## Monday, April 4, 2016

### There is no interpretation, only equation

I've run into this enough now from different places that I think it is worth a post.

Let me be clear:
Just because you write down and equation A and say (with words) that equation represents B in the model does not mean equation A represents B.
It is true that B may be consistent with A, but C could be also. It also might be the case that B has nothing to do with the equation A, or doesn't really specify A well enough -- leaving A vague.

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The best example that comes to mind is the national income accounting identity. The equation (i.e. A above) is

$$Y \equiv C + I + G + NX$$

Since $Y$ is defined as the value of all final goods and services (FGS), and the right hand side terms are defined as 1) all FGS consumed by non-government entities ($C$), 2) all FGS touched by government entities ($G$), 3) all FGS exported minus those imported ($NX$), this makes $I$ all FGS not consumed or paid for by the government or exported. That this is called "investment" doesn't make it investment in the common parlance. In fact, economists tend to take an equation like this to define "investment". But as many economists rightly point out -- this is an accounting identity (i.e. a definition) and it does not specify behavior.

In the information equilibrium view, there's probably only a $G$ term, with everything else being a residual.

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In another example, Scott Sumner wrote down a market monetarist model with the equations (i.e. A above)

\begin{align} NGDP_{t} &= NGDP_{t-1}^{F} + e_{t} \\ NGDP_{t-1}^{F} &= NGDP_{t}^{T} + SE_{t-1} \end{align}

Just because Sumner called the last error term $SE$ for 'systematic error' representing the predictable part of the central bank's policy target ($T$) failure and that $SE = 0$ for NGDP futures ($F$) targeting (i.e. B above) does not make these model equations actually mean that.

That's because we can rewrite these equations removing all reference to the NGDP futures market:

$$NGDP_{t} = NGDP_{t}^{T} + SE_{t-1} + e_{t}$$

Now NGDP at time t is just the policy target plus a zero-mean random error plus a changing nonzero-mean error term. This just represents an arbitrary decomposition of the error into a mean error plus random fluctuations. In a sense, it's an accounting identity for an error budget.

Sumner's actual claim (assumption) is

$$SE_{t}(F) \equiv \min_{T \in P} \left| SE_{t}(T) \right|$$

where $P$ is the set of policy targets. The output of the futures market is irrelevant. It is the $SE$ term doing all the work, and it's a definition.

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In another example (that is likely to get me in more trouble with the Stock-Flow Consistent [SFC] modeling mafia), in Godley and Lavoie, they wrote down two equations (plus an identity)

\begin{align} H - H_{-1} & = G - T \equiv Y_{D} - C \\ C & = \alpha_{1} Y_{D} + \alpha_{2} H_{-1} \end{align}

In the text of Chapter 3, there are all kinds of claims about these equations, from saying they represent a toy model (therefore do not take the equations seriously, which is funny to me ... if there are problems with the model, let's just not talk about them) to saying this model has no banks and defines high powered money ($H$). There have been seemingly no end to the comments about this (on these posts [1], [2], [3]). But not matter how strenuously G&L say in their text or their defenders say in comments, saying equations A represent B does not make it so.

One of the key bits is in the second equation. Consumption of FGS is proportional to after tax household and firm income ($Y_D$) plus a piece proportional to the total stock of savings in the previous period ($H_{-1}$). G&L call this high powered money and give it the label $H$, but it is really the stock of savings because $Y = C + S + T$, or another way, the stock of government debt.

Much like Sumner saying the futures markets get NGDP right, G&L insist that there are no banks or other forms of money in this model. Households spend part of their "after tax income" and part of their "savings". That is consistent with those equations, but not actually nailed down by them.

The second equation simply says after tax income and the stock of government debt are proportional to a fraction of consumption. Households could be paid in goods, wherein the first term represents barter. Or they could be paid in scrip. The second term could be trade in actual government bonds (one transaction per time period), or it could be a "wealth effect" where households create scrip (like the babysitting coop) proportional to their holdings of government bonds to trade.

Even though they say there are no banks, these equations are perfectly consistent with banks that issue their own money (aka free banking). No net assets are produced because each bank note is an asset for the household that holds it and a liability for the bank that issued it. IMHO, this is the most sensible interpretation of the second equation (as opposed to bartering part of household income plus trading financial assets).

And once you realize this, you realize that these equations are not as general as they should be. They assume the rate of production of scrip is limited to the rate of production of government bonds and that the velocity of scrip is fixed to the velocity of bonds. Since scrip (bank notes) produced via free banking is neutral in terms of assets and liabilities, it doesn't appear in the SFC matrix.

There is some assumed resistance to producing scrip, and in one possible way to make that resistance more obvious is to use a coefficient:

\begin{align} H - H_{-1} & = \Gamma (G - T) \equiv \Gamma (Y_{D} - C) \\ C & = \alpha_{1} Y_{D} + \alpha_{2} H_{-1} \end{align}

In this set of equations, $\Gamma = 1$ says that bank notes can only be created at the rate of production of government debt and exchanged for goods and services once per quarter. Having $\Gamma < 1$ means more resistance to bank note creation (risk averse bankers, a lower level of economic activity -- i.e. velocity -- relative to $\Gamma = 1$, or perhaps discounted future expectations). Having $\Gamma > 1$ means less resistance (better expectations, less risk averse banks or more economic activity). Interestingly, $\Gamma \sim 10$ leads to oscillatory behavior -- too much scrip is produced leading to something that looks like a boom bust cycle (or better, Dornbusch overshooting) that fades away in the steady state.

In G&L's interpretation (their description B that goes with the equations A), the economy SIM is a highly regulated economy where everyone goes to the Transaction Bureau once per quarter and trades part of their measured output (reduced by some fraction for 'taxes'), plus a part of their allotment of government bonds for a fraction of everyone else's output. I'm not allowed to buy my friend's new album (nor is she allowed to say it's available) except once per quarter when our local branch of the transaction bureau is open. Using terms like "government" and "household" and "money" for a situation that better resembles 1984 or a Soviet command economy is like economists' use of the terms "investment" and "savings" -- words totally dissociated from their colloquial meanings. The weird part is that a lot of SFC modeling is done because the practitioners say economists don't know how the real banking system works.

That dystopian vision can be replaced with something that could be consistent with a much more realistic economy by adding in the constant $\Gamma$. With $\Gamma$, households are paid with direct deposits at banks that are backed by their holdings of government bonds via fractional reserve banking. People buy and sell stuff at any point during a quarter. Velocity of scrip is still proportional to the "velocity" of government bonds ... but as G&L say, this is a toy model.

I'm sure some commenters might object to this (possibly uncharitable) characterization of the model (Bill?), but the key thing to understand is that it doesn't matter what Godley, Lavoie, you or I say about the meaning of the equations. The equations represent something independent of the verbal interpretations. In this case, the verbal interpretations of G&L are actually at odds with the equations they wrote down.

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My conclusion is that you should always be wary of the interpretations of equations, and that in the case of a disparity, you should give deference to the equations, not the words. I take this seriously enough that I actually think that the equations in a model represent a kind of reality. For example, in many New Keynesian models, the central bank is modeled with a Taylor rule. For me, that means the central bank literally is a black box that enforces the Taylor rule. It doesn't conduct meetings to discuss policy, or have board members. It doesn't speak in public. If you think those things about a model that has a central bank described by a Taylor rule, you might make a mistake!

Now this isn't to say I think math is more awesome than reasoned argument. I accept that sometimes ideas might not have useful mathematical representations -- potentially, ever, but especially in their early stages. Rather, it's a cautionary tale about the interpretations of equations once you have them. Just because you used a mental model to construct a set of equations does not mean that mental model was translated into those equations.

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PS In physics, this is all much easier in a day-to-day sense. The things in the models are the representations of reality. An electron is not some "thing" that we've decided to model with a massive spinor representation of the Lorentz group with a U(1) charge. It literally is a massive spinor representation of the Lorentz group with a U(1) charge. In a simpler non-relativistic quantum theory, an electron is a wavefunction with some quantum numbers.

Neither of these things are consistent with, say, a tiny ball with an electric charge even though that is a useful model sometimes. In fact if you write down a model for an electron as a hard sphere that's too small to measure, you shouldn't think of it as a wavefunction with some quantum numbers -- except to understand how your model will break down in some circumstances -- because that will interfere with the interpretation of your equations that were derived for a hard sphere.

In a sense, there is no interpretation (i.e. a "B") in physics. There are only the equations (i.e. the "A's"). Physicists sometimes talk about interpretations -- the most famous instances are the interpretations of quantum mechanics (which are mostly just manifestations of the interpretations of probability and interpretations of causality). However, those interpretations have zero impact on the calculations of quantum mechanics. And interpretations that do have an impact on something observable have tended to get that observable wrong!

You could interpret (ha!) my post as taking the "shut up and calculate" view, but really I'm saying you should be wary of the possible disparities between your mental model and the equations you write down.

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PPS The title reference is to Ghostbusters. ... "There is no Dana, only Zool." It's a forced joke and doesn't really mean there is no interpretation -- only that there is not necessarily a single or definitive interpretation of any set of equations and that the source of the equations is not necessarily the best source for the interpretations.

1. Text: "They {G&L} assume the rate of production of scrip is limited to the rate of production of government bonds and that the velocity of scrip is fixed to the velocity of bonds. Since scrip (bank notes) produced via free banking is neutral in terms of assets and liabilities, it doesn't appear in the SFC matrix.

"There is some assumed resistance to producing scrip, and in one possible way to make that resistance more obvious is to use a coefficient:

H−H−1=Γ(G−T)≡Γ(YD−C)

C=α1YD+α2H−1

"In this set of equations, Γ=1 says that bank notes can only be created at the rate of production of government debt and exchanged for goods and services once per quarter. Having Γ<1 means more resistance to bank note creation (risk averse bankers, a lower level of economic activity -- i.e. velocity -- relative to Γ=1, or perhaps discounted future expectations). Having Γ>1 means less resistance (better expectations, less risk averse banks or more economic activity)."

I see that you are closer to operationalizing Γ. As I anticipated long ago, to do so you assume private banks. Which is why I pointed out at that time that there are no private banks in the SIM economy.

You're welcome. :)

1. As I anticipated long ago, to do so you assume private banks. Which is why I pointed out at that time that there are no private banks in the SIM economy.

Nope.

Private banks are just the most intuitive way to understand it. Without private banks, Γ is the rate at which households ramp up their bartering an amount equal to their wealth effect.

In fact, the model is consistent with no money changing hands ever. As I say in the text, it could all be barter.

Just ask yourself -- why is the rate at which the economy approaches the steady state what it is? There is no answer besides an assumption that bonds (or bartered goods, or scrip) don't change hands more than once per time period.

It doesn't matter what it is. Whatever it is, it is assumed to change hands once per time period. And because of that, Γ=1.

2. Jason:

"Just ask yourself -- why is the rate at which the economy approaches the steady state what it is? There is no answer besides an assumption that bonds (or bartered goods, or scrip) don't change hands more than once per time period."

G&L make no such assumption. In fact, even in the SIM model money changes hands a number of times within each time period. They state:

"The causal chain is set off by a stream of payments by the government. These government expenditures generate income, a tax yield, a money supply and a consumption stream. The government has suddenly come in, and decides to order $20 worth of services from the production sector. These services are paid for by the creation of 20 units of cash money, that is$20. The money created is then circulated within the system in the following way.

"First, producers will pay households with these 20 units of cash. Households will then be forced to pay taxes on 20% of that, that is, they will have to pay 4 units in taxes. These 4 units of money are thus destroyed, as soon as the taxes are paid back to government. Households then purchase consumer services from one another, using 60% of the remaining 16 units of cash money, that is, 9.6 units, while the rest, 40% of the 16 units, will be put aside to accumulate wealth, in the form of cash balances. But the 9.6 units of consumption now generate production and an income equal to 9.6 units. Out of this income, more taxes will be paid, more cash will be accumulated, and more consumer expenditures will be carried out. But these expenditures will lead to more production and more income being distributed, all this within the very same period.

"The initial $20 government injection thus has ripple effects throughout the economy. The government injection has a multiple effect on income. This is the well-known Keynesian multiplier process, to be found in all elementary macroeconomics textbooks." (pp. 68-69). This multiplier effect continues until a short term equilibrium is reached within each time period. (SIM has two equilibrium processes, a short term process within each time period and a different, long term process across time periods. Within each period money (H) thus has a velocity which, in their example in which the long term equilibrium is approached from below, is always greater than one. 3. I think this is a matter of semantics, but I'll go ahead and cede that money doesn't change hands more than twice in a "single period". How can you tell? You can re-write part of the SIM model as: $$\Delta C = \frac{\alpha_{1} (1 - \theta) \Delta G + \alpha_{2} \Delta H_{-1}}{1 - \alpha_{1} + \alpha_{1} \theta}$$ You can see that you don't get terms of higher order than$\alpha_{1} \theta$, which means at most two transactions of the sort G&L describe in that quote over the course of a time period (e.g. at the beginning and end). But regardless of these details, the main point is that as it is written, the rate of approach to the steady state is an assumption buried in the model. You change it by changing "$\Gamma$". Even Ramanan accepted that you could change the rate of approach to the steady state (although he erroneously thought you could do it by changing the alphas). Why is this rate a fundamental parameter of the model that derives from "accounting" ... it doesn't make any sense. 4. Jason: "I think this is a matter of semantics, but I'll go ahead and cede that money doesn't change hands more than twice in a "single period"." I don't see that it matters, but let's look at their example in Table 3.4, period 2. At the start of period 2 the government creates and spends 20 dollars into the economy, and immediately taxes away 20% of that, or 4 (dollars understood), leaving 16. It will tax away an additional 3.7 by the end of the period, leaving 12.3. This process is indicated on pp. 68-69. It is not spelled out in detail, however, but it is plain that the maximum amount of cash in the economy in period 2 is 16 and the minimum is 12.3. The nominal GDP in period 2 is 38.5. That means that the minimum velocity of money in period 2 is 38.5/16 = 2.41. Jason: "But regardless of these details, the main point is that as it is written, the rate of approach to the steady state is an assumption buried in the model. You change it by changing "Γ"." Well, I still don't know what you mean by Γ except a parameter for altering the rate of approach to a steady state. I suspect that you are talking about a different model and a different economy; IOW talking past G&L et al. I do not see how you have critiqued the G&L models except to say that you prefer something else. Jason: "Even Ramanan accepted that you could change the rate of approach to the steady state (although he erroneously thought you could do it by changing the alphas). Why is this rate a fundamental parameter of the model that derives from "accounting" ... it doesn't make any sense." Can you change the rate of approach by changing the alphas? Let's see. First, what do we mean by changing the rate of approach? If we approach a steady state from below, starting from zero, as G&L do, then I think that the things to look at are the percentages of the asymptotic values for C and H. In their example with a tax rate of 20%, alpha-1 of 0.6, and alpha-2 of 0.4, those values are 80 and 80, and at the end of period 3 they have reached 34.9% and 28.4%, respectively of their asymptotic values. What happens if we keep the tax rate at 20% and change alpha-1 to 95% and alpha-2 to 72%? As before during period 1 everything is zero. At the end of period 2 C = 63.33 and H = 3.33; at the end of period 3 C = 73.33 and H = 4.67. The asymptotic values are 80 and 5.56. So after period 3 they have reached 92% and 78% of their asymptotic values, respectively. :) 5. You ignored my argument. If you change the alphas you change the steady state so that is irrelevant. I have now gone through this model literally dozens of times and not found any error in my reasoning despite being challenged by several people. I am not adverse to correcting my mistakes. But as there aren't any. I feel a bit like I'm telling people there is a constant C you get when you integrate a function and people are adamant that C = 0. 6. Jason: "If you change the alphas you change the steady state so that is irrelevant." Well, there is a certain ambiguity there. I thought that your point was about changing the alphas changing the rate of approach to the steady state, **whatever it was**, not about whether changing the alphas changed the value of H in the steady state. To quote you again, "the main point is that as it is written, the rate of approach to the steady state is an assumption buried in the model." "Buried in the model" isn't very clear, is it? It isn't clear at all. And it was not even deeply buried. I find it hard to believe that you and Ramanan were arguing about whether changing the alphas changes the eventual supply of cash in the economy. But now that I see that your complaint is that the alphas and other parameters of SIM determine not only the values of the nominal Y, C, H, and other variables in the steady state, but also the rate of convergence to that state, my reaction is the same as before: a big so what, good buddy. The parameters of the model determine its behavior. Oh, the horror! I have a separate comment, but it will wait. 7. Actually, I have a question that I can state briefly. Jason: "I feel a bit like I'm telling people there is a constant C you get when you integrate a function and people are adamant that C = 0." Why do think that people are adamant that Γ = 1? 8. Here are a couple of questions that I think may be easy for you to answer. :) First, assume that G = 20 in every period, and that Θ = 0.2 in every period; also that the alphas are undetermined. (We are interested in what happens if we change the alphas.) Question 1: In that case, what do you mean by the steady state? Question 2: In that case, what do you take as the measure of the distance between the steady state and another state? Thanks. :) 9. Hi Bill, You said: "I find it hard to believe that you and Ramanan were arguing about whether changing the alphas changes the eventual supply of cash in the economy." We were not. Ramanan said you could account for any change in Γ with a change in the alphas or theta. That is not true. The alphas have constraints that prevent you from matching any value of Γ, and where you do "match" it's only an approximation. "But now that I see that your complaint is that the alphas and other parameters of SIM determine not only the values of the nominal Y, C, H, and other variables in the steady state, but also the rate of convergence to that state" The idea is that the choice of Γ = 1 controls the rate of approach to the steady state. You can also make some changes to the alphas that also control the rate of approach to the steady state, but it's not the same thing. Also, while Γ has no impact on the SIM economy once it reaches the steady state, the alphas and theta still do. It's different -- it's a different degree of freedom. Imagine controlling the volume of your stereo by adjusting the volume (Γ) or adjusting the left-right balance (alphas). Ramanan was saying you could control the volume with only the stereo balance. However, that can only adjust the volume to be between say 100 dB and 97 dB (one speaker off, balance set to left). Only adjusting the volume (Γ) gets you the full range from 0 to 100 dB. Now Γ = 1 is just a label for a degree of freedom in the model that is assumed away; you could probably implement that degree of freedom it in a number of ways. "Why do think that people are adamant that Γ = 1?" Because they think it is an accounting identity, but it's really a model assumption. It's generally a resistance to exchange so that exchanges only happen at the beginning and end of a time period. I've used the analogy that it is resistance to producing enough scrip since that is intuitive to me, but resistance to barter is another possible explanation. 10. Question 1: No idea. Without defining the alphas, we don't know what the steady state is. Question 2: I don't think anyone has ever discussed a metric for the distance between steady states. I would default to the Euclidean metric where you take the norm of the difference between two vectors d = |(H1, C1, G1, YD1, Y1, T1) - (H2, C2, G2, YD2, Y2, T2)| You should check out Tom Brown's blog; he's set up a several versions of SIM that allow you to change the alphas and "Γ". http://banking-discussion.blogspot.com/2016/03/sim6-updated-sim-to-preserve-time.html 11. Jason: "I would default to the Euclidean metric where you take the norm of the difference between two vectors d = |(H1, C1, G1, YD1, Y1, T1) - (H2, C2, G2, YD2, Y2, T2)|" Can we take the vector, (H*, C*, G*, YD*, Y*, T*) as definitive of the stable state? 12. Jason: "The idea is that the choice of Γ = 1 controls the rate of approach to the steady state. You can also make some changes to the alphas that also control the rate of approach to the steady state, but it's not the same thing. Also, while Γ has no impact on the SIM economy once it reaches the steady state, the alphas and theta still do." I can see why you might prefer a model that has Γ, but I fail to see an economics case for Γ. That's why I keep asking you for an operational definition. So far all I see is that it is a parameter that allows you to tune the convergence of the model without changing the alphas. That's nice, but . . . . Bill: "Why do think that people are adamant that Γ = 1?" Jason: "Because they think it is an accounting identity, but it's really a model assumption." I think that one possible reason is that H stands for cash. Sure, that is an assumption of the model. We could have other models without cash, or models with cash and other kind of money, or models with money and bonds, and, in fact, G&L do have other, more complex models. But SIM has cash, represented by H. In SIM, government spending (G) and taxing (T) are done in cash, so ΔH = G - T represents an equation in terms of cash. When you say that ΔH = Γ(G - T) the equation is no longer in terms of cash. So we no longer have a cash economy. What do we have? That is unclear. It is true that, if Γ = 1, the model acts as if it were a cash economy, but it isn't really. 'Γ = 1' is not an assumption of SIM, because Γ does not exist in SIM. SIM has a cash economy. A model with Γ does not have a cash economy. 13. "SIM has a cash economy." There is literally nothing in the model equations that says that. There are no agents and no bits of cash that change hands. All we have are some aggregates. They say we spend something proportional to H. Taking ΔH = G - T is literally the same mistake as taking PY = M instead of PY = MV or k PY = M There's a (change in) stock on one side of the equation and a flow on the other side. You can choose how fast to spend H. There is a degree of freedom. There's effectively a derivative that isn't specified. I put Γ in the equation ΔH = Γ(G - T) because that is easiest for me to see. Apparently it confuses you because you see ΔH = G - T as an accounting identity instead of an assumption on the rate of adjustment to the steady state. Fine. But you can move it back into some other equations if you'd like. How about here: $$\Delta C = \frac{\alpha_{1} (1 - \theta) \Delta G + \alpha_{2} \Delta H_{-1}/\Gamma}{1 - \alpha_{1} + \alpha_{1} \theta}$$ Does that make it any clearer? In the version up above in this comment thread, the ratio of delta G to delta H going into consumption is fixed by the alphas and theta. But it's not. There's a freedom that you have unless exchange happens only at the time steps. If I get money and can only spend it on Jan 1, Apr 1, Jul 1 and Oct 1, then Γ = 1. Otherwise Γ is not 1. 14. Bill: "SIM has a cash economy." Jason: "There is literally nothing in the model equations that says that. There are no agents and no bits of cash that change hands." Let me refer you once more to the text of G&L, p. 59: "The balance sheet matrix for Model SIM, given by Table 3.1, is extremely simple as there is only one item – money (H) – which is a liability of the government and an asset of households. This money is printed by government: we can assume it consists of banknotes, that is, what is usually called **cash** money." (Emphasis mine.) Jason: "All we have are some aggregates. They say we spend something proportional to H." I believe that the equation about private spending is this, which refers to spending within each period: C = α1 · YD + α2 · H(previous) Without subscripts I used "(previous)" instead of the subscript "-1". Anyway, C is not generally proportional to H. Jason: "Taking ΔH = G - T is literally the same mistake as taking PY = M instead of PY = MV or k PY = M "There's a (change in) stock on one side of the equation and a flow on the other side. You can choose how fast to spend H. There is a degree of freedom. There's effectively a derivative that isn't specified." Actually, ΔH = G - T is not about private spending of H. It is about government spending and taxation. Government spending takes place at the beginning of each period, but taxation occurs within it, depending upon private spending and, hence, income. G&L do not go into detail, but, to quote them once more, on p. 69: "The initial$20 government injection thus has ripple effects throughout the economy. The government injection has a multiple effect on income. This is the well-known Keynesian multiplier process, to be found in all elementary macroeconomics textbooks."

The government taxes its initial spending of 20USD, leaving an initial increase of H by 16USD. Households now spend according to the Keynesian multiplier. Money circulates throughout the period. Its average velocity in the period, V, is given by NGDP/M, which in G&L is written Y/H.

It is true that G&L do not specify their model well enough for us to calculate V precisely, but they do allow us to set limits on V. For instance, in a steady state where H* = 4 and Y* = 100 (not their example), within each period H varies between 20 at the beginning of the period and 4 at the end, so that V lies between 5 and 25, depending upon the details of spending and taxation.

Jason: "I put Γ in the equation ΔH = Γ(G - T) because that is easiest for me to see. Apparently it confuses you because you see ΔH = G - T as an accounting identity instead of an assumption on the rate of adjustment to the steady state. "

I am not confused. ΔH = G - T is well defined in G&L. In your model, Γ indeed affects the rate of convergence to the steady state. However, as I said, and as you have not disagreed about, Γ takes us out of a cash economy. What is H in your model? You have not spelled that out clearly.

If you want to make a different model that you believe is superior to theirs, fine! But the burden of proof is yours. If you think that they have made a mistake, the burden of proof is yours. You claim: "the verbal interpretations of G&L are actually at odds with the equations they wrote down." The burden of proof is yours.

I am a sympathetic audience for you, as I am one of your supporters. But you have not convinced me that you have gotten to first base.

15. To be clear, G&L have the overall burden of proof for their models and approach. However, you have made specific claims that put the burden of proof for them on you.

2. Jason,

I agree with a lot of the points you make (I don’t have any strong views on the maths of SFC models and I mostly agree with your behavioural points). However, when you talk about accounting identities, I think that you are mostly wrong. This comment draws an analogy with chemistry to try to explain how the difference of views arises; makes a couple of comments on your recent post on ‘saving’; and offers you a simple challenge.

Imagine that macro-economists devise accounting identities for macro-chemistry involving the sum total across an accounting period of all chemistry experiments which create water from its constituent elements.

Imagine that they define an identity which says that, at a macro level (rather than the simple micro level at which dumb experimental chemists live), it takes three parts of hydrogen and one part of oxygen to create one part of water. They also claim that the identity is true by definition as they defined the identity.

I imagine that the dumb chemists who live at the micro level would have a problem with this. They would argue that the micro-accounting of chemistry says that it takes two parts of hydrogen and one of oxygen to make one part of water. As the macro view is just the sum total of millions of different micro-level experiments, the economists’ macro-identity must be wrong. The macro-economists would dismiss this criticism as irrelevant as their macro-identity is true by definition.

The chemists might try again and suggest that, as the length of the macro accounting time period tends to zero, there would be fewer and fewer experiments in each period. Eventually, we would reach a period length so short that there would be only one experiment in the period. At that point, the macro identity would have to match the result of the single experiment, so either the macro identity or the micro results of that one experiment must be wrong. The macro-economists would dismiss this criticism as their view of micro-foundations involves the motivation of a representative chemist.

Whose side would you be on in this debate?

Or imagine instead that macro-economists said that, at a macro level, it takes two parts of hydrogen and one part of a residual to make one part of water (where the residual includes all of the elements other than hydrogen required to make water).

I imagine that the dumb chemists who live at the micro level would have a problem with this too. They would argue that the micro-accounting of chemistry says that the residual must be oxygen as nothing else would make sense, and they would accuse the economists of causing confusion. The macro-economists would dismiss this criticism as irrelevant and assume that the dumb chemists were even dumber than they had thought.

Whose side would you be on in this debate?

Or imagine that macro-economists agreed that, at a macro level the identity involves two parts of hydrogen and one part of oxygen for each one part of water. However, as there are three terms in the identity (hydrogen, oxygen and water), there must be separate micro-events corresponding to each term in the identity i.e. there is one type of event which creates water; a second independent type of event which destroys hydrogen; and a third independent type of event which destroys oxygen. In combination, these three types of event produce the identity.

I imagine that the dumb chemists who live at the micro level would have a problem with this too. They would point out that the macro-economists had completely missed the point of chemistry. There are not independent event types for each term in the identity. There is only one type of event, experiments, which transform all three terms together (or two types if we include experiments which convert water back to its constituent elements). The macro-economists would dismiss this criticism as irrelevant.

Whose side would you be on in this debate?

(cont’d)

3. Returning to Keynes’ identities, the problem is that macro-economists consistently make the equivalent of the three errors in my macro-chemistry analogy. Most mainstream economists do not appear to understand basic accounting at a micro-level, so they don’t understand that their ‘true by definition’ statements are wrong.

A different point. GDP covers all activities from mining of raw materials through to manufacturing of goods, as well as the sale of the newly produced goods and services to households. Your articulation of the identities appears to ignore everything other that the sale of final goods and services. Where do you think that the final goods and services come from? It’s not clear. Real-world accounting must obey the laws of physics.

Another point. In an earlier post on the term ‘saving’, you said that you agreed with Nick Rowe’s definition of the term. Nick said that saving includes:

“buying a newly-produced investment good, buying land, buying a used car, buying financial assets, and sticking $100 under the mattress”. There are three problems with this over and above the general point that making up ad-hoc definitions of the terms in these identities is precisely the sort of behaviour that has caused 80 years of confusion. First, the identities we are dealing with relate to GDP and not the entire economy. Trading of existing assets (such as land, used cars or existing financial assets) by households is outside the scope of the model, so Nick has a basic scope issue. (Also, even if existing assets were included (e.g. on the business side of the identity), the sale of an existing asset by one business would be accompanied by the purchase of the same asset by another business so the accounting entries would cancel out at the macro level. Nick seems to be thinking about only one half of the transaction). Second, as I said on an earlier post, accounting is about things you HAVE and things you DO. For example: At the start of a period I HAVE €100. I then EARN €200. As a result, I now HAVE €300. I then SPEND €175. As a result, I now HAVE €125. My saving for the period is the €125 I HAVE at the end of the period minus the €100 I HAD at the start of the period i.e. €25. It’s not complicated and is analogous to a chemistry experiment. Saving is something you HAVE. It is not something you DO. When Nick suggests that “sticking$100 under the mattress” is saving, he is trying to turn it into something you DO. That is wrong. The saving (and dissaving) occurs through the activities of EARNing and SPENDing. The mattress is irrelevant. Keynes understood this. Nick doesn’t.

Third, Nick says that “buying a newly-produced investment good” is SAVING. However, you say (in comments in your post on saving) that INVESTMENT “includes non-government buying of non-consumption goods (houses, production machinery)”. These are not consistent so at least one of you is wrong.

You seem to see accounting as a trivial modern contrivance. However, (according to Wikipedia) double-entry bookkeeping dates from around AD 600 in the Muslim world and from the end of the 13th century in Europe. The essence of accounting is the concept of conservation. Arguably, chemistry only escaped the nonsense of alchemy when it bought into the discipline of accounting and the concept of conservation. When economists make up their own incoherent version of macro-accounting, they are ignoring over a millennium of accounting at the micro-level.

Laughably, when they’re not talking about accounting identities, macro-economists lecture the rest of the world on the need for micro-foundations in economics to ensure that the macro view is built in a way that is consistent with the micro view. You couldn’t make this stuff up!

(cont’d)

1. These are not consistent so at least one of you is wrong.

If there are no exports, and in the event of zero budget deficit, S = I, so Nick and I are totally consistent. Without exports, there are:

C + S + T = C + I + G

if G = T (no budget deficit), then S = I.

My statement is equivalent to saying if Y = C + I + G, then Y - C - G = I. It's just accounting :)

...

How does accounting deal with the endowment effect? If I buy a bike for €100, it's suddenly worth (to me), say, €120. Where did that €20 come from?

2. "If I buy a bike for €100, it's suddenly worth (to me), say, €120. Where did that €20 come from?"

All skandhas are empty. :)

3. Hi, Jamie. :)

Here is a hint. Do not use the dollar sign in your comments here. (In case you had not figured that out. ;))

4. OK, so here is my challenge. In my discussion on macro-chemistry, I said that:

“The chemists might try again and suggest that, as the macro accounting time period tends to zero, there would be fewer and fewer experiments in each period. Eventually, we would reach a period so short that there would be only one experiment in the period. At that point, the macro identity would have to match the result of the single experiment …”.

If we replace ‘experiment’ with ‘transaction’ then the same thing is true for macro-economic accounting identities. We can consider the micro-accounting for any single GDP-related transaction and ask how that micro-accounting relates to the macro-level accounting identity. That will show us how the macro-identity builds up.

To keep it simple, let’s ignore both government and overseas and consider only transactions involving businesses and households. That means that the relevant Keynesian accounting identity is:

Investment + Consumption = Consumption + Saving

Here are three VERY simple scenarios. Accounting is not difficult. It is mostly just pedantic – like science. It’s also not about human behaviour. It’s mostly just about the recording of observable events in a coherent and consistent fashion – again like science.

Scenario 1: A business has a newly manufactured bicycle which it values at €100. A household has €100. The single transaction is that the business sells the bicycle to the household for €100.

Scenario 2: A business has a newly manufactured bicycle which it values at €80. A household has €100. The single transaction is that the business sells the bicycle to the household for €100.

Scenario 3: A business has the component parts for a bicycle which it values at €50. A household has €0. The single transaction is that the business hires the household to build the bicycle from its component parts. The business pays the household €30 for this work.

How would each of these three scenarios be reflected in Keynes’ accounting identity? What are the implications of the answers for the definitions of the terms in the macro-level identity?

1. Hi Jamie,

Here are my answers; although I am under the impression that you wanted different answers (or you were trying some trick questions) ...

Scenario 1: C = 100, S = I = 0.

There is one final good produced that is purchased as a household consumption good at a price of 100.

Scenario 2: C = 100, S = I = 0.

There is one final good produced that is purchased as a household consumption good at a price of 100.

Scenario 3: C = ??, S = I = ??.

I think in this case the €50 bike parts is capital, which could have been investment/saving in the previous time period. As the bike isn't sold, it doesn't contribute to GDP. Depending on what the household does with the €30, we could have C = 30, C = 0, or something in between. The €30 paid for labor doesn't count towards GDP because if it was spent on consumption goods, it would be double counted. Sort of like how buying a stock doesn't contribute to GDP because the company may buy capital goods with it -- double counting the money.

...

Scenario 4: A business has a newly manufactured bicycle which it values at €100. A bike rental business has €100. The single transaction is that the business sells the bicycle to the bike rental business for €100.

Scenario 4: C = 0, S = I = 100.

2. Jamie: "Scenario 1: A business has a newly manufactured bicycle which it values at €100. A household has €100. The single transaction is that the business sells the bicycle to the household for €100."

Here are my thoughts, FWIW.

First, it does not matter how the business values the bike. Accounting in practice may deal with such subjective things, but they do not enter into the national accounting that we are talking about here.

Second, I think that we need to know what time period we are talking about. "Newly" is not specific enough. IIUC, if the bike existed in the previous time period, buying it is saving; if it was manufactured in the present time period, buying it is consumption. Economists may set me straight on that if I have it wrong. :)

3. (I think) if the bike is not sold in the same period, it is "inventory investment", contributing to I = S. However, when it is sold to a consumer in another period it is consumption in that period.

5. I am busy busy now, but here is something that illustrates my qualms about the approach suggested in this post. Here are a couple of equations from Brad DeLong, along with interpretations. From http://www.bradford-delong.com/2016/04/must-read-martin-wolf-negative-rates-are-not-the-fault-of-central-banks-ftcomhttpsnextftcomcontent9b1d8b.html

DeLong:

“As I told my undergraduates yesterday:

Y = μ[co + Io + NX] + μG - μ(Ir)r

where:

Y is real GDP
μ = 1/(1-cy) is the Keynesian multiplier
co is consumer confidence
cy is the marginal propensity to consume
C = co + cyY is the consumption function--how households' spending on consumption goods and services varies with consumer confidence, with their income which is equal to real GDP Y, and with the marginal propensity to consume
Io is businesses' and banks' "animal spirits"--their confidence in enterprise
r is "the" long-term risky real interest rate r
Ir is the sensitivity of business investment to r
NX is foreigners' net demand for our exports
And G is government purchases. “ (Parentheses around lr added by me, because the subscripts did not copy.)

A couple of quick notes. By real GDP DeLong does not mean a vector of quantities of goods and services. The equation for the Keynesian multiplier, μ, looks like it is the limit of an infinite process which might not be realized in a finite interval of time. The G&L models inherit that problem.

Were I in DeLong’s class I would have questions about the variables in this equation. First, how are they measured?

I suppose that Y, NX, G, and r are measured fairly straightforwardly. Maybe μ, as well. But I think that the same is not true for consumer confidence, animal spirits, and sensitivity to r. Certainly when I have asked economists how business confidence (animal spirits here, I guess) is measured, I have gotten no reply. If only one variable were not measurable, then the equation could be rewritten to define it, but three variables?

And assuming that the variables were measurable, why should we think that they have a linear relationship to Y?

It is not that consumer confidence and animal spirits are not important and relevant to GDP. **But why is their relationship to GDP expressed as an equation instead of a paragraph?** Why should we give it any more credit than this equation?

HATE + EMPATHY = LOVE

Back to DeLong:

“And as I am going to tell them next Monday, real GDP Y will be equal to potential output Y* whenever "the" interest rate r is equal to the Wicksellian neutral rate r*, which by simple algebra is:

r* = [co + Io + NX]/Ir + G/Ir - Y*/μ(Ir)” (Parentheses added)

In this equation, r* is unmeasurable (I suppose), which might be OK. But we still have co, Io, and Ir on the right side of the equation, as well as Y*, which may not be measurable, either.

Does the root of excess mathiness in economics lies in such equations?

1. Hi Bill,

Were you in DeLong’s class, you probably would have been told what all of those symbols meant and how they were measured earlier in the year or in the prerequisites for the course.

Coming into the middle of a class (any class) and saying: "you didn't tell me about what all the symbols mean and how they are measured" is expecting a bit too much. Knowledge builds on other knowledge.

If you were to walk into a physics class and the professor wrote down

ℒ = ψ(i γ·∂ - m)ψ

Would you ask what these symbols are and how they are measured? I'd assume if you'd gotten this far in physics, you might have gleaned a bit about wavefunctions and Lagrangians. But even if you hadn't, none of these symbols are actually measurable.

A Lagrangian (ℒ) is a mathematical object that represents the field content of your quantum field theory. The "d-slash" operator (γ·∂) is the covariant derivative on a spin manifold (a pure mathematical object). The mass (m) is actually a mass operator that only with all of the quantum corrections represents the (measurable) mass of an excitation of the spinor field. And the Grassmann valued quantum field (ψ) really is more of a bookkeeping device, but can be related to a wavefunction which is unobservable.

Did that help?

Or is physics excessively mathy? Before answering, note that theory is accurate to 17 decimal places.

There is a difference between questioning something after you've learned a bit about it and questioning something without having bothered to learn about it.

If you've studied a bit of economics, you'd know what GDP is and how it is measured (these things are widely described on the internet and the BEA has lots of references). The same goes for real versus nominal variables.

The output gap and the natural (Wicksellian) rate of interest are also basic Keynesian economics concepts. They are measured by looking at the response of the economy to policy -- which is to say they are effectively parameters in the theory.

Economics isn't like physics in the sense that is hasn't been figured out yet, so the answers are not all at the back of the book. The Keynesian theory DeLong describes might not be correct. Maybe my information equilibrium theory is really the correct approach. Maybe something else is.

But if you're claiming economics is "mathy" because you haven't bothered to study the math, well I can't help you.

Additionally, Romer's mathiness means something completely different than your use here. Coming from his example, Romer would call the way physicists use math mathiness because it (usually) isn't as rigorous as a mathematician's math.

2. Thanks, Jason. :)

Then let me ask you. How is Io, businesses' and banks' animal spirits measured?

3. Jason: "Or is physics excessively mathy? Before answering, note that theory is accurate to 17 decimal places."

You could not make that statement if physics were only equations. The equations have to be interpreted.

6. Sorry for the delay in replying. Real life intervened. Sorry also about the dollar sign as well. I usually use € but I was quoting Nick Rowe and forgot to change his dollar to a €.

I have included my answers at the end of a slide pack at the link below. My answers are not the same as your answers. The rest of the slide pack is my diagrammatic notes to myself regarding how Keynes’ identity must work in order to be consistent with micro accounting and some notes about the dynamics of recessions from a business perspective which follow from the identity accounting logic.

There are no tricks. I am merely trying to illustrate the difference in thinking on these identities between mainstream economists and heterodox economists where your views are similar to the mainstream.

The assumption is that the specific transactions in each scenario are the only transactions that take place in the economy is a particular period. When I say ‘newly manufactured’ I meant that the bicycle was manufactured in the prior period so it already exists at the start of the current period. All that remains is for the bicycle to be sold in the current period.

Jason: “Scenario 4: A business has a newly manufactured bicycle which it values at €100. A bike rental business has €100. The single transaction is that the business sells the bicycle to the bike rental business for €100.

Scenario 4: C = 0, S = I = 100”

No that is wrong. If a business sells something that it values at €100 to another business for €100 then it represents a disinvestment of €100 for the selling business and an investment of €100 for the purchasing business so the I term nets out to 0. There is no net saving either. You have to account for BOTH parties in each transaction.

Bill: “First, it does not matter how the business values the bike. Accounting in practice may deal with such subjective things, but they do not enter into the national accounting that we are talking about here”

No that is wrong and it’s not subjective. Businesses value short-term inventory investments at cost so the valuation represents what the business spent to create the investment. When the business values a bicycle at €80 and sells it at €100, it makes €20 profit. Profit is business saving which, as you will see from my slide pack, I have separated out from the S term in the identity. (Mainstream economists never make clear whose saving the S term represents and often appear to ignore profit).

Irrespective of whether you find my answers convincing, the real-world accounting versus ‘economists accounting’ is one of the key things that is at the heart of the mainstream Keynesian versus Post Keynesian debates. You will at least understand the debate better even if you reject my answers and continue to side with the mainstream.

Here is the slide pack. I’ll leave it as published for a few days until you have read it.

1. Thanks, Jamie! :)

Jamie: "The assumption is that the specific transactions in each scenario are the only transactions that take place in the economy is a particular period. When I say ‘newly manufactured’ I meant that the bicycle was manufactured in the prior period so it already exists at the start of the current period. All that remains is for the bicycle to be sold in the current period. . . .

"Businesses value short-term inventory investments at cost so the valuation represents what the business spent to create the investment. When the business values a bicycle at €80 and sells it at €100, it makes €20 profit."

OK, you are saying that the business bought the bike for €80 in the previous time period, but sell it for €100 in the current time period, right?

In that case isn't the €80 transaction included in the accounting for GDP in the previous time period? It may be relevant to the business and its profits or losses, but what is its relevance to current GDP?

2. Hi Jamie,

Those are some nicely put together slides.

Of course I answered in terms of what economists mean by the accounting identities. If you ask about the theory of gravity, I would assume you mean General Relativity. There are a couple of other theories out there: 11-d supergravity, loop quantum gravity, causal dynamical triangulations. But I don't assume you mean them if you start talking about gravitational field strength. In the same way, if you just say investment and savings on an economics blog, I assume you mean the standard definitions: e.g. in the US, the NIPA definitions that lead to the BEA data.

https://en.wikipedia.org/wiki/National_Income_and_Product_Accounts#Production_accounting

1. You should probably say "post-Keynesian consumption", "post-Keynesian savings" and "post-Keynesian investment". I try to say "information equilibrium" instead of just "equilibrium". I understand it is annoying, but mainstream economics is just that: the mainstream. Therefore using mainstream terminology just leads to confusing writing and differences are just assumed to be mistakes.

2. When you state (I am assuming with G = 0, NX = 0)

C + I - RP = C + S = Y

You are either at a minimum changing the definition of I and total income Y, or RP ≡ 0. However, since the definition of I is basically "stuff that contributes to Y that isn't C", you must be changing the definition of I. Additionally, you say the C and I are business on one side, and C and S are households on the other, but I includes residential investment that is attributed to both households and rental agencies. Consumption is done by households only. For businesses, buying printer paper is investment, since it ostensibly is used in the creation of their product. There is no business "consumption". I'm not saying this to say you are wrong (maybe your relabeling is helpful in some way) -- I am saying this to say how much you have changed the definitions. And there aren't a lot of Post-Keynesian data aggregation services out there, so I'm not sure what data you can use. I have the same issues: not all governments release "M0" data (the US government doesn't release seasonally adjusted M0 to my continued consternation).

3. Changing the definitions of Y and I means you can't use the widely available data, since it is all computed using the mainstream definitions.

4. How do you incorporate private (business) valuations of assets? Mark-to-market? Marginal product? What about depreciation?

5. Do these changes in definitions lead to anything useful? Are recessions intimately connected to profit? Well, as they're intimately connected with income in the standard definitions, this just seems like we've re-labeled stuff.

3. continued ...

I am almost certain that the standard definitions going into the national income accounting identity

Y = C + I + G + NX

are going to turn out to be flawed. They were basically invented in the 1930s, 80+ years before the advent of the true fundamental theory -- information equilibrium. I'm only half joking.

I wrote what I thought was a really good post here:

http://informationtransfereconomics.blogspot.com/2016/03/does-saving-make-sense.html

Basically, the reason to use any particular identity is that you think the terms in it move in highly correlated ways. The best example is G. In:

Y = C + I + G + NX

G -- made of thousands of line items in the budget -- tends to move up or down as a big block. And that big block can move independently of the other components.

Let's say:

Y = C + I - RP

Does RP move in a correlated way independently of the other components? Then it's a useful sub-component. But in recessions, C, I and RP all seem to move together. I'd need to see some evidence that RP is special to break it out of/include it in income.

I've advocated (in the link above) the income identity:

Y = X + G

where X is everything except government expenditures.

Given how terrible macroeconomics is at describing empirical reality, we should really retreat to much simpler descriptions of the economy.

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.