Rwanda’s Economic Health
(A study of three significant slices of the Rwandan economy in three different papers)
Nzeyimana Parfait
March 2022
Kigali, Rwanda
DEDICATE
This book is dedicated to:
My family
Young economist
Writers Space Africa- Rwanda
Rwanda’s Economic Health
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Foreword
A healthy economy is equitable, participative, growing, sustainable, and stable. This
book consists of three research papers touching on the topics labeled as Estimating timevarying volatility in consumer prices in Rwanda (Feb2009-May2021), The effect of
government expenditures on inflation in Rwanda (2006Q1-2019Q4) and Forecasting the
industrial output in Rwanda using the Box-Jenkins methodology(BJ) (2006Q1-2020Q4).
All those studies combined in this book showcase the health of the Rwandan economy in
the studied period on those aspects of growth, sustainability, and stability.
This book has an interest in providing fact-based evidence on the health and status of the
Rwandan economy in the studied period, it provides analysis and policy
recommendations to continue improving policy-making and sustainable development in
Rwanda.
The first article focuses on estimating time-varying volatility in CPI main components
and its impact on economic growth. The volatility was assessed using the ARCH family
models where the GARCH (1,1) models were used using monthly data ranging from the
period of February 2009 to May 2021 obtained from the National Institute of Statistics of
Rwanda, the National Bank of Rwanda, and the U.S Energy Information Administration.
The three main contributors to the CPI in Rwanda were the ones that were considered for
analyzing the volatility and its persistence in the CPI components. More to that, this study
did look at also how inflation volatility plays a role in predicting the level of economic
growth in Rwanda. From the estimations, we found that for housing CPI volatility is not
persistent as its coefficient of persistence is 0.843901 less than one, while for transport and
food & non-alcoholic beverages they are persistent with their coefficients being 1.137753
and 1.348036 respectively, we have also found that CPI volatility has a significant impact
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in predicting the level of economic growth mainly the nominal gross domestic product
with its coefficient of persistence being 1.0237 as further explained in the findings.
The second article focuses on the effects of the government expenditure on inflation in
Rwanda where, to understand the effect of government expenditures on inflation in
Rwanda we have used the autoregressive distributed lag (ADRL) model to investigate
the relationship between them. In that framework, we found evidence that the two are
related and that the increase in government spending in Rwanda lead to a decrease in
inflation both in the short and the long-run. However, referring to the theoretical and
empirical literature used in this study, it is seen that in different cases the government
expenditures have an opposite effect on inflation as to the case of Rwanda. Thus efforts
should be made by policymakers to diversify the ways through which they finance the
government expenditures, so that they do not rely on the traditional ways to finance the
government spending including taxation and external borrowing.
The third article focuses on forecasting the industrial output in Rwanda using the BoxJenkins methodology(BJ), The interest of this study is to find an ARIMA model which is
most appropriate to forecasting industrial growth in Rwanda using Eviews. The BoxJenkins methodology is the one that was used in this paper and based on the research
obtained, we identified the model appropriate to forecasting industrial output in Rwanda
as ARIMA (2,1,10). And based on the model selected the estimated forecast of the
industrial output in Rwanda will increase on minimum average of 0.35 percent quarterly
in the period of 2021Q1 to 2023Q1 and on minimum average of 0.34 percent from 2023Q2
to 2023Q4. The results of the forecasting unit price of industrial output using Eviews
software on 2021Q1– 2023Q4 are stable enough.
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Disclaimer;
Comments, suggestions and questions can be send on
parfaitnzey@gmail.com.
This book is open for discussion and constructive
criticism.
Nzeyimana Parfait.
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Table of content.
Dedicate ........................................................................................Pg1
Foreward........................................................................................Pg2-3
Disclaimer......................................................................................Pg4
Estimating time-varying volatility in consumer prices in Rwanda
(Feb2009-May2021).................................................................Pg6-33
Effects of government expenditures on inflation in Rwanda
(2006Q1-2019Q4)......................................................................Pg34-65
Forecasting the industrial sector growth in Rwanda using Box–
Jenkins (BJ) methodology.....................................................Pg65-126
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Estimating time-varying volatility in
consumer prices in Rwanda (Feb2009May2021)
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Abstract
This study dealt with estimating time-varying volatility in CPI main components and its
impact on economic growth. The volatility was assessed using the ARCH family models
where the GARCH (1,1) models were used using monthly data ranging from the period
of February 2009 to May 2021 obtained from the National Institute of Statistics of Rwanda,
the National Bank of Rwanda, and the U.S Energy Information Administration.
The three main contributors to the CPI in Rwanda were the ones that were considered for
analyzing the volatility and its persistence in the CPI components. More to that, this study
did look at also how inflation volatility plays a role in predicting the level of economic
growth in Rwanda.
From the estimations, we found that for housing CPI volatility is not persistent as its
coefficient of persistence is 0.843901 less than one, while for transport and food & nonalcoholic beverages they are persistent with their coefficients being 1.137753 and 1.348036
respectively, we have also found that CPI volatility has a significant impact in predicting
the level of economic growth mainly the nominal gross domestic product with its
coefficient of persistence being 1.0237 as further explained in the findings.
Keywords: CPI inflation, Transport CPI, food & nonalcoholic CPI, exchange rate, housing
CPI, Core inflation, Gross domestic product, time-varying volatility, and variance.
1. Introduction
The unforeseen component in the time series of inflation that emerges from recurrent
shocks is described by inflation volatility.
The literature on variability or volatility of inflation is thin. Although the extant literature
provides strong evidence on the adverse effects on economic welfare, it says little about
the empirical features of inflation volatility across the economies. The current literature
also lacks a theoretical analysis of the fundamental determinants of inflation volatility.
Furthermore, in the sparse research on inflation volatility, there are more studies based
on advanced countries and less for developing countries (Shesadri and Banerjee, June
2013).
Therefore, since the adoption of the price-based monetary policy in 2019 in Rwanda, it is
very important to assess the volatility in consumer prices (CPI) inflation.
Thus, a forward-looking approach to monetary policy implementation requires, among
other things, enhanced forecasting capacity. During the preparation phase that preceded
the adoption of the price-based monetary policy, the National Bank of Rwanda (NBR)
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has explored a variety of inflation forecasting tools to guide monetary policy decisions.
The tools include near-term forecasting models such as short-term inflation forecasting
(STIF) and the Autoregressive Moving Average (ARMA), as well as the Quarterly
Projection Model (QPM) of the forecasting and policy analysis system (FPAS).
(Maniraguha F,Karangwa M, Mwenese B and Bagabe J, 2019)
Econometric literature shows that the short-term forecasting using ARMA-type models
becomes limited when price series are volatile due to their restrictive assumptions of
linearity and homoscedastic error variance (Lama, A. Jha, G., R. Paul, B. Gurug, 2015).
Therefore, given the observed magnitude of price volatility in Rwanda, there is an
increasing demand for the assessment of volatility to improve the quality of accuracy of
short-term forecasts. (Maniraguha F,Karangwa M, Mwenese B and Bagabe J, 2019).
More to solve the issue of thin literature on consumer price volatility in Rwanda which
is necessary as Rwanda in using the price-based monetary policy, this study will also
address the issue of improving the quality accuracy of short term forecast in inflation
volatility in Rwanda. To understand that this study will consider the main drivers or the
fundamental volatility determinants of consumer price volatility in Rwanda which
includes the transport CPI, housing, electricity, gas, and other fuels CPI as well as food
and non-alcoholic beverages.
By understanding the dynamics of volatility in these CPI components we will be able to
understand the persistence of the shocks in these components which will help to model
and control the resulting volatility in the total CPI which is the headline inflation. And if
we can then model the headline inflation or at least the core part of it this will help in
predicting the level of inflation which supports the price-based monetary policy as the
central bank will be able to set appropriate policies in its main mission of controlling
inflation.
2. Literature review.
The Consumer Price Index (CPI) is a measure that examines the weighted average of
prices of a basket of consumer goods and services, such as transportation, food, and
medical care. It is calculated by taking price changes for each item in the predetermined
basket of goods and averaging them. Changes in the CPI are used to assess price changes
associated with the cost of living (Jason . F and Peter. W, 2021).
The CPI is one of the most frequently used statistics for identifying periods of inflation
or deflation. It may be compared with the producer price index (PPI), which instead of
considering prices paid by consumers looks at what businesses pay for inputs (Jason . F
and Peter. W, 2021).
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In this section in which we are talking about different kinds of literature that are related
to our study. However, there are only two studies that talk about the time-varying
volatility in consumer prices in Rwanda, and worldwide the existing literature is very
scarce. Nevertheless, the literature on price volatility on the stock market is abundant and
we shall also include it as it has a weight of relevancy in terms of determining the
methodology and estimation of the time-varying volatility in consumer prices. Which is
the reason why we have consulted a variety of studies and research which will help us in
this paper.
Inflation is undoubtedly one of the most largely observed and tested economic variables
both theoretically and empirically. Its causes, impacts on other economic variables, and
cost to the overall economy are well known and understood. There could be arguments
for having, or not, moderate inflation in the economy and its pros and cons, nonetheless,
if the debate focuses on inflation uncertainty or inflation volatility instead of inflation
level, economists have almost consensus about its negative impact over some of the most
important economic variables, like output and growth rate via different channels. (Syed,
Kumail, Abbas, and Rizvia, 2013).
Discussions are ongoing on the cause of inflation uncertainty; some researchers opined
that monetary policy is the key in the determination of inflation uncertainty since it
originates from the uncertainty of the monetary policy regime, commonly termed
“regime uncertainty”. They argued that when there are high inflation policymakers
confront a dilemma, i.e., at one end, they want to bring down inflation, at the other end;
they are scared that it may trigger a recession in the economy. Since the public is not
aware of the direction of policymakers, it becomes highly uncertain of the future course
of inflation. They further stated that the uncertainty rises further as a result of the
announcement of unrealistic stabilization programs by the governments in the face of the
increase in high inflation. However, inflation uncertainty arises due to the unknown size
of the change in price level because of a certain change in the money supply. (Bamanga,
Muhammad A. et al., 2016).
Using GARCH model, (Thornton, 2006) used monthly data of South African Consumer
Price index from 1957:01 to 2005:09 to examine the relationship between inflation and
inflation uncertainty. The result supports Friedman`s hypothesis that high inflation leads
to more variable inflation.
(Kotonikas, 2004) looked at the inflation and inflation uncertainty and the impact of the
explicit targeting in the context of the UK economy using the GARCH model and came
up with the findings that there exists a positive relationship between past inflation and
uncertainty about future inflation, in line with the Friedman-Ball causal link.
(Conrad, C.and Karanasos, M., 2005) in their work used the ARFIMA-FIGARCH model
which generates long memory in both the conditional mean and variance of inflation
using monthly CPI data of the USA, Japan, and the UK to examine the relationship
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between inflation and inflation uncertainty. Their findings indicated that inflation
significantly raises inflation uncertainty as
predicted by Friedman’s hypothesis. (Rizvi, S.K and Naqvi, B., 2010) examined the
relationship between inflation and uncertainty in Pakistan using quarterly data from
1976:01 to 2008:02. They modeled Inflation to be determined by real growth rate and M2
growth rate and inflation uncertainty as time varying process using GARCH framework.
The study analyzed asymmetric behavior of inflation uncertainty using GJRGARCH and
EGARCH models and then asymmetry and leverage effects employing news impact
curves. The authors investigated the causality between inflation and inflation uncertainty
using bivariate Granger-Causality test. They found strong evidence that the FriedmanBall inflation uncertainty hypothesis holds for Pakistan.
(Balcilar , M. and Ozdemir, A., 2013) employed Granger causality tests within a
conditional Gaussian Markov switching vector autoregressive (MS-VAR) model using
monthly CPI data for G-7 countries (Canada, France, Germany, Japan, United Kingdom,
and the United States) covering the period 1959:12–2008:10 to examine the relationship
between inflation and inflation uncertainty. The study found evidence in favor of the
Friedman hypothesis for Canada and the United States.
(Hegerty, 2012) used an Exponential GARCH and monthly CPI data from 1976 – 2011 to
examine the relationship between inflation and inflation uncertainty in nine African
countries (Burkina Faso, Botswana, Cote d’Ivoire, Ethiopia, Gambia, Kenya, Nigeria,
Niger and South Africa) and found that the Friedman hypothesis holds true in all the
countries. (Valdovinos, C.F. and Gerling, K, 2011) also found that increased inflation
raised inflation uncertainty by examining links between inflation and inflation
uncertainty in WAEMU countries (Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau,
Mali, Niger, Senegal, and Togo) using monthly CPI data for the period of 1994 to 2009.
In a recent study on inflation volatility in Nigeria (Omotosho, B.S and Doguwa, S. I.,
2013), used three components of monthly CPI (core, food and headline) from1996 to 2011
and investigated the dynamics of inflation volatility in Nigeria employing three GARCH
type models i.e. symmetric GARCH, asymmetric TGARCH, and EGARCH. The authors
found that the asymmetric TGARCH (1, 1) was appropriate for explaining the dynamics
of headline and core CPI volatilities in Nigeria. However, the symmetric GARCH (1, 1)
was adequate for decomposing the volatility in food CPI. The study, however, was silent
on investigating the relationship between inflation and inflation uncertainty.
3. Methodology
This paper is estimating the time-varying volatility in consumer prices and accounts on
the effects of inflation volatility in Rwanda and its importance in predicting the level of
inflation in Rwanda as Rwanda is using the inflation targeting framework on her journey
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to control inflation. The study design and data analysis methods will be focused on as we
will be using secondary data which was collected from the national institute of statistics
of Rwanda and the national bank of Rwanda. The period that this paper will be covering
is from February 2009 to May 2021.
3.1.
Empirical Model
For this particular study we have chosen the GARCH models as our econometric model
to estimate the volatility in consumer prices.
The generalized autoregressive conditional heteroskedasticity (GARCH) process is an
econometric term developed in 1982 by Robert F. Engle, an economist and 2003 winner
of the Nobel Memorial Prize for Economics (Will. K and Margaret.J, 2020).
Heteroskedasticity describes the irregular pattern of variation of an error term, or
variable, in a statistical model. Essentially, where there is heteroskedasticity, observations
do not conform to a linear pattern. Instead, they tend to cluster. The result is that the
conclusions and predictive value drawn from the model will not be reliable. GARCH is a
statistical model that can be used to analyze a number of different types of financial data,
for instance, macroeconomic data. Financial institutions typically use this model to
estimate the volatility of returns for stocks, bonds, and market indices. They use the
resulting information to determine pricing, judge which assets will potentially provide
higher returns, and forecast the returns of current investments to help in their asset
allocation, hedging, risk management, and portfolio optimization decisions (Will. K and
Margaret.J, 2020).
The general process for a GARCH model involves three steps. The first is to estimate a
best-fitting autoregressive model. The second is to compute autocorrelations of the error
term. The third step is to test for significance. GARCH processes differ from
homoskedastic models, which assume constant volatility and are used in basic ordinary
least squares (OLS) analysis. OLS aims to minimize the deviations between data points
and a regression line to fit those points (Will. K and Margaret.J, 2020).
With the consumer prices, the volatility varies depending on or during certain periods
and this volatility depends on past variance, which makes a homoskedastic model suboptional.
GARCH processes, because they are autoregressive, depend on past squared
observations and past variances to model for current variance. GARCH processes are
widely used in finance due to their effectiveness in modeling asset returns and inflation.
GARCH aims to minimize errors in forecasting by accounting for errors in prior
forecasting and enhancing the accuracy of ongoing predictions (Will. K and Margaret.J,
2020).
Our study uses the GARCH as it considers the time-varying volatility explained by its
past deviations as well as its past volatility which is disregarded by the ARCH model
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3.2.
Model specification
3.2.1. Housing CPI model specification
Mean equation: 𝑙𝑜𝑔ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡 = 𝜌 + 𝜎𝑙𝑜𝑔𝑒𝑛𝑒𝑟𝑔𝑦 + 𝛽𝑙𝑜𝑔𝑎𝑔𝑟𝑖𝑔𝑑𝑝 + 𝜀𝑡 (1)
2
Volatility equation: ℎ𝑡 = 𝜑 + 𝜔ℎ𝑡−1 + 𝜙𝜇𝑡−1
(2)
In the above equations, the 𝑙𝑜𝑔ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡 shows the housing inflation CPI at time t, where
𝜌, 𝜎 𝑎𝑛𝑑 𝛽 are the constant and coefficient of the model.
𝑙𝑜𝑔𝑒𝑛𝑒𝑟𝑔𝑦 𝑎𝑛𝑑 𝑙𝑜𝑔𝑎𝑔𝑟𝑖𝑔𝑑𝑝 are the independent variables (explanatory variables) of the
specified model and 𝜀𝑡 which is the error term.
After estimating the mean equation of the housing inflation CPI a GARCH equation is
estimated where 𝜑, 𝜔, 𝑎𝑛𝑑 𝜙 are the constant and coefficients of the GARCH term and the
ARCH term respectively.
3.2.2. Transport CPI model specification
Mean equation:
𝑙𝑜𝑔𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑡 = 𝜌 + 𝜎𝑙𝑜𝑔𝑒𝑥𝑐ℎ𝑡−1 + 𝛽𝑙𝑜𝑔𝑜𝑖𝑙_𝑝𝑟𝑖𝑐𝑒𝑠𝑡−2 +
𝜂 log 𝑛𝑜𝑛𝑎𝑔𝑟𝑖𝑔𝑑𝑝𝑡−2+ ∅𝑙𝑜𝑔𝑐𝑜𝑟𝑒𝑡−2 +𝜀𝑡 (3)
2
Volatility equation: ℎ𝑡 = 𝜑 + 𝜔ℎ𝑡−1 + 𝜙𝜇𝑡−1
(4)
In the above equations, the 𝑙𝑜𝑔𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑡 shows the transport inflation CPI at time t,
where 𝜌, 𝜂, 𝜎 , 𝛽 𝑎𝑛𝑑 ∅ are the constant and coefficient of the model.
Log 𝑒𝑥𝑐ℎ𝑡−2 , 𝑙𝑜𝑔𝑜𝑖𝑙_𝑝𝑟𝑖𝑐𝑒𝑠𝑡−2 , 𝑙𝑜𝑔𝑛𝑜𝑛𝑎𝑔𝑟𝑖𝑔𝑑𝑝𝑡−2 𝑎𝑛𝑑 𝑙𝑜𝑔𝑐𝑜𝑟𝑒𝑡−2 are the independent
variables (explanatory variables) of the specified model and 𝜀𝑡 which is the error term.
After estimating the mean equation of the transport inflation CPI a GARCH equation is
estimated where 𝜑, 𝜔, 𝑎𝑛𝑑 𝜙 are the constant and coefficients of the GARCH term and the
ARCH term respectively.
3.2.3. Food and non-alcoholic beverages model specification
Mean equation:
𝑙𝑜𝑔𝑓𝑜𝑜𝑑𝑡 = 𝜌 + 𝜂 log 𝑛𝑜𝑛𝑎𝑔𝑟𝑖𝑔𝑑𝑝 + 𝜎𝑙𝑜𝑔𝑒𝑥𝑐ℎ𝑡−1 + 𝛽𝑙𝑜𝑔𝑓𝑟𝑒𝑠ℎ𝑝𝑟𝑜𝑑𝑢𝑐𝑡 + 𝜀𝑡 (5)
2
Volatility equation: ℎ𝑡 = 𝜑 + 𝜔ℎ𝑡−1 + 𝜙𝜇𝑡−1
(6)
In the above equations, the 𝑙𝑜𝑔𝑓𝑜𝑜𝑑𝑡 shows the food inflation CPI at time t, where
𝜌, 𝜂, 𝜎 𝑎𝑛𝑑 𝛽 are the constant and coefficient of the model.
𝑙𝑜𝑔𝑒𝑥𝑐ℎ𝑡−1 , 𝑙𝑜𝑔𝑓𝑟𝑒𝑠ℎ𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑎𝑛𝑑 𝑙𝑜𝑔𝑛𝑜𝑛𝑎𝑔𝑟𝑖𝑔𝑑𝑝 are the independent variables
(explanatory variables) of the specified model and 𝜀𝑡 which is the error term.
After estimating the mean equation of the food inflation CPI a GARCH equation is
estimated where 𝜑, 𝜔, 𝑎𝑛𝑑 𝜙 are the constant and coefficients of the GARCH term and the
ARCH term respectively.
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3.2.4. GDP model specification.
To understand how alienating the ideal that inflation volatility have an impact on
predicting economic growth in Rwanda we have specified an additional equation to the
main ones already specified above in the model specification section, this one holding the
GDP as the dependent variable with the headline CPI and the core CPI as the
independent variables. Running the model, we have observed the presence of the ARCH
effects in the residuals thus we used the GARCH models instead of the Ordinary Least
Squares method with our mean equation as : 𝑙𝑜𝑔𝐺𝐷𝑃𝑡 = 𝜌 + 𝜂 log ℎ𝑒𝑎𝑑𝑡−1 +
2
𝜎𝑙𝑜𝑔𝑐𝑜𝑟𝑒𝑡−1 + 𝜀𝑡 (7) and our volatility equation as: ℎ𝑡 = 𝜑 + 𝜔ℎ𝑡−1 + 𝜙𝜇𝑡−1
(8)
In the above equations, the 𝑙𝑜𝑔𝐺𝐷𝑃𝑡 shows the Gross Domestic Product at time t, where
𝜌, 𝜂 𝑎𝑛𝑑 𝜎 are the constant and coefficient of the model.
Log ℎ𝑒𝑎𝑑𝑡−1 𝑎𝑛𝑑 𝑙𝑜𝑔𝑐𝑜𝑟𝑒𝑡−1 are the independent variables (explanatory variables) of the
specified model and 𝜀𝑡 which is the error term.
After estimating the mean equation of the gross domestic product a GARCH equation is
estimated where 𝜑, 𝜔, 𝑎𝑛𝑑 𝜙 are the constant and coefficients of the GARCH term and the
ARCH term respectively.
3.3.
Data source, treatment, and variable description
In this study, the data were treated in different ways where we collected the data from
different sources and in different formats. In the CPI publication by the national institute
of Statistics, we selected the monthly data of the consumer price index on our selected
CPI components and put them in one excel sheet prior to testing.
We also collected quarterly GDP data from GDP publications from the national institute
of statistics and we transformed it into monthly data using excel formulas, therefore we
put them together with the CPI data in the same excel sheet prior to testing.
We have also taken exchange rate data in monthly format from the National bank of
Rwanda and we also put them together with the previously collected data in the same
excel sheet for prior testing. Finally, we took oil prices data from U.S Energy Information
Administration (EIA)s in a monthly format and put them together with the previously
collected data in the same excel sheet prior to testing.
After tabulating and transforming the data in one excel spreadsheet these were analyzed
using EVIEWS-9 software in order to reach the ultimate purpose of the study.
4. Results
This section of the study is providing the answers to the research questions and
hypothesis testing.
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4.1. Stationarity results
Noting that all the series (variables) prior running the models for the sake of ensuring
stationarity they were all subject to the ADF test, to test for their stationarity and they
were all found to be stationary (integrated) at first difference. See results of the ADF
below.
Table 1. Unit root test using ADF test results at level
Series/ unit root test at level
LOGAGRIGDP
LOGCORE
LOGENERGY
LOGEXCH
LOGFOOD
LOGFRESH_PRODUCT
LOGGDP
LOGHEAD
LOGHOUSING
LOGNONAGRIGDP
LOGOIL_PRICES
LOGTRANSPORT
Prob./individual
intercept
0.7199
0.9361
0.7773
0.9964
0.7233
0.5836
0.8258
0.8593
0.9034
0.8152
0.1905
0.2719
Prob./
trend
and intercept
0.1847
0.1984
0.0183
0.2613
0.1752
0.0171
0.0277
0.0719
0.0112
0.0320
0.0735
0.0084
Prob./none
0.9999
1.0000
0.9927
1.0000
0.9907
0.9775
1.0000
0.9999
0.9995
1.0000
0.6947
0.9139
Source: Authors calculation using EVIEWS 9
As it can be clearly seen the above table all the tested time series at level have the
probability higher than 5% which means that we can accept the null hypothesis that those
series have unit root at level hence not stationary and thus we can proceed testing for the
unit root at first difference.
Table 2. Unit root test using ADF test at first difference
Series/ unit root test at first
difference
D(LOGAGRIGDP)
D(LOGCORE)
D(LOGENERGY)
D(LOGEXCH)
D(LOGFOOD)
D(LOGFRESH_PRODUCT)
D(LOGGDP)
D(LOGHEAD)
D(LOGHOUSING)
D(LOGNONAGRIGDP)
D(LOGOIL_PRICES)
D(LOGTRANSPORT)
Prob./indiv
idual
intercept
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
Prob./
trend and
intercept
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
Prob./none
0.0000
0.0000
0.0000
0.0079
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
Source: Authors calculation using EVIEWS 9
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As it can be clearly observed in the table above all the series have the probability less than
5% at 1% which means that we can reject the null hypothesis suggesting that there is the
presence of unit root. Thus we can conclude that our series are stationary(integrated) at
first difference.
4.2. Estimation results for the analysis of the Heteroskedasticity test (the
ARCH effect).
In order to use the ARCH/GARCH models in any research, there have to be some
conditions or assumptions which are fulfilled, and that assumption is the presence of the
ARCH effect or simply the heteroskedasticity. To be able to do such, we have to estimate
the equations using Ordinary Least Square methods and then test their residuals
(heteroskedasticity test) in order to verify if really there is ARCH effect so that we can use
or not use the ARCH family models.
Therefore, we estimated the below equations so that we can determine whether or not
the ARCH family models are appropriate.
Figure 1. Estimation outputs for headline CPI using OLS method.
Source: Authors estimation using eviews 9
As it can be observed from the above output energy and agricultural GDP have a very
significant relationship with the housing CPI at 1% level of significance, where a 1%
increase in energy will lead to anincrease of 0.35% in housing CPI and a 1% increase in
agricultural GDP will lead to an increase of 0.12% in housing CPI. The R_squared of the
model is 0.98 % which means that our model is fit.
However, this estimation does not tell us much to wether we will be using the the ARCH
family models to understant the volatility in consumer prices of this this component of
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inflation. Reason why we have to test for the residuals so that we can confirm the presence
of the heteroskedasticity or not in our model so that we can go ahead with the ARCH
familiy models or not to explain the the volatility in the housing CPI.
Figure 2. Residuals for headline CPI
Source: authors estimation using EVIEWS9
After estimating the residual test for testing the presence of conditional
heteroskedasticity in our model we have found that basing on the above figure the
probability of Chi-square at lag 1 is very significant at 1% level of significance and that
the probability for the residuals are also strongly significant at 1% level of significance
which confirms that in our model there is the presence of heteroskedasticity and gives us
a go ahead to use the ARCH family models for the analysis of volatility in the housing
CPI.
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Figure 3. Estimation output for the food & non-alcoholic beverages using OLS
Source: authors estimation using EVIEWS9
As it can be observed from the above output the fresh product CPI and exchange rate
have a very significant relationship with the food and non-alcoholic beverage CPI at 1%
level of significance, where a 1% increase in fresh product CPI will lead to anincrease of
0.75% in food and non-alcoholic beverage CPI and a 1% increase in echange rate will lead
to an increase of 0.24% in food and non-alcoholic beverage CPI. However, the non
agricultural CPI though it seemingly have a negative relationship with the food and nonalcoholic beverage CPI that raltionship is not significant. The R_squared of the model is
0.99 % which means that our model is fit.
However, this estimation does not tell us much to wether we will be using the the ARCH
family models to understant the volatility in consumer prices of this this component of
inflation. Reason why we have to test for the residuals so that we can confirm the presence
of the heteroskedasticity or not in our model so that we can go ahead with the ARCH
familiy models or not to explain the the volatility in the food and non alcoholic beverages
CPI.
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Figure 4. Estimation output for the residuals of food & non-alcoholic beverages
Source: authors estimation using EVIEWS9
After estimating the residual test for testing the presence of conditional
heteroskedasticity in our model we have found that basing on the above figure the
probability of Chi-square at lag 1 is very significant at 1% level of significance and that
the probability for the residuals are also strongly significant at 1% level of significance
which confirms that in our model there is the presence of heteroskedasticity and gives us
a go ahead to use the ARCH family models for the analysis of volatility in the food and
nonalcoholic beverages CPI.
Figure 5. Estimation output for transport CPI using OLS.
Source: authors estimation using EVIEWS9
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As it can be observed from the above output the core CPI and non-agriculture GDP have
a very significant relationship with the transport CPI at 1% level of significance, where a
1% increase in core CPI will lead to anincrease of 1.85% in transport CPI and a 1% increase
in non agricultural GDP will lead to an decrease of 0.26% in transport CPI. However, the
oil prices and exchange rate though they seemingly have a negative and positive
relationship with the transport CPI that raltionship is not significant. The R_squared of
the model is 0.79 % which means that our model is fit.
However, this estimation does not tell us much to wether we will be using the the ARCH
family models to understant the volatility in consumer prices of this this component of
inflation. Reason why we have to test for the residuals so that we can confirm the presence
of the heteroskedasticity or not in our model so that we can go ahead with the ARCH
familiy models or not to explain the the volatility in the transport CPI.
Figure 6. Estimation output for residuals for transport CPI
Source: authors estimation using EVIEWS9
After estimating the residual test for testing the presence of conditional
heteroskedasticity in our model we have found that basing on the above figure the
probability of Chi-square at lag 1 is very significant at 1% level of significance and that
the probability for the residuals are also strongly significant at 1% level of significance
which confirms that in our model there is the presence of heteroskedasticity and gives us
a go ahead to use the ARCH family models for the analysis of volatility in the transport
CPI.
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Figure 7. Estimation output of the GDP using OLS
Source: authors estimation using EVIEWS9
As it can be observed from the above output core CPI have a very significant relationship
with the gross domestic product at 1% level of significance, where a 1% increase in core
CPI will lead to anincrease of 0.55% in GDP and the hadline CPI have a positive but non
significant relationship where a 1% in headline CPI will lead to an increase of 0.55% in
GDP. The R_squared of the model is 0.98 % which means that our model is fit.
However, this estimation does not tell us much to wether we will be using the the ARCH
family models to understant the volatility in consumer prices of this this component of
inflation. Reason why we have to test for the residuals so that we can confirm the presence
of the heteroskedasticity or not in our model so that we can go ahead with the ARCH
familiy models or not to explain the the volatility in the gross domestic product.
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Figure 8. Estimation output of the residuals for the GDP output
Source: authors estimation using EVIEWS9
After estimating the residual test for testing the presence of conditional
heteroskedasticity in our model we have found that basing on the above figure the
probability of Chi-square at lag 1 is very significant at 1% level of significance and that
the probability for the residuals are also strongly significant at 1% level of significance
which confirms that in our model there is the presence of heteroskedasticity and gives us
a go ahead to use the ARCH family models for the analysis of volatility in the gross
domestic product.
Table 3. Summary for the results of the heteroskedasticity test.
ARCH effect test for the specified equations
Equation
Prob. F(1,444)
Prob. Chi-square
RESID^2(-1)
housing
0.000
0.000
0.000
Food&
non-alcoholic 0.000
beverages
0.000
0.000
Transport
0.000
0.000
0.000
GDP
0.000
0.000
0.000
Source: Authors calculation using EVIEWS 9
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From the above results one can observe that there is the ARCH effect in the equations
tested, therefore we cannot use the ordinary least squares method to analyze and run the
models. Thus in this study we will be using the ARCH/GARCH family models.
4.3. Behavior of CPI volatility in Rwanda
As prior explained above, the consumer price volatility is the difference in price of the
commodity’s day to day percentage and it describes the fluctuations in commodities
prices. For us to understand this behavior we plot the residuals for the CPI volatility as
shown below;
Figure 9. Residuals for headline CPI
4.9
4.8
4.7
4.6
4.5
.02
4.4
.01
4.3
.00
-.01
-.02
-.03
09
10
11
12
13
Residual
14
15
16
17
Actual
18
19
20 21
Fitted
Source: Authors computation using EVIEWS9
As it can be observed on the above graph the inflation volatility is high and variant, with
period of high volatility followed by periods of high volatility and those of low volatility
followed by those of low volatility as indicated by the residuals. Observing the actual or
the inflation itself we can observe that inflation have been increasing but with different
variations over the selected period of February 2009 to May 2021.
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Figure 10. Residuals for core CPI in Rwanda.
4.9
4.8
4.7
.04
4.6
.03
.02
4.5
.01
4.4
.00
-.01
-.02
09
10
11
12
13
Residual
14
15
16
Actual
17
18
19
20 21
Fitted
Source: authors calculation using EVIEWS9
Similarly, as the headline CPI inflation, the slope of core CPI in Rwanda is upward and
rising and the residuals of this CPI is also fluctuating and variant however, though they
present similar conditions in the conditions of variance where periods of high volatility
are followed by periods of high volatility and those of low volatility followed by those of
low volatility, they do present major differences notably because even if there are
fluctuations they are different in that, on the headline CPI there is a very high volatility
compared to the core inflation which seems to be stable along the time with very low
volatility or fluctuations because this kind of inflation is controlled by the central bank.
However, it can be clearly noticed that in May of the 2020, the core CPI was at its pick
and this effect is not seen on the side of the headline inflation while the core inflation is
part of the headline inflation. To understand the reason behind this one need to first know
that the headline inflation is the core inflation and the prices of fresh products
(agricultural products) as well as energy including oil prices all together.
During the period of May 2020 in Rwanda as well as the world until date we were are
facing covid-19 pandemic which has affected our economy negatively and it was in that
period where Rwanda was in lock down and this have caused the core CPI to rise in its
components due to the consequent increase in imports while the exports were drastically
reduced, this was also due to the speculation and the high level of demand of products
of first necessities during that period which explains the pick in volatility in core inflation
due to that negative shock.
Nevertheless, this significant pick doesn’t appear in the headline inflation series as it was
curbed by the prices of oil, energy and fresh products which were very low at the period
due to the pandemic plus then significant drop in demand of oil due to the lockdowns.
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As prior mentioned above that the core inflation is the type of inflation that can be
controlled by the government as well as the central bank, this was also seen in that period
as different price controlling mechanisms that were put in place specially to deal with the
speculation and other controllable factors that were pushing up the level of prices mainly
of the core inflation, and this explains why in the month of June 2020 the prices started to
reduce and then reach to its volatile pick downward in October 2020 only to be stable
again in December of 2020 due to that positive shock induced by the price controlling
mechanisms by both the government (mainly through the ministry of commerce and
industries (MINICOM)) and the national bank of Rwanda (BNR).
4.4. Testing the first Hypothesis
Ho: Consumer price volatility has an effect on the economic growth in Rwanda
H1: consumer price volatility has no effect on the economic growth in Rwanda
When the market value of services and goods which are produced within an economy
increases or is increasing then we can talk about the economic growth. And the main
measure of economic growth is GDP (gross domestic product). In order to understand
well the impact of the CPI we estimated the equation (9) and (10).
4.4.1. Estimations output for the GARCH (1,1) pre-models for GDP.
In order for us to choose the best fitting model which can explain our hypothesis testing
we have to estimate all the equations using different error distributions so that we can
test their residuals so that we can determine the best fitting model.
Figure 11. GARCH (1,1) model estimation for GDP using normal distribution of
errors
Source: Authors estimation using EVIEWS9
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From the above output we can observe that the model output has very significant mean equation
where the lagged value of the headline inflation and the lagged value of the core inflation have
very significant coefficients at 1% level of significance which entails that a 1% increase in headline
and core inflation will cause an increase in GDP of 0.56% and 2.5% respectively.
The variance equation has also very significant ARCH and GARCH term at 1% level of
significance which means that the gross domestic product depends both on its past deviations
and its past volatility. The coefficient of persistence is also significant where it is of 1.0237 which
means that the present shocks will be seen in the forecasts for many periods ahead.
Figure 12. GARCH (1,1) model estimation for GDP using correlogram squared
residuals
Source: Authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
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Figure 13. GARCH (1,1) model estimation for GDP ARCH LM test
Source: Authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
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Figure 14. GARCH (1,1) using student’s t distribution of errors
Source: Authors estimation using EVIEWS9
From the above output we can observe that the model output has very significant mean equation
where the lagged value of the headline inflation and the lagged value of the core inflation have
very significant coefficients at 1% level of significance which entails that a 1% increase in headline
and core inflation will cause an increase in GDP of 0.56% and 2.5% respectively.
The variance equation has also very significant ARCH and GARCH term at 1% level of
significance which means that the gross domestic product depends both on its past deviations
and its past volatility. The coefficient of persistence is also significant where it is of 1.0332255
which means that the present shocks will be seen in the forecasts for many periods ahead.
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Figure 15. GARCH (1,1) correlerogram squared residuals
Source: Authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
Figure 16. GARCH (1,1) for GDP ARCH LM test.
Source: Authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
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Figure 17. GARCH (1,1) estimation output for GDP using generalized error distribution
Source: Authors estimation using EVIEWS9
From the above output we can observe that the model output has very significant mean equation
where the lagged value of the headline inflation and the lagged value of the core inflation have
very significant coefficients at 1% level of significance which entails that a 1% increase in headline
and core inflation will cause an increase in GDP of 0.51% and 2.59% respectively.
The variance equation has also very significant ARCH and GARCH term at 1% level of
significance which means that the gross domestic product depends both on its past deviations
and its past volatility. The coefficient of persistence is also significant where it is of 1.002822 which
means that the present shocks will be seen in the forecasts for many periods ahead.
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Figure 18. GARCH (1,1) correlerogram squared residuals
Source: Authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
Figure 19. GARCH (1,1) for GDP ARCH LM test.
Source: Authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
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4.4.1. Summary for residual diagnostics
In order to choose the best and fit model to represent the impact of CPI in predicting the
economic growth in Rwanda we have conducted different tests including those specified
above in the validity and reliability tests.
Table 4. Diagnostic tests for the GDP equation
Normal
Distribution
Significant coefficients
Five
ARCH significant
Yes
GARCH significant
Yes
Log like hood
284.2932
Adjusted R2
0.981954
Schwartz I C
-3.664244
Autocorelleration (ARCH LM test & None
Correlogram squared residuals)
Source: authors calculations using EVIEWS 9
Student t
Five
Yes
Yes
284.0342
0.982012
-3.626771
None
Generalized
Error (GED)
Five
Yes
Yes
286.4261
0.981695
-3.659314
None
Form the above results we can observe that the GARCH (1,1) model estimated using the
Normal(Gaussian) distribution is the one which is more fit than the others and which can
explain better how the CPI can play a role in predicting the level of economic growth in
Rwanda. As it has the Schwartz criterion which is very small compared to the other
similar models estimated.
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Figure 20. Estimation output for the chosen of the GDP equation
Source: authors calculations using EVIEWS9
The above mean equation results are suggesting that GDP is explained by healine CPIand
core CPI inflation. As a matter of fact one percent increase in the headline CPIincreases
the value of GDP by 0.56 percent and also that a one percent increase in core CPI will
increase the value of the GDP by 2.5 percent.
The results entails that there is a positive relationship between inflation and economic
growth in Rwanda, and these results are in line with the findings of (Ananias G, Mathias
K and KASAI N,, 2018) Where they found that there is existence of a non-linear
relationship between GDP growth and inflation in Rwanda and the optimal level was
estimated at 5.9% at the time which is where the GDP in Rwanda would be maximized .
This non-linear relationship between GDP growth and inflation in Rwanda means that
the economic growth and inflation in Rwanda have a positive consistent relationship up
to a certain point or threshold level of inflation where, if it goes over that point the
economic growth in Rwanda will start to decline.
More to that, the threshold inflation varies between 1.0% – 3.0% for developed countries,
11.0% – 12.0% for developing countries and 9.0% for all countries, respectively. For SubSaharan Africa, Ndoricimpa (2017) estimated the inflation threshold at 9.0% for lowincome countries, 6.5% for middleincome countries and 6.7% for all countries taken
together as per ( Khan, M. S. and A.S. Senhadji, 2000).
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Additionally, in the chosen period inflation in Rwanda wether the headline CPI or the
core CPI they did not exceed the threshold band for the deveoping countries and even
the core CPI have not also exceeded the the inflationary band set by the central bank of
5 ± 3 and this can explain the results in our mean equation where inflation have a
significant and positive relationship with the economic Growth .
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) using the normal Gaussian distribution of errors is the one which is more
appropriate to estimated and explain the GDP volatilty, and from the results above it is
noticed that both the ARCH and the GARCH term are significant which means that the
GDP volatility depends both on its past deviations as well as it past volatility. The
persistance coeffcient (sum of ARCH and GARCH parameters) (𝜔 + 𝜙) equivalent to
C(6) and C(5) respectively in the estimation output is 1.0237 which is above the
conditions of stationarity which is set as 𝜔 + 𝜙 should be less than one and in our case it
is not fullfiling the conditions which means that the effects of todays schocks in GDP dies
away slowly and remains in the forecasts of variance for many periods in the future.
Thus we can conclude by accepting the null hypothesis that the CPI volatility have an
impact in predicting the economic growth in Rwanda as the coeffients of the mean
equation are very significant in predicting the economic growth togther with the
significant GARCH and ARCH terms whose also the persistant volatility as present
shocks last long in the forecasts of many periods ahead.
This implies that given that inflation in Rwanda is maximizing the econmic growth this
will favor investiments, employment creation, innovations, the competitiveness to
exports and etc
However, if the volatility in that GDP is highly volatile and persitent to an extent where
the optimal inflation level is surpased this will affect the aggregate demand and the
investiments as well as firms which by the fear of paying higher rates in raising capital
will be less likely to hire new employees or undertake new capital investiments.
3.5. Testing for the second hypothesis testing
As afore mentioned above our hypothesis goes like;
Ho: There is persistence in CPI volatility in Rwanda
H1: There is no persistence in CPI volatility in Rwanda
And to test this hypothesis we picked four main components of the CPI in Rwanda and
considered them as the dependent variables as explained and elaborated in chapter 2
section 2.5. regarding the model specification. Therefore, in this section we are going to
test the hypothesis that CPI is persistent in Rwanda on each of the specified models.
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4.4.1. Estimations outputs for the GARCH (1,1) pre-models for housing CPI.
In order for us to choose the best fitting model which can explain our hypothesis testing
we have to estimate all the equations using different error distributions so that we can
test their residuals so that we can determine the best fitting model.
Figure 21. GARCH (1,1) model estimation for housing CPI using normal distribution
of errors
Source: authors calculations using EVIEWS9
The above mean equation results are suggesting that housing CPIis explained by energy
CPI and agricultural GDP as they are all very significant at one percent level of
significance . As a matter of fact one percent increase in the energy CPI increases the value
of housing CPI by 0.36 percent and one percent increase in agricultural GDP will increase
the value of the housing CPI by 0.12 percent. And these results are very significant which
means that the explanatory variables have a very high level of significance in predicting
the level of housing CPI inflation.
Considering the variance equation we can observe that the estimated GARCH(1,1) it is
noticed that only the ARCH term is significant which means that the housing CPI
volatility depends only on its past deviations but not on it past volatility. The persistance
coeffcient (the ARCH term in this case) is 0.635147 which is fullfiling the conditions of
stationarity which should be less than one and in our case it is fullfiling this condition
which means that the effects of todays schocks in housing CPI dies away quickly and
doesn’t remains in the forecasts of variance for many periods in the future
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Figure 22. GARCH (1,1) model estimation for housing CPI using correlogram squared
residuals
Source: authors calculations using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
Figure 23. GARCH (1,1) model estimation for housing CPI ARCH LM test
Source: authors calculations using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
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significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
Figure 24. GARCH (1,1) using student’s t distribution of errors
Source: authors estimation using EVIEWS9
The above mean equation results are suggesting that housing CPIis explained by energy
CPI and agricultural GDP as they are all very significant at one percent level of
significance . As a matter of fact one percent increase in the energy CPI increases the value
of housing CPI by 0.36 percent and one percent increase in agricultural GDP will increase
the value of the housing CPI by 0.11 percent. And these results are very significant which
means that the explanatory variables have a very high level of significance in predicting
the level of housing CPI inflation.
Considering the variance equation we can observe that the estimated GARCH(1,1) it is
noticed that only the ARCH term is significant and behaving normally which means that
the housing CPI volatility depends only on its past deviations but not on it past volatility.
The persistance coeffcient (the ARCH term in this case) is 1.070386 which is not fullfiling
the conditions of stationarity which should be less than one and in our case it is not
fullfiling this condition which means that the effects of todays schocks in housing CPI
dies away slowly and remains in the forecasts of variance for many periods in the future.
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Figure 25. GARCH (1,1) correlerogram squared residuals
Source: authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
Figure 26. GARCH (1,1) for housing ARCH LM test.
Source: authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
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Figure 27. GARCH (1,1) estimation output for housing using generalized error
distribution
Source: authors estimation using EVIEWS9
The above mean equation results are suggesting that housing CPIis explained by energy
CPI and agricultural GDP as they are all very significant at one percent level of
significance . As a matter of fact one percent increase in the energy CPI increases the value
of housing CPI by 0.40 percent and one percent increase in agricultural GDP will increase
the value of the housing CPI by 0.11 percent. And these results are very significant which
means that the explanatory variables have a very high level of significance in predicting
the level of housing CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) using the generalized distribution of errors is the one which is more
appropriate to estimated and explain the time-varying volatility in housing CPI inflation,
and from the results above it is noticed that both the ARCH and the GARCH term are
significant which means that the housing CPI volatility depends both on its past
deviations as well as it past volatility. The persistance coeffcient (sum of ARCH and
GARCH parameters) (𝜔 + 𝜙) equivalent to C(6) and C(5) respectively in the estimation
output is 0.843901 which is fullfiling the conditions of stationarity which is set as 𝜔 + 𝜙
should be less than one and in our case it is fullfiling this condition which means that the
effects of todays schocks in housing CPI dies away quickly and doesn’t remains in the
forecasts of variance for many periods in the future.
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Figure 28. GARCH (1,1) correlerogram squared residuals
Source: authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are less than the 10% thus we can conclude that there is
autocorelleration in our model.
Figure 29. GARCH (1,1) for housing ARCH LM test.
Source: authors estimation using EVIEWS9
From the above figure we can confirm that there is autocorelleration in our model as
both the Chi-square and the WGT_residual probability is less the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model cannot be considered for further selection.
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Table 4. Summary for the diagnostic test for housing CPI
Normal
Distribution
Significant coefficients
Four
ARCH significant
Yes
GARCH significant
No
Log likehood
489.4255
2
Adjusted R
0.983957
Schwartz I C
-6.411269
Autocorelleration (ARCH None
LM test & Correlogram
squared residuals)
Source: authors calculations using EVIEWS 9
Student t
All
Yes
Yes
490.5212
0.982798
-6.392311
None
Generalized Error
(GED)
All
Yes
Yes
497.8066
0.982914
-6.490761
yes
Form the above results we can observe that the GARCH (1,1) model estimated using the
Normal distribution of errors is the one which is more fit than the others and which can
explain better the behavior in time-varying volatility in the housing CPI in Rwanda. As
it has the highest R-squared value and the Schwartz criterion which is very small
compared to the other similar models estimated.
Figure 30. Estimation output for the chosen housing CPI model
Source: Authors calculations using EVIEWS9
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The above mean equation results are suggesting that housing CPIis explained by energy
CPI and agricultural GDP as they are all very significant at one percent level of
significance . As a matter of fact one percent increase in the energy CPI increases the value
of housing CPI by 0.36 percent and one percent increase in agricultural GDP will increase
the value of the housing CPI by 0.12 percent. And these results are very significant which
means that the explanatory variables have a very high level of significance in predicting
the level of housing CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) using the normal distribution of errors is the one which is more appropriate
to estimate and explain the time-varying volatility in housing CPI inflation, and from the
results above it is noticed that only the ARCH term is significant which means that the
housing CPI volatility depends only on its past deviations but not on it past volatility.
The persistance coeffcient (the ARCH term in this case) is 0.635147 which is fullfiling the
conditions of stationarity which should be less than one and in our case it is fullfiling
this condition which means that the effects of todays schocks in housing CPI dies away
quickly and doesn’t remains in the forecasts of variance for many periods in the future.
Thus we can conclude by rejecting the null hypothesis that CPI is not persistant in the
case of housing inflation even though as prior mentioned the periods of high volatility
are followed by those of high volatility and vice versa, but the schocks in this component
of CPI are not long lasting in the periods ahead.
The housing variable index is calculated together with water, electricity, gas and other
fuels and those are essential goods and services that the househlds depends on day to
day for their activities and survival. Most of them like housing, water and electricity it is
very hard to substitue them, which means that even if there is an increase in in their prices
people will still have to consume. And given the important weight of this component in
the CPI basket of 2,075 in Rwanda. Thus, even a slight increase in that component CPI
will be noticable in the overall inflation inflation in Rwanda. Therefore, if there is a high
increase in this component’s CPI which is significantly persistant it can drive the inflation
higher and though that effect won’t be longlasting in periods ahead as seen above with
the persistance coefficient.
However, as is very difficult to control the energy prices and the agricultural gross
domestic product for they are affected by wide range of factors that the central bank
cannot control, their should be a coordination between the central bank’s policies and the
government policies. Where the government can set policies that can curb the rise in the
energy prices as well as the drop down of the output in the agricultural production i.e.
sacrificing some revenues that the government could get through taxes from gas, energy,
fuel in the period of high volatility in prices for those commodities so that they prices can
not go higher on the market which can lead to the rise in housing CPI as seen in the model
and many more.
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4.4.2. Outputs for the GARCH (1,1) pre- models for food and non-alcoholic beverages
CPI.
In order for us to choose the best fitting model which can explain our hypothesis testing
we have to estimate all the equations using different error distributions so that we can
test their residuals so that we can determine the best fitting model.
Figure 31. GARCH (1,1) model estimation for food& non-alcoholic CPI using normal
distribution of errors
Source: authors estimation using EVIEWS9
The above mean equation results are suggesting that food& non-alcoholic CPI is
explained by a one month lagged value of exchange rate, fresh products prices and nonagricultural GDP as they are all very significant at one percent level of significance . As a
matter of fact one percent increase in the exchange rate increases the value of food& nonalcoholic CPI by 0.24 percent , one percent increase in fresh product CPI increases the
food& non-alcoholic CPI by 0.68 percent and one percent increase in non-agricultural
GDP CPI will lead to a decrease of food& non-alcoholic CPI of 0.017 percent. And these
results are very significant which means that the explanatory variables have a very high
level of significance in predicting the level of headline CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) using the normal Gaussian distribution of errors is the one which is more
appropriate to estimated and explain the food& non-alcoholic CPIvolatilty, and from the
results above it is noticed that both the ARCH and the GARCH term are significant which
means that the headline CPI volatility depends both on its past deviations as well as it
past volatility. The persistance coeffcient (sum of ARCH and GARCH parameters) (𝜔 +
𝜙) equivalent to C(9) and C(8) respectively in the estimation output is 1.1377.53 which
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is not fullfiling the condition of stationarity which is set as 𝜔 + 𝜙 should be less than one
and in our case it is not fullfiling this condition which means that the effects of todays
schocks in food& non-alcoholic CPI in dies away slowly and remains in the forecasts of
variance for many periods in the future.
Figure 32. GARCH (1,1) model estimation for food& non-alcoholic CPI using
correlogram squared residuals
Source: authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
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Figure 33. GARCH (1,1) model estimation for food& non-alcoholic CPI ARCH LM
test
Source: authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
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Figure 34. GARCH (1,1) using student’s t distribution of errors
Source: authors estimation using EVIEWS9
The above mean equation results are suggesting that food& non-alcoholic CPI is
explained by a one month lagged value of exchange rate, fresh products prices and nonagricultural GDP as they are all very significant at one percent level of significance. As a
matter of fact, one percent increase in the exchange rate increases the value of food& nonalcoholic CPI by 0.24 percent, one percent increase in fresh product CPI increases the
food& non-alcoholic CPI by 0.68 percent and one percent increase in non-agricultural
GDP CPI will lead to a decrease of food& non-alcoholic CPI of 0.017 percent. And these
results are very significant which means that the explanatory variables have a very high
level of significance in predicting the level of headline CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) using the normal Gaussian distribution of errors is the one which is more
appropriate to estimated and explain the food& non-alcoholic CPI volatility, and from
the results above it is noticed that both the ARCH and the GARCH term are significant
which means that the headline CPI volatility might depend both on its past deviations as
well as it past volatility however, the GARCH term behaves poorly which means that the
model depends on its past deviations only. The ARCH term is equivalent to 1.093137
which is not fulfilling the condition of stationarity which should be less than one and in
our case it is not fulfilling this condition which means that the effects of today’s shocks in
food& non-alcoholic CPI in dies away slowly and remains in the forecasts of variance for
many periods in the future.
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Figure 35. GARCH (1,1) correlerogram squared residuals
Source: authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
Figure 36. GARCH (1,1) for food and non-alcoholic beverages ARCH LM test.
Source: authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
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Figure 37. GARCH (1,1) estimation output for food and non-alcoholic beveages using
generalized error distribution
Source: authors estimation using EVIEWS9
The above mean equation results are suggesting that food& non-alcoholic CPI is
explained by a one month lagged value of exchange rate, fresh products prices and nonagricultural GDP as they are all very significant at one percent level of significance. As a
matter of fact, one percent increase in the exchange rate increases the value of food& nonalcoholic CPI by 0.23 percent, one percent increase in fresh product CPI increases the
food& non-alcoholic CPI by 0.68 percent and one percent increase in non-agricultural
GDP CPI will lead to a decrease of food& non-alcoholic CPI of 0.013 percent. And these
results are very significant which means that the explanatory variables have a very high
level of significance in predicting the level of headline CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH (1,1) using the normal Gaussian distribution of errors is the one which is more
appropriate to estimated and explain the food& non-alcoholic CPI volatility, and from
the results above it is noticed that only the ARCH term is significant which means that
the headline CPI volatility depends only on its past deviations. The ARCH term is
equivalent to 1.093137 which is not fulfilling the condition of stationarity which should
be less than one and in our case it is not fulfilling this condition which means that the
effects of today’s shocks in food& non-alcoholic CPI in dies away slowly and remains in
the forecasts of variance for many periods in the future.
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Figure 38. GARCH (1,1) correlerogram squared residuals
Source: authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
Figure 39. GARCH (1,1) for food& non-alcoholic ARCH LM test.
Source: authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 5% level of
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significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
Table 5. Summary for the diagnostic test for food& no-alcoholic beverages
Normal
Distribution
Significant coefficients
All
ARCH significant
Yes
GARCH significant
Yes
Log like hood
441.9095
2
Adjusted R
0.990327
Schwartz I C
-5.774734
Autocorelleration (ARCH None
LM test & Correlogram
squared residuals)
Source: authors calculations using EVIEWS 9
Student t
Six
Yes
Yes
446.1959
0.990185
-5.799104
None
Generalized Error
(GED)
Five
Yes
No
444.6511
0.990307
-5.778087
None
Form the above results we can observe that the GARCH (1,1) model estimated using the
Normal(Gaussian) distribution is the one which is more fit than the others and which can
explain better the behavior in time-varying volatility in food& non alcoholic beverages
CPIin Rwanda. As it has the highest adjusted R squared which all coefficients being
significant. However, though the model estimated using the student t error distribution
has the lowest Schwartz criterion compared to the other similar models estimated its
GARCH term behaves poorly as it has sign bias being negative.
Figure 40. Estimation output for the chosen food &non-alcoholic
beverages CPI model
Source: Authors calculations using EVIEWS9
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The above mean equation results are suggesting that food& non-alcoholic CPI is
explained by a one month lagged value of exchange rate, fresh products prices and nonagricultural GDP as they are all very significant at one percent level of significance . As a
matter of fact one percent increase in the exchange rate increases the value of food& nonalcoholic CPI by 0.24 percent , one percent increase in fresh product CPI increases the
food& non-alcoholic CPI by 0.68 percent and one percent increase in non-agricultural
GDP CPI will lead to a decrease of food& non-alcoholic CPI of 0.017 percent. And these
results are very significant which means that the explanatory variables have a very high
level of significance in predicting the level of headline CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) using the normal Gaussian distribution of errors is the one which is more
appropriate to estimated and explain the food& non-alcoholic CPIvolatilty, and from the
results above it is noticed that both the ARCH and the GARCH term are significant which
means that the headline CPI volatility depends both on its past deviations as well as it
past volatility. The persistance coeffcient (sum of ARCH and GARCH parameters) (𝜔 +
𝜙) equivalent to C(9) and C(8) respectively in the estimation output is 1.1377.53 which
is not fullfiling the condition of stationarity which is set as 𝜔 + 𝜙 should be less than one
and in our case it is not fullfiling this condition which means that the effects of todays
schocks in food& non-alcoholic CPI in dies away slowly and remains in the forecasts of
variance for many periods in the future.
Thus we can conclude by acepting the null hypothesis that CPI is persistant in the case
of food& non-alcoholic inflation even though as prior mentioned the periods of high
volatility are followed by those of high volatility and vice versa, it is also observed that
the schocks in this component of CPI are long lasting in the periods ahead.
Given that the food and non-alcoholic beverages have the biggest weight in the CPI
basket of 2,738 a high and persistent volatility in that component of the CPI is not good
as this can affect the people’s purchasing power on food and non-alcoholic beverages and
can drive easily the overall inflation high.
And as it is difficult to control the fresh products CPI, the government should ensure that
there are appropriate policies i.e. helping farmers have good irrigation means and large
modern warehouses. So that even in in time of climatic hardiships or bad seasons can not
affect the fresh product prices as well as the food and non-alcoholic CPI.
4.4.2. Estimations output for the GARCH (1,1) pre-models for transport CPI.
In order for us to choose the best fitting model which can explain our hypothesis testing
we have to estimate all the equations using different error distributions so that we can
test their residuals so that we can determine the best fitting model.
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Figure 41. GARCH (1,1) model estimation for transport CPI using normal distribution
of errors
Source: authors estimation using EVIEWS9
The above mean equation results are suggesting that transport CPIis explained by a one
month lagged value of exchange rate, two month lagged value of core CPI inflation, two
months lagged value of oil prices and two months lagged value of non agricultural GDP
as they are all very significant at one percent level of significance . As a matter of fact one
percent increase in the exchange rate decreases the value of transport CPI by 0.030 percent
, one percent increase in core CPI will increase the value of the transport CPI by 1.70
percent, one percent increase in oil prices decreases the transport CPI by 0.04 percent and
one percent increase in non agricultural GDP will lead to an decrease of transport CPI of
0.21 percent. And these results are very significant which means that the explanatory
variables have a very high level of significance in predicting the level of transport CPI
inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) and from the results above it is noticed that only the ARCH and GARCH
term are significant which means that the transport CPI volatility depends on its past
deviations and on its past volatility. The persistance coeffcient (sum of ARCH and
GARCH parameters) (𝜔 + 𝜙) equivalent to C(9) and C(8) respectively in the estimation
output is 1.504611 which is not fullfiling the conditions of stationarity which is set as 𝜙
should be laying between zero and one therefore in our case it is not fullfiling this
condition which means that the effects of todays schocks in headline CPI in dies away
slowly and does remains in the forecasts of variance for many periods in the future.
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Figure 42. GARCH (1,1) model estimation for transport CPI using correlogram squared
residuals
Source: authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are less the 10% thus we can conclude that there is autocorelleration
in our model.
Figure 43. GARCH (1,1) model estimation for transport CPI ARCH LM test
Source: authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
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significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model cannot be considered for further selection.
Figure 44. GARCH (1,1) using student’s t distribution of errors
Source: authors estimation using EVIEWS9
The above mean equation results are suggesting that transport CPIis explained by a one
month lagged value of exchange rate, two month lagged value of core CPI inflation, two
months lagged value of oil prices and two months lagged value of non agricultural GDP
as they are all very significant at one percent level of significance . As a matter of fact one
percent increase in the exchange rate decreases the value of transport CPI by 0.018 percent
, one percent increase in core CPIwill increase the value of the transport CPI by 1.60
percent, one percent increase in oil prices increases the transport CPI by 0.032 percent
and one percent increase in non agricultural GDP will lead to an decrease of transport
CPI of 0.14 percent. And these results are very significant which means that the
explanatory variables have a very high level of significance in predicting the level of
transport CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) and from the results above it is noticed that only the ARCH term is
significant which means that the transport CPI volatility depends on its past deviations
but not on its past volatility. The ARCH term coeffcient 𝜙 equivalent to C(7) respectively
in the estimation output is 1.348036 which is not fullfiling the conditions of stationarity
which is set as 𝜙 should be laying between zero and one therefore in our case it is not
fullfiling this condition which means that the effects of todays schocks in headline CPI in
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dies away slowly and does remains in the forecasts of variance for many periods in the
future.
Figure 45. GARCH (1,1) correlerogram squared residuals
Source: authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
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Figure 46. GARCH (1,1) for transport ARCH LM test.
Source: authors estimation using EVIEWS9
From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
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Figure 47. GARCH (1,1) estimation output for housing using generalized error
distribution
Source: authors estimation using EVIEWS9
The above mean equation results are suggesting that transport CPIis explained by a one
month lagged value of exchange rate, two month lagged value of core CPI inflation, two
months lagged value of oil prices and two months lagged value of non agricultural GDP
as they are all very significant at one percent level of significance . As a matter of fact
with the exception of exchange rate where one percent increase in the exchange rate
increases the value of transport CPI by 0.012 percent but is not significance , one percent
increase in core CPI will increase the value of the transport CPI by 1.45 percent, one
percent increase in oil prices increases the transport CPI by 0.038 percent and one percent
increase in non agricultural GDP will lead to an decrease of transport CPI of 0.18 percent.
And these results are very significant which means that the explanatory variables have
a very high level of significance in predicting the level of transport CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) and from the results above it is noticed that only the ARCH term is
significant which means that the transport CPI volatility depends on its past deviations
but not on its past volatility. The ARCH term coeffcient 𝜙 equivalent to C(7) respectively
in the estimation output is 1.348036 which is not fullfiling the conditions of stationarity
which is set as 𝜙 should be laying between zero and one therefore in our case it is not
fullfiling this condition which means that the effects of todays schocks in headline CPI in
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dies away slowly and does remains in the forecasts of variance for many periods in the
future.
Figure 48. GARCH (1,1) correlerogram squared residuals
Source: authors estimation using EVIEWS9
From the figure above one can notice that the correlegram squared residuals have
probabilities which are above the 10% thus we can conclude that there is no
autocorelleration in our model.
Figure 49. GARCH (1,1) for transport ARCH LM test.
Source: authors estimation using EVIEWS9
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From the above figure we can confirm that there is no autocorelleration in our model as
both the Chi-square and the WGT_residual probability is above the 10% level of
significance. Plus, the model has passed both the correlegram squared residuals and
ARCH LM tests which means that our model can be considered for further selection.
Table 6. Summary of diagnostic test for transport CPI
Normal
Distribution
Student t
Generalized
Error (GED)
Significant coefficients
Six
Seven
Six
ARCH significant
Yes
Yes
Yes
GARCH significant
Yes
No
Yes
Log like hood
273.0926
291.0037
273.9224
Adjusted R2
0.752298
0.759479
0.716811
Schwartz I C
-3.467920
-3.679144
-3.445153
None
None
Autocorelleration (ARCH Yes(with
LM test & Correlogram correlegram
squared residuals)
squared residuals)
Source: authors calculations using EVIEWS 9
Form the above results we can observe that the GARCH (1,1) model estimated using the
student t error distribution as it is the one which is more fit than the others and which
can explain better the behavior in time-varying volatility in transport CPIin Rwanda. As
it has the highest adjusted R squared, log likehood and the Schwartz criterion which is
very small compared to the other similar models estimated.
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Figure 50. Estimation output for choosen transport CPI model
Source: Authors calculations using EVIEWS9
The above mean equation results are suggesting that transport CPIis explained by a one
month lagged value of exchange rate, two month lagged value of core CPI inflation, two
months lagged value of oil prices and two months lagged value of non agricultural GDP
as they are all very significant at one percent level of significance . As a matter of fact one
percent increase in the exchange rate decreases the value of transport CPI by 0.018 percent
, one percent increase in core CPIwill increase the value of the transport CPI by 1.60
percent, one percent increase in oil prices increases the transport CPI by 0.032 percent
and one percent increase in non agricultural GDP will lead to an decrease of transport
CPI of 0.14 percent. And these results are very significant which means that the
explanatory variables have a very high level of significance in predicting the level of
transport CPI inflation.
Considering the variance equation (volatility equation) we can observe that the estimated
GARCH(1,1) using the student t distribution of erro is the onthatch is more appropriate
to estimated and explain the transport CPIvolatilty, and from the results above it is
noticed that only the ARCH term is significant which means that the transport CPI volatil
depends n its past deviations but not on its past volatility. The ARCH tercoefficientnt 𝜙
equivalent to C(7) respectively in the estimation outpu is 1.348036 which is notfulfillingg
the conditions of stationarity which is set as 𝜙 should be laying between zero and one
therefore in our case it is not ulfilling this condition which means that the effects of
today’s shocks in headline CPI in dies away slowly and does remain in the forecasts of
variance for many periods in the future.
Thus we can conclude by accepting the null hypothesis that CPIis persistent in the case
of transport inflation even though as prior mentioned the periods of high volatility are
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followed by those of high volatility and vice versa, it is also observed that the shocks in
this component of CPIare long-lasting in the periods ahead.
Despite the weight of 1,245 of the transport CPI in the CPI basket, an increase in transport
prices affects enormously the economy in terms of movement of people, goods, and
delivery of services as transport is a major factor of economic growth, therefore, the
government could put price regulating mechanismsms’s that can help in regulating the
transport prices so that their volatility cannot be very high which can affect even the
overall inflation or even stagnate the economic growth.
5. Conclusion and policy recommendations
For the sake of understanding inflation dynamics in Rwanda, this research paper estimates the
magnitude and persistence in consumer price indices in Rwanda by considering housing, food
&non-alcoholic beverages and transport CPI in the period between 2009 and 2021 using monthly
data obtained from the National Institute of Statistics of Rwanda, the National bank of Rwanda
and the U.S Energy Information Administration.
After running the data, answering the different research questions, and testing the hypothesis
this study has reached the following conclusions:
The inflation volatility is high and variant, with periods of high volatility followed by periods of
high volatility and those of low volatility followed by those of low volatility as indicated by the
residuals of the headline and those of the core CPI and by observing the actual or the inflation
itself we can observe that inflation has been increasing but with different variations over the
selected period of February 2009 to May 2021.
There non-linear relationship between GDP growth and inflation in Rwanda where the economic
growth and inflation in Rwanda have a positive consistent relationship up to a certain point or
threshold level of inflation where, if it goes over that point the economic growth in Rwanda will
start to decline. These also indicated that the effects of todays’ shocks in GDP dies away slowly
and remains in the forecasts of variance for many periods in the future as its persistence
coefficients exhibit the conditions of stability thus the model being explosive as the persistence
coefficient was 1.0237 above one than one and all the coefficients of the mean equation were
significant at one percent level thus the null hypothesis was accepted.
For the housing CPI the the null hypothesis was rejected as the CPI is not persistent as the shocks
in this component of CPI are not long-lasting in the periods ahead as the persistence coefficient
of the model is less than one which means that it fulfills the pre-requisite condition for stability
as the persistence coefficient was 0.843901 less one than one and all the coefficients of the mean
equation were significant at one percent level thus the null hypothesis rejected accepted.
For the transport CPI and the food& non-alcoholic beverages the null hypothesis was accepted
as the CPI is persistent as the shocks in this component of CPI are long-lasting in the periods
ahead as the persistent coefficient of the model does not fulfill the pre-requisites condition for
stability as the persistence coefficient was 1.137753 and 1.348036 respectively above one than one
and all the coefficients of the mean equation were significant at one percent level thus the null
hypothesis was accepted.
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More to that, for the transport CPI, it was seen that this component of inflation does not depend
on its past volatility but instead on its past deviations as the GARCH term is not significant.
As a matter of recommendation; further research should be made in this area because so far there
is very little literature in analyzing consumer price volatility and the available papers are very
scarce to date, thus further research incentives on this subject will bring more innovations and
understanding of the discussed matter.
As Rwanda is now using inflation targeting (price-based monetary policy), the study of consumer
price volatility needs more attention as it helps a lot in understanding the inflation dynamics.
Therefore, the national bank of Rwanda, individual researchers, and policymakers should bring
more interest on this subject.
Additionally, in forecasting and predicting the inflation and inflation volatility alongside the
currently used models including the NTFS and ARMA the ARCH family models should also be
considered as they can increase accuracy in the near term forecast for the consumer prices.
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Works Cited
Adam and Khadija. (2020, November 11). Econometrics. Retrieved from Investopedia:
https://www.investopedia.com/terms/e/econometrics.asp
Arora, S. K. (2021, may 27). What is Data Analysis? Methods, Techniques & Tools. Retrieved from
hackr.io: https://hackr.io/blog/what-is-data-analysis-methods-techniques-tools
Awogbemi C.A and A.I Oluwaseyi . (2011). modeling volatility in financial time series. Evidence from
Nigeria inflation rate. Ozean journal of appled sciences VOL4(3): 340-344.
Ananias G, Mathias K and KASAI N, (2018). Optimal inflation for economic growth in Rwanda. BNR
economic Review 13.
Balcilar , M. and Ozdemir, A. (2013). Asymmetric and time varying causality between inflation and
inflation uncertainity in G7 countries . scottish journal of political economy , 60(1).
Bamanga, Muhammad A. et al. (2016). Inflation and inflation uncertainty in Nigeria: A test of. CBN
Journal of Applied Statistics, 24.
Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity,. Journal of
Econometrics, 31, 307–327.
Cariolle.J. (2012). measuring macroeconomic volatity: Applications to export revenue data, 1970-2005.
fondation pour les etudes et recherche sur le development. international working paper series N0 114.
Chow, G. C., and Lin, A. L. (1971). Best linear unbiased interpolation, distribution, and extrapolation of
time series by related series. The Review of Economics and Statistics, 53(4), 372-375.
Conrad, C.and Karanasos, M. (2005). on the inflation-uncertainity hypothesis in the USA, Japan, UK;
a dual long memory approach . Japan and the world economy , 17: 327-343.
Edge, M. (2021). Statistical Thinking from Scratch. A Primer for Scientists.
Engle, R.F., and Ng, V.K. . (1993). Measuring and testing the impact of news on volatility. Journal of
Finance,, 48, 1749–1777.
Fernando, J. (2021, september 07). consumer price index. Retrieved 09 11, 2021, from investopedia:
https://www.investopedia.com/terms/c/consumerpriceindex.asp
Fisher, I. (1911). The Purchasing Power of Money. London: Macmillan., 200.
Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: John Wiley and Sons. ISBN 0471-28715-6.
Goudarzi and Ramanaryanan. (2010). modelling and estimation of volatility in indian stock market.
International journal of business and managment vol5(21;85-98.
Rwanda’s Economic Health
Page 62
Hegerty, S. (2012). Does High Inflation lead to increased inflation. African Economic and Business
Review, 10(2).
ILO, i. l. (2004). consumer price index manual: theory and practice . Geneva : Publications of the
International Labour Office, the International Monetary Fund, the Organisation for.
James, C. (2021, june 28). time-varying volatility.
https://www.investopedia.com/terms/t/time-varying-volatility.asp
Retrieved
from
investopedia:
Jason .F and Peter.W. (2021, july 13). Consumer Price Index (CPI). Retrieved july 31, 2021, from
investopedia: https://www.investopedia.com/terms/c/consumerpriceindex.asp
John, C. .. (2018, MAY 7). How to Perform a Heteroskedasticity Test. Retrieved from Magoosh Statistics
Blog: https://magoosh.com/statistics/how-to-perform-a-heteroskedasticity-test/
Judson.R and A.Orphanides. (1999). Inflation volatility and growth. journal of international finance
vol.2(1): 117-138.
Kendra Cherry and Amy Morin, LCSW . ( 2020, September 08). Forming a Good Hypothesis for
Scientific Research. Retrieved 07 25, 2021, from very well mind: https://www.verywellmind.com/what-isa-hypothesis-2795239
Khalafalla. (2010). Association between inflation and uncertainity. journal of business studies Quarterly
vol2(1):36-5.
Kotonikas, A. (2004). Inflation and Inflation Uncertainty in the United. Economic Modelling.
Lama,A. Jha, G., R.Paul, B. Gurug. (2015). modeleing and forecasting of price volatility, an application
of GARCH and EGARCH models. agricutural research review vol28(1): , 73-82.
Maniraguha F,Karangwa M, Mwenese B and Bagabe J. (2019). estimating time-varying volatilty of
consummer prices in Rwanda: application of GARCH models. BNR economic review 14.
Middleton, F. (2020, june 19). The four types
https://www.scribbr.com/methodology/types-of-validity/
of
validity.
Retrieved
from
scribbr:
Middleton., F. (2021, july 16). Types of reliability and how to measure them. Retrieved from scribbr:
https://www.scribbr.com/methodology/types-of-reliability/
Mishkin F. and A. Posen. (1998). Inflation targeing: lessons from four countries. National bureaux of
Economic Research . Working paper 6126.
NISR. (july 2021). consumer price index CPI june 2021. Kigali: National institute of statistics of Rwanda.
Omotosho, B.S and Doguwa, S. I. . (2013). Understanding the Dynamics of nflation Volatility in
Nigeria: A GARCH Perspective. CBN Journal of Applied Statistics, 3(2).
Rwanda’s Economic Health
Page 63
Press, C. D. (2021, 09 10). meaning of volatility in english . Retrieved from Cambridge Dictionary :
https://dictionary.cambridge.org/dictionary/english/volatility
Rizvi, S.K and Naqvi, B. (2010). asymetric behavior of inflation uncertainities and Friedman's -ball
hypothesis : evidence from Pakistan . the Lahore journalof economics , 15(2) : 1-33.
Schwarz, E.Gideon. (1978). Estimating the dimension of a model. Annals of Statistics,, 6 (2): 461–464.
Shesadri and Banerjee. (june 2013). Essays on Inflation Volatility. 23/26 Old Elvet, Durham DH1 3HY,
UK: Durham E-Theses, Durham university.
Syed, Kumail, Abbas and Rizvia. (2013). Inflation volatility: An Asian perspective. Economic ResearchEkonomska Istraživanja, 2014, 25.
The investopedia team and C. POTTERS. (2021, April 30). R-Squared vs. Adjusted R-Squared: What's
the Difference? Retrieved from investopedia: https://www.investopedia.com/ask/answers/012615/whatsdifference-between-rsquared-and-adjusted-rsquared.asp
Thornton, J. (2006). High and Variable Inflation: Further Evidence on the. Southern African Journal of
Economics.
valdes, O. (2019, august 05). what is literature review? Retrieved July 31, 2021, from ThoughtCo.:
https://www.thoughtco.com/literature-review-research-1691252
Valdovinos, C.F. and Gerling, K. (2011). Inflation Uncertainty and Relative Price Variability in
WAEMU Countries. IMF working paper, No.11/59.
Will. K and Margaret.J. (2020, october 25). GARCH Process. Retrieved from investopedia:
https://www.investopedia.com/terms/g/generalalizedautogregressiveconditionalheteroskedasticity.asp.
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Effects of government expenditures on
inflation in Rwanda
(2006Q1-2019Q4).
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Abstract
A good government spending plan is essential and critical for an economy. A good
understanding of it is essential so as to have an efficient and evidence based planification
which is fundamental to prevent that government expenditures leads not to deficits or
even inflation due to different issues that can be associated to it as described further in
the study.
To understand the effect of government expenditures on inflation in Rwanda we have
used the autoregressive distributed lag (ADRL) model to investigate the relationship
between them. In that framework we found the evidence that the two are related and that
the increase in government spending in Rwanda lead to a decrease in inflation both in
the short and the long-run
However, referring to the theoretical and empirical literatures used in this study, it is seen
that in different cases the government expenditures have an opposite effect on inflation
as to the case of Rwanda. Thus efforts should be made by policy makers to diversify the
ways through which they finance the government expenditures, so that they do not rely
on the traditional ways to finance the government spending including taxation and
external borrowing.
Keywords: government expenditures (spending), inflation, Rwanda
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1. Introduction
Government expenditures or the government spending is the money spent by the
government or public sector in the provision of services and acquisition of goods and
services for current use which is then classified as government final expenditure different
from government investment which is where the government acquires the services and
goods for future use.
There are different ways in which the government spending is financed where one can
note the indirect and direct taxes, foreign borrowing and domestic borrowing where the
government borrows from its’ citizens.
The government, along with the cost of economic stabilization, incurs distribution and
allocation costs. However, increase in government spending in form of intervention,
going by the neo-Classical economists could result to high inflation outcomes given the
full employment assumption (Olayungbo, 2013). In general, fiscal policy in many
countries is faced with many problems which includes, Tax collection difficulties,
institutional inadequacy, problems related to access to foreign capital, Money issuing to
finance public expenditures which in turn causes inflation. Therefore, government
expenditures in addition to the impact on production can have an impact on inflation
(Georgantopoulos A., (2010)).
The literature about inflation indicates that the economists have spent plenty of time to
understand the reasons that cause inflation. The economists have succeeded to give
details about the sources of the inflation. But, until now the relation of the inflation and
the other macroeconomic variables such as the government expenditures has remained
debatable. Government expenditures according to the economic situation are changing.
According to the Keynesian view, the government needs to spend in order to achieve
stability in the economy, stimulate or increase productivity or investment (Mohsen
Mehraraa, 2016).
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In Rwanda inflation has been stable throughout the recent years but if not well managed
it can be an issue as it has a significant effect on economic variables and can crucially
impact individuals’ lives. In this matrix, we can acknowledge that the mastery of the
origins of inflation can help the authorities in designing and implementing proper
policies as to when it is making necessary spending in order to ensure stability of the
economy, improving or stimulating productivity and investment according to the
Keynesian view through income redistribution between the poor and the rich or through
direct public investment.
Using a variety of instruments such as government spending, although in both theoretical
and practical experiences of countries have been proven that increases in government
spending causes inflation, it’s one of the significant issues in the possibility of achieving
economic growth After several decades that most economists focus on monetary policy,
by the financial global crisis in 2008, again fiscal policy as a tool of economic stabilization
was considered by economists. In fact, the effects of fiscal policy on economic activity in
countries with emerging markets and developing countries are not clear in the short and
long term. Since the economies of developing countries compared to developed countries
in the business cycles are facing with more volatility and this factor makes them more
vulnerable to shocks of the financial crisis (Mohsen Mehraraa, 2016). But the monetary
and fiscal policies can help to alleviate the impact of the financial crisis when it is
occurring.
The main objective of this study is to empirically traverse the relationship present
between inflation and government expenditures in Rwanda by using the ADRL approach
based on quarterly data over the period 2006-2019.
The rest of this paper is structured as follows: section 2 analyses the government
expenditure and allocation in Rwanda, section 3 reviews the theoretical and empirical
literature on the relationship between government expenditures and inflation, section 4
presents the methodology, section5 presents results and discuss findings and section 6
concludes with policy recommendations.
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2. Government spending and allocation in Rwanda
In this section we are going to discuss on the government spending and allocation of
funds to different sectors of the economy as per NST1 (National Strategy for
Transformation 1) for the fiscal year 2019/20 in comparison to the fiscal year 2018/19
We will also look at inflation and in relation to government expenditures along the years.
2.1 Government spending and allocation structure in Rwanda
Generally speaking, the Rwanda’s government spending goes through various sectors of
the economy including agriculture, education, and others through different policies like
the policy of Nkunganire where the government provides subsidies to help farmers buy
seeds, manure and irrigation materials for the improvement of the agricultural sector
together with other facilities provided through the ministry of agriculture and livestock.
Still on that, there are many more other policies through which the government of
Rwanda spends money to support the population and economic growth as to allocating
resources to different areas or sectors of the economy as per NST1 (which is a government
strategy developed as an implementation instrument for the remainder of Vision 2020
and the first four years of the Vision 2050. The budget allocation to the three NST1 pillars
is as follows. (MINECOFIN, June 2019)).
Public Finance Management (PFM) has taken the biggest piece of the pie (it has also had
the third largest increase in budget allocation when compared to the FY18/19) as the
Government continues to ensure that both the external debt and project loans are within
acceptable limits. As priority area one under the social transformation pillar of the NST1.
(MINECOFIN, June 2019)
Education has taken the second biggest share of the pie. Priorities under the education
sector are to focus on improvement of access to quality education ranging from
construction of classrooms countrywide, to in-house text books production and
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distribution and promotion of STEM subjects in primary and secondly schools.
(MINECOFIN, June 2019)
Water and Sanitation had the largest increase in the budget allocation to the tune of 47%
when compared to the current year. The increase is to enable: The finalization of the
construction of two water treatment plants in Kanzenze (Bugesera) and Gihira (Rubavu).
Connecting 109 productive use areas to water including industrial parks, commercial
centres, schools and Health Centers. Undertake construction of Kigali Centralized
Sewerage System phase 1. (MINECOFIN, June 2019)
Environment and Natural Resources had the second largest increase in budget allocation
to the tune of 36% when compared to the current year. The increase is towards Rwanda’s
continued effort to preserve Natural resources and the environment in order to promote
the green economy, which presents multiple opportunities for the economy.
Key interventions to be implemented in 2019/2020 include: Rehabilitation of urban
wetlands in Kigali City; Re-afforestation and rehabilitation of the degraded area of Jali,
Mount Kigali and Rebero with 30 ha of new forest planted and 420 has of forest
maintained; Urban Forestry for Sustainable City through beatification, landscaping and
greening in urban areas; Increase the area covered by forests focusing on agroforestry;
and Implementation of flood control measures (MINECOFIN, June 2019)
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Figure 1. Government expenditures per sectors as per NST1.
Government spending per sectors in NST1
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
% shareFY18/19
% shareFY19/20
% change from FY18/19
Source: Author’s chart: Data from Sustaining the Momentum: Rwanda’s 2019/20 National
Budget Insights and Highlights
If we look at the structure of the government spending in Rwanda throughout the fiscal
year of 2019/2020 as specified in the budget we see that the government spending in
Rwanda was classified into five categories including the recurrent expenditures, the
capital/development expenditures, net lending, and accumulation of deposits and
arrears of payments.
Looking at the recurrent expenditure, the allocated amount of FRW 1,424.5bn in fiscal
year 2019/20 is 9% higher than the allocated amount in the fiscal year 2018/19. The
increase in recurrent expenditure is mainly driven by increased allocations for both wage
and nonwage related items arising from ongoing restructuring exercises including
creation of new structures in the public sector. Specifically, the increase in the allocated
amount for wages will cater for restructuring of education and health sector salaries
including new recruitments as well as increases in allowances of the security agencies.
(MINECOFIN, June 2019).
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Talking on the capital expenditure, total capital spending in the fiscal year 2019/20 has
been estimated at FRW 1,152.1bn. This figure is made up of FRW 694bn of domestically
financed expenditure and FRW458.2bn of foreign financed expenditure. With regard to
the domestically financed portion, the allocated amount is to allow the implementation
of priority projects that will increase access to electricity, water and sanitation as well as
education and health. In the case of the foreign financed portion, the allocated amount is
to cover projects in the energy, roads and agriculture sectors (MINECOFIN, June 2019).
Coming on the net lending, Outlays under net lending in the fiscal year 2019/20 have
increased by 28% from the previous year’s budget allocation. The increase in the allocated
amount is mainly for two significant spending areas: funds for the recapitalization of BRD
– which is going to be done over a three year period and funds to Rwandair to support
its expansion strategy BRD has been recapitalized to promote accelerated private sector
growth (MINECOFIN, June 2019).
Figure.2. Government spending in Rwanda fiscal year 2019/2020.
RWF'billions
Government spending fiscal year 2019/20
1,600
1,400
1,200
1,000
800
600
400
200
0
Recurrent
Budget
Development
Budget
Net lending
Arrears of
payment
Accumulation
deposits
2018/19 Billion
1,310
1,041
190
27.2
16.96
2019/20Billion
1,424.50
1,152.10
244.1
30
25.5
Source: Author’s chart: Data from Sustaining the Momentum: Rwanda’s 2019/20 National
Budget Insights and Highlights
Talking about inflation and government expenditures we can see that despite the increase
in government spending in respect to core inflation which is the type of inflation that the
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government can control, we observe that in Rwanda despite the increase of government
spending this in turn have not affected that much core inflation which remained stable
over time despite its’ slight increase.
Figure.3. Government spending and core inflation in Rwanda from period 2006 to 2019.
Government spending and core inflation
500.0
450.0
400.0
350.0
300.0
250.0
200.0
150.0
100.0
50.0
0.0
CPI_core
GVEXP
Source: Author’s chart: Data from National Institute of Statistics Rwanda (NISR).
3. Literature review.
In consideration to the main purpose of this paper, this section reviews theoretical and
empirical literature on the effect of government spending on inflation in Rwanda and
other factors that may influence the inflation to hike or decrease.
3.1. Theoretical literature.
If it is true that inflation is a “social evil”, it is true that inflation reduces the costs of the
public sector, since certain groups in society cannot defend. Moreover, the fiscal drag –
the crop that inflation gives policy-makers in countries with progressive tax systems of
type – is disappearing in many states, since the awareness of citizens in this respect has
increased in recent years (Mohsen Mehraraa, 2016).
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Therefore, following such perspectives, inflation may be observed as a weakness of the
government to execute its credit obligations. However, these governments can make use
of inflation to benefits from the rise in price. As the situation of unforeseen inflation can
be used by the government to gain profit and this can be a regular instrument for the
government in lack of financial commitment.
Brescian Turroni was the first economist who studied the relationship between budget
deficits and inflation. He came to the conclusion that the relationship between deficits
and inflation could be negative. Patinkin in 1993 showed how the pressure, including
political interests, can be a helpful to decrease the differences in nominal spending of
revenues by using inflation. In other words, he believes that when government
expenditure is larger than revenues, borrowing from the central bank to finance can be
requested. This action increases the rate of inflation and thus reduces the real expenditure
of government. The negative effect of inflation on the real costs of government, known as
Patinkin effect. (Mohsen Mehraraa, 2016)
About the role and effect of inflation on tax revenues, Tanzi discussed for the first time
that inflation reduces the real value of tax revenues (Tanzi, 1987). His belief that real value
of tax revenues decreases due to inflation was based on the fact that there is a common
delay in tax payment for developing countries and that could lead to a large deficit
known as Tanzi effect.
Tanzi and Patinkin effect showed themselves in countries with inflation experience.
Depending on economic conditions, intensity will be different. The Tanzi effect from
income and Patinkin effect from the expenditure impress the deficit. (Mohsen Mehraraa,
2016)
Based on a dynamic system analysis, the relationship between current spending, deficit,
money supply and inflation can be explained. If government expenditure increases, this
increase makes the budget situation worse and leads to deficit. On the other hand,
increasing government debt to central bank (as a source of monetary base) will bring
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increase in monetary base, and will lead to increase money supply. However, with regard
to the positive relationship between the general level of prices and liquidity, increasing
the money supply will lead to an increase in inflation. However, the inflation led to a
decrease in the real value of government spending in the next period. So this decrease
forces the government to compensate for its cost value, by increasing nominal
expenditure the next period. But increase in expenditure will increase the budget deficit
and repeat the above process. So the increase in government expenditure (deficit) and the
general level of prices, a cause and effect relationship is established (Piontkivsky R., 2001)
3.2. Empirical literature.
Different studies have explored the relationship between government expenditures and
inflation for developed and developing countries both in time of war and peace, such
extensive empirical and theoretical analysis were made to investigate that relationship.
(Han, 2002)Investigated the relationship between inflation and the size of government.
They found that inflation is significantly and positively related to the size of government
mainly when periods of war and peace are compared. Also they show a weak positive
peacetime time series correlation between inflation and the size of government and a
negative cross-country correlation of inflation with non-defense spending.
(Ezirim Ch., 2008) studies the relationship between public expenditure growth and
inflation in the U.S using the co integration analysis and Granger Causality Model
applied to time series annual data from 1970 – 2002. The results indicate that public
expenditure and inflation have a long-run equilibrium relation between them. Inflation
significantly influences public expenditure decisions in the U.S. Public expenditure
growth aggravated inflationary pressures in the country, where reduction in public
expenditure tends to reduce inflation.
(Mohammad S.D, 2009) Try to find out long run relationship among M2, inflation,
government expenditure impact and economic growth in case of Pakistan. For this
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purpose, they have used Johnson co integration and Granger causality test to find out
long run association and causality. They found a negative relation between public
expenditure and inflation. They attempted to explain that most of public expenditure is
non-development and inflation is due to adverse supply shock (cost push inflation) in
case of Pakistan.
(Pekarski, 2010) Analyzes budget deficits and inflation in inflationary economies. The
main finding is that recurrent outbursts of extreme inflation in these economies can be
explicitly explained by the hysteresis effect associated with the action of two mechanisms:
the arithmetic of the wrong side of the ITLC and the Patinkin effect. Another finding is
that changes in different items of the budget balance sheet may have very different effects
on inflation (apart from their different effects on the real economy).
(Magazzino, 2011)Examines the nexus between public expenditure and inflation for the
Mediterranean countries during the period 1970-2009, using a time-series approach. He
found a long-run relationship between the growth of public expenditure and inflation for
some countries. Furthermore, Granger causality tests results show a short-run evidence
of a directional and bidirectional relationship from expenditure to inflation for all
countries.
(Musa, 2013)Investigated and measured the long and short run relationship of monetary
and fiscal policies on economic growth in Nigeria. A VECM technique was employed to
analyze and draw policy inferences. They showed it is clear that monetary policy exacted
greater impact on the economic growth but the effects of fiscal policy had lower
magnitude more specifically when there is decrease in the inflation rate
(Surjaningsih, 2012)Examine the impact of fiscal policy on output and inflation in
Indonesia. VECM1 was applied over quarterly data, covering the period 1990 to 2009.
Empirical results showed that government spending is more effective to stimulate
economic growth especially in times of recession, compared to taxation policies. While
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the increase in government spending causes a decrease in inflation, tax increases lead to
higher inflation.
(Olayungbo, 2013)Examines asymmetry causal relationship between government
spending and inflation in Nigeria from the period of 1970 to 2010. The asymmetry
causality test shows that a unidirectional causality exists from negative government
expenditure changes (low or contractionary government spending) to positive inflation
changes (high inflation) in the VAR2 model. The finding implies that inflationary
pressure in Nigeria is state dependent, that is high inflation is caused by low or
contractionary government spending.
4. Methodology
In this section, I present how I specified the econometric model and describes the
methods I used to analyze data and also will discuss set of data used and the detailed
description of variables used.
4.1. Empirical model.
Basing on (Pesaran, 2001) we used the autoregressive distributed lag (ADRL) bound
testing to explore the cointegration or long-run relationship between inflation and
government expenditure in Rwanda.
The choice of this test is based on the following considerations. Firstly, the ARDL
cointegration technique is adopted irrespective of whether the underlying variables are I
(0), I (1) or a combination of both, and cannot be applied when the underlying variables
are integrated of order I (2). Thus, to avoid cashing of the ARDL technique, it is advisable
to test for unit roots since variables that are integration of I (2) leads to the crashing of the
technique. Secondly, if the F-statistics (Wald test) establishes that there is a single long
run relationship and the sample data size is small (n ≤ 30) or finite, the ARDL error
correction representation becomes relatively more efficient. According to Pesaran et al
(2001), to apply the bounds test procedure, a conditional Vector Error Correction Model
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(VECM) of interest can be specified to test the cointegration relationship between the
underlying variables. (Apeh Kenneth, 2019)
The econometric tools that were used for these verifications are the Augmented DickeyFuller test for stationarity, Johansen co-integration test for long term relationship and
diagnostic tests of the underlying variables. The stability of the estimated model was
verified using the CUSUM and CUSUMSQ stability tests (Apeh Kenneth, 2019)
4.2. Model specification.
The model specification used in this study permits to assess the relationship between
government expenditures and inflation in Rwanda. The applied model was inspired by
(Apeh Kenneth, 2019) and recent papers that analyzed the relationship between
government expenditures and inflation.
The functional model for this study as specified as follows:
Equation 1: COREINF= f (GVEXP, HOEXP, RGDP, EXH_AV, M3)
Where;
COREINF: is the quarterly core inflation
GVEXP: is the quarterly government expenditures
HOEXP: is the quarterly household expenditures
RGDP: is the quarterly real gross domestic product
EXCH_AV: is the average quarterly exchange rate
M3; is the quarterly broad money
From the above equation 1 we can see that core inflation is dependent to government
expenditures, household expenditures, real gross domestic product, average exchange
rate and broad money, thus the core inflation for Rwanda can be specified in log form as
follow:
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equation 2.
𝑙𝑜𝑔𝑐𝑜𝑟𝑒𝑖𝑛𝑓 = 𝛼0 + 𝛼1 𝑙𝑜𝑔𝑔𝑣𝑒𝑥𝑝 + 𝛼2 𝑙𝑜𝑔ℎ𝑜𝑒𝑥𝑝 + 𝛼3 𝑙𝑜𝑔𝑟𝑔𝑑𝑝 + 𝛼4 𝑙𝑜𝑔𝑒𝑥𝑐ℎ𝑎𝑣 + 𝛼5 𝑙𝑜𝑔𝑚3 + 𝜀𝑟
Where;
Logcoreinf is the core inflation measuring the level of prices in the economy on quarterly
basis for the core CPI, loggvexp is the government expenditures measuring the quarterly
government spending in the economy , loghoexp is the
household expenditures
measuring the level of household spending in the economy quarterly basis, logrgdp is
the gross domestic product measuring the level of national income on quarterly basis,
logexch_av is the average exchange rate measuring the level of average exchange rate of
the Rwandan franc to a dollar on quarterly basis, logm3 is the broad money measuring
the level of money supply in the economy on quarterly basis, the coefficients α= 0,1,2,3,4,5
are the long-run coefficients and the εr is the error term. The variables were chosen basing
on similar studies including (Apeh Kenneth, 2019) (Mohsen Mehraraa, 2016)
(PAHLAVANI, (2009) ) and others.
The datasets was transformed using natural log to ensure normality, stability and to
reduce skewness and kurtosis (Apeh Kenneth, 2019).
4.3. Data sources and variables description.
Data used in this paper were obtained from different sources where the data for core
inflation, government expenditure, household expenditure and real gross domestic
product were obtained from the national institute of statistics of Rwanda (NISR). And the
data for average exchange rate and broad money were obtained from the national bank
of Rwanda (BNR). All the data used are for the period ranging from 2006 to 2019 on
quarterly basis from 2006Q1 to 2019Q4.
The choice for these variables was made following the approach of other empirical
studies on the same subject as well as other factors advanced by the literature.
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As saw earlier the dependent variable in this paper is the core inflation. The values used
for this core inflation are quarterly consumer price index, with these we want to explore
the various factors that affect the core consumer price index basket or core inflation in
Rwanda and as suggested by the topic, we will focus on the effect of government
expenditure on inflation and assess to which extent it has influenced core inflation along
the selected period.
The government expenditure variable shows the level of government spending all along
the selected period quarterly basis. Where higher government spending in an economy
close to full capacity may result in higher inflationary pressures and a little increase in
GDP, this study will assess the impact of government spending on core inflation in
Rwanda along the years representing various spending by the government as in
education, debt payment, investment in infrastructures, pension spending, welfare
benefits and others.
Included is also household spending which shows the level of household spending in
relation to inflation, and its effect on the core consumer price index, this variable was
included as it is also another factor that affects inflation as higher household spending
result in the rise of in inflationary pressures.
Referring to other studies like (Apeh Kenneth, 2019) (Ezirim Ch., 2008) and the effect of
exchange rate on consumer price index, we have also included the average interest rate
in this study as this variable also affects inflation rate as when the currency keeps on
depreciating in relation to the currency of reference usually a US dollar this also favor the
rise in inflation.
Real gross domestic product (RGDP) variable was also included to assess how the real
growth in domestic product affects the core consumer price index and according to
similar studies including (Apeh Kenneth, 2019) (Ezirim Ch., 2008) (Mohsen Mehraraa,
2016) we can see that the change in domestic product have an effect on inflation and that
will also be assessed on the case for Rwanda.
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Finally, the broad money variable as used in similar studies including (Mohsen
Mehraraa, 2016) (Apeh Kenneth, 2019) and others will helps to analyze how the level of
money in circulation across the selected period have affected the level of core inflation in
Rwanda.
In short, the interaction of those variables in computation to follow, will help to assess
the effect of government spending on inflation as shown in the next section.
5. Results
In this part of the paper we will see the estimation results for the specified model above
and the various steps followed.
5.1. Empirical results.
According to (Öztürk, 2013), if one of the variables’ unit root degree is higher than I(1),
the critical values obtained by (Pesaran, 2001)and (Narayan, 2005) cannot be used in the
Autoregressive Distributed Lag (ARDL) approach. These critical values are based on I (0)
and I (1). Therefore, it is necessary to determine whether or not the variables abide by the
assumptions of the ARDL bound testing approach by performing the unit root test at the
first stage of the analysis. In the first phase of the econometric analysis in this framework,
the Augmented Dickey-Fuller (ADF) and PhillipsPerron (PP) unit root tests are to be
performed to determine the degrees of integration of the series. (ALPER2, 2016) The unit
root tests both ADF and PP results are shown in the table below:
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Table 1: unit root test results both ADF and PP test.
Variables
LOGCOREINF
Test at
ADF at level
PP at level
ADF
at
first
PP
at
difference
difference
first
T-stat
PROB
T-stat
PROB
T-stat
PROB
T-stat
PROB
INTERCEPT
-2.65
0.08
-3.88
0.00
-3.49
0.01
-3.46
0.01
TREND
2.72
0.22
-1.90
0.63
-3.99
0.01
-3.55
0.04
NONE
2.11
0.99
3.77
0.99
-2.58
0.01
-2.46
0.01
INTERCEPT
1.16
0.99
2.21
0.99
-3.26
0.02
-3.12
0.03
TREND
-2.50
0.32
-2.73
0.22
-3.80
0.02
-3.80
0.02
NONE
2.71
0.99
4.76
1.00
-1.80
0.06
-1.53
0.1
INTERCEPT
0.05
0.95
-0.72
0.83
-7.54
0.00
-20.77
0.00
TREND
-5.98
0.00
-5.89
0.00
-7.49
0.00
-23.18
0.00
NONE
3.260
0.99
5.17
1.00
-10.28
0.00
-9.68
0.00
INTERCEPT
-0.90
0.77
-1.11
0.70
-9.84
0.00
-14.01
0.00
TREND
-4.11
0.01
-4.13
0.01
-9.76
0.00
-15.22
0.00
NONE
3.11
0.99
7.53
1.00
-8.56
0.00
-8.59
0.00
INTERCEPT
-0.05
0.94
0.07
0.96
-6.74
0.00
7.06
0.00
TREND
-2.36
0.39
-2.63
0.26
-6.73
0.00
-7.29
0.00
NONE
5.45
1.00
-6.77
1.00
-4.97
0.00
-4.92
0.00
INTERCEPT
-1.79
0.37
-5.28
0.00
3.37
0.01
-10.06
0.00
TREND
-1.63
0.79
-2.85
0.1
-3.80
0.02
-10.59
0.00
2.50
0.99
-6.35
1.00
-1.39
0.1
-6.34
0.00
AND
INTERCEPT
LOGEXCH_AV
AND
INTERCEPT
LOGGVEXP
AND
INTERCEPT
LOGHOEXP
AND
INTERCEPT
LOGRGDP
AND
INTERCEPT
LOGM3
AND
INTERCEPT
NONE
Source: author’s computation using EVIEWS 9.0.
As observed in the table above, the variables used are all stationary (integrated) at first
difference. And as discussed above and according to (Pesaran, 2001), there is no need to
verify whether the regressors are stationary at level, first difference or mutually
cointegrated when finding a long-run relationship among the endogenous variable and
the explanatory variables.
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After testing for the unit root and observing that none of the variables is integrated at I
(2), we can now proceed with the ADRL bound test to observe whether or not there is a
long-run relationship between the explained and the explanatory variables as seen in the
table below showing the results for the ADRL bound test.
Table2: results of the ADRL bound test
ARDL Bounds Test
Date: 02/07/21 Time: 17:56
Sample: 2006Q3 2018Q4
Included observations: 50
Null Hypothesis: No long-run relationships exist
Test Statistic
Value
k
F-statistic
9.781302
5
Critical Value Bounds
Significance
I0 Bound I1 Bound
10%
2.26
3.35
5%
2.62
3.79
2.5%
2.96
4.18
1%
3.41
4.68
Source: Author’s computation with e-views9
As observed in the table above, we can see that the F-statistic value is greater than the 5%
critical value highlighted in yellow as well as the 1% critical value highlighted in green
upper bound. Therefore, this shows that there is a long-run relationship between the
explained and the explanatory variables. Thus, we can strongly reject the null-hypothesis
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that that there is no long-run relationship between the dependent and independent
variables.
After the bound test and knowing that there is a long-run relationship between the
explained and explanatory variables, then we can compute for the long-run coefficients
using the ADRL approach.
Table3: Long-run estimated using ADRL approach
Long Run Coefficients
Variable
Coefficient Std. Error
t-Statistic
Prob.
LOGEXCH_AV
0.212581
0.433246
0.490671
0.6264
LOGGVEXP
-0.955153 0.367434
-2.599526
0.0131
LOGHOEXP
-0.427489 0.313450
-1.363819
0.1804
LOGM3
1.063286
0.360528
2.949245
0.0054
LOGRGDP
-0.591149 0.719271
-0.821872
0.4161
C
8.215796
2.923163
0.0057
2.810584
Source: Author’s computation with e-views 9
As seen in the above table, the blue-highlighted values show that their corresponding
values are not significant and the yellow-highlighted values shows that their
corresponding values are significant at 5% level of significance.
The estimates in the above table3 for the long-run, shows that in the long-run real gross
domestic product is insignificant with inflation rate in a negative way while exchange
rate (exch_av) is also insignificant but in a positive way. The findings also show that in
the long-run government expenditures (gvexp) and broad money (m3) have a very
significant effect to inflation, even if the government have a negative effect on inflation.
Now concerning our regressors of interest which is the government expenditures (gvexp)
we see that it is highly significant with its p-value of 0.0131 and its coefficient of-0.955153
which means that a 1% increase in government spending will lead to a 0.95% decrease in
inflation on the long-run.
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After the long-run coefficient estimation we have also computed the short-run error
correction model whose results are shown in the table below:
Table4 A and B: Error Correction Model (ECM) representation for selected ADRL
model.
Table4A: ECM representation for selected ADRL model before cointegration.
Dependent Variable: LOGCOREINF
Method: ARDL
Date: 02/07/21 Time: 17:56
Sample (adjusted): 2006Q3 2018Q4
Included observations: 50 after adjustments
Maximum dependent lags: 1 (Automatic selection)
Model selection method: Akaike info criterion (AIC)
Dynamic regressors (2 lags, automatic): LOGEXCH_AV LOGGVEXP
LOGHOEXP LOGM3 LOGRGDP
Fixed regressors: C
Number of models evalulated: 243
Selected Model: ARDL(1, 1, 1, 0, 2, 0)
Variable
Coefficient
Std. Error
t-Statistic
Prob.*
LOGCOREINF(-1)
0.880360
0.037866
23.24942
0.0000
LOGEXCH_AV
-0.361420
0.265824
-1.359623
0.1818
LOGEXCH_AV(-1)
0.386853
0.256018
1.511037
0.1388
LOGGVEXP
-0.052431
0.020123
-2.605563
0.0129
LOGGVEXP(-1)
-0.061843
0.019525
-3.167363
0.0030
LOGHOEXP
-0.051145
0.034578
-1.479118
0.1471
LOGM3
-0.032034
0.035288
-0.907765
0.3696
LOGM3(-1)
0.095499
0.036136
2.642772
0.0118
LOGM3(-2)
0.063745
0.033978
1.876083
0.0681
LOGRGDP
-0.070725
0.072450
-0.976191
0.3350
C
0.982937
0.267259
3.677840
0.0007
R-squared
0.997528
Mean dependent var
4.517415
Adjusted R-squared
0.996894
S.D. dependent var
0.172353
S.E. of regression
0.009606
Akaike info criterion
-6.261309
Sum squared resid
0.003599
Schwarz criterion
-5.840663
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Log likelihood
167.5327
Hannan-Quinn criter.
-6.101125
F-statistic
1573.511
Durbin-Watson stat
1.321350
Prob(F-statistic)
0.000000
Table B: ECM cointegrating form representation for the selected ADRL model after
cointegration.
ARDL Cointegrating
Dependent Variable: LOGCOREINF
Selected Model: ARDL(1, 1, 1, 0, 2, 0)
Date: 02/07/21 Time: 18:30
Sample: 2006Q1 2019Q4
Included observations: 50
Cointegrating Form
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(LOGEXCH_AV)
-0.361420
0.265824
-1.359623
0.1818
D(LOGGVEXP)
-0.052431
0.020123
-2.605563
0.0129
D(LOGHOEXP)
-0.051145
0.034578
-1.479118
0.1471
D(LOGM3)
-0.032034
0.035288
-0.907765
0.3696
D(LOGM3(-1))
-0.063745
0.033978
-1.876083
0.0681
D(LOGRGDP)
-0.070725
0.072450
-0.976191
0.3350
CointEq(-1)
-0.119640
0.037866
-3.159567
0.0030
Cointeq = LOGCOREINF - (0.2126*LOGEXCH_AV -0.9552*LOGGVEXP
-0.4275*LOGHOEXP + 1.0633*LOGM3 -0.5911*LOGRGDP + 8.2158 )
Source:
both
tables
A
and
B
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By observing the estimated values above in the table 4A the short-run we can see that the
R2 value which equals to 0.997528 this shows that 99% of the variation of inflation rate
are explained by the explanatory variables and this shows that the model is overall fit
and acceptable.
Still looking at the table 4A the p-values 0.0000, 0.0129, 0.0030, 0.0118 indicates that three
of the explanatory variables are highly significant at 1% level in explaining inflation in
Rwanda.
In table4A, we can also observe that one lagged value of inflation is positively significant
at 1%level of significance in explaining inflation in Rwanda and this means that inflation
in Rwanda has a cumulative impact as a 1% unit increase in a year, will also increase
inflation by 0.88% in the subsequent year. And at the same time we can see that
government expenditure has also a lagged value which negatively affect inflation and
which is highly significant at 1% level of significance as one 1%-unit increase in
government spending in a year will decrease inflation by 0.05% in the subsequent year.
Also we can observe that there is a lagged value for broad money which is highly
significant at1% level of significance positively and this means that a 1%-unit increase in
broad money in a year will lead to 0.09% increase in inflation in the subsequent year. This
emphasizes that inflation in Rwanda is positively responsive to broad money and
negatively to government spending.
The ECM coefficient noted as cointEq(-1) in table4B is negative and highly significant.
This shows that the model has a self-adjusting mechanism to adjust the short-run
dynamics of variables with their corresponding long-run values. According to (Afolabi
J.A, 1995) a stable long-run relationship is further proved by a highly significant error
correction term. The Durbin Watson statistic which is 1.321350 shows that there might be
a positive serial autocorrelation among variables, but as we can observe the R-square is
less than the Durbin Watson statistic which means that our data are not spurious.
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To assess more of the relevance of the data we used, we proceeded with the diagnostic
and stability test.
For the Diagnostic tests we have carried out; the Breusch-Godfrey Serial correlation LM
test, Heteroskedasticity test ARCH and the Jarcque-Bera test. The results from those tests
were as follows:
Table5: Breusch-Godfrey Serial correlation LM test
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
1.121566
Prob. F(15,24)
0.3896
Obs*R-squared
20.60516
Prob. Chi-Square(15) 0.1499
Source: Authors computation using e-views9.
The results from the serial correlation test carried on the model shows that there is no
serial correlation as the chi-square probability highlighted in green above in table5 is
greater than 10%. Thus the model is good for forecasting.
Table6: Heteroskedasticity test ARCH
Heteroskedasticity Test: ARCH
F-statistic
1.621083
Prob. F(2,45)
0.2090
Obs*R-squared
3.225891
Prob. Chi-Square(2)
0.1993
Source: Authors computation using e-views9.
From the above test testing for hoteroskedasticity we can observe that its probability as
highlighted in red is greater than 10% thus we can conclude that our model is
homoscedastic as the variance of the residual is constant.
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Figure4: Jarque-Bera test.
8
Series: Residuals
Sample 2006Q3 2018Q4
Observations 50
7
6
5
4
3
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
-2.09e-16
-0.000312
0.027100
-0.019197
0.008570
0.381163
3.704396
Jarque-Bera
Probability
2.244408
0.325562
2
1
0
-0.02
-0.01
0.00
0.01
0.02
Source: Authors computation using e-views9.
The Jarque-Bera test for normality show that the residuals are normally distributed as its
probability as shown in the graph above is greater than 10% and from that we can
conclude that the population is normally distributed.
For the stability test we carried out the test of stability for the long-run model as seen in
the output graphs below showing the CUSUM and CUSUMQ test performed. These tests
of cumulative sum of recursive residuals (CUSUM) and CUSUM square when applied to
residuals they evaluate the stability of the model, the expectations are that both the
CUSUM and CUSUMQ graphs should be within the critical boundaries at 5% level of
significance for the model to be acceptable as being stable.
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Figure5: Graph of CUSUM test for coefficient stability of ADRL long-run
20
15
10
5
0
-5
-10
-15
-20
2009
2010
2011
2012
2013
2014
CUSUM
2015
2016
2017
2018
5% Significance
Source: Authors computation using e-views9.
Figure6: Graph of CUSUMQ test for coefficient stability of ADRL long-run
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
2009
2010
2011
2012
2013
2014
CUSUM of Squares
2015
2016
2017
2018
5% Significance
Source: Authors computation using e-views9.
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From figure 5 and figure 6 we can see that both the CUSUM and CUSUMQ graphs are
within the critical boundaries at 5% level of significance and this entails that the model is
overall stable and therefore can be used for policy formulation.
6. Conclusion and Policy recommendations.
The main focus of study is to evaluate how the level of government expenditures affect
inflation in Rwanda, this was assessed using the autoregressive distributed lag with
quarterly data from the National Institute of Statistics of Rwanda (NSIR) and the National
Bank of Rwanda (BNR) for the period 2006Q1 to 2019Q4. Though study mainly focused
on the nature of relationship between inflation and government spending, it also assessed
other factors that could affect inflation along the chosen period.
In the short run the results shows that the lagged values of inflation and broad money
had a positive and significant effect on inflation, it also shows that there is a lagged value
of government expenditures that has a significant a negative effect on inflation, which
implies that those variables have a cumulative impact on inflation in Rwanda.
In the long-run the results shows that money supply (broad money) has a strong positive
impact on inflation and these findings are in line with the finding found in a similar study
in Iran by (PAHLAVANI, (2009) ) showing that the level of money supply was positively
related to in inflation in Iran. Regarding government expenditure it is found that it has
a strong negative impact respectively in explaining inflation in Rwanda and these
findings are in line with a similar study made in Nigeria by (Apeh Kenneth, 2019)
showing that government spending was negatively related to inflation in Nigeria.
The negative relationship between inflation and government spending shows that in
Rwanda there is still large spare capacity as the industries in Rwandan economy are
operating under the maximum level of production, where we observe that most
industries or businesses have increased their capacity without matching it with the
increase in demand, this through introducing new technologies while expecting the rise
in demand over investing in fixed assets.
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Lower demand can also explain this negative relationship, where there is loss of market
share as this one gets too competitive as better products are introduced by competitors.
Inefficiency can also be noted as this non efficient of factors of production by industries
creates a problem which leads to less competitiveness and less unit cost than the
competition.
Thus, this spare capacity in Rwanda portrays that the un-utilized factors of production
were used to increase the level of national product (income) which in turn didn’t cause
inflationary pressures, as though there is increase in government spending, there is no
increase in unit cost, and the additional consumer expenditure as well as investment that
shifts the aggregate demand curve further to the right won’t cause inflation because of
the spare capacity.
In that perspective we have concluded that inflation in Rwanda is negatively responsive
to money supply as a unit increase in government spending leads to a decrease in
inflation in Rwanda. We also noticed that inflation is positively responsive to money
supply as a unit increase in government expenditures leads to an increase in inflation.
Therefore, based on the above findings, concerning the issue of broad money the National
Bank of Rwanda should ensure effective monetary policy where there is efficient money
supply mechanisms to ensure that the positive responsiveness between inflation and
money supply does not become an issue in the coming future.
Concerning the issue of government spending, though along the years there have been a
negative relationship between inflation and government expenditures where increase in
government spending have led to a decrease in inflation both in the short and the longrun run, policy makers should keep making good use of the best theoretical and empirical
literatures on hand or available to analyze the best government spending designed to
encourage growth for the probability of achieving that effect.
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The potential consequences of uncertain data or assumptions should be fully explored
and analyzed before setting policies involving government spending as inefficient
government spending may lead to misallocation of resources and this can lead to larger
government spending with less efficiency as government expenditures are taking place
of private sector expenditures and this might lead to large budget deficits.
The policy makers, should also assess the way through which they finance the
government spending, they should not rely on taxes and external borrowing as to finance
their spending as in the long-run this can cause inflationary pressures or even inflation
rate to rise ,in such case the rise in government spending would be synonym of rise in
taxes or external debt which in turn will negatively affect the economy and the general
increase in prices, as in such case government spending will no longer be reducing the
rate of inflation but increasing it.
Efforts should made by the government to increase more it’s borrowing from the
National Bank of Rwanda, as voluntarily the lenders who lends to the government will
not decrease their consumption as they uses their savings but the inverse would happen
when they are paying higher taxes as people are unwilling to go into debt or reduce their
savings.
Government borrowing from the public tends to restricts private spending as much as
higher taxes could do under the same conditions, and the selling and buying of the
government securities will provide the National Bank of Rwanda with means of
controlling the money supply hence this will be essential for efficient monetary policy.
This does not only help with the monetary policy but also this avoids the bad outcomes
that taxes might have on incentives, if taxes are increased above what the tax payers are
accustomed to.
In that perspective one can say that borrowing will permit the government spending to
be higher than it could be feasible using taxes,
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Finally, policy makers should diversify the ways they finance the government
expenditures, by increasing the government borrowing from the National Bank of
Rwanda as well as other ways that are possible, they should also ensure efficient
spending by basing on reliable data and assumptions, so that increase in government
spending may not affect inflation positively but contribute to a healthy economic growth.
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Works Cited
Afolabi J.A, O. S., 1995. An Assessment of the Impact of Inflation on Financial Intermediation
in Nigerian Banking Sector, s.l.: NDIC Quarterly, 5 (1):29-48. .
ALPER2, A. P. D. F. Ö., 2016. RELATIONSHIP BETWEEN INFLATION AND
UNEMPLOYMENT: THE ARDL BOUND TESTING APPROACH FOR TURKEY1, s.l.: s.n.
Apeh Kenneth, A. M. A. N. O. N., 2019. An Econometric Assessment of the Impact of
Exchange
Rate
Depreciation
on
Inflation
in
Nigeria
(1981-2017)..
Preprints
(www.preprints.org).
Ezirim Ch., M. M. I. E. U., 2008. " Inflation versus public expenditure growth in the us:
AN EMPIRICAL INVESTIGATION. North American Journal of Finance and Banking
Research 2(2); 26-40 .
Georgantopoulos A., T. A., (2010). "The Interrelationship between Money Supply, Prices
and Government Expenditures and Economic Growth: A Causality Analysis for the Case
of Cyprus". International Journal of Economic Sciences and Applied Research, 5(3), 115-128,
Volume 5(3).
Han, S. &. M. C. B., 2002. "Inflation and the Size of Government, s.l.: (Vol. 2, No. 1). Divisions
of Research & Statistics and Monetary Affairs, Federal Reserve Board.
Magazzino, C., 2011. "The nexus between public expenditure and inflation in the Mediterranean
countries". s.l.:MPRA Paper No. 28493, .
MINECOFIN, June 2019. Sustaining the Momentum: Rwanda’s 2019/20 National Budget
bulletin, kigali-Rwanda: s.n.
Mohammad S.D, W. S. L. I. H. A., 2009. An Empirical Investigation between Money
Supply, Government Expenditure, output & Prices: the Pakistan Evidence" Issue 17.
European Journal of Economics, Finance and Administrative Sciences. [.
Mohsen Mehraraa, M. B. S. S. R., 2016. The Impact of Government Spending on Inflation
through the Inflationary Environment, STR approach. world scientific news.
Rwanda’s Economic Health
Page 95
Musa, Y. &. A. B. K., 2013. "Long and Short Run Relationship Analysis of Monetary and
Fiscal Policy on Economic Growth in Nigeria: A VEC Model Approach. Research Journal
of Applied Sciences, Engineering and Technology 5(10): 3044-3051.
Narayan, P. K., 2005. The saving and investment nexus for China: evidence from
cointegration tests. Applied economics, 37(17), 1979-1990.
Olayungbo, D. O., 2013. Government Spending and Inflation in Nigeria: An Asymmetry
Causality Test,. International Journal of Humanities and Management Sciences, 1(4)., Volume
International Journal of Humanities and Management Sciences, 1(4)..
Öztürk, I. &. A. A., 2013. The long-run and causal analysis of energy, growth, openness
and financial development on carbon emissions in Turkey. Energy Economics, 36, 262-267.
.
PAHLAVANI, M. R. M., (2009) . SOURCES OF INFLATION IN IRAN: AN
APPLICATION OF THE ARDL APPROACH. International Journal of Applied Econometrics
and Quantitative Studies , Volume Vol.6-1.
Pekarski, S., 2010. Budget Deficit and Inflation Feedback, Structural Change and Economic
Dynamics.. s.l.:s.n.
Pesaran, M. S. Y. S. R., 2001. Bounds Testing Approaches to the Analysis of Level
Relationships. Journal of Applied Econometrics, , pp. 16, 289-326.
Piontkivsky R., B. A. K. M. &. S. T., 2001. The impact of the budget deficit on inflation in
Ukraine"., s.l.: International Association for the Promotion of Cooperation with Scientists
from the New Independent States of the Former Soviet Union (INTAS) Research Report,
95, 0273.
Surjaningsih, N. U. G. A. D. T. B., 2012. "The Impact Of Fiscal Policy On The Output And
Inflation". Bulletin of Monetary Economics and Banking 367, April 2012. .
Tanzi, V., 1987. quantitative characteristics of the tax systems of developing countries.. s.l.:s.n.
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Forecasting the industrial sector growth in
Rwanda using Box–Jenkins (BJ) methodology
(2006Q1-2020Q4)
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Abstract
The government of Rwanda makes projections of its revenues in order to model its
monetary and fiscal policy for it to achieve that objective it is better to have a model that
can estimate the future values of revenues that can be generated from the industrial sector
as one of the three main sectors that makes up the economy of Rwanda.A successful time
series forecasting is emperatively dependent on an appropriate fitting model.
Industrial sector in Rwanda is one of important factors of the economic growth in
Rwanda, with the development of the industrial sector in Rwanda, predicting the future
behavior of this sector
output comprises uncertainty due to the ignorance of
mathematical and statistical techniques while doing predictions.
The interest of this study is to find an ARIMA model which is most appropriate to
forecasting industrial growth in Rwanda using Eviews. The Box-Jenkins methodology is
the one which was used in this paper and based on the research obtained, we indentified
the model appropriate to forecasting industrial output in Rwanda as ARIMA (2,1,10).
And based on the model selected the estimated forecast of the industrial output in
Rwanda will increase on average of 0.35 percent quarterly in the period of 2021Q1 to
2023Q1 and on the average of 0.34 percent from 2023Q2 to 2023Q4. The results of the
forecasting industrial outpout in Rwanda using Eviews software on 2021Q1– 2023Q4 is
stable enough.
Keywords: time series, industry, box-jenkins methodogy, stationarity, forecasting.
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1.Introduction
In the three main sectors that constitute a country’s economy we find the industrial sector
regarded as the secondary sector of the economy after the agricultural sector which is the
primary sector of the economy.
This sector of the economy comprises of economic activities performed by companies,
organizations and people engaged in the production of services and goods in a given
field reason why industries are categorized according to the goods and services they
produce.
It is the industrial sector where the final(finished) products that can be used by the
consumer are produced, it most of the time uses agricultural sector’s completed products
which are sent for further processing.
This sector of the economy can be classified into two main types where we have
large(heavy) industries and small(light) industries where most of them transform raw
materials into end products that can be consumed.
In Rwanda the industrial sector have been developing since the last tweenty seven years,
though it doesn’t contributed as the agricultural and service sector, it does contribute a
significant share to the gross domestic product in Rwanda where for example in the last
four quarters the industrial sector contributed 18,19,21 and 19% respectively as acoording
to (NISR, 2021).
The government of Rwanda makes projections of its revenues in order to model its
monetary and fiscal policy for it to achieve that objective it is better to have a model that
can estimate the future values of revenues that can be generated from the industrial sector
as one of the three main sectors that makes up the economy of Rwanda. A successful time
series forecasting is emperatively dependent on an appropriate fitting model.
Industrial sector in Rwanda is one of important factors of the economic growth in
Rwanda, with the development of the industrial sector in Rwanda, predicting the future
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behavior of this sector
output comprises uncertainty due to the ignorance of
mathematical and statistical techniques while doing predictions.
The main purpose of this study is to help Rwandan policy makers and planners in getting
a fitted model for forecasting the future evolution of the industrial sector. The second
interest of this paper is to improve the knowledge of readers who misunderstand the use
of statistical knowledge in Economic Institutions. The third purpose of this paper is to
study the contribution of the industrial sector to the gross domestic product. The fouth
interest of this paper is to analyse the influence that the past values in the industrial sector
have on its future values.The last objective of this study is to provide the tools for future
researchers interested in the same fields.
The rest of this articcle is made as follow; section 2 studies the industrial sector n Rwanda,
section 3 reviews the literature reviews, section 4 shows the methodology, section5
presents the results and discuss findings and section 6 concludes with policy
recommendations.
2. Industrial sector in Rwanda.
Rwanda’s industrial sector is made of five main subsectors which are mining and
quarrying, manufacturing, electricity, water and waste management,and construction.
Figure: sectorial performance in Rwanda 2006Q1 to 2020Q4
Source: authors’ chart using data from NISR R_GDP national accounts 2019Q3 and 2020Q4
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From the above chart, one can observe that compared to other sectors of the Rwandan
economy, the industrial sector have been laging behind well as the service sector did
perform well over all other sectors except in 2020 where due to the covid-19 pandemy,
this sector slowed down because of the lockdowns while the agricultural sector growed
faster than other sectors highly as the goververnment policies favired the agricultural
sector in the period of total lockdown, so as to prevent food insecurity in the country.
2.1. Mining and quarrying
Mining is the second largest export sector in the Rwandan economy after tourism. The
mining sectorin Rwanda has untapped potential that presents lucrative investiment
opportunities in the entire value chain from exploration to value addition, in its NST1(
national strategy for transformation 1) Rwanda recently set an ambitious target of
generating USD 1.5B in export revenues by 2024 (RDB, 2021).
Figure: mining and quarrying in Rwanda from 2006Q1 to 2020Q4.
Source: authors’ chart using data from NISR R_GDP national accounts 2019Q3 and 2020Q4
From the above chart one can observe that the mining& querrying subsector of the
idustrial sector in Rwanda have been performing well all along the years with a staedy
grwoth from 2006Q1 to 2019Q4 but observed a downfall from 2020Q1 to 2020Q3 which
is due to a schock caused by the covid19 pandemy which forced the countr to enter in a
period of lockdowns and shutdowns of diverse activities.
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2.2. Manufacturing
Rwanda’s manufacturing sector is largaely undervisified, and is concentrated in seven
sub-sectors: Food, beverages & tobacco,textiles, clothing & leather goods, wood & paper;
printing, chemicals, rubber & plastic products, non-metallic mineral products, metal
products, machinery & equipment, furniture & other manufacturing (NISR, 2021)
The primary industrial activities involve mainly the processing of coffee, tea, bananas,
beans, sorghum, potatoes and other agricultural commodities. Other smaller scale
industrial products include cement, small-scale beverages, soap, furniture, shoes, plastic
goods, textiles and cigarettes. The majority of goods manufactured in Rwanda are
produced for domestic consumption; in order to limit the country’s reliance on imports.
The vast majority of manufacturing companies in Rwanda are located in the capital city,
Kigali. Sulfo Rwanda Industries is the second largest manufacturing company in
Rwanda, located in Kigali. Sulfo Rwanda produces a wide range of consumer goods for
the domestic market, these include: soap, lotions, skin lightening products, washing
detergents and sweets (commonwealth, 2013).
Rwanda is a large exporter of metal ores, comprised of mainly tin ores; ore exportation
makes up 43% of the country’s total yearly exports. The country also exports a large
amount of unroasted coffee beans, which make up over 25% of total yearly exports.
Rwanda’s major export partners include Switzerland 16%, China 14%, Hong Kong 7%
and the US 7%. Rwanda’s development aims are outlined in Vision 2020; objectives
include targeting growth and development, which focus on economy-wide
improvements in productivity. The overall goal is to have transformed Rwanda’s
economy by 2020, moving away from subsistence agriculture towards increased
manufacturing, services and commercial agriculture (commonwealth, 2013).
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Figure: manufacturing sector performance in Rwanda 2006Q1 to 2020Q4
Source: authors’ chart using data from NISR R_GDP national accounts 2019Q3 and 2020Q4
From the figure above one can observe that in the manufacturing sector in Rwanda, food,
beverage& tobacco and textile,clothing and leather goods are ones performing well
compared to the remaing subsectors in the manufacturing subsector of the industrial
sector.
2.3. Electricty
Electricity availability and consumption is a critical input for economic, social and
political development of a country. It is therefore of utmost importance that a country
has adequate and reliable electricity supply to meet its demand, based primarily on the
existing resources. The development of a least-cost generation development plan
provides a realistic guide as to how demand for electricity can be met in the medium and
long-term at a minimized cost (REG, 2019).
Acording to Rwanda Energy Group (REG, 2019), in selecting appropriate technological
supply alternatives for the expansion of the Rwandan electricity generation system, the
following important aspects are to be considered:
• Rwanda is endowed with a myriad of natural resources, the most dominant of which
include water, sunshine, methane at the bottom of Lake Kivu and peat reserves in the
southern part of Rwanda. It is therefore important that these resources are identified and
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utilized for electricity production in the most cost-efficient manner, while meeting
demand and reserve margin needs. This LCPDP is dedicated to identifying the potential
output from maximum and economically feasible utilization of national resources, based
on cost variables such as extraction costs/emissions constraints, where applicable (REG,
2019).
• Currently, peak demand and reserve during peak are served by mainly diesel-powered
power plants (Jabana II, Jabana I and 10 MW of SO Energy), as well as seasonal inputs
from the big hydro storage power plants on the system. The use of diesel during these
hours hikes up the generation cost, and consequently the electricity tariff. Due to the
existence of the Shango-Mirama interconnecting line from Rwanda to Uganda, the
possibility of import of power from Uganda to reduce the generation cost prior to Hakan
entry in 2020 was considered (REG, 2019).
• A power network analysis12 was done on existing and planned interconnectors
(including planned power plants per technology type per country), amongst the 6 Nile
Equatorial Lakes Subsidiary Action Plan (NELSAP) member countries, i.e. Burundi,
Democratic Republic of Congo, Kenya, Rwanda, Tanzania and Uganda to evaluate the
potential future behaviour of the interconnected system over the period 2016 – 2021.
Results from this analysis showed countries with potential to be both peak and off-peak
customers for excess power from Rwanda up to 2021. This therefore was one of the key
scenarios considered within the plan – power trade as a strategy to increase company
earnings (REG, 2019).
• In line with the Paris Agreement and the 7th Sustainable Development Goal set by the
United Nations (i.e. affordable and clean energy), policies existing within the Rwanda
energy sector target increased contribution of renewable energy to the national electricity
production. A policy target of 60% by and after 203013 was set to ensure compliance with
global trends towards decarbonization of the energy sector. This was therefore an
important factor to consider during scenario development. Within all developed
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scenarios, compliance with this ambitious target was monitored throughout the planning
horizon (REG, 2019).
Figure: electricty subsector development in Rwanda 2006Q1 to 2020Q4
Source: authors’ chart using data from NISR R_GDP national accounts 2019Q3 and 2020Q4
From the above figure one can observe that the electricty subsector of the industrial sector
in Rwanda have been growing upward in recent years from 2006 to 2020 and this growth
is expected to continue in the years to come, but though there is that increase this subsctor
is also facing different challenges as according to the Rwanda energy group, until the
Hakan peat to power facility begins operation in 2020, Rwanda will have limited
generation resources especially during the dry season when many hydro power plants
face water shortage problems. During this period, rental diesel generation is used to
supply the peak demand, and this generation comes at a high cost. The optimal expansion
program indicates that there is an immediate need for the import of approximately 45
MW in the last half of 2019, based on an estimated annual uniform electricity demand
growth of 10% (REG, 2019).
A study conducted by Israel Electric considered different annual growth rates of 8% (low
growth), 10% (base case) and 12% (high growth) due to the uncertainty of forecasts.
Electricity demand forecasts were then calculated in line with recent historical trends,
using existing hourly load curves for the years 2015-2016. Peak and energy demand
forecasts over the next 20 years were calculated as shown in table below (REG, 2019).
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Table: Annual Peak & Energy Demand Growth for Different Growth Rates
source: REG, Rwanda least cost power2019
An additional econometric assessment and forecast of annual consumption growth rates
based on the available data on residential consumer consumption levels and electrical
appliance use provided an estimate of 9.8% for the years 2016-2040. Bearing the
uncertainties associated with demand forecasting and the different results presented by
these studies, it was decided that an annual demand growth rate of 10% be used for
Rwanda’s generation expansion scenario development and expansion planning (REG,
2019).
The remaing subsectors, water &waste managmnet and construction have also kept on
growing where notably construction kept on growing faster in the recent years
contributing largely to the Rwanda’s gross domestic product, though it was hindered by
the covid19 pandemy.
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Figure: water and waste management subsector in Rwanda 2006Q1 to 2020Q4.
Source: authors’ chart using data from NISR R_GDP national accounts 2019Q3 and 2020Q4
As it can be observed in the chart above the water and waste managenment subsector in
indudustrial sector have been growithing though out the recent years years where it have
also observed a constant growth from 2019Q2 to 2020Q2.
Figure: construction 2006Q1 to 2020Q4
Source: authors’ chart using data from NISR R_GDP national accounts 2019Q3 and 2020Q4
Based on the above graph one can observe that there was an a steady increase in
construction subsector which contributed a lot to the gross domestic product of Rwanda
but this sector as mentioned above have witnessed a schock because of the covid19
pandemy which have lead to its downfall, though it is recovering due to the recovery
policy strategies put in place by the government of Rwanda including the quick recovery
fund.
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3. Literature review.
Considering the main purpose of this study, this part reviews theoritcal and empirical
literature on the on the contribution of industrial sector on development and the
forecasting methodology used in this paper.
3.1. Theoritical literature.
Industrialization is often essential for economic growth, and for long-run poverty
reduction. The pattern of industrialization, however, impacts remarkably on how the
poor benefit from growth. Pro-poor economic and industrial policies focus on increasing
the economic returns to the productive factors that the poor possess, e.g. raising returns
to unskilled labour, whereas policies promoting higher returns to capital and land tend
to increase inequality, unless they also include changes in existing patterns of
concentration of physical and human capital and of land ownership. Use of capitalintensive methods instead of labour-intensive ones tends to increase income disparities,
as does the employment of skill-biased technologies, especially where the level of
education is low and human capital concentrated. Also, the location of industrial facilities
has an impact on overall poverty reduction and inequality (Kniivilä, 2009).
After World War II, China adopted a development strategy that included deliberate
insulation from the world economy, industrialization and economic dominance of the
state. As the country was falling far behind Western countries, however, it began
reforming its closed and centrally planned economy in 1978. Since reforms, growth has
accelerated and in the 1980s and 1990s GDP growth rates were the highest in the world,
9.9 per cent and 10.3 per cent respectively, up from 6 per cent in the 1970s (Worldbank,
2004a)
In its reforms, China has followed a model similar to that of other successful East Asian
countries. Growth has been based on rapid industrialization, increased trade openness
and exports, and gradual liberalization of financial markets. Growth has been import-
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export led: technology and know-how have been imported from abroad and adapted to
the domestic resources, in particular to the abundant labour force (Dutta, 2005).
This has made the extensive production of export goods possible. The high domestic
savings rate coupled with large foreign direct investment inflows have made massive
investments in infrastructure possible. In addition, labour markets have been
increasingly deregulated, facilitating labour mobility (Kniivilä, 2009)
The economic development strategy that India chose after the Second World War was
very similar to China’s – near autarky, industrialization and the dominance of the state
in the economy. Development was considered synonymous with industrialization and
industry was concentrating mainly on basic goods like steel and machinery. Private
capital was not seen as an efficient motor for development, and it was considered to have
a tendency towards monopolization. Because of that, state control was considered to be
essential. The chosen development strategy was one of import substitution. Development
policies included licensing of industrial activity, the reservation of key areas for state
activity, controls over foreign direct investment, and interventions in the labour market
(Kaplinsky, 1997).
3.2. Empirical literature.
One of the main tasks of the economy watcher is to extract reliable signals from
highfrequency indicators to provide the decision-maker with an early picture of the
short-term economic situation. The index of industrial production (IPI) is probably the
most important and widely analysed high-frequency indicator, given the relevance of
manufacturing activity as a driver of the whole business cycle. This can be seen by the
extensive comments and reactions of business analysts as soon as the IPI is published.
Indeed, the IPI is a crucial variable in the forecasting process of the short-term evolution
of GDP in most countries (Guido Bulligan, 2009).
However, the IPI itself is characterised by a significant publication delay, which limits its
usefulness and motivates the great efforts to compute reliable and updated forecasts. The
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efforts of statistical institutes to shorten the delay of the first release imply a greater
degree of revision of the early estimates, which leads to the usual problem of assessing
the ability of alternative forecasting methods using real-time data (Guido Bulligan, 2009).
The publication by Box and Jenkins of Time Series Analysis: Forecasting and Control (op.
cit.) ushered in a new generation of forecasting tools. Popularly known as the Box–
Jenkins (BJ) methodology, but technically known as the ARIMA methodology, the
emphasis of these methods is not on constructing single-equation or simultaneousequation models but on analyzing the probabilistic, or stochastic, properties of economic
time series (Damodar N. Gujarati, 2009).
Box-Jenkins forecasting models are based on statistical concepts and principles and are
able to model a wide spectrum of time series behavior. It has a large class of models to
choose from and a systematic approach for identifying the correct model form. There are
both statistical tests for verifying model validity and statistical measures of forecast
uncertainty. In contrast, traditional forecasting models offer a limited number of models
relative to the complex behavior of many time series with little in the way of guidelines
and statistical tests for verifying the validity of the selected model (Dr. Joseph K.
Mung’atu, 2018).
4. Methodology.
In this section is presented how the econometric model is specified and the methodology
used to to analyze and forecast, it also descuss the set of data used and and describes the
variables used.
4.1. Empirical model.
4.1.1. Model building
The ARIMA methodology is carried out in three stages described by Box and Jenkins
(1976), viz. identification, estimation and diagnostic checking. Parameters of tentatively
selected ARIMA Model at the identification stage; parameters are estimated at the
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estimation stage and adequacy of tentatively selected model is tested at the at the
diagnostic checking stage. If the model is found to be inadequate, the 3 stages are
repeated until satisfactory ARIMA model is selected for the time series under
consideration, to end up with a specific formula that replicates the patterns in the series
as closely as possible and also produces accurate forecasts. Software packages EVIEWS
contain programs for fitting of ARIMA models (Dr. Joseph K. Mung’atu, 2018).
4.1.2. Indentification stage
A preliminary Box-Jenkins analysis with a plot of the initial data should be run as the
starting point in determining an appropriate model. The input data must be adjusted to
form a stationary series; one whose values vary more or less uniformly about a fixed level
over time. Apparent trends can be adjusted by having the model apply a technique of
"regular differencing," a process of computing the difference between every two
successive values, computing a differenced series which has overall trend behavior
removed (Dr. Joseph K. Mung’atu, 2018).
The class of ARMA models is quite large and in practice we must decide which of these
models is most appropriate for the data at hand n Y1, Y2 ,Y3 ,..., Yn . The correlogram and
partial correlogram are two simple diagrams which can help us to make this decision (i.e.
to identify the model) (Damodar N. Gujarati, 2009).
The correlogram for MA model and the partial correlogram for an AR model both cut off.
As we know, the correlogram for AR model dies down (but does not cut off).it can be
shown that the partial correlogram for an MA model dies down as well. Thus, if both
diagrams die down, we can conclude that the appropriate model is ARMA. (Damodar N.
Gujarati, 2009).
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Table: characteristics of a stationary model.
Model
ACF
AR(p)
Tails
PACF
off
towards
zero Cuts off to zero after lag p
(exponential decay)
MA(q)
Cuts off to zero after lag q
Tails
off
toward
zero(exponential decay)
ARMA(p,q)
Tails off toward zero
Tails off toward zero
Source: Basics of econometrics 5th edition.
Another guiding principle in model identification is that of parsimony, the total number
of parameters in the model should be as small as possible, this will almost certainly
produce the best forecasts, and we can obtain more precise (stable) parameter estimates
if the number of parameters is small (Damodar N. Gujarati, 2009).
4.1.3. Estimation stage
At the identification stage one or more models are tentatively chosen that seems to
provide statistically adequate representations of the available data. Then we attempt to
obtain precise estimates of parameters of the model by least squares as advocated by Box
and Jenkins (Damodar N. Gujarati, 2009).
According to (Dr. Joseph K. Mung’atu, 2018) & (Damodar N. Gujarati, 2009) a good model
fits the following characteristics:
1) It is parsimonious: fits the available data adequately without using any unnecessary
coefficients.
2) It is stationary: Stationarity condition on coefficient
𝐴𝑅(𝑝) = ∅1 𝑌𝑡−1 + ∅2 𝑌𝑡−2 + ⋯ + ∅𝑝 𝑌𝑡−𝑝 + 𝜀𝑡
If p=0: we have a pure MA model or white noise ARMA (0, q) and always MA and white
noise are stationary. If p=1: AR(1) or ARMA(1,q) stationarity condition is required where
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the absolute value of ∅1 must be less than 1. If p=2 : AR(2) or ARMA(2,q) stationarity
condition are required where absolute value of ∅2 must be less than 1, ∅1 +∅2 <1 and ∅2 ∅2<1 . If p>2, we check this condition ∅1 +∅2 +…+∅p<1 .
3) It is invertible:
Invertibility conditions on coefficients:
𝑀𝐴(𝑝) = ⍬1 𝐵1 − ⍬2 𝐵2 − ⋯ − ⍬𝑞 𝐵𝑞
If q=0, we have a pure AR or a white noise. all pure AR or white noise are invertible` If
q=1,MA(1) or ARMA(p,1) ,invertibility require that the absolute value of ⍬1 <1. If q=2,
MA(2) or ARMA(p,2),condition for invertibility are stated as follow: the absolute value
of ⍬2<1 , ⍬1 +⍬2 <1 and ⍬2 -⍬2<1 I f q>2, we check this condition ⍬1 +⍬2 +…+⍬q<1 .
4) It has statistically independent residuals
An important assumption is that the random shocks 𝜀(𝑡) are independent in a process.
We test the shocks for independence by constructing an acf using the residuals as input
data. If residuals are statistically independent, this is important evidence that it cannot
improve the model further by adding more AR or MA terms.
5) It fits the available data satisfactorily (available data sufficiently well at the estimation
stage)
Of course no model can fit the data perfectly because there are random-shocks elements
present in the data. The analyst must decide in each case if an ARIMA model fit available
data well enough to be used for forecasting. Box-Jenkins suggest a minimum of 50
observations.
6) It produces sufficiently accurate forecasts (small forecast errors).
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Though a good forecasting model will usually fit the past well, it is more important that
it forecast the future satisfactorily. To evaluate a model by this criterion we must monitor
its forecast performance.
4.1.4. Diagnostic checking stage
Once a model has been identified and estimated, it is usually taken to the true model and
forecast can be obtain accordingly .to protect against disastrous forecasting errors, the
least we can do is to check that the fitted model is a satisfactory one. The most commonly
used method is to examine the correlogram of the residuals from the fitted model to see
if the residuals are a white noise (as they should be if the model is correct). Box et al
(1994). Once the appropriate ARIMA model has been fitted, we can examine the goodness
of fit by means of plotting the ACF of residuals of the fitted model. If the ACF and PACF
of earlier lags are not in general within ±2√𝑁 band around 0 then there is probably left
over serial dependence in the residuals or conditional heteroscedasticity (Damodar N.
Gujarati, 2009).
4.1.5. Determining the Best Model
To determine the best model of several models of ARIMA can be used several criteria,
among others: criteria for Mean Square Error (MSE), Akaike's Information Criterion
(AIC) and Schwartz’s Bayesian Criterion (SBC). The best model was chosen that the
value of the smallest message (Aswi, 2006).
4.1.6.Forecasting future values
According to Newborn and Granger (1974)‖it is better to sort out the individual model
to derive a preferred model that contains the useful features of the original model‖ Once
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a model has been created for a time series; EVIEWS can use it to forecast future values
beyond the end of the series (Dr. Joseph K. Mung’atu, 2018).
4.2. Data source and analysis.
The data used in this study were from the national institute of statistics of Rwanda
(NISR), in the National accounts of 2019Q3 and 2020Q4. These data ranges from the
period of 2006 to 2020 on quartely basis. The varible that is going to be analyzed is the
industrial oupt from that period which is is going to be forcasted for 2021,2022 and 2023.
These data are analysed using the EVIEWS software, with the Box-Jenkins‘s methodology
which consist of three parts:
a) The autoregressive part consists of a linear regression that establishes how past values
of price per kilogram of coffee exported are related to future values, b) The ―Integrated‖
part refers to how many times we have to take a difference to get a stationary series, and,
c) The moving average part consists of how past forecast errors are related to future
values of price per kilogram of coffee exported (Damodar N. Gujarati, 2009)
An ARIMA model was developed using the Box-Jenkins‘s methodology that will take
into account past values and forecast errors to predict future coffee exportation levels.
The Box-Jenkins‘s methodology aids in identifying a forecast model, estimating its
parameters, checking the model‘s performance, and finally using it to forecast (Aswi,
2006). All of these steps are illustrated below as I develop a simple model to forecast
industrial sector output .
5. Results.
In this section of the paper, we will see the estimation of the model that can be used to
forecast the industrial sector output, and the results of the forecast of quaterly industrial
output for the seven years ahead.
5.1. Model indentification
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The serial data of industrial output in Rwanda are plotted in the figure below which
shows that the series kept on aising through time, and this means that they may not be
stationary. But deciding if the mean is not stationary just by looking at the graph below
can be misleading.
Figure: Industrial growth in Rwanda 2006Q1 to 2020Q4.
Source: Author’s estimation in Eviews9
5.1.1Correlogram of data at level
Source: Author’s estimation using Eviews9
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The correlegram shows that the data are not stationary as the spikes are not within the
boundaries both for Autocorrelation and partial autocorrelation. The Q statitics is
highly signficant ; the residuals are not white noise.
5.1.2. Unit root test at level for the industrial sector output series
Unit root test will help us to know if our data are stationary or not using Augmented
Dickey-Fuller and including intercept, Trend and Intercept or none of these (no intercept,
no Trend). If the absolute values of calculated ADF are greater than the absolute values
of 5% critical value, this means that there is stationarity. When the critical value is greater
than ADF value; so we do not reject the null hypothesis (H0: non-stationarity) (Damodar
N. Gujarati, 2009).
Figure: unit root test at level
Source: Author’s estimation using Eviews9
The unit root test above shows that there is the presence of unit root in our series, thus
they are not stationary at level , therefore one can proceed to test the unit root test after
transforming our data into first difference to see wether our series are integrated.
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5.1.2.1. Unit root test at first difference
Figure: unit root test at first difference
Source: Authors computation using Eviews9
The unit root test above indicates that there is no presence of unit root in our series, thus
they are integrated at first difference, therefore one can proceed with the indentification
of tentative models..
5.1.2. Indentification of tentative models.
Figure: correlogram of industrial output at first difference
Source: estimation by the author using Eviews9
The ACF have large spike at first, second and third lag and the PACF has large spike at
first and second lag; this can be an ARI(p,d) or IMA(d,q) or ARIMA(p,d,q) model. Now
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based on the output of our correlegram at second difference one can choose the
following tentative models as shown in the table bellow;
Table :Tentative models &overfiting models
Model
AIC
SC
HQC
ARIMA (2,1,2)
-2.494964
-2.387435
-2.453174
ARIMA (2,1,4)
-2.446043
-2.338514
-2.404254
ARIMA(2,1,6)
-2.438996
-2.331467
-2.397206
ARIMA (2,1,8)
-2.439547
-2.332018
-2.397757
ARIMA(2,1,10)
-2.637549
-2.530020
-2.595759
ARIMA(5,1,2)
-2.327034
-2.216535
-2.284419
ARIMA(5,1,4)
-2.136355
-2.025856
-2.093740
ARIMA(5,1,6)
-2.230198
-2.119698
-2.187582
ARIMA(5,1,8)
-2.347775
-2.237276
-2.305160
ARIMA(5,1,10)
-2.527686
-2.417187
-2.485071
Source: author’s extimation using eviews9.
After choosing the tentative models as in the above table, we extimate each model and
then choose the best tentative models that can be used for forcast, as accrding to (Aswi,
2006)& (Damodar N. Gujarati, 2009), we do this process by looking at the tentative model
which have the lowest AIC, SC and HQC , and based to our output we can observe that
we have a model which is ARIMA(2,1,10). We can now proceed by estimating the
equations and choose the best that can be used to forecast future output of the industrial
sector in Rwanda.
5.1.3. Model estimation.
From the above comprising the tentative and overfitting models we have choosen the
model ARIMA(2,1,10) after that we estimate the equation and the output is shown in
the figure below;
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Figure: results of estimation of ARIMA(2,1,10)
Source: author’s extimation using eviews9.
From the above output, one can observe that all the coeffients are signficant and from
the above output one can estimate the equation as:
𝑌𝑡 = 0.021491 − 0.445741𝑌𝑡−2 + 0.063083𝜀𝑡 − 0.834418𝜀𝑡−10
5.1.4. Diagnostic checking of residuals.
At this stage of the testing done to see if the selected model is already pretty well
statistically. The trick is to test whether the residual estimation results already are white
noise. When residual already white noise means the model is just right (Winarno, 2011)
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Figure : correlogram of residuals ARIMA(2,1,10)
Source: Author’s estimation using eviews 9
Looking at the above figure of ARMA structure it appears that the residual is already
random. This is shown by the graph where all dots are all located inside the circle. From
the independence of the residual test results, a models of ARIMA (2, 1, 10) is qualified
white noise therefore it can be used for forecasting.
5.1.5. Forecasting.
After a diagnostic test using ARMA structure method, the next step is to do forecasting
by using models that have been chosen, namely ARIMA (2,1,10).
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Figure: industrial forecast from 2006Q1 to 2023Q4
Source: authors’ calculation using eviews9
Based on the model estimated the forecasted industrial output in Rwanda will increase
on average of 0.35 percent quarterly in the period of 2021Q1 to 2023Q1 and at the average
of 0.34 percent from 2023Q2 to 2023Q4.
6. Conclusion and policy recommendation
The industrial sector in Rwanda is one of the three main sectors of the Rwandan economy,
but the output of this sector is still low compared to the other remaining sectors of the
economy as viewed in the (NISR, 2021) report of quarterly GDP. The aim of this study
was to analyze the quarterly output of the industrial sector data obtained from National
institute of statistics of Rwanda which was collected on quarterly basis.
This research as mentioned above used the Box-Jenkins methodology (BJ), (ARIMA
model) in modeling the output of the industrial sector in Rwanda. The stationarity
assumptions were tested using the Dickey-Fuller (ADF) statistical test and the AIC, SSE
and the SBC test were used to select a good model among the tentative ARIMA models.
In national accounting, policy makers are frequently confronted with decision making
situation in which time is a very important factor and it is very risky to do economic
planning without projecting for the future.
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Forecasting, which is one technique that country leaders may rely on as an aide in
supervising present operations and in planning for future necessities, plays a crucial role
in industry, agriculture, service, business, Government and Constitutional planning since
any efficacy they do depends on the capacity to anticipate future events and outcomes.
The right to ARIMA Model forecasting industrial output in Rwanda is model ARIMA
(2,1,10). The model ARIMA (2,1,10) is a better model when compared to the other
tentative models. This is indicated by the parameters in the model are already significant,
the value of the AIC, SC and HQC indicating that it is model which is smaller in compared
to other models and it already meets the test of independence.
The analysis done using the data collection from the secondary data of Rwanda national
accounts for GDP on quarterly basis, industry output is important since its forecasts of
the future evolution of the industrial output can be applicable to the economic activities
government policy makers and financial institutions.
And as observed in this paper, based on the model selected the estimated forecast of the
industrial output in Rwanda will increase on minimum average of 0.35 percent quarterly
in the period of 2021Q1 to 2023Q1 and on the minimum average of 0.34 percent from
2023Q2to 2023Q4.
The Box-Jenkins methodology (ARIMA model) is most powerful and popular in
analyzing time series data. We would recommend different and various researchers to
use it. These suggestions are addressed to the planners of industrial output in Rwanda in
order to improve the evolution of the industrial sector in Rwanda. The policy makers
should take into consideration the results found in the study in order to make a good
decision about the strategies and policies that can be made and put in place to improve
and manage the evolution of the Rwandan industrial sector. They should keep
conducting researches each year in order to control the evolution of Rwandan industrial
output so that they can implement fact based policies that will foster the wide growth of
the industrial sector in Rwanda, as the pace path taken indicates that its being done
gradually and this same pace should be kept for the years to come so as to assure
sustainability.
We are suggesting for further research. Even though much effort has been put in this
paper, there are still many things to study in the domain of industrial sector, notably the
government institutions and financial institutions using the statistical knowledge which
will be studied by other researchers in the same field of the interest.
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Works Cited
Aswi, S. (2006). Analisis Deret Waktu. Makassar: Andira publisher.
commonwealth. (2013). Find Industry and Manufacturing expertise in Rwanda. Retrieved may 15,
2021, from commonwealth network: https://www.commonwealthofnations.org/sectorsrwanda/business/industry_and_manufacturing/#
Damodar N. Gujarati, D. C. (2009). basics of econometrics. McGraw-Hill/Irwin,.
Dr. Joseph K. Mung’atu, M. J. (2018). Forecasting the Unit Price of Coffee Export in Rwanda Using
Arima Model. International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064.
Dutta, M. (2005). China’s industrial revolution: challenges for a macroeconomic agenda. . Journal
of Asian Economics, Vol. 15, pp. 1169-1202.
Guido Bulligan, 1. R. (2009). Forecasting industrial production: the role of information and
methods . IFC Bulletin No 33 .
Kaplinsky, R. (1997). India’s industrial development: an interpretative survey. . World
Development, Vol. 25, No. 5, pp. 681-694. .
Kniivilä, M. (2009). Industrial development and economic growth: Implications for poverty reduction and
income inequality. helsinki: Pellervo Economic Research Institute, Helsinki, Finland.
NISR. (2021). R_GDP national accounts 2020Q4. kigali: National institute of statistics of Rwanda.
RDB. (2021). mining. Retrieved april 29, 2021, from RDB.rw: http://www.rdb.rw
REG. (2019). RWANDA LEAST COST POWER . kigali: Rwanda Energy Group.
Winarno, W. W. (2011). Analisis ekonometrika dan statistika degan Eviews. Edisi Ketiga.
Yogyakarta : unit Penerbit dan Percetakan (UPP STIM YKPN).
Worldbank. (2004a). World Development Indicators 2004. CD-ROM. world bank.
Rwanda’s Economic Health
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