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Modeling changes in US monetary policy with a time-varying nonlinear Taylor rule

  • Anh D. M. Nguyen EMAIL logo , Efthymios G. Pavlidis and David A. Peel
Published/Copyright: April 3, 2018
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Studies in Nonlinear Dynamics & Econometrics
From the journal Studies in Nonlinear Dynamics & Econometrics Volume 22 Issue 5

Abstract

The monetary economics literature has highlighted four issues that are important in evaluating US monetary policy since the late 1960s: (i) time variation in policy parameters, (ii) asymmetric preferences, (iii) real-time nature of data, and (iv) heteroskedasticity. In this paper, we exploit advances in sequential monte carlo methods to estimate a time-varying nonlinear Taylor rule that addresses these four issues simultaneously. Our findings suggest that US monetary policy has experienced substantial changes in terms of both the response to inflation and to real economic activity, as well as changes in preferences. These changes cannot be captured adequately by a single structural break at the late 1970s, as has been commonly assumed in the literature, and play a non-trivial role in economic performance.

Keywords: asymmetric objective; monetary policy rules; particle filter; real-time data; stochastic volatility; Taylor rule; time-varying parameter model
JEL Classification: C32; E52; E58

Funding source: Economic and Social Research Council

Award Identifier / Grant number: ES/J500094/1

Funding statement: Nguyen acknowledges the support of the UK Economic and Social Research Council [ES/J500094/1].

Acknowledgement

We are thankful to the editor and the referee for their comments. We also thank Konstantinos Theodoridis, Ivan Paya, John Barrdear, Jeremy Chiu, Mihnea Constantinescu, Timo Teräsvirta, Julien Chevallier and participants at the 3rd International Workshop on Financial Markets and Nonlinear Dynamics (Paris, France), the 2017 Royal Economic Society Annual conference (Bristol, UK), the 2015 Money Macro and Finance conference (Cardiff, UK) and the Bank of Lithuania seminar (Vilnius, Lithuania) for comments and suggestions. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of Lithuania or the European System of Central Banks.

A Appendix

A.1 Forecasting the contemporaneous variance of inflation

We detail the procedure to forecast the contemporaneous variance of inflation series as follows:

  • Step 0, Initiation: We start with the 1965Q4 period, set i ↝ 1965Q4.

  • Step 1, Estimation: Let Ii be the information set at time i which includes available monthly inflation and the unemployment gap to the last month of the quarter i − 1. Given Ii, Equation (20) is estimated with GARCH(1,1) errors.

  • Step 2, Forecast: Based on the estimated-GARCH process, we forecast the conditional variances of inflation for the three months of quarter i. Take the average of those forecasts and save it as σπi|Ii2.

  • Step 3, Termination: If i ≠ 2007Q4, move to the next period i = i + 1 and follow step 2. Otherwise, the procedure stops and we collect the expected variance of inflation σπi|Ii2 for i = 1965Q4, …, 2007Q4.

Table 1 report the means, the standard deviations and the correlation matrix of different estimates of the expected variance of inflation by applying the four-step procedure outlined above. The measures are different in terms of the number of lags of inflation (n) and the measure of output gap (yt) which are used in Equation (20).

Table 1:

Summary statistics for forecasts of inflation variance: 1965Q4–2007Q4.

MeansM0M1M2M3M4M5
Standard deviations0.1020.1000.1040.1020.0990.098
Correlation matrix0.0550.0560.0590.0580.0510.052
M01.0000.9940.9930.9910.9920.988
M10.9941.0000.9840.9950.9870.995
M20.9930.9851.0000.9930.9780.973
M30.9910.9950.9931.0000.9780.984
M40.9920.9870.9780.9781.0000.994
M50.9880.9950.9730.9840.9941.000

  1. The measure M0 is associated with three lags of inflation n = 3 and the output gap yt proxied by the five-year moving average unemployment gap. For M1, n = 6 and yt proxied by the five-year moving average unemployment gap. For M2, n = 3 and yt proxied by the historical average unemployment gap. For M3, n = 6 and yt proxied by the historical average unemployment gap. For M4, n = 3 and yt proxied by the three-year moving average unemployment gap. Finally, for M5, n = 6 and yt proxied by the three-year moving average unemployment gap.

A.2 Estimates of time-invariant parameters

The estimates of time-invariant parameters are presented in Table 2.

Table 2:

Means and standard deviations of time-invariant parameters.

ParametersMeansStandard deviations
σa0−0.860.11
σa1−2.220.08
σa20.630.11
σa3−2.230.14
σa4−1.100.07
σa5−1.280.08

  1. The table presents the estimates of the time-invariant parameters of the state space system:

    it=11+exp(−a5,t)it−1+exp(−a5,t)1+exp(−a5,t)(a0,t+a1,tπt|t+a2,tσπt|t2+a3,tyt|t)+exp(a4,t)εt,ak,t=ak,t−1+exp(σak)εak,t,k=0,1,…,5.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2017-0092).

Published Online: 2018-04-03

©2018 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/snde-2017-0092
Keywords for this article
asymmetric objective; monetary policy rules; particle filter; real-time data; stochastic volatility; Taylor rule; time-varying parameter model

Articles in the same Issue

  1. Interview
  2. An Interview with Timo Teräsvirta
  3. Research Articles
  4. Nonlinear and asymmetric pricing behaviour in the Spanish gasoline market
  5. Testing for misspecification in the short-run component of GARCH-type models
  6. Closed-form estimators for finite-order ARCH models as simple and competitive alternatives to QMLE
  7. Time-varying asymmetry and tail thickness in long series of daily financial returns
  8. Modeling changes in US monetary policy with a time-varying nonlinear Taylor rule
  9. Financial fragmentation and the monetary transmission mechanism in the euro area: a smooth transition VAR approach
  10. P-star model for India: a nonlinear approach
  11. Can a Taylor rule better explain the Fed’s monetary policy through the 1920s and 1930s? A nonlinear cliometric analysis
  12. Modeling time-variation over the business cycle (1960–2017): an international perspective
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