4\beta}}{2} \gt 1 \] Yes, this is a special case. The persistence of the shocks is just equal to one of the roots of the model. Here \(\delta_0\) is just a parameter describing how big the monetary policy shock is.
Now, solve the model by any standard method for the unique locally bounded solution. The answer is \[ \pi_{t} = \delta_0 \lambda_1^{-t}, \] \[ \kappa x_{t} = \delta_0 (1-\beta \lambda_1^{-1}) \lambda_1^{-t} \] \[ i_t = 0 \]
Thursday, September 3, 2015
Historical Fiction
Steve Williamson has a very nice post "Historical Fiction", rebutting the claim, largely by Paul Krugman, that the late 1970s Keynesian macroeconomics with adaptive expectations was vindicated in describing the Reagan-Volker era disinflation.
The claims were startling, to say the least, as they sharply contradict received wisdom in just about every macro textbook: The Keynesian IS-LM model, whatever its other virtues or faults, failed to predict how quickly inflation would take off in the 1970, as the expectations-adjusted Phillips curve shifted up. It then failed to predict just how quickly inflation would be beaten in the 1980s. It predicted agonizing decades of unemployment. Instead, expectations adjusted down again, the inflation battle ended quickly. The intellectual battle ended with rational expectations and forward-looking models at the center of macroeconomics for 30 years.
Just who said what in memos or opeds 40 years ago is somewhat of a fodder for a big blog debate, which I won't cover here.
Steve posted a graph from an interesting 1980 James Tobin paper simulating what would happen. This is a nicer source than old memos or opeds from the early 1980s warning of impeding doom. Memos and opeds are opinions. Simulations capture models.
The graph:
I thought it would be more effective to contrast this graph with the actual data, rather than rely on your memories of what happened.
The black lines are the Tobin simulation. The blue lines are what actually happened. (I'm not good enough with photoshop to superimpose the graphs, so I read Tobin's data off his chart.)
The two curves parallel in 81 to 83, with reality moving much faster. But In 1984 it all falls apart. You can see the "Phillips curve shift" in the classic rational expectations story; the booming recovery that followed the 82 recession.
And you can see the crucial Keynesian prediction error: After the monetary tightening is over in 1986, no, we do not need years and years of grinding 10% unemployment.
So, conventional history is, it turns out, right after all. Adaptive-expectations ISLM models and their interpreters were predicting years and years of unemployment to quash inflation, and it didn't happen.
The claims were startling, to say the least, as they sharply contradict received wisdom in just about every macro textbook: The Keynesian IS-LM model, whatever its other virtues or faults, failed to predict how quickly inflation would take off in the 1970, as the expectations-adjusted Phillips curve shifted up. It then failed to predict just how quickly inflation would be beaten in the 1980s. It predicted agonizing decades of unemployment. Instead, expectations adjusted down again, the inflation battle ended quickly. The intellectual battle ended with rational expectations and forward-looking models at the center of macroeconomics for 30 years.
Just who said what in memos or opeds 40 years ago is somewhat of a fodder for a big blog debate, which I won't cover here.
Steve posted a graph from an interesting 1980 James Tobin paper simulating what would happen. This is a nicer source than old memos or opeds from the early 1980s warning of impeding doom. Memos and opeds are opinions. Simulations capture models.
The graph:
![]() |
| Source: James Tobin, BPEA. |
The two curves parallel in 81 to 83, with reality moving much faster. But In 1984 it all falls apart. You can see the "Phillips curve shift" in the classic rational expectations story; the booming recovery that followed the 82 recession.
And you can see the crucial Keynesian prediction error: After the monetary tightening is over in 1986, no, we do not need years and years of grinding 10% unemployment.
So, conventional history is, it turns out, right after all. Adaptive-expectations ISLM models and their interpreters were predicting years and years of unemployment to quash inflation, and it didn't happen.
Monday, August 31, 2015
Whither inflation?
(Note: This post uses mathjax to display equations and has several graphs. I've noticed that the blog gets picked up here and there and mangled along the way. If you can't read it or see the graphs, come back to the original .)
The news reports from Jackson Hole are very interesting. Fed officials are grappling with a tough question: what will happen to inflation? Why is there so little inflation now? How will a rate rise affect inflation? How can we trust models of the latter that are so wrong on the former?
Well, why don't we turn to the most utterly standard model for the answers to this question -- the sticky-price intertemporal substitution model. (It's often called "new-Keynesian" but I'm trying to avoid that word since its operation and predictions turn out to be diametrically opposed to anything "Keyneisan," as we'll see.)
Here is the model's answer:
The blue line supposes a step function rise in nominal interest rates. The red line plots the response of inflation and the black line plots output. The solid lines plot the answer to the standard question, what if the Fed suddenly and unexpectedly raises rates? But the Fed is not suddenly and unexpectedly doing anything, so the dashed lines plot answers to the much more relevant question: what if the Fed tells us long in advance that the rate rise is coming?
According to this standard model, the answer is clear: Inflation rises throughout the episode, smoothly joining the higher nominal interest rate. Output declines.
The news reports from Jackson Hole are very interesting. Fed officials are grappling with a tough question: what will happen to inflation? Why is there so little inflation now? How will a rate rise affect inflation? How can we trust models of the latter that are so wrong on the former?
Well, why don't we turn to the most utterly standard model for the answers to this question -- the sticky-price intertemporal substitution model. (It's often called "new-Keynesian" but I'm trying to avoid that word since its operation and predictions turn out to be diametrically opposed to anything "Keyneisan," as we'll see.)
Here is the model's answer:
![]() |
| Response of inflation (red) and output (black) to a permanent rise in interest rates (blue). |
The blue line supposes a step function rise in nominal interest rates. The red line plots the response of inflation and the black line plots output. The solid lines plot the answer to the standard question, what if the Fed suddenly and unexpectedly raises rates? But the Fed is not suddenly and unexpectedly doing anything, so the dashed lines plot answers to the much more relevant question: what if the Fed tells us long in advance that the rate rise is coming?
According to this standard model, the answer is clear: Inflation rises throughout the episode, smoothly joining the higher nominal interest rate. Output declines.
Tuesday, July 28, 2015
Mankiw and Conventional Wisdom on Europe
Greg Mankiw wrote a week ago in the Sunday New York Times, ably explaining the conventional view that the Euro is a bad idea, and that even countries as small as Greece (11 million people) need national currencies. Excerpt:
Short: I am also a big meter fan. I don't think each country needs its own measure of length, or to shorten it when local clothiers are having trouble and would like to raise cloth prices.
Monetary union works well in the United States. No economist suggests that New York, New Jersey and Connecticut should each have its own currency, and indeed it would be highly inconvenient if they did. Why can’t Europeans enjoy the conveniences of a common currency?I am a big euro fan. This seems a good moment to explain why I don't accept this conventional view, despite its authority from Milton Friedman to Marty Feldstein and Greg Mankiw and even to Paul Krugman.
Two reasons. First, unlike Europe, the United States has a fiscal union in which prosperous regions of the country subsidize less prosperous ones. Second, the United States has fewer barriers to labor mobility than Europe. In the United States, when an economic downturn affects one region, residents can pack up and find jobs elsewhere. In Europe, differences in language and culture make that response less likely.
As a result, Mr. Friedman and Mr. Feldstein contended that the nations of Europe needed a policy tool to deal with national recessions. That tool was a national monetary policy coupled with flexible exchange rates. Rather than heed their counsel, however, Europe adopted a common currency for much of the Continent and threw national monetary policy into the trash bin of history.
Making matters worse, however, was the common currency. In an earlier era, Greece could have devalued the drachma, making its exports more competitive on world markets. Easy monetary policy would have offset some of the pain from tight fiscal policy. Mr. Friedman and Mr. Feldstein were right: The euro has turned into an economic liability that has exacerbated political tensions. For this, the European elites who pushed for the currency union bear some responsibility.
Short: I am also a big meter fan. I don't think each country needs its own measure of length, or to shorten it when local clothiers are having trouble and would like to raise cloth prices.
Wednesday, July 15, 2015
Behavioral Public Choice
In a number of blog posts, (here ) I've complained about the lack of behavioral public choice theory, and highlighted some efforts in that direction.
Much behavioral economics documents that people do stupid things, and then jumps to the conclusion that parternalistic government can do things for us better. But wait, those government functionaries are also human, also behavioral, and placed in group and social settings that psychology as well as economics warns us are particularly prone to bad outcomes.
Marginal revolution highlights an interesting new paper that breaks in to this field, Behavioral public choice: The behavioral paradox of government policy by Ted Gayer and W. Kip Viscusi. A quote:
I am interested that behavioral economics seems so focused on mistakes of individual decision making, as nicely summarized in the quote. In fact the most obvious thing about humans is that we are social animals, not that we are poor individual decision-makers. I would think that behavioralists would be bringing social psychology more than individual decision making to economics. But maybe this just reveals how little I know about either.
Much behavioral economics documents that people do stupid things, and then jumps to the conclusion that parternalistic government can do things for us better. But wait, those government functionaries are also human, also behavioral, and placed in group and social settings that psychology as well as economics warns us are particularly prone to bad outcomes.
Marginal revolution highlights an interesting new paper that breaks in to this field, Behavioral public choice: The behavioral paradox of government policy by Ted Gayer and W. Kip Viscusi. A quote:
In this article we examine a wide range of behavioral failures, such as those linked to misperception of risks, unwarranted aversion to risk ambiguity, inordinate aversion to losses, and inconsistencies in the tradeoffs reflected in individual decisions. Although such shortcomings have been documented in the behavioral literature, they are also reflected in government policies, both because policymakers are also human and because public pressures incorporate these biases. The result is that government policies often institutionalize rather than overcome behavioral anomalies.I haven't read it, but it seems interesting, and the field seems wide open. The defense of freedom never was that freedom is perfect, merely that government control is worse.
I am interested that behavioral economics seems so focused on mistakes of individual decision making, as nicely summarized in the quote. In fact the most obvious thing about humans is that we are social animals, not that we are poor individual decision-makers. I would think that behavioralists would be bringing social psychology more than individual decision making to economics. But maybe this just reveals how little I know about either.
Monday, July 6, 2015
Calomiris and sticky prices
Charles Calomiris has a very interesting Forbes oped on Greece, with a much deeper insight.
"an across-the-board redenomination would lower prices throughout the economy"? Not necessarily. Why would any store lower prices just because it gets to lower wages and rent? Prices are not a "contract."
Thus, the redenomination should probably come with a (say) one week price control. Every price must be lowered 30% over what it was the previous day, for a week, Just long enough for each store to see that its competitors and suppliers has also really lowered prices. Then stores can do what they want.
My proposal begins with government action to write down the value of all euro-denominated contracts enforced within Greece. This “redenomination” would make all existing contracts – wages, pensions, deposits, and loans – legally worth only, say, 70% of their current nominal value. This policy would kill several birds with one stone. It would significantly reduce pensions, relieving fiscal pressure and satisfying troika demands for fiscal sustainability. It would do so in a way that would also mitigate the purchasing power consequences for pensioners, because an across-the-board redenomination would lower prices throughout the economy, making the reduction in nominal pensions more bearable. By applying redenomination to deposits and loans, banks’ health would be revived – their loans would now be payable and therefore more valuable, and their net worth would consequently rise. The 30% wage reduction would further reduce fiscal problems and make Greek producers competitive, and operate as an “internal devaluation” to raise demand for Greek products and tourism. Most importantly, this internal devaluation – by solving the problems of fiscal deficits, non-competitiveness and bank insolvency – would inspire confidence in Athens’ ability to stay within the eurozone, which should bring deposits back into the banking system to fuel a rebirth of lending.I think this is about half right, but a very good idea lies in here.
"an across-the-board redenomination would lower prices throughout the economy"? Not necessarily. Why would any store lower prices just because it gets to lower wages and rent? Prices are not a "contract."
Thus, the redenomination should probably come with a (say) one week price control. Every price must be lowered 30% over what it was the previous day, for a week, Just long enough for each store to see that its competitors and suppliers has also really lowered prices. Then stores can do what they want.
China crash?
Meanwhile, on the other side of the world, China is doing everything in the textbook to ignite a "bubble."
I dislike that usually undefined term, which carries a lot of normative baggage. But there are a set of steps that governments often take unwittingly and are later criticized for. China's doing them on purpose. And these steps quite often precede large market declines.
Short sales ban: Financial Times: "opened a probe into market manipulation" ... "The investigation is likely to focus on short selling." The usual witch hunt, with Chinese characteristics. Owen Lamont has a splendid paper on what often follows short-sales bans. The weekend before TARP and Lehman, the US instituted a short-sales ban on bank stocks, just in case there was someone out there who did not know banks were in trouble and they should sell now. Europe instituted a CDS selling ban in the first PIGS crisis...
Lending to encourage highly leveraged speculation: Wall Street Journal: "Under the planned move, China’s central bank will indirectly help investors borrow to buy shares in a market that had already seen a rapid buildup in debt from so-called margin financing." Procyclical credit supply is named by just about every account of a "bubble" followed by a crash.
Prices depend on supply and demand. As well as increasing demand, limit supply: "A halt to new stock listings."
And more. Quartz offers "A complete list of the Chinese government’s stock-market stimulus (that we know about)" including "People’s Bank of China will “provide liquidity assistance” to China Securities Finance Corp., a company owned by the stock regulator. The company will use the money to lend to brokerages, which could then make loans to investors to buy stocks."
This scenario often ends badly.
The only thing I can think of that can actually stop a crash is for the central bank to directly print money to buy stocks. And not just a little bit. A pre-announced and limited quantity won't work. The US QE took billions to alter bond prices a few basis points at most. One has to commit to a price floor and a "do what it takes" amount of money, no matter how large or inflationary. I don't know of it ever being tried. It will be interesting to see if China goes that far. They could hide the fact with extensive bailouts of people "borrowing" to buy stocks, or otherwise cover losses or promise to cover losses.
Of course, the right strategy is to leave it alone. The whole point of stocks is that they go down on occasion, without runs, without defaults, and without financial distress. Unless the people and institutions holding them are highly leveraged. Didn't we just learn this lesson?
I dislike that usually undefined term, which carries a lot of normative baggage. But there are a set of steps that governments often take unwittingly and are later criticized for. China's doing them on purpose. And these steps quite often precede large market declines.
Short sales ban: Financial Times: "opened a probe into market manipulation" ... "The investigation is likely to focus on short selling." The usual witch hunt, with Chinese characteristics. Owen Lamont has a splendid paper on what often follows short-sales bans. The weekend before TARP and Lehman, the US instituted a short-sales ban on bank stocks, just in case there was someone out there who did not know banks were in trouble and they should sell now. Europe instituted a CDS selling ban in the first PIGS crisis...
Lending to encourage highly leveraged speculation: Wall Street Journal: "Under the planned move, China’s central bank will indirectly help investors borrow to buy shares in a market that had already seen a rapid buildup in debt from so-called margin financing." Procyclical credit supply is named by just about every account of a "bubble" followed by a crash.
Prices depend on supply and demand. As well as increasing demand, limit supply: "A halt to new stock listings."
And more. Quartz offers "A complete list of the Chinese government’s stock-market stimulus (that we know about)" including "People’s Bank of China will “provide liquidity assistance” to China Securities Finance Corp., a company owned by the stock regulator. The company will use the money to lend to brokerages, which could then make loans to investors to buy stocks."
This scenario often ends badly.
The only thing I can think of that can actually stop a crash is for the central bank to directly print money to buy stocks. And not just a little bit. A pre-announced and limited quantity won't work. The US QE took billions to alter bond prices a few basis points at most. One has to commit to a price floor and a "do what it takes" amount of money, no matter how large or inflationary. I don't know of it ever being tried. It will be interesting to see if China goes that far. They could hide the fact with extensive bailouts of people "borrowing" to buy stocks, or otherwise cover losses or promise to cover losses.
Of course, the right strategy is to leave it alone. The whole point of stocks is that they go down on occasion, without runs, without defaults, and without financial distress. Unless the people and institutions holding them are highly leveraged. Didn't we just learn this lesson?
Wednesday, June 3, 2015
Asset Pricing Summer School
I’m going to offer my online course “Asset Pricing” over the summer. The intent is a “summer school” for PhD students, either incoming or between the first year of foundation courses and the second year of specialized finance courses.
At least one university is going to use this more formally: Require completion of the class for their PhD students (either incoming or between first and second year,) and organize a TA and group meetings around the class. We have found that this sort of social organization helps a lot for students to get through online classes.
At least one university is going to use this more formally: Require completion of the class for their PhD students (either incoming or between first and second year,) and organize a TA and group meetings around the class. We have found that this sort of social organization helps a lot for students to get through online classes.
Friday, May 29, 2015
On writing well
The WSJ notable and quotable picked a lovely snippet from “On Writing Well” (1976) by William Zinsser, who died May 12 at age 92.
From the New York Times Obituary
Measure your time. You may think you're a social scientist, but in fact you're a writer.
Clutter is the disease of American writing. We are a society strangling in unnecessary words, circular constructions, pompous frills and meaningless jargon.
Who can understand the clotted language of everyday American commerce: the memo, the corporate report, the business letter, the notice from the bank explaining its latest “simplified” statement? What member of an insurance plan can decipher the brochure explaining the costs and benefits? What father or mother can put together a child’s toy from the instructions on the box? Our national tendency is to inflate and thereby sound important. The airline pilot who announces that he is presently anticipating experiencing considerable precipitation wouldn’t think of saying it may rain. The sentence is too simple—there must be something wrong with it.
But the secret of good writing is to strip every sentence to its cleanest components. Every word that serves no function, every long word that could be a short word, every adverb that carries the same meaning that’s already in the verb, every passive construction that leaves the reader unsure who is doing what—these are the thousand and one adulterants that weaken the strength of a sentence. And they usually occur in proportion to education and rank.Though each sentence is spare, Zinsser includes some long and concrete lists. Notice how effective that combination is.
From the New York Times Obituary
His advice was straightforward: Write clearly. Guard the message with your life. Avoid jargon and big words. Use active verbs. Make the reader think you enjoyed writing the piece.
He conveyed that himself with lively turns of phrase:
“There’s not much to be said about the period except that most writers don’t reach it soon enough,” ...
“Abraham Lincoln and Winston Churchill rode to glory on the back of the strong declarative sentence,” ..Zinsser's book was an inspiration to me. I highly recommend it to economists and PhD students. (My reading list for a PhD writing workshop.)
Measure your time. You may think you're a social scientist, but in fact you're a writer.
Thursday, May 28, 2015
Small shoes and headroom
I talked with Kathleen Hays and Michael McKee on Bloomberg Radio last week, and they asked (twice!) a question that comes up often in thinking about Fed policy: shouldn't the Fed raise rates now, so it has some "headroom" to lower them again if another recession should strike?
I could only answer with my standard joke: That's like the theory that you should wear shoes two sizes too small because it feels so good to take them off at the end of the day.
But the question comes up so often, it's worth thinking about a little more seriously. Under what views about the economy does this common idea make any sense?
I could only answer with my standard joke: That's like the theory that you should wear shoes two sizes too small because it feels so good to take them off at the end of the day.
But the question comes up so often, it's worth thinking about a little more seriously. Under what views about the economy does this common idea make any sense?
Monday, April 27, 2015
Unit roots in English and Pictures
After my unit roots redux post, a few people have asked for a nontechnical explanation of what this is all about.
Suppose there is an unexpected movement in any of the data we look at -- inflation, unemployment, GDP, prices, etc. Now, how does this "shock" affect our best estimate of where this variable will be in the future? The graph shows three possibilities.
Suppose there is an unexpected movement in any of the data we look at -- inflation, unemployment, GDP, prices, etc. Now, how does this "shock" affect our best estimate of where this variable will be in the future? The graph shows three possibilities.
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.)
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.)
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