Raise interest rates to raise inflation? Lower interest rates to lower inflation? It's not that simple.
A correspondent from an emerging market wrote enthusiastically. His country has somewhat too high inflation, currency depreciation and slightly negative real rates. A discussion is going on about raising rates to combat inflation. Do I think that lowering rates in this circumstance is instead the way to go about it?
As you can tell, posing the question this way makes me very uncomfortable! So, thinking out loud, why might one pause at jumping this far, this fast?
Fiscal policy. Fiscal policy deeply underlies monetary policy. In my own "Fisherian" explorations, the fiscal theory of price level is a deep foundation. If the government is printing up money to pay its bills, the central bank can do what it wants with interest rates, inflation is coming anyway.
Conversely, underlying the decline in inflation in the US, Europe, and Japan is an extraordinary demand for nominal government debt.
Bond markets seem to think we'll pay it off. And that is not too terribly an irrational expectation. Sovereign debts are self-inflicted wounds. A little structural reform to get growing again, tweaks to social security and medicare, and next thing you know we're back in the 1990s and wondering what to do when all the government bonds are paid off. Also, valuation is more about discount rates than cashflows. People seem happy -- for now -- to hold government debt despite unusually low prospective returns.
My correspondent answers that his country is actually doing well fiscally. However, his country is also a bit low on reserves and having exchange rate and capital flight problems.
But current deficits are not that important to inflation either in theory or in fact. The fiscal policy that matters is expectations of very long term stability, not just a few years of surpluses. Also, contingent liabilities matter a lot. If investors in government debt see a government that will bail out all and sundry in the next downturn, or faces political risks, even temporary surpluses are not an assurance to investors. (Craig Burnside, Marty Eichenbaum and Sergio Rebelo's "Prospective Deficits and the Asian Currency Crises, in the JPE and ungated here is a brilliant paper on this point.)
Rational expectations. The Fisherian proposition also relies deeply on rational expectations. In the simplest version, \( i_t = r + E_t \pi_{t+1} \), people see nominal interest rates rise, they expect inflation to be higher, so they raise their prices. As a result of that expectation inflation is, on average, higher. (Loose story alert.)
How do they expect such a thing? Well, rational expectations is sensible when there is a long history in one regime. People see higher interest rates, they remember times of high interest rates in the past, like the late 1970s, so they ratchet up their inflation expectations. Or, people see higher interest rates, and they've gotten used to the Fed raising interest rates when the Fed sees inflation coming, so they raise their expectations. The motto of rational expectations is "you can't fool all of the people all of the time," not "you can never fool anyone," nor "people are clairvoyant."
The Fisherian prediction relies on the interest rate change to be credible, long-lasting, and to lead to the right expectations. A one-off experiment, that might be read as cover for a dovish desire to boost growth at the expense of more inflation, and that might be quickly reversed doesn't really map to the equations. Europe and Japan, stuck at the zero bound, with a fiscal bonanza (low interest costs on the debt) and slowly decreasing inflation expectations is much more consistent with those equations.
Liquidity. When interest rates are positive and money does not pay interest, lowering rates means more money in the system, and potentially more lending too. This classic liquidity channel, which goes the other way, is absent for the US, UK, Japan and Europe, since we're at the zero bound and since reserves pay interest. (Granted, I couldn't get the equations of the liquidity effect to be large enough to offset the Fisher effect, but that depends on the particulars of a model. )
Successful disinflations. Disinflations are a combination of fiscal policy, monetary policy, expectations, and liquidity. Tom Sargent's classic ends of four hyperinflations tells the story beautifully.
Large inflations result from intractable fiscal problems, not central bank stupidity. In Tom's examples, the government solves the fiscal problem; not just immediately, but credibly solves it for the forseeable future. For example, the German government in the 1920s faced enormous reparations payments. Renegotiating these payments fixed the underlying fiscal problem. When the long-term fiscal problem was fixed, inflation stopped immediately. Since everybody knew what the fiscal problem was, expectations were quickly rational.
The end of inflation coincided with a large money expansion and a steep reduction in nominal interest rates. During a time of high inflation, people use as little money as possible. With inflation over, real money demand expands. There was no period of monetary stringency or interest-rate raising preceding these disinflations.
So these are great examples in which the Fisher story works well -- lower interest rates correspond to lower inflation, immediately. But you can see that lower interest rates are not the whole story. The central bank of Germany 1922 could not have stopped inflation on its own by lowering rates. I suspect the same is true of high inflation countries today -- usually something is wrong other than just the history of interest rates.
So, apply new theories with caution!
To the raising interest rates question for the US and Europe, some of the same considerations apply. We won't have any liquidity effects, as central banks are planning to just pay more interest on abundant reserves. Higher real interest rates will raise fiscal interest costs, which is an inflationary shock by fiscal theory considerations. The big question is expectations. Will people read higher interest rates as a warning of inflation about to break out, or as a sign that inflation will be even lower?
Thursday, March 31, 2016
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 \(\sigma=1, \kappa=1\):
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.
Friday, March 25, 2016
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:
The ECB
What's wrong with this?
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
(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:
"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 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,"
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
Oh, and on negative rates:
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.
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?"
.. 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!
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.
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.
(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.
Tuesday, March 8, 2016
Deflation Puzzle
Larry Summers writes an eloquent FT column "A world stumped by stubbornly low inflation"
So why is inflation slowly declining despite our central banks' best efforts? Here is a stab at an answer. I emphasize the central logical points with bullets.
In normal times, to raise interest rates, the central bank sells bonds, which soaks up money. Less money drives up interest rates as people bid to borrow a smaller supply, and less money also reduces "demand," which reduces inflation. In the long run, higher inflation and higher interest rates go together, as they did in the 1980s.
However, we are now in a classic "liquidity trap." Interest rates have been zero since 2008. Money and bonds are perfect substitutes. The proof of that is in the pudding: the Fed massively increased excess reserves from less than $50 billion to almost $3,000 billion, and inflation keeps trundling down.
The liquidity effect will remain absent as the Fed starts raising interest rates, and would remain absent if the Fed were to cut rates or reduce them below zero as other central banks are doing. You can't have more than perfect liquidity.
The Fed isn't even planning to try. It plans to keep the $3,000 billion of excess reserves outstanding and raise interest rates by raising the interest rate on reserves. There will be no open market operations, no "tightening" associated with this interest rate raise. But even if it did, we're $2,950 billion of excess reserves away from any liquidity effect, so it wouldn't matter.
Central banks thought they were raising inflation by lowering interest rates, following experience from the normal-times liquidity-effect correlation between lower interest rates and higher inflation. But that experience does not apply when its liquidity effect is turned off.
With no liquidity effect, lowering interest rates further below zero can only, slowly, lower inflation further. Central banks desiring inflation may have followed a classic pedal mis-application.
Do I "believe" this story? Belief has no place in science. It is the simplest coherent story that explains the last few years, not needing lots of frictions, irrationalities, and other assumptions. I have some equations to back it up. But we don't "believe" anything at least until it's published and has survived critical examination, replication and dissection. Still, I think it merits consideration.
Shh. I like zero inflation. If central banks have the wrong pedal but are driving the right speed anyway, why wake them up? Even Larry seems to have given up on the Phillips curve:
There is no sign of the dreaded "deflation vortex," any more than there is any sign of dreaded monetary hyperinflation. We're drifting down to the Friedman rule. As Larry emphasizes, don't get excited over forecasts from models that rather spectacularly did not forecast where we are today.
Central banks' desire for 2% inflation, and the Fed's rather puzzling interpretation of its "price stability" mandate to mean perpetual 2% inflation may also be relics of the bygone liquidity-effect regime.
Appreciate the first half of the column which turns the signs around. It's a great bit of rhetoric.
I have to register mild disagreement with Larry's "solution" to the supposed "problem,"
He doesn't say which monetary policies would work, given they have not done so yet. But these are topics for another day.
(Note: If quote and bullet formatting doesn't show up, come back to the original.)
Market measures of inflation expectations have been collapsing and on the Fed’s preferred inflation measure are now in the range of 1-1.25 per cent over the next decade.
Inflation expectations are even lower in Europe and Japan. Survey measures have shown sharp declines in recent months. Commodity prices are at multi-decade lows and the dollar has only risen as rapidly as in the past 18 months twice during the past 40 years when it has fluctuated widely
And the Fed is forecasting a return to its 2 per cent inflation target on the basis of models that are not convincing to most outside observers.
Central bankers [at the G20 meeting] communicated a sense that there was relatively little left that they can do to strengthen growth or even to raise inflation. This message was reinforced by the highly negative market reaction to Japan’s move to negative interest rates.
So why is inflation slowly declining despite our central banks' best efforts? Here is a stab at an answer. I emphasize the central logical points with bullets.
- Interest rates have two effects on inflation: a short-run "liquidity" effect, and a long-run "expected inflation" or "Fisher" effect.
In normal times, to raise interest rates, the central bank sells bonds, which soaks up money. Less money drives up interest rates as people bid to borrow a smaller supply, and less money also reduces "demand," which reduces inflation. In the long run, higher inflation and higher interest rates go together, as they did in the 1980s.
However, we are now in a classic "liquidity trap." Interest rates have been zero since 2008. Money and bonds are perfect substitutes. The proof of that is in the pudding: the Fed massively increased excess reserves from less than $50 billion to almost $3,000 billion, and inflation keeps trundling down.
- In a liquidity trap, the liquidity effect is absent.
The liquidity effect will remain absent as the Fed starts raising interest rates, and would remain absent if the Fed were to cut rates or reduce them below zero as other central banks are doing. You can't have more than perfect liquidity.
The Fed isn't even planning to try. It plans to keep the $3,000 billion of excess reserves outstanding and raise interest rates by raising the interest rate on reserves. There will be no open market operations, no "tightening" associated with this interest rate raise. But even if it did, we're $2,950 billion of excess reserves away from any liquidity effect, so it wouldn't matter.
- When the liquidity effect is absent, the expected inflation effect is all that remains. Inflation must follow interest rates.
Central banks thought they were raising inflation by lowering interest rates, following experience from the normal-times liquidity-effect correlation between lower interest rates and higher inflation. But that experience does not apply when its liquidity effect is turned off.
With no liquidity effect, lowering interest rates further below zero can only, slowly, lower inflation further. Central banks desiring inflation may have followed a classic pedal mis-application.
Do I "believe" this story? Belief has no place in science. It is the simplest coherent story that explains the last few years, not needing lots of frictions, irrationalities, and other assumptions. I have some equations to back it up. But we don't "believe" anything at least until it's published and has survived critical examination, replication and dissection. Still, I think it merits consideration.
Shh. I like zero inflation. If central banks have the wrong pedal but are driving the right speed anyway, why wake them up? Even Larry seems to have given up on the Phillips curve:
...suppose that officials were comfortable with current policy settings based on the argument that Phillips curve models predicted that inflation would revert over time to target due to the supposed relationship between unemployment and price increases.
There is no sign of the dreaded "deflation vortex," any more than there is any sign of dreaded monetary hyperinflation. We're drifting down to the Friedman rule. As Larry emphasizes, don't get excited over forecasts from models that rather spectacularly did not forecast where we are today.
Central banks' desire for 2% inflation, and the Fed's rather puzzling interpretation of its "price stability" mandate to mean perpetual 2% inflation may also be relics of the bygone liquidity-effect regime.
Appreciate the first half of the column which turns the signs around. It's a great bit of rhetoric.
I have to register mild disagreement with Larry's "solution" to the supposed "problem,"
In all likelihood the important elements will be a combination of fiscal expansion drawing on the opportunity created by super low rates and, in extremis, further experimentation with unconventional monetary policies.
He doesn't say which monetary policies would work, given they have not done so yet. But these are topics for another day.
(Note: If quote and bullet formatting doesn't show up, come back to the original.)
Wednesday, March 2, 2016
Premium increase insurance
Marginal Revolution and the Wall Street Journal both pass on a great quote from Warren Buffett:
You may say BH doesn't want the risk, but in a previous letter Buffett explained that BH was selling 99 year put options. And being hugely diversified is precisely what allows a company like this to take some risk.
If it doesn't want to hold the risk it could sell it. Surely there are lots of investors who are skeptics of climate change -- not warming, but the claim that warming will give rise to more extreme weather and higher insurance payouts; people who cheered at that quote in the WSG -- and would be happy to put their money where their mouths are in the reinsurance market.
(These thoughts are obviously related to health insurance, premium increase insurance and long-term guaranteed renewable contracts that solve the preexisting conditions problem.)
It’s understandable that the sponsor of the proxy proposal believes Berkshire is especially threatened by climate change because we are a huge insurer, covering all sorts of risks. The sponsor may worry that property losses will skyrocket because of weather changes. And such worries might, in fact, be warranted if we wrote ten- or twenty-year policies at fixed prices. But insurance policies are customarily written for one year and repriced annually to reflect changing exposures. Increased possibilities of loss translate promptly into increased premiums. . . .
Up to now, climate change has not produced more frequent nor more costly hurricanes nor other weather-related events covered by insurance. As a consequence, U.S. super-cat rates have fallen steadily in recent years, which is why we have backed away from that business. If super-cats become costlier and more frequent, the likely—though far from certain—effect on Berkshire’s insurance business would be to make it larger and more profitable.
As a citizen, you may understandably find climate change keeping you up nights. As a homeowner in a low-lying area, you may wish to consider moving. But when you are thinking only as a shareholder of a major insurer, climate change should not be on your list of worries.The puzzle to me is, why doesn't Berkshire Hathaway write ten- or twenty-year policies at fixed prices? Or, better, why does it not offer a second contract, that ensures you against the event that your regular insurance will be repriced every six months? If people are worried about it, and nobody else is doing it, it would seem they could charge a huge premium.
You may say BH doesn't want the risk, but in a previous letter Buffett explained that BH was selling 99 year put options. And being hugely diversified is precisely what allows a company like this to take some risk.
If it doesn't want to hold the risk it could sell it. Surely there are lots of investors who are skeptics of climate change -- not warming, but the claim that warming will give rise to more extreme weather and higher insurance payouts; people who cheered at that quote in the WSG -- and would be happy to put their money where their mouths are in the reinsurance market.
(These thoughts are obviously related to health insurance, premium increase insurance and long-term guaranteed renewable contracts that solve the preexisting conditions problem.)
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