Taylor Rule
This material was originally created for
Starting Point: Teaching Economics
and is replicated here as part of the SERC Pedagogic Service.
and is replicated here as part of the SERC Pedagogic Service.
Initial Publication Date: January 30, 2015
Summary
This case computes a Taylor rule for monetary policy over time. This activity can be used as either (a) an instructor-led example in which the instructor shows –either on paper or a screen– the data and students analyze them, or (b) as a student exploration in which students find the specified data. Instructors with less time could use option (a) and instructors interested in their students learning about the FRED database could use option (b).
This activity plots a Taylor rule-determined target interest rate for monetary policy as a function of a price index (the Consumer Price Index for All Urban Consumers) –expressed in growth rates- and the unemployment gap (the difference between the Civilian Rate of Unemployment and the Natural Rate of Unemployment (Long-Term)). The secular trend and the cyclical behavior of this target interest rate can be compared to the Federal Funds Rate that the Federal Reserve System actually targeted.
This activity is suitable for addressing each of the following issues:
1. How are different macroeconomic magnitudes factored into a standard Taylor rule?
2. How similar are the Federal Funds Rate and the Taylor rule-determined target interest rate?
3. How did the rule-determined and the actual target interest rate evolve after the 2008-2009 recession?
Learning Goals
After the completion of this module students will be able to:
1. Use FRED graphs to perform data manipulations.
2. Use FRED graphs to perform a visual data comparison
3. Assess how monetary policy interest rate targets change in value over time.
4. Assess the evolution of monetary policy interest rate targets during economic expansions and contractions.
1. Use FRED graphs to perform data manipulations.
2. Use FRED graphs to perform a visual data comparison
3. Assess how monetary policy interest rate targets change in value over time.
4. Assess the evolution of monetary policy interest rate targets during economic expansions and contractions.
Context for Use
Ideally, this module should be directed to an intermediate macroeconomics or financial economics class. It can be used as either (a) an instructor-led example in a large lecture or (b) student groups can be assigned to replicate it outside of class as a basis for a short assignment. Between the presentation of the data and the ensuing discussion, instructors should allocate 20-30 minutes of classroom time. The discussion could focus on the mismatch between the rule-determined interest rate target and the one effectively adopted by the Federal Reserve System and on why, sometimes, the rule-determined interest rate target is negative.
Note that a more advanced treatment of this topic may compute Taylor rules for different time horizons of the natural rate of unemployment (e.g. short-run vs. long-run) or employ a measure of the output gap (e.g. the difference between the real potential GDP and the real GDP). These exercises may be used to illustrate how the choices made regarding data can either support or undermine a theoretical construct.
Prerequisite skills: Graph literacy
Prerequisite concepts: Unemployment rates; Inflation rates; the Taylor rule
Note that a more advanced treatment of this topic may compute Taylor rules for different time horizons of the natural rate of unemployment (e.g. short-run vs. long-run) or employ a measure of the output gap (e.g. the difference between the real potential GDP and the real GDP). These exercises may be used to illustrate how the choices made regarding data can either support or undermine a theoretical construct.
Prerequisite skills: Graph literacy
Prerequisite concepts: Unemployment rates; Inflation rates; the Taylor rule
Description and Teaching Materials
The following is a description of this activity being used as an instructor-led example. For a basic step-by-step description of this activity –also suitable for a student-led exploration of the topic– please see the Handout.
Within a lecture discussing monetary policy, an instructor will use this module to help students understand the concepts of intermediate monetary policy targets and the Taylor rule and to guide a discussion of their quantification.
(Step 1)
The instructor will first present a graph of the Effective Federal Funds Rate (FEDFUNDS) (Category: Money, Banking & Finance > Interest Rates > FRB Rates > Effective Federal Funds Rate)
Note
- The instructor should "Edit Data Series 1 > Frequency" and select "Quarterly". Decreasing the data frequency makes for a smoother plot and facilitates the visual interpretation of the series.
The instructor should point out that after 1981 the trend value of the nominal Federal Funds rate has been declining. Narrowing the range of the data set to 1980-present will make that pattern more obvious. A discussion of the cyclical nature of this intermediate target of monetary policy should pay attention to the lack of an apparent cyclical behavior between 1980 and 1990. This fact could be discussed in the context of nominal vs. real interest rates.
(Step 2)
The instructor will then "Add a Data Series > Add New Series", graphing the Consumer Price Index for All Urban Consumers (CPIAUCSL) (Category: Prices > Consumer Price Indexes > Consumer Price Index for All Urban Consumers: All Items)
That will become Series (a)
Note
- The instructor should "Edit Data Series 2 > Units" and select "Percent", transforming the Consumer Price Index into the CPI Inflation Rate allows for both series to be plotted in the same units.
- As above, the instructor should "Edit Data Series 2 > Frequency" and select "Quarterly".
(Step 3)
Next, the instructor will "Add a Data Series > Modify Existing Series > Data Series 2", graphing the Civilian Unemployment Rate (UNRATE) (Category: Population, Employment, & Labor Markets> Current Population Survey (Household Survey)> Unemployment Rate> Civilian Unemployment Rate)
That will become Series (b)
Note
- The instructor should "Edit Data Series 2 > Units" and select "Percent", as the website resets the default units to the last selection.
(Step 4)
Next, the instructor will "Add a Data Series > Modify Existing Series > Data Series 2", graphing the Natural Rate of Unemployment (Long-Term) (NROU) (Category: Population, Employment, & Labor Markets> The Natural Rate of Unemployment (Long-Term))
That will become Series (c)
These steps are needed in order to have three series as part of the same database object and allow for their manipulation. This manipulation is accomplished by selecting "Create Your Own Data Transformation > Formula > 1+(1.5*a)-(1*(b-c)) > Apply"
The instructor should point out how the choice of parameters in the formulation of the rule will have major implications for monetary policy interest rate target-setting. Besides purely methodological issues related to the determination of the parameters the instructor can discuss how the dual mandate of the Employment Act of 1946 is embodied in the Taylor rule.
Note
- The value of the parameters in the Taylor rule above are used by Nechio (2011) and Malkin and Nechio (2012) in two separate Economic Letters published by the Federal Reserve Bank of San Francisco. See full references under Resources.
The graph now plots the Taylor rule for monetary policy as function of a constant, a multiple of the inflation rate, and the unemployment gap. The historical values of the effective federal funds rate are also plotted for purposes of comparison.
The following is a list of questions that could be asked:
* How closely does the effective Federal Funds Rate match the Taylor rule for monetary policy? Are there time periods when the two of them overlap? Why is that not frequently the case?
* Notice the evolution of the Taylor rule between the third quarter of 2008 and the second quarter of 2013. What does it mean, in terms of monetary policy, for the Taylor rule to dictate a negative target interest rate? How could that be achieved?
Further sophistications:
* Plot a Taylor rule employing the Natural Rate of Unemployment (Short-Term) (NROUST) instead of the Natural Rate of Unemployment (Long-Term) (NROU). How does the choice of time-horizon on the estimate of the natural rate of unemployment impact the Taylor rule?
* Plot a Taylor rule employing the Real GDP (GDPC1) and the Real Potential Gross Domestic Product (GDPPOT) instead of the Civilian Unemployment Rate (UNRATE) and the Natural Rate of Unemployment (Long-Term) (NROU). How should the parameters of the Taylor rule be re-calibrated in order for the rule to remain a practical instrument of policy guidance?
Activity Handout for Taylor Rule (Microsoft Word 31kB Jan21 15)
Within a lecture discussing monetary policy, an instructor will use this module to help students understand the concepts of intermediate monetary policy targets and the Taylor rule and to guide a discussion of their quantification.
(Step 1)
The instructor will first present a graph of the Effective Federal Funds Rate (FEDFUNDS) (Category: Money, Banking & Finance > Interest Rates > FRB Rates > Effective Federal Funds Rate)
Note
- The instructor should "Edit Data Series 1 > Frequency" and select "Quarterly". Decreasing the data frequency makes for a smoother plot and facilitates the visual interpretation of the series.
The instructor should point out that after 1981 the trend value of the nominal Federal Funds rate has been declining. Narrowing the range of the data set to 1980-present will make that pattern more obvious. A discussion of the cyclical nature of this intermediate target of monetary policy should pay attention to the lack of an apparent cyclical behavior between 1980 and 1990. This fact could be discussed in the context of nominal vs. real interest rates.
(Step 2)
The instructor will then "Add a Data Series > Add New Series", graphing the Consumer Price Index for All Urban Consumers (CPIAUCSL) (Category: Prices > Consumer Price Indexes > Consumer Price Index for All Urban Consumers: All Items)
That will become Series (a)
Note
- The instructor should "Edit Data Series 2 > Units" and select "Percent", transforming the Consumer Price Index into the CPI Inflation Rate allows for both series to be plotted in the same units.
- As above, the instructor should "Edit Data Series 2 > Frequency" and select "Quarterly".
(Step 3)
Next, the instructor will "Add a Data Series > Modify Existing Series > Data Series 2", graphing the Civilian Unemployment Rate (UNRATE) (Category: Population, Employment, & Labor Markets> Current Population Survey (Household Survey)> Unemployment Rate> Civilian Unemployment Rate)
That will become Series (b)
Note
- The instructor should "Edit Data Series 2 > Units" and select "Percent", as the website resets the default units to the last selection.
(Step 4)
Next, the instructor will "Add a Data Series > Modify Existing Series > Data Series 2", graphing the Natural Rate of Unemployment (Long-Term) (NROU) (Category: Population, Employment, & Labor Markets> The Natural Rate of Unemployment (Long-Term))
That will become Series (c)
These steps are needed in order to have three series as part of the same database object and allow for their manipulation. This manipulation is accomplished by selecting "Create Your Own Data Transformation > Formula > 1+(1.5*a)-(1*(b-c)) > Apply"
The instructor should point out how the choice of parameters in the formulation of the rule will have major implications for monetary policy interest rate target-setting. Besides purely methodological issues related to the determination of the parameters the instructor can discuss how the dual mandate of the Employment Act of 1946 is embodied in the Taylor rule.
Note
- The value of the parameters in the Taylor rule above are used by Nechio (2011) and Malkin and Nechio (2012) in two separate Economic Letters published by the Federal Reserve Bank of San Francisco. See full references under Resources.
The graph now plots the Taylor rule for monetary policy as function of a constant, a multiple of the inflation rate, and the unemployment gap. The historical values of the effective federal funds rate are also plotted for purposes of comparison.
The following is a list of questions that could be asked:
* How closely does the effective Federal Funds Rate match the Taylor rule for monetary policy? Are there time periods when the two of them overlap? Why is that not frequently the case?
* Notice the evolution of the Taylor rule between the third quarter of 2008 and the second quarter of 2013. What does it mean, in terms of monetary policy, for the Taylor rule to dictate a negative target interest rate? How could that be achieved?
Further sophistications:
* Plot a Taylor rule employing the Natural Rate of Unemployment (Short-Term) (NROUST) instead of the Natural Rate of Unemployment (Long-Term) (NROU). How does the choice of time-horizon on the estimate of the natural rate of unemployment impact the Taylor rule?
* Plot a Taylor rule employing the Real GDP (GDPC1) and the Real Potential Gross Domestic Product (GDPPOT) instead of the Civilian Unemployment Rate (UNRATE) and the Natural Rate of Unemployment (Long-Term) (NROU). How should the parameters of the Taylor rule be re-calibrated in order for the rule to remain a practical instrument of policy guidance?
Activity Handout for Taylor Rule (Microsoft Word 31kB Jan21 15)
Teaching Notes and Tips
There is an ever-growing trove of Economic Letters by the Federal Reserve Bank of San Francisco discussing the recent evolution of monetary policy in the United States and in Europe, frequently against a benchmark of a Taylor rule-determined interest rate target (see full references under Resources). These are great resources to carry the discussion further.
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Assessment
The recommended method for assessment for an intermediate macroeconomics or financial economics class would be to have students write up a short memo where they discuss the historical evolution of different classes of nominal and real interest rates. This should be a take-home assignment.
References and Resources
"Monetary Policy When One Size Does Not Fit All" by Fernanda Nechio
Federal Reserve Bank of San Francisco Economic Letter 2011-18, June 13, 2011
http://www.frbsf.org/economic-research/publications/economic-letter/2011/june/monetary-policy-europe/
"U.S. and Euro-Area Monetary Policy by Regions" by Israel Malkin and Fernanda Nechio
Federal Reserve Bank of San Francisco Economic Letter 2012-06, February 27, 2012
http://www.frbsf.org/economic-research/publications/economic-letter/2012/february/us-europe-monetary-policy/
"The Fed's Monetary Policy Response to the Current Crisis" by Glenn D. Rudebusch
Federal Reserve Bank of San Francisco Economic Letter 2009-17, May 22, 2009
http://www.frbsf.org/economic-research/publications/economic-letter/2009/may/fed-monetary-policy-crisis/
Federal Reserve Bank of San Francisco Economic Letter 2011-18, June 13, 2011
http://www.frbsf.org/economic-research/publications/economic-letter/2011/june/monetary-policy-europe/
"U.S. and Euro-Area Monetary Policy by Regions" by Israel Malkin and Fernanda Nechio
Federal Reserve Bank of San Francisco Economic Letter 2012-06, February 27, 2012
http://www.frbsf.org/economic-research/publications/economic-letter/2012/february/us-europe-monetary-policy/
"The Fed's Monetary Policy Response to the Current Crisis" by Glenn D. Rudebusch
Federal Reserve Bank of San Francisco Economic Letter 2009-17, May 22, 2009
http://www.frbsf.org/economic-research/publications/economic-letter/2009/may/fed-monetary-policy-crisis/