Monday, November 30, 2015

300 years of interest rates

In this post I just did a bit of educated guessing about where the monetary regime breaks should go over the past 300+ years in the UK (time series from here). Turns out all but one (in 1790) roughly correspond to points where interest rates changed from being/not being "pegged" (see here, here, and here):

I plan on doing a future post where I see if I can make this into a more scientific proposition rather than some vague empirical eyeballing ...

Principal component = information equilibrium model?

John Cochrane has an interesting paper/blog post about forecasting interest rates. I'm not sure I've absorbed it all quite yet, but I have a quick take.

The key point Cochrane is making is that the reason adding an inflation term to forecast models of interest rates improves them is really just because inflation has a trend -- a trend that roughly follows the first principal component term (PC1 at the link). Adding a trend (with principal components) allows you to get a really good fit -- and in fact it is this trend that captures most of the forecasting capability of the model. Cochrane says this means there a strong one-factor model of bond yields across all maturity. Basically, one interest rate describes them all pretty well.

This is just a cheesy overlay on the principal component graph, but that first principal component seems to be well described by the information equilibrium model:

Sunday, November 29, 2015

Maximum entropy better than game theory (again)

Today Nick Rowe mentions the dictator/ultimatum game (I choose to divide a pot and if you refuse the division, we both get nothing ... or the dictator version where you get no input). It's another case where the maximum entropy guess is better than game theory. Game theory says the solution is 99.9% (or more) for the dictator and x = 0.1% (or less) for the other person if people were truly rational. Maximum entropy guesses x ≈ 50%, but allows x ≤ 50% if information transfer is non-ideal. It also would guess x = 33% for three players, x = 25% for four, etc.

More on the rest of Nick's post later, but it brings up this again. And this.

Saturday, November 28, 2015

Department of Huh? Rent control edition

From Wikimedia Commons.

I got a couple paragraphs into this post at Project Syndicate by Brad DeLong and hit a stumbling block:
The reason that rent control is disliked is that it forbids transactions that would benefit both the renter and the landlord. When a government agency imposes a rent ceiling, it prohibits landlords from charging more than a set amount. This distorts the market, leaving empty apartments that landlords would be willing to rent at higher prices and preventing renters from offering what they are truly willing to pay.
Huh? DeLong is usually quite good at this sort of thing, so it's possible I'm missing something.

Why would a landlord choose zero rent and an empty apartment over renting at the rent ceiling? It's possible upkeep costs more than the rent ceiling with a renter rather than leaving the apartment empty, but I thought this was Econ 101 analysis.

And why would getting an apartment at the rent ceiling rate be worse for the renter than getting an apartment at the market rate? Sure Veblen goods come to mind (a thousand dollar a month NY loft apartment isn't as 'impressive' as a ten thousand dollar one ... to those who care about such things), as well as the ability to outbid someone else for the apartment.

I was under the impression that the reason price ceilings were bad in the Econ 101 sense is that they discouraged the building of new supply and acted as an implicit subsidy (basically producing shortages). If you can only get five hundred dollars a month for a one bedroom, it doesn't necessarily make as much sense to build a new building as it would if you could get a thousand. But additionally, more people are able to afford apartments, so fewer would be available. The result isn't empty apartments, but no apartments. And that's also what Wikipedia says.

So what does Info Econ 101 have to say about price ceilings?

In the case of a price minimum p0, there's a pretty simple solution. You basically restrict the price to p ∈ [p0, ∞) rather than p ∈ (0, ∞). However as the two spaces  (0, ∞)  and  [p0, ∞) are diffeomorphic to each other (except for the single point p0), you really end up with the same solution, just shifted. We can ignore the tiny detail of the single point at p0.

Taking the price to have a maximum value p0 is basically restricting the price to the domain (0, p0], which is more complicated. However there is a great function for mapping the space  (0, ∞) to (0, p0) where we'll again ignore the detail of including p0. We'll use an arctangent map so that the differential equation for the price with a price ceiling is the same as the differential equation without a price ceiling after the map arctan: (0, ∞) → (0, p0). This introduces an extra scale parameter (the "width" of the arctangent transition), but it can essentially be absorbed into the information transfer index. Now there are three regimes for the price ceiling. The first is where the ceiling is well above the equilibrium price:

The dashed line represents the demand curve with no price ceiling and the solid curves are the supply and demand curves with the price ceiling. For small shifts, this case is not very different than the original solution where the equilibrium price is marked with a black dot.

If the ceiling is comparable to (and below) the equilibrium price, you get a new equilibrium that is below -- but close to -- the ceiling:

And finally, if the price ceiling is well below the equilibrium, you get the standard Econ 101 result where the price is basically at the ceiling and the market is unresponsive to supply or demand shocks:

Update 11/29/2015

I just want to add that I am not advocating rent control, but rather the naive Info Econ 101 approach to understanding the effects that is more well-defined than the naive Econ 101 approach -- best would be a much more complex model.

Generally, my intuition is that a subsidy (or progressive taxation) would probably be the optimal approach. But it's also just a complex problem since space/land is genuinely limited.

Non-deflation non-surprise

Why didn’t the sustained high unemployment after 2008 push us into deflation? There are some popular stories — downward nominal wage rigidity that makes the long-run Phillips curve non-vertical at low inflation rates, “anchored” inflation expectations — and I cite those stories myself. But standard discourse on macroeconomics has not fully taken the non-deflation surprise into account.
That was Paul Krugman in his post from today.

Non-deflation isn't as much of a surprise in the information equilibrium model. Over time the response to inflation from output shocks has become approximately zero. And it's related to the liquidity trap -- the lack of a response to the price level from monetary expansion.

Thursday, November 26, 2015

The minimum wage in Info Econ 101

I added an update to this post about using supply and demand diagrams for the minimum wage, but thought it would be good to do a post on its own. The traditional Econ 101 use of supply and demand diagrams looks like this:

If you set a price above the equilibrium price P* then the new equilibrium market solution becomes the intersection of the demand curve and the minimum wage and the difference between the intersection of the demand curve and the supply curve with the minimum wage value is the amount of unemployment.

Some questions arise:

Why the demand curve intersection point? Why not the supply curve intersection point? This basically assumes that employers are at their limits, rather than say people are staying out of the labor force because a minimum wage job at a lower minimum wage isn't worth it.

What do the curves below the minimum mean? These represent the "illegal" supply and demand for labor -- the desire to employ people at less than the legal minimum wage. I personally would like to drive well over the speed limit, but that piece of the solution space doesn't necessarily enter into my speed decisions that are more based on traffic and road conditions. I'd really like to go a speed that is impossible for my car to attain ... but that should have even less impact.

Anyway, the Info Econ 101 (or Info Econ 1100101, ha! there's a nerd joke for you) picture is different:

The original solution to the information equilibrium condition is no longer a solution in the case of a minimum wage. The intersection point with the minimum wage and the original demand curve (or supply curve) is no longer a meaningful point. The general information equilibrium solution just says both supply and demand go up ... at least in the simplified presentation. There could be all kinds of more complex factors going on.

However that is the point. The Econ 101 analysis is not just oversimplified but wrong according to data. The Econ 101 view above is also wrong in the Info Econ 101 view which is itself simplified, but isn't inconsistent with data.
Econ 101: simple but inconsistent with data
Info Econ 101: simple and consistent with data

Wednesday, November 25, 2015

Speaking of math ...

... maybe you should prefer to use the IT model for quantitative predictions of things like inflation.

The new core PCE data for October says 0.1% inflation. The error is looking pretty good for the IT model as well (the IT model is doing as well as a model that consists of a smoothed version of the data -- gray dashed line):