Tuesday, December 11, 2007

Lies, Damn Lies, and ... Economics?

Today I'm going to venture out of any field that I have the slightest expertise in and flounder about in the field of basic macro-economics.

But before I demonstrate my utter lack of knowledge, I'm going to touch on a subject that I at least have some familiarity with -- mathematics. I'm going to share with you a math problem that I cannot solve. It looks something like this:


A A'
--- = 111 = ----
B B'


B = B' * 1.41

What is the ratio between A and A'?
Elementary algebra would seem to imply the answer should be 1.41:

A A'
--- = ----
B B'

A * B' = A' * B

A * B' = A' * B' * 1.41 ==> A = A' * 1.41

By itself, I would have expected this problem would be trivial.
However, what perplexes me is that the observed value for the ratio between A and A' is nowhere near 1.41, but rather approximately 1.0.

And here is where I demonstrate my lack of understanding in the field of economics...

The thing that has been puzzling me for years (even before the recent foreign exchange craze) is that the U.S. dollar has experienced fairly consistent inflation for these 13 years while the Japanese Yen has experienced almost none, yet the exchange rate remains the same.

You see, A' / B' is the average value of the Japanese Yen in U.S. dollars for November 2007. And A / B is the average value of the Japanese Yen in U.S. dollars for April 1994. Both ratios just happen to be approximately 111. (Source: Board of Governors of the Federal Reserve System)

The ratio B' / B is the purchasing power of the U.S. dollar in 2007 relative to dollars in 1994. That is, one 1994 dollar (B) is worth 1.41 2007 dollars (B'). (Source: Bureau of Labor Statistics)

The ratio A' / A is the purchasing power of the Japanese Yen in 2007 relative to yen in 1994. It so happens that one Japanese yen buys the same amount in 2007 that it did in 1994. (Source: Japanese Ministry of Internal Affairs and Communications)

How can this be?
How can two currencies can have different inflation rates, but yet maintain the same conversion rate?

I'm no economist, but I cannot help but wonder if the answer lies outside of math and in the realm of human irrationality. Or that the CPI values uses to calculate the purchasing power of a currency are inconsistent and/or flawed. Actually, I know that CPI calculation methods differ amongst countries, but for some reason I expected Japan to have used to the calculation method that U.S. does. I admit I haven't investigated that explanation yet.

Does anyone have a better explanation (preferably one that does not violate basic math principles)? I would love to put this puzzle to rest.


BenjaMinster said...

Short answer: Purchasing power across currencies doesn't make sense. Also, the dollar is overvalued. :)

I'm no economist either, but I'd say it's probably incorrect to treat the exchange rates as ratios of quantities that exist independent of the rate. While that thinking is natural if you are converting from one currency to another at a known rate, that isn't how people calculate or adjust exchange rates.

Also, I would assume that a comparison of inflation measures is apples-to-oranges unless I could read up on the calculations used.

There are a lot of people worried about the strength of the dollar on account of things like the federal debt and the (ever-widening) trade deficit. The vague idea that I tend to agree with is that the dollar won't be hit too bad as long as it is still being used for the pricing of oil and certain countries continue buying up chunks of debt.

I really want to make a graph of the EUR to USD conversion rate and the price of oil in USD vs. time. Though the pricing of oil is still in USD, it would be interesting to see if the two track each other.

Kelly Yancey said...

Thanks for the comment. I'm curious why purchasing power across currencies would't make sense. The staples obviously vary by culture, but the cost to live at an equivalently comfortable level should be estimable. Or are you suggesting that the estimates are just horribly off?

Unfortunately, I know for a fact that the EU uses a different CPI measure so it makes comparison between the Euro and the US Dollar very difficult.

Part of what fascinates me about the Yen/Dollar inconsistency is that Japan's national debt far outstrips the U.S. in proportion to their GDP. The national debt ratio in the U.S. hovers around 62% of GDP where as Japan's is currently at 170%. And yet the consensus seems to be to say that the U.S. dollar is overvalued.

If anything, the ratio between the U.S. dollar and the Japanese yen seems to imply the opposite is true: that the yen is overvalued (compared to the U.S. dollar) by approximately 40%. Go figure.

Could it be that the national debt is meaningless and only the foreign trade deficit really affects the relative value of currencies?

Speaking of which, if we accept that we cannot compare purchasing power across currencies, then how can anyone determine whether one currency buys "more" -- and hence is worth more -- than another currency? It would seem that the entire premise of one currency being (inherently) worth more than another is predicated on being able to compare purchasing power.