TUBERÍAS DE ENTRADA Y SALIDA DE PRODUCTO

This study utilizes three main econometric methods to help in answering the three research questions: (1) Co-integration Analysis, (2) Granger Causality and (3) Ordinary Least Squares (OLS). It is important to state here that before making use of any of the tests, the researcher established that the data is stationary by carrying out a stationarity test to check for the presence or absence of unit roots in the time series. Unit root tests have increasingly become a popular path for determining the elements of macroeconomic time series variables. This development is as a result of the fact that most macroeconomic time series variables display non-stationarity behaviour, which is capable of nullifying the quality of empirical conclusions drawn from such estimates if no suitable measures are taken. Therefore, one class of econometric instrument that has been vital in guarding against the pitfall of spurious regression results arising from non-stationarity of time series variables is the unit

developed by Dickey and Fuller (1981); and the Phillip-Perron test developed by Phillip and Perron, 1988), among others. Taking the foregoing into cognisance, this study commenced its empirical analysis by establishing the stationarity properties of the variables. In this regard, the ADF test was used to infer the number of unit roots (if any) or non-stationarity of the variables, before the co-integration test among the variables were examined. The results of the ADF test are reported in chapter 5 under descriptive data analysis.

4.4.1. Co-integration

Economic and financial time series often exhibit trends. Trends can either be deterministic (i.e. a function of time) or stochastic (i.e. a persistent but random long- term movement) (Fabozzi et al, 2014). To reveal a relationship among economic variables, it is imperative to model changes in stochastic trends over time. Cointegration is used to identify common stochastic trends among different economic variables. If economic variables are cointegrated, it means that they exhibit a long-run relationship. Recall that OLS method requires that variables be covariance stationary. A covariance stationary variable is one in which its mean and variance are constant, and its autocorrelations are finite and do not change over time (Hamilton, 1994; Johansen, 1988, 1995; Fabozzi, et al., 2014). When variables are not covariance stationary, Cointegration analysis provides a framework for interpretation, estimation and inference. Many economic time series appear to be “first-difference stationary” instead of being covariance stationary. This implies that the level of a time series is not stationary, but its first difference is. First difference stationary processes are also referred to as integrated processes of order 1, or I(1) processes. Covariance-stationary processes are I(0). But removing the trend through differencing variables only allows the researcher to make statements about the changes in these variables (i.e. Xt--- Xt-1) rather than the level of these variables, Xt, which is usually of major interest. In addition, if the variables are subject to a stochastic trend, then a focus on the changes in the variables will lead to an error of specification in the regressions. Cointegration technique can be used to examine variables that share the same stochastic trend and at the same time avoid problems of spurious regression.

Since this study aims to examine the financial markets/financial development channel through which FDI may be beneficial to growth, it is important to first

examine the joint movement of FDI, financial development and economic growth. Hence, Johansen’s co-integration analysis (Johansen, 1988; 1995) will be employed to find out if there is a long run relationship between FDI, financial development and economic growth. The Johansen’s co-integration approach is chosen for this study because it allows for more than one co-integrating relationship, unlike the Engle-Granger (Engle and Granger, 1987), which is based on a linear combination of two co-integrating time series, which must be stationary. Johansen’s test is however, subject to asymptotic properties, i.e. large samples. According to Pesaran, Shin and Smith (2001), if the sample size is too small then the results will not be reliable, and Auto Regressive Distributed Lags (ARDL) becomes inevitably necessary. However, since the sample size for this study is greater than 30 (i.e.

T=45), the Johansen-Julius approach will be used to estimate the vector error correction model (VECM). The Engle and Granger two-step Error Correction Model (ECM) is used to check the direction of long run causality where the Johansen's test show cointegration between a dependent variable and the set of independent variables.

4.4.2 Granger Causality

To address research question (1), the Granger Causality test will be adopted in this research study to find out whether FDI is the one that Granger causes growth or whether growth is the one that Granger causes FDI and a period of 45 years (1970- 2014) will be used for this analysis. The Granger Causality approach measures the precedence and information provided by a variable (X) in explaining the current value of another variable (Y). According to Granger (1969), a variable Y is said to be granger-caused by X if given the past values of Y, the past values of X helps in predicting the value of Y. A common method for testing Granger causality is to regress Y on its own lagged values as well as on lagged values of X. The null hypothesis H0 tested is that the lagged values of X do not granger-cause Y. Rejecting the null hypothesis is equivalent to accepting the alternative hypothesis H1 that the lagged values of X actually Granger-cause Y. In other words, the lagged values of X must be statistically significant for causality to exist. Given that the level of impact FDI has on growth may be subject to a minimum threshold level of financial development, it is thus appropriate to check whether FDI itself could contribute to financial development and, in doing so, enhance its chances in stimulating growth (e.g. Omran and Bolbol, 2003). The causality between financial development and

question (3). However, using Granger causality is not without limitations. Lin (2008) show that for causality to hold, two assumptions must be met: (1) The future value of X cannot predict the value of Y. That is, only the past causes the present or future. This largely ignores the role of expectations in shaping the behaviour of economic variables. (2) A cause contains unique information about an effect not available elsewhere.

4.4.3. Ordinary Least Squares (OLS)

The main method used in this study to investigate research question (2) is the ordinary least squares (OLS) technique. OLS will be used to examine the direct effect of FDI and financial development on economic growth and then will also be used to ascertain the role of financial sector development in enhancing the contributions of FDI on economic growth using FDI-Financial Development interaction terms. OLS method is used for estimating the unknown parameters in a linear regression model. The objective of OLS is to closely "fit" a function with the data. It does so by reducing the sum of squared residuals (or errors) from the data (Gujarati, 2003). OLS makes key assumptions about the statistical properties of the data in order for model estimates to be valid and reliable. First, it assumes zero mean value of the disturbance term (ui). That is, given the value of the regressor

(X), the mean or expected value of the random term ui is zero (i.e. E(ui |Xi) = 0).

Second, OLS assumes equal variance or homoscedasticity of ui. Given the value of

X, the variance of ui is the same for all observations. That means, the conditional

variances of ui are identical. Third, OLS assumes no autocorrelation between the

disturbances. Given any two X values, Xi and Xj (i≠ j), the correlation between any

two ui and uj (i≠ j) is assumed to be zero. Fourth, the regression model is specified

correctly.

Alternatively, there is no error or specification bias in the model used in conducting the empirical analysis. Here, the bias refers to choosing the wrong functional form. Fifth, there is no perfect multicollinearity. That means, there are no perfect linear relationships among the explanatory variables. These and many other assumptions must not be violated if OLS technique is to be reliable and valid (Gujarati, 2003). As noted in chapter 2, there are several problems encountered when estimating a typical Cobb-Douglas production function or economic growth models using OLS techniques, including problem of collinearity, the mix of stationary and non- stationary variables as well as endogeneity. Some of the measures taken in this study to overcome all these problems include conducting preliminary tests for

normality, unit root, multicollinearity and other postestimation tests to check the shape of the residuals (error terms). Key variables which did not follow a normal distribution were transformed while non-stationary variables were made stationary before running the regressions. In addition, duplicate variables that were highly collinear were either treated or removed to avoid any spurious regressions.