# Monthly Archives: February 2015

## More on Germany

Tony Yates has a new post speculating on Germany’s attitude toward fiscal policy. Tony’s assumption is that the German’s opposition to a deal with Greece is rooted in their beliefs about the macroeconomy. In particular, the New Keynesian consensus never really took hold in Germany and therefore they don’t tend to look favorably on stabilization policies. Some might view Tony’s post as a condemnation of Germany, but I don’t view it as such. If you’re a New Keynesian, you probably think this is a bad thing. If you’re not a New Keynesian, or if you’re otherwise opposed to stabilization policy, you probably think this is a good thing. But regardless of whether it is good or bad, this is a possible explanation. Nonetheless, I don’t find this explanation all that convincing.

As I wrote in my previous post on the topic, I think that macroeconomists tend to look at the negotiations between Germany (and the EU more broadly) and Greece all wrong. Naturally, as macroeconomists, we tend to think about these negotiations in terms of the “big picture”. In other words, when macroeconomists look at the negotiations, they often think about the macroeconomic effects of a financial market collapse in Greece and the possible damage that results from various interlinkages. Those who see these costs as being very large then tend to advocate the importance of coming to an agreement. In addition, those who advocate stabilization policies think that such an agreement should also allow Greece to defer the costs until they have a chance to improve their economy through (you guessed it) stabilization policies.

I think that this is the wrong way to think about the negotiations. The negotiations have to be viewed in the context of game theory. The Germans and the Greeks are playing a dynamic game. Thus, Germany has an incentive to make sure that any deal that is reached between the EU and Greece is one that prevents these types of negotiations from happening in the future. In other words, Germany is trying to minimize the costs associated from moral hazard in the future. This isn’t just about Greece, this is about setting a precedent for all future negotiations. When you think about the negotiations in this context, I think that you come up with a better understanding of Germany’s behavior.

But I also think that once you think about the negotiations in terms of game theory, the supposed German opposition to fiscal stabilization doesn’t hold up very well as an explanation of the German response. For example, suppose that the Germans do believe in fiscal stabilization policies. Wouldn’t it then make sense to use austerity as a punishment mechanism for the bailout? If Germany’s true desire is to prevent such negotiations from taking place in the future, then they have an incentive to enact some sort of punishment on Greece in any deal that they reach. Imposing austerity would be one possible punishment. Even if the Germans don’t believe in fiscal stabilization, they know that the Greeks do. As a result, this threat is still a credible way of imposing costs in the game theoretic context because the expected costs to Greece are conditional on Greece’s expectations.

In short, whether or not Germany believes in economic stabilization policy, they are likely to pursue the same strategy within a game theoretic context. Thus, viewing this strategy on the part of the Germans doesn’t necessarily tell us anything about German beliefs.

## Resolving the Glasner-Sumner Dispute

David Glasner and Scott Sumner are arguing about whether saving = investment is an identity or an equilibrium condition. So I thought I would step in and resolve this dispute. Instead of using textbook accounting identities, let’s consider a framework everyone is familiar with — a two-period consumption model.

1. Consider a Robinson Crusoe economy. There is one guy on an island with production opportunities, but no market opportunities. For simplicity, think of a two-period model. In the first period, the individual receives an endowment, Y. The individual can invest that endowment to generate future production or consume the endowment. The individual transforms Y into P1, production now, and P2, production later. It follows that investment is defined as I = Y – P1. Savings is defined as S = Y – C1, where C1 is consumption in the first period. Since there is only one guy on the island, it must be true that P1 = C1. These decisions are both determined by the individual’s rate of time preference. Thus, S = I is an identity.

2. Consider the same guy on an island, but who now has market opportunities. Now we have the same definitions for saving and investment. Saving is

S = Y – C1
I = Y – P1

Note that with exchange opportunities, it is very unlikely that C1 = P1. Thus, at the individual level, savings probably doesn’t equal investment. Combining these conditions, we get

S = I + P1 – C1

for the individual. Now sum across all terms and we get

$\sum S = \sum I + \sum P1 - \sum C1$

Now in equilibrium, market-clearing requires that total production equals total consumption. Thus, market clearing implies that total savings is equal to total investment:

$\sum S = \sum I$

Saving = Investment is therefore an equilibrium condition.

3. Finally, David’s issue is that he doesn’t think that gross domestic income and gross domestic expenditure are the same thing. Empirically, he’s correct. This is why we have GDP Plus.

## Germany, Greece, and Rent-Seeking

Greece is currently seeking a bailout from the European Union. However, negotiations (at least as I write this) are at a standstill. Greece wants a bailout, but the new Greek government has indicated that it is unwilling to enact so-called austerity reforms. During the negotiations, the European Central Bank has given emergency funding to the Greek financial system. However, this funding is conditional on the negotiations between Greece and the EU. The finance ministers of various EU countries want Greece to commit to reducing their debt in line with their 2012 commitments. Since Greece appears unwilling to meet those requirements, the support from the ECB is likely to stop by the end of the month. Thus, Greece could face a significant financial crisis if no deal is reached.

In the midst of these negotiations, some have argued that the EU, and Germany specifically, do not appear to understand the magnitude of the situation. Paul Krugman, for instance, writes

As long as it stays on the euro, then, Greece needs the good will of the central bank, which may, in turn, depend on the attitude of Germany and other creditor nations.

But think about how that plays into debt negotiations. Is Germany really prepared, in effect, to say to a fellow European democracy “Pay up or we’ll destroy your banking system?”

[…]

Doing the right thing would, however, require that other Europeans, Germans in particular, abandon self-serving myths and stop substituting moralizing for analysis.

This last statement is particular telling. Many commentators agree with Krugman and view the Germans and other members of the EU as moralizing. In other words, they are not using economic analysis, but rather relying on their own views about right and wrong and how a government should operate. However, I would submit that rather than assuming that the Germans and other members of the EU are vindictive moralizers, an understanding of economics can actually teach us why EU members have taken their current position. But to understand why, we need to know something about rent-seeking.

Suppose that there are two countries, Germany and Greece. In addition, suppose that each of these countries have an endowment of resources, $R_i$, where $i=1$ will refer to Germany and $i=2$ will refer to Greece. Now let’s assume that each country can devote some amount of resources to production, $P_i$ and some amount of time to fighting with each other, $F_i$. It follows that each country has a resource constraint:

$R_i = P_i + F_i$

Now, let’s assume that the total production between the two countries is given as

$Y = (P_1^{1/s} + P_2^{1/s})^s$

where $s \geq 1$ is a measure of complementarity in production. One way to think about $s$ is that the higher its value, the most closely linked the two countries are in terms of international trade, production, etc.

Thus, we see that the countries can commit their resources to production or to fighting. The more each country contributes to production, the higher the total level of production. However, fighting with one another can also provide benefits (this obviously doesn’t have to refer to actual fighting, it could refer to negotiations like those that are ongoing). However, whereas increased production will cause an increase in the amount of production/income that is generated, fighting will only have an effect on the distribution of income.

Thus, each country faces a trade-off. The more resources they commit to production, the higher the level of income that is generated. The more resources they commit to fighting, the greater the distribution of the existing income they receive (but there is less income as a result). Thus each country has to choose the share of resources that they want to commit to production and fighting.

We will assume that there is a contest success function (as in Tullock, 1980) that is a function of the amount of resources that each country commits to fighting. For Germany, we assume that the contest success function is given as

$\mu_1 = {{F_1^m}\over{F_1^m + F_2^m}}$

where $m$ is an index of the decisiveness of the conflict. Correspondingly, for Greece $\mu_2 = 1 - \mu_1$.

Given these definitions, we can then define the distribution of income:

$Y_1 = \mu_1 Y$
$Y_2 = \mu_2 Y$

Now let’s assume that each country wants to maximize their own income $Y_i$, taking what the other country is doing as given. Thus, each country wants to maximize the following

$\max\limits_{P_i, F_i} {{F_i^m}\over{F_i^m + F_j^m}} [(P_1^{1/s} + P_2^{1/s})^s]$
$\textrm{s.t.} \hspace{2mm} R_i = P_i + F_i$

In equilibrium, it follows that

${{F_2 P_2^{(1-s)/s}}\over{F_1^m}} = {{F_1 P_1^{(1-s)/s}}\over{F_2^m}}$

Now let’s use this equilibrium condition to understand the interaction between Germany and Greece. Suppose that we simply choose resource endowments of $R_1 = 100$ and $R_2 = 50$ thereby assuming that Germany has twice as many resources as Greece. Now let’s consider the implications under two scenarios. First, we will consider the scenario in which $s = 1$. In this case, total production is just the sum of German and Greek production. It follows from equilibrium that

$F_1 = F_2$

Thus, in this case, Germany and Greece devote the same amount of resources to the fighting. However, since Germany has twice as many resources as Greece, it follows that Greece is devoting a larger percentage of their resources to fighting. In devoting resources to fighting, the two countries produce less total production. To see this, consider that if each country devoted all of their resources to production, total production would be 100 + 50 = 150. If we assume that $m = 1$, then $F_1 = F_2 = 37.5$. Thus, total production is 62.5 + 12.5 = 75. And yet this is their optimal choice given what they expect the other country to do!

As a result of the percentage of resources devoted to fighting, Greece gets 1/2 of the resulting production, despite only having 1/3 of the total resources. It should therefore be straightforward to understand why Greece is devoting so many resources to getting a larger bailout without bearing the costs of so-called austerity measures. In addition, it is important to note that it is in Germany’s best interest to devote resources to fighting, given what they expect Greece to do.

It is straightforward to show two other results with this framework. First, as $s$ increases, the weaker side has less of an incentive to fight whereas the stronger side has a greater incentive to fight. In other words, when production becomes more complementary, then the poorer side has less of an incentive to fight because of the linkages in production between their production effort and the other country. While the richer country has an incentive to fight more, the total resources devoted to fighting will fall.

Again, this informs the discussion about Germany and Greece in comparison to other countries. If you want to understand why there seems to be a greater conflict between Germany and Greece than between Germany and other EU countries, consider that Greece is Germany’s 40th largest trading partner, just after Malaysia and just ahead of Slovenia. All else equal the model described above suggests that we should expect more resources devoted to conflict.

The second characteristic has to do with the decisiveness of conflict. As $m$ increases, the conflict between the two countries can be considered more decisive. As the conflict becomes more decisive, the model predicts that the sides will have more of an incentive to devote to fighting. Thus, if Germany believes that this is (or should be) the last round of negotiations with Greece, then we would expect them to devote more resources to fighting.

So what is the point of this exercise?

The entire point of this exercise is to understand that Germany is, in fact, acting in their own economic interest given what they expect Greece to do. If we want to understand the positions of Germany and Greece, we need to understand strategic behavior. Germany’s refusal to simply give in to Greece’s demands and “do what’s best for Europe” ignores a lot of the aspects of what is going on here. Those who think that Germany is being too harsh ignore some of the key aspects of the framework discussed above.

First, one should note that the distribution of income in the framework above is always more equal to the distribution of resources. Thus, it pays for Greece to fight. However, Germany knows that it pays for Greece to fight and therefore Germany’s best strategic decision is to devote resources to fighting as well.

Second, by claiming that Germany is failing to do what is in the “best interests of Europe”, the critics are presuming that they know the social welfare function that needs to be maximized. Perhaps they are correct. Perhaps they are not. But even if these critics are correct, this doesn’t mean that Germany’s behavior is incomprehensible or that it is based on something other than economics. Rather the confusion is on the part of the critics who fail to understand that a Nash equilibrium may or may not be the socially desirable equilibrium. Germany’s rhetoric might be moralizing, but we can understand their behavior through an understanding of economics. And this is true whether you like Germany’s behavior or not.

[This post is an application of Hirshleifer’s Paradox of Power model. See here.]