Tuesday, May 14, 2019

Accounting identities and conservation laws

David Glasner brought me into a twitter thread that resulted in a disagreement between Noah Smith and myself which is unfortunate because I think we're saying the same thing regarding "accounting identities" in economics being arbitrary definitions. Noah just seems to think that conservation laws aren't also (direct consequences of) definitions. First, let me get all relativistic (in both senses).

Newton's laws are basically a series of definitions that say "I am defining a quantity called momentum (1st and 2nd laws) that is conserved by definition (3rd law)" [1].  This turned out to be one of the most useful definitions in science — though it was counterintuitive at the time. Imagine people reading the 1st law about objects tending to stay in motion when everything in their life usually ground to a halt due to friction.

This definition of momentum led to being able to predict the orbits of comets and the paths of projectiles pretty well. Emmy Noether eventually discovered the reason: it's because the universe has an approximate translational symmetry such that laws of physics at a point x is the same as the laws of physics at a point x + dx. It gets a few things wrong, like the orbit of Mercury — that's because the actual symmetries are Lorentz invariance and general covariance. But by "actual" here, we mean that they dynamics that result from the definition of momentum that arises from assuming Lorentz invariance (4-momentum) gives the results we measure. We also often arbitrarily separate the momentum conserved due to rotational symmetries (angular momentum) from the momentum conserved due to translational ones.

But the universe doesn't care about momentum or its conservation — we humans defined it based on a way we decided to decompose the universe that we found useful. And in the end, it comes down to the definition of what a derivative is. That x + dx is directly related to the momentum operator d/dx and the better definitions of momentum that are conserved have covariant derivative momentum operators. So, it's really our human definition of calculus.

As we found issues with the definition of momentum, we've expanded it and made it more nuanced — because the purpose of the definition of momentum is to get empirically accurate theories, not hold on to Newton's definition.

Now not being an economist I may get this wrong but Simon Kuznets' original definition of GNP/GDP as the market value of final goods and services produced in a quarter (or year, or other time period) was so defined because people thought it would be useful as a measure of production related to the current level of employment. If a Starbucks barista made you a coffee this morning, it'll be in this quarter's GDP. If I sell you my vintage 1980s Dougram collection, it doesn't employ anyone in the current period so it's not in GDP.

Just like how momentum was defined in order to try and produce a useful theory of motion ("physics"), GDP was defined in order to try and produce a useful theory of employment ("macro"). It's just a definition:
GDP = (your cup of Starbucks Coffee) + (my cup of Starbucks Coffee) + ... (other Non-Coffee final goods and services produced in 2019 Q2)
We can also arbitrarily group (partition) them:
GDP = C + NC
That arbitrary grouping is probably not useful. But this one has stuck around for a long time:
GDP = C + I + G + NX
We call this arbitrary grouping a national income accounting identity. Now just because it has stuck around doesn't make it right, but it does capture one useful aspect of modern economies — G tends to move all at once with changes in government fiscal policy and can move in the same or opposite direction relative to e.g. C. Empirical data appears to show that changing G can be used to offset the collapse in C during a recession, for example. In a long-ago blog post, I discussed how it might be useful to think of an additional financial sector (which redefines C, I, and NX a bit) so that:
GDP = C + I + F + G + NX
That's another arbitrary grouping that's purely a definition. But like our evolving definition of momentum that's been found wanting on occasion, we can evolve our definition of the national income accounting identity to pick out a financial as well as a government sector. Why? Because the financial sector is also large and may move in the same direction all at once like in 2008. If we think of the distribution of growth rates of various companies and government entities in terms of their contribution to GDP, the whole collection will have some average growth rate based on the average of that distribution:

GDP growth will be the ensemble average. Like partitioning down to the individual coffee level, this may or may not be useful. However, if we group the financial sector into one big box (gray) and the government sector into another (blue), we instead have maybe something like this:

If there's a financial crisis, then maybe the whole financial sector shrinks:

and the new ensemble average growth rate results in a GDP that declined in that quarter. Shifting the government sector up could potentially offset that a bit. Again, maybe this arbitrary grouping is useful and maybe it isn't — a lot depends on the interactions of the various pieces (I talk about that a bit more here).

The main point is that definition of GDP and the accounting identity partition of it are both completely arbitrary, but like the arbitrary definition of momentum (which is based on our calculus-based approach to physics) they might be useful.

It's true per Noah's original tweet in the thread that we don't want to put too much weight on what is essentially an arbitrary definition that might not be useful. And you definitely want to be careful about reasoning from the identity alone — also because calculus:

This graphic lays out the possibilities for the interaction of those sectors (including the little boxes) in the distribution pictures above (but this graphic is for levels, while the distribution is for growth rates). The picture I showed in the distributions is the upper right where the change in the financial box doesn't do anything to the other boxes.

Macroeconomics is a nascent science compared to physics — Newton's definition of momentum is from 1687 while Kuznets' definition of GDP is from 1934. So yes, by all means recognize that the definition of GDP and its various accounting identities are arbitrary definitions. GDP seems to be a useful macro definition for studying employment and fiscal policy does seem to have an effect on the economy warranting a separate G term. Maybe there are better — more useful — definitions. But don't go too far in the other direction and think that the enormously successful definition of momentum as a conserved quantity makes it not arbitrary. It's still just a label we humans applied to the universe.



[1] Actually Newton's Lex II was a bit vague:
Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.
A somewhat direct translation is:
Second Law: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
The modern understanding is:
Second Law: The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.
Where momentum and impulse now have very specific definitions as opposed to "motive force" and "motion". This is best interpreted mathematically as

I ≡ Δp

where I is impulse and p is the momentum vector. The instantaneous force is (via the fundamental theorem of calculus, therefore no assumptions of relationships in the world)

I = ∫ dt F

F ≡ dp/dt

where p is the momentum vector. The alteration of "motion" (i.e. momentum) is Δp (or infinitesimal dp), and the rest of the definition says that the vector (and impulse vector I) is parallel to the vector. Newton would have written in his own notes something like f = ẋ using his fluxions (i.e. f = dx/dt).

Monday, May 13, 2019

Wage growth forecast continues to perform (unemployment, too)

The dynamic information equilibrium model (DIEM) wage growth forecast from over a year ago now continues to perform a bit better than Jan Hatzius's forecast from six months ago:

For some reason, I didn't put the latest unemployment rate report on the blog (and labor force participation) — let me correct that:

Tuesday, May 7, 2019

JOLTS: a continuing deviation from the trend

There's not much to say about the JOLTS data except that it's continuing the negative deviation it has been on for awhile now. The most robust deviation is actually in separations, with hires — the most robust indicator of a future recession (about 5 months in advance of indications in the unemployment rate) still showing no deviation. Based on this model which puts hires as a leading indicator, we should continue to see the unemployment rate fall through August of 2019 (5 months from March 2019). As always, click to enlarge ...

Wednesday, May 1, 2019

Economic weakness in the West?

I noticed that the unemployment rates for two west coast states — Washington state (where I live) and California (the largest state by population) — have shown a noticeable uptick recently. Now state level unemployment rates have large fluctuations. However, the unemployment rate for the West Census Region (defined here) is a bit smoother and is also showing that same turnaround. So I decided to try the dynamic information equilibrium model (DIEM) on it:

This shows the last few months of data rising up a bit over the expected non-recession (dynamic equilibrium) path. I tried a few counterfactual estimates: a free parameter shock (A), a shock with a fixed center date at 2019.7 and other parameters free (B), and a typical magnitude/duration shock with a free center parameter (C).

First, it should be noted that typically the non-equilibrium shocks are underestimated in their magnitude during the leading edge, and then overestimated until the shock center has passed. This is probably the reason for scenarios A and B being small relative to the average size of a recession shock.

Scenario A could potentially be showing us the end of the 2014 mini-boom (that end appears clearly in the WA unemployment rate, but at the end of 2015, not 2019). But the mini-boom shows up clearly in JOLTS hires data (again, here) — which we can look at for the West region. In that data (using the DIEM), it appears to end in mid-2016, far earlier than late-2018/early-2019:

It's not implausible that we're just seeing the end of the mini-boom (which does not appear to have ended for the country as a whole).

The latest JOLTS data also appears to be skirting the bottom edge of the hires data. Scenarios B and C both show what a counterfactual recession would look like that's consistent with the deviation from the DIEM since 2018, but — depending on the shock width — shocks to the hires time series precede shocks to the unemployment rate by about 5 months or so. In this case, the hires data is a bit noisy and just might not see the a shock yet.

More data will be coming out in mid-May that might clarify things a little more. It will be interesting to see the unemployment data that comes out on Friday and whether or not this uptick will start to appear nationally.

Tuesday, April 30, 2019

Wage growth and tight labor markets

Ernie Tedeschi put up a version of a chart today I think I saw from Adam Ozimek about a year ago showing a linear relationship between 25-54 year-old employment population ratio (which I updated yesterday) and the employer cost index that's a measure of wage growth:

I have some issues with this being called a "wage Phillips curve" because what this really shows is just economic growth: as the economy grows, employment grows as well as wages. It's kind of just supply and demand here. As non-engaged labor becomes scarce, wage growth go up. The Phillips curve is a relationship between prices of goods and employment — lower unemployment causes some measure of the price of goods to increase. This requires an additional step beyond the labor market picture where e.g. higher wages chase scarce goods causing their prices to increase — the wage-price spiral.

But as I talked about last year, I don't think this simple linear relationship is the true relationship between these variables — it's actually somewhat spurious. Back then, I projected (based on the DIEM [1]) what continued economic growth would look like on this graph and the data would follow a line of much lower slope. And sure enough (click to enlarge) —

I used different data for wages (Atlanta Fed's Wage Growth Tracker) because it has a longer time series and is reported monthly (like EPOP) instead of ECI's quarterly frequency. The addition of the data from before 1994 (yellow) also helps show that this isn't just a simple line. The data since last year (black) have followed the expected non-recession trendline (gray). In fact, if you look at the last 3 years of data, it's even more clear that the lower slope from the dynamic equilibrium is correct, not the linear fit:

This supports the conclusion that what's being seen here is just a consequence of economic growth. Wages tend to grow and employment rate tends to rise (and unemployment tends to fall) between recessions [2]. 



[1] The graph is made from a parametric plot of the wage growth DIEM and the EPOP DIEM:

[2] The rates these change at are different — their units are different, so they're not really even commensurate! Wage growth (or ECI growth) is % change per year (therefore changes if you change the time scale) while EPOP or unemployment are just fractions (%, or pure numbers). 

Monday, April 29, 2019

Employment-population ratio and labor force participation rate

I haven't updated the forecasts of labor force participation for ages 25-54 or the employment population ratio by gender in awhile. I was prompted by this tweet from Ernie Tedeschi about how labor force participation hasn't abated — but it shouldn't show any signs until after a recession has already hit (here, here). Here are the updated models for labor force participation and women's employment-population ratio:

For some reason I don't fully understand, the code for men's employment-population ratio had the dynamic equilibrium hard coded to 0.007/year when the actual solution from the entropy minimization was 0.005/year. It's the latter value that matches the original fit while also fitting the post-forecast data, but I'll present both graphs — the 0.007/year value is the one that shows recent data lagging the forecast. My guess for the reason was that I was comparing the value for the fit for women in the graph above (which is 0.007/year) and forgot to change it back or document it. Anyway, here's the E-POP ratio for men with both dynamic equilibria:

Last but not least is the employment population ratio for everyone in the labor force — which has a forecast from the CBO to compare to (again, via Ernie Tedeschi) ...

... that's doing poorly.

I added the CBO's August 2018 projection from Ernie's graph. Here's the longer run (the graph above was made to match Ernie's tweet):

Core PCE inflation: three cheers for DSGE

Core PCE inflation data — the measure commonly believed to be the most closely watched by the Fed — was released today. To be a bit of a troll, my Twitter headline for this post is going to be that the NY FRB DSGE model is remarkably accurate (black is post-DIEM forecast data):

... at least in its forecast mean. Given that the error bands are smaller for the dynamic information equilibrium model (DIEM), we'd say it improves our Bayesian prior more than the DSGE model does despite the near zero deviation from the mean forecast. Here's the year-over-year measure for the monthly data:

Of course, I really dislike year-over-year measures. Sure, they help eliminate seasonal variations, but the introduce correlated errors ... i.e. the present value depends on the measured value — including its error — from a year ago. And since there are undoubtedly seasonal/annual/multi-annual fluctuations, year-over-year measures make an implicit assumption that your measurement error has no seasonal variation which is unlikely. This is why lots of year-over-year measures tend to increase the order of the AR processes that can be used to estimate them in the short run. Of course, the benefit is that overall error is usually smaller than when you take derivatives (which only impact the points right next to each other) because much of the uncorrelated error over the course of a year is averaged out.

Note: this should not in any way be read as disparaging the performance of the DSGE model above — it would likely be just as right about other measures. It's mostly about reading anything into the individual time series points (i.e. saying core PCE inflation has fallen over the past couple quarters).

Here's the continuously compounded annual rate of change (aka log-derivative) versions alongside some other forecasts from the FOMC (purple points with error bars representing the "central tendency") and Jan Hatzius (lavender dots):

This white dots with black outlines represent the annual averages. Here's the quarterly version:

Overall, the DIEM forecast is performing well — as well as a fancy DSGE model. However, the path — being relatively constant — isn't very challenging.

Friday, April 26, 2019

GDP data!

I have some NGDP and RGDP dynamic information equilibrium model forecasts I've been tracking the performance of. These, unfortunately, aren't very exciting because GDP data is (surprise) super noisy. Or at least it's noise in the DIEM view. Some people tend to think of the fluctuations of GDP from one quarter to another as somehow meaningful. I'll probably hear about it on APM/NPR's Marketplace tonight. At least it's working better than the NY Fed's DSGE model which predicts about the same average path but with much larger error bands.

Anyway, here's the latest:

Wednesday, April 24, 2019

Happy birthday to the blog!

I started this blog with its first post six years ago today. At the time, I had derived supply and demand diagrams from an information theoretic approach [1] that I thought might be publishable if it weren't for the institutional roadblocks. For one, I'm not an economist, and while I love the earnestness of "econophysicists" no one listens to them, nor do they (in general) provide a good reason for doing so. The work is sometimes referred to as "heterodox", a) I don't really think it is because that's its own thing (q.v. Carolina Alves) and b) I didn't really know about it at the time — therefore that community isn't/wasn't necessarily a viable alternative to mainstream publication.

I decided to just present the results on this blog — the draft paper I had written was presented in the first few posts here. Eventually those results would be incorporated and expanded on in my first econ pre-print, originally on the arXiv in q-fin.EC (there's a re-post of it at SSRN). That first pre-print contained the model in the forecast above that's been doing well for almost 4 yearsAnother pre-print followed a couple years later containing its own forecast (of unemployment and JOLTS data) that's also been doing well.

And here we are — six years later. To celebrate, I made an animation of one of the forecasts that I've been tracking the longest — more than half the time this blog has been in existence. The model itself was first written down in February of 2014, less than a year after the blog started — though there general concept was written down in August of 2013.

The interesting thing about this model is that it's a simple idea: the interest rate is the "price of money" and NGDP (~ aggregate demand) is the "demand for money" — with the monetary base being the "supply of money". (It's also a component of the information equilibrium IS/LM model.) It's possible it's not correct (or is only an "effective theory") and what we really have is a dynamic information equilibrium model. But it's still working for now!

Thanks everyone for reading! 



[1] And which Thomas Mikaelsen has recently been checking my math on!

Friday, April 19, 2019

Wage growth forecast continues to do well

The Atlanta Fed updated their wage growth tracker a few days ago while I was at Coachella, so I didn't have a chance to update it at the time. The post-forecast data continues to be pretty much in line with the original forecast from February 2018 (as always, click to enlarge):

Plus, despite being paid a fraction of what Jan Hatzius of Goldman Sachs is paid, my forecast for the same set of variables is looking a bit more informative than his:

That blue dashed line is the nominal GDP dynamic equilibrium and is part of my "limits to wage growth" hypothesis where nominal wage growth is halted by a recession if it starts to exceed nominal economic growth (and therefore eats into profits on average/in the aggregate). It's a speculative part of the information equilibrium "macro model". We did appear to skirt the edge of it towards the end of 2016 before the data dipped a bit. Given the noise in the data, it is difficult to tell if that was the fading "mini-boom" of 2014 or the beginnings of a genuine downturn that was averted. Job openings was showing a similar downturn at the time that was significant enough (alongside yield curve flattening) for me to posit a coming recession in late 2019 to early 2020 — but might have faded away in subsequent job openings data and revisions. However, the downturn is still present in quits and separations so basically we're still in a situation where only time will tell.

Thursday, April 11, 2019

Median interest rate spread inverted

We're at edge of the two sigma band where a recession occurs after the monthly median interest rate data manifests a yield curve inversion. The median daily interest rate data showed a brief inversion at the end of March — about two weeks ago:

The gray band is where the interest rate spread indicator points to a recession based on a simple linear extrapolation (blue)/AR process (red) based on median (which in this case is basically equal to the principal component) of multiple spreads.

Note that except for the 2001 recession, these median rate spreads started to head back up by this point over the past few recessions — reminding us that we will probably see the Fed lower rates (increasing the short-long rate spread) before a recession starts. Or maybe the yield curve will prove to be a false alarm — to be placed on the scrapheap of indicators that lose their predictive ability as soon as they're widely recognized.

Wednesday, April 10, 2019

CPI inflation forecast still holding up after 2 years (plus useless forecasts)

Here's the latest CPI data (all items, post-forecast data in black) and the dynamic information equilibrium model (DIEM) forecast from 2017:

Note that the dashed line is the revised parameters from this post (from one year ago) — but given the revised line falls entirely within the error band it's really a trivial correction (more on this below). Especially when we look at the inflation rate:

Useless forecasts from the Peterson Institute

When I saw a forecast from the Peterson Institute, I was initially excited to have another model with which I could compare the dynamic information equilibrium model. However, it turns out that not only was it for core CPI inflation (which is far less interesting than headline inflation shown above — it's constant, so I stopped tracking it), but it was also a useless forecast for core CPI inflation (clue and red dashed lines):

Going by a simple AR process around a constant value of inflation (a model that outperforms the most advanced DSGE models), we should expect an error band due to fluctuations in the data roughly comparable to the DIEM band shown above. That's because the DIEM is actually constant over the post-recession period and the error is estimated by taking the standard deviation of the model residuals — i.e. basically the process for AR process estimation [1].

So Collins and Gagnon (the authors) should have known that. They also should have known that the prior data looks like the data in the graph above — pretty much within half a percentage point of 2% over roughly the past decade. Which also means they should have known that their forecast (and in particular the difference between their forecasts which is the focus of the article) is basically within the noise of a model with a maximally uninformative prior — i.e. useless

True, this means the DIEM for core CPI data is also useless [2] — part of the reason I stopped tracking it. In fact, I note that the re-estimation of parameters in the all item CPI was also trivial and it generates an effect comparable to the difference between these Peterson Institute forecasts. But at least I've acknowledged that it's within the noise (and given an estimate of the model error).

But this Peterson Institute forecast? It's such a small deviation, I'd almost think that they made it knowing that it probably couldn't be rejected by the data. It's basically a non-forecast.



[1] Neglecting the little bit at the beginning that effectively tracks the expected mean reversion (as described in a footnote here).

[2] The all item CPI forecast actually showed a tiny improvement over a constant model — but was also related to a lot of other dynamic equilibrium models. But also, the various DIEM models show a great deal of improvement of the error bands (here, here) — bands this Peterson Institute forecast didn't even give us.

Dynamic equilibrium in population growth

I saw some data from Brookings today (via Noah Smith) about population growth that looked almost exactly like wage growth data — and it turns out it is well-described by a dynamic information equilibrium model (DIEM):

The 1991 recession and the 2008 recession are both followed (with a lag on the order of years) by a fall in the population growth rate. The 2001 recession basically coincides with the population growth decline. However, there is a drop in population growth not associated with a recession, but rather associated with the end of Obama's term as President and the beginning of the current administration's term:

Update: Forgot the labels — they show the shock centers for the unemployment rate (u), wage growth (W), and JOLTS hires (HIR). These labels are actually centered on the shock (including the text) so the actual center is a bit to the left of the arrow.

Tuesday, April 9, 2019

JOLTS day!

The Job Openings and Labor Turnover Survey (JOLTS) data released today continues the status quo of bending slightly below the dynamic information equilibrium model (except for hires):

Click to enlarge any of these images. I wanted to see if incorporating more data in the model for job openings (which showed its largest drop since 2015 today) could handle the deviation — and it can (you can cycle back and forth between these two images on a desktop/laptop):

However, this same trick does almost nothing to total separations:

And only nudges quits:

So, as with most macro data, there's some ambiguity here. Hires (the more robust leading indicator for non-equilibrium shocks — but also only by about 5 months) is showing no deviation, quits and separations (which lagged in the past) showing robust deviations, and openings being ambiguous (and also had the largest revisions last month). According to the hires data, we should continue to see the unemployment rate fall (stay on the DIEM path) through July of 2019 (5 months from February 2019, which is the data that was released this week).