Are there "Peso Problem" recessions?

Suppose monetary policy never changed for 99 years. Suppose nothing ever changed for 99 years. Would it be possible for there to be a deficient Aggregate Demand recession for 99 years? Why wouldn't prices adjust? Wouldn't 99 years be long enough for prices to adjust?

Suppose that monetary policy never changed for 99 years, but every year people knew that there was a 1% chance that it would change that year. And that if it did change there would be a very big loosening of monetary policy. A 100% loosening -- requiring a hypothetical flexible price equilibrium price level 100% higher than the current hypothetical flexible price equilibrium price level.

So every year for 99 years, when firms set prices at the beginning of the year, they are 99% confident that monetary policy will continue unchanged, in which case they would do better by cutting their prices 1%. But there is a 1% chance that monetary policy will change, in which case they would do better by raising their prices 99%. So they leave their prices unchanged, because the expected benefits of cutting their prices by 1% are exactly balanced by the expected benefits of raising their prices by 99%.

For 99 years out of 100, firms regret they did not cut their prices 1% at the beginning of the year. For 1 year out of 100, firms regret they did not raise their prices 99% at the beginning of the year.

So, on average, a recession lasts for 99 years, during which firms' prices are 1% too high, given the monetary policy in effect during those 99 years. And, on average, there is a boom every 100 years that lasts for one year, during which firms' prices are 99% too low, given the monetary policy in effect during that one year.

(This does not necessarily mean that booms are 99 times bigger than recessions, even though they are 99 times more rare. Not everything is linear. There are supply constraints, as well as demand constraints.)

1. Do we ever observe Peso Problem recessions?

2. What would be the empirical signature of a Peso Problem recession?

3. Is it conceivable that some countries right now are in a Peso Problem recession? Is the average firm 100% confident that those who fear imminent hyperinflation are wrong? Or only 99% confident?

(This post is a restatement of a comment I made on Frances' Smaug post. Here is a good discussion of the Peso Problem, which is normally applied to exchange rates and financial markets. A Peso Problem is an extreme case of a probability distribution that is highly skewed with a fat tail on one side. A sample size large enough to reflect the whole probability distribution would be a very large sample.)

If you had told me in 2008 that the recession in some countries would last as long as it has, I would have predicted inflation in those countries would have been lower than it has in fact been. I would have been wrong.

Comments

[Alex Godofsky]

I'm skeptical of the upward price rigidity you'd need for something like this.

[Peter N]

You're more likely to see something like this on Wall St. Consider a random walk time series from a distribution with infinite variance and an absorbing barrier at 0. The perverse incentives are built in.

Even without the help of bankruptcy, death is an absorbing barrier, which gets back to your example. Any event that has a low probability of occurrence within the life of the investor will be down-weighted. This is the result of evolution. Pessimists don't reproduce enough to take advantage of their caution, just as it's difficult to profit from being right about a bubble. Keynes was correct about timing "irrational" markets.

[Vaidas]

Nick, empirical signature of such recession would be the high expected volatility of NGDP or inflation. NGDP options do not exist, but it makes sense to look at VIX.
See my post for more:
http://marketmonetarist.com/2012/12/22/guest-post-market-montarism-and-financial-crisis-by-vaidas-urba/

[Vaidas]

BTW, with NGDPLT, we could observe peso booms, where NGDP rises above trend more and more each year, until a financial crisis hits and NGDP hits the trend again.

[Vaidas]

In my peso boom example, there is a high probability of slightly-above-trend growth, and a small probability of a large crash.

[Zorblog]

This certainly is the phenomenon currently observed in Southern Europe. 25% unemployment makes no sense. Everybody would be better off if those people would work and produce something.
It is thus difficult to understand why the unemployed don't cut the wage they ask for, why businesses don't lower their prices, why owners of empty spaces don't cut the rent, why creditors don't write off the debts of those who can't pay.
Uncertainty is the obvious answer. While deflation and default looks like the most likely outcome, there still is hope for a miracle.

[Simon van Norden]

"Is it conceivable that some countries right now are in a Peso Problem recession?" Yes...without doubt.
Is there any evidence that some countries right now are in a Peso Problem recession? Not that I know of.

Nick, you are effectively asking what we know about the tails of a distribution (I think you're just asking about a monetary policy variable, but you might be asking about real variables as well.) And you want to go well out into the tails...to bound the size of events that on average happen once-per-century. Intuitively, we'll need a few centuries of data to be confident about things like that. Obviously, we don't have that for most economic series. Many of the countries we're interested in (Canada, Italy, Germany) only go back to the mid-1800s and their central banks are 20th century institutions. Even absent such problems, we'd have to seriously ask whether 19th century data is informative for what could happen in a 21st century economy (i.e. we're effectively assuming that there has been no change in the distribution during the sample.) We could try to use cross-country data to help us get more observations...but that only works to the extent that observations are independent across countries (and in a Global Financial Crisis, we recognise that things are very far indeed from independent.)

As a generally principal, we cannot rule out very small probability events with arbitrarily large impacts. This implies that we can invoke them to justify pretty much anything (...and I'm not restricting myself to economics here.)

Do you think that invoking them is a useful exercise? Do you think it is "scientific"?

[Phil Koop]

I think that Simon makes a good point, but the fact is that the Peso Problem is a popular idea, perhaps because if true it would be a simple and elegant explanation for the stylized facts that are bothering Nick.

So what empirical support might there be for this idea beyond those stylized facts? Proving the Peso Problem exists seems (to me) to require demonstrating that realized inflation is systematically higher than expected inflation. The trouble is that these expectations are not observable in market prices, being blended with a risk premium. There is a large literature attempting to quantify this risk premium in order to get at these expectations, but none of it is conclusive. (The Cleveland Fed is just the tip of the iceberg here; try googling "inflation risk premium".) Much of this work does not distinguish between market expectations and the historical probability distribution of inflation, which negates the point that we are interested in here.

In short, I think you have your work cut out for you here.

[Simon van Norden]

Expanding on what Phil Koop said, if you're interested in the literature on the inflation risk premium, one of the better recent papers is that by Yuriy Kitsul and Jonathan H. Wright (http://www.econ2.jhu.edu/People/Wright/infops.pdf), who analyse the information from US CPI option prices (inflation floors and caps.) To be sure, there is no option with a strike price anywhere near Nick's disaster scenario, but I think the qualitative nature of their results are interesting.

From their abstract
"We compare the option-implied probability densities with those obtained by time series methods, and use this information to construct empirical pricing kernels. The options-implied densities assign
considerably more mass to extreme inflation outcomes (either deflation or high inflation) than do their time series counterparts. This yields a U-shaped empirical pricing kernel, with investors having high marginal utility in states of the world characterized by either deflation or high inflation."

I read this as saying that (1) option market participants have much higher forecast probablities of extreme inflation outcomes (i.e. high or low than statistical models produce, or (2) they are willing to pay an extra premium to insure themselves against those outcomes, or (3) some combination of the above. That evidence does not disprove Nick's conjecture (I don't think anything could) but it suggests that investors are worrying about both high and low inflation. I don't think symmetric worries can explain the type of effects that interest Nick.

[Ron Ronson]

In this example firms are dealing with a 1% chance of 100% inflation. Presumably as well as this uncertainty they will face other uncertainties specific to their businesses. It may well be that this 1% uncertainty is minor compared to these other uncertainties

My point is that all businesses in deciding whether to invest will factor in uncertainty. They "insure" against this uncertainty by requiring a higher level of profit. This higher profit will translate (via a lower demand for labor) into lower wages. As some workers will probably, at the margin, choose leisure over working at this lower wage overall employment and RDGP will be lower compared to the situation with no uncertainty. However the economy will still be in equilibrium and not in recession in my view.

[Peter N]

Why don't creditors write off the debts of those who can't pay? Because they represent savers who don't want to lose the money - retirees, pension funds and the like, and the people they represent vote. Inflationary solutions are a threat to them, so that approach is blocked as well. The details in Spain are complicated, but the underlying political dynamic is clear enough.

This is just another version of how the contest between creditors and debtors over who will bear the losses prevents solutions to the problem.

[Nick Rowe]

Simon: I have never lived in a house that burned down. But I still have fire insurance. But I can check my belief in the fat-tailed skewed distribution for my house by looking at cross-section data. Every year some houses do burn down.

That example shows that it is *sometimes* possible to test this sort of thing empirically. Or, as Vaidas, and your response to Phil suggests, maybe look at data on VIX, inflation options, or something like that?

[Peter N]

Isn't this a problem in preferences and perceived marginal utility? Why do people play the lottery? Why do people buy houses in flood zones? Why do stocks sell at a premium?

People are very bad at calculations involving probabilities, and they can have nonlinear time preferences. Thus we have compulsory flood insurance (as a condition of the mortgage), which turns the risk into a cost.

[RebelEconomist]

Isn't the problem the other way round? That is that monetary policy, fiscal policy, regulatory policy, accounting policy and every other relevant policy is set close to max ease, short of an inflationary reset. The slightest mistake and the house of cards finally collapses, so no-one wants to add to their exposure. And if you are exposed, you just sit tight and hope that the normal levels of real growth and inflation will eventually relax the stress and you can survive. I suspect that the example of higher inflation and slow recovery you have in mind is the UK! I am not sure where else has higher inflation and slow recovery, but my guess is that slow recovery is often associated with some sign of bust forestalled, like slow property price falls in Spain or fiscal deficits in Japan, that everyone knows is unsustainable.

[Peter N]

Think of Japan as a corporation owned by its employees through an ESOP. The company writes down a ton of assets every year and stays in operation through issuing new stock that is bought by the ESOP. It has 0 stockholders' equity and no debt, but the stock is worthless and the company shows no signs of becoming profitable. It pays a dividend by using its new equity.

The analogy seems clear enough. What happens when the employees retire and want to cash out?

[Simon van Norden]

Nick:

"That example shows that it is *sometimes* possible to test this sort of thing empirically." Yes....esp. if you have literally billions of houses to observe. But please note my earlier comment
1) we have less then 200 countries
2) those countries do not represent independent outcomes
3) we habe less than 200 observations per country (much less if we think old data, such as that from the Gold Standard, is not applicable.)
For those reasons, we'll have less precision in our estimation of extreme events for inflation than for housing.

Regarding information from financial markets, we can at best test *joint* hypotheses of rationality and risk-neutrality. Market prices don't let us distinguish between the probability that investors assign to outcomes and the risk premium they assign to them.

But let's get back to your original post...you're asking whether a 1% scenario was conceivable. I'm pointing out that our confidence interval for what could happen that infrequently is very large. To understand how large it is, why don't you try to see what (if anything) is *inconceivable* at the 1% level. Is a severe deflation/Great Depression? World War III? What do you think you can rule in or out?

[Makrointelligenz]

"So every year for 99 years, when firms set prices at the beginning of the year, they are 99% confident that monetary policy will continue unchanged, in which case they would do better by cutting their prices 1%. But there is a 1% chance that monetary policy will change, in which case they would do better by raising their prices 99%. So they leave their prices unchanged, because the expected benefits of cutting their prices by 1% are exactly balanced by the expected benefits of raising their prices by 99%."

I think you have got it wrong here, the benefit of having prices 1% higher in case of a very high inflation which occurs just 1% of the time does not offset the drawback of having the prices 1% too low in 99% of the cases. So I think with your expectations the firms should set its prices at the lower level so that they are correct 99% of the time.

[Alex1]

"Simon: I have never lived in a house that burned down. But I still have fire insurance. But I can check my belief in the fat-tailed skewed distribution for my house by looking at cross-section data. Every year some houses do burn down.

That example shows that it is *sometimes* possible to test this sort of thing empirically. Or, as Vaidas, and your response to Phil suggests, maybe look at data on VIX, inflation options, or something like that?"

I will say something incredibly naive now, but as I understand it the question at hand is: "are firms expectations of future monetary policy/macroeconomy like x", which I would test empirically by, well, asking them. Is that crazy? Is it so much more unreliable than looking at financial market proxies? What am I missing?

[Saturos]

Isn't this basically the explanation for the Japanese slump? (as much of it as is demand-side)