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Journal of Global Economics
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Revisiting Fisher Equation in BRICS Countries

Bahmani-Oskooee M1*, Jing-Ping Li2 and Chang T3

1Department of Economics, The Center for Research on International Economics, University of Wisconsin-Milwaukee, USA

2Department of Finance and Banking, Shanxi University of Finance and Economics, China

3Department of Finance, Feng Chia University, Taiwan

*Corresponding Author:
Bahmani-Oskooee M
Department of Economics
The Center for Research on International Economics
University of Wisconsin- Milwaukee, USA
Tel: 4142294334
E-mail: [email protected]

Received date June 14, 2016; Accepted date August 26, 2016; Published date August 30, 2016

Citation: Bahmani-Oskooee M, Li JP, Chang T (2016) Revisiting Fisher Equation in BRICS Countries. J Glob Econ 4:210. doi: 10.4172/2375-4389.1000210

Copyright: © 2016 Bahmani-Oskooee M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Abstract

In this paper we test the Fisher effect by using monthly data from each of the four BRICS countries (i.e., Brazil, Russia, India, China, and South Africa). The results by applying threshold cointegration method reveal that the Fisher effect is valid in all countries except South Africa, implying that nominal interest rates adjust to inflation in the long run.

Keywords

Threshold cointegration; Fisher equation; BRICS

Introduction

According to the quantity theory of money, x% increase in the money supply results in x% inflation, in the long run. If nominal interest rate adjusts to inflation in the long run, then the Fisher effect is said to be in place. This means that both nominal interest rate and inflation rate should be cointegrated in the long run1. Therefore, the Fisher effect basically implies that in the long run nominal interest rate adjusts to inflation rate or expected rate of inflation. Alternatively, the nominal interest rate and inflation rate should have a cointegrating relationship in the long run or the real interest rate which combined the nominal interest rate and inflation rate must be mean reverting or stationary.

Most studies which have tried to test the Fisher effect have either tested for cointegration between nominal interest rate and inflation or have applied different unit-root tests to establish stationarity of the real interest rates. An implicit assumption inherent in standard unitroot tests or standard cointegration methods is the linear adjustment of variables which imply asymmetry effects. However, recent studies in asymmetry analysis which utilize nonlinear models supports the notion that macro variables do have asymmetric effects on each other. For example on the asymmetric effects of U.S. stock market on consumption see Apergis et al. [1]; on the asymmetric effects of exchange rate changes on domestic prices see Delatte [2]; on interest rate pass-through mechanism to deposit rates see Verheyen [3]; on asymmetry S-curve see Bahmani-Oskooee et al. [4]; On asymmetry effects of exchange rate changes on the trade balance see Bahmani- Oskooee et al. [5,6]; On the asymmetric effects of exchange rate changes on the demand for money see Bahmani-Oskooee et al. [7]; On the asymmetric effects of output gap on inflation see Valadkhani [8] and on the asymmetric effects of income and interest rate on housing prices in the U.S. see Bahmani-Oskooee et al. [9].

The evidence from many of the studies mentioned above indicates that the assumption of symmetric adjustments yield poor results as compared to models that deal with asymmetric effects. Since testing for asymmetric effects introduce nonlinear adjustment of variables, the new nonlinear models provide relatively more support for our theoretical expectation. As such we are motivated to apply the Autoregressive Distributed Lag (hereafter, ADL) test for threshold (asymmetric) cointegration in our study. Such test that is introduced by Li et al. [10] is applied to test the Fisher effect in BRICS countries. To that end, data are discussed in Section 4. The model and method are introduced in Section 5. Finally, while Section 6 presents our empirical results, Section 7 provides a summary.

Data

Monthly data over the period January 1996- September 2015 from each of the five BRICS countries (i.e., Brazil, Russia, India, China, and South Africa) are employed to carry out the empirical analysis. All consumer price indices, CPI (2005 = 100) and nominal interest rates are taken from the Data stream. Tables 1 and 2 report summary statistics of both nominal interest rate and inflation rate, respectively, for each country in the sample. We find that Russia and China have the highest and lowest mean inflation rates of 12% and 0.2%, respectively. Russia and China also have the highest and lowest nominal interest rate of 23.15 and 3.83, respectively.

  Brazil Russia India China South Africa
Mean 16.71 23.15 7.51 3.83 9.95
Median 15.80 13.00 6.50 2.70 9.00
Maximum 45.90 160.00 12.00 12.72 21.85
Minimum 7.11 5.25 6.00 0.99 5.00
Std. Dev. 7.43 25.68 1.82 2.84 4.21
Skewness 1.35 2.73 1.01 1.93 0.71
Kurtosis 5.08 11.51 3.07 5.67 2.62
Jarque-Bera 114.93 1009.3 40.31 216.98 21.38
Probability 0.000 0.000 0.000 0.000 0.000
Observations 237 237 237 237 237

Table 1: Summary statistics of nominal interest rate.

  Brazil Russia India China South Africa
Mean 0.005 0.012 0.005 0.002 0.004
Median 0.004 0.008 0.006 0.001 0.0039
Maximum 0.028 0.324 0.047 0.025 0.0241
Minimum -0.006 -0.004 -0.0212 -0.015 -0.011
Std. Dev. 0.003 0.023 0.008 0.007 0.0046
Skewness 1.702 10.449 0.227 0.292 0.477
Kurtosis 9.666 134.81 5.669 3.198 4.371
Jarque-Bera 550.98 175139 73.113 3.736 27.422
Probability 0.000 0.000 0.000 0.154 0.0000
Observations 237 237 237 237 237

Table 2: Summary statistics of inflationrate.

The ADL Test for Threshold Cointegration

As mentioned before, the adopted methodology in this paper is based on the threshold cointegration analysis that is introduced by Li et al. [10]. We begin first with the following specification:

image

Where, nit is the logarithm of the nominal interest rate; πt represents the inflation rate, and ut is the error term. The threshold ADL regression model of Fisher equationtakes the following form:

image

Where, It denotes two indicators, imageand image

In (2) if we adopt the first indicator, then we replace It with image and if the second indicator is adopted, then we replace It with image.In either indicator, Et is the estimated error correction term. Note that the adjustment speed which is measured by βi (i = 1, 2, 3, 4) do vary in this set up which is what makes the threshold ADL model to be different than a standard ADL specification. Here, only two lags of image are included in the regression so that we do not lose too many degrees of freedom. The lag-selection is guided by the partial autocorrelation function (PACF) of image

Two tests are proposed for threshold cointegration by Li and Lee [10]. One is due to Boswijk [11] denoted by BO test under which we test the coefficients of both image in the testing regression. The second test known as BDM test is by Banerjee et al. [12]. Under this test we add lead of πt-1 to the regression so that the asymptotic results are valid in the absence of strict exogeneity. The null hypotheses under both tests are outlined as:

image

In the absence of any rule for adopting Indicator A versus B in our model, the recommendation is to select the adjustment mechanism that is based on a set criterion such as the Akaike Information criteria (AIC) or Schwartz criteria (SC) [13].

Empirical Results and Policy Implications

Brazil image, BO stat:26.169, BMD stat :22.463,AIC=1697.926
Russia image, BO stat:48.034***, BMD stat :43.986***, AIC=2269.081
India image, BO stat:22.547*, BMD stat:16.519*, AIC =697.51
China image, BO stat:17.388, BMD stat:16.827*, AIC =1008.491
S. Africa image, BO stat:12.599, BMD stat:11.742, AIC =888.655

Table 3: Conditional threshold ADL model of fisher equation with indicator A.

Brazil -1.191, 0.153, BO stat :33.684***, BMD stat :31.905***, AIC =1691.003
Russia 0.028, 0.555, BO stat :44.095***, BMD stat :44.023***, AIC =2272.491
India -0.194, 0.148, BO stat :17.524, BMD stat :11.699, AIC =702.326
China -0.029,0.496, BO stat :15.032, BMD stat :14.384, AIC =1010.786
S. Africa 0.000, 0.521, BO stat:15.86, BMD stat :13.053, AIC =885.452

Table 4: Conditional threshold ADL model of fisher equation with indicator B.

Our findings imply that if monetary policy results in 5% inflation in BRICS, the nominal interest rate in the economy of those 4 countries (Brazil, Russia, India, and China) would eventually also increase by 5%. Therefore, a change in the money supply shouldn’t have an effect on the real interest rate. If the real interest rate isn’t affected, then all changes in inflation must be reflected in the nominal interest rate, which is exactly what the Fisher effect claims.

Summary and Conclusion

The Fisher effect asserts that monetary policy that may result in x% inflation, eventually will push the nominal interest rate up by x%, leaving the real interest rate unchanged. We employ the ADL test for threshold cointegration recently introduced by Li et al. [10] to verify the Fisher effect in BRICS countries. The Monte Carlo simulations of Li et al. [10] shows that their test do not suffer from low power and have good size properties. Our empirical results support Fisher effect in BRICS countries, except in South Africa.

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