## Matt Rognlie of the Practical Irrelevance of Friedman's "Optimal Deflation" Argument

Matt:

The practical irrelevance of the Friedman rule: In his recent Economist debate with Brad DeLong on whether the inflation target should be raised, eminent monetary economist Bennett McCallum emphasizes the Friedman rule as an important determinant of the optimal long-term rate of inflation:

First, in the absence of the ZLB, the optimal steady-state inflation rate—according to standard new Keynesian reasoning—lies somewhere between the Friedman-rule value of deflation at the steady-state real rate of interest (therefore something like –2% to 4%) and the Calvo-model value of zero, with careful calibration indicating that the weight on the latter may be considerably larger. Second, a theoretically attractive modification of the Calvo model would imply that the weight on the second of these values should be zero, so that the Friedman-rule prescription itself would be optimal (in the absence of the ZLB). Third, even when the effects of the ZLB are added to the analysis, the optimal inflation rate is (according to this line of analysis) probably negative—closer to –2 % than to 4 %…

The Friedman rule follows naturally from a basic model of monetary policy. “Money” is a good that is costless to provide, yet valuable to consumers and businesses; for the sake of efficiency, it should be priced at cost, which means that the risk-free nominal interest rate should be zero (so that you don’t lose anything from holding wealth in the form of cash rather than Treasury bills). Since real interest rates are usually positive, this means that we need long-term deflation...

This is all valid in theory. But does it have practically meaningful welfare consequences? Brad DeLong does a little arithmetic and comes out skeptical:

Say that if cash in my pocket earned the same real rate of return as bonds in my portfolio, I would carry more cash and find myself having to stop at the ATM only once a quarter rather than once a week. Say it takes me six minutes to go the ATM. Say my time is worth $30 per hour at the margin. Say that other portfolio swaps I would no longer have to do are of equal value. Then I would gain $6 per week or $300 per year from a deflation rate of 3% per year. Say I am representative of 200m American adults. That is a net welfare gain of $60 billion a year for America from this “reduced shoe leather wear” effect of having an inflation target of –3% per year. The lost production from the recession that began in 2008 has so far amounted to $2.6 trillion. The meter is still running at a current rate of $1.04 trillion per year. It will be at least $4 trillion before we are through.

This is easy to see in other ways as well.... What is a plausible estimate of the welfare loss from a change in inflation target from 2% to 4%? Let’s be extreme and say that the resulting change in steady-state nominal interest rates causes real base money demand to fall in half, from $1 trillion to $500 billion. At worst, this implies a ($500 billion)

6% = $30 billion welfare loss due to deviation from the Friedman rule.... But of course, we wouldn’t expect the demand for base money to fall in half. Laurence Ball, for instance, finds that the semi-elasticity of money demand with respect to interest rates is -0.05... which gives a maximum welfare hit of ($200 billion)6% = $12 billion. Now we’re at less than one-thousandth of GDP!It doesn’t end there. First of all, seignorage is a way for the government to collect revenue... if you’re interested in maintaining positive interest rates for some other reason, the fact that seignorage income allows you to bring down some other tax means that the true welfare cost is even lower than you’d initially estimate.

And then there’s the elephant in the room: who holds currency, anyway? There is roughly a trillion dollars of paper currency in circulation; that’s over $3000 for every man, woman, and child in America. Most of the value is held in the form of $100 bills. Clearly most of it isn’t being used for the purpose of ordinary transactions....

The Friedman rule is the ultimate example of an idea that is qualitatively true yet quantitatively irrelevant.