Factors Determining the Accuracy of the Taylor Rule

today and in the future and helps the public understand the responsibility of policy makers for LSCS decisions (Kahn 2010).

1.1.2 Taylor rule for calculating policy interest rate

The original formula of Professor Taylor (1993) is as follows: i t = π t + 0.5(y t )+ 0.5(π t – 2) + 2 (1.1)

and general form:

i t = π t + r* + α(π t – π*) + β(y t ) (1.2)

In there:

i t : Fed's LSCS

r*: Equilibrium real interest rate

π t : Average inflation rate over four consecutive quarters (Judd and Rudebusch 1998)

π*: Long-run target inflation rate y t : output gap

y= 100x

Real GDP - Potential GDP

Potential GDP

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or y t = 100 x Ln(real GDP/potential GDP) (Kozichi 1999) α: inflation bias coefficient

β: output deviation coefficient

According to Taylor (1993), if the equilibrium real interest rate is 2%, the average inflation rate over four quarters is 2%, the actual inflation level coincides with the inflation target, and actual output equals potential output (i.e. the deviations are zero), then the FFR will be 4%.

Taylor (1993) argues that it is more efficient to weight output deviations than not to weight them; however, it is unclear whether the weighting of output deviations is higher or lower than the weighting of inflation deviations. Therefore, Taylor applied a factor of 0.5 to these deviations in formula (1.2).

Transforming formula (1.2) we have the following form:

i t = π* + r* + 1.5(π t – π*) + 0.5 (y t ) (1.3)

It is easy to verify that formulas (1.2) and (1.3) are the same and that formula (1.3) has replaced the first term of (1.2) π t with π* with the inflation bias now being 1.5 instead of 0.5. Formula (1.3) means that the real interest rate (i t ) will increase (decrease) by 1.5 percentage points if the actual inflation rate is 1 percentage point higher (lower); likewise, the real interest rate will increase (decrease) by 0.5 percentage points if the GDP growth rate is 1 percentage point higher (lower) than the potential output level. This shows that the Taylor rule (1993) gives more weight to the inflation target. The “Taylor rule” associated with the Taylor rule requires that the real interest rate should increase when the actual inflation rate exceeds the inflation target (Asso, Kahn, and Leeson 2010).

The general form of (1.3) will be:

i t = π* + r* + β π (π t – π*) + β y (y t ) (1.4) In which, β π =1+α, β y = β.

Billi (2011) presents a variant of the Taylor rule that replaces the output deviation with the output growth deviation (g t – g*) as follows:

i t = π* + r* + β π (π t – π*) + β y (g t – g*) (1.5)

Where: g t is the real GDP growth rate and g* is the growth trend of real GDP measured by the average GDP growth rate over the long period.

Assume from equation (1.2):

+ If π t = π*, and real GDP = potential GDP, equation (1.2) becomes

wall:

i t = π t + r* (1.6)

Equation (1.6) is similar to Irving Fisher's formula for interest rates.

famous monetary economist of the 20th century:

i = i r + π e (Mishkin 2010, p. 84)

Where i is the nominal interest rate, i r is the real interest rate and π e is the inflation rate over the period.

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+ If π t > π* or real GDP > potential GDP (or y t > 0) then i t will increase.

+ If π t < π * or real GDP < potential GDP (or y t < 0) then i t will decrease.

+ If π t > π* and real GDP < potential GDP (or y t < 0):

Occurs when the actual inflation rate exceeds the target inflation rate while the actual output level is below potential output. This is a stagflation situation in the economy. In this case, the Taylor rule acts as a neutral between the two deviations of inflation and output, giving an appropriate indicative level of LSCS; i t increases or decreases depending on the impact of the two deviations of inflation and output along with their two corresponding deviation coefficients. LSCS determined by the Taylor rule can increase or decrease depending on the response of shocks. Considering the condition of the coefficients of inflation deviation and output deviation given, if a strong demand shock causes the inflation deviation to increase more than the reduction in economic growth, LSCS will increase to reduce inflation. However, the increase will not be higher than the case of hot growth (real GDP > potential GDP and π t > π*) due to the opposite offsetting effect from the output deviation compared to the inflation deviation. On the contrary, if the price shock has a strong impact on aggregate supply, leading to a larger decrease in output deviation than the increase in inflation, the interest rate will decrease to stimulate economic growth under the condition that the actual inflation rate is still higher than the target inflation rate. However, the interest rate will not decrease more than the case where the actual inflation rate is below the target inflation rate (π t < π* and real GDP < potential GDP) due to the offsetting effect from the inflation deviation compared to the output deviation. The interest rate according to the Taylor rule will not change when under the impact of the supply shock, the inflation deviation is equal to the output deviation. In the case of a stagnant economy, the Taylor rule has neutralized two components that occur in opposite directions: inflation and economic growth. One factor that needs to be considered is the lag in the impact of monetary policy on consumption, investment and inflation factors when planning monetary policy. The same policy has different impact lags in different periods depending on the business cycle, consumer and investor expectations, demand shocks, supply shocks and consumer psychology.

From equation (1.2) it can be seen that although the weighting of the deviations is the same at 0.5, however, through the transformation according to equation (1.3), the inflation deviation coefficient is 1.5 compared to the output deviation coefficient of only 0.5 and thus the model shows that the Fed has set

more weight on the change in the inflation rate than on the change in GDP growth rate in the period 1987-1992. High interest rates will control inflation through the interest rate transmission mechanism with the impact on the cost of consumer and business loans, limiting investment in production development. Besides, high interest rates will help increase the strength of the domestic currency, reducing inflationary pressure. The dependence of the model on the two variables of inflation and output assumes that all other growth indicators and prices have been fully reflected in the quarterly/annual inflation and output levels.

Kahn (2010) argues that the deviation coefficients may vary depending on the particular formula considered. The choice of appropriate coefficients for the Taylor rule depends on space and time (Central Bank of Iceland 2002). This is important because determining the coefficients appropriate to economic conditions allows for the calculation of the LSCS to be closer to the actual economic situation so that central banks can apply the Taylor rule as a guide for interest rate policy.

Consider the following two models:

a1. i t = π* + r* + 1.5(π t – π*) + 0.5 (y t ) a2. i t = π* + r* + 0.5(π t – π*) + 0.5 (y t )

Model (a1) is the Taylor rule (1993) of the form (1.3) and model (a2) of the form (1.4) takes the inflation deviation and output deviation coefficients as 0.5.

The difference between the two models (a1) and (a2) is defined as follows:

- i t of (a1) deviates from i t of (a2) by an amount equal to (π t – π*). This shows that when the actual inflation rate is larger than the target inflation rate, the difference between i t according to the Taylor rule (a1) is larger than i t according to the Taylor rule (a2). When interest rates become too high, it will have a strong impact on consumption and investment, credit is limited, consumption and investment spending decrease sharply, businesses are worried about unprofitable business so they do not develop production and business, goods are scarce, and the decrease in supply of goods will continue to put pressure on inflation. That explains why some central banks are cautious when applying the principle of "high interest rates against high inflation". Lee and Crowley (2010) conducted an assessment of the monetary policy of the European Central Bank (ECB) including 12 member countries of the Eurozone (excluding new members).

(Slovenia, Cyprus, Malta and Slovakia) over the period 1999 – 2009 using the original Taylor rule (1993) and found that for key member countries such as France and Germany, ECB monetary policy was close to the LSCS level suggested by the original Taylor rule. In contrast, for Greece and Ireland, two countries with relatively high inflation rates in the early years of the assessment period, ECB monetary policy was found to be too loose compared to the LSCS level suggested by the original Taylor rule.

- When π t = π*: there is no difference of i t between (a1) and (a2).

- When π t < π*: the value of i t calculated according to (a1) will be smaller than the value of i t calculated according to (a2).

In an example of the Taylor rule calculation of the Icelandic Central Bank with data for the period November 2000 to March 2001: π*=2.5%, r*=4%, π t = 9% and the estimated y t = 3%; the Icelandic Central Bank applied a 11.4% LSCS (Central Bank of Iceland 2002) which is closer to the result calculated by model (a2) of 11.25%; while the LSCS i t calculated by model (a1) would be 17.75%. The same result for Romania (Appendix 8) gives the coefficient pair (β π , β y ) of (0.5; 0.5) which is closer to the Romanian Central Bank's LSCS than the coefficient pair (β π , β y ) of (1.5; 0.5).

1.1.3 Factors determining the accuracy of Taylor's rule

1.1.3.1 Equilibrium real interest rate (r*) or Natural interest rate 3

1.1.3.1.1 Concept of natural interest rate

The LSTN is equivalent to the equilibrium real interest rate for the economy, which is the interest rate at which monetary policy is neutral, neither tightening nor loosening. (Bernhardsen and Gerdrup 2007).

According to Lundvall and Westermark (2011) “the natural rate of return is the real rate of return that can be achieved if resources are used normally in the present and expected to remain so in the future”. The level of resource use is often measured by the deviation between real GDP and potential GDP. The level of resource use at the normal level is determined when the output deviation is zero, then real GDP is equal to potential GDP.

3 These two concepts are used interchangeably. In the thesis the author uses the term natural interest rate.

The concept of LSTN was first mentioned by Knut Wicksell in a series of publications around 1899, specifically as “There is a certain rate of interest which is neutral in relation to the prices of commodities, and tends neither to increase nor to decrease them” (Wicksell 1898, p. 102), or “So long as prices remain unchanged, the central bank’s rate of interest will remain unchanged. If prices rise, the rate of interest will rise; and if prices fall, the rate of interest will fall; and so the rate of interest will remain at the new level until a new movement of prices requires a change in one direction or the other.” (Wicksell 1898, p. 189).

The LTM, under conditions of price stability, can provide a guide for a central bank in setting its LTM target. A central bank that wishes to maintain price stability should act to keep the real bank interest rate equal to the LTM. According to Amato (2005), this view has recently become an important part of the new Keynesian economic theory.

More generally, Manrique and Marque (2004) restated Bomfim's (1997) view that LSTN is defined as “the interest rate consistent with a level of output converging to the potential level of output, at which the output level is consistent with a stable level of inflation”.

1.1.3.1.2 The role of LSTN in CSTT:

When the central bank keeps the interest rate lower than the natural rate to increase the use of resources, it shows a loose monetary policy; conversely, if the central bank keeps the interest rate higher than the natural rate to limit the use of resources, it shows a tight monetary policy.

The level of the real interest rate changes over time depending on the extent of macroeconomic fluctuations affecting the economy and must be determined before a decision can be made to loosen or tighten monetary policy. The central bank will have to conduct monetary policy by finding a way to make the real interest rate less likely to deviate from the real interest rate and to make production and unemployment less likely to deviate from normal levels of resource use. A central bank pursuing an inflation-targeting policy has two reasons for influencing resource use: one is the maintenance of price stability; the other is the sustainability of the real economy.

Lundvall and Westermark (2011) argue that in practice, determining the level of LSTN is difficult, just as determining the level of potential output is difficult. When the level of economic activity changes, it takes time before the central bank can determine what underlying conditions have changed and what the consequences will be for economic growth. Resource utilization may be below or above normal before monetary policy takes effect. Furthermore, it takes time for resource utilization to return to normal through monetary policy. Thus, it is difficult to prevent resource utilization from being above or below normal.

The importance of the LSR for monetary policy is intrinsically linked to the objectives of monetary policy. The current mandate of central banks to achieve price stability and sustainable output gap is, in principle, one of the main benchmarks of monetary policy. The LSR is an obvious potential indicator for monetary policy.

Amato (2005) argues that according to the most recent LSTN theories, the central bank will move the LSCS step by step along with the change in LSTN; according to the New Keynesian school's view, LSTN is the equilibrium real interest rate that can be achieved in a fictitious replica of the economy in which the nominal adjustment has been completed and with this view, three common characteristics of LSTN have been highlighted:

(i) LSTN is the one-period interest rate;

(ii) LSTN is the equilibrium real interest rate and the equilibrium is determined for each period;

(iii) The LTN changes in the short-term and long-term periods. The long-term equilibrium LTN can change over time due to changes in the structure of the economy. Therefore, the LTN is not considered a long-term real interest rate but a short-term interest rate determined from time to time, tending to focus on the long-term interest rate, which can also change gradually over time.

Because of the important characteristics of LSTN, Professor Taylor made it reasonable to include the LSTN variable in the rule for determining LSCS.

1.1.3.1.3 Issues related to the natural interest rate r* in the Taylor rule

In equation (1.1), Taylor (1993) assumed that the equilibrium average real interest rate is a constant 2%. This assumption is likely to cause errors because the equilibrium level of the economy can change at different economic cycles, due to the impact of increasing or decreasing labor productivity, inflation or financial shocks.

Comparing the actual Fed's interest rate with the normal interest rate will show the Fed's interest rate management direction: if the actual Fed's interest rate is greater than the normal interest rate, it shows that this is a tight monetary policy. On the contrary, if the actual Fed's interest rate is lower than the normal interest rate, it shows that the monetary policy is loose and expands investment in production and business.

The LSTN view implies that the economy will eventually respond to LSTN levels.

In the Taylor rule the LSTN component is also related to the output deviation component y t .

1.1.3.1.4 How to determine the natural interest rate

Although economists have made progress in estimating LSTN, the results of the estimation depend on the choice of estimation method (Williams 2003). This is because LSTN is unobservable (Bernhardsen and Gerdrup 2007). Archibald and Hunter (2001) argue that there is no “right way” to estimate LSTN. Below are some methods for determining LSTN.

+ New Zealand Central Bank model (Archibald and Hunter 2001):

- Method 1 : Estimate LSTN based on historical interest rate values

Monetary theory and empirical research indicate that monetary policy only really affects the economy in the short and medium run. In the long run, monetary policy is neutral. Suppose that the LSTN (r n ) consists of two components: the trend (r*) and the cycle

r n = r* + c (1.7)

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