Returning to the Taylor Rule to calm the « Audit the Fed » movementRecently, members of the Fed repeatedly mentioned using (and returning to) simple monetary policy rules, such as the Taylor Rules (Janet Yellen on March 27, James Bullard on April 15, Loretta Mester on April 16, Eric Rosengren on April 16, etc.). This cannot be a coincidence, particular given that the formula they choose is often identical, even though there are many ways to write Taylor rules : Rt = RR* + πt + 0.5 (πt 2) + (U*Ut) where Rt, RR*, πt, U* and Ut respectively represent the fed funds rate, the equilibrium real interest rate, inflation, the equilibrium unemployment rate (NAIRU), and the unemployment rate. With the 2016 Presidential election on the horizon, one cannot help seeing in this return to the Taylor rule a pro forma concession to the supporters of the « Audit the Fed » movement, who want the U.S. Congress to have its say in American monetary policy, and believe that policy should be founded more on simple, mechanical monetary policy rules, such as Taylor rules. We reiterate here that Janet Yellen has said several times that she is against auditing the Fed. The concession is only pro forma, because the equilibrium real interest rate and the equilibrium unemployment rate are two unobservable variables. Even if they return to a Taylor rule, the members of the FOMC will retain some elbow room, by exploiting the fact that the equilibrium real interest rate and the equilibrium unemployment rate vary over time. To take one example, in her March 27 speech (« Normalizing Monetary Policy : Prospects and Perspectives »), Janet Yellen indicated that by setting these two variables at 2 % and 5.5 %, respectively, then the fed funds rate should be at almost 3 % right now (Taylor rule 1 in the graph opposite). But she also explained that the Fed is now assuming that both variables are currently at 0 % and 5 %, respectively, which would justify a fed funds rate at around 0.250.50 % currently. This rule would indicate that the fed funds rate would be around 0.75 % at end2015, 1.50 % at end2016, and 2 % at end2017 (Taylor rule 2 in the graph opposite). It is clear that estimating the equilibrium interest rate is crucial to understanding American monetary policy in the years ahead. Below we will examine the factors which indicate that it is lower than before. Natural rate of interest vs equilibrium real interest rateThe natural rate of interest is generally defined as the shortterm real interest rate that allows economic activity to reach its potential (see the reference paper by Thomas Laubach and John Williams, « Measuring the Natural Rate of Interest »). It is interesting to note that over the past few years, the Fed has made greater use of the term « equilibrium real interest rate », which it defines as the real fed funds rate consistent with « the economy achieving maximum employment and price stability over the medium term. » The equilibrium real interest rate corresponds to the first term of the Taylor rule equation. Economic theory holds that it is not constant over time, and that it fluctuates based on changes in agents’preferences and technological changes, and more generally, based on « economic fundamentals ». Laubach and Williams developed a methodology using Kalman filters, which simultaneously estimates the natural rate of interest and potential GDP growth. Based on their estimates (see graph opposite), the natural rate of interest is slightly below 0 %. However, as shown in a Fed study (« Estimating Equilibrium Real Interest Rate in Real Time », Clark and Kozicki, Kansas City Fed), there is serious uncertainty about how to estimate parameters when applying the LaubachWilliams methodology. As various members of the Fed including Janet Yellen have stated, there are reasons to believe that the equilibrium real interest rate dropped during the Great Recession. These reasons include the high degree of uncertainty regarding economic forecasts, which limits investment decisions for businesses and major purchasing decisions for households, due to :
The equilibrium real interest rate is lower than beforeBesides the fact that it is required reading at the Fed, the John Taylor rule in its original formulation (i.e. as presented in his original article^{1}) is very interesting in how it links together the policy rate, inflation, and growth (instead of unemployment^{2}). This is why this formulation is used here to explore and estimate the natural real interest rate (i.e. underlying or equilibrium): r = p + 0.5y + 0.5(p  2) + 2 where r is the policy rate, p inflation over the previous year, and y the difference between current and potential GDP growth. Furthermore, the inflation target is explicitly set at 2 %, while the real interest rate is explicitly set at the same 2 % level, with the understanding that this version’s estimate period covers the years 198492. Assuming that potential growth in the U.S. economy is about 2 % (a figure that many estimates agree on), the year 2014 might, with an initial estimate of 2.4 %, be characterised as having a slightly positive output gap, but ultimately is close to its longterm equilibrium. In a literal application of the rule, the slight « surplus » growth relative to 2 % potential appears to be 20 bps of monetary tightening, which would offset a 25 bps decrease justified by core inflation that is undershooting its target by ½ %, after coming out to about 1½ % for the year 2014. All in all, this simple analysis of the Taylor rule tells us that in 2014, the Fed’s nominal policy rate should be (a little over) 3½ %, or an equilibrium (or underlying) real rate of 2 % (as normatively suggested by John Taylor) plus core inflation (not counting energy and food) of 1½ %. Another way to employ the Taylor rule is to assume that the 2 % figure retained by Taylor for his equilibrium real rate is arbitrary, and to instead try to deduce it from where the U.S. economy is in its longterm equilibrium, with inflation and growth practically at their respective targets (2 % in both cases) : this gives an equilibrium real rate equal to the opposite of the inflation rate, namely 1½ %. In fact, a series of econometric analyses of longterm relationships between the policy rate, inflation, and growth (as well as the rate of return of capital and the distribution of valueadded between production factors) seems to confirm the idea that the equilibrium rate is significantly negative^{3}. Thus, an econometrically simple linear model makes it possible to show a correlation ranging from 45 % to 60 % between the real policy rate (i.e. minus core inflation – not counting energy and food – over the previous year) and the GDP growth rate since 1960 and 1985, respectively. The various models and estimation methods are very informative in that they also indicate that since 2009, the Fed has needed to keep its policy rate at a level at least 2 % lower (compared to what it would have been over the period preceding 2009) to obtain the same growth rate/inflation rate^{4}. In simple terms, inflation is far from sufficient to lower the real policy rate below the level that would allow activity to accelerate, which would appear to be about 2 % or so (if not 3 %). Likewise, an econometrically similar model shows that, in a slightly modified version of the Taylor rule (one that takes into account the growth of apparent productivity gains from capital^{5}), the Fed’s policy rate is in line with the economic rate of return of installed productive capital ; this means, in particular, that at its current level, the Fed’s policy rate does not appear to be accelerating or slowing the profitability of capital compared to its equilibrium trend. Combining the second fi nding with the previous one (in which the Fed must keep its policy rate 2 % or 3 % below the level historically required to keep price growth and production growth close to their respective trends) indicates that surplus production capacities still persist. This is because combining the findings indicates that the sustained increase in the capital intensity of production (i.e. the stock of capital relative to production) appears to be forcing a downward trend in the real (i.e. inflationadjusted) prime interest rate towards lower levels, assuming equal growth. Inflation is too low to offset a policy rate that is too high, even at 0 %, which raises a monetary policy dilemma for the FedThe observation that, at 1½ % using core inflation, the Fed’s real policy rate is too high, proceeds logically if not mechanically, from inflation being not high enough, because the nominal policy rate is stuck at 0 % and may have trouble dropping significantly into negative territory and staying there a while. This impasse seems to call for the reactivation of the substitute traditionally used by the Fed to overcome the obstacle of the zero lower bound, namely quantitative easing. However, as demonstrated by the impact of QE2 and especially QE3 (as well as that of the « Taper Tantrum », as a reaction), this strategy tends to inflate financial bubbles, and thereby financial instability, potentially causing the Fed to fail to meet its other mandate. To that end, the harmful side effects of this purely monetary reflation strategy indicate the need to complete the American macroeconomic policy mix with at least two additional tools : fiscal stimulus to complement the continuation of monetary accommodation, and for good measure and to strengthen the reflationary effect of that fiscal stimulus, a strengthening of fi nancial regulations. As these two changes are still remote (assuming they are politically feasible), the status quo seems to represent the best option for the Fed. Otherwise, given the structural elements listed above, continued monetary tightening at this point would bring the risk of slower growth and inflation. In any event, in the absence of shortterm inflationary pressure (as the risky case is actually assumed to be the opposite one, with possible secondround effects from the drop in energy prices), there is a great risk of seeing the current real rate increase when it should be staying at its current level, or even decreasing. To that end, besides a possible overestimation of the neutral rate by Janet Yellen (who puts it at 0 %, following on from the work of John Williams, whose methodology is « mechanistic »^{6} where we see it being around 2 % to 3 % instead), choosing a NAIRU of 5½ % seems just as arbitrary, as it underestimates underemployment and therefore, the chronic negative demand effects associated with a low (full) employment rate of the workingage population (and not the active population, the fraction of that population that is not discouraged enough to leave the labour market).
1 « Discretion versus policy rules in practice », John Taylor (1993). 
Our work indicates that the sustained increase in the capital intensity of production appears to be forcing a downward trend in the real prime interest rate towards lower levels, assuming equal growth Continued monetary tightening at this point would bring the risk of slower growth and inflation
At its current level, the Fed’s policy rate does not appearto be accelerating or slowing the profitability of capital compared to its equilibrium trend
The harmful side effects of this purely monetary reflation strategy indicate the need to complete the American macroeconomic policy mix with at least two additional tools:
