Friday, April 27, 2007

Channeling James Tobin

Mark Thoma (with support from Frederic Mishkin) holds with those who insist that only money can cause inflation – at least if, by inflation, one means a sustained pattern of increases in the price level. I believe that, as a formal matter, the argument is somewhat circular tautological: the conclusion is based on comparative static models in which money is the only stock variable. Fiscal policy is, almost by definition, a one-shot deal in these models, so it cannot produce a sustained pattern of change in anything.

Consider the standard closed-economy IS-LM model, as I learned it in school:

IS curve: Y = C(tY) + I(r) + G
LM curve: M/P = L(r, Y)

where
Y = national output
C = consumption
I = private investment
G = government spending
t = tax rate
r = interest rate
M = money stock
P = price level

Applying the standard assumption of a vertical long-run Phillips curve, we can take the growth rate of Y as exogenous for our purposes. Without loss of generality, let’s assume Y is constant.

Now, we want to ask, can the growth rate of P (otherwise known as the inflation rate) be positive if M is constant? You can see immediately from the LM curve that, if P were rising and M were constant, either r or Y would have to be changing. Otherwise the left-hand side of the equation would be falling, while the right-hand side would be constant. However, we have assumed that Y is constant, and a look at the IS curve shows that, if r is changing, then one of the other flow variables (Y, G, or t) must also be changing. But, again, we have assumed Y is constant, so unless there is a constantly changing fiscal policy (e.g., the tax rate constantly falling or government spending constantly rising), the equations won’t balance. So without money growth, you would really have to do something bizarre to get sustained inflation.

But suppose we introduce a new stock variable, call it “B” for bonds (government bonds, that is). The stock of government bonds grows as the government accumulates deficits (or falls as it accumulates surpluses). Using the “d” operator to indicate a rate of change, we can describe this process as:

dB = G – tY

For completeness, we can add yet another stock variable, the capital stock (“K”). Without loss of generality, I’m going to ignore depreciation and just say:

dK = I

In principle, private investment depends not directly on the government bond interest rate but on the required return on private capital. Let’s call this required return “s” (for “stock market return” as a mnemonic, although you should understand that it is the general required return on private capital, not just for the stock market).

In the standard IS-LM model, it was assumed that s and r were in some fixed relation, but in a world where government competes with the private sector for capital, the relation between the two returns need not be fixed. Government bonds and private capital have different characteristics – different risks, different degrees of liquidity, and so on. Investors may have a preferred proportion of holdings between the two, and when the relative supply of one asset increases, they will require some compensation for changing their proportions. Call the difference in returns between the two assets “e” (for “equity premium”) and recognize that it will depend on the relative outstanding stocks of government bonds and private capital. That gives us the following model:

Y = C(tY) + I(s) + G
M/P = L(r, Y)
dB = G – tY
dK = I(s)
s = r + e(B, K)

We now have a wedge between money growth and inflation. As the government runs a constant (sufficiently large) deficit, B increases relative to K. Therefore e(B, K) increases, and s falls relative to r. In order for Y to remain constant in the IS curve, s has to be constant in absolute terms, so this means r has to rise. In the LM curve, as r rises, with Y and M constant, P has to rise. Fiscal policy does cause sustained inflation.

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11 Comments:

Blogger Gabriel Mihalache said...

This looks like a good argument for calling (some) financial instruments "money". :-)

Fri Apr 27, 05:14:00 PM EDT  
Blogger knzn said...

There’s a basic problem with choosing any single definition of “money” in a “quantity theory” context. The problem is that different forms of money (and quasi-money) are not perfect substitutes. No matter what definition you choose, you’re going to end up having problems. If you choose a narrow definition, the problem is that there are substitutes available. If you choose a broad definition, the problem is that different components of the “money stock” have different demand equations. For example, if you choose to include government bonds in your definition of money, then you might think that open market operations would have no effect on aggregate demand. But of course they do. (OK, that’s not a good example; because of the fractional reserve banking system, open market operations actually change the total stock of money and bonds, but suppose you were to offset the effect of the money multiplier by changing the reserve requirement at the same time. You would still get a net effect, because bank deposits and bonds are not perfect substitutes.)

I would say (and I think most central bankers today would agree) that we should stop worrying about measures of money per se (except perhaps as indicators of potential demand) and just adjust interest rates so as to produce the intended path for the price level, given various models of the economy, economic indicators, feedback from actual prices, and some amount of intuition. If you don’t like active policy, OK, then just use a Taylor rule, or some more sophisticated variant on the Taylor rule (except I think you can do better with active policy).

If one is talking about fiscal policy, I would say that, realistically, any analysis should make monetary policy endogenous, and since bonds and base money are not perfect substitutes, a central bank that targets the price level can and will ultimately offset the inflationary effect of fiscal policy. But then the question becomes, what exactly are they trying to offset? If they think the effects of fiscal policy on the inflation rate are only temporary, they might ignore it. But…never mind, just see the end of my next post.

Sat Apr 28, 05:02:00 PM EDT  
Blogger Karl Smith said...

I am not sure we even have to get this deep. If the government spending is rising faster than taxes then it should be enough in the simple model.

Now of course this can't happen forever but if we had a steady increase in the price level over a period of 5 years I think everyone would call that inflation.

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