RE-EXAMINING THE MEAN REVERSION OF INFLATION RATE IN ECOWAS

DRAMA Bedi Guy Hervé¹

¹Department of Economics, University Peleforo Gon of Korhogo, France

Keywords:Inflation rate ECOWAS Mean-reversion PANIC The Pooled MSB Panel unit roots.

ARTICLE HISTORY: Received:13 April 2018. Revised:30 April 2018. Accepted:2 May 2018. Published:4 May 2018.

Contribution/ Originality:This study is one of very few studies which have investigated whether inflation series is mean-reverting in Economic Community of West African States from 1985 to 2015. This study originates new formula such as first and second generation panel unit root tests to evaluate the stationary properties of the inflation rate for ECOWAS. The paper's primary contribution is finding that the rate of inflation in ECOWAS is a stationary process. This study documents the originality of this article.

1. INTRODUCTION

Since the founding article of Nelson and Plosser (1982) which studied the characteristics of integration of important macroeconomic variables of the United States, the study of the characteristics of chronological series of macroeconomic variables has become a central field of research in economy. Unfortunately, the results are ambiguous in empirical literature.

In particular, the analysis of the process of unit root in the principal macroeconomic aggregates, such as joblessness rate, the real exchange rate, the real gross national product (GNP) per capita, inflation, the energy consumption or the production, is important since they throw light on the validity of relative macroeconomic theories. For example, the stationarity of the real gross national product per inhabitant, of the joblessness rate and the real exchange rate backs up the theories of convergence of stochastic income, of the natural rate of joblessness and of parity of purchasing power, respectively. There are plenty applied studies about these theories.

In this article, we are interested in the temporal characteristics of the inflation rate- in the case of ECOWAS- that is one of the main macroeconomic variables more drawing the attention of academicians in economy. The Fisher effect, the traditional model of assets’ valuation, the accelerationist hypothesis, the monetary policies of control of the growth of the money supply, the model of Phillips curves and the joblessness hysteresis are a few of research fields which have to do with inflation. Moreover, the following results lead economists to probe into the characteristics of integration of the inflation rate.  

Firstly, owing to the fact that inflation largely influences the decisions in terms of expenditure and saving, the inflation rate is generally taken into consideration in the conduct of monetary policy. The central banks are based on their knowledge of temporal characteristics of inflation to lead a monetary policy and target the inflation rate because the cost of disinflation is different when inflation rate shows I(0) or I(1) behaviour. As Arize et al. (2005) inflation is unpopular because of the real cost it imposes on economy and society, consequently, the level of inflation is generally taken into account in the conduct of monetary policy. The non-stationary inflation rate implies the inflationist shocks have a permanent effect, and then a high cost for disinflation policies. However, the stationary inflation rate will bring about a low cost for monetary authorities in the conduct of monetary policies (Cecchetti and Debelle, 2006). Thus, knowledge about the characteristics of integration of the inflation rate belongs to the decision makers in order to control inflation.

Second, “inflation is typically regarded as a key variable in many economic models, whose validity hinges critically on whether inflation is I(0) or not” (Basher and Westerlund, 2007).  For example, the Fisher effect is one of the most reliable concepts in finance theories and it validity depends on the existence of non-stationary inflation rate. The Fisher equation suggests that inflation rate should follow I(1) process and need to be integrated with the nominal interest rate in order for the real interest rate to be stationary. In addition, another main macroeconomic concept such as the expectations augmented Phillips curve model, where wages and prices share a long-run relationship, requires non-stationary inflation rate. Furthermore, the accelerationist hypothesis indicates non-stationary inflation rate. According that theory (accelerationist hypothesis), the government policy makers have to keep high level of inflation in order to maintain unemployment level below its natural rate. In addition, the rational expectation behaviour developed by Cagan (1956) stipulates that a stable money growth is followed by a stationary inflation rate unless there exist puzzles. In other words, rational expectations hypothesis suggests that stable growth of money supply implies stationary inflation rate.

Thirdly, the stationary of inflation rate is equally important in the selection of the correct economic modelling. For example, to evite wrong political decision a VAR model can be utilized in the case of stationary inflation rate to make reliable estimation. However, it is more practical to study non-stationary variables by applying a cointegration model or vector error correction (VEC) model see (Arize et al., 2005). By taking into account all these above-mentioned reasons, this study aims at contributing to literature under two aspects. Firstly, we use data about the inflation rate to analyse its characteristics in certain West African countries. Secondly, we apply second generation panel unit root recently developed. The remaining part of the paper is organised as follows. The second section is a literature review about inflation. The third section comprises the panel unit root procedure. In the fourth section, we describe the data and the variables. The fifth section presents the principal results. At last, in the sixth section, we suggest few political implications followed by the concluding part.

2. LITERATURE REVIEW

As Narayan and Narayan (2010) have indicated it, “comparatively to the documentation about unit root tests in the real gross national product and the real exchange rate, literature on the hypothesis of unit root applied to inflation rate is rare”. However, literature is very rich. We can classify them in seven bits. 

The first step of the studies uses some unvaried conventional unit root tests to prove if the inflation rate is stationary or not. For example, Lai (1997) who used the modified Dickey-Fuller test, developed by Park and Fuller (1995) on the inflation rate of the G7 countries noticed that the inflation rates were stationary. In 2005, inflation rate stationarity of 93 inflation rates in the world have been examined by Charemza et al. (2005). They applied Dickey and Fuller (1979;1981) conventional increased and have compared the results to those obtained by taking into account the symmetric stable innovations. The results showed that there is significant change in favour of the non-stationary if innovations are treated as some samples of stable symmetric paretian distribution with an infinite variance. The implementation of Dickey and Fuller unit root (1979, DF below) in the analysis of the stationary of inflation rates in 40 countries, Ball et al. (1990) showed that the null hypothesis of non-stationary could not be rejected for 38 countries over 40. The integrated nature of inflation rates in United States has been also analysed by Cook (2005) using DF and the unit root tests based on the rank. The first test indicated the rejection of the null hypothesis of the unit root, whereas this latter was not.

The second step of the studies performs the panel unit root tests method. Lee and Wu (2001) for example, used a bootstrap version of the panel unit root of Im et al. (2003) with seemingly unrelated approach of Taylor and Sarno (1998) in the analysis of the stationarity of inflation rates in 13 countries of the Organisation for Economic Cooperation and Development (OECD). They found overwhelming proof of average reversion. Culver and Papell (1997) analysed the stationary of inflation rates in 13 countries of OECD by using unvaried unit tests and some unit root tests. The results of the ADF, KPSS (Kwiatkowski et al., 1992) and sequential break tests demonstrated that in most countries covering by the study, the inflation rates followed the unit root process. However, the results of the panel data provided some reliable proof against the non-stationary. Another researcher, Osterholm (2004) showed the stationary of inflation rates in the United Stated of America by using three unit root tests, namely the IPS unit root test Im et al. (2003) the MADF Taylor and Sarno (1998) and the Johansen (1988) test of the likelihood report. Tsong et al. (2012) found reliable proof of the mean reversion of inflation rates of 19 OECD countries. For their investigation they utilise the panel unit root tests that allow a transversal dependence and the optimal test of the covariable point. In the same order, Otero (2008) using the unvaried KPSS unit root test and Hadri (2000) analysed the stationary of inflation rates in 13 OECD countries. The results of the KPSS unit root test generally showed that the inflation rates of OECD countries could be described as the I(1) process, whereas the Hadri unit root test implied the stationary.

The third step of the studies takes into account the structural ruptures during the unit root process. The unvaried unit root tests that do not take into account the structural ruptures generally indicate that the inflation rates are non-stationary, whereas the unit root tests with structural ruptures generally imply that the inflation rates are stationary. Caporale and Paxton (2013) for example, studied the stationary of inflation rates for 5 Latina American countries by using the standard ADF unit root test and the test of the Bai multiple structural rupture and Bai and Perron (1998;2003) cover the period of 1980-2004. The results of the ADF unit root test revealed that the stationary was only obtained for three countries. However, when the structural ruptures have been authorized, the five countries turned towards some stationary inflation rates. Benati and Kapetanios (2002) found that the unit root could strongly be rejected for most of the series by using a unit root test newly developed allowing until m of structural breaking up to the 23 inflation series of 18 countries. Levin and Piger (2003) used some Bayesian and classical econometric framework to characterise the dynamic behaviour of the inflation rates for 12 industrialised countries by estimating an unvaried autoregressive model for each series and by considering the possibility of structural rupture. The results show that permitted rupture induced the stationary in the inflation rates.

In addition, there also exist some studies utilizing unit root tests with structural ruptures. Narayan and Narayan (2010) for example, investigated if the inflation rate of 17 OECD countries could be modelled as a stationary process using some unvaried KPSS unit root tests and of panel allowing in the maximum five structural ruptures developed by Carrion-i-Silvestre et al. (2005). The results unvaried tests of the KPSS showed that the inflation rates were stationary in 10 of the countries. Moreover, the test of the KPSS panel provided some reliable proof favourable to the stationary of inflation rates in the panels composed of countries that have been declared non-stationary by unvaried tests. To some comparison ends, Narayan and Narayan (2010) also applied the LM unit root test of Im et al. (2005) and obtained some strong proof against the non-stationary. Basher and Westerlund (2007) used a group of unit root tests on the data of Culver and Papell (1997). They noticed that the stationary of the inflation rate was independently maintained of the transversal dependence and the structural changes.

Romero-Avila and Usabiaga (2009) used three-panel unit root tests carried out by Smith et al. (2004); Hadri (2000) and Carrion-i-Silvestre et al. (2005) for 13 OECD countries. However, the outcomes of these tests were ambiguous. Hadri (2000) demontrated a non-stationary whereas (Smith et al., 2004) provided evidence of unit root. However, the test of the KPSS panel shows strong proof of joint stationary. In addition, in this section, there exists a group of studies applying unvaried unit root tests and LM allowing some structural ruptures as in our study. For example, Im et al. (2010) made unvaried panel unit root tests and LM with two structural ruptures to test the stationary of inflation rates in 22 OECD countries. The results of the unvaried LM test indicate that 16 countries out of 22 have some stationary inflation rate. They afterwards used the LM panel unit root test and obtained some results against the non-stationary. Another study implementing the LM unit root belongs to Lee and Chang (2008). They examined the stationary of inflation rates in 11 OECD countries and in Asia and presented some results to support the stationary.

In the fourth section, we can view other studies conducted by a non-linear approach analysing the stationarity of the inflation rates. Henry and Shields (2004) for example, apply the Wald bootstrap approach developed by Caner and Hansen (2001) applied to United States inflation rates, Japan and the United Kingdom. The results imply that the inflation rates in the United Kingdom and in Japan were described as a unit root with threshold two regimes process. However, for the United States, the threshold was insignificant and the shocks on the inflation seem to be infinitely persistent. In the same order, the works of Ho (2009) depicted evidence of unit root process covering 19 OECD countries using the non-linear statistics IV that takes into account the transversal dependence. Another researcher, Zhou (2013) used the unit root test that allows the non-linearity to explore the stationarity of inflation rates in 12 European countries. The non-linearity has been observed in 8 countries over 12 and, among them, 6 countries seemed to have a non-linear stationary in their inflation rates. Arize (2011) applied some non-linear and linear unit root tests, such as the DF-GLS test developed by Elliot et al. (1996) the classic ADF unit root test, as well as the KSS non-linear unit root test of Kapetanios et al. (2003) to the inflation  rates of 34  African countries. The DF-GLS, ADF and KSS tests have not rejected the null hypothesis of stationary in respectively 17, 13 and 25 cases. Gregoriou and Kontonikas (2009) used ADF (Ng and Perron, 2001) and the non-linear ADF unit root tests Kapetanios et al. (2003) on the inflation rates of 5 OECD countries adopting the inflation targeting. The results of the ADF unit root test showed that the null unit roots could not be rejected in all the countries. Moreover, the NP test showed that the null hypothesis of unit roots could only be rejected at the level of 5% significant in two countries. However, the results of the non-linear ADF test implied a unit root process in all cases.

The fifth section of the studies analyses the stationary of inflation rates as a necessary first step while testing Fisher hypothesis. To name a few, Malliaropulos (2000) applying the ADF unit root tests and Zivot and Andrews (1992) to the inflation rate by testing Fisher hypothesis for the United States, got some favourable results to the non-stationary. However, the ZA test indicated that the inflation rate was stationary. Moreover, Atkins and Chan (2004) noticed that the nominal interest rate and the inflation rates in Canada were stationary around a determinist tendency with two ruptures in the framework of Fisher hypothesis. In addition to that, while searching the validity of the Fisher effect in the United States, Crowder and Wohar (1999) applied the ADF unit root test and noticed that the inflation rates were not stationary. Clemente et al. (2004) who used a unit root test with ruptures of inflation rates of the G7 countries to test the validity of Fisher hypothesis, had proof that the inflation was represented by a stationary variable of broken tendency.

The sixth section of the studies uses the fractional integration analysis to assess the stationarity of inflation rates. Use a fractionated analysis of integration to the inflation rates of 50 developing countries, Arize et al. (2005) for example, determined that the inflation rate was non-stationary in most the concerned countries. Bos et al. (1999) used a fractional integration test to the inflation rates of the G7 and got some results to the support of the long memory or the unit root process. In another article, Bos et al. (2001) using a fractionnaly integrated moving average model, found that the after war American inflation had a long memory, with integration order around 0,3. Gadea et al. (2004) used DF, PP, NP, and the KPSS unit root tests for the persistence of inflation rates by fractionated integration. The results of the DF, PP and NP unit root tests published the null hypothesis of unit root in all the countries.

At last, the last section consists in some studies analysing the inflation or the convergence of price levels between a group of countries by examining the stationarity of inflation differentials or by testing the relations of co-integration between the inflation rates. The convergence holds if the inflation rates are stationary. Holmes (2002) for example, using the monthly data over the period 1972-1999 studied the strong and weak convergence between the principal economies of EU. The univaried ADF unit root test demonstrated the null hypothesis of unit root has been rejected for only a few cases, whereas the t bar test suggested by Im et al. (2003) implied the stationary in its ensemble. Drine and Rault (2006) who tested the inflation convergence between the Euro area and central and oriental Europe, found some strong proof of convergence thanks to the unit root tests of the LM panel. Das and Bhattacharya (2004) tried to examine the convergence of prices in the Indian regions by using the panel unit root tests taking into account the transversal dependence. The results laid bare the convergence of the levels of the relative prices between the different regions of India.

3. PANEL UNIT ROOTS

To study the average reversion of the inflation rate in the African countries, we used several unit root tests. We divide these tests in two groups, namely the first generation of unit root tests and the second-generation unit root tests. The first generation of unit root tests applied in this study comprised the LLC test (Levin et al., 2002) the IPS Im et al. (2003) and the Hadri (2000). The second-generation tests are the two PANIC tests (Bai and Ng, 2010) and Pesaran (2007). The main difference between two generations of tests is in the hypothesis of cross independence. First generation methods suppose that all cross-sections are independent and second-generation methods relax this assumption. And the positive side of the PANIC method compared to the others second generation methods is that PANIC test main objective is to exploit the factor structure of panel data to fragment panel unit root tests, and also univariate counterparts, with advantage size and power characteristics. More precisely, its exploits the contemporaneous correlation between cross-section units to split the process in two parts: a common and idiosyncratic component.

First Generation: Cross-Sectional Independence

The basic model underlying these tests is:

The first test included in the first generation of unit root tests is the LLC test of Levin et al. (2002). This test uses the following adjusted t statistics:

Another test that we keep in the category of the first generation is the IPS test f (Im et al., 2003) that uses the statistics tˍ standardized bar based on the movement of the distribution of Dickey-Fuller:

Contrary to the precedent tests of the first generation, the test proposed by Hadri (2000) lays on the stationary null hypothesis. It is an extension of the test of stationary developed by Kwiatkowski et al. (1992) in the context of chronological series. Hadri proposes a multiplying test of Lagrange based on the residue for the null hypothesis than the individual series Y_i,t  (for i = 1,K ,N) are stationary around a determinist level or around a deterministic trend, with regard to the alternative of a unit root in the panel data. Hadri (2000) considers the two following models:

Second Generation: PANIC Pooled Tests

In their article published in 2004, Bai and Ng showed that test

See Bai and Ng (2010) for details.

Jang and Shin (2005) studied the characteristics of Pa,b for p = 0 by some simulations. But Bai and Ng (2010) proposed a theorem that provides the limitative theory for p = -1 and p = 0. They show that the t tests of the autoregressive coefficient put in common in the idiosyncratic errors are asymptotically normal. The convergence is for N and T tending to the infinite conjunctly with N / T → 0. It is therefore about a common limit according to Phillips and Moon (1999). The Pa and Pb are the analogous of t_a and t_b of Moon and Perron (2004) except that; (a) the tests are focus on some PANIC residuals and (b) the method of data’s “de factorization” is different from the method of Moon and Perron (2004).When p = -1, the parameters of adjustment used in P_a,b  are equally different from t_a,b of Moon and Perron (2004).

3.1. The Pooled MSB   

An important characteristic that distinguishes the stationary processes from the non-stationary processes is that their sampling moments require some different normalisation rates to be asymptotically limited. In the unvaried context, a simple test focused on this idea is the test of Sargan and Bhargava (1983). Stock (1990) issued the modified test of Saran and Bhargava (MSB test) to allow

(see, Bai and Ng (2010) for details) under the null hypothesis and generated at zero under the alternative. Thus, the null value is rejected when the statistics is too small. As Perron and Ng (1996) show it and Ng and Perron (2001) the MSB has a similar power to the ADF test of Said and Dickey (1984) and the Phillips-Perron test developed by Phillips and Perron (1988) for the same method of tendency. A unique characteristic of the MSB is that it doesn’t necessitate an estimation of ρ, which allows us to afterward assess the differences of power between the tests are due to the estimation of ρ. This motivates the test of non-stationary of simple panel following the idiosyncratic errors called panel PMSB test. Let us consider that p = 0; 1  got from the PANIC test. For e the statistics of the test is defined as follows: 

3.2. The MP Tests

The autoregressive coefficient ρ can also be estimated from data in levels as follow:

3.3. Another Second Generation Tests: Pesaran (2007)

As far second generation test, Pesaran (2007) proposes a test where augmented regressions of Dickey-Fuller (ADF) are augmented with the average transversal of delayed levels and the first differences of individual temporal series. In this way, the common factor is represented by the cross-sectional average Y_i,tand the shifted values. The Pesaran test uses the Cross-sectional ADF statistics (CADF), which are given below:

4. DATA AND VARIABLES

We use the annual index of prices to consumption (base =2010) for 15 African countries namely : Benin, Burkina Faso, Cabo Verde, Côte D’Ivoire, Gambia, Ghana, Guinea, Guinea Bissau, Liberia, Mali, Niger, Nigeria, Senegal, Sierra Leone and Togo over the period 1985-2015. The inflation rate is calculated as the first logarithmic difference of the index of prices to consumption1 . The data stem from the indicators of development in the world published by the World Bank (2016). The analyzed countries and the duration are provided by the data availability. 

Figure-1. Inflation rate evolution in ECOWAS

Source: Own computation

Figure 1 shows the evolution of the inflation rate for ECOWAS and its countries and the tables 1a and 1b corresponding respectively show the descriptive statistics and the unidirectional tabulation. As we see it: (i) the evolution of inflation rates in most of the ECOWAS countries is similar except in Guinea Bissau, Nigeria and in Ghana; (2i). Most of these countries had several times 50% inflation (see the table in a unique sense). (3i) many countries reach their maximum inflation level in 94. Indeed, this date corresponds of the devaluation year in Africa. This devaluation reached 07 West African countries. The concerned countries were Benin, Burkina Faso, Côte d’Ivoire, Mali, Niger, Senegal and Togo; (4i). Our results of Jarque-Bera’s test indicate that the ensembles of data are not normal in ECOWAS; since the corresponding p value is inferior to 5%.

Table-1a. Summary Statistics of Data set

Source: Own computation.

Table-1b. One-way tabulation of Inflation

Source: Own computation

5. RESULTS AND DISCUSSIONS

The first generation panel unit roots tests results applied to ECOWAS are illustrated in table 2 bellow. In applying these tests, the dependence between series has not been taken into account. The LLC and Breitung tests provide proofs to reject the null hypothesis of the base unit roots to 1% level. However, they (the LLC and Breitung unit roots tests) are criticized for their process hypothesis of common unit roots in the namely countries, the entire cross section have a characteristic of unit root. The IPS unit root goes further and softens this hypothesis by supposing an individual unit roots process. As we see it, the IPS unit tests (Fisher-ADF and Fisher-PP) provide proofs to reject the null hypothesis of unit roots for the ECOWAS countries. Contrary to the precedent tests, the Hadri unit root test rejects the null hypothesis of stationary; it is important to note that the autocorrelation leads to a severe height distortion in the Hadri test leading to an excessive rejection of the null hypothesis. Thus, based to the first generation tests, inflation rate in the Economic Community of West African States is stationary.

Table-2. First Generation Tests

Source: Own computation

The table 3 gives the results of the Moon and Perron tests with the A, B and C models as well as the nonstationarity in idiosyncratic and common components (PANIC) (Bai and Ng, 2010) and panel pooled tests. A does not suppose any deterministic component. B supposes a constant and allows a fixed effect model. C allows a constant and a trend. Since both (First and Second MP t-stat) reject the null hypothesis, we conclude the stationary of the inflation. Thus, according to the first and the second of Moon and Perron tests, the inflation rate is a mean reversion process in ECOWAS.

Table-3. PANIC Test

Source:Own computation

To make our results more robust, we completed our investigation with another second generation test depicted in table 4 bellow. In addition, as we see, Pesaran (at lag 0, 1 and 2) test in model 1 and model 2, support the mean reversion of inflation rate in the Economic Community of West African States (since they reject the null hypothesis of unit root at 5%).

Table-4.CIPS Test on Inflation

Source: Own computation

6. CONCLUDING REMARKS

The empirical test of the unit root characteristics of the inflation rate is necessary to know the behaviour of economic cycles. Moreover, this would equally allow understanding the long and short-term impact of macroeconomic policies on the consumption of lasting goods. For this, we used a group of unit root tests to evaluate the characteristics of the stationary of the inflation rate for ECOWAS. We applied the first and second-generation tests over the 1985-2014 periods.

Our analysis indicates that the null hypothesis of the unit root problem in the series of inflation rate is rejected by the LLC, Breitung, Fisher and IPS unit root tests, (first generation tests). For the 2010 PANIC tests and the Pesaran unit root test, the inflation rate as second-generation tests is a mean reversion process.  

Our results can have practical implications for econometric modelling as well as for the political decision makers in the formulation the inflation policy to back up the economic growth in certain West African Countries. Our analysis in the major part shows that the inflation rate is stationary around a deterministic trend in ECOWAS. This implies that: (i) the fluctuations of the inflation rate have a transitory effect. (ii) The inflationist shocks do not have lasting effects on ECOWAS inflation rates. Consequently, the monetary authorities of these countries would implement some disinflation policies cheaper than those of countries having non-stationary inflation rates. Moreover, the tendentious stationary of the inflation rate indicates that the inflation rate will find again its trend in time and it could be possible to foresee the future movements of the inflation rate according to its past behaviour. (iii) Since the inflation rates are stationary around a trend, only the important shocks as the governmental policies aiming at modifying the fundamentals will have lasting effects on the inflation trajectory, but the shocks only provoke some short-term deviations around a deterministic trend. In this case, the global demand policies cannot be overestimated (Lee and Wu, 2001) and the administrative policy of a government should not be to adopt some excessive interfering targets.   

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