Thursday, July 24, 2014

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.

Wednesday, July 23, 2014

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.

Tuesday, July 22, 2014

Is monetary policy best?

Simon Wren-Lewis is annoyed with market monetarists who are annoyed with Paul Krugman who said that they have no political home in the US. Putting my two cents in, Krugman is right. My family consists of pretty stereotypical conservatives, and about the only thing that would make them say that "printing money" to improve the economy is a good thing is to say Obama is against it or that we'll put Reagan's face on it.

But Wren-Lewis reiterated the idea that today's "Keynesians" and market monetarists agree that monetary policy is the best macro stabilization policy when you're not at the zero lower bound.

Is it?

The more I look into this, the less the monetarist program for macroeconomic stabilization makes sense.
Recessions appear to be discrete shocks that are on top of a long run trend

In the information transfer model, the long run trend runs roughshod right past the shock. In this picture, monetary stabilization consists of temporarily altering the trend to offset a temporary shock and then returning to trend. It's a bit like sailing a ship, getting hit by a gust of wind, and lashing the helm to new course (monetary policy) [1] instead of just turning the wheel temporarily (fiscal policy).

However, in this picture, the economy is already deviating from the trend. What makes any macroeconomist think moving the trend will mean that the deviation will come along with it? Sure, it is not entirely implausible -- in turning the ship to counter a gust of wind, there is no particular reason to believe that the wind will get stronger or weaker in response. But this means you really need a theory of the trends and the shocks [2].

Employment recoveries in recessions seem unaffected by any kind of policy

The employment recovery from a recession has a surprising regularity across many decades (see here for the US and here for Australia). The data almost pose the question themselves: Does any kind of policy actually do anything macroeconomically relevant for unemployment? People do not seem to get hired back faster if monetary policy is "loose" (1960s and 1970s) or it is "tight" (2008). Nor do they seem to get hired back faster if there is significant fiscal stimulus (2008) or not (1991).

So if neither monetary policy nor fiscal policy help speed up the fall in unemployment, then government intervention should not be assessed through macroeconomic relationships with unemployment, but rather assessed via the direct impact of the intervention.

The simplest version of direct impact is something like the Depression-era WPA: the government directly hires people. Additional measures where the government contracts with construction companies to dig holes and fill them up again also fits this bill (preventing layoffs and encouraging hiring).

However, whether you pay for this by borrowing or by printing money does not seem to have a macroeconomic impact on the decline of the unemployment rate. The key point is that the macroeconomic rationales for not using fiscal policy are therefore pretty irrelevant. Another way to put this is that the purported negative consequences of fiscal policy won't make the unemployment rate fall any slower. Crowding out? So what? That won't cause unemployment to fall any slower. Monetary offset? So what? That won't cause unemployment to fall any slower.

Yes, fiscal policy may not make the unemployment rate fall faster, but at least it helps the people that are laid off put food on the table or the people that aren't laid off keep their jobs. And maybe you can fix some of the roads while you're at it. Monetary policy doesn't help people directly -- unless you print money and give it to people.
Note:  I am not saying fiscal or monetary policy don't have an effect on the initial rise in unemployment. My intuition (guess) is that the initial rise in unemployment from the natural rate at the onset of a recession is likely entirely due to human behavior (anxiety/panic), therefore bold assertions from the government couched in the dominant economic paradigm at the time easily calm people down and arrest the rise in unemployment. (This would go part way towards explaining why there are no mini-recessions using something like the "recognition" mechanism Sumner describes.)

Monetary policy sometimes doesn't even work on the things it can affect

In the information transfer model, the impact of monetary policy becomes muted as the size of the economy and monetary base grow. Returning to the ship analogy, the effect of the helm becomes less relevant as the current grows. At that point, directly affecting the current -- e.g. the G in C + I + G + (X-M) -- becomes more relevant.

When it does work, monetary policy works by kind of a dirty trick

Although not the entirety of the argument in favor of monetary macroeconomic stabilization, the mechanism by which it operates is to use inflation to make workers accept a real wage cut while not taking a nominal wage cut (also could be applied to firms or households). Because of money illusion, humans focus on the nominal values so don't notice their real income is falling.

In the information transfer model, there is significant RGDP growth that is caused by expansion of the medium of exchange when the monetary base is small [3], so this is not necessarily true of the information transfer model. However, monetary policy advocates aren't advocating the information transfer model.
If you put these together, you get that monetary policy is a dirty trick that doesn't always work, doesn't seem to help unemployment, asks us to change the trend in response to a temporary event and requires us to swallow a bunch of theory that hasn't been empirically tested. Where do I sign up?

[1] Of course, the real idea behind the market monetarism is that you can just tell everyone on the ship you're still headed for Boston -- you don't necessarily have to turn the wheel -- and you'll eventually get there.

[2] In the market monetarist view, expectations are important. If recessions are temporary shocks then any monetary policy compensating for it will also be perceived as temporary -- and hence not work. The only way this works is if either recessions never happen so monetary policy never has to change in response to it, or if people are tricked into thinking the policy is permanent (see also the last bolded point).

[3] I actually think this is a major issue for monetary economics. How do economies get started? Well, if you create a monetary system you get an economy -- that is RGDP growth. At some point a doubling of the monetary base may just lead to inflation (according to long run neutrality), but when the base is small, a doubling of the base should have some real effect by allowing more transactions to occur.

Sunday, July 20, 2014

Rationality is beside the point

Brad DeLong has a post wherein he poses the question
Given that people aren't rational Bayesian expected utility-theory decision makers, what do economists think that they are doing modeling markets as if they are populated by agents who are?
intimating that maybe some ideal modeling scheme exists where you just need to replace the "rational Bayesian" with "behavioral". Along with most economists out there with objections to rational expectations, it seems most econoblog commenters are objecting to the "rational", rather than e.g. me who objects to the "expectations".

DeLong then quotes Andrew Gelman on how nonlinear utility functions used in economics are suspect and how students believe each step of a utility argument, but are "unhappy with the conclusion". The students seem confused by their own reasoning. Noah Smith has a post from earlier this year on other problems with utility functions. Cosma Shalizi sums it up pretty well (emphasis mine):

The foundation on which the neo-classical framework is raised, though, is an idea about rational agents: rationality means maximizing expected utility, where expectations come from maintaining a coherent subjective probability distribution, updated through Bayes's rule; moreover, the utility function is strictly self-regarding. This is a very well-specified idea, readily formalized in clean and elegant mathematics. Moreover, there's pretty much only one way to formalize it, which makes the mathematical modeler's life much easier. All of this appeals to certain temperaments, mine very much included. Alas, experimental psychology, and still more experimental economics, amply demonstrate that empirically it's just wrong.
All true.

Yet markets seem to work.

This is actually pretty remarkable. We're totally irrational potentially hyperbolic discounters subject to framing effects ... yet markets seem to work.

But! This is only pretty remarkable if you see markets as some kind of system that efficiently allocates resources. If we look at my recent post where I attempt a definition of aggregate demand using the information transfer model, then we see the efficient allocation of resources is not the proper frame. A market transfers any information, not necessarily useful, rational or efficient information. Transferring completely crazy information accurately is considered more of a success in this framework than transferring a correct prediction about the future only nine times out ten.

"Gold is going to a million dollars an ounce."

"Inflation will take off at any minute."

The market is "inefficient" when these statements are inaccurately transferred from the aggregate demand to the aggregate supply, not when they are wrong. Of course, for the information to be transferred accurately some element of the aggregate supply has to receive the information accurately. And the world might work in such a way that really crazy information is almost never received accurately -- the person on the other end of a gold transaction really just wants to make a not unreasonable amount of money and thinks gold is going to fall in value [1]. Maybe our normal cognitive biases are transferred accurately, yet markets work [2]. I don't know all the answers. 

I do know that assuming the information is transferred fairly accurately gives you supply and demand diagrams. It also does a good job predicting inflation. So maybe we shouldn't worry too much about rationality or individual utility functions.

At least, if you use the information transfer model.

[1] It is interesting that people who are selling gold seem in advertisements seem to put forward the attitude that one should have when one wants to buy gold ... it's a safe asset, you'll stay rich or become richer if you buy gold; shouldn't these sellers just hold on to their gold? This is the opposite of many other advertisements which usually say something like we have a lot of TVs and we can't possibly watch them all so we implore you to come on down to Crazy Eddie's and take them off our hands.

[2] I'd like to make the distinction between where an unfettered market leads to a Pareto efficient allocation and where an unfettered market leads to some sub-optimal allocation. In both cases, the information transfer may be "efficient" in the sense that the information received is the information transmitted. It may not be socially optimal.

Friday, July 18, 2014

US inflation predictions

If you looked carefully at the previous post, you might have noticed that the lines extended a bit beyond 2014. That was because I was also going to produce some inflation predictions for the US using the same procedure. Here is US inflation out to 2020 using predictors 5-20 years back (they turn out to be mostly consistent):

The same caveats apply as in this prediction of Canadian inflation: this assumes the log-linear extrapolation of NGDP and M0 using the prior 10 years holds.

Inflation prediction errors

Essentially following the procedure of the previous post -- fitting the price level function P to data from 1960 to a year Y, and then log-linearly extrapolating NGDP and M0 (currency) from Y to 2014 to find P(y>Y) and the inflation rate i(y>Y) = d log P/dt -- I thought I'd see how the errors evolve as you add more data. The log-linear extrapolations only used the past 10 years of data starting from Y.

In one sense, I wanted to figure out if the previous post was a fluke (it isn't), and also what the error would be on predicting inflation 2014 - Y years out.

Here are the inflation extrapolations colored in rainbow colors with red being the most recent and purple being the most distant past (the CPI inflation data is the green jagged line):

And here are the errors (absolute value of the mean difference between the prediction and the measured CPI) as function of years out the prediction is made (2014 - Y):

The graph shows the irreducible measurement errors in gray. Inflation is not a smooth curve and the measurement of CPI contains some fluctuations month to month. If one averages over shorter and shorter periods, even if you have the trend exactly right, you're going to get larger and larger errors. I estimated this effect by finding the distribution of errors around a linear fit to 1994 to 2007 inflation data (a fairly straight line) to estimate the error distribution. Using the estimated distribution, I ran Monte Carlo simulations of the absolute value of the mean error averaged over different time periods to produce the gray band of points. You can see that this accounts for much of the model prediction error over shorter time periods (red points on the left side of the graph above). Additionally, the 12 basis point error from Y = 2007 (7 years back from 2014) in the previous post is typical for extrapolation from that time period and likely represents only irreducible error.

That is a pretty startling piece of information. It means you likely can't do any better than the information transfer model in predicting inflation in the medium term (5-15 years out).

Thursday, July 17, 2014

Better than TIPS

Scott Sumner asked (in comments on his post on AD) if the information transfer model (ITM) was better at predicting inflation (gray line in the graph above) than TIPS spreads (the difference between inflation indexed treasuries and ordinary treasuries of the same maturity, red jagged line in the graph above). The TIPS spread on a given day represents the market's future expected average inflation over the maturity of the treasury (we'll use the 10-year).

Well, the ITM is better -- about 5 times better. Actually, the ITM was better at predicting inflation even though the worst economic crisis since the Great Depression intervened!

I fit the ITM model to 1960-2006 Q4 data and then did a log-linear extrapolation of NGDP  and M0 (currency in circulation) starting in 2007 to predict inflation from 2007 to 2014 Q1. That's the blue line in the graph above.

The 10-year TIPS spread from Q1 2007 represents the market's best guess at the average inflation rate over the next 10 years, and so should also represent the average inflation rate from 2007 to 2014 Q1. That's the red straight line.

The ITM model average difference from 2007 to 2014 was -12 basis points, while the TIPS model was on average off by +66 bp.

Actually, the ITM totally dominates the market prediction -- the 2007 prediction of the ITM was better than the TIPS prediction for almost every date you start the TIPS prediction. This graph shows the ITM 2007 prediction difference alongside the TIPS prediction from the given year:

The ITM prediction from 2007 was a better predictor of inflation in 2013 than the TIPS spreads from 2013! The ITM model falls apart in the last couple months, but then the past couple months only represent a couple CPI data points. The ITM model represents a long run trend, so its predictions will have a higher error over short runs of data. The market random guess TIPS spread is better at short runs because in the short run, inflation this month is about what inflation was last month.

PS It seems the TIPS spread is a good predictor of the TIPS spread though.