Aber zurück zu Krugman und seiner simple math,:
I’ve been on the warpath over Germany’s refusal to play a constructive role in European fiscal stimulus. But what does the math look like? Here’s a simple analysis — well, simple by economists’ standards — of the reason coordination is so important for the EU.
We start from the proposition that Europe is, or soon will be, in a position where interest rates are up against the zero lower bound. This means both that fiscal policy is the only game in town, and that we can use ordinary multiplier analysis.
Let m be the share of a marginal euro spent on imports — either for an individual county, or for the EU as a whole (I’ll explain in a minute). I’ll assume that m is the same for government spending and for domestic demand. Let c be the marginal propensity to consume. And let t be the share of an increase in GDP that accrues to the government in increased taxes or reduced transfers.
Consider the effects of an increase in government purchases dG. This will raise GDP directly, to the extent that it falls on domestic goods and services, and indirectly, as the rise in GDP induces a rise in consumer spending. We have:
dY = (1-m)dG + (1-m)(1-t)c dY
or dY/dG = (1-m)/[1 - (1-m)(1-t)c]
Since governments are worried about debt, it’s also important to ask how much the budget deficit is increased by an increase in government spending. It’s not one-for-one, because higher spending leads to higher GDP and hence higher tax revenue. We have
dD = dG - tdY
A crucial number is “bang for euro”: the ratio of the increase in GDP to the increase in the deficit. After a bit of grinding, it can be shown to be
dY/dD = (1-m)/[1 - (1-t)(1-m)c - t(1-m)]
OK, some numbers. The average EU country spends about 40 percent of GDP on imports, and collects about 40 percent of GDP in taxes. Let me cut corners and assume that the marginal rates are the same as the average, and also assume that the marginal propensity to consume is 0.5. That is, for an average EU country, m = 0.4, t= 0.4, c = 0.5.
We can represent a coordinated fiscal policy by looking at the numbers for the EU as a whole. The only difference is that m falls to 0.13, because two-thirds of the imports of EU members are from other EU members.
And we get the following results:
UNILATERAL FISCAL EXPANSION
Multiplier = 0.73
Bang per euro = 1.03
Multiplier = 1.18
Bang per euro = 2.23
The bang per euro is what matters: the tradeoff between increased debt and effective stimulus is MUCH better for the EU as a whole than it is for any one country.
You can play with these numbers, but I don’t think that conclusion is very sensitive to the details as long as you keep the large intra-EU trade effects in there. The lesson of this algebra is that there are very large intra-EU externalities in fiscal policy, making coordination really important. And that’s why German obstructionism is such a problem.