The Taylor Rule is a formula that gives an indication of where one can expect the Fed to set the federal funds rate.
The Taylor Rule can be written as:
Fed Funds = Neutral Real Rate + Inflation + [.50 × (Inflation – Target)] + [.50 × (Output Gap)]
where the neutral rate and inflation target are both 2%, inflation is year over year, and the output gap is a measure of how close the economy is to producing at potential. The Taylor Rule prescribes that the Fed anchor the federal funds rate at the neutral interest rate (the Neutral Real Rate + Inflation). From that anchor, the Fed should raise the funds rate by 50 bps for each percent that inflation is above target and for each percent that the economy produces above potential (and vice versa).
The below chart plots the Taylor Rule against the effective funds rate. As can be seen, following the Global Financial Crisis (the shaded portion of the chart), the Taylor Rule called to raise the funds rate several years before the Fed started raising it. This either indicates a failure by the Fed to raise rates at the appropriate time or calls into question the effectiveness of the Taylor Rule.
Working with a recent modification to the Taylor Rule provided by James Bullard, President of the St. Louis Fed, seems to produce a chart that aligns more closely with reality.
In Bullard’s modification, he changes the representation of the neutral rate. The neutral rate is a challenging inclusion in the Taylor Rule because it greatly influences the rate that the rule prescribes (since it serves as the intercept of the equation), but it is not directly observable. The San Francisco Fed defines the neutral rate as the rate that “neither stimulates (speeds up, like pushing down the gas pedal on a car) nor restrains (slows down, like hitting the brakes) economic growth." In other words, the neutral rate is the rate which holds the economy in equilibrium. With this understanding, it becomes clear just how important estimating the neutral rate is to monetary policy: Setting a policy rate that is accommodative or restrictive depends entirely on what policy rate the Fed thinks would hold the economy in equilibrium.
The original Taylor Rule sets the neutral rate at 2%. This static neutral rate assumption fails to capture the fluctuating nature of the neutral rate: namely, that the neutral rate would tend to be lower in a weaker economy versus a stronger economy. Bullard, on the other hand, constructs the neutral rate by subtracting inflation from the 1-Year Nominal Treasury to create a proxy for the market return on real assets. The return on a safe, liquid asset is one way that the neutral rate has been depicted in recent models and proves advantageous in that it fluctuates along with the economy.
The chart below shows a Taylor-type rule with Bullard’s modified neutral rate set against the effective funds rate.
The modification prescribed a sustained negative rate following the Global Financial Crisis, which would justify the lingering low rate and quantitative easing seen during that time. The modification also prescribed a rate rise about the time when the Fed raised the funds rate, as opposed to the Taylor Rule which was almost four years early. The most current data point (for 2018:Q2) prescribes a funds rate of about 2.79%, congruent with the Fed continuing to raise rates.
All of this indicates that the Fed’s decision to keep rates low for so long could have been based on the premise that a weaker economy necessitates a lower neutral rate.
Sources & Citations:
 Bullard, James. 2018. “R-Star Wars: The Phantom Menace.” Presentation at the 34th Annual National Association for Business Economics (NABE) Economic Policy Conference.
 Federal Reserve Bank of San Francisco. 2005. “What is Neutral Monetary Policy?” Accessed July 6, 2018. https://www.frbsf.org/education/publications/doctor-econ/2005/april/neutral-monetary-policy/
 Del Negro, Macro, Domenico Giannone, Marc P. Giannoni and Andrea Tambalotti. 2017. “Safety, Liquidity and the Natural Rate of Interest,” Brookings Papers on Economic Activity. 235-303.