Anmol On Fiscal Policy

Anmol on Fiscal policy

Right now, the Euro Zone debt crisis, along side the American debt crisis seems extremely serious, because both economies constantly seem on the verge of default, and any such default would lead to a world wide economic collapse. That’s why the leaders of the world will do almost anything to prevent a default. Today’s article will deal mainly with how to deal with large debt burdens, calculation of debt burdens, and interest rates of bonds. Some of the answers I find will definitely surprise you and make you think.

As a response to the Italian debt crisis, Sylvio Berlusconi forced parliament to push through austerity measures, a natural reaction, also mirrored by Republicans to the American debt crisis, but how much do these measures actually help? How much of a surplus should a government actually run when they have large debt burdens? Well, lets look at the case of country X, a hypothetical country to determine the best strategy of a government

First, we must discuss the concept of the multiplier. Let’s say I gain $1, and my marginal propensity to consume (∆consumption/∆income) is 0.8, which means I’ll spend 80¢ of that dollar. The next person has 80¢ and will spend 80¢*0.8, or 64¢ of it, and so on. As you can see, this is a geometric progression, and the formula for the total amount of money in the economy is injection (of money)/1-mpc. So any injection in the economy is multiplied by 1-mpc, which is why 1-mpc is known as the multiplier.

How do you calculate the debt burden of a country? Is it the internal debt? Is it the foreign debt? Well, it’s the internal debt multiplier*internal debt+the multiplier*foreign debt.What is the internal debt multiplier? It’s the amount the economy will lose by paying off internal debt. Lets assume that government can either spend a certain amount of money, T, or return T to bond holders. If they spend T, then growth in the economy will be T*multiplier, or T/(1-mpc), whereas if they pay T to bond holders, the injection to the economy will be T(mpc)/(1-mpc), because the amount they consume will return to the economy. Therefore the debt is (T-T*mpc)/(1-mpc), or T(1-mpc)/(1-mpc) or T. The foreign debt multiplier will be 1-mpc, because the money you use to repay foreign debt automatically leaves your economy. So total debt burden= internal debt*1+foreign debt*multiplier, or internal debt+foreign debt*multiplier.

Now, we need to calculate bond yields. Assuming there is a very small chance of default, bond yields will be close to inflation. Inflation is a function of change in consumption. ∆consumption= ∆national income*mpc. To find Inflation from ∆consumption, we use the formula, ∆consumption (as % of GDP)*G(supply)/[G (supply) + G (demand)]
G being the gradient of the curve. Assuming bond yields are near inflation, as happens often in real life, bond yields are approximately ∆consumption*Gs/Gs+Gd.

Every year, your debt burden is multiplied by your bond yields, which is then added to your net budget deficit, to calculate the debt for the next year. To follow the rest of this article, you should look at a country’s debt burden as a percentage of its GDP, and not in absolute terms, as it will make more sense that way. Lets look at an example to make it easier.

Italy’s national debt is 120% of GDP, and because more reliable data isn’t available, we’ll assume that 45% of its debt is foreign, and 75% is internal. We’ll also assume that mpc=0.7, because reliable data on that too is unavailable. The total debt burden= 75%+45%/(1-0.7), or 75%+150%, or 225% of GDP. Let’s assume that despite all the calls for austerity, the Italian government decides to resist foreign pressure, and run a deficit which adds a burden= 10% of GDP. Therefore, the economy will grow by 10% of GDP to 110% of initial GDP. Assuming Gs=Gd, then Gs/Gs+Gd=1/2, and inflation will be 0.7*10*0.5=3.5%, and bond yields will be 3.5%. Just to make this example clearer, we can assume bond yields will be 4%. The new debt will be 225*1.04+10, or 244% of GDP.

The new national debt will be 244*100/110, or 222% of GDP, lower than what it was before the deficit, which is counter intuitive to what all the pro austerity economists say. What they say makes sense, if you’re in debt, spend less, pay other people back, but the math disagrees with them. Paying off a certain amount of debt will contract your economy more than it contracts your debt, therefore increasing your burden.

Of course, this only works with very large debt burdens, and beyond a point, it stops to work. This point is given by 100*(Gd+Gs)/Gs, for the economy. Note that economic growth isn’t mentioned here, because interest rates will normally be similar to economic growth, so the two tend to cancel each other out. Even unexpected growth is irrelevant, because growth is a fraction of total GDP, so the lowest debt:GDP ratio, is still the most beneficial path. Of course, after your debts reach a certain point, the point which I call “the point of madness”, it should start running surpluses to pay off the debt, that’s the point at which the debt to GDP ratio is constant regardless of deficits, or surpluses, and the deadlock can only be broken by unexpected technology growth. Of course, how economies get beyond this point is beyond me, but some of them find a way to do it. My advice to them: spend, spend, spend.