Normally, the deviations of the real economy and inflation from our objectives are small enough that any conflicts are minor. And the well-known Taylor Rule captures normal policy adjustments well, appropriately weighting output gaps and inflation deviations in the setting of our policy rate. However, the Taylor Rule is a rule-of-thumb, whose claims of empirical validity are based on its ability to track policy during periods of relatively modest volatility.2 The current recession is outside of the empirical experience of Taylor Rules calibrated to describe Federal Reserve actions.

We need to look beyond heuristic descriptions like the Taylor Rule to a more complete analysis of optimal monetary policymaking within a dual mandate framework. This topic has been studied extensively in the macroeconomic literature. Interestingly, one of the first modern treatments is due to John Taylor in an article published in Econometrica in 1979.3 This framework continues to be a mainstay of optimal policy analysis, as evidenced by a large literature that includes work by Michael Woodford in recent years.4 Taylor expresses the central bank’s dual-mandate objective as monetary policymakers attempting to minimize the weighted sum of squared deviations of inflation and the level of output from their goal values. That is, a central bank attempts to minimize a simple quadratic loss function like the following:

L = (π – π*)2 + λ * (y – y*)2

Here π and y are inflation and the (natural) logarithm of output, and π* and y* are the policy goals for these variables. In most formulations, y* is the log of the level of potential output—the level of output at which resource slack has a neutral influence on the level of inflation. Thus, (given the properties of logarithms) y – y* is the usual output gap, the percentage difference between actual and potential output. And π – π* is the gap between the actual and desired rates of inflation. Ideally, we’d like both of these gaps to be zero, but this usually won’t be the case. We measure the costs associated with the overall deviation of actual outcomes from the ideal with the quadratic loss function L. Note that for each policy goal, this loss function equally weights same-sized misses above and below target.

The coefficient λ determines the relative weight policymakers give to their misses on real output versus those on inflation. If λ is equal to 1, then a 1 percentage point deviation of inflation from its target gets the same weight in computing the overall costs of being away from the optimum as a 1 percentage point deviation of output from its potential.

However, Ken Rogoff (1985) and others have argued that, in order to avoid inflationary biases that might creep into policy, a good, conservative central banker ought to conduct policy as if λ were less than one. 5 It’s reasonably conservative to set λ equal to ¼. That means the costs of a 1 percentage point output gap are judged to be only one-quarter as high as the costs of a 1 percentage point deviation of inflation from its goal. So a λ of ¼ puts a good deal of weight on keeping inflation near its goal.

Given that the Fed’s mandate is expressed in terms of employment, it is helpful to recall Okun’s Law, which says that a 1 percentage point gap between actual and potential output corresponds to a one half percentage point gap between unemployment and its natural rate. Making this translation in the loss function, we see that the conservative central banker attempts to minimize the equally weighted sum of squared inflation and unemployment deviations:

L = (π - π*)2 + 1 * (u – u*)2

where u and u* are the actual and natural rates of unemployment 6;

The bottom line is that a conservative and tough-minded central banker can still value deviations in unemployment from the natural rate equally with deviations in inflation from its target. Accordingly, an inflation rate of 5% against an inflation goal of 2% presents this policymaker with an equal-sized loss as a 9% unemployment rate against a conservative estimate of 6% for the natural rate of unemployment. (I call this conservative, because while we think a number of factors such as increased job mismatch and extended unemployment insurance benefits have temporarily boosted the natural unemployment rate in the U.S., these factors are not expected to persist in the long-run).

There also is an immediate corollary: If you aren’t as riled up over 9% unemployment as you would be over 5% inflation, then you either put even less weight on unemployment deviations in your loss function or you think that the natural unemployment rate is substantially higher than 6%.

I’ll address the latter possibility later. However, I now want to turn to reasons why the challenges to policymaking in the current situation are orders of magnitude larger than those we face during more normal times. To preview, these are because: (a) we find ourselves in the aftermath of a Reinhart-Rogoff type financial crisis, which has resulted in severe headwinds weighing on the recovery process; (b) the economic costs of the vast amounts of unused resources in the economy are very large; and (c) the zero lower bound is a constraint on standard monetary policy actions, requiring a broader monetary policy framework if we are to provide more policy accommodation.