More on sticky wages

Back in this post, I mentioned that the observed distribution could produce the slight deviation from from a constant price P in the market P:NGDP→NW (aggregate demand sending signals to nominal wages). I'll put a little bit of meat on that claim here. Let's start with a population with a distribution of incomes:

Now let's select some fraction of this distribution to receive a normally distributed raise. This is accomplished by drawing from a Bernoulli distribution and a normal distribution and taking the product; the 0's of the Bernoulli draw mean zero raise and the 1's mean a normally distributed raise. Here is the resulting distribution (over the entire period from 1960-2013):

Compare this with the distribution here. And here is the model result from the sticky wage post (red) alongside this simulation (black), which shows the plausibility of this observed distribution leading to the deviation from sticky wages:

Is there a sign of inequality in the price level?

When I was writing this post, I noticed that the aggregate demand-labor supply model (NGDP-LS) didn't do so well at the edges of the data (it did well from 1970s-1990s, but had deviations before and after) and it made me wonder if inequality didn't have something to do with it. In the post itself, I mentioned that the tiny amount of wage flexibility accounted for some of it. Here I want to speculate about a different mechanism: income inequality.

The mechanism would be that NGDP growth would be faster than labor supply growth as gains are taken by the rich, meaning that the derivative of the model (NGDP/LS) would be greater than the derivative of the price level P. This is what happens in the graph from the post linked above (model is blue, price level data is green):

I grabbed some inequality data from Saez to see if the ratio of the derivatives was correlated. It turns out it isn't unless you add an 18 year lag to the inequality data. It is possible it takes awhile for the price level to catch up with inequality, but I'll chalk this one up as inconclusive. Here is the relevant graph with the inequality data in green and the derivative data in blue along with a smoothing of the data:

O-Canada

Scott Sumner linked to Nick Rowe today which inspired me to run the numbers for Canada. Unfortunately I was only able to find monetary base data up to June of 2009 (any help?). At least it shows the start of the recession (which Nick Rowe says does not show up in the CPI data). Here is the reference for the model I'm using for the price level, and here is the reference for the interest rate model.

And here are the graphs (model in blue, data in green):

And here is where Canada appears in the scrum (see here for the definition of this plot):

Basically, Canada is sort of halfway between the US and Australia hence it had a mild recession instead of not having one at all (AU) or a severe one (US). Canada returned to its pre-2009 trend after the recession, having only increased its monetary base by a small amount. Since I didn't have the actual data after 2009, I did an extrapolation from the piece of the trend I did have in the graph (small dotted green line). Canada appears to still be farther away from the "liquidity trap" (indicated by the information trap criterion, the dotted black line) than the US, Japan, the UK or the EU. Here is a graph of the path of the Canadian economy in MB-NGDP space analogous to this one for the US:

The liquidity trap rate is about 0.5%, but the current rates in Canada are above 1%.

Scientific controls and sampling

I'm not sure I completely understand what Scott Sumner (or Mark Sadowski) is getting at in this post. You can't see the effect of fiscal policy if your sample has the same monetary policy (e.g. US states or EU member nations)? For reference, Sumner's description of monetary offset is laid out in the paper linked in this post. Basically, it says if fiscal policy increases AD, this will raise inflation which will cause the central bank to react to bring inflation back to target. In the long run, the AD boost is offset by monetary policy.

In the cases we are looking at (EU member nations), each has the same monetary authority (the ECB) so the monetary policy is an EU-wide aggregate while the fiscal policy is local to the member nations. While Sumner's model has a plausible mechanism for the ECB to offset the average fall in AD due to austerity, it wouldn't offset the relative fall between nations. The nations engaging in more austerity will be worse off than those engaging in less. This still makes Paul Krugman's point that austerity is bad.

On a more fundamental level, you'd think you'd want to control for monetary policy which means you'd want to have the same monetary policy in the sample population. If having the same monetary policy makes the effect you want to see unobservable, then how do you know the offset exists in the first place? A mysterious force counteracting another force resulting in no effect? It's like saying my glass of whisky here is experiencing a force to the right that is always counteracted by a force to the left [1] -- how did I ever know about either? 

Speaking of forces, I'd like to bring up the information transfer picture. It's actually a picture:

Depending on the current location of the economy in the space of monetary base (MB) and NGDP, the direction of the "force" due to fiscal shifts and monetary shifts range from almost parallel (a quantity theory economy) to orthogonal (a liquidity trap economy). In the former, you can have almost complete monetary offset. In the latter, monetary policy isn't even pushing in the right direction (it has no projection along the NGDP axis). This goes back to Krugman's sample and Sadowski's "unskewed" version: if the countries are all in a liquidity trap, then you're going to see the effects of austerity. If you're not, then monetary policy would have offset the fall in AD from the recession in the first place an no austerity would've been necessary (and if it had been tried it would have been offset).

[1] Well, it actually is from air pressure -- but we know about that from different experiments. Which is kind of my point.

The Phillips curve

Earlier this year John Quiggin made the bold claim that macroeconomics went wrong in 1958 after the discovery of the Phillips curve. I've been working over the past couple months trying to figure out how the Phillips curve comes about in the information transfer framework and I basically come to the same conclusion. Here is my bold claim:

The Phillips curve is real but barely useful regularity in the data that has been completely misinterpreted.

OK, let's begin. The curve is generally drawn as a downward sloping curve in unemployment rate-inflation rate space. In the information transfer model, this immediately says that the information source is aggregate demand (NGDP), the information destination is the supply of unemployed people (U, e.g. this metric -- and n.b. here and throughout U is the total number of unemployed, not the unemployment rate), and the price level P is detecting signals from the demand to the supply. In my notation, P:NGDP→U. Therefore we can write 

$$
\text{(1) } P = \frac{1}{\kappa} \frac{NGDP}{U}
$$

We can do a fit to the data (price level in green, model in blue)

This fit works as well as the fit to the interest rate in the IS-LM model, so it gives some hint that we may be able to extract information from it. One interesting thing to consider is that the price level curve could define a "natural rate" of unemployment (actually more of a mean level of unemployment, blue):

The graph divides the number of unemployed by the size of the civilian labor force (L) to get the unemployment rate. Here is the graph of deviations from the blue curve:

I've excised the recessions in the data points (dots) in the graph above. It becomes clear that most of the data points and nearly all of the non-recession data points represent an unemployment rate that is falling. This is a major point in understanding the Phillips curve in the information transfer framework. Of course, to get to our final destination requires a little math. Start with the price level equation (1) above and take the logarithmic derivative:
$$
\frac{d}{dt} \log P = \frac{d}{dt}\log \frac{1}{\kappa} \frac{NGDP}{U}
$$
Expanding that out a little
$$
\frac{d}{dt} \log P = \frac{d}{dt}\log NGDP -\frac{d}{dt}\log U -\frac{d}{dt}\log \kappa
$$
Identifying the inflation rate $\pi$ (borrowing from the notation in the wikipedia entry) and the NGDP growth rate $n$, and taking $\kappa$ to be constant ($\simeq 0.6$ by the way), and fiddling with the $U$ term:
$$
\pi = n -\frac{1}{U}\frac{d}{dt}U
$$

If we expand around the number of unemployed at natural rate $U^*$ (or really any fixed level of unemployed rate) and taking $dU/dt = U'$ we can write:

$$
\pi = n -\frac{U'}{U^*} + \frac{U'}{U^{*2}}(U-U^*)
$$

Or in terms of the unemployment rate $u = U/L$ where $L$ is the civilian labor force:

$$
\pi = n -\frac{U'}{U^*} + \frac{U' L}{U^{*2}}(u-u^*)
$$

Where we make the notational identifications $n -U'/U^* = \pi^e + \nu$ and $B = U' L/U^{*2}$ we finally obtain the new classical form of the Phillips curve:

$$
\pi = \pi^e + \nu + B (u-u^*)
$$

... except there's a problem: the sign of the $B$ term is "wrong". This is where the observation in the previous graph comes in. Nearly all the data has $U' \lt 0$ so in most descriptions of the data we can take $b = |U' L/U^{*2}|$ positive and write

$$
\pi = \pi^e + \nu - b (u-u^*)
$$

The regularities of the Phillips curve essentially result from the fact that recessions tend to cause unemployment to shoot up quickly and then drift back down slowly over a longer period. With this knowledge we can see what the data looks like when excluding data where $U' > 0$:

Graphs of the Phillips curve tend to be broken up into "regimes" (from the wikipedia article we have 1955-1971, 1974-1984, 1985-1992 and 2000-2013); we can see how this segmentation approximates the behavior of the parameters $b$ and $\pi^e + \nu$:

Basically, the Phillips curve "regimes" represent relatively constant segments of the parameter values. Here are the graphs of the resulting Phillips curves for the different "regimes":

This allows us to posit a reason for the failure to find microfoundations for the Phillips curve. It is a property of the unemployment rate (quick rise, slow fall) that is only marginally connected to inflation (the slow fall in unemployment occurs during a recovery hence during a temporary increase of the inflation rate from a low level brought on by the recession). The real nugget of statistical regularity is that a recession causes unemployment to rise and inflation to fall with the Phillips curve describing the subsequent return to normal (unemployment to fall and inflation to rise). Or another way, the Phillips curve is just mean reversion. And mean reversion doesn't really need microfoundations, does it?

In any case, the Phillips curve is dependent on the dominance of data where $dU/dt < 0$ after recessions.

Sticky wages

Simon Wren-Lewis calls the lack of acceptance of downward nominal wage rigidity (sticky prices) a methodological failure in macroeconomics:

I suspect nearly all economists are naturally reluctant to embrace cases where agents appear to miss opportunities for Pareto improvement ... However in most other areas of the discipline overwhelming evidence [in favor of wage stickiness] is now able to trump these suspicions. But not, it seems, in macro. 

While we can debate why this is at the level of general methodology, the importance of this particular example to current policy is huge. Many have argued that the failure of inflation to fall further in the recession is evidence that the output gap is not that large.

Paul Krugman adds his perspective to Simon's:

You see, the question of wage (and price) stickiness, and hence of real effects of changes in nominal demand, was what the great rejection of Keynesianism was all about. And I mean all about. Back in the 70s, there was hardly any discussion of the determinants of nominal demand; what Lucas and his followers were arguing was that Keynesianism must be rejected because it was unable to derive wage stickiness from maximizing behavior.

Sticky wages form the basis of the explanation of the existence of unemployment in Keynesian economics. If there is a fall in aggregate demand, basic microeconomic arguments suggest that people as maximizing agents will lower their "reserve wage" in order to keep the economy at full employment. This is not what is observed. People do not lower their reserve wage; people become unemployed. There are many reasons given for this (e.g. nominal wage cuts or hiring new employees at a lower wage are bad for morale, the coordination problem where no one person wants be the one to lower their reserve wage, etc). It is a fruitful arena for study in economics.

I had previously considered that sticky wages might be the result of imperfect information transfer, but I am going to tackle the problem from a different perspective. I'm not going to figure out the reason for sticky wages here. However, I will show how sticky wages manifest themselves in the information transfer framework.

In this earlier post, I built a model where the price level P detects signals from the aggregate demand (NGDP) to the labor supply (LS) which I denote P:NGDP→LS. The basic equations of the information transfer framework then tell us that P ~ NGDP/LS. Now what this suggests is that the number of employees responds to changes in aggregate demand. It also allows us to derive Okun's law where changes in real demand (NGDP/P = RGDP) are equal to changes in employment (see the link at the beginning of this paragraph). What would it look like if nominal wages (NW) responded to changes in aggregate demand?

Well, you'd have a market P':NGDP→NW where P' ~ NGDP/NW, but we don't know what the price P' is. Let's first have a look at NGDP (solid) and NW (dashed):

These two nominal aggregates are effectively proportional to each other with NGDP/NW = 2.1, which means that P' is a constant (which I have normalized to 1). Here are the two prices (blue, red) shown on the same graph (with the CPI in green standing in for the price level):

A constant price means we must always have the same signal from the aggregate demand to nominal wages which means falling aggregate demand causes nominal wages to fall primarily as a reduction in the number of employed people, not a change in their nominal wage. There are still some fluctuations in P' so nominal wage rigidity is not absolute, but these fluctuations are small ... which is in fact what is observed:

This is an empirical observation. There is no a priori reason that P':NGDP→NW must have a constant price P'; it could have had the changing relationship observed in the analogous graph to the one above between the aggregate demand (solid) and the labor supply (dashed):

This small variation seen in P' can be used to slightly improve the fit to the price level P by taking P→P*P'  (old fit in blue, new in purple with the price level in green):

But overall nominal wage rigidity is the observed dominant market interaction with nominal wage changes being a small effect. To reclaim the physics analogy using the Hydrogen atom from Brad DeLong, sticky prices are the Schrodinger equation and wage flexibility is the Lamb shift.

Deviations from the trend using the GDP deflator

While these results used the CPI (less food and energy), this version uses GDP deflator data. I claimed that inflation during the 1960s was unnaturally low and wanted to see if that conclusion was robust under different measures of inflation. It is:

The population, the monetary base: Is there a connection?

Ostensibly there should be an overall correlation with a larger population meaning a larger monetary base, but in the process of constructing this post, I noticed an interesting correlation in the fluctuations around that overall relationship:

Is the distance from the origin in (log MB, log NGDP) space directly related to the population size?

The effect of cohort size on income is called the Easterlin effect in sociology, see e.g. this review. The effect here is different since it looks at contemporaneous population size. The economy is farther out along the R = (log NGDP, log MB) axes than it "should" be in the 80s and 90s, and this is corresponding with a lower population. I wouldn't put very much money down on this being more than a coincidence, but I thought I'd jot it down.

Revealing the true business cycles

In an earlier post I tried to extract the deviations from the trend that are the bread and butter of economics. In that post I link to Noah Smith explaining that:

You take a jagged time-series and you smooth it out, and you call the smoothed-out series the "trend". That's it. Whatever is left you call the "cycle", and you make theories to try to explain that "cycle". 

But how much do you smooth? That's a really key question! If you smooth a lot, the "trend" becomes log-linear, meaning that any departure of GDP from a smooth exponential growth path - the kind of growth path of the population of bacteria in a fresh new petri dish - is called a "cycle". But if you don't smooth very much, then almost every bend and dip in GDP is a change in the "trend", and there's almost no "cycle" at all. In other words, YOU, the macroeconomist, get to choose how big of a "cycle" you are trying to explain. The size of the "cycle" is a free parameter.

My opinion is that this procedure is garbage.

I think the idea of the expected path I developed in my recent post is much better grounded; so what do the de-trended cycles look like according to that picture? First, here's inflation:

There were a couple of spikes in 1974 and 1979 (probably due to the oil crisis) but the big anomaly is that inflation in the 1960s was unnaturally low (as well as appearing to have some data issues). This is contra the prevailing narrative that inflation was high in the late 1960s through the 1970s and was countered by the resurgence of monetarism in 1980s.

How about RGDP growth?

The recessions (red) line up nicely with significant deviations from the mean (which is slightly less than 0 meaning that the expected RGDP growth rate is potentially an upper bound). In fact, if we excise the recessions (see this post), we get a nice random sequence:

You can see the distribution of the residuals is pretty close to normal after subtracting out the recessions (the mean is -0.6% and the standard deviation is +/- 3.1%, the skewed piece from the recessions is also pretty obvious in the black line):

Predicting out to 2030

It may be hubris, but I'm going to venture a prediction about average non-recession RGDP growth. By non-recession growth, I mean the average over the quarterly reports with the negative results deleted. (Why do this? Well, it appears that these predictions represent an upper bound from which recessions are deviations; more on this in a subsequent post.) Anyway, building on the previous post here is a self-explanatory table:

These results follow from simply extending the path S(t) in the previous post out to 2030.

The 1970s

Update 3 Feb 2014: Basically the posts stands, but I updated the graphs to use the monetary base minus reserves here.

Ah, the 1970s. In with Let It Be and out with Off the Wall. And so formative for people who were shaped by those years ... especially our current slate of economics professors, political pundits and other associated riff-raff. This is my hundredth post, so I will celebrate with a tribute to the 1970s with lots of pretty graphs and ending with the final conclusion that the 1970s was the same as any other decade.

But first, the stylized facts!

Brad DeLong has a recent post up about the "end" of the Keynesian era and the beginning of the Friedman era. The stylized facts:

B1. ... adverse energy supply shock--The tripling of world oil prices in 1973 

B2. ... adverse growth supply shock--The productivity growth slowdown ... for reasons that are still not well understood in the 1970s 

B3. ... long-run growth-- ... huge backlog of unexploited opportunities for technological improvement and capital investment ... could not be sustained beyond the mid-1970s 

B4. Political economy--institutions-- ... [labor-capital] bargain broke down in the 1970s. 

B5. Hubris--Governments believed that they could run economies at overfull employment indefinitely without de-anchoring  expectations of inflation, and in the 1970s it turned out that they were wrong

In a similar vein -- in the sense that the 1980s purportedly cured the ails of the 1970s -- I recently countered Scott Sumner's claim that supply side reforms were that cure. Now my response to Sumner was that basically the initial combination of low information transfer index and low monetary base starting after WWII basically meant that ceteris paribus the US would always grow faster than e.g. the EU years later unless a "monetary phase transition" or a "hyperinflation" episode intervened.

But in order to have a thorough trashing of the left and right's economic view of the 1970s, I'll add some of Sumner's stylized facts on how the Fed "blew it" from 1966-1981 from this post:

S1.  [Incorrect] assumption of stable Phillips Curve.

S2.  Mis-estimation of the natural rate of U, which was rising.
S3.  Confusion between nominal and real interest rates.

In order to address these issues, I will construct a conterfactual path of RGDP and inflation through the years that assumes no major changes in the economy or monetary policy from the 1960s until 2008 and show this counterfactual path actually describes the RGDP and inflation we see during that period.

I start with the 3D price level surface P = P(MB, NGDP) familiar to regular readers where the actual path of the monetary base (MB) and NGDP is shown as a black line and the information trap criterion (∂P/∂MB = 0) is shown as a dotted line. On the right, I show it in 3D as a surface plot and on the left in 2D as a contour plot:

This function P(MB, NGDP) derived from the information transfer model and fit to price level data allows us to make the plot of RGDP growth ( = d log (NGDP/P)/dt = d log RGDP/dt with the model in blue, data in green) at the top of this post. What does the gradient of this function look like?

You can see the empirical path (black) travels from areas of high gradient towards low, which means that we will see inflation will go from high in the 1960s to low in the 2000s. But we have some work to do because the gradient is the vector (∂ log P/∂MB, ∂ log P/∂NGDP) therefore we have to convert that into a derivative with respect to time ∂ log P/∂t to get the inflation rate. There's an easy way to do this --  just take the derivative of the empirical functions with respect to time by taking P(MB, NGDP) = P(MB(t), NGDP(t)) = P(t); this is where the results in the graph at the top of this post come from. However I'd like to create the counterfactual path S(t) mentioned above so we're going to end up taking a directional derivative using a measure along S(t) (i.e. the pullback of the time differential to the price level surface). We'll start with two linear fits:

On the right we have the empirical points from 1960 to 2008 as a function of the monetary base and nominal GDP and on the left we have the distance from the origin (R) of these same points in (MB, NGDP) space. I will take the linear fit in the graph on the right as the counterfactual path S(t) and the linear fit in the graph on the left will be used to linearly approximate the measure allowing us to convert from a gradient with respect to MB and NGDP to a derivative with respect to time:

ŝ ·∇ → ŝ(MB(t), NGDP(t)) · (∂R/∂MB ∂t/∂R ∂/∂t, ∂R/∂NGDP ∂t/∂R ∂/∂t)

In more comprehensible terms, I am accounting for the facts that a) while the gradient points in the direction of maximum change, the counterfactual path doesn't follow the direction maximum change (perpendicular to the contours), but instead follows S and that b) in the graph on the right you can see that 1 year increments (each dot) aren't equal to billion dollar increments so the slope of the price level surface will not be measured correctly if you don't take that information account. Anyway, the final result is given in this plot of the RGDP growth rate along the path S(t):

Now we can read off the RGDP growth rate for the counterfactual path S (I color coded the expected RGDP growth rate in reference to the previous graph, show the derivative along the empirical path in blue and show the empirical data in green):

This graph shows that RGDP growth is roughly what we should have expected following the straight line path, or another way, nothing interesting happened in the 1970s. We are going from high growth in the 1960s towards lower growth today along a continuous trend. And here's inflation (data in green, expected inflation along S(t) in blue):

Again, we're basically following the trend. There are some deviations around 1974 and then another peak in 1980 (probably due to the Oil Crises). The real question should be why was inflation so low in the 1960s?

Going back to the stylized facts at the top of this post, there is only evidence of B1. The rest are trying to explain an effect that isn't there. To see this, here is a table of the expected average RGDP growth from the linear path and the non-recession (x > 0) quarterly reported RGDP growth by decade:

1960s: expected: 5.2 actual: 5.4

1970s: expected: 4.5 actual: 5.5

1980s: expected: 4.0 actual: 4.2

1990s: expected: 3.6 actual: 3.2

2000s: expected: 3.3 actual: 3.0

The awesome growth under Kennedy and Johnson? Expected. The anemic growth under Bush? Expected. The 20% growth slowdown from 1960 to 1980? Expected. To first order it appears nothing has happened due raising or lowering taxes, loosening or tightening monetary policy, regulating or deregulating. 

The productivity slowdown (B2) that isn't understood isn't understood for a reason: it didn't happen. Or rather, it's always been happening. There was no backlog of technological developments that ran out (B3). As far as RGDP growth goes, the decline of labor unions (B4) wasn't a major factor (it could still play into wealth distribution). Inflation expectations did not become de-anchored (B5); in fact they were unnaturally low in the 1960s and only returned to the expected trend (after some oil shocks). The stable Phillips curve (S1) is in essence a restatement of (B5); again nothing happened to the relationship between inflation and RGDP growth (and therefore employment). The natural rate of unemployment was not changing (S2). I'm not even sure what confusion between nominal and real interest rates (S3) is supposed to mean, but it's likely a dig at IS-LM and Keynesian economics. I do know one thing: it didn't lead to a change in the RGDP growth path or inflation because there was no significant change!

Resolving neo-Wicksellian indeterminacies**

Via Brad DeLong, Nick Rowe has a post on neo-Wicksellian indeterminacies that makes me realize I have awhile to go before I really understand this stuff. There is at least one aspect of the problem that a) I think I understand and b) I think I can resolve. Here's Rowe:

The standard answer simply assumes that Y=Y* and p=0% and r=r* [i.e. output = long run output, etc] when the 5 years are up, and solves backwards from there. Which means both p and Y jump down and r jumps up when the bad news hits. We have deflation and a recession for 5 years, with that deflation and recession slowly ending as we approach the end of the 5 years. 

John Cochrane proposes an alternative solution to the same set of New Keynesian equations. He simply assumes that Y does not jump when the bad news hits, and solves forwards from there. If Y does not jump when the shock hits, that means that inflation must jump to 5% immediately, so that real interest rate can be minus 5% when the nominal rate is 0%. But the inflation rate can only jump to 5% if the expected present value of the output gap jumps too. Hitting the ZLB [Zero Lower Bound] causes a boom, as Y slowly rises, then slowly falls, and only asymptotes to Y* well after the 5 years are past. And inflation slowly falls, and only asymptotes to zero well after the 5 years are past. 

John Cochrane is not (as I read him) saying his solution is the right one. He is saying it is no less right than the standard solution.

Following what I did here, we have three economies with the same history of AD shocks and changes in the monetary base that start from the same starting point. The only difference is that the information transfer (IT) index (related to the unit of account function of money and whether an economy is better described by a quantity theory of money or an IS-LM model) are at three different levels (high = red, medium = gray, low = blue):

The first thing that jumps out is that, ceteris paribus, a lower IT index economy grows faster. The second thing that jumps out is that the effect of QE is strongly dependent on the IT index a the time. The same level of QE in a lower IT index country leads to growth or a lack of a slowdown (say, Sweden, Israel or Australia) while the remaining slump becomes more significant as the IT index grows. Basically, QE would have worked when Ben Bernanke wrote his thesis in 1979. Anyway, that is a rehash of this post.

I want to return to Rowe (and Cochrane) talking about the idea that the New Keynesian (NK) equations are indeterminate in the sense that hitting the ZLB can lead to a boom or a bust depending on how you solve them. So I used the NGDP curves above to model the interest rates (again, high IT index = red, medium = gray, low = blue ... interest rate data is shown in very light gray):

You can see that all three economies head towards the "ZLB"*** but you can also see in the NGDP graph above that this is associated with a boom (blue) or a protracted recession (red) depending on the IT index. Another way, the IT index is the parameter breaking the indeterminacy of NK models, choosing the equilibrium.

For completeness, here are the model solutions for the price level and interest rate for the best fit IT index (model in dark gray, data in light gray):

** The title is a reference to the Newsradio episode Airport where Mr. James is wistful about Dave's talent for "RLP" (Resolving Logical Paradoxes).

*** In the information transfer model, the zero lower bound and the liquidity/information trap are only approximately the same thing. See this post.

Exogenous and endogenous

In some previous posts I explained there were different models based on whether information sources and destinations were "floating" or "constant". I took these terms from the original paper which in an update (v3) has changed the language to "constant restriction" and "floating restriction". In either case, mathematically the come down to whether an integral is:

$$ \frac{1}{y_0} \int dy \quad \text{ or }\quad  \int \frac{1}{y} dy $$

The question is whether $y$ is set inside (floating, or the second integral) or outside (constant, or the first integral) the market.

While not a precise translation from information theory to mathematics to economics, these terms are pretty close to the terms endogenous and exogenous. Therefore, the IS-LM model has an exogenous aggregate demand, an endogenous aggregate supply and an endogenous money supply. Scott Sumner's** model (LS-MS) treats AD as endogenous in the money market but exogenous in the labor market. In the case of accelerating inflation, the model has an exogenous money supply and endogenous aggregate demand. In my model, everything is endogenous.

Again, this is not a precise translation (see endogeneity), but in the loose sense of exogenous meaning outside the model and endogenous meaning inside the model we can switch back and forth between the two languages.

** The model is not really his in the sense that he came up with it. I built it in the information transfer framework based on what he's said in his blog.

Resolving the Australian interest rate conundrum

Paul Krugman mentioned something in passing today

... that as long [a country doesn't] have large amounts of foreign-currency debt it’s very hard to tell any story in which interest rates surge and the economy slumps ...

which made me think about yesterday's problem with modeling the 3-month Australian interest rate. Was Australia's interest rate controlled by its own monetary policy during the 1980s? Sure enough, I found some data on the amount of foreign currency debt held by the Australian government and it turns out a large fraction was US dollar denominated:

If we plot the previous fit alongside the US 3-month rate, the correlation jumps out at you (AUD 3-month in green, USD 3-month in dotted green and the model based on AUD monetary base in blue):

Taking even an oversimplified picture with an extended model that is the larger of the original AUD model interest rate and the USD 3-month rate data (dotted dark blue, and the curve using the USD model is solid dark blue), you can see that the deviation is no longer that mysterious:

Eventually I might want to go back and do a better model where the two pieces are weighted by the fractions shown in the graph at the top of this post, but I think this is good enough for now.

Australia, Australia, Australia, Australia, we love you!

Scott Sumner linked to Marcus Nunes about Australia avoiding the Great Recession today which gave me as good a reason as any to do this for that country. It is an interesting case because -- at least for the interest rates -- it doesn't work as well. Anyway, let's start with the NGDP (red) and MB (blue) in billions of Australian dollars:

We can immediately do the fit to the price level (CPI less food, energy is in green and the model is in blue) and see that it is quite excellent:

However the interest rate model only works after the 1990s (3-month rate in green, model in blue):

I originally thought it might have something to do Australia floating its currency at the end of 1983 (hence the demarcation), but that doesn't seem to really account for it. I'm not sure what is responsible for the deviation. The EU shows some deviation from the model as well, but it doesn't have quite the same magnitude as we see here.

The amazing economic feat Australia has accomplished is that it hasn't had a recession since the 1990s that is attributed to the RBA. However the price level parameters put Australia somewhat farther away from the information trap: it has a very low normalized monetary base like the UK, but additionally has a much lower information transfer index like the US. I've added Australia to the graph here:

Basically Australia was much farther from the information trap criterion (black dotted curve) and so its monetary base injection didn't push the country into the information trap (liquidity trap). However, we can see that Australia (gray) has a similar information transfer index to the US (blue), so it drives home the point that the information transfer index is not the only thing to consider: