Discovering the Link between Algerian Inflation and Inflation Uncertainty Using Markov Switching Model

Inflation appears as a first challenge for recent economy performance in Algeria. This study uses the Markov Switching model to examine the relationship between Algerian Inflation and inflation Uncertainty using quarterly data for the period 1974-2014. The main result supports the Friedman-Ball hypothesis for the Algerian case that there is a positive association between the level of inflation and inflation uncertainty. This means that the increase in the level of inflation in Algeria leads to a rise in inflation uncertainty. DOI: 10.5901/mjss.2015.v6n4s3p241


Introduction 1.
The first half of the 1970's is characterized by the continuing stability of the Algerian inflation rate oscillating between 3 to 6%. However from 1975 to 1988, inflation registered high trend with an average annual rate of 9.96%. This peak can be explained by many reasons, mainly the adaptation of new Algerian exchange rate regime that has become based upon a basket of 14 currencies 1 instead of the strict begs. The second reason behind the high inflation rate during 1975-1988 is within the core inflation in itself, as measured by the dominance of food products that contributed up to 50% to the total increase in imports due to the expansion of trade openness.
As the Algerian inflation rate has been growing steadily since the 1990s, price stability became actually the main challenge of the bank of Algeria as it has a great impact on the Algerian economy and the consumer purchasing power. In fact, the average increase of the CPI turned around 18.55% in the 90's, whilst in the 20's it witnessed its lowest average at 3.2%. From the beginning of the second decade of the new millennium, inflation rates increased to ranges between 6 to 8.5% to such an extent that it has become necessary for policy makers to grasp inflation trends with their uncertainties. This study helps track inflation uncertainty at any time horizon letting policymakers decide to disinflate or increase inflation rate on local economy by capturing switching regimes of inflation uncertainty; See more Ball and Cecchetti´s (1990), Evans and Wachtel (1993), Kim and Nelson (1999), Castillo and Humala (2012). The goal of this study is to estimate a time-varying Markov Switching Model of inflation producing measures of inflation uncertainty in Algeria. In order to bring out the evolution over time of monetary policy, we shall be using the Markov Switching Model to examine the relationship between Algerian inflation and inflation uncertainty upon quarterly data for the period 1974-2014 The rest of the paper is organized as follows. In section 2 we examine a Literature Review on the subject, followed by Section 3 that presents Model and Methodology. Section 4 draws on results and discussion and Section 5 contains the main conclusion.

Literature Review 2.
Economics Research has drudged for many decades to examine inflation topics, such as the main determinants of inflation; (see Dornbusch et al. (1990), Click (1998) , Arize et al.(2004), Klein and Kyei (2009), Kandil and Morsy (2011), Ibrahim A. O and Akinwande A, (2010)). Other previous studies highlighted the relationship between inflation and economic growth. Baroo (1991), Bruno and Easterly (1998), Khan and Senhadji (2001), Nicholas (2009)… The relationship between Inflation and inflation uncertainty is grasped from many angles. Okun (1971) and Friedman 1977, Ball 1990 argued that high inflation creates more uncertainty about future inflation. Furthermore, many empirical investigations have drawn upon the positive side of the relationship between inflation and Inflation uncertainty. See: Fisher (1981), Taylor (1981), Ball and Cecchetti (1990), whilst, On the contrary of Friedman Hypothesis, Pourgerami and Maskus (1987) found a negative relation between inflation and inflation uncertainty.
Between the two arguments, Holland (1995) demonstrated that inflation raised inflation uncertainty in the United States and increased uncertainty about future monetary policy while deflation would not affect inflation uncertainty Hwang (2001) in similar study using ARFIMA-GARCH-type models over monthly US inflation for the period 1926 -1992, pointed that inflation affects negatively but slightly its uncertainty, whereas the latter affects the inflation insignificantly Fountas et al (2004) investigated the relationship between inflation and inflation uncertainty during the period 1960-1999 in six European Union countries. They found rising inflation uncertainly to cause significant inflation in these countries except for Germany.
Özcan Karahan (2012) examined the relationship between inflation and inflation uncertainty in Turkey from 2002 to 2011 using ARMA-GARCH model and Granger causality tests. His result confirmed Friedman-Ball hypothesis that inflationary period is always followed by high inflation uncertainty Many empirical studies used GARCH, ARCH family models, and ARIMA to check Friedman and Friedman-Ball hypotheses; Thornton (2006Thornton ( ,2007Thornton ( , 2008 for India, emerging markets and Argentina respectively; Qayyum (2006) for Pakistan; Brunner and Hess (1993), and Grier and Perry (1998) for G-7 countries, Jiranyakul and Opiela (2010) in the ASEAN-5 economies ….. Ricketts and Rose (1995) argue in favor of Markov Switching Models for the establishment of an elastical association between inflation and inflation uncertainly for a group of G7 countries. Simon (1996) concluded that inflation presents a good response to inflation uncertainly and output gap by applying the methodology of Markov-switching models to describe the inflation process in Australia.
Jin Kim (2004) discovered the link between inflation and its uncertainty in an empirical comparative study between Hamilton's Markov-switching heteroskedasticity and autoregressive conditional heteroskedasticity over the period 1958:1-1990:4. He found a strong relationship between studied variables when higher inflation is associated with higher long-run uncertainty.
Bia owolski et al (2005)  Castillo and Humala (2012) illustrated the link between inflation and inflation uncertainty in Peru using Markov regime-switching heteroskedasticity model and highlighted the fact that high inflation always goes with periods of short and long-run high inflation uncertainty. We shall present hereafter the model and the methodology to deal with this relationship. • Transition probabilities should satisfy the normal stochastic constraints, And A probability distribution in each of the states, Where denotes the observation symbol in the alphabet, and the current parameter vector. The Following stochastic constraints must be satisfied.

And
If the observations are continuous then we will have to use a continuous probability density function, instead of a set of discrete probabilities. In this case we specify the parameters of the probability density function. Usually the probability density is approximated by a weighted sum of M Gaussian distributions , Where: =Weighting coefficients =mean vectors =covariance matrices Should satisfy the stochastic constrains, And • The initial state distribution, where, Therefore, we can use the compact notation To denote an HMM with discrete probability distributions, while:

Results and Comment 4.
Much econometric estimations, which use the least square method (GLS), produce spurious regression and their statistics indicate false and bias elasticity (Granger and Newbold, 1974)). In this paper, Augmented Dickey-Fuller (1979 and  tests drawn from the stationary tests represented in figure 1 below, enable an acceptance at a level that signifies integration of the variables at order 1.

Figure 1: Unit Root Tests
Here, we try to check the significant association between inflation and it's uncertainly using Markov Switching (MS) of discrete hidden states according to an unobserved process, Hamilton 1989 andBia owolski (2005).
Before illustrating the results from the Markov Switching model, it would be preferable to run a Markov simple-twostate model to show the static ex-post probabilities between Algerian Inflation and inflation Uncertainty. The mathematical representation of the equation is: e 2 t = + CPI t+1+ Where e 2 t is the Markov switching exponential Standard error, CPI is consumer price index, t is time, and are parameters.
The estimation result show that the inflation Uncertainty coefficient is greater than 1:(1.06) with p-value lower than 0.05 which can be taken as an evidence to accept the alternative hypothesis, meaning that changes in inflation rates cause the inflation uncertainty to vary with great discrepancy.
In this case that characterizes time series behaviors of inflation and uncertain inflation, we can apply the Markov Switching model as it offers more advantages through two regimes  Table 01 shows that the variance for all series is close to zero. Furthermore, we observe the mean in two regimes are 0.980034 and 0.975176 respectively. On the contrary, variance of the second regime is higher than first regime, so, Friedman assumption is accepted and variability of inflation uncertain in the second regime is more persistent compared to the first regime. Regime transition Results show the stable persistence with small convergence between two regimes. During the first half of 1980s characterized by repetitive devaluation of Algerian Dinar against a stronger dollar and during Algeria war since 1990, we note high level of inflation associated with higher variance of inflation as evidenced by the Ball-Friedman hypothesis, (See Figure 2). The first half of the 1970's is characterized by the continuing stability of the Algerian inflation rate oscillating between 3 to 6%. However from 1975 to 1988, inflation registered high trend with an average annual rate of 9.96%. The average increase of the CPI turned around 18.55% in the 90's, whilst in the 20's it witnessed its lowest average at 3.2%. From the beginning of the second decade of the new millennium, inflation rates increased to ranges between 6 to 8, 5. This highvolatility and mass inflation instability during five decades allowed us to focus on the Markov-switching models for modeling inflation pressure. Our results confirm that inflation is reasonably well delineated within uncertainly inflation in Algeria.