Language games and expectations of "doing nothing"

If I make one very trivial change to Paul Krugman's model of a temporary liquidity trap, I can change the results, so that the central bank can use current monetary policy to return the economy to full employment, even if it cannot make credible commitments about future monetary policy.

I am going to change the notation.

Let me introduce a new variable m(t), which is defined as Paul's "M(t)-M(t-1)". So m(t) is simply the change in the stock of money relative to the previous period. (Or, if you prefer, define m(t) as "log[M(t)]-log[M(t-1)]", so that m(t) is the growth rate of the money supply relative to the previous period.)

Paul assumes that in period t the central bank chooses M(t). In my new notation, I assume that in period t the central bank chooses m(t). Each period the central bank decides how much money to print (so m(t) > 0), or burn (so m(t) < 0). And if it does nothing, and neither prints nor burns, then m(t) = 0, so M(t) = M(t-1).

Suppose initially that M(t) is constant at Mbar for all t, so that m(t)=0 for all t. Now suppose that the central bank "does something" in period t, but is expected to "do nothing" in all subsequent periods, because it cannot make credible commitments about its future actions.

1. In Paul's notation, that translates into: "M(t) increases above Mbar, but expected M(t+1) is unchanged and stays at Mbar".

2. In my notation, that translates into "m(t) increases above 0, but expected m(t+1) is unchanged and stays at 0".

But 1 and 2 are substantively different statements. 1 is an increase in the money supply M(t) that is expected to be temporary. 2 is an increase in the money supply M(t) that is expected to be permanent. And 1 and 2 will have very different effects.

If the central bank cannot credibly commit its future actions, so people always expect it to "do nothing" in future, we get a big difference in the effect of current actions depending on how people define "doing nothing" for future actions.

Now read Paul: "An immediate implication is that the current money supply [M(t)] doesn’t matter. The future money supply [M(t+1)] matters, because it can affect the future price level, so a permanent increase in M can affect the economy [today] — but that effect works entirely through expectations." [my additions, bold added.]

If he were using my notation, but exactly the same model, Paul would say instead:

"An immediate implication is that the current money supply growth rate [m(t)] DOES matter. The future money supply growth rate [m(t+1)] also matters, because it can affect the future inflation rate, so a permanent increase in m can also affect the economy today — but that effect works entirely through expectations."

Each monetary policy regime has a different definition of "doing nothing". The gold standard defined "doing nothing" as "leaving the price of gold unchanged". And so people expected the price of gold to remain unchanged, unless the central bank did something. Nowadays, we expect the price of gold to change in response to shocks, unless the central bank does something to stop it changing.

Paul says: "So if you are convinced that monetary expansion must work, please tell me why. Don’t push words around; as I said, you’re probably engaged in deceptive word games, even if that’s not your intention. Give me a careful analysis of what people are doing, and how the frictions, whatever they are, cause the basic result of monetary impotence to go away."

Paul (or the reader) might say that I am playing word games here. I would prefer to say that I am recognising the reality of there being more than one possible language game. Each monetary policy regime has its own language game. In particular, the meaning of "doing nothing" depends on the monetary policy regime. The effect of current actions on expectations about the future (the meaning of those current actions) depends on the monetary policy regime.

I'm rigging the language game my way; Paul is rigging the language game his way. But which language game would we prefer a central bank to play? Mine. Because a central bank that plays the language game my way can escape a liquidity trap.

A Nash equilibrium is where each player has no incentive to act differently given the expectation that the other players "do nothing" in response. But "doing nothing" means something quite different in the Cournot game than in the Bertrand game. (In Cournot it means "do not change output", and in Bertrand it means "do not change price".) So the Cournot-Nash equilibrium is quite different from the Bertrand-Nash equilibrium. (Cournot-Nash has lower output than Bertrand-Nash.) Language games matter.

Comments

[Lord]

Some see things as they are ... some see things as they could be ...

[Nick Rowe]

Lord: true. But how things are now, is how things could have been in the past. Things weren't always like this, and they won't always be like this.

[Peter Summers]

Nick,

I think you're conflating levels & growth rates here. In particular, what do each of you mean by "...but expected x(t+1) is unchanged"? In Paul's notation, if M(t) increases but expected M(t+1) is unchanged, that's a level shift, assuming 'unchanged' means 'from its value at time t", that is M(t+1) = M(t). But in your notation the equivalent would be that m(t+1) = m(t-1): money growth was 0 until t-1 was (say) 5% in t, and is then 0 thereafter. Said another way (and this is literally off the top of my head), are you mixing money neutrality with super-neutrality?

PS

[Nick Rowe]

Pete: I have edited the post slightly, to clarify what I meant.

[louis]

So both you and Krugman have the same diagnosis- that the central bank cannot *mechanically* lift an economy out of a recession at the zero lower bound, and that monetary policy can work only if the central bank increases expectations of the future money supply, which requires them to back away from promises to target inflation rates once the economy leaves the liquidity trap. The only difference is that you say "so get the CB to drop the inflation rate targeting" and he says "good luck doing that, time for fiscal policy".
Am I missing some other distinction?
Also, if you were convince the central bank was inflexible in its policy rules, would you consider fiscal policy the next efficacious option? I.e. do you doubt the effectiveness of government deficits to boost AD in that monetary backdrop, and/or do you see other policy options getting better traction?

[Nick Rowe]

louis: but if the central bank sticks to the same inflation target, fiscal policy won't work either. The central bank will offset it.

[Max]

Krugman lost me with:
"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."

Is he really saying that fiscal policy works (in this model) by increasing the future price level? If that is even possible, it's surely not what any normal person means by fiscal policy. Setting the price level is monetary policy.

[Nick Rowe]

Max: "Is he really saying that fiscal policy works (in this model) by increasing the future price level?"

No, he's not saying that. He's saying that Y=C+G, and C depends only on the future price level, so a $1 increase in G causes a $1 increase in Y.

[Majromax]

> Setting the price level is monetary policy.

Is it? This is the fuzzy middle of language. To finance writers, setting interest rates is monetary policy. To gold bugs, setting the price of gold is monetary policy.

Krugman is operating from the assumption that the CB "can't" (with respect to its available tools) change the future price level by itself. That in turn means that it can't actually be setting the price level by monetary policy.

[Max]

Nick, okay, good. My next puzzlement is, what counts as G in this model? Krugman was assuming no investment, so would the government have to purchase consumer goods and distribute them?

[Nick Rowe]

Max: that won't work, because if the government buys one loaf of bread and gives it to me, that simply means that I buy one less loaf of bread, and consume the same total amount of bread. It simply means the government is doing my shopping for me. It has to be something I would not have bought myself. (But if it's something I don't want, then Y goes up, but utility does not go up, because all the extra G is wasted. So it has to be some sort of public good, that priveds utility to people, but people can't buy for themselves.)

[louis]

Nick - presumably the CB is missing its inflation target in the current period, or more importantly, some growth in AD would still be consistent with hitting the inflation rate target. That's what makes the liquidity trap meaningful. If fiscal policy closes the output gap, the cb need not offset the effect on output if the rate of inflation hasn't moved above target.
And there's no need for a monetary offset in future periods, because the fiscal stimulus is temporary by its nature.
We're used to talking about offsets when the monetary authority has the power to create full employment on its own, but that is less meaningful once we've ruled that out.

[Max]

Nick, I see. That really narrows the possibilities for what G could be. War would qualify.

[Nick Rowe]

Max: yes, but also stuff like roads and sewers.

I wish I could remember a lovely quote from P.J. O'Rourke, speaking to happy east europeans after communism collapsed. Something like "Government is supposed to be about boring stuff, like making sure the sewers work."

[Min]

It seems to me that you are interpreting "doing nothing" as "doing what you usually do". E. g., under a gold standard the usual thing is to redeem notes with specie (or maybe bullion) at a set ratio. Today, the usual thing is not to redeem notes with specie or bullion at all. No?

[Min]

Nick Rowe: "I wish I could remember a lovely quote from P.J. O'Rourke, speaking to happy east europeans after communism collapsed. Something like "Government is supposed to be about boring stuff, like making sure the sewers work."

Too bad he wasn't talking to US politicians. They haven't been taking care of the boring stuff for a long, long time.

[W. Peden]

"presumably the CB is missing its inflation target in the current period, or more importantly, some growth in AD would still be consistent with hitting the inflation rate target. That's what makes the liquidity trap meaningful."

Now I'm confused, because we were told that the UK was in a liquidity trap back in the early years of the decade, but while it was true that the Bank of England was missing its inflation target, it was OVERSHOOTING its target from January 2010 to February 2012. So what happens when we relax the idealisation of below-target inflation?