Tuesday, March 26, 2019

The beginnings of an information equilibrium macro model

I've been trying to put together a summary of the information equilibrium/dynamic information equilibrium models that comprise a single (still preliminary) macro model. It's mostly for my own notes. At the top of this post is a graphical representation (click the graphic enlarge) of several posts. This recent post explains the relationship between information equilibrium and dynamic information equilibrium (there is also this "tour of information equilibrium" presentation) — these are represented by blue double arrows and purple single arrows, respectively. The gray dashed lines represent vague "links" (obviously NGDP is related to NGDP/L, it being in the numerator, but the "limits to wage growth" connection is more speculative). The black line relates NGDP with its growth rate by a mathematical operation (log-derivative a.k.a. the continuously compounded annual rate of change). There are two "exogenous shock" inputs — one is the business cycle (which is behind recessions, possibly based on the "limits to wage growth"), and the other are social factors (women entering the workforce, Baby Boomers retiring after the Great Recession).

We have:

I left out the interest rate models because they're not terribly relevant at this level. Not that interest rate signals are irrelevant — it's entirely possible the limit to wage growth mechanism functions because the Fed raises rates until wage growth stagnates at a level at or below NGDP growth, so then starts to lower rates which sends a signal to markets that a bear market is approaching creating a self-fulfilling prophesy. I'm still agnostic on that.

However, all the IE and DIEM  relationships (blue double and purple single lines) above are empirically valid. It's essentially the connection between the top half and the bottom half of the graphic that is speculative.


Update 27 March 2019

If you were wondering where we are regarding that "limits to wage growth" picture:

The Hatzius band is from this post. The dashed line is the mean NGDP growth rate from a dynamic information equilibrium model.


The various abbreviations:

HIR = JOLTS hires rate
JOR = JOLTS job openings rate
u = unemployment rate (UNRATE on FRED)
U = unemployment level
L = employment level (PAYEMS on FRED)
NGDP = nominal gross domestic product
K = "capital"
PCE = personal consumption expenditures
PI = personal income
CLF = civilian labor force (CLF16OV on FRED)
W = wages (wage growth is Atlanta Fed wage growth tracker)


  1. It's interesting to see graphically how it all ties together.

  2. I've followed your work on the connection between labor trends and inflation with interest.

    Wondering if you've explicitly addressed anywhere what you see as the relationship between your work and what Keynes believed his framework would predict as far as how increases in employment would be associated with increases in the price level in conjunction with increases in effective demand? Is it possible you've simply captured empirically and consistently via your own theory the same effect Keynes claimed would result as (if I understand his General Theory correctly) an influx of new workers would correspond to diminished returns relative to the status quo and a lowering of real wages across all workers, which would then show up as inflation?

    I guess I'm just struck by how forcefully both you and Keynes have drawn the connection between the mere increase in workers in an economy and inflation, while what I have been exposed to in popular accounts of inflation (as I am not a serious student of economics) would appear to barely see any role for employment except for when "full employment" had already come into view.

    Keynes builds his arguments throughout his General Theory, of course, but in his clearly titled Ch. 21, "The Theory of Prices," he is as clear as anywhere that, under more realistic assumptions:

    "[T]he increase in effective demand will, generally speaking, spend itself partly in increasing the quantity of employment and partly in raising the level of prices. Thus instead of constant prices in conditions of unemployment, and of prices rising in proportion to the quantity of money in conditions of full employment, we have in fact a condition of prices rising gradually as employment increases."

    Sorry if this is well-known to you and anyone else who might read your blog and others like it, but part of what I find so promising in your work is the actual model-building consistent with parameters that you have empirically measured or derived. For instance, just as Keynes was excited to have an empirical estimate of his investment multiplier for the U.S. ca. 1930, I suspect he'd be delighted to have your empirical estimates for the parameters which appear to have governed the relationship between labor force participation and rates of inflation in recent decades. Again, sorry if this isn't adding anything that isn't already in your work or discussions about your work, and thanks for all your work.

    1. Question pertaining to the above: Would your model/theory predict that inflation would have slowed on its own once the demographic shift (i.e., women entering labor force) was complete in the 1960-80s timeframe, or once inflation expectations are set, does it require Volcker-type moves in the money supply and in interest rates for the inflation expectations to be reset?

      More broadly, these issues would seem to complicate any central bank mandate that would ostensibly combine "full employment" with "stable prices," yet the problem would only be apparent if getting to "full employment," which I presume is the socially desirable place to end up, would only entail inflation on a transitory and transitional basis. Meanwhile, even with the approach promoted by the likes of Kashkari at the Fed, the assumption seems to be that inflation shouldn't be allowed to increase because any gains on the employment side will be more than offset by the inevitable harm involved when money supply and effective demand are eventually contracted in order to bring inflation back down under the assumption that that will be the only way inflation will come down (i.e., it is not a transitory but always a persistent phenomenon once begun). Of course, if modern central banking is correct in its outlook, then "full employment" perhaps only comes to mean "maximum employment under stable prices," which is not what Keynes had in mind given his more common sense definition of the level of employment at which no one would like more work at the prevailing wage level (if I understand him correctly).

      I suppose I'm probably just wishful that there is one more misconception/superstition out there that, were we to eliminate it, would yield a marked improvement in our economic system, like the progress made when modern central banking finally decoupled from gold.

    2. Sorry for the delay in getting back to you (this week has been busier than usual) and thank you for reading! I'll answer your questions in a series of responses as I get a chance.

      To answer one of your questions about inflation coming down naturally without central bank interventions, I believe this is the case — and not for just the US, but for Canada and New Zealand:


      That you could predict the inflation rate to fall in Canada and New Zealand before any monetary changes were put in place makes it unlikely they had the effect they are claimed to have. The exact same trick can't be used for the US because Volcker's changes come in the 80s rather than the 90s, but given that inflation had already begun to fall and the tight link with labor force participation — coupled with the observations of other countries (aforementioned ones and Japan) — we pretty much have a story where Volcker just happened to be the Fed chair at the right time.

    3. Regarding the relationship between inflation and employment, I am under the impression that inflation is something very different from what economics (going all the way back even beyond Keynes to Adam Smith or Hume) has said it is in terms of a relationship between supply and demand. There are two main factors that explain the variation in inflation over the post-war era (and to some degree earlier, but data is spotty):

      1. labor force participation
      2. the unemployment rate when labor force participation is increasing faster than population growth

      Component 1 is governed by the model above, but there's an additional component that looks much more like the traditional Phillips curve. However, component 2 fades away as the demographic surge ends. I have some speculation about this:




      But overall, the price level appears to be a measure of the size of the economy in terms of the economic state space (which is a more information-theoretic measure). I'm not certain, but I think the link between labor force size, output and inflation is simply due to the fact that a huge number of people in a country live similar lives in terms of consumption and income (i.e. at each level of the income distribution, people buy the same stuff, live in the same places, and generally live similar lives — rich people in a country live one way surrounded by the same stuff, and poor people in that country live another way). That means as you add jobs to a country's economy, you basically add another undifferentiated unit (except by income scale). And that part might explain a bit of why demographic changes show up in inflation because you're changing those "undifferentiated units" — which for the US in the 1950s was white & male (in the US), but changed in the 60s and 70s to become increasingly more female.

    4. Again, that last bit is speculation.

      I'll think about effective demand a bit more.

    5. Thanks for the extensive response. First, a quick point of clarification. "Volcker just happened to be the Fed chair at the right time." Do you mean "right time" for the sake of informing today's conventional wisdom, or "right time" for the sake of the reality at the time. I would infer from your comments on the NZ case that you meant the former, in which case, is it possible that "right time" might have been more like "wrong time" as it meant that we didn't get to learn what would have happened to the price level without such an intervention?

      The only other thing I had in mind that I'm not clear on is where you'd come down on central bank policy. If inflation will tend to taper on its own following the influx of workers to an economy – provided the system isn't pushed all the way to a condition where the quantity of money begins to dominate – I wonder why we wouldn't just keep rates at 0% at all times (combined with a set of socially acceptable, if not optimal, macroprudential policies). Under Keynes's theory, if one assumes a reality conforming to your beliefs regarding inflation and a weak propensity and capacity for fiscal management, it seems one would simply want to maximize investment in the private sector and that the best we could do in this respect is ZIRP + macroprudential at all times (leaving aside negative rates for the time being). Obviously, this position would appear to depend strongly on being correct that large changes in price levels are merely transitional. Presumably the reason Keynes didn't push for a simple zero-rate policy is that he subscribed to a more conventional perspective on the sources of inflation and assumed that the neutral rate might be materially higher than 0%, but it's hard to read Keynes and not feel like he thought there was a way to reconcile actual "full employment" with "price stability." Note that moving to such a zero-rate paradigm would entail its own transitional effects having social and political costs and risks, making it hard to get there even if it ended up being the optimal policy (e.g., rentiers crying that they can't get the returns they're accustomed to; a relatively modest rise in equilibrium debt levels as the cost of servicing the debt falls to a new steady-state; a potential increase in so-called wealth inequality as future returns are capitalized at modestly lower rates, although I would argue this is a one-time and, to a significant extent, notional effect). I feel like we saw all of these occur in the years following the GFC when the Fed kept rates at the zero-bound.

      From the alternate perspective of the status quo, what I find difficult to tell is how close to optimal (and to Keynes's vision) modern central banking may have already come. The Fed, for instance, might already be doing a brilliant job relative to what is actually feasible and what Keynes was hoping to achieve with his ideas – although you might infer that I'm in the camp that was not able to see the benefit of the rate increases in the current cycle given that we weren't even at the point of having to confront the question of whether a higher level of inflation might be tolerable, let alone perhaps temporary. It seems obvious we'd want to have more workers (to the extent that the available wages would exceed their disutility of employment) along with abundant capital, rather than a happy rentier class enjoying "risk-free" returns for no reason other than tradition and superstition, if those traditions and superstitions have no grounding in reality.

      But I'm a layperson, so I hope my thinking on this subject is coherent enough that you feel you can share a perspective that might help. Thanks, as always.

    6. By "right time" I meant that it was the "right time" for Volcker's personal career and legacy — whoever was the Fed chair at the time would have gotten credit.

      As for central bank policy, I'm not sure it does anything except act as a coordination point, and when people act in a coordinated way (e.g. panicking together) that can cause (typically negative) non-equilibrium economic shocks.


      It does seem that Fed choices about interest rates can e.g. cause markets to crash. However, as a side note, fixed (pegged) interest rates seem to be associated with high inflation. Generally, the Fed does not seem to control long term rates, and when they let the short rate get above the long term rate (yield curve inversion), there's an economic downturn that follows. But maybe there's something else that happens?

      Basically when it comes to interest rates and their effects:


      There are definitely bad choices because of what people think about how interest rates work — i.e. it's a social phenomenon rather than an economic one.

    7. Thanks for your views. Appreciate you taking the time.


Comments are welcome. Please see the Moderation and comment policy.

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.

Note: Only a member of this blog may post a comment.