Taylor rule

The Taylor rule is named after its inventor, the U.S. economist John B. Taylor, named. The aim of the rule is to determine the monetary policy or the policy rate set by the central bank.

Taylor tried to understand, according to what laws the U.S. central bank, the Federal Reserve System (Fed ), the target value for its main monetary policy instrument, the short-term interest rate ( federal funds rate ) on the money market, shall determine. In contrast to the European Central Bank, the U.S. central bank approach, along with the goal of stable prices and high employment and moderate long-term interest rates. To quantify the response of the Fed to change rates of the real economy and inflation accurately and thus derive a target-oriented interest rate, John B. Taylor developed in 1993 this formula. It presents an empirical approach based on economic studies. Basically, the studies refer to the G8 countries and their success in order to achieve its monetary policy objectives. For this reason, the rule can be transmitted in an adapted form in many other countries. The Taylor rule is supposed to be a sort of guide to action for central banks.

Taylor's intention

Originally, it was Taylor's intention to establish a rule that was suitable to trace the interest rate policy of the Fed ( Federal Reserve System). Thus he had the goal to design an alternative to the definition of short-term interest rate of the monetary policy. He attached great importance to its simplicity and robustness. It should serve as a means to capture the monetary policy of the central bank and adequately assessed. But it should be a concept as a guide to policy decisions by central banks simultaneously. From a legal position of the United States (Fed must price level and economic development into account ) was his premise that central banks set their interest rate policy as a function of the current rate of inflation and the economic situation.

Components of the Taylor formula and its interpretation

  • Expected rate of inflation
  • Real equilibrium interest rate r *
  • " Inflation gap" difference between expected inflation (measured by the GDP deflator ) and the inflation target (those that sought by the Central Bank in the medium term )
  • " Output gap " or " output gap " ( like protein YgaP ) is the logarithmic difference between the actual real GDP and potential output (defined as production volume corresponding to the long-term growth rate)

The expected inflation rate ( ) and the equilibrium real interest rate (r * ) supply based on the Fischer equation, a benchmark for short-term interest rate, the level compatible with the achievement of the inflation target () is at full load ( y = y *). The price stability and economic growth and the economic stabilization are summarized in the production and inflation gap. If the inflation target is exceeded in the inflation gap, this requires an increase in the short-term interest rate on the benchmark, and vice versa. The output gap captures economic aspects and price outlook. Here we recommend a reduction in short-term interest rate in unused capacity (y y *). Both indicate how strongly the central bank deviations from potential output and variations in the desired inflation target for monetary policy evaluated. α and β indicate how strongly monetary policy to changes in the inflation rate from its target or production should respond by the production level. After Taylor is thereby fixed to a height of α > 1. Thus, the central bank may shows signs of inflationary pressure the real interest rate can rise, so that the balance can be restored. The use of expected inflation on the right side of this equation shows that as a monetary policy instrument, although acts of the nominal short -term interest rates, but it ultimately comes to the influence of the real interest rate.

The Taylor rule as a further development of the IS-LM model

In the Taylor rule classical monetarist - Keynesian elements and elements of the "new classical macroeconomics " interrelated. He sets the interest rate is a function of the deviations from targets for monetary policy deemed relevant macro variables. This makes the IS- LM model, the LM condition superfluous, because this is the recursive determination of the nominal money supply. In the new version of the IS -LM model, the coordinates measure the real interest rate (y -axis) and real output (x -axis). The IS curve is based on the usual hypotheses. Furthermore, the aggregate demand reacts opposite direction to the real interest rate. This has the consequence that the position of the line is determined by the demand component and the economic goods offer at any time demand follows. The location of the new MP - line (MP = monetary policy) is dependent on the current inflation rate and the monetary policy target rate. Regarding the Taylor rule, the central bank follows a simple variant. If the inflation rate is above the monetary policy target, it increases the real interest rate (and vice versa). The bank knows the expected rate of inflation (through the adoption of rational expectations ) and controls by the nominal interest rate to affect the real interest rate. Here, however, it is based solely on the current inflation rate. In the figure it becomes clear that there is always a unique and opposite relationship between level of output and inflation.

Process steps for the derivation of a suitable control

To influence deviations from the price and output targets, the short-term interest rate can be determined by means of derivation by individual process steps. For this, the monetary policy rule to be tested is inserted into the selected model and dissolve by the choice of possible solution algorithm. The next step is to analyze the stochastic distribution of the variances of the individual variables ( input, output, underemployment ). Finally, following the evaluation of the monetary policy rule with the fixed properties and checking the robustness of the model. This can be done by a comparison with other models.

Possibilities of application of the Taylor rule

The Taylor rule is very changeable and can thus be adapted to many different political circumstances. They can be regarded as the basis of monetary s political decisions. Furthermore, model calculations on the variation of the coefficients for weighting the expected inflation rate and the Outputgap are possible.

Forms of the Taylor rule

The original Taylor rule

Shall be the rate of inflation and the inflation target, from whose difference is the inflation gap. The output gap is characterized by y. As production potential, the long-term development of GDP are called at normal capacity utilization of existing capacity. The variables α and β describe again the equilibrium quantities and the equilibrium real interest rate is described by.

Applied to the Fed Taylor describes the following rule:

If the equation adapted to the already used by our variables, it reads:

The expectation that past inflation coincides with the future rate of inflation is marked with. The Outputgap () is the deviation of the long-term growth path. The Inflationsgap is determined by calculating the deviation of the observed inflation rate in the past four quarters of the assumed inflation target of 2%. Also the height of the short-term interest rate is determined by the Inflationsgap (difference between the current and the desired rate of inflation). As described above, the coefficients ( α and β = 0.5) Again, the policy -response parameters. From the formula it can be concluded, the greater the gap the Outputgap and Inflationsgap of target value, the greater the interest rate policy scope of monetary policy. Votes inflation and Outputgab with the target values ​​match, there is no deviation from the long -term growth path. Consequently, there is the nominal interest rate is the sum of the same real interest rate and the inflation target. If you look at this equation a little closer to, you may find that real interest rates rise above the equilibrium value, if the inflation target is exceeded or the capacities are overloaded. The signs of exuberant economy is inflationary effects will arise in which the interest rate will increase. However, the economy is in a crisis, is expected to decline in the inflation rate. Through the expression of the two weights α and β the different objective functions of central banks can be clarifies. The higher this is, go the more differences in the interest rate policy with a. Specifically, the Taylor rule implies that increases the federal funds rate by 1.5 percentage points with an increase in the inflation rate by one percentage point. If GDP by one percentage point below potential GDP, the federal funds rate by 0.5 % percentage points lower. This should be ensured by a controlled inflation pressure occurring, that monetary policy is more restrictive, thus allowing an increase in the real interest rate. The Taylor rule can thus be understood in a positive and normative sense. In a positive sense, the rule provides an explanation for the temporal evolution of a short-term controllable by the central bank interest rate. As a rule of action of the reaction function, it can be understood in a normative sense.

A more general Taylor rule

(of the European Central Bank, Jarchow, Schinke and Shepherd )

The equilibrium real interest rate is described by r, the current inflation rate and the target inflation rate. The output gap (yy * ) is equal to the previous rules. The policy -response parameter can be applied depending on the weighting of inflation and growth component. This can, for example, under heavy weight for α and 1.5 for the output coefficient β to be 0.5. This weighting depends entirely on which priority is given to the individual sizes. In the present rule, the interest rate is the greater, the more the rate of inflation exceeds the target inflation rate and the stronger the production potential is busy (and vice versa). It can be seen that the economy is in equilibrium when there is no deviation of GDP from potential output is present and corresponds to the target inflation of expected inflation. A difference to the original Taylor rule is that the desired nominal interest rate is not determined from current inflation and real interest rate gleichgewichtigem, but from the target inflation and the equilibrium real interest rate. A further modification to the original rule is that instead of actual inflation, expected inflation is employed. The reason for this is to note the time delay, which is subject to the effect of monetary policy on inflation.

Application of the Taylor rule for the euro area

( comes through the analysis of the Bank for International Settlements ( 1999) on the application )

The balance rate is assumed constant. The altered rate of inflation over the previous year 's. Other components of the formula are as usual the Outputgap (), the target inflation rate ( ) and the current inflation rate (). A simplified form of the general equilibrium model for the representation of the general economic situation as a function of shocks and temporal expectations can be represented in two equations.

The equation describes the supply side and thus the output. The destination is the current production decision. In the first clip of the real interest rate is derived by the nominal interest rate () minus the expected inflation rate for the next period (). The expectations of future production conditions () have a positive impact on the nominal interest rate. With the variable is a stochastic error term is taken into account. The parameters and are > 0 With this equation, the evolution of aggregate demand is shown for a given strategy.

For the inflation rate results, which corresponds to the demand side. The current inflation rate resulting from price adjustments that are made due to the expectations for future inflation, and the current capacity utilization rates ( roughly equivalent to the output gap and a disturbance term ). Since only a part of the companies to make adjustments, the values ​​are from, and always between 0 and 1

Solving both equations for now and on, we obtain: Short-term rates in the current period are referred to as r * and the target inflation. The Inflationsgap ( ) refers to the deviation of the expected future inflation from the inflation target, which is weighted by α. Since the formula can lead to instability and arbitrary expectations, the ECB considers that the application not recommended. One reason for this may be the rising of the stability problem when the forecast horizon k increases. It can cause extreme fluctuations of the results in light sensitivity of monetary policy. For this reason, the stabilizing properties of the Taylor rule are lost. But the change in expectations can lead to economic developments. Consequently, it is unclear for economic entities, such as the monetary system responds to exogenous shocks. Finally, by going the anchor effect of the Taylor rule lost, which the ECB prompted to use them only as a guide to achieve monetary s political goals.

The Taylor rate in Germany

In Germany, inflation gap and the output gap are equally weighted with 0.5 and the inflation rate is based on the West German price index for the preservation of life. The in deriving the monetary targets of the Bundesbank underlying inevitable inflation (or the price from 1985 standard) serves as the inflation target. The output gap is based on the potential appreciation of the West German Bundesbank. The equilibrium real short-term interest rate is set at 3.4%. This is consistent with the average of the real funds rate over the observed period of 1st quarter 1979 to 4th quarter 1998. If the Taylor Rule, should be considered when interpreting that other averages are acceptable. In the figure it can be seen that the observed interbank interest rate is smoother than the calculated Taylor rate. Had the Bundesbank is based on the Taylor rate, this would, ceteris paribus, more movements in interest rates implies when it allowed its concept into reality. The reason for the strong fluctuations is that the Taylor interest rate does not take into account the negative consequences of an activist monetary policy. Despite everything, both interest rates have followed similar trends. It is surprising that they went so similar, as the output gap has played a major role in the Bundesbank policy. This can be explained by the similarities of the Taylor rule and the monetary targeting strategy. That is, if GDP grows more slowly than potential output, provides the central bank with falling interest rates more money available than would be required to finance its ongoing growth.

A Taylor rule for the United Kingdom

( postulated by Nelson, 2000)

The short-term equilibrium interest rate for a uniform growth is marked with i * and the target inflation rate. The Inflationsgap is weighted with a policy -response barometer of 1.5. The Outputgap is weighted weaker by 0.5.

The consideration of the exchange rates

The inflation rate is shown here again and by the Outputgap by. The parameter et taking the place for the exchange rates. An increase indicates an appreciation of the domestic currency. Political interference reflect δ and ρ. A decreasing weighting of past real exchange rates to each other corresponds to the ratio of the two coefficients. This is caused by the impact of price rigidities imports and exports on inflation rates. According to Taylor, it does not matter whether anticipated or actual inflation rates are taken because they are on the one hand often very similar and because anticipated inflation rates of the assumed transmission mechanisms depend. Especially for small countries, it is useful to consider the exchange rate, because the coefficients and depend on exchange rate policies as responses.

Reception

Transmission mechanisms

Theses

Meeting all or tend to:

  • The lower the Inflationsgap (or less inflation rate ), the greater is the liquidity injection derEZB
  • The lower the Outputgap ( or the lower economic growth ), the greater is the liquidity provided by the ECB
  • Price adjustments react with economic growth delay
  • Wages delayed reaction to the economic growth
  • Short-term interest rates respond to the expected deviations between the inflation rate and the target inflation rate
  • Taylor rule is suitable for the assessment of the monetary policy environment

Do not apply to:

  • Taylor - rule can be applied as a rule- bound form of monetary policy does not apply to the Euro - currency system, because shocks require a discrete interest rate management
  • According to Taylor, it is not decisive role, whether the expected or actual inflation rate is applied
  • Causes in the euro area slightly worse results ie a greater variance of interest

Strengths and weaknesses of the Taylor rule

Strengthen

One advantage of the Taylor rule is its relative simplicity. It provides a relatively clear structure -money market political argument. In addition, it offers many degrees of freedom in the choice of price variables and is therefore flexible. In addition to the price stability Taylor also refers to the economic development in the formula. He continues to believe that the central bank controls only the short-term interest rate and this results in endogenous money supply. Another positive aspect is that it is relatively easy to use by the central bank and its application for policy- Experts is relatively easy to understand in the private sector. This facilitates communication on monetary policy orientation. The followers of the forecast-based version even go as far to say that in all the relevant information for monetary policy decisions are predetermined.

Weaken

One of the biggest problems is the determination of the equilibrium interest rate. Taylor has the long-term growth rate (GDP ) is used in place of the equilibrium interest rate of the U.S. economy. The two are indeed interdependent, but not the same. The growth rate of GDP is no interest rate. It is therefore not excluded that the central bank would have created a different monetary policy a different growth rate. Consequently, the interest rate policy of the central bank would have produced a different equilibrium interest rate. The interest rate is a result of monetary s political decisions and thus not derived from the real economy size. With this fact, the Taylor rule loses its anchor of interest provision and thus also their handlungsanleitende control function.

The determination of the coefficients with which the production and inflation gap are weighted, is debatable. Specifies a central importance to a strict inflation-fighting, it is the inflation rate gap higher than the output gap. The determination of an appropriate weighting can not be determined correctly, because it depends on several factors, such as the " inflation culture " or the labor market constellation. Consequently, these variables have to be estimated, which can be very risky. It would for example also possible that the weighting should be determined by the policy. Furthermore, it is not certain whether the inflation gap is to be determined on the basis of Bip deflator or on the basis of the price index for living. The determination of the level of the output gap is not unproblematic. It all depends on which method is used for calculation. The result will always be different, no matter whether one uses the log - linear trend, the Hodrick -Prescott trend, or the estimation of a production function. This will be reflected immediately in the level and in the course of the Taylor interest rate.

A negative aspect is that the application of the Taylor rule could cause by relatively large fluctuations in the interest rate slightly higher economic volatility than the prevailing practice.

Another weakness is that the time lags of the interest rate policy signals according to the experience in many countries are difficult to predict and thus the pro-cyclical effect can not be excluded. Also, for example, requires a stock market crash short-term monetary measures, but must not have the effect that the central bank returns generally of a monetary bound monetary policy to a discretionary monetary policy. Even in the case of a single price increase - such as due to an increase in VAT - shows in principle for action. Also, the nominal interest rate used leads to frequent criticism since it can not be negative. So it falls to a low level, it is no longer possible the Taylor rule, to ensure the binding of the system to the monetary policy objectives.

Furthermore, an assumption of constancy of the real interest rate is critical. The factors to be considered these variables are the (expected ) rate of return on fixed assets, the overall propensity to save, the general assessment of the uncertainties in the economy and the degree of credibility of the central bank. An important point that is not taken into account, is the necessity of predictive behavior.

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