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DESCRIPTIONPAIR WISE CAUSALITY
On Pairwise Granger causality Modelling and Econometric Analysis of Selected Economic Indicators
Olushina Olawale Awe
Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
The goal of most empirical studies in econometrics and other social sciences is to determine whether a change in one variable causes a change in or helps to predict another variable. Granger causality modeling approach is quite popular in experimental and non-experimental fields which involve some dynamic econometric time series methodologies. In this paper, Granger causality and co-integration tests were employed in the empirical modelling of seven economic indicators in Nigeria. The results alternated between bi-directional, uni-directional and no causality among the economic indicators considered.
Prior to the Granger causality tests, we tested for stationarity in the variables using the Augmented Dickey-Fuller (ADF) procedure. The variables proved to be integrated of either I(1) or I(2). Johansen co-integration test reveals that at 5% level of significance, we have at least four co-integrating pairs among the variables. This verifies the fact that when two or more time series are co-integrated, there must be either bi-directional or uni-directional Granger causality between them.
Our findings reveal that Government Investment, Real Money Supply and Government Expenditure Granger causes output growth in Nigeria. We finally relate these results with popular postulations in economic theory.
Key Words: Causality, GDP, Co-integration, Prediction, Economic theory.
Causality can be described as the relationship between cause and effect. Basically, the term causality suggests a cause and effect relationship between two sets of variables, say, Y and X. Recent advances in graphical models and the logic of causation have given rise to new ways in which scientists analyze cause-effect relationships (Pearl, 2012).
Runes (1962) highlighted nine basic definitions of causality which was also captured by Hinkelmann and Kempthorne (2008) as follows:
(1)A relation between events, process or entities in the same time series subject to several conditions.
(2)A relationship between events, processes or entities in a time series such that when one occurs, the other follows invariably.
(3)A relationship among variables such that one has the efficacy to produce or alter another.
(4)A relationship among variables such that without one, the other could not occur.
(5)A relationship between experienced events, processes or entities and extra-experimential events, processes or entities.
(6)A relation between something and itself (self-causality).
(7)A relation between an event, process or entity and the reason or explanation for it.
(8)A relation between an idea and an experience and
(9)A principle or category incorporating into experience one of the previous ones.
However, in recent times, Granger causality modelling has received considerable attention and use in many areas of research. Since the concept of Granger (non) causality was introduced by Granger (1969), it has become a popular concept in econometrics and many other fields of human endeavour.
In line with most of the literatures in econometrics, one variable is said to Granger cause the other if it helps to make a more accurate prediction of the other variable than had we only used the past of the latter as predictor. Granger causality between two variables cannot be interpreted as a real causal relationship but merely shows that one variable can help to predict the other one better.
Given two time series variables Xt and Yt, Xt is said to Granger cause Yt if Yt can be better predicted using the histories of both Xt and Yt than it can by using the history of Yt alone. In this paper, we model selected economic indicators using Pairwise Granger causality analysis as proposed by Granger (1969).The rest of the paper is structured as follows: Section two discusses the literature review, section three is on the data and methodology used in the study, section four is on the empirical analysis and results while section five discusses the results and concludes the paper.
2.0 Literature Review.
Many researchers in the field of Time Series Econometrics have used Granger causality procedure to study the causal interactions that exists among economic indicators in various countries of the world. Moreover, several intelligent articles have surfaced in literature on the use of Granger causality tests to analyze time series data since its introduction by Granger(1969).
Some of the articles include: Granger CWJ(1969), Granger CWJ(1980), Granger CWJ( 1988), Swanson and Granger(1997), Entner et al (2010), Mohammed et al(2010), Chu and Chymour (2008), Arnold et al (2007), Eichler and Didelez(2009), Clarke and Mirza (2006), Erdal et al (2008), Pearl(2012) just to mention a few. Others include: Shojaie and Michailidis (2010), Moneta et al (2011),Chen and Hsiao (2010),White et al(2011), Zou et al (2010), Havackova-Schindler et al (2007), Haufe et al (2010), Eichler and Didelez (2007),Cheng(1996),Cheng et al(1997),Toda et al (1994) etc.
Although, flurries of articles have been written on the topic, regrettably, the comparison is usually done among smaller groups of variables. This study tends to contribute to the theoretical and empirical literature on the topic and examines the Pairwise Granger causality analysis of selected economic indicators in Nigeria. We also offer some theoretical economic underpinnings of the related variables involved in the study.
3.0 Data and Methodology.
We used secondary data obtained from the Central Bank of Nigeria Statistical Bulletin in this study.
Data on seven economic indicators were obtained for a period of 35years (1970-2004). The Economic variables considered are: Gross Domestic Product, Money Supply, Investment, Exchange Rate, Inflation Rate, Government Expenditure, and Interest Rate on Lending.
Data on these variables collected over a period of 35 years were subjected to econometric analysis to determine Granger causality by use of bi-variate Vector Autoregressive (VAR) Models. Traditionally, most economic variables are non-stationary; hence unit root tests were performed on all the variables. All the variables were found to be non-stationary and integrated of either I(1) or I(2).
Johansens co-integration test reveals that at 5% level of significance there is at least four co-integrating equations in the study.
Vector auto-regressive modelling approach was used to model the variables.
We determine the best lag length by the use of Akaike Information Criteria (AIC) and Schwartz Information Criteria(SIC).Therefore, we used a lag length of 2 in the study.
Prior to the Pairwise Granger causality tests, we first conduct unit root tests to determine if the variables are stationary and to detect their order of integration.
Granger and Newbold (1974) noted that the regression results from the VAR models with non-stationary variables will be spurious.
We use Johansen and Juselius (1990) test to check for the presence of co-integration among the series. Two time series are co-integrated if there is a long run relationship between them. We then capture the interrelationships among the variables with Pairwise Granger causality tests.
3.1 Steps involved in testing for Granger causality (Gujarati, 1995).
The steps involved in testing for the direction of causality between two economic series say, and are as follows:
1. Regress current on all past values and other variables, but do not include the lagged variables in this regression. Hence, from this regression, obtain the residual sum of squares.
2. Now run the regression including the lagged variable(unrestricted regression).From this regression, obtain the unrestricted residual sum of squares()
3. Test the null hypothesis Ho: i.e. lagged terms do not belong in the regression. 4. To test this hypothesis, we apply the F-test given by;
F = .. (3) This follows the F-distribution with M and N-K degrees of freedom. M is the number of lagged terms and K is the number of parameters of parameters estimated in the restricted regression.
5 If the F-value exceeds the critical F-values at the chosen level of significance, or if the P-value is less than the alpha level of significance, we reject the null hypothesis in which case the lagged values belong in the regression. This is another way of saying that Granger causes . Gujarati (1995) 6 Step 1-5 can be repeated to test model (2) i.e. to test whether Granger causes Xt.
This methodology is highly sensitive to lag length selection when conducting a Granger causality analysis.
4.0 Empirical Analyses and Results.
This section contains the various fundamental results of analysis from this research.
4.1 Unit root tests.
Traditionally, most economic variables are non-stationary; hence we test for the presence of unit-roots using the Augmented Dickey-Fuller tests.
Dickey(1976) and Fuller (1976) noted that the least squares estimator of the VAR model in the Granger causality analysis is biased in the presence of unit root and this bias can be expected to reduce the accuracy of forecasts.
Given an AR (p) process:
which can be written through recursive replacement with differenced terms, as