The Simple Analytics of Monetary Impotence (Wonkish)

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I’ve been having a back-and-forth over monetary policy at the zero lower bound, some of it in public and some in private correspondence, which is basically a continuation of a conversation that reaches back many years. And it occurred to me that even many of the economists I’m talking to don’t know about an analytical approach that, it seems to me, lets you cut through most of the confusion here. It’s the basis of my old 1998 model, but I don’t think people are reading that piece even when I direct them to it. So let me lay out the core insight that changed my own mind about monetary policy in a liquidity trap (and is useful for fiscal policy too.)

What I did in my old analysis was to radically simplify the dynamics by imagining an infinite-horizon model in which all the action takes place in period one. That is, there may be shocks to consumer preferences, or fiscal policy, or monetary policy, but they all take place “now”; after period 2 everything stays the same. What this in turn means is that we can take the period 2 price level and level of consumption as given. In what follows I’ll use an asterisk to refer to period 2 and subsequent values — P* is the period 2 price level, C* the period 2 consumption level — and let un-asterisked symbols refer to period 1.

I also, as a first pass, assume that there is no investment, just consumption.

Now ask the question: what determines period 1 consumption?

Well, if we have rational expectations and frictionless capital markets — which we don’t, but let’s see what would happen if we did — the answer is that the ratio of marginal utility in period 1 to marginal utility in period 2 must equal the relative price of consumption in the two periods, where the relative price is the real discount rate, the rate at which one unit of consumption now can be converted into units of consumption in the future. If r is the nominal one-period interest rate, this says that

MU/MU* = (P/P*)(1+r)

To make things even simpler, assume logarithmic utility, so that marginal utility is 1/C. Then this becomes

C*/C = (P/P*)(1+r)

or

C = C*(P*/P)/(1+r)

So we have an Euler equation that lets us read off current consumption from future consumption, current and future price levels, and the interest rate. And we can take future consumption as given.

Now suppose that we’re in a New Keynesian world in which prices are temporarily sticky; so P is given. And suppose we’re at the zero lower bound, so r=0. Then there’s only one moving part here: the expected future price level. Anything you do — monetary or fiscal — affects current consumption to the extent, and only to the extent, that it moves the expected future price level. Full stop, end of story.

An immediate implication is that the current money supply doesn’t matter. The future money supply matters, because it can affect the future price level, so a permanent increase in M can affect the economy — but that effect works entirely through expectations. What you do now matters only to the extent that people take it as an indication of what you will do in the future. Don’t talk to me about monetary neutrality, or how it stands to reason that money must matter, or helicopter money, or even money-financed deficits; we’ve taken all of that into account en passant with the Euler equation.

Now, if we let households be liquidity-constrained, giving them transfer payments can affect current spending; but that’s a fiscal point, not really about money.

Another perhaps less immediate implication is that there is no crowding out from temporary fiscal expansion. Suppose the government goes out and buys a bunch of stuff while we’re at the zero lower bound. This doesn’t affect future consumption, and therefore doesn’t affect current consumption either. Notice that this is in an approach with full Ricardian equivalence; so every economist who claimed that Ricardian equivalence makes fiscal expansion ineffective has actually shown that he doesn’t understand the concept.

Again, I’m not claiming that this Euler equation is The Truth. If you want to make arguments about policy that rely on some failure of the assumptions, especially imperfect capital markets, fine. But that’s not what I hear in most of this discussion; what I hear instead are attempts to talk things through that end up being, unintentionally, word games. Instead of telling a specific story about what people are supposed to be doing and why, economists try to reason in terms of concepts like monetary neutrality that aren’t as well-defined as they think, and end up fooling themselves into believing that they’ve demonstrated things they haven’t.

Now, one good exception is Brad DeLong’s argument that money does too work in a liquidity trap because such traps are always the result of disrupted financial markets. What I’d say is that they are *sometimes* caused by financial disruption. But is this one of those times? As the chart shows, we had a lot of disruption in 2008-9. Is that still a major factor in our economic weakness? Do we think that Japan’s problems have been rooted in the banking system all these years?

Anyway, that’s how I see it. If you disagree, please try to put your argument in terms of what the people in your model are doing — not in terms of catchphrases.