Friday, August 1, 2014

When will information theory influence economics?

Easy. By the end of 2015.

That's a joke; I'm celebrating the highest monthly pageview total I've gotten so far (still pretty small -- big blogs get as many per day), so I decided to project when my pageviews would reach the level of Scott Sumner's blog themoneyillusion.com. Since Sumner managed to influence the the post-financial crisis debate and even got Ben Bernanke talking about NGDP targeting, I thought that would be a good guide to the required number of pageviews per month**. I wasn't able to get a firm number, but on a log scale it doesn't matter so much. Luckily, my pageviews are pretty log-linear, so the extrapolation is easy:


Special thanks to Tom Brown for his advocacy and linking back to me here. Thanks also to the Feedly readers, Twitter followers and Google+ followers for your regular check-ins. (Sorry to the Feedly readers for the math being messed up and the pictures always coming out huge, messing up the flow of the text.)

** It doesn't really matter the quality of the arguments, just the number of people who see them, right? (Again, joking.)

Zen kōan inflation targeting

Tyler Cowen suggests the rather silly "target 4% to achieve 2% inflation" monetary policy for the ECB. I'm not sure if he actually meant it as a joke or not, but it certainly illustrates the utter ridiculousness of model-independent expectations that aren't the constrained "rational expectations" typically used in economic models.

Rational expectations are perfectly fine: you have an underlying model and the economic agents expect e.g. the level of inflation predicted by the model. In some sense, rational expectations make the economic agents superfluous. If the agents are just going to parrot back the expected values of model random variables, why not just say they aren't there. A better word for "rational" expectations would be model-dependent expectations, which I contrast with model-independent (MI) expectations above. These MI expectations are those typically invoked by e.g. Scott Sumner and Nick Rowe.

Cowen suggests that the ECB could target 2x% in order to achieve x% inflation relying on MI expectations. With MI expectations however, if the ECB doesn't keep this a secret, the agents will learn 2x really means x, and then the 4% inflation target will really be a 1% inflation target since 4% means the ECB is aiming for 2% so will only achieve 1%. Okay, then.

But here's where it really gets silly. If you see the ECB's current 2% target as not credible, then aiming for 4% and resulting in 2% manufactures a credible 2% inflation target out of an incredible one by renaming "two" as "four". Incredible!

Another solution, proposed by Scott Sumner, is that the ECB doesn't actually want 2% inflation, even though it says it does, but rather the ECB communicates its inflation targets by talking about unemployment and competitiveness. Yes, the official inflation target is 2%, but that is irrelevant: the actual inflation target is 1% because that is what makes the PIIGS competitive.

[*slice*]

Yes, that was Occam's razor.

Sure, countries seem to be able to achieve their inflation targets most of the time (in fact, the quantity theory of money works for a lot of cases), but now we have a series of countries that seem to be undershooting them a bit: Japan, US, EU, Canada ... etc. Maybe there is a maximum achievable inflation rate i* for an economy? For countries with inflation targets below this maximum, inflation targeting works: the central bank says 2%, it gets 2%. For countries with inflation targets above this level, all you get is the maximum i*.

The information transfer model produces this result. At every point on the price level surface (see e.g. here, or at the top right of this blog if you're not viewing it on a mobile device), there is a maximum gradient (inflation rate). This is the inflation limit at that point. During the 1960s in the US, this maximum inflation rate was 10% or more.

EU i* is predicted to be low by this model (almost zero) -- below their target of 2%. For the US, i* is just below 2%.

Where does this maximum come from? Money has two purposes: it is the medium of exchange, allowing transactions to occur and it is the unit of account, Fisher's measuring stick. In the information transfer model, money allows people to exchange information and measure the units of the information. As you increase the amount of money, the relative impact of these different capacities changes. You can imagine the unit of account as a box that gets smaller as more money is added to the system, while the medium of exchange is the number of boxes. The height of that stack is proportional to the price level. And it looks something like this:


Japan is on the right side of this diagram, while, say, China in on the left. The maximum inflation rate i* is the slope, higher on the left and lower on the right.

This is Cowen's "most economical model".

The economic future of China is so bright (I gotta wear shades)

Another request from Jon Prince in comments, this time for a projection of the future of China's economy with the information transfer model. His particular questions were about whether China's growth rate was sustainable and how long before the Chinese economy reaches information trap/liquidity trap conditions. I don't have data on interest rates for Chinese government debt, so this prediction it will only be based on the slowing of NGDP and the price level with respect to currency growth.

This will be based on the model in this post and starts with an extrapolation of NGDP and currency (M0):


This path results in the following predictions for RGDP growth, inflation, NGDP growth and the price level:





Although there is a slow fall in growth, these graphs show above 8% RGDP growth (and above 10% NGDP growth) through 2020. There will still be some fairly large fluctuations around these predictions, though. Overall, this is a pretty good position for an economy and I don't see any liquidity traps in China's near future. China's very mild economic deceleration will probably be attributed to many things in the mainstream economic media: slowing growth as the economy runs out of catch-up growth opportunities, moving of low cost manufacturing to poorer countries, economic inequality, etc. The real reason is that it's just a manifestation of a universal behavior of large economies -- at least if the information transfer model is right.

Prediction update: not bad for five parameters

I made some predictions back in March about the path of the US economy, so with the release of unemployment data today, I thought I'd update the plots from that post to see how the information transfer model is doing. Overall, it's doing just fine.

This first graph wasn't a prediction of the model, but instead the projected path of NGDP and money that forms the basis of the inflation, RGDP and interest rate predictions. It turns out the economy has followed these reasonably well:


That means the predictions of the model should still apply. However, it appears now that there was a fairly large NGDP shock coming from the sequester:


This is contra Sumner's view that NGDP actually did better in 2013 than 2013, and shows the importance of having a model. NGDP can have the same path for both Sumner and myself, but he sees growth (despite the data) and I show a large shock following the sequester.

Here is year over year (YoY) inflation:


A bit high, but well within the normal fluctuations for YoY inflation. Inflation and NGDP come together to give us YoY RGDP growth:


Here are the interest rates:


10 year rates are a bit above the expected value (I used the "upper bound' version of the interest rate model in the prediction).

And finally, we come to the unemployment rate. The information transfer model only says that the blue rectangular area is the economy's "natural rate", so the predicted curve is only a quadratic extrapolation. The prediction is that unemployment will start to flatten out when the prediction reaches the blue band (i.e we should start to see "positive curvature")


Overall, the model seems to be working just fine.

PS: There are actually seven parameters M0, γ, α, κi, c (interest rate), κL, and κU, but the normalization of the price level is arbitrary (α could be redefined to be 1 by picking a different year as the base of the price level -- and it actually drops out of all the predictions above) and κL and κU only appear as the ratio u* = κL/κU. Therefore there are only five meaningful parameters: M0, γ, κi, c, and u*.

Thursday, July 31, 2014

I do not think that calculation means what you think it means

It took me a minute to figure out exactly how Sumner came up with this result. I assume that Sumner meant 2013 Q4 as the ending point of his second period starting at 2014 Q4, so that wasn't the problem. The problem is that Sumner calculated the NGDP growth at some point between 2011 Q4 and 2012 Q4 and at another point between 2012 Q4 and 2013 Q4, not the average growth during those two period (or any other meaningful number).

See, Sumner took the end points of the time periods and calculated the % change between them. I show more digits to give some evidence that I did the same calculation Sumner did:

2011 Q4 to 2012 Q4: 3.46652% (Sumner rounds to 3.47%)
2012 Q4 to 2013 Q4: 4.56636% (Sumner rounds to 4.57%)

According to the mean value theorem, taking the slope between the endpoints of a curve only means the slope of some presumably continuous curve achieved that value somewhere in between those end points. It is not the average growth for the period (or really anything at all).

Of course, this isn't the way you should do this. NGDP is a number with some measurement error, so relying on only the two end points means that you massively increase the error in the derived quantity.

What is the (omitted) error on Sumner's measurement? I assumed a log-linear model of GDP from 2009 Q4 to 2014 Q2 and calculated the error bands. The result is plotted here:


If we use these error bars to predict the error on Sumner's measurement, we get

2011 Q4 to 2012 Q4: 3.8 ± 1.6%
2012 Q4 to 2013 Q4: 3.8 ± 1.6%

That isn't a typo. The two periods have exactly the same growth rate. The difference between the two periods is entirely measurement error.

We can try a different method: average the growth rate numbers. The period starting from 2009 Q4 also has an average growth rate of 3.8% by this method, however the error is larger at ± 1.9%. Here is a graph:


If you look at this last graph, you can start to see how misleading the numbers in Sumner's post are. I see almost constant growth with random fluctuations around it. If you average these numbers for Sumner's two periods, you end up with another inconclusive result:

2011 Q4 to 2012 Q4: 3.7 ± 1.3%
2012 Q4 to 2013 Q4: 3.9 ± 1.7%

There was no failed experiment and market monetarism didn't pass any test. It's all inconclusive.

PS Sumner's commenter Kailer Mullet is incorrect: the single decimal precision (nearest 0.1%) is exactly how much precision is warranted by these numbers. Adding another decimal place is pure noise and taking one away loses information.

Tuesday, July 29, 2014

On travel again

I'm out in the middle of nowhere for the next two weeks, so blogging will be bursty as I have little else to do in the evenings, but will be busy at the real job all day. I'm working on the piece about the history of expectations and human behavior in economics hinted at in comments on this post.

Monday, July 28, 2014

Chinese statistics seem just fine

I got a request to run the model for China in an email from Jonathan Prince, so here it is. I half expected to get nonsensical results; the "conventional wisdom" in the US is that Chinese statistics are suspect (see here for example). However, after running the model using data from FRED (derived from OECD and IMF data), it turns out that aside from potentially understating inflation in the late 90s/early 2000s, the results for China are largely in line with other countries. Here are the NGDP-M0 and P-M0 plots I've been showing lately with China added:


Here is the actual model fit with parameters (everything below shows model calculations in blue and data in green):


You can see the understatement of inflation in 1999-2000. The information transfer index is high, but constant, meaning that the Chinese economy roughly follows something like the quantity theory of money (however the rate of change of the price level is smaller than the rate of change in the money supply, i.e. log P ~ k log M0 with k < 1):


Due to the seasonal effects and the lack of quarterly NGDP data or "core" CPI data, the year over year inflation is a bit noisy, but the model seems to give us something that looks like "core" CPI:


Again, inflation seems to be understated in 1999-2000. Overall, China seems like a pretty typical high-growth large economy, like the US in the 1960s.