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Risk-free no more (part I)

My main objection against the euro stems from the realization (post fact I must admit) that the common currency has resulted in an increase of macro and systemic risks across the countries of the eurozone, despite the initial intention of eliminating currency risk and harmonizing monetary policies across the region. One risk that sharply increased in significance the moment the EZ countries adopted the euro is sovereign risk and in this post I will try to illustrate why.

I start with creating a (very) simple model of money flows in a country that uses its own currency and in which the state borrows 100 currency units at time T=0 through the issuance of bonds in order to pay for some services (e.g. civil servants’ salaries). The sale of the bonds creates an equal amount of money (figure 1) with which the newly issued debt is eventually going to be repaid.

Figure 1

Figure 1

We now try to follow the course of these 100 currency units from the moment they leave the state’s bank account at time T=1 till the moment they return. Let’s assume for simplicity, that out of every transaction that occurs thereafter the state is able to collect a fixed 25% in the form of taxes, whether indirectly (e.g. through VAT) or directly (through income tax). Our preferred unit of time is going to be a single transaction, so if money velocity turned out to be equal to 2, then the money that we try to keep track of would change hands twice in a year. In this case the unit of time coincides with a half-year period.

Figure 2 shows the amount of tax revenue the state receives out of each subsequent transaction and the cumulative tax revenue after a sufficiently large number of transactions.

Figure 2

Figure 2

After the 100 currency units are initially spent at time T=1, those who received it (e.g. civil servants) will use this money to purchase various goods or services. Once all 100 currency units have been expensed once, the state stands to receive 25 currency units through taxation. The remaining 75 currency units are used subsequently for the purchase of other goods and services and after they are expensed once more, the state stands to collect 18.75 additional currency units, for a total of 43.75 currency units. The process continues indefinitely until the whole amount of 100 currency units is received.

Although it is not shown in this diagram, the interest that the state pays on these bonds is recirculated in the economy creating income (for the bondholders), demand and tax revenue in exactly the same process as above. And similarly, after a large number of transactions the state ends up with the full amount necessary to pay also the interest on the bonds it has issued. Here it is also worth noting that whether money is spent on imports is irrelevant, since every currency unit spent on imports must return in the economy in the form of investment.

What would happen though if the citizens didn’t pay taxes or if firms used various loopholes to avoid paying taxes? Let’s assume that as much as one third of annual production occurs in the black market, then the state is going to miss tax revenue from one out of every three transactions in our model. The treasury will care much less than what you might have thought, as figure 3 shows.

Figure 3

Figure 3

It may take a little longer for the Treasury to receive the full amount it needs to repay its liability, but given enough time it will. When people or businesses avoid paying taxes, the money they save can still be used in the economy and eventually is being taxed when it leaves the black market. The state will eventually receive the same amount of money, even though it might need more time to collect it. A state with a lower tax rate, say 18% and zero tax evasion, would collect the required amount in approximately the same time.

Now we are going to add some more complexity in the model by considering that the country of our example is divided in two regions, one in the South and one in the North. The state uses the proceeds of the bonds to spend 20 currency units in the Southern region and 80 in the Northern region. Let’s assume for now that the two regions do not trade at all with each other and repeat the previous exercise. The results are shown in figure 4.

Figure 4

Figure 4

As trade occurs only within each individual region, South and North will end up paying in taxes exactly the amounts initially received from the state, 20 and 80 currency units respectively.

But clearly assuming that no trade is conducted between the two regions is unrealistic, so in the next step we can relax this assumption and see what happens if the Southerners decided after the fourth transaction of our example to spend 5 currency units in purchases from the North (they could also be investing 5 currency units in the North which would not make any difference in our example). Just like taxes, the expense of the 5 currency units is going to reduce demand in the subsequent periods in the South, the exact opposite of what will happen in the North. The example is illustrated in figure 5.

Figure 5

Figure 5

Interestingly, the state ends up receiving the same amount again in taxes (100) but the North contributes 85 currency units to the state’s revenues while the South only 15. So even though the South had a cash outflow of 5 throughout the test period, it recovers this amount to the last cent by paying less in taxes. The opposite holds true for the North.

This case is representative of what happens in every country around the world. Surpluses and deficits of regional balances-of-payments are over time compensated by fiscal transfers. The temporary imbalances can help the regions self-adjust, by suppressing and boosting demand in the appropriate regions. The system might seem unfair to those regions that happen to overproduce, but it makes absolute sense that additional income originating from domestic exports should give rise to a higher tax liability. The more I earn, the more I should pay in taxes.

And lastly, what if we assumed that the two regions in the last example are different countries within the Eurozone? At time T=1 the Southern country runs a budget deficit of 20 euros and the Northern country a budget deficit of 80 euros. Then the South spends 5 euros in imports from the North. The numbers in figure 5 won’t change, the only thing that will change is the recipient government. The Southern government will only be able to receive 15 euros from taxes, whereas the Northern government will receive 85. The former goes broke, while the latter becomes a fiscal poster child. Sound familiar?



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