Exchange rate expectations in a liquidity trap

Bottom line:  Since we don't know much about how an economy can escape a deflationary spiral by itself, we don't know the counterfactual conditional, and so can't estimate the effect of a fiscal expansion on the future price level and the rational expectation of the future exchange rate under PPP. The assumption of static expectations of exchange rates might be the best we can do, and roughly rational. If so, a fiscal expansion will not affect net exports, and protectionism is not needed.

What determines the exchange rate in a liquidity trap? The answer matters, among other reasons, because the effects of fiscal policy, and protectionism, will depend on how the exchange rate responds to these policies.

Unless international capital mobility is zero (and it isn't), the current exchange rate depends on the expected future exchange rate. If people suddenly expect the Canadian dollar to be worth more in the future, they buy it now, and it becomes worth more now.

The simplest assumption about exchange rate expectations is static expectations. People expect the future exchange rate to be the same as it is now. Stephen Gordon reminds me that it is hard to beat a random walk empirically in forecasting exchange rates, so static expectations (which is what a random walk tells you to expect) is not a bad assumption. It can also be a rational expectation, if there is no reason to expect the future to be any different from the present. So if s is the exchange rate (a rise in s means appreciation), this means that E[s(t+1)]=s(t).

The simplest assumption about international capital mobility is that it's perfect. A bit extreme, perhaps, but simple, and commonly used. If i is the domestic nominal  interest rate, and i* the foreign, this means that i + E[s(t+1)]-s(t) = i*.

In a liquidity trap, domestic and foreign interest rates are exogenous, both stuck at zero. They don't adjust to changes in the current exchange rate (as they normally would), because the domestic and foreign central banks want to push interest rates lower, but can't.

Put those three simple assumptions (static expectations, perfect capital mobility, and exogenous interest rates) together, and the result is a mess. At best, the exchange rate is indeterminate, because it is equal to whatever people expect it to be, and they expect it to be whatever it is now, so anything is an equilibrium. At worst (with the smallest risk premium, or smallest interest rate differential) there is no equilibrium.

One way to escape that unpleasant conclusion is to assume imperfect capital mobility. That was my previous strategy. With exogenous interest rates, and zero expected change in the exchange rate, the capital account of the balance of payments is also exogenous. With no intervention by central banks, the current account deficit must be equal to the capital account surplus, and so is also exogenous. Therefore the exchange rate must adjust to keep net exports fixed, and fully offset any effect of fiscal policy on imports.

Paul Krugman provides another way to escape. Keep perfect capital mobility, but replace static expectations. Assume instead that people expect the liquidity trap to be temporary, and that at some future time interest rates will be endogenous again, and the exchange rate will be determined in the same way it normally is. I like his approach. But it's not clear how it will affect my results about fiscal policy and net exports.

If we assume that the future exchange rate, when we escape the liquidity trap and return to normal times, call it s*, is exogenous with respect to current fiscal policy, then my results about fiscal policy are wrong, and his are right. If E[s(t+1)]=s* is exogenous, and i and i* are exogenous, then the current exchange rate s is also exogenous with respect to current fiscal policy. Even though exchange rates are flexible, it is exactly as if we had fixed exchange rates.

But will s* be unchanged by changes in current fiscal policy? That depends: on the future fundamentals that affect s*; and on whether current fiscal policy affects those future fundamentals.

One very simple theory of those fundamentals is Purchasing Power Parity: s* is determined by relative domestic and foreign price levels, so that s* = P*/P. So, will current fiscal policy affect the future price level P?. If so, it will affect s*, and so affect the current exchange rate by an equal amount.

An expansionary fiscal policy today will increase aggregate demand, and cause some increase in inflation. More properly, it will prevent as much deflation as would otherwise occur. Analysing this question properly is hard, because we don't know what would happen otherwise, if we waited for some deus ex machina to rescue the economy from a deflationary spiral. (And we don't really want to find out). We don't know the couterfactual conditional, because the economics of how economies escape a deflationary spiral all by themselves is, let's say, underdeveloped.

So let's suppose (and we can do little better than suppose), that without an expansionary fiscal policy there would be a (say) cumulative 20% deflation before a miraculous recovery. And with an expansionary fiscal policy the price level would (say) remain stable. That means the fiscal policy causes a 20% higher future price level than would otherwise occur. And a 20% decrease in s*. And therefore a 20% depreciation in the current exchange rate.

Would a 20% depreciation of the current exchange rate be enough to offset any effect of current fiscal policy on net exports? Probably. And if so, I'm right: an expansionary fiscal policy will have no effect on net exports. It's just like assuming static expectations.

Of course, I just made up that 20% number. But that's all we can do. Or we assume static expectations.

Comments

[MattYoung]

"Since we don't know much about how an economy can escape a deflationary spiral by itself"

Either we have never had a deflationary spiral, or we are not here.

[Nick Rowe]

There was a deflationary spiral in the 1930's, but I don't think it was the same. The big difference was that the 1930's had the gold standard. When you have a fixed stock of international reserves (gold), deflation has one beneficial effect: it increases the real quantity of international reserves, and so allows the global real money supply to increase. (I am NOT saying that deflation doesn't have bad consequences, but in the 1930's there was one good consequence to at least partially offset them). Currency devaluations against gold had the same effect. Fortunately, we don't seem to have to worry about shortage of international reserves and global money supply this time. But it also means that lessons from the 1930's are always helpful. Or you could say that WW2 was the deus ex machina.

[Nick Rowe]

Correction: should be: "But it also means that lessons from the 1930's are NOT always helpful."

[Patrick]

Say we accept that the mess is not too far from current reality. It might explain all the flailing going on. Since the mess is unstable and must resolve somehow maybe policy makers get to choose?

Coming from a math/physical sciences background, unstable dynamic systems scare me. When you poke them, they have a tendency to reconfigure themselves in a unexpected ways - sometimes tearing themselves to pieces in the process.

[calmo]

Atleast in the early phase, the power structure resisting the forces that eventually shift this framework are successful in denying that there is any threatening force.
Holding onto the microphone in these modern times is a significant advantage to the modern power structure with a few voices speaking somewhat authoritatively to many --as opposed to many unorchestrated voices speaking somewhat more interactively to smaller audiences yesterday. (The "on message" scripts of the Bush administrations from various principals in the WH should make this abundantly clear, yes? These people were delivering...not receiving feedback.)
Or so I would argue against Nick's "gold standard": the reliance on this precious metal having everything to do with custom and tradition (as Hume might argue)[as calmo gathers respectable figures seein how small his mike is...how small his gold pile is too...] --confidence not reinforced (and somewhat undermined by the very process) by a central banking authority "guaranteeing" your deposits in the bank.
But characterizing the "sameness" or "the difference" between now and 1930s, important given the outcome (WWII).
We are beyond just handing over our confidence to prominent figures who have recently demonstrated their incompetence...and we are listening to many other smaller voices --not for direction(s) especially, but to find out if they are listening or...just directing. Sorta.
We have become "difficult"....a jazzy version of "We are all subprime now."

[Nick Rowe]

But, but, but: what about expectations of exchange rates? How do they get determined? It matters.

[Don the libertarian Democrat]

Nick, I might ask something else, but this puzzles me:

"because the domestic and foreign central banks want to push interest rates lower, but can't.'

I don't understand why the Fed couldn't"
1) Add a fee to these bonds
2) Discount them over time

In other words, add a disincentive to buy and hold them.

[Nick Rowe]

Hi Don: it's technically possible. But people would just hold cash under the mattress, or in safety deposit boxes, and get zero interest rates that way. (There are various schemes always floated to tax cash, or make it expire, etc., but they always come across as a bit sci-fi.)

[Don the libertarian Democrat]

OK. Wait. The importance of the Flight to Safety is the guarantees. The fact that the government will insure these bonds can be redeemed.I can understand people actually going and withdrawing cash in waves at, say, -5%. But at -1 to -3 % I'm not so sure. Also, mightn't it be better to force people to cash? I'm not even saying that you'd have to actually do it. The other thing that I'm suggesting is using this for exchange rates. What exactly is China going to do with their money if they don't put it in US Treasuries? They're obviously willing to receive nothing for explicit guarantees.

"In a liquidity trap, domestic and foreign interest rates are exogenous, both stuck at zero. They don't adjust to changes in the current exchange rate (as they normally would), because the domestic and foreign central banks want to push interest rates lower, but can't."

I'm suggesting that, in the case of China, you could. Am I wrong?

[Nick Rowe]

The government guarantee only means the government guarantees they will be converted into cash. Ten $100 US banknotes is the same as a $1,000 US T-bill, except the former can be used as a medium of exchange, if needed.
At below 0% interest, China would just hold US$ banknotes instead.

We don't want to force people into cash (that usually works, but has stopped working). We want to force people out of cash, and out of bonds, and into newly-produced goods and services. There are 2 ways to do this: flood the market with bonds+cash (so they've got so much they decide to spend some); create expectations of inflation, which is a way to tax cash+bonds, create a negative real (inflation-adjusted) interest rate on cash+bonds.