Optimal Rate of Inflation for the Gambia

1

Optimal Rate of Inflation for the Gambia: A Relationship between Economic Growth and

Inflation.

An empirical research

Dodou Saidy1

Submitted to the School of Business and Public Administration University of The Gambia, in Fulfillment of Honours Requirements for a Bachelor of Science Degree in Economics.

MARCH 2013

1 I am a final year student, pursuing a BSC in Economics and Finance from the University of the Gambia.

2

Approval

I certify that I have supervised this paper and I am of the opinion that it meets the acceptable

standards of scholarly work and is adequate in quantity and quality as a research project for the

fulfillment of Honors requirements for the Bachelor of Science in Economics.

……………………………………………….

Mr. Yaya s. Jallow

(Supervisor)

This research project is submitted to the school of business and public administration, university of

the Gambia in fulfillment of the Honours Requirements for the Bachelor of Science in Economics.

………………………………………….

Mohammed Jammeh

Ag. Head of Department of Economics

and Management Sciences

3

Declaration

I hereby declare that the work done in this paper was done by me with the exception of

references to other people’s works that have been duly acknowledged. This paper, either in

whole or part has not been presented elsewhere for any other degree.

…………………………………………….

(Student) Dodou Saidy

…………………………………………

Mr. Yaya S Jallow

(Supervisor)

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Dedication

To Allah the almighty for letting me to successfully complete this work to the best of my ability

and to my family for their support and encouragements.

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Acknowledgments

I would like to thank the almighty Allah, for allowing me to do such a challenging work in good

health. As always in such a research, at undergraduate level, there are many people to thank.

My special thanks and appreciation goes to Mr. Yaya S. Jallow, my able supervisor whose

untiring advice and constructive criticism helped me accomplished this work. He was the first

person to task me with such a work and it was from there that I got the confidence in doing

such a work. I would also say a big thanks to my colleagues in the Forecasting for Business class

for their sharing of ideas in group discussions and etc. I am grateful to Mr. Christopher Belford

for he always asked me about the progress of my work; this gave me a lot of motivation in my

research. It would be a crime without acknowledging the support giving to me by Binta D.

Sanyang, in helping me arrange my data into Microsoft excel. This reduced the work load on

me, by enabling me to focus on other aspects of the research. I would also convey my gratitude

to World Bank for making data available to, not only me but to everybody, without which, this

work cannot go ahead. I am also indebted to each and everyone who helps me in one way or

the other in doing this study. I will not do justice without thanking and praying for my family for

their unflinching support.

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ABSTRACT

Using macroeconomic data on the Gambia, obtained from the World Bank website for the

period 1990 to 2011, this study investigates the optimal rate of inflation2 for the Gambia. I

adopted a four step approach in determining the long run and short run relationship between

inflation and economic growth. I first test for structural breaks in the real GDP growth rate,

second I test for stationarity of the variables to avoid spurious regression using the Augmented

Dickey Fuller test, third, I tested for cointegration between the variables and finally I run both

an Error Correction Model (ECM) and an OLS regression to determine the threshold level.

However, the relationship between inflation and growth is not linear. Thus a conditional least

square estimation (gradient search) was employed. A set of six different ECMs and OLS were

estimated and the optimal rate is determined by the K3 that has the highest R square (lowest

RSS). The results from the regressions indicate an inflation rate of 6% as the optimal rate of

inflation for the Gambia. Similarly the OLS results show a 7% rate of inflation as conducive for

economic growth.

2 The inflation rate that is conducive for sustained economic growth 3 This are the various rates of inflation that I suspect, could be the optimal rate of inflation for the Gambia, it ranges from 4 to 9 percent

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Table of contents

Approval ..................................................................................................................................... 2

Declaration ................................................................................................................................. 3

Dedication .................................................................................................................................. 4

Acknowledgments ......................................................................................................................... 5

Abstract ....................................................................................................................................... 6

CHAPTER 1 .................................................................................................................................... 9

1.1 Background of the study ........................................................................................................... 9

1.2 Problem Statement ................................................................................................................ 10

1.3 Research Questions ................................................................................................................ 11

1.3 Research Objective ................................................................................................................. 11

1.4 Significance of the Study ......................................................................................................... 11

1.5 Research Hypotheses.............................................................................................................. 12

1.6 Scope of the Study ................................................................................................................. 12

CHAPTER 2 .................................................................................................................................. 13

2.0 Literature Review ................................................................................................................... 13

2.1 Theoretical Framework ........................................................................................................... 13

2.1.1Keynessian growth theory ..................................................................................................... 13

2.2 Empirical Evidence ................................................................................................................. 17

CHAPTER 3 .................................................................................................................................. 20

3.0 Methodology ......................................................................................................................... 20

3.1 Model specification ................................................................................................................ 21

3.1.1 Error Correction Model ........................................................................................................ 21

3.2 Techniques of Estimation .................................................................................................... 22

3.3 Dataset and Variables ............................................................................................................. 24

3.4 Definition of Variables ............................................................................................................ 24

3.5 Aprior Results ........................................................................................................................ 25

CHAPTER 4 .................................................................................................................................. 28

4.0 Pre and Post Estimation test results and analysis ....................................................................... 28

4.1 Structural Breaks test ............................................................................................................. 28

4.2 Unit Root Test ........................................................................................................................ 28

4.3 Test for Serial correlation, Normality and Stability ..................................................................... 28

CHAPTER 5 .................................................................................................................................. 30

5.0 I NTERPRETATION AND ANALYSIS OF RESULTS ........................................................................... 30

5.1 Pair wise Granger Causality Test .............................................................................................. 30

5.2 The optimal Inflation Rate Results ............................................................................................ 30

5.3 Estimated Short run Relationship between Inflation and Economic Growth .................................. 31

5.3.1 Cointegration test ................................................................................................................ 32

5.3.2 Impulse Response Function and Forecast Error Variance Decomposition Results ........................ 32

5.4 Cumulative Impulse Response Function .................................................................................... 33

5.5 Estimated Long run Relationship Between Inflation and Economic Growth ................................... 34

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5.6 Ordinary Least Squares Results ................................................................................................ 36

CHAPTER 6 .................................................................................................................................. 37

6.0 Conclusion and Recommendations ........................................................................................... 37

6.1 Conclusion............................................................................................................................. 37

6.2 Recommendations ................................................................................................................. 37

7.0 References ............................................................................................................................ 39

8.0 Appendix ............................................................................................................................... 42

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Chapter 1

INTRODUCTION

Background

High and sustained economic growth parallel with moderate inflation is are two most vital goals

of economic policy. Policy makers all over the world are concerned with this challenging task of

simultaneously achieving both goals, which sometimes seems daunting to achieve. Hence,

Monetary Authorities in the Gambia are not left behind in their pursuit of maintaining price

stability, economic growth couple with other goals of economic policy such as: high

employment, exchange rate stability, etc. Thus, during the period under study, Real GDP

declined from an average of 5.9 percent between year 2003 and 2006 to 4.7 percent in 2007. In

2009 Real GDP grew by 6.3 percent, led by strong growth in agriculture, tourism and the

construction industry. However, economic growth retards a little bit from 6.1 percent in 2010

to 4.3 percent in 2011, this contraction in GDP growth is attributed mostly to the crop failure

caused by lack of sufficient rainfall for agricultural productivity. However, the Gambian

economy is expected to grow by 5.5 percent in 2012 and by 10 percent in 2013, with strong

growth expected in agriculture and the tourism sector (budget speech 2013).

Similarly, Inflationary pressures in the country, continued to ease for the period under study

despite an increase in international commodity prices. Nevertheless, inflation rose from 3.9

percent in 2010 to 4.7 percent in 2011. This was due to the rise in food and energy prices as the

country imports about 50 percent of its basic food stuffs, it led to the depreciation of the dalasi

against all major currencies during this period (MPC report for February 2013). The monetary

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policy committee stated that inflation is forecasted to rise slightly to 4.8 percent and 5.0

percent in 2012 and 2013 respectively, in line with the monetary policy target of 5.0 percent.

This is attributed mostly to heightened inflationary expectations within the country. With these

developments, the MPC is committed to keeping the rediscount rate at 12.0 percent. However,

the committee will continue to monitor price movements and are committed to keeping

inflation low and non volatile (MPC report February 2013).

Problem Statement

Inflation is an interesting and important macroeconomic phenomenon because it affects

everything from wages to the price of basic food stuffs, monetary policy and has a significant

impact on the economy. It is barely just few months’ back that the Gambian currency (the

dalasi) suffered from speculative attacks4. This caused the dalasi to depreciate and as a result it

led to hiking of prices in the country. It makes foreign goods more expensive to Gambians and

Gambian goods cheaper to the rest of the world. The Gambian economy, being an import base

economy, experienced a fall in its term of trade (TOT)5 and in effect worsens the overall welfare

of the country. Furthermore, higher inflation rate is attributed to uncertainty about the future

price levels, which reduces efficiency of investment and discourages potential investors, causes

unpredictable real interest rate and discourages domestic financial saving. Similarly very low

inflation reduces company’s profit margin unless cost fall further than final consumer prices.

4 Is a change in investors’ perceptions that makes the fixed exchange rate untenable speculative attack relies entirely on the

market reacting to the attack by continuing the move that has been engineered, in order for profits to be made by the attackers 5 The value of a country's exports relative to that of its imports.

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This can lead to higher unemployment as firms seeks to reduce their costs. Low asset prices

weaken household wealth and confidence, leads to further decline in aggregate demand and a

rise in savings.

Research Questions

Is there an inflation rate in the Gambia that will enable optimal economic growth

holding other factors constant?

If there is such an inflation rate, is it a single or double digit number?

Does inflation have a statistically significant effect on economic growth?

Research Objectives

The main objective of this study is to determine the inflation rate in the Gambia that will enable

sustained economic growth. I was motivated by the fact that monetary policy makers in the

Gambia don’t have a specific inflation rate at which they are committed to keep the inflation

rate at that point.

Significance of the study

If the optimal rate of inflation is established in the Gambia, it could be a tool for the monetary

authorities in conducting monetary policy and to target inflation more explicitly. Establishing

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the threshold level should reduce uncertainty in terms of interest rates, exchange rate and

above all investments in the country. It will also help policy makers to come up with credible

policy that will be trusted by the public, thus minimizing the time inconsistency problem6.

Research Hypothesis

Inflation has no effect on economic growth.

There is no single inflation rate that is conducive for economic growth.

Structure of the paper

The rest of the paper is set as follows, chapter 2 deals with theoretical and empirical literature.

Chapter 3 deals with methodology of the study. Chapter 4 deals with the pre and post

estimation test. Chapter 5 gives an interpretation and analysis of the results and the paper

concludes with recommendations and conclusion.

6 The problem that arises when a decision maker, especially a policy maker, prefers one policy in advance but a different one

when the time it implement arrives. Knowing this, others will not find the commitment to the first policy, hence, caused

economic inefficiency.

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Chapter 2

LITERATURE REVIEW

THEORETICAL FRAMEWORK:

GDP and inflation are both considered important economic health indicators. It is widely

believed that there is a relationship between the two. The problem is that there are

disagreements as to what that relationship is or how it operates. As a result, when

governments make decisions based on these pieces of information, the outcome often cannot

be guaranteed. Exploration of the relationship between GDP and inflation is best begun by

developing an understanding of each term individually. GDP which is the value of a nation's

goods and services during a specified period is the main indicator of an economy’s health.

Inflation on the other hand refers to a situation where price levels increase on average, as a

result, money has less purchasing power. There are many theories about Economic Growth and

its relationship with inflation, ranging from the classical school of thought to the modern

theories of growth, thus, I will only talk about the Keynesian Idea of economic growth and its

relationship with inflation.

KEYNESIAN ECONOMICS

Keynesian economics theory focused on total spending in the economy and its effects on

output and inflation. It was pioneered by British economist John Maynard Keynes in his book,

The General Theory of Employment, Interest and Money, in 1936. Keynesian economists

believe that since private sector decisions sometimes lead to market failure, it requires an

active policy response by government. Keynes used his income-expenditure model in arguing

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that the economy's equilibrium level of output may not correspond to the natural level of real

GDP. Total spending on goods and services in the economy is the sum of four components:

consumption, investment, government spending, and net exports this is express as:

Where, AE = aggregate expenditures C = consumption I = investment G = Government spending

NX = net exports (exports - imports).The economy is at equilibrium when aggregate output is

equal to aggregate expenditures. Firms are selling as much as they produce and households are

buying the amount they want to purchase.

Y = aggregate output, or income

In the traditional classical macroeconomic theory, equilibrium always occurs at full employment

output. However, In the Keynesian model with fixed prices we can have equilibrium when the

economy is operating below its potential of full employment. The implication was during the

Great Depression, which could continue for a long time since it represents a possible

equilibrium. The government must step in to force the economy to a new equilibrium of full

employment. When the economy is not at equilibrium aggregate output does not equal

aggregate expenditures. Firms are producing more or fewer goods than households are buying.

The relationship between consumption and income is described by the consumption function.

The consumption function represents the "planned" or "desired” level of consumption for a

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given level of income. The consumption function is express below, were weather, wealth,

interest rates, and prices are assumed constant.

Where, C = desired level of consumption spending, C0 = fixed (autonomous) level of

consumption, C0 > 0, c = constant, 0 < c < 1, also called the "marginal propensity to consume"

(MPC) and Y = total income.

Consumption is made up of two components: autonomous consumption, C0, which is

consumption that is independent of the level of income, and income induced consumption, cY

that does depend on the level of income. The MPC is derived from the consumption function

using calculus.

Autonomous Spending

There are three components of aggregate expenditure we still need to define: investment,

government spending, and net exports. We assume that all three components are exogenous,

not determined by any variable within the model. In particular, we assume these three

components are independent of the level of income and they are: Investment Spending (I = I0),

Government Spending (G = G0) and Net Exports (NX = NX0).

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Assuming that investment spending is autonomous is a controversial assumption. In normal

economic conditions we expect investment spending to be a function of interest rates, wealth,

income and other variables. But, however, Keynes observed that we should not expect

investment to respond to changes in income or the interest rate in the short run when

resources are underutilized.

The independence of government spending is more problematic as income tax revenues rises

when income increases. When government revenue goes up, government spending also

increases, but Keynes still believes government spending will not increase with income. He

advocated for proactive government intervention in the economy. During a recession when tax

revenues decline, Keynes recommends that governments should increase rather than reduce

spending; otherwise the recession would get worse. The government should be ready to accept

deficits during recessions. When income rises as the economy recovers, the government should

then run a budget surplus to pay off the earlier deficit.

The main theme of Keynesian thoughts was that those who have income demand goods and

services and in turn, help create jobs. Thus the government should find a way to boost

aggregate demand by devising fiscal policies that will boost aggregate demand. However,

modern Keynesians advocated for monetary policy in addition to using fiscal policy to boost

aggregate demand, as monetary policy affects aggregate demand by affecting private

investment and consumption demand. An increase in money supply leads to a fall in interest

rates, investment growth, and exchange rate but increase consumption, prices and growth.

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However, not only does aggregate demand generates employment but also leads to inflation.

Recently, the global financial crisis from 2007-2009 caused many governments to adopt a

Keynesian model of stimulating the economy by pumping in a lot of money into their respective

economies with the hope of stopping the crisis, most notable is the stimulus bill pioneered by

the Obama administration in United States during the 2007 to 2009 financial crisis.

EMPIRICAL LITERATURE

Many studies have been done to establish the relationship between inflation and economic

growth. Most notably within the past twenty years. These studies used different models in

establishing the optimal rate of inflation. I present a few related studies that used the non-

linear relationship between inflation and GDP to support my own methodology. Most of the

papers I reviewed used a model developed by Senhadji and Khan (2001), which was based on a

conditional least squares estimation, where optimal inflation rate is unknown and a series of

regression employing different methods ranging from ECM, VAR, OLS, Two stage least squares

and panel data fixed effects7 are employed and hence I will only mention the methods used in

estimation.

Khan and Senhadji (2001) used panel data from 1960 to 1998 incorporating 140 countries

(comprising both developing and developed countries), to determine whether the threshold

level is the same for both develop and developing countries. Their findings showed that, the

7 A regression function describes the relationship between dependent variable Y and explanatory variable(s) X. ECM, VAR, OLS, Panel Data fixed Effects are all regressions techniques.

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threshold level of (1% to 3%) and (7% to 11%) for develop and developing countries

respectively, will be conducive for economic growth. Similar study done by Barro (1996) using

both panel and OLS found that inflation and economic growth have a significant negative

correlation but the relationship is stronger in developing countries.

The optimal rate of inflation differs across ECOWAS countries as found by Ahortor et al (2010).

The authors establish a 10% rate of inflation for Ghana and 13% rate of inflation for Nigeria as

optimal for sustained economic growth in both countries. Similarly Frimpong and Oteng-Abayie

(2010), Quartey (2010) and Marbuah (2010) using ECM, VAR and OLS respectively determined

an inflation rate of 9%, 11% and 10% respectively as conducive for economic growth in Ghana.

Using an ECM to determine the threshold level of inflation for South Africa, Phiri (2010)

ascertain an inflation rate of 8% above which it will be detrimental to finance and economic

growth. In a parallel fashion, Selenteng (2005) estimated the optimal level of inflation in

Lesotho and instituted a 10% rate of inflation to spur economic growth. Furthermore, Alqahtani

et al (2011) using the same technique, determined a 4% rate of inflation as optimal for

economic growth in the kingdom of Saudi Arabia.

Searching the threshold inflation rate for India Singh (2010) used both VAR and ECM in

estimating the optimal inflation rate, and discovered that both techniques yielded an inflation

rate of 6%. However, Ghosh and Phillips (1998) using panel data regression technique and

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allowing for a nonlinear specification found a statistically and economically significant negative

relationship between inflation and growth for both develop and developing countries.

Judson and Orphanides (1996), re-examines the relationship between inflation, inflation

volatility and growth using cross country panel data within United States for the past 30 years.

With respect to the level of inflation, in contrast to the same work done by the authors in 1994

based on cross sectional time average regression comparisons, revealed a strong negative

correlation between inflation and income growth in the United States. Bruno and Easterly

(1998) did a similar study and they discovered an inflation growth correlation is only present

with high frequency data and with extreme inflation observations; but there is no cross

sectional correlation between long run averages of growth and inflation.

Furthermore, Mubarik (2005) argued that very high inflation and too low inflation is bad for

economic growth in Pakistan. Using an ECM and employed annual data on Pakistan for the

period 1973 to 2000 and established 9% threshold level of inflation above which inflation will

retard economic growth. In contrast, Hussain (2005) improving on the data used by Mubarik

(2005) suggested that targeting inflation exceeding the range of 4% to 6% would be detrimental

to growth and development in Pakistan.

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Chapter 3

METHODOLOGY

In this part, we present the empirical methodology used in investigating the optimal inflation

rate for the Gambia. The objective is to establish the optimal inflation threshold that will spur

economic growth in the Gambia.

We have adopted four steps in establishing the optimal inflation rate. First, we conduct a

structural break8 test on real GDP growth rate to determine whether there are breaks in the

growth rate so that I can control for it, using the Zivot and Andrews test for structural break

developed by Zivot and Andrews (1992). This is done to make sure breaks in the data can be

accounted for, to avoid biased results.

Second, we test for the stationarity9 of all the variables using the widely used augmented dickey

fuller test. It helps in knowing the order in which my variables are integrated. Furthermore the

test is conducted to avoid spurious regression10 problems.

Third, we conducted a Granger causality test, to establish the casual effect of inflation and

growth on each other. Using the Granger causality test developed by Granger (1969), this test

will help in answering the following questions: is inflation causing economic growth or is

economic growth causing inflation? Is the causation one way or two ways?

8 Deep reaching change detected in (GDP) a time series sample. 9 Stationarity variables don’t have a systematic change in either mean or variance in the time series. If there were such changes

an increasing or decreasing trend in the data would be present. 10 A very good regression results but having no economic meaning

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Fourth, we test for the cointegration11 of all the variables using the Johansen test for

cointegration developed by Johansen (1988). The test helps in establishing whether my

variables have a long run relationship and hence a regression using the variable will be spurious

or unbiased. Thus it is the first step in determining whether to use an ECM.

Finally, we estimate the optimal inflation rate at different samples and under various cases,

employing an error correction model (ECM).

Model specification

Error Correction Model (ECM)

A Vector Error Correction model is accounting for cointegrated variables. If two or more

variables are non stationary time series and have a common long run path (equilibrium), we can

test for cointegration. A test for cointegration is a test, to determine whether a linear

combination of the series is stationary or not. If for instance two time series are cointegrated by

a common factor (cointegrating vector), we have to account for this relationship and use an

Error-Correction Model to get correct results.

Hence the model is specified below:

Where ……….. Eq… (1)

11 Two or more variables are said to be cointegrated if they have a long run equilibrium relation, thus a regression between the variables will not be meaningless.

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Thus - Will be stationary. In an error correction model we need

non-stationary data and a long run relationship between the variables.

However with all my variables being integrated at order zero12, we are still using an ECM why?

The reason for using an ECM with the condition of my variables was supported by the study

done by Keele and D. Boef (2004). They used analytical results from an Autoregressive

Distributed Lag Model and an ECM on stationary data. The results of the two techniques yield

the same result. The authors argued that ECM was developed prior to the theory of

cointegration and is flexible enough to model stationary data that are long memoried.

Hence this model will help in establishing both the long run and short run relationship between

inflation and economic growth. However in the short run there may be disequilibrium and the

error term in equation (1), serves as the equilibrium error. This error term is used to tie the

short run and long run value.

Techniques of Estimation:

I adopted the model used by Khan and Senhadji (2001), Mubarik (2005), Hussain (2005), Gokal

and Hanif (2004), Phiri (2010), Marbuah (2010), Seleteng (2005), Quartey (2010), a non linear

threshold of inflation is estimated. If the optimal rate is known the model could be estimated

by OLS (khan and senhadji 2001). However since the optimal level of inflation is unknown, a

non linear least square is adopted. Inflation enters the regression in a non linear and non

differentiable fashion. A gradient search technique to implement the non linear least squares is

12 This is an indication of all my variables are stationary or they have a constant mean and variance, thus, a relationship between them will be meaningful.

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appropriate (khan and senhadji 2001). The estimation has been carried out with a method

called conditional least squares (khan and senhadji 2001). For any inflation rate (K) a model is

estimated, yielding R square (sum of squared residuals). The optimal rate of inflation is found

by selecting the inflation rate, which minimizes RSS or gives the highest R squared.

The ECM is specified as follows:

y = RGDP growth, INF = inflation rate, k = is the different value of K we chose to test whether

they are the optimal rate of inflation, X = is a vector containing investment, population growth

and another dummy for structural breaks: that takes on the value: D = 1 after the break and

zero otherwise.

The parameter or threshold value K has a unique property that expresses the inflation and

growth associated as low inflation and high inflation ( + ). The implications of high

inflation here mean that when long-run inflation estimates is significant, then ( + ) will

impact on growth at the threshold level of inflation. The value of k is chosen arbitrarily for

estimation purposes in ascending order from 4% to 9% to estimate the threshold model

meaning a total of six ECM regressions will be estimated. We chose this range, because it is

clearly stated in both theory and practice that both very low and very high inflation is not good

24

for economic growth. This is clearly manifested by the Central Bank of the Gambia (CBG)

mission statement of: keeping inflation at a single digit number. The optimal inflation rate (K), is

then obtained by finding the corresponding K value which minimizes the residual sum of

squares (RSS)13 in each estimated regression model. In other words, it is the point at which the

coefficient of determination (R Square) is maximized. It is at this level that inflation has a

significant impact on growth (Mubarik, 2005, Salami and Kelikume, 2010). We also estimated an

OLS regression to check whether the results will be the same.

Data Set and Variables:

In this study, we use the dataset from the World Bank data base on the Millennium

Developments Goals (MDGs) indicators. We collected annual data for the period of 22 years

ranging from year 1990 to 2011 on the Gambia. Which is not long enough to carry out a

meaningful research, hence the Denton method of disaggregation was used to break the data

into quarters. This method has the advantage over other methods of disaggregation as the sum

of the quarterly variables adds up to the yearly data. In this study we control for variables such

as real GDP growth rate, inflation rate, population growth rate and investment.

13 The residual sum of squares is a measure of the amount of error remaining between the regression function and the data set

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Definition of Variables:

Ygrowth: this is the Real GDP growth rate for the Gambia.

Inflation: this the inflation rate for the Gambia measured by the consumer price index

base year = 2004.

Population: this is the population growth rate for the Gambia.

Investment growth: gross capital formation growth rate is used as a proxy14 of

investment growth rate.

INFk: this is a dummy taking the value of one if inflation is less than the optimal rate

and zero otherwise

Strbreak: this is also a dummy to account for structural breaks and takes on the value of

one if the observation is after the break and zero otherwise.

Aprior Results:

Theoretically I expect the following relationship to emerge.

We expect inflation at lower levels to have a positive effect on GDP but,

however, if inflation surpasses the optimal rate we expect the relationship

to be negative. Low inflation may help an economy recover from an

economic recession. Low inflation will restore investor confidence as it will

reduce uncertainty couple with high interest rates will increase investment

and economic growth. However, high inflation rates are regarded as harmful

to economic growth. It adds inefficiencies in the market, and makes it

14 A measurable variable that is used in place of a variable that cannot be measured

26

difficult for companies to do long-term planning. Inflation can affect

productivity as companies are forced to shift resources away from

production of goods and services in order to minimize losses from inflation.

Uncertainty about the future purchasing power of money discourages

investment and saving.

We also expect investment growth to have a positive effect on GDP in the long

run. GDP increases when businesses invest in infrastructure, real estate, new

product development and other physical operations. Accordingly, when

businesses and other private sector investments fall, GDP tends to follow suit.

Again we expect population growth to have a positive effect on GDP in the short

run; however in the long run the effect could be positive or negative. Because a

large population means more man power available to develop the economy at a

faster rate, however, in the long run, population growth exerts a lot of pressure

on economic and natural resources as a result consuming resources at a faster

rate. Therefore, if the population is consuming more than what nature is

providing for us the sign will be negative or otherwise.

Strbreak, we expect the dummy to have a positive effect on GDP. Because since

the turn of the new millennium all the key sectors with significant contribution

to GDP have experienced structural changes. Such as, in the service sector the

numbers of banks increased from 3 to 14 banks, the GSM industry was born etc.

In the agricultural sector with the aid of the Taiwanese technical mission, new

variety of crops with early maturity have been introduced. The tourism sector

27

has also seen a number of high quality hotels start operations in the country,

tour operators also increase etc. For human capital, university of the Gambia

also started producing highly qualified Gambian and hence increasing the human

capital based of the country. Other sectors such as energy, infrastructure,

manufacturing etc has all experience structural changes, even the consumer

price index based year15 have been changed to year 2004. Hence the structure of

the Gambian economy since the turn of the new millennium is significantly

different from the period before it (Page 2011).

15 The CPI or Consumer Price Index is a measure of the cost of goods purchased by average U.S. household, using a particular y year’s prices call the base year.

28

Chapter 4

PRE AND POST-ESTIMATION RESULTS

To make sure the results are unbiased, reliable and efficient, several tests have been conducted

all geared towards better output of result such as:

STRUCTURAL BREAKS TEST

Zivot and Andrews test for structural breaks, the results shown on the graph indicates that,

break in GDP happen in the second quarter of year 2001 (April to June). This could be attributed

to the coming of many Nigerian banks, the birth of GSM industry in the Gambia (May 2001),

new road constructions etc. See graph 1 at the appendix.

UNIT ROOT TEST

We conducted an Augmented Dickey Fuller test for stationarity of all the variables, using two

lags and all the variables were integrated at I (0). The results of the Augmented Dickey Fuller

test are reported at the appendix. See table 7

NORMALITY, SERIAL CORRELATION, AND STABILITY TEST

The test for normality, serial correlation, and stability16 are all conducted and the result

indicates that: the residuals are normally distributed with a p-value of less than 5%, the null

16

Normality is features of variables with values clustered around the mean which is equal to the median and mode and fall off smoothly in either side of it. Serial correlation: the correlation of a variable with itself over successive time intervals. Stability refers to the absence of excessive fluctuations in the variable.

29

hypothesis is rejected at the 95% confident interval. For serial correlation with a P-value of less

than 5%, the null hypothesis is rejected at the 95% confident interval. Meaning the error term

in my model is serial correlated, however this does not have any significant effect on the

reliability and efficiency of the results. A stability test result shows that all the dots are within

the band and hence the model is stable. The results of all the above mention tests are reported

at the appendix. See table 6

30

Chapter 5

INTERPRETATION AND ANALYSIS OF RESULTS

Pair wise Granger Causality test:

The test statistic shows the null hypothesis (Ygrowth does not Granger cause inflation) is not

rejected with a p- value of 0.299, which means that Ygrowth does not granger cause inflation.

The second null hypothesis (inflation does not granger cause Ygrowth) is rejected with a p-

value of 0.038, which means inflation does Granger cause Ygrowth. See appendix table 3 for the

result.

The results from the estimation of the Optimal Inflation Rate:

As stated above, the decision criterion is the optimal rate (k), with the highest R square or

lowest RSS is the optimal rate of inflation for the Gambia. The table below shows the optimal

inflation rates ranging from 4% to 9%.

Optimal inflation

rate % (k)

R squared

4 0.4356

5 0.4653

6 0.4712

7 0.4666

31

8 0.4534

9 0.4428

From the results above, the optimal inflation rate for the Gambia is 6% as it is the Inflation rate

that best explains the variation in economic growth and it is statistically significant at the 95

percent confidence interval. This result is in line with the mean reversion17 concept, as the

mean of inflation for the period used for the study was 5.9%, which is almost 6%.

Because we succeeded in estimating the optimal inflation rate for the Gambia, this gives me the

right to report only the short run and long run relationship between inflation and economic

growth at the optimal rate of inflation (the regression involving the 6% inflation rate), that we

have estimated.

Estimated Short-Run relationship between inflation and economic growth (ECM):

Before reporting and interpreting the results of the short run relationship between inflation

and economic growth. We would report the cointegration test results that we have estimated.

17 A theory suggesting that, values of variables eventually move back towards the mean or average.

32

Cointegration Test:

The study adopts the Johansen multivariate maximum likelihood method; using this

cointegrated process to test whether the variables have long term equilibrium relationship. To

examine rank of vector that is testing how many of non-zero of characteristic roots exists in the

vector. The Johansen test results indicate that all the variables are cointegrated as the trace

statistics and maximum Eigen value statistics indicates the presences of at least three

cointegration vectors between Ygrowth and its determinants. Results of the test are at the

appendix. See table 8

Impulse Response Function (IRF) and Forecast Error Variance Decomposition (FEVD) Results:

Analysis.

Impulse is inflation and Response is Ygrowth.

The results are of the expected sign for (IRF), a one percent shock in inflation rate measured by

CPI, will leads to a rise in economic growth by 1.3771% over one year and increase to a

maximum of 1.74058% over two years. The small percentage effect of inflation on growth in

short run is expected and it is of the expected sign. However the effect of inflation on growth

should be more significant in the long run. See results at appendix table 4.

FEVD measures the percentage of variation in economic growth that is explained by a

percentage shock in inflation rate. The FEVD result indicates that 4.8% of variation in economic

33

growth is explain by a one percentage shock in inflation over one year and rise to a maximum of

12% over 2 years. Again the short run effect of inflation on economic growth is of the expected

sign and effect, but the effect should be large in the long run. This results shows that inflation

and economic growth have a positive relationship in the short run, but the effect of inflation on

economic growth is not that much large, but however in the long run inflation is expected to

impact more on growth. See results at appendix table 4.

Cumulative Impulse Response Function (CIRF) Result: Analysis

CIRF represents the impact on economic growth of a one percent shock to inflation after a

period of time. It does measure the cumulative effect of inflation on economic growth. The CIRF

of 3.66948% represents the impact on economic growth of a one percent shock in inflation

after 4 quarters and increase to a maximum of 10.2972% after 8 quarters. CIRF GRAPH also

shows that there is a positive relationship between inflation and economic growth, the

relationship between the two is small in the short run but however becomes more significant in

the long run see graph 2 at the appendix. This is an indication of a strong relation between

inflation and economic in the long run. See table 5 and graph 2 at the appendix for

comprehensive results.

34

Estimated long-run relationship between inflation and economic growth:

The result form the cointegration test is an indication of a long run relationship between

inflation and economic, this is also evident in the CIRF graph which shows a positive

relationship between inflation and economic growth as the relationship prolongs. The

estimated long run relationship is presented below:

(-2.16)* (2.48) * (-1.03)

(7.50)** (1.17)

No. of obs = 86, R squared 0.4712, Sample:1990q3-2011q4, F-stat = 14.087,

* p<0.05; ** p<0.01 T-stat: are enclosed in parentheses

The results show that lower inflation rate has a negative relationship with economic

growth: as a one percent increase in inflation decreases economic growth by -2.13%.

However, the results also indicates that higher inflation spurs economic growth by

3.38% (-2.128805 + 5.512891) after a one percent increase inflation above the optimal

rate.

The effect of population on economic growth indicates that in the long run, a one

percent increase in population growth will reduce economic growth by 11.56968%, but

it is not statistically significant.

In the long run a one percent increase in investment boost economic growth by 1.2

percent and it is highly significant.

35

Strbreak dummy shows that economic growth after the year 2001 and beyond is more

than the periods before it by 1.83 percent, but it is not statistically significant. See table

1 at the appendix for comprehensive results of the long run relationship.

The result of the long run relationship between inflation and economic growth, and the other

variables, shows that contrary to my expectation lower inflation had a negative effect on

economic growth. This could be attributed to slowdowns in the economy caused by falling

aggregate demand which leads to small profit margins and business closure, hence the negative

relationship. Inflation above the optimal rate shows a positive relationship between inflation

and economic growth this is not of the expected sign. This could also be attributed to the fact

that, if people believe that prices are going to rise in the future, they may spend more at

present, since money that is not spend will lose value. And, because inflation reduces the real

value of debts, people’s debt burdens would fall and hence increase aggregate demand and

growth. This was the main reason for the United States stimulus bill in year 2008 to trigger

some inflationary pressure. However, there is an inflexion point, beyond which persistent

increase will render the currency worthless and retard growth, Zimbabwean economic crisis of

year 2008 is an example. Investment is of the expected sign and is highly significant in the long

run, thus showing a strong relation between it and economic growth. However population and

strbreak dummy are not significant and population is not of the expected sign as we expect

there long run relationship to be positive. However this could be attributed to the fact that high

population growth exerts a lot of pressure on economic and natural resources. Thus we are

consuming at a faster rate than nature is able to produce for us and hence affect economic

growth. Also to explain the insignificance of population growth in my model, the neoclassical

36

growth theory states that at the golden state only technological innovations affect economic

growth, hence rendering population growth insignificant in economic growth.

Ordinary Least Square (OLS) Results:

However we also conduct an ordinary least square estimation of the model, the aim of this was

to check whether the results from the ECM will be the same as that of OLS. However from the

six regressions we conducted, the results show that inflation rate of 7% is the optimal inflation

rate for the Gambia and both higher and lower inflation are both significant. These results were

supported by the fact that, in all the six regression we ran all the variables are not significant

except for the model including inflation rate of 7%. Hence inflation should be target between

the ranges of 6% to 7%. The OLS results are reported at the appendix. See table 2

37

Chapter 6

CONCLUSIONS AND RECOMMENDATIONS

CONCLUSIONS

By obtaining data for my study from the World Bank database for the period of 22 years from

1990 to 2011. The study seeks to estimate the optimal rate of inflation in the Gambia, which we

successfully established at 6%. This study was conducted, controlling for the effect of high

inflation rate, population growth, investment growth and structural breaks in economic growth.

A potential downside of this study is the limited availability of time series data the covers a

larger span. This leads to the process of disaggregating the data (breaking it into quarterly data)

to increase the sample size as the study with a larger span could yield better results. The

unavailability of data is always a major issue in conducting research of this magnitude in the

Gambia. This leads me to use gross capital formation as a proxy for investment growth, which

is not actually investment growth.

RECOMMENDATIONS

After modeling and estimating the threshold level of inflation for the Gambia. And the results

speak for themselves. I would recommend that the monetary authorities in targeting inflation

not to target inflation at very low level in the long run. The government of the Gambia should

38

also come with strategies to promote investment in the country as this will spur economic

growth. One way to do this is by empowering GIEPA which is responsible for investment

promotion in the country. The central bank of the Gambia should come with monetary policies

that will protect the value of the dalasi. Policies such as: a tighter monetary policy will

strengthen the dalasi as it will push the interest rate up, make domestic investment attractive

and increase the demand for the dalasi and growth. Fiscal policy should also be aimed at

protecting the dalasi as budget deficit stimulate economic growth. Since government must

borrow to finance a budget deficit the demand for loanable funds will increase and also pushes

the interest rate up. Hence, the government should also come up with strategies to support

development of new product which will be attractive in the world market.

39

REFERENCES

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Boef, L. K. ( 2004, December 16). Not Just for Cointegration: Error Correction Models with

Stationary Data.

Christian R. K. Ahortor, A. A. (2010). An Estimate of Inflation Threshold inthe WAMZ: The Case

of Ghana and NIGERIA. JEL Classification: .

DIEGO RODRÍGUEZ PALENZUELA, G. C.-M. ( 2003). Price stability, inflation costs and benefits,

downward nominal rigidities, inflation differentials, deflation. WORKING PAPER .

Eakins, F. S. (2012). financial markets and institutions. (s. edition, Ed.) pearson.

FosuOteng-Abayie, J. M. (2010). When is Inflation Harmful? Estimating the Threshold Effect for

Ghana. American Journal of Economics and Business Administration .

Gambia, C. B. (2013). Monetary policy committee report February. Banjul.

Garriga, J. B. (2012). Demographics, Redistribution, and Optimal Inflation.

GREENE, w. H. (2003). ECONOMETRICS ANALYSIS. PEARSON EDUCATION LIMITED.

GUJARATI. (2004). Basic Econometric. The McGraw−Hill.

Hanif, V. G. (2004, December 04). RELATIONSHIP BETWEEN INFLATION AND ECONOMIC

GROWTH.

40

Hussain∗, M. ( 2005, October). INFLATION AND GROWTH: AN ESTIAMTION OF THRESHOLD

POINT FOR PAKISTAN. PBR .

Kahn, B. R. (2008). What Is the Optimal Inflation Rate?

MANKIW, G. N. (2010). MACROECONOMICS. (S. EDITION, Ed.) Library of Congress Cataloging-in-

Publication.

marbuah, g. (2010). on the inflation-growth nexus: Testing for the optimal rate of inflation for

Ghana. JEL Classification .

Mubarik∗, Y. A. (2005). Inflation and Growth: An Estimate of the Threshold Level of Inflation in

Pakistan. SBP-Research Bulletin .

Olivier Coibion, Y. G. (2011). The Optimal Inflation Rate in New Keynesian Models: Should

Central Banks Raise Their Inflation Targets in Light of the ZLB? JEL codes: .

Omar Masood, B. A. (2009). An empirical study on Banks profitability in the KSA: A co-

integration approach. African Journal of Business Management .

Palley, T. I. (1998). Zero is not the Optimal rate of Inflation.

Phiri, A. (2010). AT WHAT LEVEL IS INFLATION LEAST DETRIMENTAL TOWARDS FINANCE-

GROWTH ACTIVITY IN SOUTH AFRICA? Journal of Sustainable Development in Africa .

Quartey, P. (2010). Price Stability and the Growth Maximizing Rate of Inflation for Ghana*.

Modern Economy, .

41

Safar AlQahtani1, A. E. (2011). Estimating the Optimal Level of Inflation (Inflation Threshold) In

the Kingdom Of Saudi Arabia.

Seeteng, M. (2005). inflation and economic growth: An estimate of an optimal rate of inflation

in lesotho.

Senhadji, M. S. (2001). Threshold effects in the relationship between inflation and growth. IMF

Staff papers , 48.

Tsoulfidis, P. L. (2010). competing schools of thoughts. Springer-Verlag Berlin Heidelberg .

University, H. Y. (2008). What is the Optimal Rate of Inflation for Long-Run Growth? A Cross-

Country Analysis*.

Uribe, S. S.-G. ( 2010, January 30). The Optimal Rate Of Inflation. NBER .

Uribe, S. S.-G. (2009). The Optimal Rate of Inflation.

wooldridge, j. introductory econometrics.

42

APPENDIX

Below is the estimated long run relationship between my variable, focusing on Ygrowth and inflation.

DEPENDENT VARIABLE: Ygrowth Number of observations 88

Table 1

Optimal inf variables coefficient Std. Error T- statistic p-values R

Squared

4% Inflation 2.357158 1.002677 2.35 0.019 0.4356

Inf4 -6.07354 2.177637 -2.79 0.005

Investment 1.228964 0.1675289 7.34 0.000

Population -36.00975 11.42543 -3.15 0.002

strbreak -1.411447 1.549519 -0.91 0.362

cons 23.78593

5% Inflation -1.677093 1.401393 -1.20 0.231 0.4653

Inf5 4.972407 3.09406 1.61 0.108

Investment -2.113809 .2574473 -8.21 0.000

Population 28.39393 17.49608 1.62 0.105

strbreak -.194854 2.276296 -0.09 0.932

cons -19.37268

6% Inflation -2.128805 .9868393 -2.16 0.031 0.4712

Inf6 5.512891 2.221492 2.48 0.013

Investment 1.203061 .1603199 7.50 0.301

Population -11.56968 11.18767 -1.03 0.000

strbreak 1.8271 1.556812 1.17 0.241

43

cons 6.707345

7% Inflation 14.05998 2.039701 6.89 0.000 0.4666

Inf7 -36.35168 5.691367 -6.39 0.000

Investment -1.56673 .2965757 -5.28 0.000

Population 70.80478 23.83609 2.97 0.003

strbreak -4.660689 2.694842 -1.73 0.084

cons -60.07334

8% Inflation 1.97589 .5864877 3.37 0.001 0.4534

Inf8 -6.250122 1.614144 -3.87 0.000

Investment -.6377332 .0853118 -7.48 0.000

Population 1.961348 5.957737 0.33 0.742

strbreak -1.070751 .7843653 -1.37 0.172

cons -3.099428

9% Inflation 2.017821 .8294968 2.43 0.015 0.4428

Inf9 -9.239368 2.595275 -3.56 0.000

Investment -1.025063 .1296564 -7.91 0.000

Population 23.47207 9.295693 2.53 0.012

strbreak -.3760328 1.171145 -0.32 0.748

cons -18.66934

44

This table below contains the OLS results obtain in estimating the optimal rate of inflation at different inflation

rate.

DEPENDENT VARIABLE: Ygrowth rate Number of observations 88

Table 2

Optimal inf variables coefficient Std. Error T- statistic p-values R

Squared

4% Inflation .1002753 .1605379 0.62 0.534 0.0961

Inf4 .2060409 .2719168 0.76 0.451

Investment -2.071064 1.321531 -1.57 0.121

Population .0316968 .0181746 1.74 0.085

strbreak .2003918 .2026987 0.99 0.326

cons 2.154195 .9338711 2.31 0.024

5%

Inflation .2145354 .1469853 1.46 0.148 0.0955

Inf5 -.177976 .2450409 -0.73 0.470

Investment -1.882954 1.214395 -1.55 0.125

Population .0330238 .0184705 1.79 0.077

strbreak .1383749 .2286596 0.61 0.547

cons 2.040999 .860381 2.37 0.020

6% Inflation .3772194 .1815498 2.08 0.041 0.1565

Inf6 -.713644 .3705393 -1.93 0.058

Investment .0378092 .0191601 1.97 0.052

Population -1.320416 1.192263 -1.11 0.271

45

strbreak -.0375605 .2903948 -0.13 0.897

cons 1.647254 .8507928 1.94 0.056

7% Inflation .4553191 .1858232 2.45 0.016 0.1748

Inf7 -1.110659 .4906286 -2.26 0.026

Investment .0316572 .0185776 1.70 0.092

Population .316336 1.399308 0.23 0.822

strbreak .1292271 .2247387 0.58 0.567

cons .2889657 1.017964 0.28 0.777

8% Inflation .0013776 .1691839 0.01 0.994 0.1174

Inf8 .6228007 .4060464 1.53 0.129

Investment .0300741 .0180617 1.67 0.100

Population -2.440441 1.276042 -1.91 0.059

strbreak .2091833 .2115121 0.99 0.326

cons 2.541424 .9143294 2.78 0.007

9% Inflation -.0123747 .1398726 -0.09 0.930 0.1335

Inf9 .8301861 .4437497 1.87 0.065

Investment .0306176 .0179522 1.71 0.092

Population -2.675927 1.338524 -2.00 0.049

strbreak .1293531 .2131015 0.61 0.546

cons 2.775051 .9945704 2.79 0.007

46

Table 3, below depicts the results of the granger causality between inflation Ygrowth.

Pair wise granger causality tests.

Sample: 1990q1 to 2011q4

Table 3

Null hypothesis: Ygrowth does not granger cause inflation

Equation Exclusion Chi2 Df prob > chi2

Ygrowth inflation 2.4157 2 0.299

Ygrowth all 2.4157 2 0.299

Null hypothesis: inflation does not granger cause Ygrowth

inflation Ygrowth 6.5584 2 0.038

inflation all 6.5584 2 0.038

Table below are the IRF and FEVD RESULT

Table 4

steps IRF (1) FEVD (1)

0 0 0

1 .367896 0

2 .790841 .007335

3 1.13364 .025356

4 1.3771 .047975

5 1.53918 .070603

47

The Table below is the CIRF results.

Table 5

steps Cirf (1) Fevd (1)

0 0 0

1 .367896 0

2 1.15874 .007335

3 2.29238 .025356

4 3.66948 .047975

5 5.20865 .070603

6 6.85123 .090952

7 8.55667 .108285

8 10.2972 .122628

6 1.64257 .090952

7 1.70544 .108285

8 1.74058 .122628

48

DIAGNOSTIC TESTS

Diagnostic tests were done for all five estimated equations however, only diagnostic results for the optimal level of

inflation is reported

Table 6

.

This table below reports the result of the unit root test, using the augmented dickey fuller test:

Table 7

Equation TEST FOR TEST STATISTIC CONCLUSION

Inf-6 Normality test (JB) 0.00000 Residual normally

distributed

Stability test Within band stable

Test for serial correlation

(LM TEST)

0.00239 There is serial correlation

variables Integrated order P- values conclusion

Augmented dickey

fuller test at (lag 2)

Inflation 0 0.0090 No unit root

Ygrowth 0 0.0289 No unit root

Population 0 0.0000 No unit root

investment 0 0.0000 No unit root

49

Results show in the table below indicates that no matter whether it is trace test or max Eigen value statistic shows

that all the four equations have long term equilibrium relationship.

Table 8

H0:

Eigen values rank<=(r)

(lambda) r

H1:

Max-lambda Trace

statistics statistics

(rank<=(r+1)) (rank<=(p=4))

.27347245 0 27.794663 41.368521

.0736524 1 6.6559987 13.573859

.05052176 2 4.5103119 6.9178601

.02729358 3 2.4075482 2.4075482

50

I will now report the graphs that I use in estimating and analyzing my results.

Graph 1

GRAPH 2: CIRF graph

-6-5

.8-5

.6-5

.4-5

.2-5

Bre

akp

oin

t t-

sta

tistics

1990q1 1995q1 2000q1 2005q1 2010q1year

Min breakpoint at 2001q2

Zivot-Andrews test for ygrowth, 1994q1-2008q3

0

5

10

0 2 4 6 8

ordera, inflation, ygrowth

stepGraphs by irfname, impulse variable, and response variable

51

GRAPH 3: Stability test graph

-1-.

50

.51

Imag

inary

-1 -.5 0 .5 1Real

The VECM specification imposes 5 unit moduli

Roots of the companion matrix