EMPIRICAL EXAMINATION OF THE TAYLOR

RULE FOR THE UNITED STATES

Monika Bohnke (I6068362), Wiktor Owczarz (I6052598)

Bianca Vermeer (I6075302)

Macroeconomics and Economic Policy (EBC2040)Tutor: Lennart Freitag, Tutorial 4

Word count: 2 809Maastricht University

School of Business and Economics

April 10, 2015

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Contents

1 Introduction 3

2 Economic Overview to the United States 42.1 Development of the output gap . . . . . . . . . . . . . . . . . 42.2 Development of the effective federal funds rate . . . . . . . . 62.3 Development of the inflation rate, GDP deflator . . . . . . . . 7

3 Monetary policy goals in the United States 8

4 The original Taylor Rule 9

5 Estimating the Taylor Rule 105.1 Empirical analysis for the United States . . . . . . . . . . . . 105.2 Exclusion of misspecification and spurious regression . . . . . 13

5.2.1 Normality test . . . . . . . . . . . . . . . . . . . . . . 135.2.2 Homoscedasticity . . . . . . . . . . . . . . . . . . . . . 135.2.3 Spurious regression . . . . . . . . . . . . . . . . . . . . 13

6 Conclusion 14

7 Appendix 197.1 Empirical Estimation of the Taylor Rule . . . . . . . . . . . . 19

7.1.1 Misspecification tests . . . . . . . . . . . . . . . . . . . 207.1.2 Spurious Regression Examination . . . . . . . . . . . . 20

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1 Introduction

Table 1: Estimation results : regress

Variable Coefficient (Std. Err.)

str -2.280∗∗ (0.519)Intercept 698.933∗∗ (10.364)

N 420R2 0.051F (1,418) 19.259

Significance levels : † : 10% ∗ : 5% ∗∗ : 1%

Decisions by the Federal Reserve (central bank of the United States) have

been and will continue to be of notable national and international interest.

In effect, as the US dollar is the currency most used for worldwide transac-

tions, many countries observe the strategic focus of monetary policy in the

United States on a regular basis. Especially the recent economic and finan-

cial crisis demanded a thorough approach. Low interest rates were needed

to stabilise and boost the American economy. Hence, the Federal Reserve

set target levels for the federal funds rate close to zero and implemented a

programme of large-scale asset purchases that should facilitate the access

to money. How extensive such quantitative easing measures should be and

how nominal interest rates should be chosen to induce the desired effects,

are nonetheless crucial questions. In particular, the latter issue mattered to

economists like John B. Taylor who formulated a monetary policy rule in

the early nineties of the last century. Taylor investigated a relationship that

describes how to set nominal interest rates depending on the natural real

rate of interest, inflation and the output gap in the United States from 1982

- 1991. He estimated a simple formula that should help to guide monetary

policy. His findings are widely known as the ”Taylor Rule”. However, did

the Taylor Rule hold as well over a longer time span, including the latest

financial crisis?

The purpose of this paper is to elaborate whether the Taylor Rule is an

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adequate theory to support and facilitate the decision-making processes of

the Federal Reserve. It gives a brief overview of the economic situation in the

United States and highlights the developments of the output gap, the federal

funds rate and the inflation rate over time. Further, this paper discusses

a period of disinflation initiated by Paul Volcker in 1979 and emphasises

the latest goals of monetary policy. Moreover, the original Taylor Rule is

presented and an estimation on the basis of quarterly data from 1980 - 2014

is conducted. Finally, this paper accounts for problems like misspecification

and spurious regression to justify its overall results.

2 Economic Overview to the United States

2.1 Development of the output gap

According to the latest OECD Economic Outlook, the US has been recov-

ering from the financial crisis and has experienced an increase in economic

growth. This is mainly due to the fact that industry output is on a steady

growth path. Furthermore, net wealth of households has risen in the past

few years, partly because of increasing asset prices. Contrary to the increase

in aggregate demand, gradual fiscal contraction is taking place to ensure fis-

cal sustainability and even further narrowing of the federal budget deficit in

the coming years can be expected (OECD, 2014). The net effects of the de-

velopment of output with respect to its natural level are depicted in Figure

1 below.

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Figure 1: Development of the output gap over time

Source: Federal Reserve Economic Data.

The fluctuations around the horizontal line at 0% show the deviations

of output from it’s natural level. For example the low in 2010 represents a

negative output gap of approximately -3% that was due to a large decline

in aggregate demand after the financial crisis started. However, this graph

is based on estimations with the help of a Hodrick-Prescott filter, since

the natural level of output cannot be observed empirically. An interesting

feature of Figure 1 that should be highlighted is that fluctuations are overall

smaller after the mid 1980s than they were ever before. The largest decrease

in output occurred from 1979 until 1982, which resulted from a period of

disinflation that was initiated by Paul Volcker as is explained in the following

sections.

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2.2 Development of the effective federal funds rate

Figure 2: Development of the federal funds rate over time.

Source: Federal Reserve Economic Data.

In Figure 2, the development of the effective federal funds rate is shown

from 1954 until 2014. The Federal Reserve targets the federal funds rate in

its monetary policy. This is the interest rate at which banks charge each

other for overnight loans of federal funds, balances held at Federal Reserve

Banks (FRED, 2014). As is shown in the graph, the interest rate had a

major peak in the 1980s. This high nominal interest level is a result of the

policies implemented by Paul Volcker, which aimed to stop the stagflation

crisis (Boivin, 2005). Afterwards, interest rates decreased gradually towards

a current level of around 0%. This is a result of the Federal Reserve policies

implemented to boost consumption and investment after the financial crisis

(Federal Reserve, 2014).

6

2.3 Development of the inflation rate, GDP deflator

Figure 3: Development of the GDP deflator over time

Source: Federal Reserve Economic Data.

Figure 3 presents the development of inflation (GDP deflator) over time,

starting from the third quarter of 1954 until the third quarter of 2014. The

inflation rate was on a high level throughout the 1970s, while the output

growth rate was low and the unemployment rate was high. The main cause

for the rapid increase in US inflation was the disproportionate loose mone-

tary policy. An increase in inflation was typically associated with a smaller

increase in the nominal interest rate, which led to a lower real interest rate

(Boivin, 2005). Moreover, the oil crises had a major impact on price levels.

In 1979, the Iranian revolution led to an even further increase in oil prices

that raised inflation rates dramatically (Goodfriend & King, 2005). In the

same year, Paul Volcker was appointed as the new chair of the Federal Re-

serve. Inflation was above 10% by then. He started a period of disinflation

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by first increasing the interest rates rapidly. As interest rates were increased,

investing and borrowing money became less attractive. This way the econ-

omy slowed down, output decreased and the unemployment rate increased.

This policy resulted in the early 1980s recession, which did not only affect

the US, but also other OECD nations (Goodfriend & King, 2005). However,

Volcker’s policy also effectively led to a decrease in inflation, as shown in

the third graph; there is a dramatic drop in the inflation rate from the third

quarter of 1980 onwards. Because of high unemployment and low output

there was a downward pressure on wages which in turn led to disinflation

(Gottfries, 2013). By the end of 1982, inflation had fallen to around 5%.

The Federal Reserve decided to manage the interest rate more closely and

to create a policy to close the output gap that had been created during the

disinflation. The interest rates were decreased, which ended the recession in

November 1982 (Goodfriend & King, 2013).

3 Monetary policy goals in the United States

Since 1913, the Federal Reserve has been in charge of setting monetary

policy. Besides current means to determine the discount rate and reserve

requirements, its key tools are open market operations, conducted by the

Federal Open Market Committee (FOMC). Following from the latest “State-

ment on Longer-Run Goals and Monetary Policy Strategy”, the primary

goals of monetary policy in the United States are to promote maximum

employment, stable prices and moderate long-term interest rates (Board of

Governors of the Federal Reserve System, 2014). However, not all of these

intentions are directly feasible with their given means. In effect, Gottfries

(2013) proves that monetary policy cannot influence the long-run level of

production and employment. Hence, there is no fixed goal for employment,

but still the FOMC is required to assess their decision-making with respect

to maximised employment in future periods. Concerning stable prices, they

are more explicit and announce an official target rate of 2% over the medium-

term. (Board of Governors of the Federal Reserve System, 2014). Neverthe-

less, this has not been the case in the past. The United States were mostly

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said to follow an implicit target (Thornton, 2012). To actually control for

inflation, the Federal Reserve generally has two options. Since prices are

sticky in the short-run it can either determine the money supply or set the

nominal interest rate. Both are possible strategies, but the central bank of

the US decided to direct the latter, since a policy that holds money supply

constant leads to vast fluctuations in interest rates every time a shock af-

fects money demand. This is clearly not consistent with moderate long-term

interest rates. Consequently, the FOMC uses its monetary tools to influence

the federal funds rate, which in turn affects the amount of money demand,

other short-term and long-term interest rates in the financial markets, for-

eign exchange rates and many other variables. The federal funds rate was

already introduced above (Figure 2) and is further used in the analysis of

the Taylor Rule as the representative interest rate of the Unites States.

4 The original Taylor Rule

Taylor was not the first economist that suggested a rule to facilitate mone-

tary policy for central banks. Irving Fisher, Knut Wicksell or Milton Fried-

man were only a few others that proposed monetary policy rules before him.

However, Taylor’s approach was different insofar as he was one of the first

to account for rational expectations and sticky prices (Taylor & Williams,

2010). He gathered quarterly data from 1982 - 1991 and estimated a mon-

etary policy rule, whereby his idea of setting short-term interest rates (i)

took the following form:

i = r + π + 0.5(π − π∗) + 0.5Y (1)

Here r denotes an estimate of the natural real interest rate, π denotes

inflation, π∗ denotes the implicit inflation target of the Federal Reserve and

Y denotes an estimate of the output gap. In his paper, Taylor assumes both

the implicit inflation target and the natural real interest rate to be at 2%

(Taylor, 1993). Including these figures in the previous equation, his formula

can be rewritten as:

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i = 0.01 + 1.5π + 0.5Y (2)

Taylor supposed that the nominal interest rate should be set at a level

that is at least as big as 1.5 times the level of inflation plus 0.5 times the

level of the corresponding output gap. In his view, shocks to either the

expected level of inflation or shocks that deviate output from its natural

level should be counteracted with a strong interest rate reaction. If inflation

was higher than the target level, a high real interest would be needed to

reduce consumption and investment. This could be achieved by raising the

nominal interest rate more than in proportion with the level of inflation. The

resulting decrease in aggregate demand then leads to a decline in output and

employment. Unemployment increases and firms lower their wages which in

turn decreases money demand and inflation. However, this process might

take up to two years to reach a maximum effect of lower inflation (Gottfries,

2013). The most interesting aspect of his work is whether he was actually

right with his assumptions and how well his rule describes real monetary

policy decisions.

5 Estimating the Taylor Rule

5.1 Empirical analysis for the United States

This part of the paper estimates the Taylor Rule for the United States

again, using a broad sample of quarterly data from 1954 (quarter 3) until

2014 (quarter 3). The purpose is to examine whether the interest rate re-

sponded in line with Taylor’s suggestions to changes in the inflation gap and

the output gap.

All corresponding data presented in the following were extracted from

the Federal Reserve’s database. The variables that could not be obtained

directly, were generated with the help of statistical methods and macroeco-

nomic theory. So, the real interest rate for example was calculated employing

the Fisher equation (r ≈ i−π). Moreover, the natural rate of interest (r) and

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the natural level of output (Yn) were estimated using the Hodrick-Prescott

Filter to obtain a smooth long-run trend (with λ = 1600 due to a quarterly

frequency of the data). Finally, the output gap could be determined from

the estimated natural level of output1.

Substituting (β1, β2) for the coefficients in front of the inflation gap and

the output gap, equation (1) can be rewritten as follows:

i = r + π + β1(π − π∗) + β2Y (3)

i = −β1π∗ + (1 + β1)π + r + β2Y (4)

Equation (4) allows for an estimation of the implicit inflation target

and the approximated influence of the output gap and the inflation gap

on the nominal interest rate. The natural rate of interest is due to its

composition characteristics assumed to have a weight of 1, which is in line

with John B. Taylors assumptions in the paper, ”Discretion versus policy

rules in practise”. However, taking the full sample (1954Q3 - 2014Q3) into

consideration, leads to inconclusive results.2 Further, the equation should

be reshuffled in a way that fulfills the econometric linearity condition to

perform a break-point analysis. Substituting (α = −β1π∗) leads to the

following result:

i = α+ (1 + β1)π + r + β2Y (5)

After the Quandt-Andrews unknown break point test was applied to

equation (5), one could observe a clear and significant break point in 1980Q4.

This coincides with Paul Volcker’s disinflation in the United States that was

described earlier.3 Many economists that actually addressed the Taylor

1Y = Y −YnYn∗ 100

2For the full sample regression table please see the table 3 in the appendix.3The Quandt-Andrews unknown break point test is reproduced in Table 4 in the

appendix.

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Rule in their work found similar results. According to Boivin (2005), “the

pre-Volcker conduct of monetary policy did not satisfy the so-called Taylor

principle“ (p. 4).

Consequently, decreasing the sample size from 1954Q3 to 1980Q4 as a

starting date should lead to more robust results. The estimation results of

equation (4) with a sample from 1980Q4 until 2014Q3 are shown below.

Table 2: Taylor Rule estimation: i = −β1π∗ + (1 + β1)π + r + β2Y

Note: c(1)=β1, c(2)=β2, c(3)=π∗

Substituting the estimated results from the table above into equation (4)

gives the Taylor Rule for the United States from period 1980Q4 to 2014Q3:

i = −0.216π∗ + (1 + 0.216)π + r + 0.386Y (6)

i = π + 0.216(π − π∗) + r + 0.386Y (7)

The regression output also shows the implicit inflation target that was

followed by the Federal Reserve (π∗ = 2.324), which is not entirely differ-

ent from the 2% that Taylor assumed when he developed his rule in 1993.

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Moreover, conclusions about the effects of the inflation gap and the output

gap can be drawn. Contrary to Taylor’s original analysis presented above,

the new estimation reveals that fluctuations above the inflation target of 1%

should result in an increase of the nominal interest rate by 0.216 percentage

points, rather than 0.5 percentage points. Furthermore, a 1% increase in

the output gap should lead to an increase in the nominal interest rate of

0.386 percentage points, instead of 0.5 percentage points.

5.2 Exclusion of misspecification and spurious regression

In this section, tests about possible regression misspecifications are analysed

to show that the conclusions above about the estimated parameters are

not biased, since the independent variables are only significant if certain

population properties are met.

5.2.1 Normality test

Although the dataset from 1980Q4 - 2014Q3 contains a significant outlier

and therefore looks slightly skewed to the right, the Jarque-Bera test con-

firms that the regression residuals are normally distributed with an average

mean of zero.4

5.2.2 Homoscedasticity

To test for the presence of heteroscedasticity the White test was used. The

results show that the null hypothesis of a constant variance cannot be re-

jected at the 5% significance level in favour of homoscedasticity (Diebold,

2007).

5.2.3 Spurious regression

The results of the regression analysis presented in Table 2 arouse concerns

that the estimated regression might be spurious, due to a high R2 of 0.955.

Moreover, the Augmented Dickey Fuller test shows that three out of four

4For the Jarque-Bera test please see the appendix, Figure 4

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analysed variables are stationary in their first differences (the nominal inter-

est rate, the natural rate of interest and the inflation rate). Hence, they are

non-stationary and furthermore, they are cointegrated, because the residu-

als of model i = −β1π∗ +(1+β1)π+ r+β2Y are trend stationary. However,

since the output gap is trend stationary, this might result in a spurious re-

gression. Therefore, the Augmented Dickey Fuller test had to be conducted

on the residuals of the simple linear regression between the nominal interest

rate and the inflation rate. The results show that the residuals of the OLS

(i = π + εt) which have no unit root are trend stationary. Consequently, it

is likely that the equation (4) (i = −β1π∗ + (1 + β1)π + r+ β2Y ) shows the

coefficients of a long-run equilibrium.5

6 Conclusion

Contrasting the estimation results (Table 2) with the original Taylor Rule,

one can conclude that Taylors’ assumptions and argumentations were fairly

reasonable. On average a 1% increase in inflation was followed by an increase

in the nominal interest rate of 1.216 percentage points, which is markedly in

favour of Taylor’s theory that a deviation from the inflation target should

be responded by a strong interest rate (more than in proportion). However,

there is evidence that this effect is not as large as 1.5. The null hypothesis

that assumes β1 to be equal to 0.5 can be clearly rejected at the 1% signifi-

cance level [0.216−0.50.042 = −6.7]. Similar results hold for the coefficient on the

output gap. Here, the null hypothesis that β2 was 0.5, can be rejected at

the 5% significance level [0.386−0.50.054 = −2.1]. Overall, the estimated Taylor

Rule in this paper describes monetary policy in the United States from 1980

- 2014 extremely well. The fit of the regression is very high and proven to

be unbiased. In addition, the implicit inflation target (π∗) seems not to be

different from 2% [2.324−20.342 = 0.95], which is in line with Taylors assumption

and the recent explicit inflation target of the US. All in all, the Taylor Rule

is widely accepted and yet other countries have estimated it as a general

rule of thumb. Taylor himself remarked in an interview with A. Steelman

5For the elaborated analysis, please see the appendix.

14

from the Region Focus: ”The way I think about it is that the Fed’s actions

have been largely consistent with the rule without using it explicitly” (Taylor,

2012). Hence, the Taylor Rule proves to be an adequate guide for monetary

policy.

15

References

[1] Board of Governors of the Federal Reserve System. (2014, January

28). Statement on Longer-Run Goals and Monetary Policy Strategy,

Retrieved December 1, 2014, from http://www.federalreserve.gov/

monetarypolicy/files/FOMC_LongerRunGoals.pdf

[2] Boivin, J. (2005). Has U.S. monetary policy changed? Evidence from

drifting coefficients and real-time data, Journal of Money, Credit and

Banking, vol. 38 (5), pp. 1149-1174

[3] Diebold F.X. (2007). Elements of forecasting, 4th edition, Thomson.

[4] Federal Reserve. (2014, November 3). Why are interest rates being kept at

a low level? Retrieved from http://www.federalreserve.gov/faqs/

money_12849.htm.

[5] Federal Reserve Economic Data. (2014). Effective Federal Funds Rate

[Data file]. Retrieved from http://research.stlouisfed.org/fred2/

series/FEDFUNDS

[6] Federal Reserve Economic Data. (2014). Gross Domestic Product: Im-

plicit Price Deflator [Data file]. Retrieved from http://research.

stlouisfed.org/fred2/series/GDPDEF

[7] Federal Reserve Economic Data. (2014). Real Gross Domestic Product

[Data File]. Retrieved from http://research.stlouisfed.org/fred2/

series/GDPC1

[8] Goodfriend M. & King R.G. (2005), The incredible Volcker disinflation,

Journal of Monetary Economics, vol. 52 (5), pp. 981-1015.

[9] Gottfries N. (2013). Macroeconomics, Palgrave Macmillan.

[10] OECD (2014), OECD Economic Outlook November 2014, vol. 96, Paris.

[11] Taylor, J. B. (1993) .”Discretion versus Policy Rules in Practice”.

Carnegie-Rochester Conference Series on Public Policy 39: 195-214.

16

[12] Taylor, J. B. (2012, February 24). Interview John B. Taylor (A. Steel-

man, Interviewer). Retrieved from http://www.richmondfed.org/

publications/research/region_focus/2012/q1/pdf/interview.

pdf

[13] Taylor, J. B., & Williams, J. C. (2010). Simple and Robust Rules for

Monetary Policy, Retrieved from National Bureau of Economic Research

website: http://www.nber.org/papers/w15908.pdf

[14] Thornton, D. L. (2012). How did we get to Inflation Targeting and

where do we need to go to now? A perspective from the U.S. ex-

perience (94(1)), Retrieved from Federal Reserve Bank of St. Louis

website: http://research.stlouisfed.org/publications/review/

12/01/65-82Thornton.pdf

17

[?, ?, ?, ?, ?, ?, ?]

List of Figures

1 Development of the output gap over time . . . . . . . . . . . 5

2 Development of the federal funds rate over time. . . . . . . . 6

3 Development of the GDP deflator over time . . . . . . . . . . 7

4 Normality Test . . . . . . . . . . . . . . . . . . . . . . . . . . 20

List of Tables

1 Estimation results : regress . . . . . . . . . . . . . . . . . . . 3

2 Taylor Rule estimation: i = −β1π∗ + (1 + β1)π + r + β2Y . . 12

3 Full sample regression: i = −β1π∗ + (1 + β1)π + r + β2Y . . . 19

4 Unknown break point test . . . . . . . . . . . . . . . . . . . . 19

5 White heteroscedasticity test . . . . . . . . . . . . . . . . . . 20

6 ADF test on the nominal interest rate . . . . . . . . . . . . . 21

7 ADF test on the inflation . . . . . . . . . . . . . . . . . . . . 21

8 ADF test on the natural rate of interest . . . . . . . . . . . . 21

9 ADF test on the output gap . . . . . . . . . . . . . . . . . . . 22

10 ADF test of the residuals of the i = −β1π∗+(1+β1)π+ r+β2Y 22

11 Simple OLS estimation i = π + εt . . . . . . . . . . . . . . . . 23

12 ADF test on the residuals of i = π + εt . . . . . . . . . . . . . 23

18

7 Appendix

7.1 Empirical Estimation of the Taylor Rule

Table 3: Full sample regression: i = −β1π∗ + (1 + β1)π + r + β2Y

Note: c(1)=β1, c(2)=β2, c(3)=π∗

Table 4: Unknown break point test

A break point in 1980Q4 is found.

19

7.1.1 Misspecification tests

Figure 4: Normality Test

We fail to reject the Jarque-Bera H0 : at a 5% significance level, with a

p-value of 0.49, so the residuals seem to be normally distributed.

Table 5: White heteroscedasticity test

We fail to reject the White H0 : at a 5% significance level, with a p-value of

0.092, so the variance is likely to be constant.

7.1.2 Spurious Regression Examination

In this section it is examined if concerns about spurious regression are jus-

tified. First the Augmented Dickey Fuller tests are conducted and it is

found that all series, except the output gap (Y ), are trend non-stationary.

Moreover, the two step Engel-Granger test shows that the combination of

20

variables leads to the lower order of integration in the residuals, hence the

series are cointegrated.

Table 6: ADF test on the nominal interest rate

Table 7: ADF test on the inflation

Table 8: ADF test on the natural rate of interest

21

Table 9: ADF test on the output gap

To check if our series are cointegrated, an ADF test on the residual of

the i = −β1π∗ + (1 + β1)π+ r+ β2Y is preformed, showing that there is no

unit root:

Table 10: ADF test of the residuals of the i = −β1π∗ + (1 + β1)π+ r+ β2Y

Afterwards, the order of integration of the residuals in i = π+ εt is anal-

ysed. The result of the unit root test leads to the conclusion that concerns

can be rejected that i = −β1π∗+(1+β1)π+ r+β2Y is a spurious regression.

22

Table 11: Simple OLS estimation i = π + εt

Table 12: ADF test on the residuals of i = π + εt

23