A Brief Survey of Stochastic Properties of Real Interest Rates

Procedia - Social and Behavioral Sciences 109 ( 2014 ) 130 – 134

1877-0428 © 2014 The Authors. Published by Elsevier Ltd.Selection and peer review under responsibility of Organizing Committee of BEM 2013.doi: 10.1016/j.sbspro.2013.12.432

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2nd World Conference On Business, Economics And Management- WCBEM 2012

A brief survey of stochastic properties of real interest rates

Korhan Gokmenoglua *

a Department of Economics, University of California, San Diego, CA 92093-0508, USA

Abstract

Real interest rate is one of the most important economic variables. This variable plays a central role in decision-making process of households, firms and government, and main policy tool of many central banks. Stochastic properties of real interest rate is basic ingredient of several econometric models and has some important implications on basic assumptions of many important financial and macroeconomic models such as Consumption Based Asset Pricing Model, Fisher Hypothesis and some growth models. Because of its vital importance for the economy and economic-financial theories, time series properties of real interest rate have been investigated intensely. However, studies those investigate stochastic properties of real interest rates of developing countries is comparatively limited.

1. Introduction

Real interest rate has substantial affect on economy and other macroeconomic variables. This variable is the main policy instrument of central bank and basic ingredient of several monetary models. Many macroeconomic and financial theories are based on some assumptions about stochastic properties of real rate. Time series properties of real rate have also upmost importance for econometric forecasting models. For these reasons there is a vast literature on stochastic properties of interest rate, their implications on monetary-macroeconomic theories and importance for the whole economy. However, for developing countries, including Turkey, research on stochastic properties of real rates relatively limited and studies are mainly pertinent to relationship of real rates with other macroeconomic variables.

2. Early Studies

In his controversial paper Fama (1975) claims that ex-post real rate of US is stable for 1953 and 1971 periods. The finding of constant interest rates is incompatible with basic assumptions of several macroeconomic theories including Fisher Hypothesis, Purchasing Power Parity, and Efficient Market Hypothesis. However, this study was criticized by many researchers (Shiller, 1980; Nelson and Schwert, 1977) and following Fama (1975) the idea of constant real interest rate was rejected by almost all studies (Fama, 1981; Mishkin, 1981). During 80's many studies

* Corresponding Author: Korhan Gokmenoglu. Tel.: +1-480-359-9258 E-mail address: [email protected]

Keywords: Real interest rate, unit root, structural breaks, persistence, and half-life;

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© 2014 The Authors. Published by Elsevier Ltd.Selection and peer review under responsibility of Organizing Committee of BEM 2013.

131 Korhan Gokmenoglu / Procedia - Social and Behavioral Sciences 109 ( 2014 ) 130 – 134

support that real interest rates are stationary (Huizinga-Mishkin, 1986); however some cannot reject unit root hypothesis, which show that real rate, has unit root (Mankiw and Miron, 1986).

Rose (1988) can be considered as a milestone for studies on real interest rate. Rose employs conventional unit root tests and find that nominal interest rate and inflation series are I (1) and (0) processes respectively for USA and 18 OECD countries investigated. According to these findings, under the assumptions of inflation expectations are stationary, real rate must be non-stationary for all these countries. Findings of Rose contradict with many previous studies and also are not in accordance with basic assumptions of several macroeconomics theories For example non stationary interest rates violate Intertemporal Euler Equation of Consumption Based Asset Pricing Model. This controversial finding would be a motivation for new studies on unit root properties of real rate.

King et al. (1991) apply ADF tests to investigate unit root properties of US real rates for 1949-1988 periods, and are unable to reject unit root hypothesis for real rate. Mishkin (1992) investigates unit root properties of US real interest rates by analyzing 1 and 3 months Treasury bill and consumer price index series with ADF and AEG tests. This study asserts that US real interest rate is stationary for 1953-1990 periods. During 90's several studies obtain evidence for stationary US ex-post real rate (Mishkin, 1992; Crowder and Hoffman, 1996), however others do not agree with this finding (Koustas and Serletis, 1999). It is hard to claim that there is a consensus.

Many researches conduct multi state analysis. Engsted (1995) employs ADF test to investigate unit root properties of 13 OECD countries interest rate, and his results are somewhat mixed for 1962-1993 periods. Lai (1997) tries to reveal unit root properties of real rate by analyzing data of 8 developed and 8 developing countries with the help of ADF and KPSS tests. This study has strong evidence for mean reverting process and long-term memory for real rates.

3. Structural Breaks

Perron (1989) proves that structural breaks are indispensable parts of many financial and macroeconomic variables and not taking into account potential breaks may result to obtain incorrect evidence about the stationary properties of these variables. For the last two decades almost all researchers agree with the idea that real interest rates have structural breaks due to the exogenous events either political or economic and unit root test has to take into account these breaks to prevent bias.

There many voluminous studies to investigate stochastic properties of US real rate by taking into account potential structural breaks. Garcia and Perron (1996) find that US real rates have 3 structural breaks. They divide the series into four subsamples according to the break dates and find that for each sub samples real rates are almost constant. They assert that U.S. real interest rate is a stationary process around an infrequently shifting means, which makes it difficult to reject the unit root null hypothesis.

Caporale and Grier (2000) obtain evidence of four structural breaks at the mean level of US real rate between 1961-1992 by applying Bai and Perron (1998, 2002) method. Lai (2004) investigates unit root properties of US real interest rates for 1978-2001 periods with ADF test that allows structural breaks and can reject the null hypothesis.

Clement et al. (1998) use long-term government bond and consumer price index to analyze unit root properties of US and UK real interest rates. ADF test that allow two structural breaks reveals that both series are stationary.

Rapach and Wohar (2005) employ Bai-Perron approach (1998, 2002) to examine structural breaks for real rate of US and 13 industrialized countries. For postwar period for all the countries analyzed evidences of structural breaks are found. The number of breaks varies from two to five.

Lai (2008) utilizes from ADF test that allows structural breaks to analyze the data of 8 developed and 8 developing countries from 1974 to 2001. For most of the series evidence for structural breaks is found and unit root hypothesis can be rejected for interest rates.

Ozdemir et al. (2013) reexamine the persistence of real interest rates for 13 countries by employing Lumsdaine and Pappell (1997) unit root test. They can reject unit root hypothesis for the samples investigated when structural breaks are incorporated into the analysis.

According to these findings it can be argued that structural breaks are indispensible part of real interest rates and if structural breaks are taken into account it is more probable to reject unit root hypothesis.


The studies on causes of structural breaks are relatively lesser. Political (Caporale and Grier, 2000) and economic factors such as inflation (Koustas and Serletis, 1999) are main factors mentioned. Rapach and Wohar (2005) test for multiple structural breaks in the mean real interest rate for 13 industrialized countries and find that the timing and direction of the structural breaks are often similar across countries. So they claim that these breaks might have a common source and inflation is the best potential candidate.

4. New Approaches

Some more recent studies find that US real interest rates have long memory and mean reverting tendency (Tsay, 2000; Karanasos et al., 2006). Rapach and Weber (2004) employ a number of econometric methods including ADF, Phillips z, Ng and Perron (2001) unit root and cointegration tests to examine real rates of 16 developed countries. Results are somewhat mixed. Study reveals that findings are sensitive to the employed method that is a very important, result needs to be mentioned.

It is widely accepted that unit root tests have power and size problems and also have difficulty to distinguish non-stationary and very high persistent processes from each other (Faust, 1996). On the other hand unit root tests cannot reveal enough information about persistence of real rates. To have better understanding on stochastic properties of real rates, several techniques other than conventional unit root and stationary tests can be applied.

Unit root tests can only give information whether integration coefficient of a series is one or less than one. However, integration coefficients of 0.1 and 0.9 both represent stationary processes those have very different properties. Fractional integration analysis let cointegration coefficient be any number between 0 and 1, which might be more informative about persistence (Granger and Joyeux, 1980). Pipatchaipoom et al. (2005) test for fractional integration in the U.S. ex-ante real rate for monthly data from 1971 to 2003 and estimate integration coefficient as about 0.8, which is an evidence of long memory and mean-reverting behavior.

On the other hand, in addition to unit root and fractional integration test tests, it might be preferred to estimate a confidence interval for point estimates of integration coefficient to obtain more robust findings. Karanosos et al. (2006) use long span data, 1876-2000, to investigate US real interest rates. They estimate confidence interval for integration coefficient as (0.97-0.99) which implies that series investigated does not have unit root, has mean reversion tendency, and however is highly persistent.

Rapach and Weber (2004) use conventional bootstrap and Hansens’ (1999) grid bootstrap methodologies to construct confidence interval for point estimates of integration coefficient of 13 developed countries interest rates. They also employ two different techniques, namely sub sampling and half-life based on impulse response function to obtain more evidence. Their results show that series are stationary but highly persistent.

Some researchers focus on nonlinear behavior and threshold dynamics in real rates. Threshold model is based on the notion of equilibrium relationship. This model let the series move freely inside a specific interval however, when series is sufficiently far from the equilibrium, an adjustment process occur towards the long-run equilibrium. Koustas and Lamarche (2005) investigate interest rates of G7 countries for 1960 and 2004 periods and claim that for Canada, France and Italy ex-post real interest rates can be modeled with SETAR model.

Christopoulos and Leon-Ledesma (2007) use US series from 1960 to 2001 and divide the series into two. They assert that for the first subsample, that covers 1960-78 periods, ESTR model and for the second sub sample LSTR model give best estimates.

5. Literature on Turkey

There are many studies that investigate the effect of Turkish interest rates on the other economic variables and the Turkish economy. However, literature on stochastic properties of Turkish interest rates is relatively limited (among others, Aydın and Metin-Ozcan, 2005; Alper et al., 2007; Onel, 2005)

Gokmenoglu (2012) investigates stochastic properties of Turkish real interest rates by employing Lee-Strazicich (2003) unit root test. This study reveals that Turkish real rate has three structural breaks those happen in 1994, 2001 and 2006 and when these breaks are taken into account unit root hypothesis can be rejected. After application of


other econometric techniques study concludes that Turkish real rate has mean reverting behavior, is stationary but highly persistent. This finding is in compatible with basic assumptions of several macroeconomic theories and has also policy implications.

6. Conclusion

Stochastic properties of real rate are well documented for developed countries; however for developing countries there are fewer studies. Similarly, there are many studies to investigate persistency of interest rate; however reasons of the persistency have been elaborated lesser in the literature. The affect of stochastic properties of real rates on economic theories, their policy implications and also reasons of persistency are important topics, which have to be analyzed further.

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A Brief Survey of Stochastic Properties of Real Interest Rates

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