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.