Multipliers in a liquidity trap; fixed vs. flexible exchange rates. Disagreeing with the IMF.

In a liquidity trap, interest rates are stuck at zero, so increases in government spending do not raise interest rates. What are the government spending multipliers in a liquidity trap? Closed/open economies; fixed/flexible exchange rates.

Suppose c is the marginal propensity to consume, and m is the marginal propensity to import. Ignore taxes for simplicity (or just substitute "c(1-t)" wherever I write "c").

The multiplier in a closed economy (like the world) is 1/(1-c).

The multiplier in a small open economy with fixed exchange rates (or a common currency with its trading partners) is 1/(1-c+m). The multiplier is smaller than for a closed economy, because increased income will cause increased imports and so reduced net exports.

The multiplier in an open economy (small or large) with flexible exchange rates is 1/(1-c). The multiplier is the same as in a closed economy, because the exchange rate will depreciate to offset the increased imports, so that net exports stays the same.

This result for flexible exchange rates does not rely on any assumption about the degree of capital mobility (as long as it is not infinite). It does assume that the expected rate of future exchange rate depreciation will stay the same, so that (with no change in interest rates) net capital outflows stay the same. Since net exports are equal to net capital outflows, net exports will also stay the same. I discussed this in a previous post.

As Paul Krugman explained, if countries don't like deficits, the fact that the closed economy multiplier is larger than the open economy fixed exchange rate multiplier is an argument for fiscal policy coordination within the Eurozone. (We might consider China/US coordination important as well). For countries with flexible exchange rates, however, there is no similar argument for fiscal policy coordination, because the open and closed economy multipliers are the same. An increase in government spending in Canada will not increase demand in the rest of the world.

If I am right, then the IMF is wrong:

"On who should do it, fiscal stimulus should be undertaken widely. While each country will need to consider its own circumstances, because of trade relations, the more countries that engage in stimulus, the smaller will be the actions that any individual country will need. And of course it is politically easier for countries to act together than to act alone.
It is also important that all countries that can stimulate do so, because not every country can. There are some emerging market countries that have financing constraints—either high costs or inability to finance deficits at all—which mean that they need to contract their budgets rather than expand them. Others are constrained from fiscal stimulus by high levels of debt."

Canada is fortunate in having a low debt/GDP ratio compared to other countries, and can more easily run an expansionary fiscal policy if needed. But if my result is correct, this does not mean that Canada should run a bigger deficit to try to help the rest of the world. In a liquidity trap, it won't help the rest of the world.

On the other hand, if we got ourselves out of the liquidity trap, then the multiplier goes to zero (assuming perfect capital mobility), and an increased Canadian deficit would only help the rest of the world, not Canada.

Comments

[Andrew]

Thanks. If that model is correct, I guess it really clarifies our motivation. It seems to me that now would be a good time to catch up on deferred maintenance in the public sector.

As far as avoiding short-term pain: should we be bailing out autos, forestry, mining? It seems either alternative (bail out or don't bail out) is unappealing.