Debt

I do not have any debt, which is nice.  My tuition is... well, let's not get into how it's paid for, but it is paid for without my having to take out any student loans.

But, if I did have to take out loans, I would.  The reason being is such:  the investment in my education would like give out greater returns than the debt I incurred, interest included.  The result would be a net gain in my total wealth.

This, in general, is the proper way to consider debt. It's a kind of inverse investment. As long as the money you borrow goes to purchasing you something of greater value, than you should take out the loan. As a concrete example, imagine we have a  company named Firm A.  Firm A does one thing and one thing only. It borrows money from individuals or banks who wish to save and it invests that money. Because Firm A is rather large, it's portfolio is diversified and every year it averages returns of about 4-5%.  It borrows money at an interest rate of about 2-3%. How much money should Firm A borrow?

As much as it can possibly invest.  Let's say it can only borrow $100 and it invests that $100 for a year.  At the end of the year, it owes $102 - $103 and has $104-$105.  It's made a net profit of $1-$3.  If it borrows twice that, it doubles the amount it earns.  Clearly, the way to maximize profit is to borrow as much money at that rate as the Firm can invest.

Let us assume we have a small country called Country A.  Country A's economy grows at a rate of 4%.  Its government offers bonds at a rate of 2%.  How much money should Country A's government borrow?

As much as it can pour into its economy and still have its economy grow at a rate greater than 2%.

Let's assume Country A has $100 in its economy (total GDP).  Tax rate is 10%.  So, the government collects $10, which it then spends right back in the economy.  GDP is still $100.  The government borrows $20, then spends it.  Total GDP is still $100 (total assets minus liabilities, $120 - $20).  Government borrowed at 2% interest rate.  Economy grows at 4%.  Next year, the government owes $20.40, and the economy has assets of $124.80.  "Fiscal conservatives" enter office, and all taxes now go to paying back the debt.  They even raise taxes to  16.35% (roughly) to pay off the debt.  All $20.40 has been paid off, and the total GDP is $104.40.

What would have happened if the government had never borrowed money at all?  Then the total GDP would have been $104. The country is richer because it went into debt.

What happens if the fiscal conservatives don't enter office?  The government, instead of paying off the debt, borrows another $20 and pays off the interest.  So, debt stands at $40 and total GDP stands at $144.80.  Another year passes.  The national debt is at $40.80 and assets are at $150.592 (we'll round to $150.60 to make it easier).  As a percentage of GDP,   the debt has gone from 0% (first year) to 19.5% (second year) to 37.15% (third).  And yet the total GDP, the wealth of the nation, has grown at a faster rate than it would have if there was no debt at all.

What the hell is going on?

What you are witnessing is two different compound interests battling each other.  And much like sumo wrestling, real wrestling, rugby scrums, and black hole collisions, the larger one always wins.  As long as the GDP growth rate remains above the interest rate, as long as assets exist to pay off the debt, and as long as lenders believe the first two are true, then a country can borrow money until the sun explodes and the universe either collapses into another Big Bang or entropies itself into heat death.  Interestingly enough, current physics seems to indicate the latter is more likely.

Guess what the GDP growth rate for the last quarter of 2010 in the US was? 3.10%
Guess what the interest rate on the national debt for the last quarter of 2010 is? 0.25%
Guess how much I'm concerned about deficits? Not at all.

[1] - Data taken from Trading Economics.  I have no knowledge of their possible biases.

Simpson's Paradox

Simpson's Paradox is a particularly well known statistical paradox. At least, it's well known among statisticians.  It is less well known among everyone else.

A layman's version goes something like this: imagine there are two ways of transporting emergency patients to the hospital.  One is by helicopter, the other is by ambulance.  50% of patients who go to the hospital by helicopter die, while only about 21% of patients who go by ambulance die. Clearly, there is something wrong with helicopters, we should make all patients go the hospital by ambulance.

But wait! There are two categories of emergency patients at this hospital, those in normal condition and those who are in critical condition. Of those who travel to the hospital in normal condition by ambulance, 12.5% die while only 10% of normal patients who by helicopter die.  Likewise, of those who travel to the hospital by ambulance in critical condition, 75% of them die while only 70% of critical patients who by helicopter die. What's going on?

	Normal	Normal died	Critical	Critical died	Total	Total died
Helicopter	100	10	200	140	300	150
Ambulance	600	75	100	75	700	150
Total	700	85	300	215	1000	200

What happens is that two thirds of critical patients go by helicopter while only one seventh of normal patients do.  Since normal patients die at a much lower rate than critical patients (roughly 12% as compared to roughly 72%), this skews the data to make ambulance looks much safer than helicopters, even though helicopters are way safer.

Most of the time, that is.

The fascinating moral of this story:  don't immediately assume a relation based on a single correlation. Look deeper for causes.