## Thursday, July 24, 2014

### Beware implicit modeling

One of the difficulties you have when you are steeped in a subject for a long time is that you forget when you are making implicit modeling assumptions. Nick Rowe claims that the accounting identity Y = C + I + G + NX is useless, in opposition to the "first-order Keynesian" view that if government spending G → G + δG during a recession we will get real output Y → Y + δG. He's making a claim for the null hypothesis, but it's really hard to say which is a less informative prior. Does a signal from G make it to Y or does it get absorbed by C, I and NX?

I probably didn't make it exactly as clear as I would have liked in my comment on the page, but the idea was that the identity is useless is as much a modeling assumption as the first-order Keynesian view. If G → G + δG, then

Y → C + (∂C/∂G) δG  + I + (∂I/∂G) δG + G + (∂G/∂G) δG + NX + (∂NX/∂G) δG

= Y + δG + (∂C/∂G) δG  + (∂I/∂G) δG + (∂NX/∂G) δG

The "first-order Keynesian" view assumes that (during a recession)

|∂C/∂G| , |∂I/∂G| , |∂NX/∂G| << 1

The "useless accounting identity" view assumes that

|∂C/∂G| , |∂I/∂G| , |∂NX/∂G| ~ 1

The only way you can't know what happens if G → G + δG is if it is possible for some offsetting effect or some amplifying effect of equal magnitude that makes δY < δG or δY > δG, respectively. Note that these are structurally similar assumptions about the dependence of the other variables on changes in G.

Nick also says that the first-order Keynesian view could be used to say that because Y = C + S + T, we could raise taxes (T) to get more real output. However, that is not what that equation states; it states that increasing tax revenue [1] would lead to more real output. Does raising taxes increase tax revenue in a recession? That becomes a modeling assumption. "Raising taxes" is analogous not to increasing government spending but rather to e.g. increasing the number of fixed-price RFP's the government puts out. While increasing the number of fixed price RFP's could lead to more businesses submitting bids and an increase in government outlays so that G → G + δG, it may be such that no business considers any of the potential contracts to be a good deal.

The first-order Keynesian assumes in this case is that:

|∂C/∂T| , |∂S/∂T| ~ 1

While the Rowe reductio ad absurdum assumes

|∂C/∂T| , |∂S/∂T| << 1

Again, these are structurally similar assumptions.

Rowe believes it is "warped" not to assume the same general dependence of C, I and NX on G as you do for C and S on T.

Update 7/24, 9pm PDT: I think I'd like to make this a little stronger. Rowe's claim is that e.g. consumption C depends to first order on government spending G, i.e.

C = a + b G + ...

with b ~ 1. [2] (This could also apply to I and/or NX, or all three.)

For taxes T, C ~ a + b T makes sense: my personal consumption is basically C = a - S - T (consumption is what is left over after savings and taxes). But for government spending? I'm pretty sure when the stimulus passed, I didn't change my behavior. Maybe I "expected" it to pass and priced it in already.

Another way of putting this is that Rowe is saying the basket of goods comprising C isn't actually at a local maximum or minimum with respect to the given level of government spending. Maybe that is true, but then, that's a model assumption. Consumption isn't utility, but if you take consumption to be proportional to utility, then Rowe is assuming that utility isn't maximized at a given fixed level of government spending. It's still implicit modeling whatever you call it.

[1] More tax revenue could mean we have more output (hence causality went the other way), or that the market took raising taxes as a sign that the recession is over, creating expectations of an improved economy. All kinds of theories could be at work.

[2] It is possible that C = a + c G^2 + ... with an unnatural coefficient c >> 1, but that is an unnatural assumption.

1. Jason: the identity (by itself) is useless because it would be equally true for *all* modelling priors.

Suppose I wrote the same identity as: C=Y-I-G-NX. Does that tell us that if G goes up it causes C to go down? No. If we do think it tells us that, we are being fooled by our own math.

My whole point was that writing down a particular identity in a particular way can fool us into implicit modelling.

1. Hi Nick,

I could see saying something like "Y = C + I + G + NX may be useless", but saying "Y = C + I + G + NX is useless" precludes the "first order Keynesian" interpretation. The particular partition of Y is useful in Keynesian analysis with some implicit modeling assumptions; asserting its uselessness is assuming the Keynesian view is wrong based on the identity alone.

Rearranging so that C = Y - ... simply rearranges the implicit modeling assumptions so that interaction between C and G is mathematically easier to represent. However it ignores the implicit assumptions in the partition itself. Y is an aggregate made of four not completely nebulous components. I could see making a forceful argument against the "Keynezians" who say Y = X + Z where Z is everything that has a Z in it. The Keynesian partition could be represented

(1) Y = uncoordinated expenditure (C + I + NX) + coordinated expenditure (G)

Coupling the implicit modeling assumptions above with the microeconomic coordination problem gives a generic Keynesian view. However asserting that partition is as useless as Y = X + Z means that you've made some implicit modeling assumption that includes very strong interactions between the components -- e.g. government spending crowds out private investment ( |∂I/∂G| ~ 1 ) or monetary offset can negate fiscal stimulus ( ∂Y/∂G = 0 ).

The identity may be useless. But that isn't known as an unambiguous fact, so you can't say the identity is useless.

2. Jason, O/T: Sumner quoted from part of an interview between David Andolfatto and Michael Woodford. I pointed out the ending of the interview (which was not Scott's focus). No surprise that Scott doesn't agree with Woodford there, but this was the bit that confused me:

"We haven’t even scratched the surface of what monetary policy can achieve. For instance NGDPLT is 100 times more potent than fiscal stimulus."

How do you suppose he calculated that?

1. Expectations are X times more powerful than fiscal stimulus where X is the expected value E[X] of the power of monetary policy relative to fiscal stimulus.

2. And does the value for X come straight out of one's a-posteriori? :D

3. Wait... then X = E[X]? Does that imply X is not a random variable? You were telling me about something like that in the information transfer paper...

Knowing you, you meant it just like that. Probably another layer to the joke that I'm not getting. (BTW, I'm assuming you are joking!).

4. A posteriori -- ha!

And yes, if there are a large number of particles, the fluctuations around a random variable are very small so that the ensemble average E[X] can be taken to be just a normal variable X ... and yes it was a joke :)

3. Another O/T: The title of this Marcus Nunes post caught my eye:

Also, thanks for pointing me to that Noah Smith post on why macro doesn't work very well... that and the one he did on John Cochrane's speech (or article?) along the same lines that he links to were really good.

1. I think Nunes is doing that thing where he's not putting the lines at the right time. Japan didn't start implementing Abenomics until about three weeks into Q1 (when they announced the new monetary targets). I'll have to look at it more closely, but I think that puts Abenomics starting halfway up the rise in exchange rates.

4. ... Also Sumner has a good question for you:

http://www.themoneyillusion.com/?p=27169#comment-359068

5. Jason, some implicit modeling to be ware of perhaps?:

http://mainlymacro.blogspot.com/2014/07/understanding-fiscal-stimulus-can-be.html?showComment=1406510473153#c8785886174733652719

1. Expectations are still doing all the heavy lifting in both Nick's and Simon's models. If people expect the economy to improve when the government spends more for silly reasons, then it will in both models. Why would we want to disavow people of this and replace it (for no good reason) with the new silly belief that the economy will improve when the Fed puts forth expansionary monetary policy?

That was kind of a joke. However, it seems that if people genuinely believed government spending will improve the economy without trade-offs, then both Nick's and Simon's models are incorrectly specifying expectations (Simon says there is a trade off that people expect and Nick says conditions will only improve if people expect expansionary monetary policy).

6. This may or may not be a surprise, but Sumner does not agree that macro data is largely uninformative (2nd comment to me):

http://www.themoneyillusion.com/?p=27174&cpage=1#comment-359182

1. I think he's is confusing "uninformative" with "not agreeing with the data". Sumner says:

"Tom, No I don’t agree that macro data is largely uninformative. If I viewed the world through the lens of IS-LM then I’d strongly agree with Noah, as the data doesn’t even come close to being consistent with the IS-LM approach."

Noah isn't saying that the data is inconsistent with IS-LM; Noah is saying the data doesn't tell us whether to reject IS-LM or really any macro model. There isn't enough data to confirm any model (we've only had like 6 or 7 "business cycles" -- not nearly enough to explain macro) ... that's not something that is up for debate.

As Sumner doesn't have a quantitative model of his own, we can't really answer the question of whether we can keep his model or reject it either, but not because the data is uninformative. It is likely that the data would be uninformative if there was such a model.

2. I should have said "6 or 7 business cycles in the post war period with decent data" ...