CHAPTER III RESEARCH METHODOLOGY
3.6 Panel Data Model
Panel data combines cross-sectional data and time series data which is also known as longitudinal data. Its observations involve the cross-section dimension (indicated by subscript i) and time series dimension (indicated by subscript t). A panel is said to be a balanced panel when each subject has the same number of observation and conversely, it is an unbalanced panel when there is different number of observation of each entity. When the number of cross-sectional subjects N is greater that the time periods T, it is knowns as a short panel; when T is greater than N, then it is a long panel. There are few advantages of using panel data analysis. Panel data normally provide more informative data, more efficiency and more variability by combining both cross-sectional and time series data.
Besides, panel data includes the information on both the intertemporal dynamics and the individuality to the entities may allow one to control the effects of missing or omitted variables (Hsiao, 2007; Gujarati & Porter, 2009). This method can achieve the specific objective one and two of the study (for NR world production and consumption models).
3.6.1 Fixed Effect Model (FEM)
Fixed effect model (FEM) is a statistical model that in that particular model, the parameters are fixed (non-random) quantities. FEM is used normally when we want to analyze the impact of variables that vary over time, and it also explore relationship between predictor and outcome variables within an entity (country, company, person, etc.). In a FEM, the unobserved variables are
tolerable to have any associations whatsoever with the observed variables. FEM also control for, or partial out, the effects of time-invariant variables with time- invariant effects (Wooldridge, 2001; Verbeek, 2008). The equation for the FEM is as shown below:
(3.6)
Where is the unknown intercept for each entity (n entity-specific intercepts); is the dependent variable where i = entity and t = time;
represents one independent variable; is the coefficient of independent variable;
and is the error term.
3.6.2 Random Effect Model (REM)
Unlike FEM, in random effect model (REM), the variation across entities is assumed to be random and uncorrelated with the predictor or explanatory variables in the model (allows individual effect). REM could be used when it is believed that differences across entities have some influence on the dependent variable. The crucial distinction between fixed and random effects is whether the unobserved individual effect embodies elements that are correlated with the regressors in the model, not whether these effects are stochastic or not (Wooldridge, 2001; Verbeek, 2008). An advantage of random effects is that you can include time invariant variables such as gender; in the FEM, these variables are absorbed by the intercept. The equation for the REM is as shown below:
(3.7)
Where the is between-entity error while is within-entity error.
3.6.3 Hausman Test
Hausman (1978) has suggested a test to examine whether FEM or REM is preferred for the panel data analysis. Hausman Test is sometimes described as a test for model misspecification. It is usually applied by researchers to test for FEM and REM and compare directly the random effects estimators to the fixed effects estimators . The null hypothesis is that the preferred model is a REM and the alternative is that the FEM is preferred. Test hypotheses are as follows:
H0: REM is preferred HA: FEM is preferred
It basically tests whether the unique errors are correlated with the regressors, the null hypothesis is that they are not, while the alternative is that they are correlated. In the presence of a correlation between the individual effects and the regressors, the GLS estimates are inconsistent, while the OLS fixed effects results are consistent. If there is no correlation between the fixed effects and the regressors, both estimators are consistent, but the OLS fixed effects estimator is inefficient (Wooldridge, 2001; Verbeek, 2008; Gujarati &
Porter, 2009). In this study, before moving to data analysis part, data has been used to test run the models. Results from Hausman test showed that FEM will be preferred in this study.
3.6.4 Panel Cointegration Test
Like the panel unit root tests, panel cointegration testes can be motivated by the search for more powerful tests than those obtained by applying individual time series cointegration tests (Verbeek, 2008). There are several cointegration tests developed in panel data such as the Kao (1999) test, Pedroni (1999, 2004) test.
Kao (1999) and Pedroni (1999, 2004) extend the Engle-Granger framework to test involving panel data. The basic ideas of Engle Granger are to examine two I(1) series and to see if the residuals of the spurious regression involving these I(1) series are I(0). If this is so, then the series are said to be cointegrated; but If the series are I(1) then the variables are not cointegrated. A test for the null hypothesis of no cointegration can be based on an ADF type unit root test based on residuals.
Firstly, the Kao (1999) test is developed to test the cointegration in homogeneous panels. The Kao test statistics are calculated by pooling all the residuals of all cross-sections in the panel, and it is assumed that in Kao’s test that all the cointegrating vectors in every cross-section are identical. The regression equation is as below:
(3.8) Where individual constant is term and is the slope parameter. On the other hand, Pedroni (1999, 2004) suggested several panel cointegration tests
tolerate heterogeneity. The benefits of Pedroni’s tests are: it allows multiple regressors, for the cointegration vector to vary across different sections of the panel, and also for heterogeneity in the errors across cross-sectional units. The panel regression model that Pedroni proposes is as below:
(3.9) Where t=1,2,...,T and n=1,2,…,N and m=1,2,…,M. Y and X’s are assumed to be integrated of order one I(1). The individual and trend effect
may be set zero if desired.