Taylor rule

The Taylor rule is one kind of targeting monetary policy used by central banks. The Taylor rule was proposed by the American economist John B. Taylor, economic adviser in the presidential administrations of Gerald Ford and George H. W. Bush, in 1992 as a central bank technique to stabilize economic activity by setting an interest rate.
The rule is based on three main indicators: the federal funds rate, the price level and the changes in real income. The Taylor rule prescribes economic activity regulation by choosing the federal funds rate based on the inflation gap between desired (targeted) inflation rate and actual inflation rate; and the output gap between the actual and natural level.
According to Taylor, a central bank implements a stabilizing monetary policy when it raises the nominal interest rate by more than an increase in inflation. In other words, the Taylor rule prescribes a relatively high interest rate in the situation when actual inflation is higher than targeted. The main advantage of a general targeting rule is that a central bank gains the discretion to apply all means to achieve the set target. The economic model based on backwards- and forward-looking assumptions is justified.
The monetary policy of the Federal Reserve has been changing throughout the 20th century. The period between 1960s - 1970s is defined by Taylor as a period of a poor monetary policy. The inflation rate was high and increasing in the US, yet interest rates were low, which did not sufficiently restrain rising prices. Since the mid-1970s monetary targets have been used in many countries to state targets for inflation. However, since the 2000s the actual interest rate in advanced economies, especially in the US, was below the suggested by the Taylor rule.
The Taylor rule is usually opposed to discretion policy. Due to the high technicality of the rule, the inaccuracy of predictable variable and limited number of factors incorporated into the model, the Taylor rule often faces criticism.
As an equation.
According to Taylor's original version of the rule, the nominal interest rate should respond to
divergences of actual inflation rates from "target" inflation rates and of actual Gross Domestic Product (GDP) from "potential" GDP:
In this equation, formula_2 is the target short-term nominal interest rate (e.g. the federal funds rate in the US, the Bank of England base rate in the UK), formula_3 is the rate of inflation as measured by the GDP deflator, formula_4 is the desired rate of inflation, formula_5 is the assumed equilibrium real interest rate, formula_6 is the logarithm of real GDP, and formula_7 is the logarithm of potential output, as determined by a linear trend.
In this equation, both formula_8 and formula_9 should be positive (as a rough rule of thumb, Taylor's 1993 paper proposed setting formula_10). That is, the rule "recommends" a relatively high interest rate (a "tight" monetary policy) when inflation is above its target or when output is above its full-employment level, in order to reduce inflationary pressure. It recommends a relatively low interest rate ("easy" monetary policy) in the opposite situation, to stimulate output. Sometimes monetary policy goals may conflict, as in the case of stagflation, when inflation is above its target while output is below full employment. In such a situation, a Taylor rule specifies the relative weights given to reducing inflation versus increasing output.
The Taylor principle.
By specifying formula_11, the Taylor rule says that an increase in inflation by one percentage point should prompt the central bank to raise the nominal interest rate by more than one percentage point (specifically, by formula_12, the sum of the two coefficients on formula_13 in the equation above). Since the real interest rate is (approximately) the nominal interest rate minus inflation, stipulating formula_11 implies that when inflation rises, the real interest rate should be increased. The idea that the nominal interest rate should be raised "more than one-for-one" to cool the economy when inflation increases (that is increasing the real interest rate) has sometimes been called the Taylor principle.
The historical perspective.
The policy rule emerged in the era of the broad debate on the policy rules versus discretion. The discourse among economists and policymakers started at the beginning of the 19th century. The first forum for debate was launched in the 1920s by the House Committee on Banking and Currency. In the hearing on the Strong bill in 1923, the conflict in the views on the monetary policy clearly appeared. New York Fed Governor Benjamin Strong Jr., supported by Professors John R. Commons and Irving Fisher, was highly concerned about the practices used by the Fed to control the price stability. In his opinion, Federal Reserve policy regarding the price level was unstable and could not guarantee long-term stability. After the death of the congressman, a political debate on changing the Fed's policy was suspended. The Fed was dominated at that time by Strong and his New York Reserve Bank.
Only after the Great Depression hit the country, the Fed policies started to be debated again. Irving Fisher compressed that “this depression was almost wholly preventable and that it would have been prevented if Governor Strong had lived, who was conducting open-market operations with a view of bringing about stability”. Later on, such monetarists as Friedman and Schwartz, confirmed that the economic dichotomy and the high inflation could be bypassed if the Fed followed more precise the constant-money-rule.
The recession in the US in the 1960s was accompanied by relatively high-interest rate. After Bretton Woods collapse the policy-makers were focused on keeping a low-interest rate, which had a negative impact on inventory process and resulted in the Great Inflation of 1970.
Since the mid-1970s monetary targets have been used in many countries to state targets for inflation. Many advanced economies, such as the US and the UK, their policy rates were broadly consistent with the Taylor rule in the period of the “Great Moderation” between the mid-1980s and early 2000s. The Great moderation period was characterized by the limited inflation and stability of prices. Thus, many central banks started to adjust their policies. The first mover was New Zealand, where the inflation target was introduced in 1984. The Reserve Bank of New Zealand was reformed to prioritize the price stability, besides, it gained more independence. After that, the Bank of Canada in 1991 and by 1994 the banks of Sweden, Finland, Australia, Spain, Israel and Chile were given the mandate to target inflation.
However, since the 2000s the actual interest rate in advanced economies, especially in the US, was below the suggested by the Taylor rule. The deviation can be explained by the fact that the central banks were supposed to mitigate the outcomes of financial busts but should intervene only when there are inflation expectations. The economics shocks were accompanied by the fall of the interest rate.
Alternative versions of the rule.
While the Taylor principle has proved very influential, there is more debate about the other terms that should enter into the rule. According to some simple New Keynesian macroeconomic models, insofar as the central bank keeps inflation stable, the degree of fluctuation in output will be optimized (Blanchard and Gali call this property the 'divine coincidence'). In this case, the central bank does not need to take fluctuations in the output gap into account when setting interest rates (that is, it may optimally set formula_15.) On the other hand, other economists have proposed including additional terms in the Taylor rule to take into account financial conditions: for example, the interest rate might be raised when stock prices, housing prices, or interest rate spreads increase.
Alternative theories.
Solvency rule: the alternative theory to the Taylor equation. The new perspective on the rule was presented by Emiliano Brancaccio after the financial crises of 2008. The central banker follows a 'rule' aimed to control the solvency conditions in the economic system. The inflation target and output gap are neglected, while the interest rate is put under the conditionality to the solvency of workers and firms that represent financial stability. Opposite to stricter Taylor rule the solvency rule represents more a benchmark than a mechanistic formula.
McCallum rule: The rule created by economist Bennett T. McCallum at the end of the 20th-century targets the nominal gross domestic products. In the idea of McCallum the Fed should stabilize the nominal GDP to achieve economic stability. Although the same monetary policy objectives can be reached by McCallum rule as by Taylor rule, the McCallum rule uses the precise financial data. Thus, the McCallum rule can overcome the problem of the unobservable variables.
Empirical relevance.
Although the Federal Reserve does not explicitly follow the Taylor rule, many analysts have argued that the rule provides a fairly accurate summary of US monetary policy under Paul Volcker and Alan Greenspan. Similar observations have been made about central banks in other developed economies, both in countries like Canada and New Zealand that have officially adopted inflation targeting rules, and in others like Germany where the Bundesbank's policy did not officially target the inflation rate. This observation has been cited by Clarida, Galí, and Gertler as a reason why inflation had remained under control and the economy had been relatively stable (the so-called 'Great Moderation') in most developed countries from the 1980s through the 2000s. However, according to Taylor, the rule was not followed in part of the 2000s, possibly leading to the housing bubble. Certain research has determined that some households form their expectations about the future path of interest rates, inflation, and unemployment in a way that is consistent with Taylor-type rules.
Limitations of the Taylor rule.
The Taylor rule is highly debated in the discourse of the rules vs. discretion. There are a few main limitations of the Taylor rule.
1) "Technical reasons." For economic models, the period of 4 months was widely used. However, the period is not accurate for tracking the real price changes, and the period is too long for setting the fixed interest rate. Further, the formula incorporates unobservable parameters that can be easily misevaluated. For example, the output-gap could not be precisely estimated by any bank.
2) "The inaccuracy of forecasted variables", such as the inflation and output gaps, which depend on different scenarios of economic development.
3) "Difficulty to assess the state of the economy in real time." 
4) "The discretionary optimization" that leads to stabilization bias and a lack of history dependence.
5) "The limited number of factors in the model." The model does not outlook the financial parameters. Thus, in the period of the financial boost the Taylor rule might tend to underestimate the interest rate, and opposite, during the financial busts overestimate.
6) "Does not reflect the usability of other monetary policy instruments" such as reserve funds adjustment, balance sheet policies.
7) "The relationship between the interest rate and aggregate demand is questioning" by Kriesler and Lanoie, 2007.
However, Taylor in his economic work highlighted that the rule should not be implicated mechanically: “…There will be episodes where monetary policy will need to be adjusted to deal with special factors.” On another hand, the Taylor rule is opposed to the discretion approach since it aimed to overcome the limitation of the purely discretionary approach. Hence, although the Taylor rule gives the room for manoeuvre, it is encouraged to treat the Taylor rule as a policy rule that required the strict implementation of the policy based on the incoming economic parameters.
Criticisms.
Athanasios Orphanides (2003) claims that the Taylor rule can misguide policy makers since they face real-time data. He shows that the Taylor rule matches the US funds rate less perfectly when accounting for these informational limitations and that an activist policy following the Taylor rule would have resulted in an inferior macroeconomic performance during the Great Inflation of the seventies.
In 2015, financial manager Bill Gross said the Taylor rule "must now be discarded into the trash bin of history", in light of tepid GDP growth in the years after 2009. Gross believed low interest rates were not the cure for decreased growth, but the source of the problem.