Thursday, March 31, 2016

Neo-Fisherian caveats

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.

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.

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 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.

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.

Tuesday, March 8, 2016

Deflation Puzzle

Larry Summers writes an eloquent FT column "A world stumped by stubbornly low inflation"
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.  

Wednesday, March 2, 2016

Premium increase insurance

Marginal Revolution and the Wall Street Journal both pass on a great quote from Warren Buffett:
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.)