Since that first publication, this has been a major area of research for academics, central bankers, and market economists. As a result, there is now a wide variety of policy rules that are now generically described as “Taylor Rules.” I prefer to use a wide definition of a Taylor Rule. Using control systems engineering terminology, a Taylor Rule is a feedback rule for the interest rate which is proportional to state variables (which are not necessarily directly measured), or the “P” component of a “PID controller” (Proportional-Integral-Derivative).
Standard FormatThe standard class of Taylor Rules (which includes the [Taylor 1993] rule), is given by the decomposition below. The nominal policy rate is the sum of the following terms.
- The “natural” real rate of interest. This could be a fixed constant ([Taylor 1993] used 2%), or it could vary over time.
- Short-term inflation expectations. This could either be an actual inflation expectations series (either from a survey or based on what is priced into inflation-linked bond markets), or historical inflation rates. (The [Taylor 1993] rule used a measure of historical inflation, the annual rate of change of the GDP deflator.) The use of historical inflation is justified on the theory that people’s estimates of inflation are going to be close to observed inflation over the short run. Economists within the English-speaking world would now generally use “core” inflation (the inflation rate excluding the effect of energy and food prices), as the effect of energy price movements are seen as transitory. Inflation-phobic continental European economists will tend to use the higher value of the all-item inflation (“headline inflation”) or core inflation. This is why the European Central Bank hiked rates in 2008 in response to an oil price spike, just ahead of the greatest financial crisis since the 1930s. Finally, it is important that this is short-term inflation expectations, not long term. Because inflation-targeting central banks objective is to keep long-term inflation expectations stable (which has roughly been the case since 1994 in places like the United States and Canada), using long-term inflation expectations would result in this term being roughly constant.
- Inflation deviation from target. Inflation expectations enter the expression again, but now as a deviation from central bank’s target. ([Taylor 1993] used 2% as an implicit inflation target for the Fed.) Although the previous two terms are fairly homogeneous across proposed rules, this term and the next is where the deviations start. The rule needs to attach a weighting to this term, [Taylor 1993] used a weighting of ½. That is, if inflation expectations are increased by 1%, the suggested interest rate increases by ½% (“all else equal”). If inflation expectations are below target, the suggested interest rate is similarly lowered. The weighting constant used can be chosen by the researcher constructing the rule, about the only constraint is that it is greater than zero. It needs to be positive to allow the real interest rate to increase as inflation expectations rise above target; the higher real interest rates are assumed to eventually depress inflation so that expectations will return to target. (The fact that this weighting needs to be positive is referred to as the Taylor Principle.)
- Output gap. The rule also needs to take into account the state of the economy, and not just inflation expectations. If the economy is depressed, interest rates need to be lowered, even if inflation expectations are near target (as has been the case for previous years). This is usually expressed as adding a constant times the output gap. [Taylor 1993] used a factor of ½ of the deviation of real GDP from trend, measured as a percentage of real GDP. Once again, different rules use different weighting constants. Additionally, researchers may use other variables that act similarly to the output gap, such as the unemployment gap.
ExampleThe chart below gives an updated version of the original [Taylor 1993] rule. There is a key difference, in that I have used the output gap as calculated by the Congressional Budget Office; [Taylor 1993] used a measure of GDP deviation from trend. The Taylor Rule policy rate follows similar patterns to the actual rate decisions of the Federal Reserve, but the gap between the rule output and the actual rate can be significant.
The formula for the Taylor Rule above is:
n(t) = 2% + p(t) + 0.5 O(t) + 0.5(p(t)-2%),where n(t) is the nominal interest rate, p(t) is the annual inflation of the GDP deflator, and O(t) is the (CBO) output gap (as a percentage of real GDP). The “natural real interest rate” is assumed to be a constant 2%, and the Fed is implicitly assumed to be targeting a 2% rate of inflation in the GDP deflator. One can attempt to get a better fit by choosing alternatives for these components. For example, the natural real interest rate could vary over time.
Taylor Rule ResearchThree broad strands of research are associated with Taylor rules.
- Determining a rule that best fits how a central bank reacts to data (widely known as the “reaction function”), and then using this rule to forecast the policy rate. This is extremely common in market research.
- Dynamic Stochastic General Equilibrium (DSGE) models use the assumption that economic outcomes are the result of optimising decisions of households. Since the optimisation is forward-looking (in the extreme, until time goes to infinity), households need to embed a reaction function for the central bank, as otherwise the future trajectory of interest rates is undefined. Therefore, every DSGE model has to have a reaction function, which are commonly some variant of a Taylor Rule (although more complicated dynamics are possible, such as “optimal control” rules). Since DSGE model work is mainly driven by the needs of central banks, the properties of reaction functions are heavily scrutinised.
- Is rules-based policy superior to “discretionary” policy? This was the focus of the [Taylor 1993] paper, and Professor Taylor has continued this argument since then. For example, he argues that the housing bubble of the 2000s was driven by too low policy rates; that is, the actual path of the fed funds rate was below what was predicted by a Taylor rule after 2003.
Usefulness Limited By AmbiguityIn principle, an accurate Taylor Rule would be an extremely valuable tool for a fixed income analyst. All you would need to do is to forecast the components, and you could then then come up with an accurate forecast for the path of the policy rate. This in turn would make rates investing into a proverbial money-printing machine. Unfortunately, any experience with market research tells you that any halfway-competent economist has a Taylor Rule that validates their view of policy rates – no matter what that view is.
A Taylor Rule is an economic Rorschach Test, in which economists can project whatever their views are onto the final result. Almost every term within a standard Taylor Rule is “squishy,” and these terms are tied together by somewhat arbitrary parameters. Either the terms are not directly measured (like the natural rate of interest, or the output gap), or there is no obvious consensus on what measured variables to use (market inflation expectations, core versus headline inflation, etc.). The freedom to choose the weighting parameters (within limits) means that there is considerable ability to get the output of the rule near historical policy rates. The researcher can then data mine the possible inputs so that the deviation at the endpoint matches their (or their bosses’) preconceived view as to where the policy rate should be right now. The Taylor Rule can then be “improved” when its fit deteriorates, or the desired output changes.
In summary, the output of a Taylor Rule is only suggestive. Their value (if any) lies in the fact that they tells us what factors a central bank is probably looking at when setting rates. This may have been useful when central bank rate setting was shrouded in secrecy, but its usefulness is debatable when analysts are inundated with central bank research and policy maker jawboning.
Note: This article is a first draft of content that appeared in the BondEconomics report Interest Rate Cycles.
(c) Brian Romanchuk 2015