64 

© 2020 Adama Science & Technology University. All rights reserved 

Ethiopian Journal of Science and Sustainable Development  

e-ISSN 2663-3205                                                                           Volume 7 (2), 2020 

Journal Home Page: www.ejssd.astu.edu.et  ASTU  

Research Paper 

Comparative Analysis of Inflation Dynamics of Three African Countries: Ethiopia, 

Kenya and South Africa 

Desa Daba Fufa 

 

Department of Statistics, College of Computing and Informatics, Haramaya University, P.O. Box138, Dire Dawa, Ethiopia 

Article Info  Abstract 

Article History: 

Received 3 February 

2020 

Received in revised form 

22 April 2020 

Accepted 17 Jun 2020 

 

 This paper examines a comparative view of the inflation dynamics in three African countries. 

The study used monthly data from January 2007 to April 2018. To achieve the objectives, the 

study was deployed varieties of econometric methods. The exploratory analysis reveals that 

inflation of the sampled countries exhibits similar trends over the long run. The Johansson 

Co-integration test result evince that inflation, oil price and exchange rate of Ethiopia and 

South Africa had a long run relationship. Exchange rates had significant positive effects on 

inflation dynamics of both countries while world oil price contributes positively in Ethiopia 

but negatively in South Africa. In the short run, inflation in Kenya was found to be a sign of 

Ethiopia’s inflation. Likewise, in South African inflation was an indicator of the inflation in 

Kenya whereas inflation in Kenya and Ethiopia could not predict inflation would occur in 

South Africa. Furthermore, the outcome of the impulse response function demonstrates that 

exchange rates and oil price shocks affected inflation dynamics of the sampled countries at 

different stages both directly and indirectly. In the short run, shocks to inflation have an 

interaction effect across the selected countries. The findings also report that world oil prices 

are not equally contributes for inflation dynamics in the sampled countries. 

Keywords:  

Co-integration  

Granger causality  

Inflation dynamics  

Impulse response function 

Interaction effect  

1. Introduction 

Inflation refers to the continuous upsurge in the 

aggregate level of prices of goods and services in an 

economy (Romer, 2012). It is clearly known that 

different economies in different parts of the world 

experience inflation. The severity level may differ from 

one country to another due to a number of historical 

country-specific causes. Majority of developing 

countries experienced elevated inflation. Even if 

Ethiopia has had a historically low inflation rate 

compared to other developing countries, in recent time 

it is experiencing a high inflation rate. High inflation is 

often linked with lesser growth and financial crises. As 

Al-Shammari and Al-Sabaey (2012) stated, emerging 

                                                           


Corresponding author, e-mail: dabadesa6@gmail.com 

https://doi.org/10.20372/ejssdastu:v7.i2.2020.197 

countries are disposed to currency and financial crises 

more than the industrialized countries. The surge of 

price is further associated with non-proportional 

production and consumption of goods and services. This 

can be due to insufficient investments and steady 

population growth.   

High inflation can be a serious problem for many 

economies worldwide. Currently, majority of the 

African countries like Ethiopia, South Sudan, 

Zimbabwe, Kenya, etc. experienced elevated inflation 

(Durevall and Sjö, 2012; Gudina et al., 2018; Okara and 

Mutuku , 2019). Knowing the causes of soaring inflation 

and it’s the dynamic nature of inflation has always been 

http://www.ejssd.astu.edu/
https://doi.org/10.20372/ejssdastu:v7.i2.2020.xxxxxx


Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

65 
 

a key concern of academics and monitory policymakers 

around the world. 

A large body of literature has documented the 

challenges posed by spiraling inflation on the countries’ 

economy and factors that contribute to rising inflation 

dynamics (Chou and Tseng, 2011; Durevall et al., 2012; 

Misati et al., 2013; Abounoori et al., 2014; Brahmasrene 

et al., 2014; Kargi, 2014; Christine et al., 2015; 

Habtamu, 2015; Kavila, and Le Roux, 2016; Anh, et al., 

2017). These researchers have identified some driving 

forces of inflation: world food prices, world energy 

prices such as oil price, domestic food prices, excess 

money supply, exchange rates, and domestic 

agricultural supply shocks. Durevall and Sjö (2012) 

found that inflation dynamics in Ethiopia and Kenya 

were driven by similar factors; of which world food 

prices and exchange rates had a long-run impact, 

whereas money growth and agricultural supply shocks 

had short-to-medium run effects.  

Even though numerous researches have been done, 

there has been no agreement on the sources of high 

inflation experienced in recent years and no study 

scrutinized the interaction effects of inflation dynamics 

across the countries which are the focus of this study. 

Inflation dynamics across countries may move together 

due to some common shocks (for instance world oil 

price shock, demand and supply shocks) and they may 

have interaction effects on each other if countries have 

integrated market system, economic and geographical 

ties (Eickmeier and Kühnlenz, 2018). Economic and 

trade integration in Africa is not a recent phenomenon. 

Particularly, many of the economic and trade integration 

agreements between Ethiopia and Kenya were signed at 

various times, and they have warm trade relations. For 

example, the 2017 import and export data from the 

Ethiopian Revenues and Customs Authority shows that, 

Ethiopia exported $ 67,717 to Kenya and $ 10,532 to 

South Africa. It also imported $ 35,685 and $ 203,974 

from Kenya and South Africa respectively.  

Ethiopia is the only country that shares borders with 

all the other countries in the Horn of Africa and is the 

headquarters of the African Union. Since the selected 

countries have strong economic and commercial ties, 

this research examined the inflation dynamics and 

interaction effects among Ethiopia, Kenya and South 

Africa.  

The study tried to address the following research 

questions and extends the literatures by considering the 

research questions: a) To what extent the impacts of the 

world oil price shock on inflation differ across the 

selected countries?; b) What are the drivers of domestic 

inflation dynamics?; and c) Is there any factual 

interaction effects of inflation dynamics across the 

selected countries? 

The research was carried out to investigate the trend 

of inflation, illustrate the granger causal relationship of 

inflation dynamics and identify the major driving 

force(s) of high inflation dynamics in three African 

countries. Finally, it suggested the best strategies to 

manage the variability of inflation for the policy makers 

and other stakeholders. 

2. Methods  

Ethiopia, Kenya and South Africa were purposively 

selected as the focus of this research, for they strong 

trade integration and economic ties. Kenya and South 

Africa are top trading partners of Ethiopia. Thus, the 

researcher considered Ethiopia’s, Kenya’s and South 

Africa’s inflation dynamics for analysis. 

For this study, monthly time series data spanning the 

period from January 2007 to April 2018 concerning 

Ethiopian consumer price index (ETHCPI), Kenyan 

consumer price index (KCPI) and South African 

consumer price index (SCPI), exchange rates 

((Ethiopian Birr/USD Exchange rate (ETHEXR), 

Kenyan Shilling/ USD exchange rate (KEXR) and 

South African Rand/USD exchange rate (SEXRT)) and 

world oil price were collected from National Bank of 

Ethiopia and International Monitory Fund.  

Various parameters such as Consumer Price Index 

(CPI), Wholesale Price Index (WPI) and Sensitive Price 

Indicator (SPI) were used for measuring inflation. 

Consumer Price Indexes (CPI) were used as a proxy for 

inflation. Consumer prices are very much linked with 

the world oil prices because oil products are not only 

used as a final product but are also used as an input in 

many of the production processes and economic 

activities. From 2000 to 2008, world oil prices created 

new records that severely affected the economy of every 

country of the world (Asghar and Naveed, 2015). 

The study used both descriptive and inferential 

statistics for data analysis. 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

66 
 

2.1. Econometric Model Specification and Tests 

2.1.1. Tests of stationarity 

In econometric analysis involving time series data, 

before any kind of econometric estimation takes place, 

the collected data should be tested for their stationarity. 

For this purpose, the Augmented Dickey-Fuller (ADF) 

test and Phillip-Perron (PP) tests were used to tests for 

the stationarity. The ADF test avoids the problem of 

Dickey-Fuller because it corrects for serial correlation; 

by adding lagged difference terms (Gujariti, 2004). The 

ADF test can be represented as: 

∆𝑌𝑡 = 𝛾1 + 𝛾2𝑡 + 𝛿𝑌𝑡−1 + ∑ 𝛼𝑖

𝑝

𝑖=1

∆𝑌𝑡−𝑖 + 𝑡               (1) 

where, 𝛾1, 𝛾2, 𝛿, and 𝛼 are the coefficients, t is the 

stochastic trend, 𝑡  is a white noise error term and 

∆𝑌𝑡−1=𝑌𝑡−1-𝑌𝑡−2, ∆𝑌𝑡−2=𝑌𝑡−2-𝑌𝑡−3, etc. The test 

statistic is given below: 

)ˆ(

ˆ





SE
Z

t


 

where, )ˆ(SE standard error of ̂ . Hypothesis tests: 

0: Ho where, 1  . To perform the tests, 

conventional F-test is used but compares the test statistic 

with the critical F-values developed by Dickey and 

Fuller.  

The Phillips-Perron test is an alternative method for 

unit root tests. A PP test ignores any serial correlation in 

the error term without adding lagged difference terms 

and they use the standard DF or ADF test but adjust the 

t-ratio so that the serial correlation does not affect the 

asymptotic distribution of the test statistic. 

2.1.2. Co-integration tests 

Many macroeconomic variables are not stationary at 

a level but a linear combination of two or more non-

stationary series may be stationary and these series are 

said to be co-integrated. If integrated of order one 

variables are co-integrated, they are moving together so 

that there is some long run relationship between them. 

Traditional time-series models have failed to fully 

capture the behavior of such complex relationship: 

The Johansen's approach takes its initial point in the 

vector auto regression (VAR) order p specified by: 

o 1 1 2 2
... (2)

t t t p t p t
Y Y Y Y 

  
       

The above VAR (p) can be re-specified as: 

tt

p

t

itt
YYY  







  1
1

1

1o

 
where, 





p

ij

ji

p

t

i
andI

11

  

If the coefficient matrix   has reduced rank r<n, then 
there exist nxr matrices α and β each with rank r such 

that   = αβ′ and β’Yt is stationary at level. r is the 
number of co-integrating relationships, the elements of 

α are known as the adjustment parameters in the vector 

error correction model and each column of β is a co-

integrating vector. It can be shown that for a given r, the 

maximum likelihood estimator of β defines the 

combination of Yt−1 that yields the r largest canonical 

correlations of ΔYt with Yt−1 after correcting for lagged 

differences and deterministic variables when present. 

Johansen proposes two different likelihood ratio tests of 

the significance of these canonical correlations and 

thereby the reduced rank of the  matrix: the trace test 
and maximum eigenvalue test, shown as follows 

respectively. 

1

ˆ (3)ln(1 )
n

trace i
i r

J T 
 

  
 

max 1
ˆln(1 ) (4)
r

J T 


    

where, T is the sample size and i̂  is the i
th largest 

canonical correlation. The trace test tests the null 

hypothesis of r co-integrating vectors against the 

alternative hypothesis of n co-integrating vectors. The 

maximum eigenvalue test, on the other hand, tests the 

null hypothesis of r co-integrating vectors against the 

alternative hypothesis of r +1 co-integrating vectors.  

2.1.3. Lag Length Selection 

The lag length for the VAR (p) model may be 

determined using model selection criteria. The general 

approach is to fit VAR (p) models with orders p = 0, 1, 

2…, p max and choose the value of p which minimizes 

some model selection criteria. The three most common 

information criteria are the Akaike (AIC), Schwarz-

Bayesian (BIC) and Hannan-Quinn (HQ): 

2

2

2

2ˆ( ) ln ( ) (5)

ln( )ˆ( ) ln ( ) (6)

2 ln lnˆ( ) ln ( ) (7)

AIC p p pk
T

T
BIC p p pk

T

T
HQ p p pk

T

  

  

  

 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

67 
 

The AIC criterion asymptotically overestimates the 

order with positive probability, whereas the BIC and HQ 

criteria estimate the order consistently under fairly general 

conditions if the true order p is less than or equal to pmax. 

2.1.4. Vector Autoregressive (VAR) Model Specification 

The vector autoregression (VAR) model is one of the 

most successful, flexible, and easy to use models for the 

analysis of multivariate time series. It is a natural 

extension of the univariate autoregressive model to 

dynamic multivariate time series. The VAR model has 

proven to be especially useful for describing the 

dynamic behavior of economic and financial time series 

and for forecasting. It often provides superior forecasts 

to those from univariate time series models and 

elaborate theory-based simultaneous equations models. 

A VAR model applies when each variable in the system 

does not only depend on its lags, but also the lags of 

other variables. 

The VAR model has proven to be especially useful 

for describing the dynamic behavior of economic and 

financial time series and for forecasting. A multivariate 

time series Yt is a VAR process of order p or VAR (p) 

for short if it follows the mode: 

o 1 1 2 2
...

       , p > 0, t = 1,..., T (8)

t t t p t p t
Y Y Y Y 

  
        

where, Yt is a vector of length k, 
o

 is a k-dimensional 

vector, Φ is a k × k matrix of autoregressive coefficients 

for j = 1, 2, ……, p. , and { 
t
 } is a sequence of serially 

uncorrelated random vectors with mean zero and 

covariance matrix Σ. Yt is a vector of length k. There are 

k equations. The coefficient matrix Φ measures the 

dynamic dependence of Yt and are unknown and to be 

estimated from the observed data.  

2.1.5. Vector Error Correction Model (VECM) 

The use of Vector Autoregressive Models (VAR) and 

Vector Error Correction Models (VECM) for analyzing 

dynamic relationships among financial variables has 

become common in the literature. From the above VAR 

(p) model specification, we can rewrite as a VECM. 

∆y
t
=ϑ+ Π𝑦𝑡−1+ ∑ Γ𝑖

𝑝−1

𝑖=1

∆𝒚𝑡−𝑖 + 𝜺𝑡                          (9) 

where, Π𝑖  =  αβ′,Γ𝑖 = − ∑  𝑗
𝑝
𝑗=𝑖+1  and  𝐼𝑛is an 

identity matrix. 

 Π and the short-run parameter Γ𝑖 i=1, 2,…, p-1 are p × 

p matrices of coefficients. The VECM expressed above 

is convenient because the hypothesis of cointegration 

can be stated in terms of the long-run impact matrix, Π. 

2.1.7. Granger Analysis 

This study uses Engle-Granger causality test to 

analyze the relationship between the selected variables. 

Let Xt and Yt be two stationary (after possible 

transformations) time series of length T. A variable Xt is 

said to Granger causes another variable Yt, if Yt can be 

better predicted from the past of Xt and Yt together than 

the past of Yt alone, other relevant information being 

used in the prediction (Pierce, 1977). Likewise the 

researcher was interested to see the grander causality of 

inflation dynamics between the selected countries and 

other selected variables.  

2.1.8. Impulse Response Function 

The VAR model can be used for structural inference 

and policy analysis. In structural analysis, certain 

assumptions about the causal structure of the data under 

investigation are imposed, and the resulting causal 

impacts of unexpected shocks or innovations to 

specified variables on the variables in the model are 

summarized. Granger-causality may not tell us the 

complete story about the interactions between the 

variables of a system. In applied work, it is often of 

interest to know the response of one variable to an 

impulse in another variable in a system that involves a 

number of further variables as well. These causal 

impacts are usually summarized with impulse response 

functions and forecast error variance decompositions. 

Identification of the underlying structural shocks is 

necessary if we are to estimate the effects of an 

exogenous shock to a single variable on the dynamic 

paths of all of the variables of the system, which we call 

impulse-response functions (IRFs). The impulse 

response function can be plotted as the period 

multipliers against the lag length. An impulse response 

function traces the response of a variable of interest to 

an exogenous shock. Often the response is portrayed 

graphically, with horizon on the horizontal axis and 

response on the vertical axis. It traces the effect of a one 

standard deviation shock to one of the innovations on 

current and future values of the endogenous variables. 

A shock to the i
th
 variable directly affects the j

th
 variable, 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

68 
 

and may also transmit to all of the endogenous variables 

through the dynamic structure of the VAR. Any 

covariance stationary VAR (p) process has a Wald 

representation of the form: 

The impulse response function (IRF) of a dynamic 

system is its output when presented with a brief input 

signal, called an impulse. More generally, an impulse 

response refers to the reaction of any dynamic system in 

response to some external change. 

A VAR was written in vector MA (∞) form as:  

1 1 2 2
... (10)

t t t t
Y      

 
      

Thus, the matrix
s

  has the interpretation 
s

t

st
Y










'
that 

is, the row i, column j element of 
s

  identifies the 

consequences of one unit increase in the j
th
 variable’s 

innovation at date t ( jt ) for the value of the i
th
 variable 

at time t+s(
sit

Y


), holding all other innovations at all 

dates constant. 

ti

sti
Y

'


  as a function of s is called the impulse response 

function. It describes the response of 
sit

Y


a one-time impulse 

in
tj

Y  with all other variables dated t or earlier held constant. 

 

 

3. Results and Discussions 

3.1. Descriptive analysis  

Figure 1 depicts the consumer price index (inflation) 

of the selected countries and world oil price. The 

graphical plot of the three variables (CPI) shows an 

upward increasing trend in which the co-movement 

showed greater similarity starting from the beginning 

onwards. This graphical plot confirms the finding of 

Durevall and Sjö (2012). They found that inflation in 

both Ethiopia and Kenya has increasing patterns. The 

world oil price is more fluctuated over the given period 

than inflation. The price increased to higher values in 

2008 and it does not show a clear trend which contrasts 

the finding of Ademe (2015). Domestic inflation of 

Ethiopia had a similar trend with that of world oil price. 

The fluctuation in oil prices led to the fluctuation of 

inflation. The oil prices which were higher will be 

immediately followed by the rising prices of oil 

products including gasoline and fuel oil, which were 

used by the consumer.  

The exchange rate of the three countries, generally, 

showed an increasing trend with high fluctuation 

(Figure 2). The fluctuation is low in the case of Ethiopia 

compared to the other countries. This low fluctuation 

may be due to the fact that Ethiopian exchange rate is 

characterized by a managed floating regime. 

 

 

Figure 1: Graphical representation of inflation 

Time in Month

C
P

I(
E

th
io

p
ia

)

2008 2012 2016

2
0

4
0

6
0

8
0

1
2
0

Time in Month

C
P

I(
K

e
n
y
a
)

2008 2012 2016

8
0

1
2
0

1
6
0

Time in Month

C
P

I(
S

o
u
th

 A
fr

ic
a
)

2008 2012 2016

6
0

8
0

1
0
0

Time in Month

 P
ri
c
e
 o

f 
O

il

2008 2012 2016

4
0

8
0

1
2
0

Time in Month

C
P

I(
E

th
io

p
ia

)

2008 2012 2016

2
0

4
0

6
0

8
0

1
2
0

Time in Month

C
P

I(
K

e
n
y
a
)

2008 2012 2016

8
0

1
2
0

1
6
0

Time in Month

C
P

I(
S

o
u
th

 A
fr

ic
a
)

2008 2012 2016

6
0

8
0

1
0
0

Time in Month

 P
ri
c
e
 o

f 
O

il

2008 2012 2016

4
0

8
0

1
2
0



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

69 
 

3.2. Tests of stationarity 

Augmented Dickey-Fuller (ADF) and Philips Perron 

(PP) tests were used to test the stationarity properties of 

the series. The summary of the result is given in Table 

1a) and b). The result indicates that the null hypothesis 

of the presence of unit root has failed to reject at 5 

percent level of significances. This implies that the 

series is not stationary at level. On the other hand, all the 

variables at 5 the percent level of significance are 

statistically significant in the first difference. We thus 

realize that all the series over time is stationary in first 

difference. 

 

 

 

 

 

 

 

 

 

 

 

Table 1a): ADF tests of stationary 

 At a level At the first difference 

Variables  Test Statistic  Critical value at 5%  P-values Test Statistic Critical value at 5% P-values 

Oil price -1.631 -2.888 0.4669 -5.279 -2.888 0.000 

ETHEXR 0.690 -2.888 0.9896 -7.814 -2.888 0.000 

ETHCPI 0.906 -2.888 0.9932 -5.772 -2.888 0.000 

KEXR -1.419 -2.888 0.5732 -8.412 -2.888 0.000 

KCPI 0.221 -2.888 0.9734 -6.425 -2.888 0.000 

SEXR -0.527 -2.888 0.8867 -6.421 -2.888 0.000 

SCPI 0.361 -2.888 0.9800 -8.068 -2.888 0.000 

Source: Own computation results on sample data 

Table 1b): PP tests of stationarity 

 

Variables  

At a level At first difference 

Test Statistic  Critical value at 5%  P-values Test Statistic Critical value at 5% P- values 

Oil price -1.878 -2.888 0.3424 -7.480 -2.888 0.000 

ETHEXR 0.546 -2.888 0.9862 -9.108 -2.888 0.000 

ETHCPI 0.714 -2.888 0.9901 -7.808 -2.888 0.000 

KEXR -1.138 -2.888 0.6997 -8.559 -2.888 0.000 

KCPI -2.491 -2.888 0.1176 -10.901 -2.888 0.000 

SEXR -1.225 -2.888 0.6629 -21.732 -2.888 0.000 

SCPI 0.707 -2.888 0.9900 -8.405 -2.888 0.000 

Source: Own computation results on sample data 

Figure 2: Exchange rate of the selected 

countries 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

70 
 

3.3. Optimal lags determination 

Table 2 reports optimal lags order selection statistics. 

In this Table the minimum values from each of the 

information criteria are given by star sign (*).The result 

shows the optimal lag length is one. So, we precede 

further tests and estimations with lag (1). Hence, the 

VAR (p) and VECM (P) models which are used are 

VAR (1) and VECM (1). 

3.4. Co-integration analysis 

Having confirmed the existence of unit root at a level 

in the series in Table 1, co-integration tests were 

conducted by Johansson test of co-integration. Table 3 

reports the co-integration analysis outputs. The result 

shows that the trace test didn’t reject the null hypothesis 

of zero co-integrating vector at 5% level of significance 

(22.2364*) in Kenya in favor of at most one co-

integrating vectors in case of Ethiopia and South Africa 

(13.8785* and 11.7716*) respectively. Therefore, the 

computed trace statistics that are greater than the critical 

trace values at a 5 percent level of significance explains 

the rejection of the null hypothesis of zero co-

integrating vectors. This implies that inflation in the 

case of Ethiopia and South Africa has a long run 

relationship with respective to their exchange rate and 

world oil prices.  

3.5. Estimation of the Vector Autoregressive (VAR) 

Model  

Table 4 comprises the result of inflation dynamics 

computed by using VAR model. The computed values 

indicate that the past value of the endogenous variable 

information in Ethiopia is positive significant effect in 

determining its own current values (33.76%) at five 

percent significant levels. From the results, it is also 

clearly inferred that the past values of inflation in Kenya 

(93.74%) and other constant variables (35.42%) have 

significant effect in determining the current values of 

inflation in Ethiopia keeping other variables constant. 

For the equation of inflation in Kenya, the past values of 

KCPI and SCPI have positive significant effect on the 

current values of KCPI at five significant levels. 

3.6. Vector error correction model estimation 

The presence of co-integration suggests a long run 

relationship among the variables under consideration. 

To discuss the long run equilibrium relations and short-

run adjustment processes, the researcher estimated 

vector error correction model. The long run relationship 

and short-run adjustment processes among inflation, 

exchange rates and world oil price for 1 co-integrating 

vector for Ethiopia are shown in Table 5. The 

coefficients of exchange rate and world oil price at the 

first lag were significant at 5% level of significance. 

From the Table, it is inferred that there was no long-run 

causality between inflation and its first lag. When we 

consider the first equation (inflation) the coefficient 

error correction term values are non-negative and not 

significant. The values do not confirming long run 

causality. The coefficient of error correction term of 

exchange rate equation and world oil prices equation 

values are negative and significant at 5%. The 

coefficient values are -22.58 and -27.08 percent 

monthly, meaning that the system corrects the previous 

period disequilibrium at a speed of 22.58 and 27.08, 

respectively. The error correction term which is the 

normalized co-integrating equation obtained from the 

VEC model is as follows: 

 

Table 2: Optimal Lags Determination 

     Source: Own computation results on sample data 

 

Lag LL LR df p FPE AIC HQIC SBIC 

0 -1555.630    55.835 23.888 23.950 24.041* 

1 -1471.540 172.190 49 0.000 31.726* 23.321 23.821* 24.550 

2 -1424.500 94.079 49 0.000 32.886 23.351 24.288 25.656 

3 -1377.370 94.258 49 0.000 34.365 23.380 24.753 26.760 

4 -1341.740 71.262* 49 0.021 43.416 23.584 25.394 28.039 

ΔETHCPI = -45808 ΔETHEXR + 0.3035 ΔWorld 

oil price – 144395 



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71 
 

Table 3: Johansson Co-integration Tests 

Johanson Co-integration Tests in case of Ethiopia (ETHCPI,ETHEXR and World oil price) 

Maximum    Trace  5%  critical 

Rank Parms LL Eigenvalue Statistic value 

0 3 -671.7423  . 38.8071 29.68 

1 7 -659.278 0.0589 13.8785* 15.41 

2 11 -653.23229 0.0582 1.7871 3.76 

3 12 -652.33874 0.01315   

 Johansson Co-integration Tests in case of Kenya (KCPI,KERT and World oil price) 

Maximum    Trace  5%  critical 

Rank Parms LL Eigenvalue Statistic value 

0 3 -855.7808  22.2364* 29.68 

1 7 -848.1779 0.1073 7.0305 15.41 

2 11 -844.6693 0.0510 0.0132 3.76 

3 12 -844.6693 0.0001   

Johansson Co-integration Tests in case of South Africa (SCPI, SEXR and World oil price) 

Maximum    Trace  5%  critical 

Rank Parms LL Eigenvalue Statistic value 

0 3 -551.944 . 39.0134 29.68 

1 7 -538.323 0.184 11.7716* 15.41 

2 11 -532.444 0.084 0.0124 3.76 

3 12 -532.438 0.000   

Johansson Co-integration Tests of Inflation across the Sampled Countries 

Maximum    Trace  5%  critical 

Rank Parms LL Eigenvalue Statistic value 

0 3 -412.5450 . 19.7748* 29.68 

1 7 -405.3309 0.10136 5.3466 15.41 

2 11 -403.4722 0.0272 1.6291 3.76 

3 12 -402.6576 0.0120   

Source: Own computation results on sample data 

Table 4: Output of VAR model for inflation of the sampled countries 

 Coef. Std. Err.   Z P>z [95% Conf. Interval] 

D_ETHCPI  

ETHCPI- LD 

KCPI-LD. 

SCPI- LD. 

 Cons 

 

0.3376 

0.9374 

0.0780 

0.3542 

 

0.0844 

0.0387 

0.2615 

0.1384 

 

4.00 

24.17 

0.30 

2.56 

 

 0.000  

0.000  

0.766 

0.011 

 

0.1722 

0.8614 

-0.4345 

0.0829 

 

0. 5030 

1.0134 

0.5904 

0.6256 

D_KCPI  

ETHCPI -LD 

KCPI-LD. 

SCPI-LD. 

Cons 

 

-0.0130 

0.4880 

0.5851 

0.2210 

 

0.0719 

0 .0731 

0.2228 

0.1180 

 

-0.18 

6.68  

2.63 

1.87 

 

0.857 

0.000 

0.009  

0.061 

 

-0.1539 

0. 3138 

0.1483 

-0.0101 

 

0.1279 

0.6312 

 1.0219 

0.4523 

D_SCPI  

ETHCPI-LD. 

KCPI-LD. 

SCPI-LD. 

Cons 

 

0.0311 

0.0268 

0.2681 

0.2615 

 

0.0280 

0.0285 

0.0870 

0.0460 

 

1.11 

 0.94 

3.08 

5.68 

 

0.268  

0.347 

0.002 

0.000 

 

-0.0239 

-0.0290 

0.0976 

0.1712 

 

 0.0861 

 0.0827 

 0.4387 

 0.3518 

    Source: Own computation results on sample data 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

72 
 

According to normalized equation, exchange rate 

and world oil price contributes to inflation in the long-

run. Table A-2 (appendix) reports the VEC output of 

inflation in South Africa. The result shows that the 

coefficients of error correction terms are significant at 

5% significant level. As understood from the VECM 

model results, exchange rate contributed negatively in 

the long run to the inflation in Ethiopia and South 

Africa. That is, contribute negatively to decrease the 

exchange rate aggravated inflation of the mentioned 

country. Conversely, world oil price contributes to 

inflation positively in the long run in case of Ethiopia 

and but negatively to that of South Africa. The increase 

in oil prices led to rising inflation and vice versa, which 

contrasts the finding of Sek et al. (2015). The study 

found that oil prices have a considerable effect on 

domestic prices in developing countries which are 

highly oil dependent. 

3.7. Granger causality tests 

Recall that even though a co-integration test shows 

long run relationship among variables, it does not 

specify the direction of a causal relation. Chi-square 

statistics and probability values constructed under the 

null hypothesis is rejected if the probability value is 

more than 5% significance level. Table 6 provides the 

VAR & VEC Granger Causality tests results. VEC-

Granger causality analyses of inflation, exchange rate, 

and world oil price in case of Ethiopia provides the 

existence of unidirectional causality running from the 

world oil price to inflation at the 5% significance level 

(0.0021). Moreover, there is unidirectional causality 

running from the joint exchange rate and world oil price 

to inflation. This evinces that past values of joint world 

oil price and exchange rate enabled to predict the present 

values of inflation. In the case of South Africa, the VEC 

Granger causality/block exogeneity Wald tests indicate 

the existence of unidirectional causality running from 

world oil price to inflation at 5% of significance level. 

These results are in agreement with the finding of 

Brahmasrene et al., (2014). They documented that any 

changes in international oil price will cause a change in 

inflation. Similarly, the VAR granger causality Wald 

tests results  regarding inflation in the sampled countries 

show the unidirectional granger causality running from 

inflation in Southern Africa to inflation in Kenya. This 

implies that in the short run inflation in South Africa is 

one of the driving forces of inflation in Kenya in 

addition to other macro-economic variables. In addition, 

unidirectional granger causality running from inflation 

in Kenya to Ethiopia was observed. World oil price has 

no equal contribution for the inflation fluctuation across 

the selected countries. 

 

Table 5: output of VECM in case of Ethiopia 

 Coef. Std. Err.  Z P>z [95% Conf. Interval] 

D_ETHCPI       

CE1_1 0.0071 0.0100 0.72 0.474 -0.0124 0.0267 

Cons 0.7240 0.0871 8.32 0.000 0.5531 0.8946 

D_ETHEXR       

CE1_2 -0.2258 0.0881 -2.56 0.010 -0.0532 -0.3984 

Cons 0.1376 0.028713 4.79 0.000 0.0813 0.1938 

D_Oil price       

CEl_3. -0.2708 0.0602 -4.50 0.000 -0.3888 -0.1528 

Cons 0.0181 0.5259 0.03  0.973 -1.0128 1.0490 

 Johansen normalization restriction imposed  

Beta Coef Std. Err. Z P>|z| [95% Conf. Interval] 

ETHCPI 1      

ETHEXR  -4.5808 0.3470 -13.20 0.000 -5.2609 -3.9007 

Oil Price 0.3035 0.0685 4.43 0.000 0.1692 0.4377 

Cons -14.4395      

Source: Own computation results on sample data 

 

 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

73 
 

 

Table 6: VAR &VEC granger causality tests results 

VEC Granger Causality/Block Exogeneity Wald Tests in case of Ethiopia 

Equation Excluded chi2 Df Prob>chi2  

D.ETHCPI D.Ethexr 0.1940 1 0.6596 

 D.Oil price 9.4180 1 0.0021 

 All 9.5626 2 0.0084 

D.ETHEXR D. ETHCPI 0.0230 1 0.8796 

 D.Oil price. 0.1560 1 0.6929 

 All 0.2653 2 0.8758 

D.Oil price D.ETHEXR 0.1195 1 0.7295 

 D. ETHCPI 0.1769 1 0.6741 

 All 0.3105 2 0.8562 

VEC Granger Causality/Block Exogeneity Wald Tests in case of South Africa 

Equation Excluded chi2 Df Prob>chi2  

D. SCPI D. SEXR  2.5478 1 0.1104 

 D.Oil price 8.648 1 0.0033 

 All 11.7925 2  0.0027 

D. SEXR D. SCPI 0.9112 1 0.3398 

 D.Oil price. 8.0359 1 0.0046 

 All 10.7764 2 0.0046 

D. Oil price D. SCPI 0.8433 1 0.3585 

 D. SEXR  0.0492 1 0.8244 

 All 1.0237 2 0.5994 

VAR Granger Causality/Block Exogeneity Wald Tests in case of Kenya 

Equation Excluded chi2 Df Prob>chi2  

D. KCPI D. KEXR  2.3925 1 0.1219 

 D.Oil price 3.2667 1 0.0707 

 All 4.0564 2  0.1317 

D. KEXR D. KCPI 3.6663 1 0.0555 

 D.Oil price. 0.2595 1 0.6105 

 All 4.7924 2 0.0911 

D. Oil price D. KCPI 0.3027 1 0.5822 

 D. KEXR  1.3963 1 0.2373 

 All 3.8442 2 0.1463 

VAR Granger Causality/Block Exogeneity Wald Tests of inflation in case of Selected Countries 

Equation Excluded chi2 Df Prob>chi2  

D. ETHCPI  D. KCPI  6.1847 1 0.0194 

 D. SCPI 0.0889 1 0.7660 

 All 2.0275 2 0.3630 

D. KCPI D. ETHCPI .03252 1 0.8570 

 D. SCPI. 6.8917 1 0.0090 

 All 7.2409 2 0.0270 

D. SCPI D. ETHCPI 1.2269 1 0.2680 

 D. KCPI  0.8835 1 0.3470 

 All 3.8442 2 0.1463 

Source: Own computation results on sample data 

3.8. Impulse response function 

An impulse response function traces the effect of a 

one-time shock to one of the innovations on current and 

future values of the endogenous variables. Figure 3 

displays the estimated impulse response of inflation in 

Ethiopia toward the change of world oil price and 

Ethiopian Birr/USA Dollar exchange rate. The figure 

reveals that inflation responds positively over the whole 

period with slightly increasing when a positive shock 

given to an exchange rate, which supports the finding of 

Habtamu Getnet (2015). He has found that the exchange 

rate has a direct effect on the increments or decrements 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

74 
 

of domestic inflation of Ethiopia. Figure 4 reports the 

estimated VAR impulse response function of inflation 

across the sampled countries. The result shows a one 

standard error shock of Ethiopian inflation positively 

influenced Kenyan’s inflation, but a positive shock of 

the inflation in Kenya affected the inflation in Ethiopia 

negatively. From this, it is evident that when there is 

positive shock to Ethiopia’s inflation, inflation in Kenya 

is increasing. Nevertheless, the inflation in Ethiopia 

decreases if Kenya’s inflation gets a shock. It also 

understood that a greater real trade integration and 

border ties could increase the sensitivity of inflation to 

cross border shocks.  

Figure A-1 (annex) shows that the impulse response 

function of inflation dynamics in Kenyan to Shilling/ 

USA Dollar exchange rate and world oil price. The 

figure reveals that the response of inflation to a unit 

standard deviation shock to exchange rate is positive 

and almost with increasing movements which contrasts 

the finding of Okara and Mutuku (2019). They found 

that a shock given to exchange rate has negative effects 

on inflation. Also, the response of inflation to a unit 

standard deviation shock to world oil price is positive. 

In other words, when there is a positive innovation given 

to exchange rate and oil price increases the inflation in 

that country.  

Figure A-2 (annex) exhibits impulse response 

function of inflation in South Africa towards Rand/USA 

Dollar exchange rate and world oil price received. The 

plot shows that the response of inflation in South Africa 

was positive when exchange rate faced a shock. 

Exchange rate shocks had a similar positive effect on 

inflation in both Ethiopia and Kenya, yet negative in 

South Africa. The response of inflation towards the 

world oil price is similar in all selected countries over 

the given time horizon. Furthermore, the response of 

inflation for itself innovation has little effect for the 

selected countries.

0.0

0.4

0.8

1.2

1.6

1 2 3 4 5 6 7 8 9 10

Response of ETHCPI to ETHCPI

0.0

0.4

0.8

1.2

1.6

1 2 3 4 5 6 7 8 9 10

Response of ETHCPI to ETHEXR

0.0

0.4

0.8

1.2

1.6

1 2 3 4 5 6 7 8 9 10

Response of ETHCPI to OIL

.0

.1

.2

.3

.4

.5

1 2 3 4 5 6 7 8 9 10

Response of ETHEXR to ETHCPI

.0

.1

.2

.3

.4

.5

1 2 3 4 5 6 7 8 9 10

Response of ETHEXR to ETHEXR

.0

.1

.2

.3

.4

.5

1 2 3 4 5 6 7 8 9 10

Response of ETHEXR to OIL

-4

-2

0

2

4

6

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to ETHCPI

-4

-2

0

2

4

6

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to ETHEXR

-4

-2

0

2

4

6

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to OIL

Response to Nonfactorized One S.D. Innovations

 

Figure 3: Impulse response functions of inflation in case of Ethiopia 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

75 
 

-10

-5

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

Response of ETHCPI to ETHCPI

-10

-5

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

Response of ETHCPI to KCPI

-10

-5

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

Response of ETHCPI to SCPI

-0.4

0.0

0.4

0.8

1.2

1 2 3 4 5 6 7 8 9 10

Response of KCPI to ETHCPI

-0.4

0.0

0.4

0.8

1.2

1 2 3 4 5 6 7 8 9 10

Response of KCPI to KCPI

-0.4

0.0

0.4

0.8

1.2

1 2 3 4 5 6 7 8 9 10

Response of KCPI to SCPI

-.2

-.1

.0

.1

.2

.3

.4

1 2 3 4 5 6 7 8 9 10

Response of SCPI to ETHCPI

-.2

-.1

.0

.1

.2

.3

.4

1 2 3 4 5 6 7 8 9 10

Response of SCPI to KCPI

-.2

-.1

.0

.1

.2

.3

.4

1 2 3 4 5 6 7 8 9 10

Response of SCPI to SCPI

Response to Cholesky One S.D. Innovations ± 2 S.E.

 

Figure 4: VAR Impulse Response Function of Inflation across the selected countries 

4. Conclusions 

This study empirically presents the comparative 

view of inflation dynamics among three African 

countries. Even though the main driving forces of high 

inflation across the sampled countries varies, the 

exploratory analysis of monthly data spanning from 

January 2007 to April 2018 shows the inflation trend is 

similar in the long run. The result of Johansen Co-

integration test revealed that the CPI, exchange rates and 

oil price have co-integration relationship in Ethiopia and 

South Africa case. In the long run, inflation in both 

countries is driven by exchange rates and world oil 

price. Exchange rates have positively significant effects 

on inflation dynamics of both countries while world oil 

price contributes positively in Ethiopia but negatively in 

South Africa.    

In the short run, inflation in Kenya has a predicting 

power about inflation in Ethiopia and inflation in South 

Africa has a predicting power about inflation in Kenya. 

On the other hand, inflation in Kenya and Ethiopia do 

not have a predicting power about inflation in South 

Africa. Furthermore, the outcome of impulse response 

function demonstrates that exchange rates and oil price 

shocks affects inflation dynamics of the sampled 

countries at different stages both directly as well as 

indirectly. Shocks to inflation in South Africa have 

positive impact on inflation in Ethiopia while shocks to 

inflation in Kenya have negative in the short run. 

Inflation across the sampled countries has no long run 

interactive relationship.  

There are numerous policy implications that can be 

drawn from this analysis. First, there is growing 

evidence that exchange rates are a driving force for high 

inflation for the selected countries. So, establishment of 

Monitory union is recommended to stabilize this high 

inflation variability by managing exchange rate 

variability. Second, fluctuation of oil price is also 

observed as it is a driving force of high inflation. Low 

income countries like Ethiopia and Kenya are unlikely 

to have the resources to have stocks to take advantage 

of periods of low prices or insurance against rises, so 

that they will be affected by price increases. Therefore, 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

76 
 

it is a mandatory for the interference of central bank to 

stabilize the high variability of oil price by taking into 

account those countries. Finally, increased economic 

and trade integrity is likely to lead greater sensitivity of 

aggregate inflation dynamics to costs of imported 

inputs, especially when cost changes are large in 

magnitude. This issue should be a concern of 

macroeconomic policies coordination because no single 

country can on its own assure stability to the 

international economic system. 

 

Annex: 
Table A-1: The output of VAR (1) in the case of Kenya 

 Coef. Std. Err.  Z P>z [95% Conf. Interval] 

D_KCPI       

KCPI |LD. 0.5255 0.0720 7.30 0.000 0.3830 0.6679 

KEXR |LD. 0.0241 0.0384 0.63 0.532 -0.0518 0.1000 

oil |LD. 0.0187 0.0112 1.67 0.097 -0.0035 0.0410 

_cons 0.4136 0.0921 4.49 0.000 0.2314 0.5958 

D_kexr       

KCPI|LD. 0.0983 0.1610 0.61 0.542 -0.2201 0.4168 

KEXR |LD. 0.2721 0.0858 3.17 0.002 0.1024 0.4418 

oil |LD. -0.0237 0.0251 -0.94 0.348 -0.0733 0.0260 

_cons 0.0885 0.2059 0.43 0.668 -0.3188 0.4958 

D_oil       

KCPI | LD. -0.3095 0.5272 -0.59 0.558 -1.3526 0.7336 

KEXR |LD. -0.4966 0.2809 -1.77 0.079 -1.0524 0.0592 

oil | LD. 0.3541 0.0822 4.31 0.000 0.1915 0.5167 

_cons 0.4250 0.6743 0.63 0.530 -0.9090 1.7589 

 

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

1 2 3 4 5 6 7 8 9 10

Response of KEXR to KEXR

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

1 2 3 4 5 6 7 8 9 10

Response of KEXR to KCPI

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

1 2 3 4 5 6 7 8 9 10

Response of KEXR to OIL

-0.4

0.0

0.4

0.8

1.2

1 2 3 4 5 6 7 8 9 10

Response of KCPI to KEXR

-0.4

0.0

0.4

0.8

1.2

1 2 3 4 5 6 7 8 9 10

Response of KCPI to KCPI

-0.4

0.0

0.4

0.8

1.2

1 2 3 4 5 6 7 8 9 10

Response of KCPI to OIL

-8

-4

0

4

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to KEXR

-8

-4

0

4

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to KCPI

-8

-4

0

4

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to OIL

Response to Cholesky One S.D. Innovations ± 2 S.E.

 

Figure A-1: Impulse Response Function of Inflation Dynamics in case of Kenya Appendix 



Desa Daba.                                                                                                                    Ethiop.J.Sci.Sustain.Dev., Vol. 7 (2), 2020 

77 
 

Table A-2: Output of VECM in case of South Africa 

 Coef. Std. Err.  Z P>z [95% Conf. Interval] 

D_SCPI       

_ce1 |L1 -0.0063 0.0022 -2.84 0.004 -0.0107 -0.0020 

_cons 0.4164 0.0280 14.89 0.000 0.3616 0.4713 

D_SEXR       

_ce1 |L1 0.1087 0.0048 2.27   0.023 0.0015 0.0203 

_cons 0.0354 0.0601 0.59 0.556 -0.0824 0.1532 

D_oil       

_ce1 | L1. 0.1638 0.0427 3.83 0.000 0.0800 0.2475 

_cons 0.0138 0.5359 0.03 0.979 -1.0365 1.0641 

 Johansen normalization restriction imposed  

Beta Coef Std. Err. Z P>|z| [95% Conf. Interval] 

_SCPI 1      

SEXR -10.826 0.9508 -11.39 0.000 -12.6899 -8.9630 

Oil -0.5498 0.0980 -5.61 0.000 -0.7418 -0.3577 

_cons 64.1050      

Source: Own computation results on sample data 

 

-.1

.0

.1

.2

.3

.4

.5

1 2 3 4 5 6 7 8 9 10

Response of SCPI to SCPI

-.1

.0

.1

.2

.3

.4

.5

1 2 3 4 5 6 7 8 9 10

Response of SCPI to SEXR

-.1

.0

.1

.2

.3

.4

.5

1 2 3 4 5 6 7 8 9 10

Response of SCPI to OIL

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10

Response of SEXR to SCPI

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10

Response of SEXR to SEXR

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10

Response of SEXR to OIL

-8

-4

0

4

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to SCPI

-8

-4

0

4

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to SEXR

-8

-4

0

4

8

1 2 3 4 5 6 7 8 9 10

Response of OIL to OIL

Response to Cholesky One S.D. Innovations

 

Figure A-2: Impulse Response Function of inflation in case of South Africa 

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