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ISHAKU, NYIPUTEN RIMAMTANUNG
PG/MSC/12/64567
THE IMPACT OF INFLATION ON PRIVATE
CONSUMPTION EXPENDITURE AND
ECONOMIC GROWTH IN NIGERIA
FACULTY OF SOCIAL SCIENCE
DEPARTMENT OF ECONOMICS
Azuka Ijomah
Digitally Signed by: Content manager’s Name
DN : CN = Webmaster’s name
O= University of Nigeria, Nsukka
OU = Innovation Centre
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THE IMPACT OF INFLATION ON PRIVATE CONSUMPTION
EXPENDITURE AND ECONOMIC GROWTH IN NIGERIA
BY
ISHAKU, NYIPUTEN RIMAMTANUNG
PG/MSC/12/64567
PHONE: +234(0) 8026055103
E-Mail: [email protected]
DEPARTMENT OF ECONOMICS
UNIVERSITY OF NIGERIA, NSUKKA
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SUPERVISOR: PROF. C.C AGU
AUGUST, 2015
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TITLE PAGE
THE IMPACT OF INFLATION ON PRIVATE CONSUMPTION EXPENDITURE
AND ECONOMIC GROWTH IN NIGERIA
BY
ISHAKU, NYIPUTEN RIMAMTANUNG
REG: PG/MSC/12/64567
AN M. SC. PROJECT SUBMITTED TO THE DEPARTMENT OF ECONOMICS,
UNIVERSITY OF NIGERIA, NSUKKA, IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE (M.Sc.) DEGREE
IN ECONOMICS
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CERTIFICATION
This is to certify that, ISHAKU, NYIPUTEN RIMAMTANUNG a post-graduate student of the
Department of Economics, University of Nigeria, Nsukka, whose registration number is
PG/M.Sc/12/64567 has satisfactorily completed the requirement for the award of Master of
Science (M.Sc.) in Economics.
Prof. C.C AGU Prof. C.C AGU
Supervisor Head of Department
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APPROVAL PAGE
This project has been approved for the award of the Degree of Master of Science (M.Sc.) of
the Department of Economics, University of Nigeria, Nsukka.
Prof. C.C AGU Prof. C.C AGU Supervisor Head of Department
Prof. I.A MADU External examiner
Dean, Faculty of Social Sciences
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DEDICATION
This Project is dedicated to God Almighty for his love, mercy, grace and protection and my
late parents Mr. and Mrs. Ishaku Nyiputen.
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ACKNOWLEDGEMENT
My sincere gratitude goes first to God Almighty for his love, mercies, grace, and protection
throughout this course of study.
I appreciate the contribution of my supervisors Prof. C.C Agu for his attention, patience,
advice and encouragement toward the successful completion of this work. I specially
acknowledge my senior colleagues Mr. Aladejare Samson for his immense contributions,
scrutiny and advice. Equally deserving are my lecturers Prof. F. E. Onah, Prof. Ikpeze, Prof.
Madueme, Prof. Ichoku, Dr. Innocent, Dr. Tony Orji, Dr. Nwosu, Dr. Urama, Dr. Asogwa,
Dr. Ezebuilo for their commitment and hard work. I also appreciate all the non-academic staff
of the department.
I would like to acknowledge the helpful comments and contributions of my post graduate
colleagues and friends: Henry, Aduku, Innocent, and Ogbonna. And to all other friends,
whose names did not appear here, be assured that your effort and contributions are highly
appreciated.
I am also indebted to my beloved Brothers and Sisters for their support and assistance, Mr.
and Mrs. Asher Ishaku, Mr. and Mrs. Ephraim Ishaku, Mr. and Mrs. Nahum Ishaku and Mr.
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and Mrs. Mark Ishaku. Finally, I acknowledge the enthusiastic and excellent support of my
beloved wife Mrs. Victoria Rimamtanung Ishaku and my beloved son Michael (Rimamchika)
Rimamtanung Ishaku. May the Almighty God bless you all in Jesus Name.
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TABLE OF CONTENTS
Title page……………………………………………………………………………… i
Approval page………………………………………………………….......................... ii
Certification…………………………………………………………………………… iii
Dedication…………………………………………………………................................ iv
Acknowledgement……………………………………………………………................. v
Table of Contents…………………………………………………………….................. vi
List of Tables…………………………………………………………………………… viii
Abstract………………………………………………………………………................. ix
CHAPTER ONE: INTRODUCTION
1.1 Background of the Study …………………………………………………………… 1
1.2 Statement of the Problem………………………………….......................................... 2
1.3 Research Questions ……………………………………………………………………… 4
1.4 Objective of the Study…………………………………………………………………… 4
1.5 Research Hypothesis …………………………………………………………………… 5
1.6 Significance of the Study…………………………………………………..…………… 5
1.7 Scope of the Study ……………………………………………………………………… 6
CHAPTER TWO: LITERATURE REVIEW
2.1 Conceptual Framework…………………………………………………………………… 7
2.1.1 The concept of inflation………………………………………………………………… 7
2.1.2 Private consumption expenditure……………………………………………………… 8
2.1.3 Economic growth……………………………………………………………………… 8
2.2 Theoretical literature……………………………………………………………………… 9
2.2.1 The Keynesian Theory of Inflation …………………………………………………… 9
2.2.2. Modern Theory of Inflation ………………………………………………………… 10
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2.2.3. Keynesian Theory …............................................................................................. 12
2.2.4. Endogenous Growth Theory ………………….………………………….………… 13
2.2.5. Monetary Theory …………………………………………………………………… 14
2.3 Empirical Literature ……………………………………………………………………… 15
2.3.1 Foreign Evidence ……………………………………………………………………… 15
2.3.2 Nigerian Evidence ……………………………………………………………………… 20
2.4 Summary of Literature and Value Added ……………………………………………… 22
CHAPTER THREE: RESEARCH METHODOLOGY
3.1 Theoretical framework...........................................................................................................25
3.2 Model Specification…………………………………………………………………… 26
3.3 Estimation Technique …………………………………………………………………… 28
3.3.1 Data, Sources and Software………………………………………………………… 28
3.3.2 Stationary Test…………………………………………………………………… 29
3.3.3 Co-integration Test……………………………………………………………… 30
3.3.4 The Vector Error Co- integration Mode…………………………………………………… 30
3.3.5 VEC Granger Causality…………………………………………………………… 31
CHAPTER FOUR: RESULT PRESENTATION AND ANALYSES
4.1 Unit Root Test Results……………………………………………………………… 33
4.2 Johansen Cointegration Test Result……………………………………………………… 34
4.3 lag Length Selection Criteria……………………………………………………………… 36
4.4 VECM Estimated Result…………………………………………………………………… 37
4.5 VEC Granger Causality Result......................................................................................... 41
4.6 Impulse Response Analysis......................................................................................... 44
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION
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5.1 Summary…………………………………………………………………………… 48
5.2 Conclusion………………………………………………………………………………… 48
5.3 Recommendation…………………………………………………………..………… 49
5.4 Suggestions for Further Study……………………………………………………… 50
References …………………………………………………………………………….. 51
APPENDIX
LIST OF TABLES
Table 1.1: Average growth rate of inflation, private consumption expenditure and economic
growth in Nigeria ………………………………………………………… 3
Table 4.1 Unit Root Test Results………………………………………………………… 33
Table 4.2a Unrestricted Cointegration Rank Test (Trace)…………………………… 35
Table 4.2d Unrestricted Cointegration Rank Test (Maximum Eigenvalue…..………… 35
Table 4.3 Lag length selection criteria…………………………………………………… 36
Table 4.4: Estimated VECM Result…………..………………………………………… 37
Table 4.5: VEC Granger Causality/Block Exogeneity Wald Tests…………..………… 41
Table 4.6: Impluse Response………………………………………………..………… 44
Table 4.7: Residual auto correlation test…………………………………..…………… 45
Table 4.8: Residual serial correlation test……………………………………..……… 46
Table 4.9: VEC residual normality Test……………………………………………… 47
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ABSTARCT
This study empirically examine the impact of inflation on private consumption
expenditure and economic growth in Nigeria using an annual time series data spanning
from 1981-2012. In this study, modern time series econometric methodology such as Unit
Root Testing, Johansson Co-integration test, Vector error co-integration granger
causality test(VEC) and Vector Error Correction Model (VECM) where employed to
model both the long run and short run relationships between inflation, economic
growth, interest rate as (explanatory variables) and private consumption expenditure as
(dependent variable). Augmented Dickey- Fuller (ADF) and Phillips–Perron (PP) test
were conducted and the results show that all the data are not stationary at a level but
after the first difference they become stationary. The Johansson co-integration test
indicates that there exists a long run relationship between the variables for the period of
study. However, the VEC Granger Causality result shows that inflation is positively
granger causes private consumption expenditure for the period of study and there
happens to be no causality flowing from inflation to economic growth, neither is there
causality from economic growth to inflation in the short run. However, the long-run
model result shows a negative impact of inflation on economic growth for the study
period. It implies that I per cent increase in inflation will result in 0.69 decreases in
economic performance (RGDP). It could therefore be recommended that Government
together with the central Bank of Nigeria should develop and pursue prudent monetary
and fiscal policies that would aim at reducing and stabilizing both the micro and
macroeconomic indicators especially inflation targeting, so as to boast the growth of the
economy.
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CHAPTER ONE
INTRODUCTION
1.1 Background of the Study
The management of the economy is a major concern of governments all over the world.
Governments of countries feel compelled to ensure, through appropriate policies that their
economies are managed to achieve desirable macroeconomic objectives. These objectives
include: price stability; economic growth; full employment; and balance of payments
equilibrium. The achievement of stable prices and attainment of sustainable economic growth
had been the central objectives of macroeconomic policies for most countries in the world
today. This is so because the achievement of other objectives like full employment and
balance of payment equilibrium are also determined by the achievement of price stability and
economic growth. (Ohale & Onyema, 2002)
Economic growth is dependent upon the productive effort of a society and investment of
resources. An increase in production and investment will lead to economic growth. A
country’s rate of growth can be affected by inflation through its effect on investment. An
increase in inflation rate reduces the return on investment, both on physical and human
capital. Lower returns mean less accumulation and innovation and hence a lower rate of
growth. Growth in output of goods and services is a good way of bringing material benefits to
the citizens. This is through fostering those developments such as increased investment,
technical progress, increase in demand, amongst others, which are conducive to the growth of
the economy. Investment is required to maintain output per head in the face of an increase in
the size of labour force. Moreover, increase in consumption expenditure makes producers to
respond by increasing their capacity and by so doing, promote economic growth.
Nevertheless, as the level of economic activities increase, an economy experiences growth
(Ohale & Onyema, 2002; and Apere, 2006).
Private consumption expenditure constitutes the largest component of total consumption
expenditure in Nigeria and accounts for more than 65% of the Gross Domestic
Product, GDP ( National Bureau of Statistics, 2010). Thus, private consumption expenditure
is a core component of aggregate demand. Although consumption is determined by other
factors such as interest rate, relative prices, capital gains, wealth, attitude and expectation and
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availability of consumer credit. The major determinant of consumption expenditure is
income. Individuals increase their consumption expenditure as income increases. A little
disturbance in this component will have a far reaching effect on the nation’s aggregate
demand. A consumption-led growth will in turn result into increase in production and
investment-led growth and eventual move the economy to a higher growth trajectory. An
increase in private consumption expenditure causes a rise in GDP, other things being
unchanged (Mishra & Fasoranti, 2013).
The impact of inflation on private consumption and economic growth reflects through its
impact on income redistribution, profits, investments and efficiency of firms. Inflation affects
real value of wages, salaries, rents and interest. The result of this is that the quantity of goods
and services which money income can buy is affected. In other words, private consumption
can be affected by inflation through its effects on real value of wages, salaries, rents and
interest. The effect of inflation on profit however depends on the type of inflation. Demand
pull inflation leads to an increase in the level of profits. This may therefore encourage
investment. On the other hand, cost push inflation tends to squeeze profit. This is because
there will be no excess demand; and firms will find it difficult to pass along their rising cost
in the form of higher prices to customers. This discourages production. Inflation could affect
economic growth through its effect on investment; it impairs investment if it encourages
spending instead of lending. This is because it will reduce loanable funds. This is seen from
the point that reduction in funds that are loanable will lead to increase in the rate of interest as
creditor’s demand for higher returns, to guide against the falling value of money.
From the above, one can see that the impact of inflation on private consumption expenditure
and economic growth is motivated by the relevance of private consumption and economic
growth and the consequences of inflation in the economy.
1.2 Statement of the Problem
The relevance of private consumption expenditure and economic growth to the economy of
any nation is also the rationale why government focuses on ensuring improved standard of
living and a steady rate of economic growth. The study of the impact of inflation on private
consumption and economic growth however became necessary because; price instability may
impede government’s effort to achieve improved living standard and a steady growth rate if
not checked empirically and then formulate appropriate policies. The outcome of policies on
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inflation may be misleading without investigating its impact on consumption and growth
within a given period of time.
Governments of countries put in place different policies and programme over time to ensure
the achievement of stable prices. Nigeria in an attempt to ensure price stability, since the
attainment of independence in 1960, implemented various anti-inflationary policy measures.
From 1993 attention and objectives of policy makers shifted to the achievement of single
digit inflation (Essien & Eziocha 2002). Both monetary and fiscal policies as well as wage
freeze, price control, exchange rate and other measures have been employed to stem the tide
of sustained increase in the general price level. In retrospect, it appears that in spite of these
efforts; the achievement of price stability objective has been limited.
Kumapayi,(2012) reveals that over the last few decades, high inflation in Nigeria has caused
yield on investment to decline while government policy objectives has been adversely
affected as the real size of its budget shrinks with rising inflation which has hampered
economic growth. On the contrary, Omotosho and Doguwa(2013) found that the periods of
high inflation volatility in Nigeria are associated with periods of specific government policy
changes, shocks to food prices and lack of coordination between monetary and fiscal policies.
The table below depicts on average, the growth rate of inflation, private consumption
expenditure and economic growth.
Table 1.1: Average growth rate of inflation, private consumption expenditure and
economic growth in Nigeria
Periods Variables
CPI PCX RGDP
1981-1990 4.54 -0.30 0.31
1991-2000 9.41 0.24 0.25
2001-2010 0.35 0.37 0.80
Source: Central Bank of Nigeria: Statistical Bulletin, 2012 Edition.
As it is shown in the table above, the average growth rate of consumer price index in Nigeria
for the periods 1981-1990 was 4.54. It increased by 107.27% (from 4.54 to 9.41) between the
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periods 1991-2000. This increase was followed by a sharp decrease of 96.28% (from 9.41 to
0.35) for the periods 2001-2010. A look at the private consumption expenditure reveal a
similar trend with CPI during the periods 1991-2000, as it recorded an increase of 225%. This
however was not the case between the periods 2001-2010; it increase further by 54.17%.
Finally for RGDP, the trend was different from CPI and PCX. A decrease of 19.35% was
recorded during 1991-2000. For the periods 2001-2010, though similar in trend with PCX in
the sense that an increase was recorded; but was still different as a tremendous increase of
220% was observed compared to CPI and PCX during this period.
Though, rise in prices is extrinsic in the growth process. Inflation is there with the growth of
the economy and it is expected to be moderate and gradual. Stable and low prices overtime
brings about economic growth. But Nigeria’s inflation has not been moderate and gradual.
For example, the increase in CPI was very high (107.27%); and during this period the
average growth rate of RGDP decreased. However the period CPI decreases, the growth rate
of RGDP became very high. In addition, when CPI rises during the periods 1991-2000, PCX
also rises. This is however not the expectation. It is expected that prices should be stable or
low overtime to bring about economic growth; and an increases in prices (inflation) should
lead to fall in consumption expenditure. These therefore raise puzzles about the impact
inflation has on private consumption expenditure and economic growth in Nigeria.
There is no doubt whatsoever that a lot of empirical studies exists on the area of impact of
inflation on economic growth but few on impact of inflation on private consumption
expenditure in Nigeria. Most studies conducted on the impact of inflation on economic
growth used OLS and granger causality techniques (see Osuala & Onyeike, 2013; Taiwo &
Muritala, 2011; Inyiama, 2013; Chimobi, 2010; Akekere & Yousuo 2012; and Oduh, 2012).
None of the studies examined the link between inflation, private consumption expenditure
and economic growth in Nigeria simultaneously. Therefore, this study simultaneously
examining the impact of inflation on private consumption expenditure and economic growth
in Nigeria along side with other control variables in the same model. Few or none of these
studies adopted vector error correction model (VECM) techniques which this study did. The
inclusion of private consumption expenditure which in most studies reviewed by this work
was omitted was found to be a significant variable in understanding the relationship between
inflation and economic growth in Nigeria. The variable is important because its play a dual
role in determining the relationship between inflation and economic growth. This is because
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of the catalyst role it plays in growing the economy of a nation; while on the other hand
giving rise to the problem of inflation. Moreover it accounts for about two-thirds of domestic
final spending, and thus it is the primary engine that drives future economic growth. Thus it
will be a value added to the literature, especially in Nigeria.
1.3 Research Questions
The study seeks to answer the following questions:
i. What is the impact of inflation on private consumption expenditure in Nigeria?
ii. What is the impact of inflation on economic growth in Nigeria?
1.4 Objective of the Study
The broad objective of this study is to examine the impact of inflation on private
consumption expenditure and economic growth in Nigeria. The Specific objectives include:
i. To examine the impact of inflation on private consumption expenditure in Nigeria.
ii. To examine the impact of inflation on economic growth in Nigeria.
1.5 Research Hypothesis
The study shall be guided by the following hypotheses which are stated in their null
forms:
H01: inflation has no significant impact on private consumption expenditure in Nigeria.
H02: inflation has no significant impact on economic growth in Nigeria.
1.6 Significance of the Study
This study is relevant for the fact that it will simultaneously establish the link between
inflation, private consumption expenditure and economic growth in Nigeria, which very few
or no study has examined. The methodological approach adopted for the study is also new to
study based on empirical findings related to Nigeria. The inclusion of private consumption
expenditure which in most studies reviewed by this work was omitted was found to be a
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significant variable in understanding the relationship between inflation and economic growth
in Nigeria. The variable is important because its plays a dual role in determining the
relationship between inflation and economic growth. This is because of the catalyst role it
plays in growing the economy of a nation; while on the other hand giving rise to the problem
of inflation. Moreover it accounts for about two-thirds of domestic final spending, and thus it
is the primary engine that drives future economic growth. Thus it will be a value added to the
literature, especially in Nigeria. The results of the study will be significant to the monetary
authorities. This is because it will provide relevance information on the effect of inflation on
the variables under study. In other words, it will reveal the effectiveness of her policy on
price stability as a macroeconomic policy objective. The study would also serve as guide to
the monetary authorities on the appropriate policies to adopt and at any given time. The
results of the study will also be relevance to government and other stakeholders as well as
policy makers. This is because it will reveal the performance of the monetary authorities.
This therefore will enable the government to take appropriate decision on whether to change
leadership of the current monetary authority or not. Finally, the results of the study will also
provide a platform for further studies on inflation, private consumption and economic growth.
1.7 Scope of the Study
This research work is concentrating on the Nigerian economy. For relevance and in-depth
analysis, the study intends to investigate empirically the impact of inflation on private
consumption expenditure, and economic growth in Nigeria with data spanning from 1981 to
2012. The choice of this period of reference is significant because inflation trend within the
period under study constitute a matter of serious policy consideration. The period witnessed a
steady and positive growth in money supply. The period also encompasses the major
landmark in our national economy; between 1981 to early part of 2001, stringent economic
stabilization measures were in operation as a result of the dramatic down-turn of the
international oil prices. Availability of data is an important factor that was considered in
choosing the terminal year of 2012. This study intends to use the following variables: CPI as
proxy for inflation, real GDP as a proxy for economic growth, and private consumption
expenditure as the main variables while interest rate is used as control variables.
CHAPTER TWO
LITERATURE REVIEW
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This chapter covers the conceptual framework, followed by the theoretical and empirical
literatures as it relate to the study.
2.1 Conceptual Framework
This kind of study would often raise some conceptual issues which require clarification for
better understanding and smooth presentation of issues under discussion. The key concepts
in this study are inflation, private consumption expenditure and economic growth. In what
follows, we shall peruse through the literature on the conceptual issues relating to the
aforementioned concepts.
2.1.1 The concept of Inflation
Inflation is define as a persistence rise in the general price level of goods and services in a
country over a long period of time (Umaru & Zubairu, 2012). They state that Inflation has
intrinsically linked to money, as captured by the often heard maxim “inflation is too much
money chasing too few goods” The neo-classical and their follower’s believed that inflation
is fundamentally a monetary phenomenon. In the words of Friedman, inflation is always and
everywhere a monetary phenomenon and can be produced only by a more rapid increase in
the quality of money than output”. But economists do not agree that money supply alone is
the cause of inflation. Economists, therefore, define inflation in terms of a continuous rise in
prices. Johnson defines inflation as a sustained rise in prices. Brooman defines it as “a
continuing increases in the general price level. Shapiro also defines inflation in a similar way
as a “persistent and appreciable rise in the general level of prices. Dernberg and MCDougall
are more explicit when they write that “the term inflation usually refers to a continuing rise in
prices as measured by an index such as the consumer price index (CPI) or by the implicit
price deflator for gross national product. However, it is essential to understand that a
sustained rise in prices may be of various magnitudes. As a result, different names have been
given to inflation depending upon the rate of rise in prices e.g., creeping walking, running
and hyperinflation.
But this study adopted definition given by Dernberg & Medougall which define inflation as
the persistence or continuing rise in the general price level as measured by an index such as
the consumer price index (CPI), or by the implicit price deflator for gross national product.
This is so, because there are number of different measures of inflation in use, but the most
frequently quoted are the (CPI) and the retail prices index (RPI). Each looks at the prices of
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hundreds of things we commonly spend money on, such as bread, cinema tickets, and prints
of bear and track how these prices changed over time.
Inflation has three components viz: headline inflation which is measured by all items CPI,
core inflation, measured by all items less food CPI, and food inflation, which measured by
the food CPI. The focus of this study is the headline inflation because it measured all items
CPI, so the study will adopt the all items consumer price index as a proxy for inflation.
2.1.2 Private consumption expenditure
Private consumption expenditure can also be referred to as household final consumption
expenditure. This is the market value of all goods and services, including durable products
(such as cars, washing machines, and home computers), purchased by households. It excludes
purchases of dwellings but includes imputed rent for owner occupied dwellings. It also
includes payments and fees to governments to obtain permits and licenses. For the purpose of
this study, private consumption expenditures (PCX) are the primary measure of consumer
spending on goods and services in the Nigerian economy. It accounts for about two-thirds of
domestic final spending, and thus it is the primary engine that drives future economic growth.
PCX shows how much of the income earned by households is being spent on current
consumption as opposed to how much is being saved for future consumption.
2.1.3 Economic growth
Economic growth has been defined as an increase in economic activities. There are many
proxies used in measuring economic growth viz: per capita GDP and real GDP. But for
purpose of this study the researcher focus on real GDP as a proxy for economic growth. Real
GDP measures changes in physical output in the economy between different time periods by
valuing all goods produced in the two periods at the same prices or in constant dollars
(Dornbusch, 2003). Real GDP can also be measured as GDP by current market price.
The links between private consumption expenditure, (PCX) economic growth and inflation
rest on the notion that; PCX is a determinant factor of economic growth, because it measures
the market value of goods and services; durable and non-durable goods consumed in a
country within a particular period of time. While inflation causes money to lose its real value,
making people to consume less and save more, thereby reducing aggregate demand. When
20
aggregate demand falls, firms reduced production capacity, thereby lying- off some staff
which in turn reduces their real per capita income thereby affecting economic growth.
The impact of inflation on private consumption and economic growth reflects through its
impact on income redistribution, profits, investments and efficiency of firms. Inflation affects
real value of wages, salaries, rents and interest. The result of this is that the quantity of goods
and services which money income can buy is affected. In other words, private consumption
can be affected by inflation through its effects on real value of wages, salaries, rents and
interest. The effect of inflation on profit however depends on the type of inflation. Demand
pull inflation leads to an increase in the level of profits. This may therefore encourage
investment. On the other hand, cost push inflation tends to squeeze profit. This is because
there will be no excess demand; and firms will find it difficult to pass along their rising cost
in the form of higher prices to customers.
The study adopts Consumer Price Index (CPI), Real Gross Domestic Products (RGDP), as a
proxy for inflation and economic growth respectively. While private consumption
expenditure will be used directly. These statistics are often published in the CBN statistical
bulletin, annual reports, quarterly reviews, etc.
2.2 Theoretical literature
The theories to be revealed here are: The Keynesian theory of inflation, Modern Theory of
Inflation, Keynesian Theory, Endogenous Growth Theory, and Monetary Theory
2.2.1. The Keynesian Theory of Inflation
Keynes theory of inflation is only a little more than an extension and generalization of
Wick sells view. Keynes, however, made an important departure from the classical view.
While classical economists considered an increase in money supply as the only cause of an
increase in the aggregate demand and only cause of inflation, Keynes postulated that
aggregate demand can increase also due to an increase in real factors.
Keynes expressed his view on inflation in his book, How to Pay for the War (1940),
wherein he gave the concept of inflationary gap. Inflationary gap is defined as the planned
expenditure in excess of output available at full employment. The British
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Chancellor of Exchequer defined the inflationary gap in budget speech of 1941 as “the
amount of the governments expenditure against which there is no corresponding release of
real resources of manpower or material by some other members of the community”.
The „inflationary gap is so called because it causes only inflation, without increasing
the level of output. It is important to note here Keynes linked inflationary gap and
the consequent inflation to full employment output. It implies that the expenditure in
excess of output at less-than-full-employment level is not inflationary even if prices
increase. For, such increase in price generates additional employment and output. The
additional output absorbs the excess demand ultimately without causing inflation.
2.2.2. Modern Theory of Inflation
The modern approach to inflation follows the Theory of Price Determination. The
price theory tells us that, in a competitive market, price of a commodity is determined
by the market demand and the supply of the commodity and variation in the price of the
commodity is caused by the variation in the demand and supply factors. Likewise, the
aggregate price level is determined by the aggregate demand and aggregate supply and
variation in the aggregate price level is caused by the variations in the aggregate
demand and aggregate supply. The modern theory of inflation is, in fact, a synthesis of
Classical and Keynesian Theories of Inflation. The modern analysis of inflation shows that
inflation is caused by both demand–side and supply-side factors. The demand–side factors
are called demand-pull factors, and supply-side factors are called supply-side or cost-
push factors. Accordingly, there are two kinds of inflation:
(i) Demand-pull inflation.
(ii) Cost-push inflation.
Demand-Pull Inflation: The demand-pull inflation occurs when the aggregate
demand increase much more rapidly than the aggregate supply. The demand-pull
inflation caused by monetary and real factors are provided here separately.
(a) Demand-Pull Inflation due to Monetary Factors. An important reason for demand-
pull inflation is increase in money supply in excess of increase in potential output.
Whether increase in money supply in excess of output is the cause of inflation is a
controversial issue. In reality, however, monetary expansion in excess of increase in
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real output is one of the most important factors causing demand -pull inflation. As
regards the empirical evidence of this kind of inflation, German inflation of 1922-
1923 is often cited as an example of demand-pull inflation caused by the
increase in money supply. During 1922-1923, the German government had
fallen under heavy post-war debts and reparations payment obligations. The
government, left with no option, asked its central bank to meet government payment
obligations. When the German Central Bank printed and circulated billions and
billions of paper currency, the general price level raised a billion-fold. In recent
times, the excess supply of money caused demand-pull inflation in Russia in 1990s
„when the Russian government financed its budget deficit by printing roubles.‟ Due
to rapid increase in money supply, the general level of prices had raised in Russia
during the early 1990s at an average rate of ‟25 per cent per month.‟
(b) Demand-Pull Inflation due to Real Factors. The real factors that cause demand pull
inflation are those that cause upward shift in the IS curve. The factors that cause
upward shift in the IS curve is:
(i) Increase in government spending given the tax revenue
(ii) Cut in tax rates without change in the government expenditure
(iii) Upward shift in the investment function
(iv) Downward shift in the saving function
(v) Upward shift in export function
(vi) Downward shift in the import function
Cost-Push Inflation: Inflation is not caused by the demand-side factors alone. There
are numerous instances of inflationary movement of prices which could not be fully
explained by the demand-side factors. The 1958-recession in western countries is a
famous instance. During this period of recession, aggregate demand had declined.
Therefore, the general price level should have decreased but it did not in recent
times, it is a common experience that prices generally do not decreased during
the period of recession. Furthermore, even when there is stagflation in the economy
and there is no inflationary pressure, the general price level generally continues to
increase, with a high rate of unemployment. The search for explanation to this kind
of phenomenon, particularly for the 1958-puzzel, has lead to the emergence of
supply-side theories of inflation, popularly known as cost-push theory and supply-
shock theory of inflation.
23
The cost-push inflation is caused by the monopoly power exercised by some
monopoly groups of the society, like labour unions and firms in monopolistic and
oligopolistic market setting. It has been observed that strong labour unions often succeed in
forcing money wages to go up causing prices to go up. This kind of rise in price level is
called wage-push inflation. Not only labour unions, the firms enjoying monopoly power
have also been found causing rise in the general price level. The monopolistic and
oligopolistic firms push their profit margin up causing a rise in the general price level. This
kind of inflation is called profit -push inflation. Yet another kind of cost-push inflation is said
to be caused by supply shocks. Thus, the cost -push inflation may be classified on the basis of
supply-side factors as follows.
(i) Wage-push inflation
(ii) Profit-push inflation
(iii) Supply-shock inflation
To these may be added some other kinds of supply-side factors, such as minimum-
wage legislation and administered prices. The minimum-wage legislation is an intervention
with the labour market. This prevents the downward adjustment in wages during the
period of recession. Administered prices, for instance, fixing a minimum price for
some sections of producers prevent downward adjustment in prices during the period of
good harvest and keep the prices artificially high for socio political reasons.
2.2.3. Keynesian Theory
The traditional Keynesian model comprises of the aggregate demand (AD) and aggregate
supply (AS) curves, which illustrates the inflation growth relationship.
According to this model, in the short-run, the (AS) curve is upward sloping rather than
vertical which is its critical feature. If the AS curve is vertical, changes on the demand side of
the economy affect only prices. However, if it is upward sloping, changes in AD affect prices
and output, this holds with the fact that many factors derive the inflation rate and the level of
output in the short-run. These include changes in expectations, labour force, prices of other
factors of production, fiscal and/or monetary policy.
24
In moving from the short-run to the hypothetical long-run, the above mentioned factors and
its shock, on the ‘steady state’ of the economy are assumed to be balanced out. In this ‘steady
state’ situation, nothing is changing as the name suggests. The dynamic adjustment of the
short-run AD and AS curves yields an adjustment path, which exhibits an initial positive
relationship between inflation and growth, however, turns negative towards the latter part of
the adjustment path.
The initial positive relationship between output and inflation, illustrated by the movement
from point Eo to E1 in figure 2.below, usually happens due to the time inconsistency problem.
According to this concept, producers feel that only the prices of their products have increased
while the other producers are operating at the same price level. However, in reality, overall
prices have risen. Thus, the producer continues to produce more and output continues to rise.
Blanchard and Kiyotaki (1987) also believe that the positive relationship can be due to
agreements by some firms to supply goods at a latter date at an agreed price. Therefore, even
if the prices of goods in the economy have increased, output would not decline as the
producer has to fulfil the demand of the consumer with whom the agreement was made.
Fig. 2: Relationship between output and inflation
Source: See Dornbusch, et al (1996).
Two further features of the adjustment process are also important to note. Firstly, there are
times when output decreases and the inflation rate increase, for example, between E2 and E3.
This negative relationship between inflation and growth is important as it quite often occurs
in practice, as ascertained by empirical literature. This phenomenon is stagflation, when
Infl
atio
n
.
. .
.
E3
►
▲
▼
▼
▼
E2
E1 E0
O
П1
П0
Y* Y Output
25
inflation rises as output falls or remains stable. Secondly, the economy does not move
directly to a higher inflation rate, but follows a transitional path where inflation rises then
falls. Under this model, there is a short-run trade-off between output and the change in
inflation but no permanent trade-off between output and inflation. For inflation to be held
steady at any level, output must equal the natural rate (y*). Any level of inflation is
sustainable; however, for inflation to fall there must be period when output is below the
natural rate.
2.2.4. Endogenous Growth Theory
Endogenous growth theories describe economic growth which is generated by factors within
the production process, for example, economics of scale, increasing returns or induced
technological change as opposed to outside exogenous factors such as the increase in
population. In endogenous growth theory, the growth rate has depended on one variable, the
rate of return on capital. Variable like inflation, that decreases the rate of return, which in turn
reduces capital accumulation and decreases the growth rate.
One feature accounts for the foremost difference between the endogenous growth models and
the neo-classical economics. In the neo-classical economics, the return on capital declines as
more capital is accumulated. In the simplest versions of the endogenous growth models, per-
capita output continues to increase because the return on capital does not fall below a positive
lower bound. The basic intuition is that only if the return on capital is sufficiently high, will
people be induced to continue accumulating it. Models of endogenous growth also permit
increasing returns to scale in aggregate productions, and also focus on the role of externalities
in determining the rate of return on capital.
2.2.5. Monetary Theory
Monetarism has several essential features with its focus on the long-run supply-side
properties of the economy as opposed to short-run dynamics. Milton Friedman, who coined
the term “monetarism”, emphasized several key long-run properties of the economy,
including the quantity theory of money and the Neutrality of money. The quantity theory of
money linked inflation and economic growth by simply equating the total amount of money
in existence. Friedman proposed that inflation was the product of an increase in the supply or
velocity of money at a rate greater than the rate of growth in the economy.
26
Friedman also challenged the concept of the Philip curve. His argument was based on the
premise of an economy where the cost of everything doubles. Individuals have to pay twice
as much for goods and services, but they don’t mind, because their wages are also twice as
large. Individual anticipate the rate of future inflation and incorporate its effects into their
behaviour. As such, employment and output is not affected. Economists call this concept the
neutrality of money. Neutrality holds if the equilibrium values of real variables including the
level of GDP-are independent of the level of the money supply in the long-run. Super
neutrality holds when real variables – including the rate of growth of GDP are independent of
the rate of growth in the money supply in the long run, if inflation worked this way, then it
would be harmless. In reality however, inflation does have real consequence for other
macroeconomic variables. Through its impact on capital accumulation, investment, and
exports, inflation can adversely impact a country’s growth rate. In summary, monetarism
suggests that in the long-run, prices are mainly affected by the growth rate in money, while
having no real effect on growth. If the growth in the money supply is higher than the
economic growth rate, inflation will result.
2.3 Empirical Literature
Over the years studies have been carried out to examine the impact of inflation on private
consumption and economic growth separately. In what follows, we explore the existing
literature first on global evidence and second on Nigerian evidence.
2.3.1 Foreign Evidence
On the global front, Barro (1995) made an assessment on the effects of inflation on economic
performance using data for around 100 countries over the period 1960-1970. The study
concludes that if a number of countries, characteristics are held constant, then the regression
results suggested that an increase in average inflation of 10 percent per annum reduces the
growth rate of real GDP by 0.2 to 0.3 percent per annum and lowers the ratio of investment to
GDP by 0.4 to 0.6 percent.
Bruno & Easterly (1995) examine the determinants of economic growth. Bruno and Easterly
in carrying out the research, propose a nonparametric definition of high inflation crises as
“periods when annual inflation is above 40 percent”. An annual data for 26 countries was
used. The threshold for an inflation crisis is an inflation rate of 40 percent and over. The
authors identified countries, which had high inflation crisis of 40 percent and above.
27
This was followed by assessing how the country’s growth has performed before, during
and after its high inflation crisis. The robustness of the results was examined by
controlling for other factors such as shocks including political crises, terms of trade
shocks and wars. The results found show a negative relationship between inflation and
growth, however, they found out that the case of the effects of low growth to moderate
rates of inflation very high. Moreover the results obtained indicated that causality
remained problematic, but their results are consistent with the view that costs of
inflation only become significant at relatively high rates of inflation. At lower rates of
inflation, growth and inflation may simply be jointly troubled by various demand and
supply shocks and hence shows no consistent pattern.
Andres & Hernando (1997) cross-countries studies mainly focused on the nonlinearities and
threshold effects of inflation on growth. The result found a significant negative effect of
inflation on economic growth. They also found that there exists a nonlinear relationship.
Their main policy message stated that reducing inflation by 1 percent could raise output by
0.5 and 2.5 percent.
Nell (2000) examined the issue of inflation on economic growth as detrimental to economic
growth or not; using vector Auto regressive (VAR) technique. Data for the period of 1960 to
1999 was used and his empirical results. His result suggested that inflation within the single
digit zone may be beneficial to economic growth, while inflation in double digit zone tends to
limit economic growth.
Khan & Senhadji (2001) studied the threshold effects in the relationship between inflation
and growth. The data set included 140 countries (comprising both industrial developing
countries) and generally covered the period of 1960 to 1998. The log model of inflation was
used as estimate. The estimation method used in their case was the non-linear least squares
(NLLS). The results found that, the threshold is lower for industrialized countries than it is
for developing countries (the estimates are 1-3 percent and 11-12 percent for industrial and
developing countries respectively depending on the estimation method used). The thresholds
show statistically significant relationship between inflation and growth but above the
threshold level is argued to be robust with respect to type of estimation method used. The
results in this paper provide strong evidence for supporting the view of low inflation for
sustainable growth.
28
Mallik & Chawdhury (2001) examined short run dynamics of the relationship between
inflation and economic growth for four south Asian economies; Bangladesh, India, Pakistan
and Sri-lanka. Using co-integration and error correction model and annual data retrieved from
the international monetary fund (IMF), international financial statistic (IFS), they found two
motivating results. First, the relationship between inflation and economic growth is positive
and statistically significant for all four countries. Secondly, the sensitivity of growth to
change in inflation rates is smaller than that of inflation to changes in growth rate. These
results have important policy implication that is; although moderate inflation promotes
economic growth, faster economic growth absorbs into inflation by overheating the economy.
Therefore, these four countries are on the turning point of inflation economic growth
relationship.
Faria & Carneiro (2001) examined whether high inflation affects growth in the long and short
run? The paper investigates the relationship between inflation and output in the context of an
economy facing persistently high inflation and inflation shocks. Data used consists of the
monthly inflation rate and real output for the period January 1980 to July 1995. The data was
sourced from the Brazilian institute of economics and Geography database. The authors used
bivariate time series model based on methodology following the Blanchard and Quay (1989)
decomposition. The paper aimed at estimating the long run response of output to a permanent
inflation shock. The results presented in the paper found a zero long-run response of output to
a permanent inflation shock in the content of a high inflation country in Brazil. The results
could be considered as evidence against the view that inflation and output are reliably related
in the long-run. However, in the short-run, the results indicated that, there is a negative
impact of inflation on output.
Vikesh & Hanif (2004) explored the relationship between inflation and economic growth:
case of Fiji. The objective of the paper was to determine whether a significant connection
between inflation and economic growth exists; using data spanning from 1970-2003. A
correlation coefficients and Granger causality technique was used. The results indicated that a
weak negative correlation exists between inflation and growth while the change in output gap
bears significant bearing. The causality between the two variables ran one-way from GDP
growth to inflation.
Ahmed & Mortaza (2005) empirically explored the relationship between inflation and
economic growth in Bangladesh using annual data set on real GDP and consumer price index
29
(CPI) for period of 1980 to 2005, and the co-integration and error correction models. The
evidence demonstrates that there exists a statistically significant long-run negative
relationship between inflation and economic growth for the country.
Bick & Nell (2009) empirically expended the scope of Kham & Senhadji, (2001) by
modelling a large panel data set of 124 industrialized and developing countries over the
period of 1950 to 2004, using a dynamic panel threshold model to investigate the impact of
inflation on economic growth. They found an inflation target of about 17 percent for
developing economies and 2 percent for industrialized countries. Below the 17 percent
threshold, the impact of inflation on economic growth remained insignificant, thus failing to
support the growth enhancing effect of inflation on economic growth in non-industrialized
economies.
Prasanna & Gopakumar (2009) examined an empirical relationship between inflation and
economic growth in India. In the paper, the co-integration and error correction models where
used to empirically examine long-run and short run dynamics of inflation-economic growth
relationship in India using annual data from 1972 to 2007. The objective of their study was to
examine whether a relationship exists between economic growth and inflation and if so
determine its nature. The results found that inflation and economic growth are negatively
related. Secondly, the sensitivity of inflation to changes in growth rates is larger than that of
growth to changes in inflation rates.
De Mello& Carneiro (2010) Used Euler equation-type of consumption functions to analyze
consumption behaviour in a context of persistently high inflation. It also examines how
widespread backward–looking indentation and/or total currency substitution in the case of
variation affect private consumption behaviour. The findings shows that, in the presence of
persistently high inflation widespread backward looking indexation and total foreign currency
substitution via dollarization lead to consumption volatility. Based on the findings, if the
external shocks are to have a similar impact on high inflation countries in Latin America, we
would then require that the underlying consumer spending responses to shocks should be
broadly similar.
Quartey (2010) investigated whether the revenue maximizing rate of inflation is growth
maximizing in Ghana. Using the Johansson co-integrations methodology, he found that there
is negative impact of inflation on growth. Furthermore, the study found a revenue
30
maximizing rate of inflation at 9.14 percent over the period 1970 to 2006 using the laffer
curve. He further established that the rate of inflation that is growth maximizing is not a
single digit one.
Alem & Soderbo (2010) studied Household level consumption in urban Ethiopia: the impact
of food price inflation and idiosyncratic shocks. The study used panel data to investigate how
urban households in Ethiopia coped with the food price shock in 2008 and idiosyncratic
shocks. It also aim to study how changes in food consumption and general consumption
related to household level variables. Also, self-reported data on the effects of the food price
inflation on food consumption was analyzed. Their results shows that household with low
levels of assets have been particularly adversely affected by the food price inflation. They
also find out that households headed by casual workers have been vulnerable to food price
shock.
Vaona (2011) explores the influence of inflation on economic growth both theoretically and
empirically. The author proposed to merge an endogenous growth model of learning by doing
with a new Keynesian one with sticky wages. It showed that the inter-temporal elasticity of
substitution of working time is a key parameter for the shape of the inflation growth nexus.
The study adopting various semi parametric and instrumental – variables estimation
approaches on a cross-country /time series data set. The results show that increasing inflation
reduces real economic growth, consistent with our theoretical model with a positive inter-
temporal elasticity of working time.
Wadal (2011) carried out an econometric study of private consumption function in Lebanon.
His paper examined the response of consumption to income, interest rate, inflation, and
wealth in Lebanon. The data set used covered the period of 1975 to 2007. The author used
real factors rather than nominal ones to explore the main determinants of the real private
consumption in Lebanon. The integrated nature of the series was investigated in order to
evaluate the long-run relationship between private consumption, national disposable income,
interest rate and inflation. The results showed that in the long-run real private consumption is
affected by current disposable income, anticipated inflation and wealth.
Faraji & Mwakanemela (2013) examined the impact of inflation on economic growth in
Tanzania. They used reduced form regression equation (ILS) to investigate the impact of
inflation on economic growth. Their results from regression analysis revealed that inflation
31
has a negative impact on economic growth in Tanzania. This indicated that inflation is
harmful to the economic growth of Tanzania. The same result was found by Quartey, 2010 in
Ghana.
Agalega & Acheampong (2013) examine the impact of inflation, policy rate and government
consumption expenditure on GDP growth in Ghana. Co-integration approach was adopted in
this work. The authors used annual time series data spanning from 1980-2010, and unit root
testing, co-integration and vector error correction model (VECM) were used as techniques to
models both for long and short-run relationship between the variables understudies, such that
inflation, and policy rate and government consumption expenditure and policy rate
(independent variables) and real GDP (dependent variable) the results indicated, positive
long-run relationship between inflation, and policy rate with real GDP, while government
consumption expenditure has a negative impact on real GDP in the long run. It was revealed
that inflation and government consumption expenditure have a positive effect on real GDP in
the short run. Among the variable understudies, only inflation rate had a significant impact on
real GDP while policy rate and government consumption expenditure have no significant
impact on real GDP in Ghana. It is recommended among others that the government together
with the Bank of Ghana should develop and pursue prudent monetary and fiscal policies that
would aim at reducing and stabilizing both the micro and macroeconomic indicators
especially inflation targeting so as to boast the growth of the economy.
Rutayisire (2013) this paper assumes a non linear relationship between inflation and
economic growth and attempts to identify the existence of threshold effects between these
variables in the case of Rwanda using a data set spanning the sample period 1968-2010. The
existence of a threshold level above which inflation has an adverse effect on economic
growth in Rwanda has been investigated by means of a quadratic regression model and
ordinary least square technique. The results showed that at low levels, inflation does not hurt
economic growth, while at higher levels, inflation reduces economic growth. The estimated
inflation threshold level is 14.97%.
Gilson (2013) studied public expenditure, inflation and economic growth in Cape Verde.
Using vector auto-regressive (VAR) approach, the study attempts to empirically investigate
the effects of public spending in stimulating economic growth and also inflation stabilization
in Cape Verde. The results showed that an increase in government spending does not produce
any changes in the total output of the economy, causing only an increase in inflation rate.
32
Testing the effects of public expenditure on private sector, the results also showed that
private investment does not change with changes in public expenditure; unlike consumption
which has Keynesian effects.
2.3.2 Nigerian Evidence
Nwabueze (2009) examined the causal relationship between gross domestic product and
personal consumption expenditure of Nigeria. The study employed regression analysis to
investigate the causal relationship between gross domestic product and personal consumption
expenditure of Nigeria using data from 1994-2007. The result showed that increase
consumption expenditure would lead to increase in GDP; not that increase in GDP would
result in increase in private consumption expenditure.
Aminu & Zubairu (2012) in studying the effect of inflation on growth and development of
Nigerian economy (an empirical analysis); between 1970 -2010 used ADF test for unit root
and Granger Causality test. Their result indicates that all variables are stationary and result
for causality suggests that GDP causes inflation not inflation that causes GDP. The result also
revealed that inflation possessed positive impact on economic growth, through encouraging
productivity and output level and on evolution of total factor productivity.
Chimobi (2010) investigates the existence of a relationship between inflation and economic
growth using annual data for the period 1970 to 2005, the study finds no co-integrating
relationship between the two variables. Using Granger causality tests, however, the study
established unidirectional causality running from inflation to economic growth.
Odior (2011) examined macroeconomic volatility and private consumption expenditure in
Nigeria. The paper explores the household welfare effect of macroeconomic volatility on
private consumption (PCE) in Nigeria. The study empirically model the relationship between
PCE and macroeconomic with a hybrid model, that employs a reduced form coefficients of
simultaneous equation model; to capture the dynamic interaction among the data and a
structural economic model to described the contemporaneous relationship between the
variables. Data used spanning from 1980 to 2008. The results show that volatility of
microeconomics does lead to a decline in consumption expenditure. Also economic shade to
inflation effects is stronger on the PCE at a longer horizon. The study concludes that inflation
has a negative effect on welfare.
33
Taiwo (2011) examined investment, inflation and economic growth: empirical evidence from
Nigeria. The paper attempts to empirically examine the impact of investment and inflation on
economic growth performance as well as showing the trend analysis between inflation and
investment in Nigeria from 1981 to 2006. Method of analysis used was ordinary least square
(OLS) technique. The results shows inflation has negative impact on economic growth and
investment and economic growth has positive relationship. This implies that 1 percent
increase in inflation will result in 0.09 decreases in economic growth.
Oduh (2012) explored the impact of consumers’ confidence and expectation on consumption
in Nigeria; based on a panel data analysis. The study investigated the macroeconomic
determinants of private consumption, laying emphasis on consumer confidence and
expectation by accounting for variations across the six geopolitical zones in Nigeria. The
identified macroeconomic variables in addition to consumer confidence includes: current and
expected income, prices of food and durable, nominal official exchanges rate, and deposit
rate. To realize the study objective, data from the CBN quarterly survey of consumer
confidence and expectation spanning from 2009 to 2011 was decomposed into monthly series
to improve on a number of observations. To account for variations in the zero demand
patterns, fixed effect panel regression was estimated with EGLS, accounting for cross-section
weight. The results shows strong evidence of positive relationship between consumer
confidence and household planned spending. Aside exchange rate, consumer confidence has
the highest influence on consumption accounting for about 1.7% change in planned spending;
while exchange rate account for 3.2%. Other insightful outcomes from the regression are that
consumers are more concerned with movement in the price of food items than durables, while
current and future income positively influences their consumption pattern.
Akekere & Yousuo (2012) examined the empirical analysis of change in income on private
consumption expenditure in Nigeria. The study investigated the impact of change in gross
domestic product (income) on private consumption expenditure in Nigeria, from 1981 to
2010. Using OLS technique, the result agrees with theoretical expectation of the existence of
a positive significant impact of GDP (income) on private consumption expenditure with a
slope of 0.6708253. This implies that gross domestic product (income) has a significant effect
on private consumption expenditure in Nigeria. Consumption income causal relation seems to
be almost proportional over the period under investigation.
34
Samuel& Andrew (2012) investigated the relationship between inflation, savings and output
in Nigeria, employing vector auto regression (VAR) approach. OLS and Granger causality
test were also conducted along side with VAR to augment findings and show robustness of
results using data from 1970 to 2010. The OLS result indicates that inflation tends to reduce
output, while savings actually stimulates output. The granger causality results shows that
changes in inflation may not have stimulate nor responded to output growth or savings in
Nigeria over the period of analysis. On the other hand, changes in savings effectively
stimulate output and increase in output also stimulate saving in Nigeria. The VAR result
affirmed that output changes respond more critically to changes in savings than inflation
changes, suggesting that boosting private saving will effectively stimulates output in the
Nigerian economy.
Osuala & Onyeike (2013) examined the impact of inflation on economic growth in Nigeria;
using a causality test. The study aimed at evaluating the impact of inflation on economic
growth in Nigeria using data set spanning from 1970 to 2011. Granger causality test was
employed to ascertain the direction of influence between inflation and economic growth in
Nigeria. The result shows that there exists a statistically significant positive relationship
between inflation and economic growth in Nigeria. However, there is no leading variable in
the relationship between inflation and economic growth in Nigeria. They conclude that the
effect is contemporaneous.
Inyiama (2013) his study evaluated the link between inflationary rate and economic growth
in Nigeria. It also examined the nature and forms of association between inflationary rate,
exchange rate and interest rate from 1979 to 2010. Ordinary least squares (OLS) technique
and granger causality were used in the study. The results found that inflationary rate is
negatively related with economic growth, while exchange rate and interest rate are positively
related with inflationary rate. Causality results show that there is no causality relationship
between inflationary rate and economic growth at both lag 2 and 4.
2.4 Summary of Literature and Value Added
There is no doubt whatsoever that a lot of empirical studies exists on the area of the impact of
inflation on economic growth but few on impact of inflation on private consumption
expenditure in Nigeria. Most studies conducted on the impact of inflation on economic
35
growth used OLS and granger causality techniques (see Osuala & Onyeike 2013; Taiwo
2011; Inyiama, 2013; Chimobi, 2010; Akekere& Yousuo 2012; and Oduh, 2012).
The literature review showed that none of the studies examined the link between inflation,
private consumption expenditure and economic growth in Nigeria simultaneously. Therefore,
this study departs from the previous studies by simultaneously examining the impact of
inflation on private consumption expenditure and economic growth in Nigeria; combining
inflation, private consumption expenditure and economic growth variables along side with
other control variables in the same model. The methodological approach adopted for the
study is also new to study, based on empirical findings related to Nigeria. The inclusion of
private consumption expenditure which in most studies reviewed by this work was omitted
was found to be a significant variable in understanding the relationship between inflation and
economic growth in Nigeria. The variable is important because its play a dual role in
determining the relationship between inflation and economic growth. This is because of the
catalyst role it plays in economic growth; while on the other hand giving rise to the problem
of inflation.
CHAPTER THREE
RESEARCH METHODOLOGY
This chapter contains the theoretical framework as well as the time series econometric
methods and techniques employed to carry out analysis on the impact of inflation on private
consumption expenditure and economics growth in Nigeria.
3.1: Theoretical Framework:
36
The traditional Keynesian model comprises of the aggregate demand (AD) and aggregate
supply (AS) curves, which illustrates the inflation growth relationship.
According to this model, in the short-run, the (AS) curve is upward sloping rather than
vertical which is its critical feature. If the AS curve is vertical, changes on the demand side of
the economy affect only prices. However, if it is upward sloping, changes in AD affect prices
and output, this holds with the fact that many factors derive the inflation rate and the level of
output in the short-run. These include changes in expectations, labour force, prices of other
factors of production, fiscal and/or monetary policy.
In moving from the short-run to the hypothetical long-run, the above mentioned factors and
its shock, on the ‘steady state’ of the economy are assumed to be balanced out. In this ‘steady
state’ situation, nothing is changing as the name suggests. The dynamic adjustment of the
short-run AD and AS curves yields an adjustment path, which exhibits an initial positive
relationship between inflation and growth, however, turns negative towards the latter part of
the adjustment path.
However, the structuralists argue that inflation is crucial for economic growth while
the monetarists posit that inflation is harmful to economic growth (Doguwa, 2012). To
date as opine by Ahmed and Mortaza (2005), several empirical studies confirm the
existence of either a positive or negative relationship between these two major
macroeconomic variables even as Mubarik (2005) argue that low and stable inflation
promotes economic growth and vice versa. In spite of all these view, there is no a specific
theory that explained or shows the relationship between private consumption expenditure,
economic growth and inflation simultaneously, this is why this study employed VAR
model to ascertain the relationship among inflation , private consumption expenditure and
economic growth in Nigeria.
3.2 Model Specification
The model specification adopted for this study is the Vector Autoregressive Model (VAR).
This is because structural approach to time series modelling uses economic theory to model
the relationship among the variables of interest. Unfortunately, economic theories are often
not rich enough to provide dynamic specifications that identify all of these relationships.
Furthermore, estimation and inference are complicated by the fact that endogenous variables
37
may appear on both the left and right sides of equations. These problems therefore lead to
alternative, non-structural approaches to modelling the relationship among several variables.
Taking a generalized specification of a Vector Autoregressive Model (VAR) as stated below:
𝑌𝑡 = 𝑐 + П2Yt−1 + П2Yt−2 + ⋯ + ПpYt−p + εt; t = 1, ... , T (3.1)
Where𝑌𝑡 = (𝑦1𝑡, 𝑦2𝑡 , 𝑦3𝑡, … , 𝑦𝑛𝑡 )′; n denotes the numbers of endogenous variables. p is the
lag length and Пi is an (n x n) matrix of coefficients and t is the time period.
The VAR representation of equation 3.1 can therefore be expressed as VECM as stated below
in equation 3.2 if there exist cointegration among the variables:
∆𝑌𝑡 = 𝛤1∆𝑌𝑡−1 + 𝛤2∆𝑌𝑡−2 + … + 𝛤𝑝−1∆𝑌𝑡−𝑝+1 + Ω𝑌𝑡−1 + +휀𝑡 t=1, …,T (3.2)
where: 𝛤𝑖 = −(1 − 𝛱1 − ⋯ − 𝛱𝑖), (𝑖 = 1, … , 𝑝 − 1) and 𝛺 = −(1 − 𝛱1 − ⋯ −
𝛱𝑝) 𝛺 = 𝜙𝛽1
Where ϕ represents the speed of adjustment to disequilibrium and β is a matrix of long-run
coefficients. Therefore, the term β1 Yt-1 embedded in equation (3.1) is equivalent to the error
correction term in a single-equation, except that β1 Yt-1 contains up to (n-1) vectors in a
multivariate model.
It should be noted that we can determine the long run and short run causality from the
VECM. If ϕ is statistically significant and different from zero, it implies the existence of long
run causality. The short run causality is determined following the VAR- Granger causality
framework. It is important to note the following about the application of VECM.
38
Assuming Yt is a vector of non-stationary I(1) variables, then all the terms in equation
(1) that involve ∆Yt-1 are I(0) while ΩYt-1 must also be stationary for et ~ I (0) to be
white noise
When all the variables in Yt are in fact stationary, which is not likely to happen in
reality, it implies that there is no problem of spurious regression and the appropriate
modelling strategy is to estimate the unrestricted VAR model in levels.
When there is no cointegration at all, it implies that there are no linear combinations
of Yt that are I (0) and consequently, Ω is an (n x n) matrix of zeros. In this case, the
appropriate model is a VAR model in first- differences involving no long-run
elements.
When there exists up to (n-1) cointegration relationships, it implies that ΩYt-1 ~ I (0)
and therefore, there are linear combinations of Yt that are I(0). In this instance, we can
have r cointegration vectors in which case r ≤ (n-1). Therefore, we can estimate both
unrestricted VAR and VECM to obtain long-run and short-run causal relationships
respectively in addition to other useful diagnostics.
For simplicity, we can specify a four system VECM model as follows:
∆𝑦1𝑡 = 𝑏1 + ∑ 𝜋𝑖11∆𝑦1𝑡−𝑖
𝑝𝑖=1 + ∑ 𝜋𝑖
11∆𝑦2𝑡−𝑗𝑝𝑗=1 + ∑ 𝜋𝑖
11∆𝑦3𝑡−𝑘𝑝𝑘=1 + ∑ 𝜋𝑖
11∆𝑦4𝑡−𝐿 +𝑝𝐿=1
𝜑1𝐸𝐶𝑀1𝑡−1 + 휀1𝑡 (3.3)
∆𝑦2𝑡 = 𝑏2 + ∑ 𝜋𝑗21∆𝑦1𝑡−𝑖
𝑝𝑖=1 + ∑ 𝜋𝑗
22∆𝑦2𝑡−𝑗𝑝𝑗=1 + ∑ 𝜋𝑘
23∆𝑦3𝑡−𝑘𝑝𝑘=1 + ∑ 𝜋𝑗
24∆𝑦4𝑡−𝐿 +𝑝𝐿=1
𝜑2𝐸𝐶𝑀2𝑡−1 + 휀2𝑡 (3.4)
∆𝑦3𝑡 = 𝑏3 + ∑ 𝜋𝑘31∆𝑦1𝑡−𝑖
𝑝𝑖=1 + ∑ 𝜋𝐾
32∆𝑦2𝑡−𝑗𝑝𝑗=1 + ∑ 𝜋𝐾
33∆𝑦3𝑡−𝑘𝑝𝑘=1 + ∑ 𝜋𝐾
34∆𝑦4𝑡−𝐿 +𝑝𝐿=1
𝜑3𝐸𝐶𝑀3𝑡−1 + 휀3𝑡 (3.5)
∆𝑦4𝑡 = 𝑏4 + ∑ 𝜋𝐿41∆𝑦1𝑡−𝑖
𝑝𝑖=1 + ∑ 𝜋𝐿
42∆𝑦2𝑡−𝑗𝑝𝑗=1 + ∑ 𝜋𝐿
43∆𝑦3𝑡−𝑘𝑝𝑘=1 + ∑ 𝜋𝐿
44∆𝑦4𝑡−𝐿 +𝑝𝐿=1
𝜑4𝐸𝐶𝑀4𝑡−1 + 휀4𝑡 (3.6)
39
Where:
Δ = the difference factor
b = Constant term
φ = Speed or rate of adjustment
𝜋 = Parameter coefficient
p = lag length for the VECM
휀 = white noise disturbance error term
3.3 Estimation Technique
The investigative approach adopted by this study consists of four major steps. First the
Augmented Dickey-Fuller (ADF) and Phillips-Perron statistics were used to test the
stationarity or non-stationarity of the variables and their order of integration. Second; the
Johansen cointegration technique is used to test for long run relationship between the
variables. Thirdly, if the variables are cointegrated, the VECM equation estimated the short
and long run relationship whereas the VEC Granger-Causality tests estimated the direction of
causality in each equation. Finally various residual tests would be conducted on the residuals
of the models to ensure compliance with linear model estimations.
3.3.1 Data, Sources and Software
The dataset for this study is drawn from the Central Bank of Nigeria (CBN) Statistical
Bulletin 2012 edition and the World Bank Development Index Databank for 2013 for the
period 1981 to 2012.The variables of interest in the study are: inflation rate (using consumer
price index as a proxy), Gross Domestic Product Growth Rate, private consumption
expenditure, and Real Interest Rate.
The Microsoft excel software for windows will be used for data entering and E-Views will be
used for the estimation.
40
3.3.2 Stationarity Test
Unit Root are routine tests on time series data to ascertain if individual series are stationary
which aid the application of the appropriate estimation technique. In practice, the choice of
the most appropriate unit root test is difficult. Enders (1995) suggested that a safe choice is to
use both types of unit root tests —the Augmented Dickey– Fuller (ADF) (1981) test and the
Phillips–Perron (PP) (1988) test. If they reinforce each other, then we can have confidence in
the results. Therefore, to test for series stationarity, the two widely used methods of unit root
tests—the ADF and the Phillips–Perron (PP) test were conducted. The unit root tests were
performed at level and at first difference for both with the intercept, and with the intercept
and trend term. The test is based on three forms of regression equations;
When series is without constant and trend we have the following:
∆𝑌𝑡 = 𝜕𝑌𝑡−1 + 𝑢𝑡 (3.7)
When series is with constant we have:
∆𝑌𝑡 = 𝛼 + 𝜕𝑌𝑡−1 + 𝑢𝑡 (3.8)
When series is with constant and trend we then have the following:
∆𝑌𝑡 = 𝛼 + 𝛽𝑡 + 𝜕𝑌𝑡−1 + 𝑢𝑡 (3.9)
The hypothesis is:
H0: δ=0 (unit root)
H1: δ≠0
To test the hypothesis, the regression equation are estimated using ordinary least square and
examined using the Augmented Dicky-Fuller(ADF) tau statistic t* (critical value) that δ is
equal to zero.
Decision rule;
If t*> ADF/PP do not reject null hypothesis – series is non-stationary
If t*< ADF/PP reject null hypothesis – series is stationary
41
The essence of this test is to avoid spurious regression (statistically significant relationship
when there is none) when non stationary series are used in a regression model. Gujarati
(2009), explain spurious regression as follows; “in regressing a time series variable(s), one
often obtains a very high R2 (in excess of 0.9) even though there is no meaningful
relationship between the two variables. Sometimes we expect no relationship between two
variables, yet a regression of one on the other variable often shows a significant relationship.
This situation exemplifies the problem of spurious, or nonsense, regression”. However, a
non-stationary series can be made stationary by taking the lag of the series (trend stationary
process) or taking the difference of the series (difference stationary process).
3.3.3 Cointegration Test
Due to the properties of most time series, it is customary to perform unit root test on the
series in the VAR model. If the series are stationary, then the results obtained from the VAR
model are valid. However, if the series are non-stationary, then it becomes imperative to
carry out cointegration test to verify whether the series in the VAR model are cointegrated or
not. The prominent cointegration test for VAR model is the Johansen System Cointegration
test. If the Johansen Cointegration test indicates the existence of cointegration in the model,
then the VAR model gives the long run causality which is analogous to the long run
relationship in a single-equation model. Similarly, the short run dynamics of the VAR model
are captured with the Vector Error Correction Model which is similar to the short run
adjustment.
3.3.4 The Vector Error Correction Model
A VEC model is a restricted VAR designed for use with non-stationary series that are
known to be cointegrated. The VEC has cointegration relations built into the specification so
that it restricts the long-run behaviour of the endogenous variables to converge to their
cointegrating relationships while allowing for short-run adjustment dynamics. The
cointegration term is known as the error correction term since the deviation from long-run
equilibrium is corrected gradually through a series of partial short-run adjustments.
42
Thus, the study VECM can be represented as shown below:
𝐺𝐷𝑃𝑅𝑡 = 𝛼1 + ∑ 𝛿𝑖𝐺𝐷𝑃𝑅𝑝=4
𝑖=1 𝐺𝐷𝑃𝑅𝑡−𝑖 + ∑ 𝛽𝑗𝐺𝐷𝑃𝑅𝑙𝑛𝐶𝑃𝐼𝑡−𝑗
𝑝=4𝑗=1 + ∑ 𝛾𝑘
𝐺𝐷𝑃𝑅𝑙𝑛𝑃𝐶𝑋𝑡−𝐾𝑝=4𝐾=1 +
∑ 𝛽𝐿𝐺𝐷𝑃𝑅𝑙𝑛𝐼𝑁𝑇𝑅𝑡−𝐿
𝑝=4𝐿=1 + 𝜑1𝐸𝐶𝑀1𝑡−1 + 휀1𝑡 (3.10)
𝑙𝑛𝐶𝑃𝐼𝑡 = 𝛼2 + ∑ 𝛿𝑖𝐶𝑃𝐼𝑝=4
𝑖=1 𝑙𝑛𝐶𝑃𝐼𝑡−𝑖 + ∑ 𝛽𝑗𝐶𝑃𝐼𝐺𝐷𝑃𝑅𝑡−𝑗
𝑝=4𝑗=1 + ∑ 𝛾𝑘
𝐶𝑃𝐼𝑙𝑛𝑃𝐶𝑋𝑡−𝐾𝑝=4𝐾=1 +
∑ 𝛽𝐿𝐶𝑃𝐼𝑙𝑛𝐼𝑁𝑇𝑅𝑡−𝐿
𝑝=4𝐿=1 + 𝜑2𝐸𝐶𝑀2𝑡−1 + 휀2𝑡 (3.11)
𝑙𝑛𝑃𝐶𝑋𝑡 = 𝛼3 + ∑ 𝛿𝑖𝑃𝐶𝑋𝑝=4
𝑖=1 𝑙𝑛𝑃𝐶𝑋𝑡−𝑖 + ∑ 𝛽𝑗𝑃𝐶𝑋𝑙𝑛𝐶𝑃𝐼𝑡−𝑗
𝑝=4𝑗=1 + ∑ 𝛾𝑘
𝑃𝐶𝑋𝐺𝐷𝑃𝑅𝑡−𝐾𝑝=4𝐾=1 +
∑ 𝛽𝐿𝑃𝐶𝑋𝑙𝑛𝐼𝑁𝑇𝑅𝑡−𝐿
𝑝=4𝐿=1 + 𝜑3𝐸𝐶𝑀3𝑡−1 + 휀3𝑡 (3.12)
𝑙𝑛𝐼𝑁𝑇𝑅𝑡 = 𝛼4 + ∑ 𝛿𝑖𝐼𝑁𝑇𝑅𝑝=4
𝑖=1 𝑙𝑛𝐼𝑁𝑇𝑅𝑡−𝑖 + ∑ 𝛽𝑗𝐼𝑁𝑇𝑅𝑙𝑛𝐶𝑃𝐼𝑡−𝑗
𝑝=4𝑗=1 +
∑ 𝛾𝑘𝐼𝑁𝑇𝑅𝑙𝑛𝑃𝐶𝑋𝑡−𝐾
𝑝=4𝐾=1 + ∑ 𝛽𝐿
𝐼𝑁𝑇𝑅𝐺𝐷𝑃𝑅𝑡−𝐿𝑝=4𝐿=1 + 𝜑4𝐸𝐶𝑀4𝑡−1 + 휀4𝑡
(3.13)
Where:
GDPR = Gross Domestic Product Growth Rate
CPI = Consumer Price Index
PCX = Private Consumption Expenditure
INTR = Interest Rate
α = Constant term
φ = Speed or rate of adjustment
43
𝛿, 𝛽 and 𝛾 = Parameter coefficients
p = lag length for the VECM
휀 = white noise disturbance error term
ln= Natural logarithm
3.3.5 VEC Granger Causality
A test of causality is whether the lags of one variable enter into the equation for another
variable (Enders, 1995). Considering a case of two series: {Xt}and{Yt}. If better predictions
of {Yt} can be obtained by adding to lagged values of {Yt}, the current and lagged values of
another variable {Xt}; then {Xt} is said to Granger cause {Yt}. Stated differently, { Xt} is said
to precede temporally {Yt} in that changes in {Yt} follow the changes in {Xt} . Thus, if {Xt}
does not improve the forecasting performance of {Yt}, then {Xt} does not Granger cause {Yt}.
When making choice of lag length to use; in general, it is better to use more rather than fewer
lags, since the theory is couched in terms of the relevance of all past information. Selecting a
lag length l that corresponds to reasonable beliefs, about the longest time over which one of
the variables could help predict the other for all possible pairs of (x, y) series in the group.
𝑦𝑡 =∝0+∝1 𝑦𝑡−1 + ⋯ +∝𝑙 𝑦𝑡−𝑙 + 𝛽1𝑥𝑡−1 + ⋯ + 𝛽𝑙𝑥𝑡−𝑙 + 휀𝑡 (3.14)
𝑥𝑡 =∝0+∝1 𝑥𝑡−1 + ⋯ +∝𝑙 𝑥𝑡−𝑙 + 𝛽1𝑦𝑡−1 + ⋯ + 𝛽𝑙𝑦𝑡−𝑙 + 𝜇𝑡 (3.15)
The reported F-statistics are the wald statistics for the joint hypothesis for each equation.
Where: 𝛽1 = 𝛽2 = ⋯ = 𝛽𝑙 = 0
The null hypothesis is that x does not Granger-cause y in equation 14 and that y does not
Granger-cause x in equation 15.
All of the possible permutations of the two variables are:
• Unidirectional Granger causality from variables {Xt} to variables {Yt},
• Unidirectional Granger causality from variables {Yt} to variables {Xt},
• Bi-directional casualty,
• No causality
44
In all possible cases, a common assumption is that the data are stationary. Stationarity in a
Random Process implies that its statistical characteristics do not change with time. If not the
Granger causality on non-stationary time data can lead to false casual relation (Cheng, 1996).
45
CHAPTER FOUR
RESULT PRESENTATION AND ANALYSES
There are several tests such as unit root test (ADF and PP), Johansen co-integration test, VEC
serial correlation test, Residual auto correlation test, VEC residual normality test were
performed to examine the data characteristic. This was done to avoid spurious results and
make sure that the estimation technique of VECM and VEC Granger causality chosen is
appropriate for the study. The result of the study is presented thus: unit root, Johansen co-
integration, and finally VECM and VEC Granger causality result.
4.1 Unit Root Test Results
In this study, the Augmented Dickey-Fuller (ADF) and Philip Perron (PP) tests were
employed to test the time series properties of the variables in the model. The null hypothesis
is that the variables under investigation have a unit root against the alternative that it does
not. The unit root test results of the variables under study are displayed in Table 4.1 below.
Table 4.1: Unit Root Test Results
Variables ADF at Levels
ADF at (first
difference)
PP level PP at (first
difference)
RGDP (-4.968177)
-3.661661*
-2.960411**
(-8.378555)
-3.670170*
-2.963972**
(-5.067107)
-3.661661*
-2.960411**
(-10.22660)
-3.670170*
-2.963972**
PCX (-0.054423)
-3.670170*
-2.963972**
(-7.438999)
-3.670170*
-2.963972**
(-0.480588)
-3.661661*
-2.960411**
(-7.438999)
-3.670170*
-2.963972**
CPI (-0.792061)
-3.661661*
-2.960411**
(-5.877528)
-3.670170*
-2.963972**
(-0.749594)
-3.661661*
-2.960411**
(-5.959628)
-3.670170*
-2.963972**
46
INTER (-2.890121)
-3.661661*
-2.960411**
(-5.734927)
-3.679322*
-2.967767**
(-2.836305)
-3.661661*
-2.960411**
(-7.002300)
-3.670170*
-2.963972**
Note:
*denotes critical value at 1% confidence levels
** denotes critical value at 5% confidence levels
Values in ( ) represent ADF and PP test statistics
Table 4.1 presents the results of ADF and PP unit root tests. The ADF test indicates that all
the data series with the exception of Real Gross Domestic Product (RGDP) are non-stationary
at levels. Thus, the null hypothesis could not be rejected. Statistically it could be observed
from Table 4.1 that the ADF test statistic at levels for PCX, CPI and INTR was smaller (in
absolute terms) than the critical values at both 1% and 5% confidence levels (see second
column). After first differencing, all the data series become stationary. This is also shown by
the higher ADF test statistic as compared with the critical values at both 1% and 5%
confidence levels (see third column).the third column in the table shows the results of Philip
Perron unit root tests. The PP test indicates that all data series with the exception of RGDP
are non-stationary at levels. Thus, the null hypothesis could not be rejected. But after first
differencing, all that data series were found to be stationary. This is also shown by the higher
PP test statistic as compared with the critical values at both 1% and 5% confidence level.
4.2 Johansen Cointegration Test Result
Due to the properties of most time series, it is customary to perform unit root test on the
series in the VAR model. If the series are stationary, then the results obtained from the VAR
model are valid. However, if the series are non-stationary, then it becomes imperative to
carry out cointegration test to verify whether the series in the VAR model are cointegrated or
not. The prominent cointegration test for VAR model is the Johansen System Cointegration
test. If the Johansen Cointegration test indicates the existence of cointegration in the model,
then the VAR model gives the long run causality which is analogous to the long run
relationship in a single-equation model. Similarly, the short run dynamics of the VAR model
47
are captured with the Vector Error Correction Model which is similar to the short run
adjustment.
The Johansen co-integration test utilizes two statistics test namely: the trance test and the
maximal Eigen value test. However both the trace test and maximal Eigen value test
indicated one co-integration equation. The result is presented below in Table 4.2A and Table
4.2B.
Table 4.2A Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.603046 54.11515 47.85613 0.0115
At most 1 0.419295 26.39709 29.79707 0.1173
At most 2 0.272722 10.09170 15.49471 0.2737
At most 3 0.017783 0.538291 3.841466 0.4631
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Table 4.2.1B Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.603046 27.71806 27.58434 0.0481
At most 1 0.419295 16.30539 21.13162 0.2075
At most 2 0.272722 9.553409 14.26460 0.2429
At most 3 0.017783 0.538291 3.841466 0.4631
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
GDPR PCX CPI INTR
0.128634 3.143440 -0.022536 -0.285599
48
-0.233833 -12.63250 0.037646 -0.097046
-0.238227 9.228840 -0.017900 0.091095
-0.028061 -4.788034 -0.000916 0.073434
Tables 4.2A and 4.2B Show the results of the Co-integration tests. Both the Trace test and
Rank Test (Maximum Eigenvalue) indicate that there exists at least one co-integrating
equation among the data series. This test suggests two major contentions. First, the
selected variables move along together in the long run and short terms deviations will be
corrected towards equilibrium. Secondly, co-integration literally indicates causality in at least
one direction. This implies that since there exists one co-integration equation in the model,
the use of VECM estimation is appropriate for the study because it shows that there is long
run relationship between the variables under study.
4.3 Lag Length Selection Criteria
There are many criterion of the lag length selection among which are Akaike criterion,
Schewartz-criterion information FPE, HQ and etc. Thus, the optimum lag length is 4. The
VAR lag order selection criteria are displayed in Table 4.3 below.
Table 4.3 Lag Length Selection Criteria Result
Table 4.3 lag length selection criteria.
Lag LogL LR FPE AIC SC HQ
0 -266.6467 NA 2923.455 19.33191 19.52222 19.39009
1 -221.9232 73.47426* 381.5361* 17.28023 18.23181* 17.57114*
2 -210.0770 16.07709 555.5204 17.57693 19.28976 18.10056
3 -194.9512 16.20615 731.9168 17.63937 20.11347 18.39573
4 -170.7002 19.05437 649.6492 17.05001* 20.28537 18.03909
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
49
The asterisk (*) indicates lag order selected by the criterion. There are many criterion for lag
length selection, this include: Final Prediction Error (FPE), sequential modified LR test,
Akaike information criterion (AIC), Schwarz information criterion (SC) and Hannan-Quinn
information criterion (HQ). Each of the test uses 5 percent level of significant. From the
Table 4.3 above, we can observes that there is asterisk (*) at lag 1 under LR, FPE, SC, and
HQ while the only asterisk (*) at lag 4 is under AIC this is so because in selection of lag
length, AIC is the best criterion. However the selection is best on the lowest value of AIC.
This implies that lag 4 has the lowest value of AIC of 17.05001; therefore lag 4 is selected as
the best lag for the study.
4.4 Vecm Estimated Result
A VEC model is a restricted VAR designed for use with non-stationary series that are known
to be cointegrated. The VEC has cointegration relations built into the specification so that it
restricts the long-run behaviour of the endogenous variables to converge to their cointegrating
relationships while allowing for short-run adjustment dynamics. The cointegration term is
known as the error correction term since the deviation from long-run equilibrium is corrected
gradually through a series of partial short-run adjustments. Table 4.4 below shows the
estimated result of VECM.
Table 4.4: Estimated VECM Result.
Standard errors in ( ) & t-statistics in [ ]: from the estimated result below, the values inside
this bracket () indicate the standard errors, while the values inside this bracket [ ] indicate the
t-statistics.
EXPLANAATORY
VARIABLES
DEPENDENTS VARIALES
D(GDPR) D(PCX) D(CPI) D(INTR)
D(GDPR(-1)) -0.253472 0.018871 -3.633601 -0.390032
(0.45056) (0.00437) (2.65896) (0.48054)
[-0.56258] [ 4.31560] [-1.36655] [-0.81166]
D(GDPR(-2)) -0.324878 0.014310 -7.056401 -0.440524
50
(0.61825) (0.00600) (3.64859) (0.65939)
[-0.52548] [ 2.38482] [-1.93401] [-0.66808]
D(GDPR(-3)) 0.002837 0.013171 -2.892361 -0.347755
(0.45211) (0.00439) (2.66812) (0.48219)
[ 0.00628] [ 3.00173] [-1.08405] [-0.72119]
D(GDPR(-4)) 0.068424 0.006315 -4.308833 -0.157037
(0.36098) (0.00350) (2.13035) (0.38501)
[ 0.18955] [ 1.80247] [-2.02260] [-0.40788]
D(PCX(-1)) -17.35657 -0.187003 57.95023 6.295269
(15.6272) (0.15167) (92.2237) (16.6671)
[-1.11067] [-1.23299] [ 0.62837] [ 0.37771]
D(PCX(-2)) -3.736677 0.393703 89.60632 3.945053
(14.6218) (0.14191) (86.2905) (15.5948)
[-0.25556] [ 2.77432] [ 1.03843] [ 0.25297]
D(PCX(-3)) 3.882527 -0.023093 -260.2161 -1.685581
(20.0329) (0.19443) (118.224) (21.3659)
[ 0.19381] [-0.11878] [-2.20104] [-0.07889]
D(PCX(-4)) -19.37397 -0.379270 256.1846 -12.56605
(20.3171) (0.19718) (119.901) (21.6691)
[-0.95358] [-1.92343] [ 2.13663] [-0.57991]
D(CPI(-1)) -0.018697 -0.005490 1.729187 0.048150
(0.13926) (0.00135) (0.82182) (0.14852)
[-0.13426] [-4.06232] [ 2.10410] [ 0.32419]
D(CPI(-2)) -0.006486 -0.004847 0.671306 0.076530
(0.13368) (0.00130) (0.78891) (0.14258)
[-0.04852] [-3.73630] [ 0.85093] [ 0.53677]
D(CPI(-3)) 0.171098 -0.012024 3.223772 -0.045006
(0.33899) (0.00329) (2.00056) (0.36155)
51
[ 0.50473] [-3.65479] [ 1.61143] [-0.12448]
D(CPI(-4)) -0.277787 -0.003834 1.167559 0.289961
(0.30313) (0.00294) (1.78891) (0.32330)
[-0.91640] [-1.30337] [ 0.65266] [ 0.89688]
D(INTR(-1)) -0.082329 -0.037279 8.231703 0.210469
(0.88245) (0.00856) (5.20777) (0.94117)
[-0.09330] [-4.35272] [ 1.58066] [ 0.22362]
D(INTR(-2)) -0.288898 -0.031604 9.507689 0.152339
(0.91145) (0.00885) (5.37890) (0.97210)
[-0.31697] [-3.57274] [ 1.76759] [ 0.15671]
D(INTR(-3)) -0.038910 -0.016768 6.493827 0.386136
(0.73731) (0.00716) (4.35121) (0.78637)
[-0.05277] [-2.34325] [ 1.49242] [ 0.49104]
D(INTR(-4)) -0.092702 -0.007299 2.760449 0.242300
(0.44490) (0.00432) (2.62555) (0.47450)
[-0.20837] [-1.69046] [ 1.05138] [ 0.51064]
ECM -0.060879 -0.007210 1.755086 0.175822
(0.16011) (0.00155) (0.94491) (0.17077)
[-0.38023] [-4.63947] [ 1.85742] [ 1.02960]
C 1.229263 0.155466 -30.62242 -1.620130
(4.15066) (0.04028) (24.4951) (4.42686)
[ 0.29616] [ 3.85929] [-1.25015] [-0.36598]
R-squared 0.621347 0.906322 0.652373 0.628536
Adj. R-squared -0.093887 0.729374 -0.004256 -0.073117
F-statistic 0.868733 5.121982 0.993518 0.895793
Akaike AIC 5.759628 -3.510530 9.310040 5.888475
Schwarz SC 6.623519 -2.646639 10.17393 6.752366
Long Run Cointegrating Equation Estimate on Eqn 3.2
C PCX(-1) CPI(-1) INTR(-1)
52
GDPR(-1)
1.000000 -664.5464 144.8843 -0.694471 -5.474645
(22.9476) (0.07879) (0.81238)
[ 6.31370] [-8.81441] [-6.73904]
Source: Computed using E-views
The VECM result above shows the short run as well as long run relationship existing between
the variables. It is obvious from the result that output for equation 2 happens to be most
significant (This output is contained in the 2nd column of table 4.4). This is judging base on
the corresponding T values for each of the explanatory variables in the model. A rule of
thumb absolute value of 1.63- 1.95, 1.96-2.35 and 2.36 and above were used for 1%, 5% and
10% significance levels respectively. The result also shows the single long run relationship in
the systems of equation as expressed in table 4.4 above; which was also confirmed by the
single cointegrating relationship being reported in table 4.2A and 4.2B respectively.
The ECM result for equation 3.2 happens to be the only one which is rightly signed and as
well significant; judging from its T-statistic. The ECM result shows the rate at which the
system corrects itself back to equilibrium in the case of any distortion in the system. In order
words, it shows how much of the distortion or shock, from the previous period, that is being
corrected for in the present period. The ECM for equations 3.1and 3.2 is -0.06 and
-0.01 respectively; which means that in the case of disequilibrium or distortion from the
previous period, 6% of this distortion or shock would be corrected for annually in equation
3.1. This process would continue until equilibrium is restored. Thus, the ECM value therefore
indicates that it would take the economy; sixteen years and seven months for equilibrium to
be restored in a case of distortion in the system for equation 1. While equation 3.2 ECM
value indicate it would take the economy; one-hundred years for equilibrium to be restored in
the case of distortion in the system.
The short run constant ‘C’ has a positive value of 0.155466 which is in line with Keynes
theory of consumption. Keynes postulated that the autonomous component of the
consumption function is always positive and above the zero level. This is because every
consumer must always consume irrespective of your level of income to meet basic needs
which are: food, clothing and shelter. Thus, at zero levels of the repressors’, PCX will be at
0.16 approximately.
53
The R2 for equation 3.2 which is known as the correlation coefficient which explains the
general fitness of the model, with a value of 0.906322; implies that the model is 90% linear.
While the adjusted R2 explains the extent to which the explanatory variables in equation 3.2;
that is, PCX accounted for the variation in the dependent variables such as GDPR, PCX,
CPI,and INTR.Thus;Adjusted- R2 of 0.729374 entails that 72% of the variations in the
dependent variable were accounted for by changes in PCX. The F-statistic value for equation
3.2 which is 5.121982 can be said to be statistically significant. The value shows that the
explanatory variables taken jointly, account for variations in the dependent variable (PCX)
The estimated long run relationship for equation 3.2 on table 4.4 shows that CPI and INTR
both impact negatively on economic performance. The result show that a 5.5% fall in INTR
would yield a 1% rise in GDPR in the long run. The result is true because producers favour
lower interest rate to be able to borrow fund for investment purposes; which promote
productivity in the economy, and leads to economic growth. While a 0.69% fall in CPI would
induce a 1% rise in GDPR. The result is also true to economic behaviour since a fall in
inflation raises the purchasing power of households and in turn leads to rise in aggregate
demand, thereby encouraging productivity and in turn economic growth. However, PCX
show a positive long run impact on economic performance. From the result, a 1.45% increase
in PCX would induce a 1% rise in GDPR. Which is also in line with economic theory, as
increase in aggregate private consumption would in turn lead to increase in firms’
productivity and in turn lead to economic growth.
4.5: Vec Granger Causality Result
The VEC granger causality result in Table 4.6 below shows the direction of
causality between the variables. The significant of the result is judged based on
the corresponding probability values; either when the variables causality were
observed individually or jointly. These results are presented in Table 4.6 below.
Table 4.5 Vec Granger Causality Result
VEC Granger Causality/Block Exogeneity Wald Tests
Dependent variable: D(GDPR)
Regressors Chi-sq Df P.value
D(PCX) 1.615237 4 0.8061
D(CPI) 1.920879 4 0.7503
D(INTR) 0.716293 4 0.9493
All 3.339164 12 0.9926
54
Dependent variable: D(PCX)
Regressors Chi-sq Df P.value
D(GDPR) 26.7011 3 4 0.0000
D(CPI) 20.51260 4 0.0004
D(INTR) 31.70473 4 0.0000
All 49.58548 12 0.0000
Dependent variable: D(CPI)
Regressors Chi-sq Df P.value
D(GDPR) 5.357727 4 0.2525
D(PCX) 12.92769 4 0.0116
D(INTR) 3.526606 4 0.4738
All 14.34030 12 0.2795
Dependent variable: D(INTR)
Regressors Chi-sq Df P.value
D(GDPR) 0.687198 4 0.9529
D(PCX) 0.782321 4 0.9408
D(CPI) 1.038885 4 0.9038
All 3.205966 12 0.9939
Source: Computed Using E-views
From the Table 4.5 above, it is obvious that causality flowing from the regressor to the
dependent variables (GDPR and INTR) in the first and fourth sections of the table
respectively were not significant. Either when observed individually or jointly. The result
when CPI was made dependent variable showed that GDPR and INTR do not affect CPI
individually. Put differently, real gross domestic product and real interest rate do not impact
individually on consumer price index. On the contrary, PCX has a positive and significant
impact on CPI. But when the causation of the explanatory variables was observed jointly on
CPI, the result showed a non-significant level of causation.
However, in the second section of the table, it can be deduced that GDPR, CPI, and INTR all
cause private consumption expenditure in Nigeria individually as well as jointly. The
probability values show the significance of the causation at 5% level of significance. Thus,
we can say that improvement in the performance of the economy is more of a function of
improvement in the standard of living of the citizens.
4.6 Impulse Response Analysis
The impulse response function is a shock to a VAR system. It identifies the responsiveness of
the dependent (endogenous variable) in the VAR when a shock is put to the error term. We
can alternatively say the impulse response function, measures how other variables in the
model respond; when one standard deviation positive shock is being put into a variable. In
55
this study, the behaviour of the variables was being examined when a shock is being applied
to the system within a ten year period.
The first four boxes summarize the response of GDPR to shocks in the regressors for a ten
year period. It can be observed that economic performance would respond positively to any
shock on economic performance, PCX response positively for eight years to this shock before
responds negatively for remaining two years all at 5% level of significant. This is so because
an increase in private consumption expenditure would result in increase in economic
performance or growth. However, when a shock occurs in total value of CPI, economic
performance responds positively for two and a half years before responding negatively to this
shock for the remaining period. When a shock occurs in total value of INTR, in this case, the
performance of the economy responds negatively up to a nine year period; before later
responding positively to the shock for the next one year period. These are so because an
increase in interest rate would discourage investors from borrowing of fund to invest thereby
affects economics performance.
The second row of boxes gives a picture of the behaviour of PCX, when a shock is being
applied to the regressors within a ten year period. We can also observe that private
consumption expenditure responds positively to shock in economic performance, for almost
the ten year period. Similarly PCX responded to shocks in PCX positively throughout the ten
years. However PCX responds negatively to shock from CPI for nine years, this means that
an increase in inflation, private consumption expenditure would decline. If there is any shock
from real interest rate, PCX responds positively throughout the period of ten years. Note that
all these responds is base on 5 percent level of significant.
The third row of boxes shows the response of CPI to shocks in the regressors also within a
ten year period. Unlike the first two analysed boxes; CPI respond negatively for eight years
period, to shocks in economic performance, CPI responds positively to shock on PCX almost
throughout the ten year period. While its response to itself show a positive effect for seven
and half years. In fact the response of CPI to a shock in INTR shows negative effect
56
-20
-10
0
10
20
1 2 3 4 5 6 7 8 9 10
Response of GDPR to GDPR
-20
-10
0
10
20
1 2 3 4 5 6 7 8 9 10
Response of GDPR to PCX
-20
-10
0
10
20
1 2 3 4 5 6 7 8 9 10
Response of GDPR to CPI
-20
-10
0
10
20
1 2 3 4 5 6 7 8 9 10
Response of GDPR to INTR
-.8
-.4
.0
.4
.8
1 2 3 4 5 6 7 8 9 10
Response of PCX to GDPR
-.8
-.4
.0
.4
.8
1 2 3 4 5 6 7 8 9 10
Response of PCX to PCX
-.8
-.4
.0
.4
.8
1 2 3 4 5 6 7 8 9 10
Response of PCX to CPI
-.8
-.4
.0
.4
.8
1 2 3 4 5 6 7 8 9 10
Response of PCX to INTR
-200
-100
0
100
200
1 2 3 4 5 6 7 8 9 10
Response of CPI to GDPR
-200
-100
0
100
200
1 2 3 4 5 6 7 8 9 10
Response of CPI to PCX
-200
-100
0
100
200
1 2 3 4 5 6 7 8 9 10
Response of CPI to CPI
-200
-100
0
100
200
1 2 3 4 5 6 7 8 9 10
Response of CPI to INTR
-10
-5
0
5
10
1 2 3 4 5 6 7 8 9 10
Response of INTR to GDPR
-10
-5
0
5
10
1 2 3 4 5 6 7 8 9 10
Response of INTR to PCX
-10
-5
0
5
10
1 2 3 4 5 6 7 8 9 10
Response of INTR to CPI
-10
-5
0
5
10
1 2 3 4 5 6 7 8 9 10
Response of INTR to INTR
Response to Cholesky One S.D. Innov ations
throughout the ten year period. All these response are also based on 5 percent level of
significance.
Finally, the fourth row of boxes shows the response of INTR to shock in the regressors within
a period of ten years. INTR responds positively to economic performance throughout the
period of ten years. However INTR responds to PCX positively for two years to this shock
before responding negatively for eight years all at 5% level of significance. Also INTR
respond negatively to CPI for eight years before responding positively for two years, its
response to itself is positive throughout the ten year period.
Table 4.6 Impluse Response
57
Table 4.7 RESIDUAL AUTO CORRELATION TEST
VEC Residual Portmanteau Tests for Autocorrelations
Null Hypothesis: no residual autocorrelations up to lag h
Date: 01/02/15 Time: 16:09
Sample: 1981 2012
Included observations: 27
Lags Q-Stat Prob. Adj Q-Stat Prob. Df
1 23.89996 NA* 24.81919 NA* NA*
2 43.29449 NA* 45.76528 NA* NA*
3 52.47527 NA* 56.09366 NA* NA*
4 65.62937 NA* 71.53543 NA* NA*
5 69.54526 0.0000 76.34129 0.0000 28
6 80.48298 0.0007 90.40407 0.0000 44
7 98.55145 0.0013 114.7965 0.0000 60
8 108.9134 0.0079 129.5214 0.0001 76
9 116.0558 0.0458 140.2350 0.0009 92
10 129.4747 0.0780 161.5473 0.0007 108
11 137.8146 0.1871 175.6210 0.0016 124
12 145.4608 0.3587 189.3842 0.0035 140
*The test is valid only for lags larger than the VAR lag order.
df is degrees of freedom for (approximate) chi-square distribution
Source: Computed Using E-views.
Table 4.7 gives the result of the autocorrelation test conducted on the residuals .The result of
test show that from lag one to four indicate that there is no presence of autocorrelation in the
model therefore we can accept the null hypothesis which says no residual autocorrelation up
to lag h.
58
Table 4.8 Residual Serial Correlation Test
VEC Residual Serial Correlation LM Tests
Null Hypothesis: no serial correlation at lag
order h
Date: 01/02/15 Time: 16:10
Sample: 1981 2012
Included observations: 27
Lags LM-Stat Prob
1 30.77070 0.0144
2 20.39142 0.2031
3 20.75361 0.1882
4 20.28954 0.2075
5 13.40179 0.6432
6 9.822102 0.8758
7 22.78102 0.1197
8 17.88928 0.3304
9 20.41113 0.2023
10 15.08092 0.5187
11 11.82288 0.7561
12 11.80064 0.7576
Probs from chi-square with 16 df.
Source: Computed Using E-views
Table 4.9 gives the result of the serial correlation test conducted on the residuals. Also
judging from the probability values, it is obviously clear that none of the values is significant
at the 0.05 level of significance. Thus, the null hypothesis of no serial correlation at lag order
h cannot also be rejected. This means the residuals of the study are free from serial or auto
correlation.
59
Table 4.9 VEC RESIDUAL NORMALITY TEST
VEC Residual Normality Tests
Orthogonalization: Cholesky (Lutkepohl)
Null Hypothesis: residuals are multivariate normal
Date: 01/02/15 Time: 16:11
Sample: 1981 2012
Included observations: 27
ponent Skewness Chi-sq Df Prob.
1 0.110999 0.055444 1 0.8138
2 0.121207 0.066110 1 0.7971
3 -0.127360 0.072993 1 0.7870
4 0.620333 1.731658 1 0.1882
Joint 1.926205 4 0.7493
Component Kurtosis Chi-sq Df Prob.
1 2.485575 0.297712 1 0.5853
2 2.476180 0.308685 1 0.5785
3 3.669328 0.504000 1 0.4777
4 3.899762 0.910769 1 0.3399
Joint 2.021166 4 0.7319
Component Jarque-Bera Df Prob.
1 0.353156 2 0.8381
2 0.374795 2 0.8291
3 0.576993 2 0.7494
4 2.642427 2 0.2668
Joint 3.947371 8 0.8618
Source: Computed Using E-views
The Jarque-Bera normality test in table 4.10 above shows the summary of the residual test
conducted on the residuals. The result shows that the residuals of the various models used in
this study are normally distributed. This is judging from the probability values, of which all
are greater than the 0.05 or 5% level of significance. Thus, the null hypothesis of residuals
are multivariate normal cannot be rejected.
60
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATION
This study examined the impact of inflation on private consumption expenditure and
economic growth in Nigeria for the period 1981to 2012 using modern econometrics
technique such as unit root, Johansson co-integration, vector error co-integration granger
causality test and VECM approach.
5.1 Summary
Based on the finding of this study, the specific objectives of the study where adequately
achieved.
The first specific objective was to examine the impact of inflation on private consumption
expenditure. The VEC granger causality result shows that inflation positively granger causes
private consumption expenditure for the period of the study.
The second specific objective which is to examine the impact of inflation on economic
growth was also achieved. Judging from the VEC granger causality result, there happens to
be no causality flowing from inflation to economic growth, neither is there causality from
economic growth to inflation. However, the long-run model result shows a negative impact of
inflation on economic growth for the study period. This empirical result is in line with the
results obtained by Taiwo (2011) and Inyiama (2013) and the result also agreed with the
Traditional Keynesian theory of AD and AS.
5.2 Conclusion
Based on the finding of the study, the following conclusion would be deduced from the study.
The result of the first objective indicates that inflation impact positively on PCX. This is true
because during inflationary period, money losses its value, as a result more money are going
after fewer goods. This implies that during inflationary period, people spend more money on
goods and services. For example goods that worth ten thousand naira when there is no
61
inflation in the economy would become twenty thousand naira during inflationary period.
This implies that inflation causes increase in private consumption expenditure in Nigeria for
the period of study.
The negative impact of inflation on economic growth in the long run shows that when the
problem of inflation persist in the system, small and medium scale enterprises may be
affected in terms of their operational cost. This may lead to closure of some businesses and
also reduce profits to both small and big enterprises in the country, which is not good for the
growth of the economy. Also inflation discourages both new and old investors from investing
in such economy, since money losses its value; cost of production becomes very high which
will affects economic growth.
5.3 Recommendation
Base on the finding of this work, the study therefore put forward the following
recommendations: The policy introduced by central bank of Nigeria (CBN) on the battle
to defend the naira against the dollar persists as the CBN wages on Nigeria banks have
now lowered the ATM cash withdrawals for both domestic and foreign transactions for
cards denominated in naira and foreign currency. The new cash limit on daily ATM
withdrawal is now 60000 NGN or 300 USD, down from 150000NGN per day. This
policy would help to reduce the volume of money in circulation which will reduce or
control inflationary rate in the economy.
However, the policy of CBN, in a bid to stop the naira devaluation and currency
speculation, instruct the Nigeria banks as at last week to stop the acceptance of foreign
currency cash deposits in to the domiciliary accounts. This is an action that ultimately
resulted in the rise of Nigeria currency against the US dollar. This policy would help to
appreciate the value of naira compare to US dollar or other foreign currency.
The Government together with the central Bank of Nigeria should develop and pursue
prudent monetary and fiscal policies that would aim at reducing and stabilizing
both the micro and macroeconomic indicators especially inflation targeting, so as to
boast the growth of the economy.
A demand management policies such as a reduction in real broad money supply should
be adopted as one of the recommendation to reduce inflation in the short-run; both
demand management and supply-side policies should be pursued for the control of the
rate of inflation in the long-run; exchange rate policy that ensures international
62
competitiveness of domestically produced goods should be pursued, while
economic openness policy that ensures availability of critical inputs for industry
and agriculture must be adopted for short run economic growth; and, overreliance on
imports should be reduced over the long term through aggressive export promotion to
ensure long-run economic growth.
5.4 Suggestions for Further Study
Further studies in the area could adopt the AR model to:
i. Examine the impact of private consumption expenditure on inflation and
economic growth in Nigeria.
ii. Examine the impact of private consumption expenditure on economic growth in
Nigeria.
63
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68
APPENDIX
Appendix 1A
Unit root results (ADF)
Gdpr level with intercept
Null Hypothesis: GDPR has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.968177 0.0003
Test critical values: 1% level -3.661661
5% level -2.960411
10% level -2.619160
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GDPR)
Method: Least Squares
Date: 01/02/15 Time: 13:58
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
GDPR(-1) -0.663539 0.133558 -4.968177 0.0000
C 3.055258 0.825861 3.699484 0.0009
R-squared 0.459790 Mean dependent var 0.634839
Adjusted R-squared 0.441162 S.D. dependent var 4.966721
S.E. of regression 3.712897 Akaike info criterion 5.523843
Sum squared resid 399.7825 Schwarz criterion 5.616358
Log likelihood -83.61956 Hannan-Quinn criter. 5.554000
F-statistic 24.68279 Durbin-Watson stat 2.064936
Prob(F-statistic) 0.000028
gdpr level with intercept and trend
Null Hypothesis: GDPR has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -5.353877 0.0007
69
Test critical values: 1% level -4.284580
5% level -3.562882
10% level -3.215267
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GDPR)
Method: Least Squares
Date: 01/02/15 Time: 13:59
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
GDPR(-1) -0.819576 0.153081 -5.353877 0.0000
C 1.074514 1.325283 0.810781 0.4243
@TREND(1981) 0.159370 0.085455 1.864959 0.0727
R-squared 0.519478 Mean dependent var 0.634839
Adjusted R-squared 0.485155 S.D. dependent var 4.966721
S.E. of regression 3.563755 Akaike info criterion 5.471272
Sum squared resid 355.6098 Schwarz criterion 5.610045
Log likelihood -81.80472 Hannan-Quinn criter. 5.516509
F-statistic 15.13501 Durbin-Watson stat 1.949093
Prob(F-statistic) 0.000035
gdpr 1st diff
with intercept
Null Hypothesis: D(GDPR) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -8.378555 0.0000
Test critical values: 1% level -3.670170
5% level -2.963972
10% level -2.621007
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GDPR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:01
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(GDPR(-1)) -1.316971 0.157184 -8.378555 0.0000
C 0.442491 0.786906 0.562318 0.5784
70
R-squared 0.714868 Mean dependent var -0.457000
Adjusted R-squared 0.704685 S.D. dependent var 7.857074
S.E. of regression 4.269762 Akaike info criterion 5.805334
Sum squared resid 510.4643 Schwarz criterion 5.898747
Log likelihood -85.08001 Hannan-Quinn criter. 5.835217
F-statistic 70.20018 Durbin-Watson stat 2.332668
Prob(F-statistic) 0.000000
With intercept n trend
Null Hypothesis: D(GDPR) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -8.237831 0.0000
Test critical values: 1% level -4.296729
5% level -3.568379
10% level -3.218382
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GDPR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:03
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(GDPR(-1)) -1.329366 0.161373 -8.237831 0.0000
C 1.196130 1.737068 0.688591 0.4970
@TREND(1981) -0.045162 0.092465 -0.488421 0.6292
R-squared 0.717365 Mean dependent var -0.457000
Adjusted R-squared 0.696429 S.D. dependent var 7.857074
S.E. of regression 4.329031 Akaike info criterion 5.863204
Sum squared resid 505.9937 Schwarz criterion 6.003324
Log likelihood -84.94806 Hannan-Quinn criter. 5.908029
F-statistic 34.26484 Durbin-Watson stat 2.345964
Prob(F-statistic) 0.000000
APPENDIX 1B
Unit Root test (PHILIP PERRON)
pp level with intercept
Null Hypothesis: GDPR has a unit root
Exogenous: Constant
Bandwidth: 3 (Newey-West automatic) using Bartlett kernel
71
Adj. t-Stat Prob.*
Phillips-Perron test statistic -5.067107 0.0003
Test critical values: 1% level -3.661661
5% level -2.960411
10% level -2.619160
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 12.89621
HAC corrected variance (Bartlett kernel) 10.89638
Phillips-Perron Test Equation
Dependent Variable: D(GDPR)
Method: Least Squares
Date: 01/02/15 Time: 14:04
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
GDPR(-1) -0.663539 0.133558 -4.968177 0.0000
C 3.055258 0.825861 3.699484 0.0009
R-squared 0.459790 Mean dependent var 0.634839
Adjusted R-squared 0.441162 S.D. dependent var 4.966721
S.E. of regression 3.712897 Akaike info criterion 5.523843
Sum squared resid 399.7825 Schwarz criterion 5.616358
Log likelihood -83.61956 Hannan-Quinn criter. 5.554000
F-statistic 24.68279 Durbin-Watson stat 2.064936
Prob(F-statistic) 0.000028
pp level with inter n trend
Null Hypothesis: GDPR has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 2 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -5.441396 0.0006
Test critical values: 1% level -4.284580
5% level -3.562882
10% level -3.215267
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 11.47128
HAC corrected variance (Bartlett kernel) 9.732578
Phillips-Perron Test Equation
Dependent Variable: D(GDPR)
Method: Least Squares
72
Date: 01/02/15 Time: 14:05
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
GDPR(-1) -0.819576 0.153081 -5.353877 0.0000
C 1.074514 1.325283 0.810781 0.4243
@TREND(1981) 0.159370 0.085455 1.864959 0.0727
R-squared 0.519478 Mean dependent var 0.634839
Adjusted R-squared 0.485155 S.D. dependent var 4.966721
S.E. of regression 3.563755 Akaike info criterion 5.471272
Sum squared resid 355.6098 Schwarz criterion 5.610045
Log likelihood -81.80472 Hannan-Quinn criter. 5.516509
F-statistic 15.13501 Durbin-Watson stat 1.949093
Prob(F-statistic) 0.000035
pp 1st diff intercept
Null Hypothesis: D(GDPR) has a unit root
Exogenous: Constant
Bandwidth: 2 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -10.22660 0.0000
Test critical values: 1% level -3.670170
5% level -2.963972
10% level -2.621007
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 17.01548
HAC corrected variance (Bartlett kernel) 8.536468
Phillips-Perron Test Equation
Dependent Variable: D(GDPR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:06
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(GDPR(-1)) -1.316971 0.157184 -8.378555 0.0000
C 0.442491 0.786906 0.562318 0.5784
R-squared 0.714868 Mean dependent var -0.457000
Adjusted R-squared 0.704685 S.D. dependent var 7.857074
S.E. of regression 4.269762 Akaike info criterion 5.805334
Sum squared resid 510.4643 Schwarz criterion 5.898747
Log likelihood -85.08001 Hannan-Quinn criter. 5.835217
F-statistic 70.20018 Durbin-Watson stat 2.332668
Prob(F-statistic) 0.000000
73
pp 1st diff intercept n trend
Null Hypothesis: D(GDPR) has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 2 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -10.14257 0.0000
Test critical values: 1% level -4.296729
5% level -3.568379
10% level -3.218382
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 16.86646
HAC corrected variance (Bartlett kernel) 8.152224
Phillips-Perron Test Equation
Dependent Variable: D(GDPR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:07
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(GDPR(-1)) -1.329366 0.161373 -8.237831 0.0000
C 1.196130 1.737068 0.688591 0.4970
@TREND(1981) -0.045162 0.092465 -0.488421 0.6292
R-squared 0.717365 Mean dependent var -0.457000
Adjusted R-squared 0.696429 S.D. dependent var 7.857074
S.E. of regression 4.329031 Akaike info criterion 5.863204
Sum squared resid 505.9937 Schwarz criterion 6.003324
Log likelihood -84.94806 Hannan-Quinn criter. 5.908029
F-statistic 34.26484 Durbin-Watson stat 2.345964
Prob(F-statistic) 0.000000
PCX ADF level With intercept
Null Hypothesis: PCX has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.054423 0.9457
Test critical values: 1% level -3.670170
5% level -2.963972
10% level -2.621007
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(PCX)
74
Method: Least Squares
Date: 01/02/15 Time: 14:09
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
PCX(-1) -0.004073 0.074835 -0.054423 0.9570
D(PCX(-1)) -0.334238 0.193373 -1.728459 0.0953
C 0.034704 0.404713 0.085749 0.9323
R-squared 0.111928 Mean dependent var 0.009251
Adjusted R-squared 0.046145 S.D. dependent var 0.069608
S.E. of regression 0.067983 Akaike info criterion -2.444473
Sum squared resid 0.124786 Schwarz criterion -2.304354
Log likelihood 39.66710 Hannan-Quinn criter. -2.399648
F-statistic 1.701473 Durbin-Watson stat 1.774417
Prob(F-statistic) 0.201395
75
PCX LEVEL WITH INTER N TREND
Null Hypothesis: PCX has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 2 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.989837 0.1519
Test critical values: 1% level -4.309824
5% level -3.574244
10% level -3.221728
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(PCX)
Method: Least Squares
Date: 01/02/15 Time: 14:10
Sample (adjusted): 1984 2012
Included observations: 29 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
PCX(-1) -0.424916 0.142120 -2.989837 0.0064
D(PCX(-1)) -0.192810 0.177592 -1.085688 0.2884
D(PCX(-2)) 0.232696 0.173015 1.344947 0.1912
C 2.158372 0.724401 2.979527 0.0065
@TREND(1981) 0.009072 0.002996 3.028141 0.0058
R-squared 0.431950 Mean dependent var 0.011614
Adjusted R-squared 0.337274 S.D. dependent var 0.069605
S.E. of regression 0.056664 Akaike info criterion -2.747762
Sum squared resid 0.077060 Schwarz criterion -2.512021
Log likelihood 44.84254 Hannan-Quinn criter. -2.673931
F-statistic 4.562442 Durbin-Watson stat 1.894560
Prob(F-statistic) 0.006980
ADF 1ST DIFF INTERCEPT
Null Hypothesis: D(PCX) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -7.438999 0.0000
Test critical values: 1% level -3.670170
5% level -2.963972
10% level -2.621007
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(PCX,2)
Method: Least Squares
Date: 01/02/15 Time: 14:11
Sample (adjusted): 1983 2012
76
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(PCX(-1)) -1.337622 0.179812 -7.438999 0.0000
C 0.012689 0.012326 1.029442 0.3121
R-squared 0.664022 Mean dependent var -0.000929
Adjusted R-squared 0.652022 S.D. dependent var 0.113176
S.E. of regression 0.066762 Akaike info criterion -2.511030
Sum squared resid 0.124800 Schwarz criterion -2.417617
Log likelihood 39.66546 Hannan-Quinn criter. -2.481147
F-statistic 55.33870 Durbin-Watson stat 1.773676
Prob(F-statistic) 0.000000
ADF 1ST DIFF INTER N TREND
Null Hypothesis: D(GDPR) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -8.237831 0.0000
Test critical values: 1% level -4.296729
5% level -3.568379
10% level -3.218382
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GDPR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:12
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(GDPR(-1)) -1.329366 0.161373 -8.237831 0.0000
C 1.196130 1.737068 0.688591 0.4970
@TREND(1981) -0.045162 0.092465 -0.488421 0.6292
R-squared 0.717365 Mean dependent var -0.457000
Adjusted R-squared 0.696429 S.D. dependent var 7.857074
S.E. of regression 4.329031 Akaike info criterion 5.863204
Sum squared resid 505.9937 Schwarz criterion 6.003324
Log likelihood -84.94806 Hannan-Quinn criter. 5.908029
F-statistic 34.26484 Durbin-Watson stat 2.345964
Prob(F-statistic) 0.000000
PP PCX LEVEL LEVEL WITH INTER
77
Null Hypothesis: PCX has a unit root
Exogenous: Constant
Bandwidth: 3 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -0.480588 0.8821
Test critical values: 1% level -3.661661
5% level -2.960411
10% level -2.619160
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.004506
HAC corrected variance (Bartlett kernel) 0.003713
Phillips-Perron Test Equation
Dependent Variable: D(PCX)
Method: Least Squares
Date: 01/02/15 Time: 14:13
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
PCX(-1) -0.045371 0.072338 -0.627202 0.5354
C 0.253799 0.391813 0.647755 0.5222
R-squared 0.013383 Mean dependent var 0.008177
Adjusted R-squared -0.020638 S.D. dependent var 0.068699
S.E. of regression 0.069404 Akaike info criterion -2.435397
Sum squared resid 0.139691 Schwarz criterion -2.342882
Log likelihood 39.74866 Hannan-Quinn criter. -2.405240
F-statistic 0.393382 Durbin-Watson stat 2.541389
Prob(F-statistic) 0.535434
PP LEVEL INTER N TREND
Null Hypothesis: PCX has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 10 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -3.220669 0.0990
Test critical values: 1% level -4.284580
5% level -3.562882
10% level -3.215267
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.003315
HAC corrected variance (Bartlett kernel) 0.001313
Phillips-Perron Test Equation
78
Dependent Variable: D(PCX)
Method: Least Squares
Date: 01/02/15 Time: 14:14
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
PCX(-1) -0.342614 0.112997 -3.032066 0.0052
C 1.752484 0.583266 3.004604 0.0056
@TREND(1981) 0.006905 0.002177 3.172001 0.0037
R-squared 0.274196 Mean dependent var 0.008177
Adjusted R-squared 0.222353 S.D. dependent var 0.068699
S.E. of regression 0.060582 Akaike info criterion -2.677882
Sum squared resid 0.102764 Schwarz criterion -2.539109
Log likelihood 44.50718 Hannan-Quinn criter. -2.632646
F-statistic 5.288946 Durbin-Watson stat 2.548049
Prob(F-statistic) 0.011258
PP 1ST DIFF INTER
Null Hypothesis: D(PCX) has a unit root
Exogenous: Constant
Bandwidth: 0 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -7.438999 0.0000
Test critical values: 1% level -3.670170
5% level -2.963972
10% level -2.621007
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.004160
HAC corrected variance (Bartlett kernel) 0.004160
Phillips-Perron Test Equation
Dependent Variable: D(PCX,2)
Method: Least Squares
Date: 01/02/15 Time: 14:16
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(PCX(-1)) -1.337622 0.179812 -7.438999 0.0000
C 0.012689 0.012326 1.029442 0.3121
R-squared 0.664022 Mean dependent var -0.000929
Adjusted R-squared 0.652022 S.D. dependent var 0.113176
S.E. of regression 0.066762 Akaike info criterion -2.511030
Sum squared resid 0.124800 Schwarz criterion -2.417617
Log likelihood 39.66546 Hannan-Quinn criter. -2.481147
F-statistic 55.33870 Durbin-Watson stat 1.773676
Prob(F-statistic) 0.000000
79
PP 1ST DIFF INTER N TREND
Null Hypothesis: D(PCX) has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 3 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -7.636059 0.0000
Test critical values: 1% level -4.296729
5% level -3.568379
10% level -3.218382
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.003830
HAC corrected variance (Bartlett kernel) 0.004216
Phillips-Perron Test Equation
Dependent Variable: D(PCX,2)
Method: Least Squares
Date: 01/02/15 Time: 14:16
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(PCX(-1)) -1.408205 0.181679 -7.751042 0.0000
C -0.022418 0.025968 -0.863284 0.3956
@TREND(1981) 0.002171 0.001423 1.525936 0.1387
R-squared 0.690696 Mean dependent var -0.000929
Adjusted R-squared 0.667785 S.D. dependent var 0.113176
S.E. of regression 0.065232 Akaike info criterion -2.527086
Sum squared resid 0.114892 Schwarz criterion -2.386966
Log likelihood 40.90629 Hannan-Quinn criter. -2.482260
F-statistic 30.14638 Durbin-Watson stat 1.746864
Prob(F-statistic) 0.000000
CPI ADF LEVEL INTER
Null Hypothesis: CPI has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.792061 0.8074
Test critical values: 1% level -3.661661
5% level -2.960411
10% level -2.619160
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
80
Dependent Variable: D(CPI)
Method: Least Squares
Date: 01/02/15 Time: 14:18
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
CPI(-1) -0.046905 0.059218 -0.792061 0.4348
C 7.528992 5.381449 1.399064 0.1724
R-squared 0.021175 Mean dependent var 4.518387
Adjusted R-squared -0.012578 S.D. dependent var 21.07847
S.E. of regression 21.21061 Akaike info criterion 9.009221
Sum squared resid 13046.81 Schwarz criterion 9.101736
Log likelihood -137.6429 Hannan-Quinn criter. 9.039379
F-statistic 0.627361 Durbin-Watson stat 2.150132
Prob(F-statistic) 0.434757
CPI ADF LEVEL INTER N TREND
Null Hypothesis: CPI has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.483991 0.3331
Test critical values: 1% level -4.284580
5% level -3.562882
10% level -3.215267
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(CPI)
Method: Least Squares
Date: 01/02/15 Time: 14:23
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
CPI(-1) -0.345445 0.139068 -2.483991 0.0192
C -10.72961 9.277354 -1.156537 0.2572
@TREND(1981) 2.338791 1.000230 2.338252 0.0267
R-squared 0.181081 Mean dependent var 4.518387
Adjusted R-squared 0.122587 S.D. dependent var 21.07847
S.E. of regression 19.74427 Akaike info criterion 8.895369
Sum squared resid 10915.41 Schwarz criterion 9.034142
Log likelihood -134.8782 Hannan-Quinn criter. 8.940606
F-statistic 3.095715 Durbin-Watson stat 1.909858
Prob(F-statistic) 0.061006
81
CPI ADF 1ST DIFF INTER
Null Hypothesis: D(CPI) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -5.877528 0.0000
Test critical values: 1% level -3.670170
5% level -2.963972
10% level -2.621007
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(CPI,2)
Method: Least Squares
Date: 01/02/15 Time: 14:24
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(CPI(-1)) -1.108242 0.188556 -5.877528 0.0000
C 5.117568 4.034380 1.268489 0.2151
R-squared 0.552325 Mean dependent var 0.501000
Adjusted R-squared 0.536336 S.D. dependent var 31.83061
S.E. of regression 21.67437 Akaike info criterion 9.054478
Sum squared resid 13153.79 Schwarz criterion 9.147892
Log likelihood -133.8172 Hannan-Quinn criter. 9.084362
F-statistic 34.54534 Durbin-Watson stat 2.031876
Prob(F-statistic) 0.000003
CPI ADF 1ST DIFF INTER N TREND
Null Hypothesis: D(CPI) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -5.771820 0.0003
Test critical values: 1% level -4.296729
5% level -3.568379
10% level -3.218382
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(CPI,2)
Method: Least Squares
Date: 01/02/15 Time: 14:27
Sample (adjusted): 1983 2012
82
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(CPI(-1)) -1.108192 0.192000 -5.771820 0.0000
C 4.588623 8.713641 0.526602 0.6028
@TREND(1981) 0.032045 0.465542 0.068833 0.9456
R-squared 0.552403 Mean dependent var 0.501000
Adjusted R-squared 0.519248 S.D. dependent var 31.83061
S.E. of regression 22.07016 Akaike info criterion 9.120970
Sum squared resid 13151.48 Schwarz criterion 9.261089
Log likelihood -133.8145 Hannan-Quinn criter. 9.165795
F-statistic 16.66108 Durbin-Watson stat 2.032239
Prob(F-statistic) 0.000019
CPI PP LEVEL INTERCEPT
Null Hypothesis: CPI has a unit root
Exogenous: Constant
Bandwidth: 1 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -0.749594 0.8192
Test critical values: 1% level -3.661661
5% level -2.960411
10% level -2.619160
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 420.8648
HAC corrected variance (Bartlett kernel) 385.4552
Phillips-Perron Test Equation
Dependent Variable: D(CPI)
Method: Least Squares
Date: 01/02/15 Time: 14:29
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
CPI(-1) -0.046905 0.059218 -0.792061 0.4348
C 7.528992 5.381449 1.399064 0.1724
R-squared 0.021175 Mean dependent var 4.518387
Adjusted R-squared -0.012578 S.D. dependent var 21.07847
S.E. of regression 21.21061 Akaike info criterion 9.009221
Sum squared resid 13046.81 Schwarz criterion 9.101736
Log likelihood -137.6429 Hannan-Quinn criter. 9.039379
83
F-statistic 0.627361 Durbin-Watson stat 2.150132
Prob(F-statistic) 0.434757
CPI PP LEVEL INTER N TREND
Null Hypothesis: CPI has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 1 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -2.516951 0.3183
Test critical values: 1% level -4.284580
5% level -3.562882
10% level -3.215267
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 352.1100
HAC corrected variance (Bartlett kernel) 366.5665
Phillips-Perron Test Equation
Dependent Variable: D(CPI)
Method: Least Squares
Date: 01/02/15 Time: 14:29
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
CPI(-1) -0.345445 0.139068 -2.483991 0.0192
C -10.72961 9.277354 -1.156537 0.2572
@TREND(1981) 2.338791 1.000230 2.338252 0.0267
R-squared 0.181081 Mean dependent var 4.518387
Adjusted R-squared 0.122587 S.D. dependent var 21.07847
S.E. of regression 19.74427 Akaike info criterion 8.895369
Sum squared resid 10915.41 Schwarz criterion 9.034142
Log likelihood -134.8782 Hannan-Quinn criter. 8.940606
F-statistic 3.095715 Durbin-Watson stat 1.909858
Prob(F-statistic) 0.061006
CPI 1ST DIFF INTER
Null Hypothesis: D(CPI) has a unit root
Exogenous: Constant
Bandwidth: 3 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -5.959628 0.0000
Test critical values: 1% level -3.670170
5% level -2.963972
10% level -2.621007
84
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 438.4598
HAC corrected variance (Bartlett kernel) 351.1989
Phillips-Perron Test Equation
Dependent Variable: D(CPI,2)
Method: Least Squares
Date: 01/02/15 Time: 14:30
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(CPI(-1)) -1.108242 0.188556 -5.877528 0.0000
C 5.117568 4.034380 1.268489 0.2151
R-squared 0.552325 Mean dependent var 0.501000
Adjusted R-squared 0.536336 S.D. dependent var 31.83061
S.E. of regression 21.67437 Akaike info criterion 9.054478
Sum squared resid 13153.79 Schwarz criterion 9.147892
Log likelihood -133.8172 Hannan-Quinn criter. 9.084362
F-statistic 34.54534 Durbin-Watson stat 2.031876
Prob(F-statistic) 0.000003
CPI PP 1ST DIFF INTER N TREND
Null Hypothesis: D(CPI) has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 3 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -5.841964 0.0002
Test critical values: 1% level -4.296729
5% level -3.568379
10% level -3.218382
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 438.3828
HAC corrected variance (Bartlett kernel) 350.8427
Phillips-Perron Test Equation
Dependent Variable: D(CPI,2)
Method: Least Squares
Date: 01/02/15 Time: 14:31
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(CPI(-1)) -1.108192 0.192000 -5.771820 0.0000
C 4.588623 8.713641 0.526602 0.6028
@TREND(1981) 0.032045 0.465542 0.068833 0.9456
R-squared 0.552403 Mean dependent var 0.501000
85
Adjusted R-squared 0.519248 S.D. dependent var 31.83061
S.E. of regression 22.07016 Akaike info criterion 9.120970
Sum squared resid 13151.48 Schwarz criterion 9.261089
Log likelihood -133.8145 Hannan-Quinn criter. 9.165795
F-statistic 16.66108 Durbin-Watson stat 2.032239
Prob(F-statistic) 0.000019
INTEREST RATE ADF LEVEL INTERCEPT
Null Hypothesis: INTR has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.890121 0.0580
Test critical values: 1% level -3.661661
5% level -2.960411
10% level -2.619160
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(INTR)
Method: Least Squares
Date: 01/02/15 Time: 14:34
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
INTR(-1) -0.399560 0.138250 -2.890121 0.0072
C 5.387052 1.893352 2.845247 0.0081
R-squared 0.223619 Mean dependent var 0.193548
Adjusted R-squared 0.196847 S.D. dependent var 3.704915
S.E. of regression 3.320300 Akaike info criterion 5.300328
Sum squared resid 319.7074 Schwarz criterion 5.392844
Log likelihood -80.15509 Hannan-Quinn criter. 5.330486
F-statistic 8.352799 Durbin-Watson stat 2.156316
Prob(F-statistic) 0.007220
ADF LEVEL INTERCEPT N TREND
Null Hypothesis: INTR has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.881381 0.1818
Test critical values: 1% level -4.284580
5% level -3.562882
10% level -3.215267
*MacKinnon (1996) one-sided p-values.
86
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(INTR)
Method: Least Squares
Date: 01/02/15 Time: 14:35
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
INTR(-1) -0.400903 0.139136 -2.881381 0.0075
C 6.260899 2.197816 2.848692 0.0081
@TREND(1981) -0.053525 0.067100 -0.797682 0.4318
R-squared 0.240870 Mean dependent var 0.193548
Adjusted R-squared 0.186647 S.D. dependent var 3.704915
S.E. of regression 3.341319 Akaike info criterion 5.342374
Sum squared resid 312.6035 Schwarz criterion 5.481147
Log likelihood -79.80679 Hannan-Quinn criter. 5.387610
F-statistic 4.442170 Durbin-Watson stat 2.203259
Prob(F-statistic) 0.021107
INTEREST ADF 1ST DIFF INTERCEPT
Null Hypothesis: D(INTR) has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -5.734927 0.0001
Test critical values: 1% level -3.679322
5% level -2.967767
10% level -2.622989
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(INTR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:36
Sample (adjusted): 1984 2012
Included observations: 29 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(INTR(-1)) -1.739216 0.303267 -5.734927 0.0000
D(INTR(-1),2) 0.353474 0.188519 1.874998 0.0721
C 0.155344 0.663773 0.234032 0.8168
R-squared 0.678631 Mean dependent var 0.096897
Adjusted R-squared 0.653910 S.D. dependent var 6.075646
S.E. of regression 3.574268 Akaike info criterion 5.483095
Sum squared resid 332.1601 Schwarz criterion 5.624539
Log likelihood -76.50488 Hannan-Quinn criter. 5.527394
F-statistic 27.45190 Durbin-Watson stat 1.901916
Prob(F-statistic) 0.000000
87
ADF 1ST DIFF INT N TREND
Null Hypothesis: D(INTR) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=7)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -6.070218 0.0001
Test critical values: 1% level -4.309824
5% level -3.574244
10% level -3.221728
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(INTR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:39
Sample (adjusted): 1984 2012 Included observations: 29 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(INTR(-1)) -1.900141 0.313027 -6.070218 0.0000
D(INTR(-1),2) 0.443266 0.192502 2.302659 0.0299
C 2.322360 1.538337 1.509656 0.1437
@TREND(1981) -0.127276 0.081986 -1.552409 0.1331
R-squared 0.706886 Mean dependent var 0.096897
Adjusted R-squared 0.671713 S.D. dependent var 6.075646
S.E. of regression 3.481123 Akaike info criterion 5.460029
Sum squared resid 302.9555 Schwarz criterion 5.648622
Log likelihood -75.17042 Hannan-Quinn criter. 5.519094
F-statistic 20.09706 Durbin-Watson stat 1.945794
Prob(F-statistic) 0.000001
INTEREST PP LEVEL INT
Null Hypothesis: INTR has a unit root
Exogenous: Constant
Bandwidth: 3 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -2.836305 0.0648
Test critical values: 1% level -3.661661
5% level -2.960411
10% level -2.619160
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 10.31314
HAC corrected variance (Bartlett kernel) 9.421398
Phillips-Perron Test Equation
88
Dependent Variable: D(INTR)
Method: Least Squares
Date: 01/02/15 Time: 14:41
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
INTR(-1) -0.399560 0.138250 -2.890121 0.0072
C 5.387052 1.893352 2.845247 0.0081
R-squared 0.223619 Mean dependent var 0.193548
Adjusted R-squared 0.196847 S.D. dependent var 3.704915
S.E. of regression 3.320300 Akaike info criterion 5.300328
Sum squared resid 319.7074 Schwarz criterion 5.392844
Log likelihood -80.15509 Hannan-Quinn criter. 5.330486
F-statistic 8.352799 Durbin-Watson stat 2.156316
Prob(F-statistic) 0.007220
PP LEVEL INT N TREND
Null Hypothesis: INTR has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 2 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -2.738916 0.2291
Test critical values: 1% level -4.284580
5% level -3.562882
10% level -3.215267
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 10.08398
HAC corrected variance (Bartlett kernel) 7.626894
Phillips-Perron Test Equation
Dependent Variable: D(INTR)
Method: Least Squares
Date: 01/02/15 Time: 14:42
Sample (adjusted): 1982 2012
Included observations: 31 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
INTR(-1) -0.400903 0.139136 -2.881381 0.0075
C 6.260899 2.197816 2.848692 0.0081
@TREND(1981) -0.053525 0.067100 -0.797682 0.4318
R-squared 0.240870 Mean dependent var 0.193548
Adjusted R-squared 0.186647 S.D. dependent var 3.704915
S.E. of regression 3.341319 Akaike info criterion 5.342374
Sum squared resid 312.6035 Schwarz criterion 5.481147
Log likelihood -79.80679 Hannan-Quinn criter. 5.387610
F-statistic 4.442170 Durbin-Watson stat 2.203259
89
Prob(F-statistic) 0.021107
PP 1ST DIFF INTERCEPT
Null Hypothesis: D(INTR) has a unit root
Exogenous: Constant
Bandwidth: 0 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -7.002300 0.0000
Test critical values: 1% level -3.670170
5% level -2.963972
10% level -2.621007
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 12.57447
HAC corrected variance (Bartlett kernel) 12.57447
Phillips-Perron Test Equation
Dependent Variable: D(INTR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:55
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(INTR(-1)) -1.277588 0.182453 -7.002300 0.0000
C 0.162850 0.670421 0.242907 0.8098
R-squared 0.636516 Mean dependent var 0.027000
Adjusted R-squared 0.623534 S.D. dependent var 5.982238
S.E. of regression 3.670511 Akaike info criterion 5.502879
Sum squared resid 377.2342 Schwarz criterion 5.596292
Log likelihood -80.54319 Hannan-Quinn criter. 5.532763
F-statistic 49.03220 Durbin-Watson stat 2.157665
Prob(F-statistic) 0.000000
PP 1ST DIFF INT N TREND
Null Hypothesis: D(INTR) has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 2 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -7.643887 0.0000
Test critical values: 1% level -4.296729
5% level -3.568379
10% level -3.218382
90
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 12.25079
HAC corrected variance (Bartlett kernel) 7.486628
Phillips-Perron Test Equation
Dependent Variable: D(INTR,2)
Method: Least Squares
Date: 01/02/15 Time: 14:56
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(INTR(-1)) -1.305221 0.186289 -7.006429 0.0000
C 1.267475 1.471244 0.861499 0.3965
@TREND(1981) -0.066769 0.079052 -0.844618 0.4057
R-squared 0.645872 Mean dependent var 0.027000
Adjusted R-squared 0.619641 S.D. dependent var 5.982238
S.E. of regression 3.689443 Akaike info criterion 5.543467
Sum squared resid 367.5237 Schwarz criterion 5.683587
Log likelihood -80.15201 Hannan-Quinn criter. 5.588293
F-statistic 24.62183 Durbin-Watson stat 2.180418
Prob(F-statistic) 0.000001
APPENDIX 2
JOHANSEN COINTEGRATION RESULT
Date: 01/02/15 Time: 14:58
Sample (adjusted): 1983 2012
Included observations: 30 after adjustments
Trend assumption: Linear deterministic trend
Series: GDPR PCX CPI INTR
Lags interval (in first differences): 1 to 1
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.603046 54.11515 47.85613 0.0115
At most 1 0.419295 26.39709 29.79707 0.1173
At most 2 0.272722 10.09170 15.49471 0.2737
At most 3 0.017783 0.538291 3.841466 0.4631
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
91
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.603046 27.71806 27.58434 0.0481
At most 1 0.419295 16.30539 21.13162 0.2075
At most 2 0.272722 9.553409 14.26460 0.2429
At most 3 0.017783 0.538291 3.841466 0.4631
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
GDPR PCX CPI INTR
0.128634 3.143440 -0.022536 -0.285599
-0.233833 -12.63250 0.037646 -0.097046
-0.238227 9.228840 -0.017900 0.091095
-0.028061 -4.788034 -0.000916 0.073434
Unrestricted Adjustment Coefficients (alpha):
D(GDPR) -0.677485 1.925183 1.199486 0.134891
D(PCX) -0.032508 0.011367 -0.014675 0.004735
D(CPI) -3.524366 -8.805051 4.008666 1.656383
D(INTR) 2.117983 0.280415 -0.284344 0.247953
1 Cointegrating Equation(s): Log likelihood -240.9980
Normalized cointegrating coefficients (standard error in parentheses)
GDPR PCX CPI INTR
1.000000 24.43706 -0.175191 -2.220242
(20.9406) (0.05492) (0.39383)
Adjustment coefficients (standard error in parentheses)
D(GDPR) -0.087148
(0.10318)
D(PCX) -0.004182
(0.00145)
D(CPI) -0.453354
(0.52926)
D(INTR) 0.272445
(0.06894)
2 Cointegrating Equation(s): Log likelihood -232.8454
Normalized cointegrating coefficients (standard error in parentheses)
GDPR PCX CPI INTR
1.000000 0.000000 -0.186917 -4.396851
(0.04375) (0.74207)
0.000000 1.000000 0.000480 0.089070
(0.00097) (0.01653)
Adjustment coefficients (standard error in parentheses)
D(GDPR) -0.537320 -26.44951
(0.18661) (9.10233)
D(PCX) -0.006840 -0.245783
(0.00295) (0.14372)
D(CPI) 1.605561 100.1512
(0.98775) (48.1799)
D(INTR) 0.206875 3.115411
(0.14222) (6.93708)
92
3 Cointegrating Equation(s): Log likelihood -228.0686
Normalized cointegrating coefficients (standard error in parentheses)
GDPR PCX CPI INTR
1.000000 0.000000 0.000000 0.575078
(0.32524)
0.000000 1.000000 0.000000 0.076306
(0.01340)
0.000000 0.000000 1.000000 26.59961
(4.77647)
Adjustment coefficients (standard error in parentheses)
D(GDPR) -0.823069 -15.37964 0.066272
(0.23430) (10.4513) (0.03104)
D(PCX) -0.003344 -0.381216 0.001423
(0.00380) (0.16956) (0.00050)
D(CPI) 0.650590 137.1465 -0.323803
(1.29126) (57.5977) (0.17104)
D(INTR) 0.274613 0.491242 -0.032084
(0.18950) (8.45292) (0.02510)
APPENDIX 3
LAG LENGTH SELECTION CRITERIA
VAR Lag Order Selection Criteria
Endogenous variables: GDPR PCX CPI INTR
Exogenous variables: C
Date: 01/02/15 Time: 15:40
Sample: 1981 2012
Included observations: 28
Lag LogL LR FPE AIC SC HQ
0 -266.6467 NA 2923.455 19.33191 19.52222 19.39009
1 -221.9232 73.47426* 381.5361* 17.28023 18.23181* 17.57114*
2 -210.0770 16.07709 555.5204 17.57693 19.28976 18.10056
3 -194.9512 16.20615 731.9168 17.63937 20.11347 18.39573
4 -170.7002 19.05437 649.6492 17.05001* 20.28537 18.03909
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
APPENDIX 4
VECM ESTIMATED RESULT
Vector Error Correction Estimates
93
Date: 01/02/15 Time: 15:41
Sample (adjusted): 1986 2012
Included observations: 27 after adjustments
Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
GDPR(-1) 1.000000
PCX(-1) 144.8843
(22.9476)
[ 6.31370]
CPI(-1) -0.694471
(0.07879)
[-8.81441]
INTR(-1) -5.474645
(0.81238)
[-6.73904]
C -664.5464
Error Correction: D(GDPR) D(PCX) D(CPI) D(INTR)
CointEq1 -0.060879 -0.007210 1.755086 0.175822
(0.16011) (0.00155) (0.94491) (0.17077)
[-0.38023] [-4.63947] [ 1.85742] [ 1.02960]
D(GDPR(-1)) -0.253472 0.018871 -3.633601 -0.390032
(0.45056) (0.00437) (2.65896) (0.48054)
[-0.56258] [ 4.31560] [-1.36655] [-0.81166]
D(GDPR(-2)) -0.324878 0.014310 -7.056401 -0.440524
(0.61825) (0.00600) (3.64859) (0.65939)
[-0.52548] [ 2.38482] [-1.93401] [-0.66808]
D(GDPR(-3)) 0.002837 0.013171 -2.892361 -0.347755
(0.45211) (0.00439) (2.66812) (0.48219)
[ 0.00628] [ 3.00173] [-1.08405] [-0.72119]
D(GDPR(-4)) 0.068424 0.006315 -4.308833 -0.157037
(0.36098) (0.00350) (2.13035) (0.38501)
[ 0.18955] [ 1.80247] [-2.02260] [-0.40788]
D(PCX(-1)) -17.35657 -0.187003 57.95023 6.295269
(15.6272) (0.15167) (92.2237) (16.6671)
[-1.11067] [-1.23299] [ 0.62837] [ 0.37771]
D(PCX(-2)) -3.736677 0.393703 89.60632 3.945053
(14.6218) (0.14191) (86.2905) (15.5948)
[-0.25556] [ 2.77432] [ 1.03843] [ 0.25297]
D(PCX(-3)) 3.882527 -0.023093 -260.2161 -1.685581
(20.0329) (0.19443) (118.224) (21.3659)
[ 0.19381] [-0.11878] [-2.20104] [-0.07889]
D(PCX(-4)) -19.37397 -0.379270 256.1846 -12.56605
(20.3171) (0.19718) (119.901) (21.6691)
[-0.95358] [-1.92343] [ 2.13663] [-0.57991]
D(CPI(-1)) -0.018697 -0.005490 1.729187 0.048150
94
(0.13926) (0.00135) (0.82182) (0.14852)
[-0.13426] [-4.06232] [ 2.10410] [ 0.32419]
D(CPI(-2)) -0.006486 -0.004847 0.671306 0.076530
(0.13368) (0.00130) (0.78891) (0.14258)
[-0.04852] [-3.73630] [ 0.85093] [ 0.53677]
D(CPI(-3)) 0.171098 -0.012024 3.223772 -0.045006
(0.33899) (0.00329) (2.00056) (0.36155)
[ 0.50473] [-3.65479] [ 1.61143] [-0.12448]
D(CPI(-4)) -0.277787 -0.003834 1.167559 0.289961
(0.30313) (0.00294) (1.78891) (0.32330)
[-0.91640] [-1.30337] [ 0.65266] [ 0.89688]
D(INTR(-1)) -0.082329 -0.037279 8.231703 0.210469
(0.88245) (0.00856) (5.20777) (0.94117)
[-0.09330] [-4.35272] [ 1.58066] [ 0.22362]
D(INTR(-2)) -0.288898 -0.031604 9.507689 0.152339
(0.91145) (0.00885) (5.37890) (0.97210)
[-0.31697] [-3.57274] [ 1.76759] [ 0.15671]
D(INTR(-3)) -0.038910 -0.016768 6.493827 0.386136
(0.73731) (0.00716) (4.35121) (0.78637)
[-0.05277] [-2.34325] [ 1.49242] [ 0.49104]
D(INTR(-4)) -0.092702 -0.007299 2.760449 0.242300
(0.44490) (0.00432) (2.62555) (0.47450)
[-0.20837] [-1.69046] [ 1.05138] [ 0.51064]
C 1.229263 0.155466 -30.62242 -1.620130
(4.15066) (0.04028) (24.4951) (4.42686)
[ 0.29616] [ 3.85929] [-1.25015] [-0.36598]
R-squared 0.621347 0.906322 0.652373 0.628536
Adj. R-squared -0.093887 0.729374 -0.004256 -0.073117
Sum sq. resids 132.1919 0.012452 4603.933 150.3703
S.E. equation 3.832491 0.037196 22.61743 4.087519
F-statistic 0.868733 5.121982 0.993518 0.895793
Log likelihood -59.75498 65.39216 -107.6855 -61.49441
Akaike AIC 5.759628 -3.510530 9.310040 5.888475
Schwarz SC 6.623519 -2.646639 10.17393 6.752366
Mean dependent -0.116667 0.012483 5.155926 0.074074
S.D. dependent 3.664333 0.071500 22.56945 3.945811
Determinant resid covariance (dof adj.) 86.62330
Determinant resid covariance 1.069423
Log likelihood -154.1515
Akaike information criterion 17.04826
Schwarz criterion 20.69580
APPENDIX 5
VEC GRANGER CAUSALITY RESULT
95
VEC Granger Causality/Block Exogeneity Wald Tests
Date: 01/02/15 Time: 16:17
Sample: 1981 2012
Included observations: 27
Dependent variable: D(GDPR)
Excluded Chi-sq df Prob.
D(PCX) 1.615237 4 0.8061
D(CPI) 1.920879 4 0.7503
D(INTR) 0.716293 4 0.9493
All 3.339164 12 0.9926
Dependent variable: D(PCX)
Excluded Chi-sq df Prob.
D(GDPR) 26.70113 4 0.0000
D(CPI) 20.51260 4 0.0004
D(INTR) 31.70473 4 0.0000
All 49.58548 12 0.0000
Dependent variable: D(CPI)
Excluded Chi-sq df Prob.
D(GDPR) 5.357727 4 0.2525
D(PCX) 12.92769 4 0.0116
D(INTR) 3.526606 4 0.4738
All 14.34030 12 0.2795
Dependent variable: D(INTR)
Excluded Chi-sq df Prob.
D(GDPR) 0.687198 4 0.9529
D(PCX) 0.782321 4 0.9408
D(CPI) 1.038885 4 0.9038
All 3.205966 12 0.9939
APPENDIX 6
RESIDUAL AUTO CORRELATION TES
96
VEC Residual Portmanteau Tests for Autocorrelations
Null Hypothesis: no residual autocorrelations up to lag h
Date: 01/02/15 Time: 16:09
Sample: 1981 2012
Included observations: 27
Lags Q-Stat Prob. Adj Q-Stat Prob. df
1 23.89996 NA* 24.81919 NA* NA*
2 43.29449 NA* 45.76528 NA* NA*
3 52.47527 NA* 56.09366 NA* NA*
4 65.62937 NA* 71.53543 NA* NA*
5 69.54526 0.0000 76.34129 0.0000 28
6 80.48298 0.0007 90.40407 0.0000 44
7 98.55145 0.0013 114.7965 0.0000 60
8 108.9134 0.0079 129.5214 0.0001 76
9 116.0558 0.0458 140.2350 0.0009 92
10 129.4747 0.0780 161.5473 0.0007 108
11 137.8146 0.1871 175.6210 0.0016 124
12 145.4608 0.3587 189.3842 0.0035 140
*The test is valid only for lags larger than the VAR lag order.
df is degrees of freedom for (approximate) chi-square distribution
APPENDIX 7
RESIDUAL SERIAL CORRELATION TEST
VEC Residual Serial Correlation LM Tests
Null Hypothesis: no serial correlation at lag
order h
Date: 01/02/15 Time: 16:10
Sample: 1981 2012
Included observations: 27
Lags LM-Stat Prob
1 30.77070 0.0144
2 20.39142 0.2031
3 20.75361 0.1882
4 20.28954 0.2075
5 13.40179 0.6432
6 9.822102 0.8758
7 22.78102 0.1197
8 17.88928 0.3304
9 20.41113 0.2023
10 15.08092 0.5187
11 11.82288 0.7561
12 11.80064 0.7576
Probs from chi-square with 16 df.
APPENDIX 8
VEC RESIDUAL NORMALITY TEST
97
VEC Residual Normality Tests
Orthogonalization: Cholesky (Lutkepohl)
Null Hypothesis: residuals are multivariate normal
Date: 01/02/15 Time: 16:11
Sample: 1981 2012
Included observations: 27
Component Skewness Chi-sq df Prob.
1 0.110999 0.055444 1 0.8138
2 0.121207 0.066110 1 0.7971
3 -0.127360 0.072993 1 0.7870
4 0.620333 1.731658 1 0.1882
Joint 1.926205 4 0.7493
Component Kurtosis Chi-sq df Prob.
1 2.485575 0.297712 1 0.5853
2 2.476180 0.308685 1 0.5785
3 3.669328 0.504000 1 0.4777
4 3.899762 0.910769 1 0.3399
Joint 2.021166 4 0.7319
Component Jarque-Bera df Prob.
1 0.353156 2 0.8381
2 0.374795 2 0.8291
3 0.576993 2 0.7494
4 2.642427 2 0.2668
Joint 3.947371 8 0.8618
98
APPENDIX 9
IMPLUSE RESPONSE
-20
-10
0
10
20
1 2 3 4 5 6 7 8 9 10
Response of GDPR to GDPR
-20
-10
0
10
20
1 2 3 4 5 6 7 8 9 10
Response of GDPR to PCX
-20
-10
0
10
20
1 2 3 4 5 6 7 8 9 10
Response of GDPR to CPI
-20
-10
0
10
20
1 2 3 4 5 6 7 8 9 10
Response of GDPR to INTR
-.8
-.4
.0
.4
.8
1 2 3 4 5 6 7 8 9 10
Response of PCX to GDPR
-.8
-.4
.0
.4
.8
1 2 3 4 5 6 7 8 9 10
Response of PCX to PCX
-.8
-.4
.0
.4
.8
1 2 3 4 5 6 7 8 9 10
Response of PCX to CPI
-.8
-.4
.0
.4
.8
1 2 3 4 5 6 7 8 9 10
Response of PCX to INTR
-200
-100
0
100
200
1 2 3 4 5 6 7 8 9 10
Response of CPI to GDPR
-200
-100
0
100
200
1 2 3 4 5 6 7 8 9 10
Response of CPI to PCX
-200
-100
0
100
200
1 2 3 4 5 6 7 8 9 10
Response of CPI to CPI
-200
-100
0
100
200
1 2 3 4 5 6 7 8 9 10
Response of CPI to INTR
-10
-5
0
5
10
1 2 3 4 5 6 7 8 9 10
Response of INTR to GDPR
-10
-5
0
5
10
1 2 3 4 5 6 7 8 9 10
Response of INTR to PCX
-10
-5
0
5
10
1 2 3 4 5 6 7 8 9 10
Response of INTR to CPI
-10
-5
0
5
10
1 2 3 4 5 6 7 8 9 10
Response of INTR to INTR
Response to Cholesky One S.D. Innov ations