# The Friedman Magic

One of my favorite Friedman papers is "The Effects of Full-Employment Policy on Economic Stability: A Formal Analysis" which you can find in Essays in Positive Economics.

Friedman sets up a very simple model, Z(t)=X(t)+Y(t) where Z(t) is income at time t, X(t) is what income would be if there were no counter-cyclical government policy and Y(t) is the amount added to or subtracted from X(t) by the history of government policy.

You wouldn’t think that much could come out of such a simple model but Friedman takes the model, notes that the formula for the variance of two random variables is V(Z)=V(X)+V(Y)+2 r(X,Y) Sd(X) Sd(Y) (where V is variance, r correlation and Sd is standard deviation) and proceeds to show that:

In order to cut the variance of income fluctuations in half (which would cut the standard deviation by less than a third), r(x,y) must exceed .7.

The result is powerful because once you start thinking about the correlation coefficient, r, it’s hard to see how it could be as high as .7. Very few government actions taken in time t have an effect in time t – there are lags between recognizing a problem, deciding what to do about the problem and implementing a policy. Once the policy is implemented there are lags before the policy takes effect. All of these lags are of uncertain and changing length so actions taken in t-5, t-4, t-3, and t-1, may influence Y(t) making a high correlation between X and Y unlikely. Moreover, Friedman’s bound is an upper bound, requiring optimally sized interventions – when we recognize that the size of the intervention might be too little or too much and that in both cases this will reduce the decrease in variance we have a strong case for skepticism about the efficacy of counter-cyclical policy.

But was Friedman right? In the thirty or so years after he wrote, when counter-cyclical policy was in vogue, the variance of the US economy was much lower than in the pre-World War I years. Reality it appeared, refuted Milton Friedman.

Friedman, however, lived to see his simple model proved correct (Essays in Positive Economics!). In a series of papers beginning in 1986, Christina Romer showed that the pre-WWI volatility was an artifact of the way the data was collected. Once the pre-WWI and post-WWII data were collected consistently, using the same methods, the post-WWII economy showed no big drop in volatility.

Almost nothing in, a surprising and powerful result out, and an implicit prediction proven correct after thirty years. That’s the Friedman magic.