The financial press and comments on financial developments are full of remarks about Federal Reserve policy and performance, almost to the point of obsession. While much of this commentary focuses on the latest press releases or other official announcements from the Fed, running comment in other settings frequently indulges is extreme criticism of recent Fed policy, second guesses that policy, states the author's own preferences or revisions, and frequently prophesies doom of one sort or another for the Fed's failure to follow the prescriptions of each private opinion offered. These comments very rarely cite any sort of data or provide any objective measure of Fed policy performance, and normally assume without argument that All True Scotsman agree with the writer and his objectives and principles.

The purpose of this article is to do a better job and look at serious proposed objectives to be achieved by Fed policy and to measure whether the Fed is achieving any of them, and to grade how well it is or isn't doing compared to its long run past performance on each metric. I focus most heavily on a rigorous numerical objective function that Fed staff has described in online articles as one analytic approach actually used, though it is clearly not the only such measure and is not in any way binding on Fed board members as they decide on monetary policy decisions. This objective function was published in November 2014 as part of a study on possible use of optimal control theory to Fed policy decisions. The original article can be found online here - FRB: FEDS Notes: Optimal-Control Monetary Policy in the FRB/US Model

To summarize the objective function described in that article, the idea is to minimize a cost or penalty function that measures the square deviation of three distinct series from norms desired of them. The three series are the rate of inflation as measured by a price deflator, the unemployment rate, and the fed funds rate. For the first, the measure is how far that rate of inflation is away from the Fed's standing 2% target; for the second, how far the unemployment rate is away from its cycle or long-term mean value; and for the fed funds policy rate, the measure is just the volatility of the series. This amounts to saying that the Fed tries to keep inflation close to its long run 2% target, to avoid "driving" or increasing the amplitude of cyclical swings in the unemployment rate and to "damp" that magnitude instead if possible, and to do both without moving its policy rate around too much, trying to keep it stable when possible to allow other actors in the system to calculate and plan rationally.

The paper allows that these measures can be combined with arbitrary linear weights, and also provides a discount function for expected future levels of this cost function, which effectively turns the single description into a family of possible objective functions of a set form, without actually uniquely specifying one objective. For simplicity here, I weight the three factors equally in their natural units, all weights 1.00 in terms of the formula in the paper, and I look at the current value of the measure and not its expectation under different policy paths, so the discount term can be ignored as well. To enable the units of the resulting measure to be understood intuitively, I divide the sum of squared deviations by the 3 components and take the square root of the result, which thus can be understood as a sort of average percentage deviation of each of the measures from its desired target. To be clear about that transformation (which doesn't affect its minimization), if each of the measures is 1% off its desired value, then my mixed measure will read 1.00.

In the next chart, I present the resulting time series of the Fed's own performance by its stated objective, understood in the above sense. I have also subdivided the values into half percent increments, which naturally divide the historical performance series into very good, good, middle-poor, poor and very poor performance, as is clear in the plot below. I give each its corresponding letter grade, to which the colors in the plot below correspond. There is one data point for each economic quarter.

The time domain extends from the second half of the 1950s to the 1st quarter of 2017. Notice all the blue and gold points on the lower part of the graph - those are the "A" and "B" grades for modified objective function values under 0.5% and 1.0%, respectively. Notice the large cluster of failing grades in the late 1970s and early 1980s when inflation ran out of control. Notice also the later peaks with the unemployment rate far above its cycle mean targets, with 3 quarters of "D" grades in the most recent recession and several years worth of "C" grades. Those reflect the weight that the Fed's objective function places on cycle amplitude.

Notice that the relatively mild recession in 2000-2001 never sees a grade below a "B", and the slightly harsher 1990-1991 recession sees only 2 quarters of "C" grades. I also draw attention to the blue lows mid cycle, when it is the easiest for the Fed to keep all its objective variables in their better zones. That reflects the fact that its objective is not to minimize unemployment - late cycle - but to minimize its deviation from its cycle mean, so that it returns the best objective function values as the unemployment rate reaches that mean value - assuming that inflation is also not too far from its 2% target.

The latest value of this measure is 0.4256, while the mean of the entire past is 1.0056. Simply put, the Fed is keeping its targeted variables twice as close to its objectives these days as it has usually managed in the long-term past. A Z-score for the current value is -0.7927, meaning that this measure is about 1 standard deviation better than its mean. By count of quarters, the present is at the 81st percentile; otherwise put, the Fed has been farther from its own stated targets 4 times more often than it has been closer to them in the past, than it is today. These numerical measures will be repeated in a table below, alongside similar measures grading the Fed on other proposed objective functions. Objectively, by its own standards, the Fed gets an "A" for its recent performance, and for several years it has been solidly in the A- to B+ range.

This is not a biased standard set up to be easy to pass. It gives the Fed a "D" for the cycle amplitude it allowed in the last cycle, and a mediocre several years of "C"s for how long that down phase lasted. Negotiating a recession phase without letting this measure get above 1.00 is possible in mild recessions, and that is what this objective function encourages it to aim for. Besides avoiding "driving" cycle amplitude, this objective also encourages the Fed to seek to stay in the moderate lower blue and gold ranges for as much of the time domain as possible, while either very high inflation (e.g. late 1970s) or extremes of unemployment will give it failing grades. This reflects the actual statutory "dual mandate" given to the Fed by congress. One can debate the wisdom of that mandate, of course, but the point is that the objective function whose results are shown above does faithfully reflect that mandate.

Next, I want to show how the Fed rates according to several other proposed objectives that different economic schools have proposed as more appropriate in their view, or more likely to be actually achievable. Monetarists have frequently advised that the Fed should aim exclusively at price stability, fearing that it cannot control other outcome variables and that attempts to do so may prove counterproductive. Later, some economists advised that even a goal of price stability might involve too active a role for monetary policy, and that unpredictable or unstable policy responding to changing monetary demand might "wrong foot" private planning. They therefore proposed instead a target growth rate for a monetary aggregate like M2 money supply, that the Fed should simply try to keep as stable as possible.

Last, some economists have proposed instead setting a target for nominal GDP, rather than inflation or monetary aggregates, adding money whenever nominal GDP growth falls below its long run average and trimming its rate of growth whenever nominal GDP exceeds that long run average. This is actually a recommendation tending to call for significantly greater monetary "ease" than either of the above, and frequently comes from a Keynesian rather than a monetarist perspective.

I will report how the Fed does on each of those alternate measures below. For each of those, I use 5-year average rates for the proposed target, and the objective function is to keep that averaged rate as close as possible to its target. That target is 0 in the price stability objective case ("minimize the rate of inflation", effectively), and the long run historical average rate for the other proposed approaches. After the full time series graphs, I report in a short table the current values, average historical values, Z scores and percentiles of all past values and "letter grade" the Fed would get on each of the proposed goals, with its existing behavior and performance.

First, the price stability story -

The units on the Y axis are Z scores of the past variation - in other words, how many standard deviations away from the past mean performance of inflation we are at each point in time. The X axis is time but with the plotted value depending on a five-year trailing moving average ending at that point. We readily see the period of poor performance from 1975 to 1985, understanding that the trailing moving average means that some of the bad inflation of the early 1980s extends a bit later in the graph. Notice the right end of the series, right around 1 standard deviation below the mean, and the lowest value of the series since the mid 1960s.

Next, the M2 growth rate targeting story -

In this case, the best result would be a Z score right around the Y axis, 0 standard deviations away from the mean past growth rate of M2. To the extent that this series stays on that axis, the constant M2 growth rate goal has been met; the rule counsels greater looseness than the Fed actually showed in all periods below the axis and greater tightness than the Fed actually showed in all periods above the axis. Notice that this rule would have counseled as vastly looser monetary policy in the 1990s, which arguably would have made the "internet bubble" that occurred during that decade much, much worse.

Notice also, however, that the right end of the series is right up around the 0 line and that the entire period since the last recession has been moderately below it. The supposedly great "ease" of the Fed in this period has barely sufficed to get M2 money growth back up to its long run trend rate, after it fell well below that average rate in the last recession. This is an empirical fact about recent money supply growth that many financial commentators seem not to be aware of. This targeting rule, if applied objectively, would give the recent Fed high marks, as a result.

Next, the nominal GDP targeting story -

This is another case where closely following the rule's prescription would mean that plot being near the X axis, or the Y = 0 line. One can see the sense the rule seems to have for much of the past, as most of the time series stays within the -1 to +1 Z score band, while the strong inflation period is far above the axis and greater tightness is correctly indicated. However, notice that this rule counsels systematically looser monetary policy from the early 1990s onward, including much looser policy since the 2008 recession. Since real GDP growth and the average rate of inflation both decline secularly over that period, the rule counsels reacting to those changes with ever looser monetary policy, seeking to reverse that secular trend.

Most economists do not think that the Fed can control GDP growth sufficiently, on its own, to make this a proper target for its policy. But it is worth stressing that the only defensible objective that economists have proposed for the Fed that would not look upon its present performance as outstanding, is one that regards it as having been far too tight since the last financial crisis.

Here is a summary of how recent outcomes look according to each of the proposed goals discussed above -

Each outcome line shows the average and current value of the proposed goal, how well the present looks in the historical dispersion of past values as a Z score, and the percentile of past values (with high percentiles always meaning better performance on the stated metric), and a corresponding letter grade. Only the nominal GDP targeting rule sees something to complain about in objectively rated recent Fed performance, and that in the direction of being far too tight given low recent growth in nominal GDP. Notably, the preferred monetarist measures of price stability or a stable growth rate of the M2 monetary aggregate both show equal or better performance than the Fed's more complicated objective function with its dual mandate targets.

In summary, a loose money Keynesian may find some fault with recent Fed performance as overly tight and perhaps leaving some potential nominal GDP growth unrealized, but all the other commonly defended rules for Fed policy would rate its recent performance as good. The Fed's own objective function that includes an unemployment based, cycle amplitude target is actually less forgiving of its past performance (in the last recession) than the monetarist price stability or constant M2 growth rate rules are, when objectively applied.

I would also maintain that study of the charts above shows that the Fed's more complex objective function has arguably sent fewer false signals than several of the other rules proposed. The M2 growth rate target approach would arguably have been far too loose throughout the 1990s bubble period. The nominal GDP targeting approach would arguably have grown far too loose over the last decade and a half, trying to fight a secular trend of slowing inflation and less rapid real GDP growth with purely monetary tools likely unsuited to that goal. The price stability goal appears to have the fewest such problems, but gives the recent Fed excellent grades, and if anything is too forgiving of the large amplitude of the last cycle. It only sees a falling average rate of inflation coming out of that with nothing to complain about.

I submit that most of those criticizing recent Fed policy from various points of view seldom apply their proposals with the rigor shown above, or explain why they believe their alternative proposed measures of Fed policy success would be superior to its published methods, or where and when their different proposed measures would grade recent Fed performance poorly. I invite them to do so in the comments section below, or in their own articles.

I hope this is interesting.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.