"Lowflation" is a meaningful concept

Scott Sumner is upset about using inflation to describe economies. He says that inflation doesn't describe shocks and that NGDP (of course) is a better measure. He then gives Portugal and Switzerland as an example where inflation isn't very indicative.

I thought this would be a good place to use my more precise definition of nominal shocks that takes into account monetary and fiscal impacts to NGDP. Taking this on included a pretty interesting challenge for the information transfer model: how do you describe Portugal?

In the information transfer model, one needs NGDP, CPI and currency data (M0) for the economy in question. Portugal doesn't have the last one, at least not on its own. So I posited that Portugal's M0 was αM0 for the Eurozone (i.e. Portugal has a fixed fraction of the Euro currency) where α was a free parameter. The best fit gave α = 0.052, which was sensible: Portugal is about 5% of the Eurozone economy. So here are the fits to the price level for the EU, Portugal and Switzerland from 2007-2014:

The nominal shocks follow from the price level (see the procedure outlined at the bottom of this post) by taking out the effect of the expansion of the monetary base and looking at the remainder -- this remainder is the nominal shock. Here are the nominal shocks for Switzerland and Portugal:

You can see the great recession shock at the end of 2008 and the subsequent shock to Portugal due to the post-crisis austerity measures. Since these three regions are all experiencing "lowflation", these shocks turn out to be roughly correlated with changes in NGDP. Here for example is the EU (change in NGDP is the dotted line, and the solid line is from the previous graph):

The pictures for Portugal and Switzerland are similar (I didn't want to put too many graphs in this one post). So Sumner is right: NGDP changes are a pretty good indicator. At least when inflation is low ... here is the same graph for the US going back to the 1980s:

As inflation increases, the actual nominal shocks (solid) and changes in NGDP (dotted) diverge. One benefit of the information transfer model nominal shocks is that going through zero is generally associated with a recession. Additionally, negative shocks are associated with an accelerating unemployment rate:

In particular note that the small negative shocks in the mid-to-late 1980s and after the 1991 recession (neither of which are associated with a recession) appear to arrest the fall in the unemployment rate. Although it is correlated, the change in NGDP doesn't have this meaningful zero-crossing quality.

The take-away is this: when you have "lowflation", you can say ΔNGDP ≈ nominal shocks, making NGDP a decent metric. However there is more information you can extract using the information transfer model definition of nominal shocks, and that definition is based in part on the price level.

Additionally, "lowflation" is also a good indicator of how monetary policy will affect interest rates. When an economy has low inflation, monetary expansion makes interest rates fall (the liquidity effect dominates). When inflation is high, monetary expansion makes interest rates rise (the income/inflation effect dominates).

You can't get everything from NGDP.

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 2012, 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*.

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.

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.

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.

Update 14 January 2017

There might be some issues with the unemployment rate data, however.

Beware implicit modeling

One of the difficulties you have when you are steeped in a subject for a long time is that you forget when you are making implicit modeling assumptions. Nick Rowe claims that the accounting identity Y = C + I + G + NX is useless, in opposition to the "first-order Keynesian" view that if government spending G → G + δG during a recession we will get real output Y → Y + δG. He's making a claim for the null hypothesis, but it's really hard to say which is a less informative prior. Does a signal from G make it to Y or does it get absorbed by C, I and NX?

I probably didn't make it exactly as clear as I would have liked in my comment on the page, but the idea was that the identity is useless is as much a modeling assumption as the first-order Keynesian view. If G → G + δG, then

Y → C + (∂C/∂G) δG  + I + (∂I/∂G) δG + G + (∂G/∂G) δG + NX + (∂NX/∂G) δG

= Y + δG + (∂C/∂G) δG  + (∂I/∂G) δG + (∂NX/∂G) δG

The "first-order Keynesian" view assumes that (during a recession)

|∂C/∂G| , |∂I/∂G| , |∂NX/∂G| << 1

The "useless accounting identity" view assumes that

|∂C/∂G| , |∂I/∂G| , |∂NX/∂G| ~ 1

The only way you can't know what happens if G → G + δG is if it is possible for some offsetting effect or some amplifying effect of equal magnitude that makes δY < δG or δY > δG, respectively. Note that these are structurally similar assumptions about the dependence of the other variables on changes in G.

Nick also says that the first-order Keynesian view could be used to say that because Y = C + S + T, we could raise taxes (T) to get more real output. However, that is not what that equation states; it states that increasing tax revenue [1] would lead to more real output. Does raising taxes increase tax revenue in a recession? That becomes a modeling assumption. "Raising taxes" is analogous not to increasing government spending but rather to e.g. increasing the number of fixed-price RFP's the government puts out. While increasing the number of fixed price RFP's could lead to more businesses submitting bids and an increase in government outlays so that G → G + δG, it may be such that no business considers any of the potential contracts to be a good deal.

The first-order Keynesian assumes in this case is that:

|∂C/∂T| , |∂S/∂T| ~ 1

While the Rowe reductio ad absurdum assumes

|∂C/∂T| , |∂S/∂T| << 1

Again, these are structurally similar assumptions.

Rowe believes it is "warped" not to assume the same general dependence of C, I and NX on G as you do for C and S on T.

Update 7/24, 9pm PDT: I think I'd like to make this a little stronger. Rowe's claim is that e.g. consumption C depends to first order on government spending G, i.e.

C = a + b G + ...

with b ~ 1. [2] (This could also apply to I and/or NX, or all three.)

For taxes T, C ~ a + b T makes sense: my personal consumption is basically C = a - S - T (consumption is what is left over after savings and taxes). But for government spending? I'm pretty sure when the stimulus passed, I didn't change my behavior. Maybe I "expected" it to pass and priced it in already.

Another way of putting this is that Rowe is saying the basket of goods comprising C isn't actually at a local maximum or minimum with respect to the given level of government spending. Maybe that is true, but then, that's a model assumption. Consumption isn't utility, but if you take consumption to be proportional to utility, then Rowe is assuming that utility isn't maximized at a given fixed level of government spending. It's still implicit modeling whatever you call it.

[1] More tax revenue could mean we have more output (hence causality went the other way), or that the market took raising taxes as a sign that the recession is over, creating expectations of an improved economy. All kinds of theories could be at work.

[2] It is possible that C = a + c G^2 + ... with an unnatural coefficient c >> 1, but that is an unnatural assumption.

New preprint on information transfer

Peter Fielitz and Guenter Borchardt have a new version of their paper on the information transfer model up on the arXiv. They updated it with a citation of this blog, which is quite an honor since citing blogs is a somewhat non-standard practice. The paper has an interesting discussion relevant to economics in Appendix A on the question of how you transfer information with a 1-symbol system where log 1 = 0.