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.
OK, I hope Krugman understands that interest rates are low because we are in phase 8 of the business cycle. That phase where people finally realize that too much has been consumed, while not enough has been saved so as to make available enough factors of production that produce those consumer goods. I hope he realizes that in order to accomplish the objectives of economic policy, viz. the maximization of every one’s well being in society, the government needs to do what is possibly can to let the market return to the state that the consumers are asking for in their value preferences and time preferences expressed in the form of interest rates and prices, respectively. We shall examine whether or not his recommendations even remotely accomplish this objective.
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]
Without any further analysis or detail Krugman implies that an increase in the nominal GDP is the ultimate objective of economic policy. He doesn’t go into any detail whatsoever. He passes in silence all the flaws that come with this figure and he certainly doesn’t ponder for a second what a true GDP measure should look like.
But all these amateurish shortcomings taken aside, let’s examine what the formula above really tells us. The idea behind the GDP is to approximate the total sum of the prices paid for all consumer goods and factors of production produced inside the country and consumed or used subsequently. The GDP Y is defined as Y = I + C + G + X – M, where
I = Private Investment (purchases of factors of production by domestic non government individuals),
C = Private Consumption (purchases of consumer goods by domestic non government individuals),
G = Government Expenses (purchases of consumer goods and factors of production by domestic government individuals),
X = Exports (purchases of consumer goods and factors of production by foreigners),
M = Imports (purchases of consumer goods and factors of production that were produced abroad)
Now Krugman tries to quantify the effect of additional government purchases dG on Y. dG(1-m) is that portion of government expenses that falls upon domestic consumption by the government. But for some reason he commits the unfortunate blunder of adding to that a mystical (1-m)(1-t)c dY. Where does that come from? He doesn’t even attempt to explain it. He simply assumes that the additional government purchases for some obscure reason also lead to more consumer demand due to an increase of the GDP which is … due to the increase in government expenditure. This is complete utter amateurish kindergarten nonsense.
Krugman is an intelligent person. He must have missed something here. If he wants to figure out whether or not an increase in government expenses leads to an increase in GDP then how can he commit the blunder of assuming an increase of GDP in that very same formula. This is something that not even an elementary class student would get away with. If he wants to apply the questionable GDP formula to calculate the effect of government expenses on the well being of society he should at least do that right.
First of all one has to understand, as most people hopefully do, that dG does not simply grow out of nowhere. Additional dG will have to be funded out of additional taxes. Taxes are funded by taking money from private individuals. If money is taken from private individuals it will either reduce private consumption C or private investment I or both of them by precisely the amount spent. The basic culprit is that Krugman uses variables that are dependent upon each other in the same formula. When one starts calculating derivatives for such a formula one must take that into account. Thus the following calculation is the only correct one:
Y = G + (I + C ) + X – M
<=> dY = dG(1-m) + (dI + dC – dG(1-m)) + dX – dM
<=> dY/dG = 1-m + 0 + 0 – 1 + m + 0 – 0
<=> dY/dG = 1-1
<=> dY/dG = 0
Of course he has to resort to complicated and sophisticated looking mathematic formulas because if he were to explain his hideous theory in words it would break down immediately. Even if we give Krugman the benefit of the doubt, the growth in GDP, if the government spends dG, would be exactly 0. This is the one and only correct way to calculate a change dY/dG if one understands basic elementary school mathematical concepts and if one applies simple logic and reason. Paul Krugman needs to come forward and apologize for his terrible blunder.
Even if an individual were to work and save 50% of his earnings in cash in his matress, he would not inflict the slightest harm upon his fellow men. All he does in working and saving is make available more productive capacity to everyone than he in return withdraws via consumption. By withdrawing his money and saving it for future consumption he steps back and voluntarily leaves factors of production or consumer goods available to others by not participating in the bidding process on the market. The prices for those goods would thus be lower than had he participated, but they still render the same benefit to the consumers. If the government steps in and buys the good in question, it does nothing but snatch it away from someone else and employ it in bureaucratic uses. The Trouble With Bureaucracy explains what will inevitably ensue. No one is helped in this process, only harm is inflicted.
Now, I know that a Keynesian such as Krugman would now object that the additional government expenses would not necessarily have to be funded out of taxes but rather via deficit spending. OK, let’s say the government borrows additional money from one of the participants on the market. Again, this would require that someone who would have loaned the money to someone else now loans it to the government in a credit transaction. The money will thus not be available to that marginal entrepreneur who would have borrowed it. Private investment is reduced while government expenses go up. From the kindergarten GDP formula’s point of view, the effect is 0. To those who understand bureaucracy, the effect is negative.
The diligent pseudo economist, who has meticulously studied all of Keynes’s shallow theories, will then reply: “But since we are approaching 0% interest rates, no one will lend the money, everyone will hoard it. We are in a liquidity trap!” Then we would have to reply that since we are in phase 8 of the business cycle, of course people are hoarding money. The reason being a reckless monetary and fiscal deficit spending policy. And the only way to get out of it is to swiftly abandon that policy and let phase 9, the correction, occur. But even that taken aside, what I said two paragraphs above, applies just as much in this case again. There is no way around this causality, no matter how much one tries to deny it.
Then the Keynesian will reply that the added government expenses could also be funded by having the government print money and buy goods on the market. And of course the response to that would have to be that in that case, money prices for the good purchased with the fiat money will go up and, again, will force the marginal consumer to forgo consumption of that good, while it is re-allocated to the government. The Keynesian would then reply that no one would have purchased the good if the government would not have purchased it. To that we would again have to explain to the Keynesian the basic concepts of he function of a price and that a good will be demanded at a certain price, so long as that price represents the involved parties’ value preferences. If it doesn’t then the seller needs to lower the price until it does.
But even if the price for the good was 0, what good does it do if the government prints money and gives it to someone who in return has produced a good that nobody needed? He will be the first to receive this money and bid up the prices of goods that would then not be available to other marginal consumers who would have bought it in exchange for money earned from useful labor. They will then abandon their operations which the consumers deemed useful and also begin producing that same useless good in order to obtain free money from the government. The business cycle will inevitably ensue.
It is impossible to run away from the fact that government expenses will be wasteful and by necessity lower the people’s standard of living due to the irrefutable workings behind bureaucracy. The crucial shortcoming of applying the GDP formula is the blatant disregard of the fact that the government raises money violently and against the people’s value preferences before offering goods and thus faces the inability to calculate profit and loss.
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
Now he continues with the false assumption that GDP is growing and happily concocts new formulas based on that. He doesn’t put into context the relevance of dD and, I have to assume, does not bother to view it in light of a corresponding reduction of private investment which would necessarily occur as I already pointed out above. He blithely assumes that magically a tdY appears out of nowhere and reduces the deficit. He then takes this flawed formula and incorporates it into his other flawed formula. Everything from hereon is based on sheer nonsense and requires no further comment:
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.
Krugman can’t escape the fact that his formula fails from start to finish. It sickens me that thousands of students are probably listening to him and employing his “logic” elsewhere. To anyone who still doubts my criticism, please consider the following: If the bang per Euro of deficit spending is 2.23 Euro, then why don’t we ask all European governments to spend 1,000 quadrillion Euros on deficit. This will create unprecedented wealth in Europe of 2,230 quadrillion. Then the governments can levy a tax of 1,000 quadrillion and pay off the debt. With 1,230 quadrillion Euro, this would leave Europe wealthier than ever before for years and years to come. Welcome to Krugmanland!