Interest Rate Determination & the Taylor Rule Rule_Berry_Marquez.pdf · Interest Rate Determination...
Transcript of Interest Rate Determination & the Taylor Rule Rule_Berry_Marquez.pdf · Interest Rate Determination...
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Interest Rate Determination & the Taylor Rule JARED BERRY & JAIME MARQUEZ
JOHNS HOPKINS SCHOOL OF ADVANCED INTERNATIONAL STUDIES
JANURY 2017
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Monetary Policy Rules •Policy rules form part of the “modern” approach to monetary policy where the goal is to stabilize the economy
•Definition: systematic decision process using information consistently and predictably
•Desirable properties • Rule must recognize that individuals anticipate decisions by the Central Bank • Rule must be explicit about how information is used • Rule should not be changed without a lot of forethought • Rule must be easily understood: complicated rules come across as capricious
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Taylor Rule •The Taylor rule determines a benchmark for the short-term policy rate:
𝑖 = 𝑟 + 𝜋 + 𝛽 ∙ 𝜋 − 𝜋∗ + (1 − 𝛽) ∙ (𝑦 − 𝑦∗)
•Where • 𝑖 is the federal funds rate predicted by the Taylor rule • 𝑟 is the real interest rate • 𝜋 is the current value of inflation • 𝜋∗ is the target inflation rate • 𝑦 is the measure of economic activity • 𝑦∗ is the measure of “full employment” economic activity • 𝛽 > 0 importance of inflation for monetary policy
Source: http://www.brookings.edu/~/media/Events/2015/10/15-fed-crossroads/Taylor_remarks.pdf?la=en
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Properties of the Taylor Rule •If 𝜋 > 𝜋∗ then 𝑖 ↑: If the inflation rate exceeds the target rate, then monetary policy raises the short term rate
•If 𝑦 > 𝑦∗ then 𝑖 ↑: If the economic activity exceeds its full employment level, then monetary policy should raise the short-term rate
•If 𝜋 > 𝜋∗ and 𝑦 > 𝑦∗, then 𝑖 = 𝑟 + 𝜋, which is the Fisher equation
•The “money” of monetary policy follows the interest rate
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Extensions of the Taylor Rule •Persistence:
• Monetary policy seeks to avoid large swings in policy rates • History of recent rates plays a role in setting monetary policy
•Expectations: • Changes in monetary policy do not materialize instantaneously: there is a lag • What matters are expectations of inflation and economic activity • If authorities anticipate an event that will disrupt the economy, they must act now to offset the
expected disruption
•Interdependencies: • Interest rates are not determined in a vacuum • Domestic monetary policy potentially depends on foreign monetary policy and vice versa
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Expected Inflation
Interest Rate History
Expected Growth Interest Rate
Expected Inflation
Expected Growth
Interest Rate History
Interest Rate
United States
Europe
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Generic Taylor Rule neutral rate 𝑟 + 𝜋𝑡+1 future inflation 𝛽 ∙ (𝜋𝑡+1 − 𝜋∗) future growth 1 − 𝛽 ∙ 𝑦𝑡+1 − 𝑦𝑡∗ history 𝛿 ∙ 𝑖𝑡−1 interdependence 𝜆 ∙ 𝑖𝑡𝑒
𝑖𝑡
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Implementation of the Taylor Rule •Parameters of the Taylor rule are generally unknown
•Practitioners typically assume values for the unknown parameters
•For example: • 𝛽 = 0.5: Monetary policy is equally concerned with inflation and economic activity • (𝑦𝑡+1 − 𝑦𝑡∗): output gap from the International Monetary Fund’s World Economic Outlook • Target inflation rate 𝜋∗ = 2 set and announced by the Central Bank • Real interest rate 𝑟 = 2
•Values for unknown parameters can be estimated from data
•Real interest rate and output gap can be modelled with Monte Carlo analysis
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Estimating Parameters: Rationale •Rather than assuming parameters, estimate them based on past performance
• United States and Euro Area data from 1995-2015 • Inflation and output gap from the International Monetary Fund’s World Economic Outlook • Federal funds rate from St. Louis Federal Reserve’s Federal Reserve Economic Data (FRED) • Eonia rate from European Central Bank
•How are the determinants of the interest rate actually weighted?
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Empirical Methodology •The structural model is:
𝑖𝑡𝑈𝑈 = 𝜑0 + 𝜑1 ∙ 𝑦𝑡 − 𝑦𝑡∗ + 𝜑2 ∙ 𝜋𝑡 + 𝜑3 ∙ 𝑖𝑡−1 + 𝜑4 ∙ 𝑖𝑡𝐸𝑈
𝑖𝑡𝐸𝑈 = 𝜑0𝐸𝑈 + 𝜑1𝐸𝑈 ∙ 𝑦𝑡𝐸𝑈 − 𝑦𝑡𝐸𝑈∗ + 𝜑2𝐸𝑈 ∙ 𝜋𝑡𝐸𝑈 + 𝜑3𝐸𝑈 ∙ 𝑖𝑡−1𝐸𝑈 + 𝜑4𝐸𝑈 ∙ 𝑖𝑡𝑈𝑈
•Estimate using Full Information Maximum Likelihood (FIML) method
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Estimating Parameters: Results
Independent Variable Estimated Parameters for the US Estimated Parameters for the EU
Economic Activity 𝜑1 = 0.3428** 𝜑1𝐸𝑈 = 0.1425
Inflation 𝜑2 = 0.1709 𝜑2𝐸𝑈 = 0.3951**
Interest Rate History 𝜑3 = 0.6430*** 𝜑3𝐸𝑈 = 0.5009***
Foreign Interest Rate (EU/US) 𝜑4 = 0.0000^ 𝜑4𝐸𝑈 = 0.3055*** *** p<0.01, ** p<0.05, * p<0.1
^We constrain with respect to the EONIA rate because it is statistically insignificant and negative in the unconstrained FIML estimation procedure
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Estimating Parameters: Implications •For the United States:
• Interest rate history and economic activity are most important for US rates • Inflation is less significant for the US • The US interest rate is not impacted by Euro Area rates
•For the Euro Area: • Interest rate history and inflation are most important for Euro Area rates • Economic activity is less significant for the Euro Area • The US interest rate factors heavily in the determination of Euro Area rates
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Sensitivity of Results to Changes in Exogenous Variables
•Rather than assuming values for the real interest rate, 𝑟, and potential output, 𝑦∗, model them with Monte Carlo analysis • Federal funds rate from St. Louis Federal Reserve’s Federal Reserve Economic Data (FRED) • Potential output figures from Congressional Budget Office • Determine standard deviation from historic rates and potential output
•Create random drawings for 𝑟 and 𝑦∗ to incorporate in Taylor rule
•Incorporate similarly random “shocks” to these drawings
•Generate an empirically robust range of Taylor rules
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Empirical Methodology •Recall the simple Taylor rule,
𝑖 = 𝑟 + 𝜋 + 𝛽 ∙ 𝜋 − 𝜋∗ + (1 − 𝛽) ∙ (𝑦 − 𝑦∗)
•Where 𝑟 = 2 + 𝜀1 and 𝑦∗ = 2 + 𝜀2 such that, • 𝜀1 = 𝜎𝑟 ∙ 𝜇1 + 𝜎𝑟𝑟 ∙ 𝜇2 and 𝜀2 = 𝜎𝑟𝑟 ∙ 𝜇1 + 𝜎𝑟 ∙ 𝜇2 • 𝜎𝑟 is the historic standard deviation of the federal funds rate • 𝜎𝑟 is the historic standard deviation of potential output • 𝜎𝑟𝑟 is the covariance between the two, chosen exogenously • 𝜇1 and 𝜇2 are random “shocks” normally distributed with a mean of 0 and standard deviation of 1
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Empirical Methodology •So, real interest rate and potential output are drawn such that,
𝑟𝑦 = 2
2 + 𝜎𝑟 0𝜎𝑟𝑟 𝜎𝑟
∙𝜇1𝜇2
•Draw 1,000 iterations each of 𝜇1 and 𝜇2
•Draw 1,000 subsequent iterations of 𝑟 and 𝑦 according to the equation above
•Assume 𝜎𝑟𝑟 = 0
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5 20
32
96
133
206 207
172
75
36
11 7
1.995 1.996 1.997 1.998 1.999 2.000 2.001 2.002 2.003 2.004 2.005 MORE
Freq
uenc
y Distribution of Real Interest Rate Drawings
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21
31
54
88
134
151
164
130 126
57
28
16
1.975 1.98 1.985 1.99 1.995 2 2.005 2.01 2.015 2.02 2.025 MORE
Freq
uenc
y Distribution of Potential Output Drawings
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1.95
1.96
1.97
1.98
1.99
2
2.01
2.02
2.03
2.04
1.992 1.994 1.996 1.998 2 2.002 2.004 2.006 2.008
Pote
ntia
l Out
put,
y
Real Interest Rate, r
Drawings r and y
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Monte Carlo Taylor Rule: Results •Using drawings for r and y, establish similar distributions of US Taylor rules
•Forward looking, using estimated parameters
•Forward-looking, using chosen parameters • Weight the importance of inflation and growth equally (𝛽 = 𝜃 = 0.5) • Weight persistence heavily (𝛿 = 0.9), implying “slow” adjustment of the interest rate • No interdependency (𝜆 = 0.0)
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0 3 16
59
131
212
258
169
102
39
8 3
2.1850 2.1860 2.1870 2.1880 2.1890 2.1900 2.1910 2.1920 2.1930 2.1940 2.1950 MORE
Freq
uenc
y Taylor Rule Distribution (Estimated Parameters)
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26
38
75
118 125
159
149
123
95
46
29
17
1.1748 1.1750 1.1753 1.1755 1.1758 1.1760 1.1763 1.1765 1.1768 1.1770 1.1773 MORE
Freq
uenc
y Taylor Rule Distribution (High Persistence)
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Monte Carlo Taylor Rule: Implications •Should the assumptions of the Taylor rule and projections hold, we can confidently estimate a range of possible interest rates for 2017
•Overall distribution is a reasonably tight range
•Choice parameters can be adjusted accordingly given different assumptions • “Slowness” of adjustments (persistence parameter) • Expectations vs. current data (forward-looking) • Initial value for potential growth and real interest rate
•Changes in parameters more drastically alter the distribution