Words on Numbers

Wednesday, August 17, 2005

The Federal Deficit: A big number with a little problem...

What does it mean? One of the most common misuses of numbers is publishing data that makes a nice headline, but has little meaning in and of itself.

The federal debt is the total amount of money the federal government owes. The federal deficit is the amount spent beyond revenues each year: it's the yearly change in the debt.

There's been a lot of talk about the budget deficit recently giving the latest numbers on the Federal budget deficit. The current estimate from the CBA is that we'll have a 331 billion dollar deficit in 2005. Ignoring the issues of inappropriate accuracy (can it really be estimated to 1/3 of a percent), it's not clear that this is a useful number at all.

Currently the federal debt stands at just under 8 trillion dollars according to the debt clock. Also, according to the latest numbers inflation over the past year has run at about 3.2%. So just adjusting the debt for inflation we'd expect a nominal deficit of about 256 billion dollars. I.e., if we owe 8.25 trillion dollars in 2005, we owe about the same amount of goods and services as 8 trillion dollars in 2004.

A 'nominal' deficit of 250 billion dollars actually represents a balanced budget.

By this calculation the real deficit, the additional goods and services that we owe, corresponds to a 'mere' 80 billion dollars.

So is the deficit $331B or $80B? Which number is right? Undoubtedly neither!

Of that 8 trillion dollars about 40% is owed to the federal government itself in fictions like the Social Security Trust fund. We can only really count the inflation on the 'real' debt owed outside the federal government. That's about 4.8 trillion dollars implying about 150 billion dollars of the deficit is simply inflation of the debt. That leaves a 'real' debt of about $180 billion.

So now we have three numbers ranging from a measly $80 billion to $331 billion.

It's not even the case that we can say "Well the number may not be correct, but by looking at the trends we can see what's happening." When we correct for inflation on the debt, we're taking the difference between two rather comparable quantities: the very sign of the deficit can, and in many years does, change.

It would seem elementary to correct basic discussions of economics for simple effects of inflation, but in general it does not seem to be done. Doubtless things are a lot more complex than the simple analysis done here. Nonetheless it's pretty clear that the debt numbers that see and hear discussed are not very helpful in understanding the real fiscal situation of the government.

Tuesday, August 16, 2005

Words on Numbers

Why this blog? There are excellent discussions of innumeracy on the Web, e.g., Innumeracy.com, but I haven't seen any blogs which discuss innumercy issues on a continuing basis. This blog is intended to be a venue where I can vent my own frustrations at seeing numbers and mathematical concepts misunderstood or distorted and to express pleasure on the occasions when we can see an insightful analysis. Numbers can be fun, but they are important enough in today's society to be dangerous toys.

I hope that in discussing issues with numbers and mathematics I can try to make constructive suggestions and in some small way raise awareness of issues. The topics I hope to talk about range from the great social issues of the day, e.g., the profound and deliberate misuse of numbers on all sides of the Social Security debates, to tiny issues that gratuitously make an issue difficult to understand.

My own sense is that only a small fraction of people really feel comfortable and like playing with numbers. The goal here is not to frighten people into numerical correctness, but to share the pleasure of using mathematics in daily life.