Redundancies and Macroeconomics

3/12/2013 12:00:00 PM
Krugman has a piece about how the "doctrine of immaculate transfer" is alive and well, which got me thinking about redundancies in macroeconomics. I find that a lot of erroneous causal claims about macroeconomics are due to the failure to recognize that there are certain redundancies built into the price systems of macroeconomies.

The first redundancy is between price levels and interest rates. Here's an example to illustrate why these are redundant. Suppose you have the choice of buying consumption goods today at the current price of \$1, or buying a savings bond which matures a year from now. Now consider two scenarios:
  1. The interest rate on the bond is 0% so that investing \$1 today yields \$1 next year. But, the price of that consumption good next year falls to \$0.75. That means that if you forgo one unit of consumption today, you can buy 1.5 extra units of consumption next year.
  2. In the second scenario the price of the consumption good is \$1 both today and next year, but the interest rate on the savings bond is 50%. That means if you forgo one unit of consumption today, you can buy 1.5 extra units of consumption next year. 
Although the nominal interest rate rose from 0% to 50% between the two scenarios, the real interest rate is actually the same in both: precisely 50%. In fact, both scenario's give you the exact same budget constraints. Unless your Robert Schiller, you'll admit that consumers would behave exactly the same ways under both scenarios. This is why most macro models include a "Taylor rule"--its because prices and interest rates are redundant, so at least one of these has to be exogenously specified in order for the model to predict the other. Moreover, from a policy perspective this redundancy means that there are no long-run consequences from interest rate policy--prices will eventually adjust to eliminate any economic distortions caused by interest rate setting.

That said, even though the levels of nominal interest rates and prices are redundant, they do follow very different transition paths, since nominal interest rates adjust much, much more quickly than do price levels. As a result, we do see sometimes very substantial short-run distortions from interest-rate setting. A hike in the nominal interest rate will eventually cause prices to decline (relative to what they would otherwise be), but in the meantime there will be an aggregate demand shortfall. On the other hand, if an aggregate demand shortfall arose, for whatever reason, then one way to eliminate it and restore the economy to full output would be to lower the nominal interest rate. Since interest rates move faster than price levels, this will eliminate the demand shortfall faster than waiting for prices to adjust. This is the logic of macroeconomic stabilization policy.

My point here is that I see a lot of commentators making a causal claim that "Low interest rates causes increased risk-taking." That's always a big puzzler to me, because it isn't at all clear to me what "low interest rates" even means--you have to specify what assumptions you are making about price levels as well.

A second example of macroeconomic redundancy, much along the same lines, is price levels versus exchange rates. This follows the same basic logic as above. People often make causal claims like "Higher exchange rates favor net exports." That's not a complete thought, because it isn't at all clear what a high exchange rate means. Raising the domestic/foreign exchange rate (ie, "devaluing" the currency) won't cause a net export boom if it is offset by a corresponding rise in domestic prices. Theory says that in the long-run, at least, that's exactly what will happen. Moreover, since central banks do not typically intervene directly in foreign exchange markets anymore, there is no particular reason to suppose that exchange rates would adjust anymore quickly than the overall price level in response to the bank's balance sheet operations. That's why I'm always a little puzzled when Noah Smith claims that Shinzo Abe is attempting to use monetary expansion to raise Japan's exchange rate and boost exports--unless the bank of Japan is buying foreign currencies directly, I see no reason why the Yen exchange rate would rise faster than domestic inflation. And if it doesn't there wont be an export boom. But then, I suppose the reality doesn't prohibit Abe from trying.