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Temporal aggregation and estimated monetary policy rules

  • Omer Bayar EMAIL logo
Published/Copyright: August 12, 2014
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 14 Issue 1

Abstract

Temporal aggregation alters time-series properties of high-frequency data, thereby affecting the estimation of models based on time-aggregated low-frequency data. This paper examines the effect of temporal aggregation of interest rates on forward-looking Taylor-type monetary policy rules. Results show that using quarterly-averaged interest rates in standard forward-looking structures adds a spurious bias to parameters that measure the extent of interest rate smoothing and serial correlation of shocks. Consequently, empirical interpretations of persistence in policy interest rate changes are distorted.

Keywords: federal funds rate; monetary policy rule; temporal aggregation
JEL classification: C43; E52; E58
Corresponding author: Omer Bayar, Schroeder School of Business, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722, USA, Phone: +1(812)4882867, e-mail:

Acknowledgments

I am grateful to Refet Gurkaynak, Bill Neilson, Mohammed Mohsin, Christian Vossler, seminar participants at the University of Tennessee and the Central Bank of Republic of Turkey, and three anonymous referees for helpful comments. Any remaining errors are mine.

Appendix

Previous studies show that temporal aggregation changes both the ARIMA order of a time series and the size of its autoregressive and moving average coefficients. I provide below a brief summary of past research to demonstrate how averaging affects the ARIMA order of a time series differently from sampling.

Suppose that the underlying data generating process yt can be described by the following ARIMA (p, d, q) model.

(A.1)Δdyt=a0+a1Δdyt−1+⋯+apΔdyt−p+εt+b1εt−1+⋯+bqεt−q (A.1)

where Δ=(1–L) and L is the lag operator.

It is assumed that the underlying ARIMA (p, d, q) model operates on the time interval 1, indexed by t. Temporally aggregated processes, both sampled and averaged, are observed at interval m>1, indexed by T.

A sampled sub-series {ysT} is generated from the original series {yt} by selecting values distanced at m periods such that ysT=ymt for m>1, an integer representing the sampling ratio between the original series and the temporally aggregated sub-series. Sampled sub-series {ysT} follows an ARIMA (p, d, r) process where r=(p+d)+(q–p–d)/m.[18] Moving average order of the sampled representation, if not an integer, is rounded down to the previous integer. Therefore, the number of moving average lags is p+d or p+d–1, depending on whether q>p+d or q<p+d.

An averaged sub-series {yaT} is generated by averaging every m adjacent value from the original series {yt} such that observations from the original series do not overlap. Averaged sub-series yaT=[ymt+ymt–1+…+ymt-m+1]/m follows an ARIMA (p, d, r) process where r=(p+d+1)+(q–p–d–1)/m. Consequently, the number of moving average lags in the averaged sub-series is p+d+1 or p+d, depending on whether q>p+d+1 or q<p+d+1.[19]

Evidently, number of autoregressive lags (p) and order of integration (d) remain unchanged for the two sub-series generated from the same underlying process {yt} at the same sampling ratio m. By contrast, the averaged sub-series may have one more moving average lag (q) than its sampled counterpart.

To determine the implications of this result for monetary policy evaluation, I estimate univariate ARIMA models of temporally aggregated interest rates for the same sample period from above, 1987Q4 to 2005Q. Sarno, Thornton, and Valente (2005) reports that an ARIMA (2, 1, 1) specification is satisfactory in modeling daily federal funds rate, as this structure is parsimonious and leaves no serial correlation in residuals.[20] Then, theoretical results from this section suggest that the sampled funds rate series must follow an ARIMA (2, 1, 2) process, while the averaged funds rate series must follow an ARIMA (2, 1, 3) process, where the number of autoregressive and moving average lags in the two sub-series is less than or equal to designated numbers.

Table A1 presents estimates for quarterly-averaged and end-of-quarter funds rates under alternative ARIMA specifications. Here, I consider higher-order AR and MA components to the extent implied by theory: up to two autoregressive lags in both sub-series; up to two and three moving average lags in the end-of-quarter and quarterly-averaged sub-series, respectively. Results are reported for specifications favored by a combination of factors including parsimony, Akaike and Bayesian information criteria, tests of white noise residuals, and speed of model conversion.

Table A1

Univariate ARIMA estimates for target federal funds rate.

SpecificationQAEOQ
ARIMA (1, 1, 0)
 AR (1) [p-value]0.68 [0.00]0.61 [0.00]
 AIC61.7481.13
 BIC68.6188.00
 Portmanteau (Q) test statistic [p-value]30.08 [0.87]30.97 [0.85]
ARIMA (2, 1, 0)
 AR (1) [p-value]0.69 [0.00]0.61 [0.00]
 AR (2) [p-value]–0.02 [0.90]–0.01 [0.97]
 AIC63.7183.13
 BIC72.8792.29
 Portmanteau (Q) test statistic [p-value]30.15 [0.87]31.02 [0.85]
ARIMA (2, 1, 1)
 AR (1) [p-value]1.63 [0.00]1.57 [0.00]
 AR (2) [p-value]–0.70 [0.00]–0.64 [0.00]
 MA (1) [p-value]–1.00 [0.00]–0.99 [0.00]
 AIC59.9180.23
 BIC71.3691.68
 Portmanteau (Q) test statistic [p-value]28.43 [0.92]32.68 [0.79]

AIC/BIC represent Akaike and Bayesian information criteria; smaller values indicate an improved tradeoff between goodness of fit and model complexity. Null hypothesis for the Portmanteau (Q) test is that residuals follow a white noise process.

Differences in parameter estimates remain, indicating that between sampled and averaged interest rates, indicating that averaging affects time-series properties of the daily interest rate series differently than sampling. Although this result is consistent with underlying theory, it should be taken with caution in regard to policy evaluation, as univariate models considered here disregard the main determinants of monetary policy, inflation and output gap.

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Published Online: 2014-8-12
Published in Print: 2014-1-1

©2014 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Advances
  3. Optimal portfolios with wealth-varying risk aversion in the neoclassical growth model
  4. Inventories and the stockout constraint in general equilibrium
  5. Optimal second best taxation of addictive goods in dynamic general equilibrium: a revenue raising perspective
  6. Inflation effects on capital accumulation in a model with residential and non-residential assets
  7. Optimal capital-income taxation in a model with credit frictions
  8. Contributions
  9. Interest rate fluctuations and equilibrium in the housing market
  10. News shocks and learning-by-doing
  11. Capacity utilization and the effects of energy price increases in Japan
  12. Small-scale New Keynesian model features that can reproduce lead, lag and persistence patterns
  13. Optimal policy and Taylor rule cross-checking under parameter uncertainty
  14. The impact of American and British involvement in Afghanistan and Iraq on health spending, military spending and economic growth
  15. Why does natural resource abundance not always lead to better outcomes? Limited financial development versus political impatience
  16. The skill bias of technological change and the evolution of the skill premium in the US since 1970
  17. Aggregate impacts of recent US natural gas trends
  18. Organizational learning and optimal fiscal and monetary policy
  19. Industrial specialization, financial integration and international consumption risk sharing
  20. Leverage, investment, and optimal monetary policy
  21. Public debt in an OLG model with imperfect competition: long-run effects of austerity programs and changes in the growth rate
  22. Temporal aggregation and estimated monetary policy rules
  23. International transmission of productivity shocks with nonzero net foreign debt
  24. Did the euro change the effect of fundamentals on growth and uncertainty?
  25. Topics
  26. Real factor prices and factor-augmenting technical change
  27. Monetary policy and TIPS yields before the crisis
https://doi.org/10.1515/bejm-2013-0124
Keywords for this article
federal funds rate; monetary policy rule; temporal aggregation

Articles in the same Issue

  1. Frontmatter
  2. Advances
  3. Optimal portfolios with wealth-varying risk aversion in the neoclassical growth model
  4. Inventories and the stockout constraint in general equilibrium
  5. Optimal second best taxation of addictive goods in dynamic general equilibrium: a revenue raising perspective
  6. Inflation effects on capital accumulation in a model with residential and non-residential assets
  7. Optimal capital-income taxation in a model with credit frictions
  8. Contributions
  9. Interest rate fluctuations and equilibrium in the housing market
  10. News shocks and learning-by-doing
  11. Capacity utilization and the effects of energy price increases in Japan
  12. Small-scale New Keynesian model features that can reproduce lead, lag and persistence patterns
  13. Optimal policy and Taylor rule cross-checking under parameter uncertainty
  14. The impact of American and British involvement in Afghanistan and Iraq on health spending, military spending and economic growth
  15. Why does natural resource abundance not always lead to better outcomes? Limited financial development versus political impatience
  16. The skill bias of technological change and the evolution of the skill premium in the US since 1970
  17. Aggregate impacts of recent US natural gas trends
  18. Organizational learning and optimal fiscal and monetary policy
  19. Industrial specialization, financial integration and international consumption risk sharing
  20. Leverage, investment, and optimal monetary policy
  21. Public debt in an OLG model with imperfect competition: long-run effects of austerity programs and changes in the growth rate
  22. Temporal aggregation and estimated monetary policy rules
  23. International transmission of productivity shocks with nonzero net foreign debt
  24. Did the euro change the effect of fundamentals on growth and uncertainty?
  25. Topics
  26. Real factor prices and factor-augmenting technical change
  27. Monetary policy and TIPS yields before the crisis
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