Wednesday, November 9, 2016

Blackford's information equilibrium model

Still reeling from last night's election results. I took the day off work. Maybe some of you out there need a break from coverage of the aftermath as well. I thought I would take a break and turn to something more civilized ...

Blackford has responded to my response to his response, etc. I see that we are essentially at an impasse since his response mostly repeats previous arguments or claims bafflement at my arguments rather than engaging with them. I'll call a couple pieces out, but what will probably be more interesting and constructive is my construction of Blackford's model in terms of information equilibrium at the bottom of this post (separated by asterisks).

"It is exceedingly difficult for me to understand why you insist on defending the use of Friedman's methodology in physics in criticizing my paper.  My paper is about the misuse of Friedman’s methodology in economics, not in physics. "
My argument is simple. The methodology is fine for science, therefore it is a fortiori fine for  a scientific approach to economics ...

... unless you are asserting that economics shouldn't be approached scientifically or claiming Friedman's methodology is used incorrectly (neither make any sense in the context of the original article).

As a logical argument
x is a discipline in the set of scientific disciplines S 
p(x) is the statement that effective theory (Friedman's "as if" methodology) is a valid approach for x 
e is economics 
∀x ∈ S, p(x) 
e ∈ S 
∴ p(e) 

"When I present a reasoned analysis of the historical data and a detailed explanation as to why the inevitable result of deregulating or poorly regulating the financial system leads to a catastrophe, you insist on ignoring these historical data and my reasoned argument and explanation in the absence of a mathematical model that more accurately predicts the economic data that you want to predict—data that doesn't even include the variables that I see as being crucially important to an understanding of the historical data that I try to understand and explain."
Friedman's "as if" approach was about mathematical models of data, therefore discussion of non-mathematical explanations of historical data is a non sequitur.

As an aside, saying Y is the inevitable result of X is a causal statement about economics (X causes Y). I'll leave the conclusion to Paul Krugman:
Any time you make any kind of causal statement about economics, you are at least implicitly using a model of how the economy works. And when you refuse to be explicit about that model, you almost always end up – whether you know it or not – de facto using models that are much more simplistic than the crossing curves or whatever your intellectual opponents are using.
... crossing curves ... or rational agent models.

"You boldly take this position in spite of the fact that this is the same kind of reasoning and argument used to ridicule and marginalize those economists who tried to oppose the economic policies that were responsible for blowing up the world’s economy in the first place."
This is not my argument. My argument was that Friedman's "as if" methodology is fine as science, and blaming Friedman rather than, say, the EMH (which isn't a result of "as if", and about which a defensible case could be made that belief in the EMH leads to financial crises) is barking up the wrong tree.

"I was trained as a neoclassical economist ... When I wrote Where Did All The Money Go? I wrote it as a narrative so that I could explain the financial crisis ... [to] any undergraduate student or intelligent lay person ... As a result, I did not write out equations and build econometric models in this eBook that would leave undergraduate students and lay people in a fog.  I left that to others."
So you left the economic model that purportedly backs up your ideas as an exercise for the reader? And you just sort of assumed it existed?

As an aside, I agree that equations can disrupt the narrative flow (I'm minimizing them in my book), but they shouldn't be ignored. Interested (especially younger) readers would aspire to understand equations relegated to an appendix or cited in references. I bought a copy of Bergmann's Theory of Relativity (review here [pdf]) when I hadn't yet completed calculus because I aspired to understand it.

"At the same time, I attempted to explain ... why my [theory] cannot be examined within the standard neoclassical model ..."
How do you know this if you left the equations/models to others?

"Given your bravado in discussing the methodology of economics, I *assumed* you would be able to make that translation into whatever economic paradigm you view the economy ... "
You assumed I could do it, much like you assumed others would be able to fill in the gaps in your theory and compare it to data to see if it's right.

However, this wasn't the complaint I had. You said you had some theory at your references that backed up your claims about Friedman's "as if" methodology for mathematical theories (and mainstream economics) that are compared to data, and at the references I saw no mathematical theory or comparison with data. I guess you assumed I would click on your links, read your references, derive your theory, compare it to data, and then realize you were right all along?

We have now gone far afield from directly discussing Friedman's as if methodology. But it sounds fun (or at least more fun, and possibly instructive) to write up an information equilibrium model of your work.

*  *  *

Let's get started! See here for basic definitions.
"if the levels of employment, output, income, and prices are to be stable (not change or be in equilibrium, your choice), ..."
Well, this isn't very specific because being stable, not changing, or being in equilibrium are not necessarily all synonyms (see e.g. here for definitions of dynamic unemployment or dynamic employment equilibria). Regardless, I will take this to mean these quantities are related by, or the result of, information equilibrium relationships.
" ... the amount of money people chose to spend to purchase the output that is produced must be exactly equal to the total income generated in producing that output. (Actually, it’s the rate at which people choose to spend money that must equal the rate at which income is generated ..."
Money spent to purchase currently produced output is consumption C, and let's call income W [2]. This statement is the assumption that C and W are in information equilibrium C ⇄ W, but since the rates are equal, we have an information transfer index k = 1. And therefore C = α W. Since these are supposed to be equal at some point, we should say α = 1, but in reality α ~ 1.5 over most of the available data.
"This presents a problem because not all people chose to spend all of their income on currently produced output ... the amount of money people chose to spend to purchase the output that is produced must be less than the total income generated in producing that output."
This basically says that our information equilibrium relationship can fail, and become a non-ideal information transfer relationship C → W, so that we have C ≥ α W. This creates a pathway for shocks due to e.g. panic -- and subsequent herding behavior -- over debt levels.
"... This must be compensated for by an equal amount of money spent by other people who choose to spend in excess of their income if the levels of employment, output, income, and prices are to be stable. ... the primary mechanism by which it takes place in our modern economy is through the creation of debt, ... there exists a specific rate of debt creation that must occur in order to maintain a specific level of income."
So now we have C ≥ α W generally, but assume W + D = C (where D is debt) in equilibrium. I will re-write this in terms of the debt to income ratio ρ ≡ D/W so that

C = W (1 + ρ)

following from the new information equilibrium system

C ⇄ W
C ⇄ 1 + ρ

Again with IT index assumed equal to 1 for each (basically Cobb-Douglas form with both exponents equal to 1). Let's look at a scenario where growth is constant. Call the growth of income ω, the growth of consumption γ, and the growth of 1+ρ to be r. We can say using the equilibrium ansatz e.g. W ~ exp ω t

γ = ω + r

i.e. consumption growth is equal to income growth plus debt (ratio) growth. We also have

1 + ρ = exp r t

so that

D = W₀ exp ω t (exp r t  1)

And for r t >> 1 (long run) the growth rate of debt δ is

δ ~ ω + r

And so we have γ = δ for r t >> 1. This is generally consistent with what Blackford says (he actually talks about δ > ω leading to instability). How well does this model work so far? Here I plot W, C, and 1 + ρ normalized to 1991 (the debt number from FRED only goes back to 1990s, but that's sufficient for our purposes):

And here are the growth rates (y-axis here and below is percent per annum):

And here are the growth rates of C, W, and W (1 + ρ) (i.e. γ , ω , and ω + r):

Also, we can see that δ ~ ω + r is a decent approximation

Actually, it looks like W ⇄ C is a decent model on its own. In fact, adding debt makes the model worse in quantitative ways: it reduces from 0.74 to 0.53 and increases RMS error from 157 bp to 342 bp (the former being centered at zero, the latter being biased high)

Now it is true that Blackford's theory is that deregulation of the financial sector lead to δ > ω, which lead to the crash of 2008. And it is true that δ > ω:

However, the Graham-Leach-Bliley Act (Financial Services Modernization Act of 1999) based on EMH arguments that tears down Glass-Steagall doesn't come until November of 1999, whereas δ > ω since well before. So the big deregulation didn't cause δ > ω. Additionally, the difference (area between the curves) is larger before the dot-com crash of 2000 (and subsequent early 2000s recession) than the dot-com crash until the 2008 financial crisis (and subsequent Great Recession). However, former recession was far less damaging than the latter. Shouldn't we have built up more debt before a bigger crisis?

But here we also have an illustration of a point I made in my original response:
"... again we have an example of assumptions [about accumulating debt] made because Blackford thinks they should be included, but doesn't provide us with a more empirically accurate theory based on their inclusion."
We've included debt, but the theory

C ⇄ W
C ⇄ 1 + ρ

it isn't any more empirically accurate than

C ⇄ W

It's actually worse! It's supposed to give a better account of the Great Recession, but the simpler model accounts for it just as well (i.e. a fall in income leads to a fall in consumption). Actually, the simpler model works best if we don't assume the IT index k = 1, but rather closer to k = 1.1 [2]. In any case, we have consumption growth γ approximately equal to income growth ω over the entire post-war period for which there is good data:

This means that the debt D that Blackford includes in order to bring W + D growth into equilibrium with consumption growth C isn't really doing much besides making the model less empirically accurate and setting up the exactly conditions that Blackford says lead to a financial crisis.

Let's follow through the steps. Blackford originally says

1) "the amount of money people chose to spend to purchase the output that is produced must be exactly equal to the total income"

The level version of this isn't true (C ~ 1.5 W), but he say's it really the rate version which is empirically true (ω ~ γ) as shown above. We've set up a decent (albeit simplistic) model of consumption and income that is consistent with the empirical data. But then he says:

2) "the amount of money people chose to spend to purchase the output that is produced must be less than the total income"

3) "there exists a specific rate of debt creation that must occur in order to maintain a specific level of income"

In the discussion above, I've taken this to mean W + D = C (i.e. debt financed consumption, spending more that income) [1]. However, since W and C grow at the same rate, this implies that maintaining this condition requires that D grows at that same rate -- ω ~ γ ~ δ. However we see above that δ > ω, which means that the additional debt growth (i.e. r = δ - ω) leading to the financial crisis does not come from maintaining a specific level of income (a behavioral relationship). However, Blackford says that maintaining the level of income (consumption) is what requires us to take on debt:
This phenomenon is perfectly normal and is an essential mechanism by which the system functions, but it does pose the possibility of a serious problem. Namely, if the rate at which debt must be created in order to maintain the level of income that corresponds to the full employment of our resources is greater than the rate at which income increases when the system is at full employment it means that full employment can only be maintained with an increase in debt relative to income. Maintaining full employment in this situation is unsustainable in the long run as the need to service the debt out of income must eventually overwhelm the system and cause it to become unstable.
Blackford's emphasis. He is saying we take on debt to maintain W + D = C, but if we take on debt too quickly, it ends up being unsustainable. But if we're taking it on to maintain W + D = C, why would we take it on too quickly? One needs to add in an additional (behavioral) effect to explain the fact that the empirical data says we take on debt too fast to be taking it on just to maintain W + D = C (for which it isn't needed). That behavioral effect is the lack of regulation. However, all of this is due to deciding to add a debt mechanism to the model in the first place that makes the original model worse empirically, and simply serves to set up the conditions Blackford defines as causing instability.

Adding effects (e.g. debt) to a model that not only make it worse at describing the empirical data, but additionally only serve to set up the condition you posit leads to a financial crisis is petitio principii --question begging, in the original sense of assuming the initial point. In order to explain the financial crisis, we added debt in such a manner that it makes δ > ω (i.e. δ ~ ω + r with r positive) and observe that δ > ω would be unstable leading to a financial (debt) crisis.

This is not to say that there isn't some kind of debt mechanism behind the financial crisis. It's that this one seems like a degenerative research program. We add an auxiliary hypothesis about debt (and also inequality, not discussed here) in order to handle the financial crisis, but it doesn't result in greater explanatory power (C ⇄ W did well on its own, and adding C ⇄ 1 + ρ just made it worse empirically). This is exactly what is meant by a degenerative research program:
The difference between a progressive and a degenerative research programme lies, for Lakatos, in whether the recent changes to its auxiliary hypotheses have achieved this greater explanatory/predictive power or whether they have been made simply out of the necessity of offering some response in the face of new and troublesome evidence.

*  *  *


[1] In the following, it is hard to see if Blackford means there is debt-financed consumption (C = W + D, consumption C, income W, and debt D) or debt financed income (W = C + D). However, luckily for us, it doesn't matter (you can re-label W into C or vice versa, since they form an information equilibrium relationship). I took the interpretation where we have debt financed consumption C = W + D because W < C, so it is not prima facie incompatible with empirical evidence.

[2] Here's the general information equilibrium model C ⇄ W (i.e. with k = 1.1):


  1. "∀x ∈ S, p(x)

    e ∈ S

    ∴ p(e) "

    Entirely tautological.

    1. It should be. It is a logical argument. All true logical arguments are tautologies, otherwise they'd be falsehoods.

      However, the initial premise ∀x ∈ S, p(x) (assumed in the logical statement) is actually from experience. Basically, in order to argue against the conclusion, you need to argue against the premise ∀x ∈ S, p(x) which states:

      "Friedman's 'as if' methodology is valid for all scientific approaches"

      You'd basically have to show that "as if" isn't the same as effective theory.

  2. "it isn't any more empirically accurate than

    C ⇄ W"

    Maybe that just says something about your model rather than that debt was incorporated?

    1. It's true!

      I said as much at the end.

      This is not to say that there isn't some kind of debt mechanism behind the financial crisis.

      i.e. some other model might exist. But Blackford never put forward a model, and said that I could use my framework to figure it out.

      My model does say pretty general things about growth rates that should always apply (i.e. you could actually make the same argument without ever resorting to information equilibrium, but just argue about the growth rates).

      And since Blackford's model is just defined by relating growth rates of different variables, the information equilibrium model is sufficient to describe all possible such models.