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Panel data, also called longitudinal data or cross-sectional time series data, are data where multiple cases (people, firms, countries etc) were observed at two or more time periods. There are two kinds of information in cross-sectional time-series data: the cross-sectional information reflected in the differences between subjects, and the time-series or within- subject information reflected in the changes within subjects over time. Panel data regression techniques allow taking advantage of these different types of information23.

3.4.2 Fixed Effects Regression

Fixed effects regression is the model to use when we want to control for omitted variables that differ between cases but are constant over time. It lets us to use the changes in the variables over time to estimate the effects of the independent variables on our dependent variable, and is the main technique used for analysis of panel data. In order to decide which method we should use we applied the Hausman test which is proposed by Hausman (1978) about the correlation between regressors and the individual effect. This is an important test to check weather observed and unobserved explanatory variables are correlated. Even the estimators are correlated with the individual effect fixed effect estimator is consistent but random effect

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is not. So we test null hypothesis that individual effect and explanatory variables are uncorrelated against the alternative hypothesis where individual effects and explanatory variables are correlated. Based on the Hausman test we reject the null hypothesis and statistically prefer the fixed effect estimation.

3.4.3 Generalized Method of Moment (GMM)

As suggested by Anderson and Hsiao (1981) Generalized Method of Moment can be used to estimate the dynamic model with instrumental variables in the first differenced fixed effect model.

The generalized method of moments is a very general statistical method for obtaining estimates of parameters of statistical models. It is a generalisation, developed by Lars Peter Hansen of the method of moment. The GMM estimator is widely used in the estimation of the dynamic panel data model in recent years (Bond et al, 1997; Hall et al, 1998;Ozkan, 2001). GMM can be used to estimate the dynamic model with instrumental variables in the first differenced fixed-effect models suggested by Anderson and Hsiao(1981). We now move on to the discussion of this method24.

3.4.3. 1 Description

The idea of the GMM is to use moment conditions that can be found from the problem with little effort. Like any other estimation methods, such as OLS and maximum likelihood (ML), require a theoretical relation that the parameters should satisfy. By choosing parameter

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estimates, the sample correlation between the instruments and the function of parameters is satisfied as closely as possible. The theoretical relation is replaced by its sample counterpart and the estimates are chosen to minimize the weighted difference between theoretical and actual value.

3.4.3.2 GMM estimator in the first difference equation

There is evidence25 that OLS method is inappropriate to estimate our dynamic model. First, the serial correlation test reveals that the assumption of serially uncorrelated errors is violated and this suggests some degree of misspecification. Second, there is evidence of a negative coefficient of the lagged dependent variable in the OLS level specification. This is surprising since the lagged dependent variable is expected to be biased upward due to correlation with the unobservable fixed effects. In the presence of firm specific effects OLS coefficients are biased assuming that α is unobservable and covariances between regressors and α are nonzero (Hsiao, 1986). Also, OLS will result in inconsistent estimation of the coefficient parameters since yi,t-1will becorrelated withαi which is constant. In order to eliminate the specific effects

it is required to take the difference and avoid this problem. OLS regression does not consistently estimate the parameters because (yi,t-1- yi,t-2) and (ɛit - ɛi,t-1) are correlated through

terms yi,t-1 and ɛi,t-1. Anderson and Hsiao(1982) recommended a consistent estimation

technique which requires using ∆yi,t-2 = (yi,t-2- yi,t-3) or yi,t-2 as instruments for the first

difference of the lagged dependent variable where both are correlated with (yi,t-1- yi,t-2) but

uncorrelated with (ɛit - ɛi,t-1). If the error term ɛit in levels is not serially correlated the

instrumental variable estimation will result in consistent estimates. As it fails to utilize all the

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available moment conditions the instrument variables estimation does not essentially lead to efficient estimates of the model parameters.

Generalized Method of Moments (GMM) estimation technique use Arellano and Bond (1991) which employs additional instruments obtained by utilizing the orthogonality conditions that exist between the lagged values of the dependent variable and disturbances. They study the performance of these estimators and show that the GMM estimates result in smaller variances than those associated with the Anderson and Hsiao type instrumental variable estimators. The GMM estimators allows the instruments to use in each period to increase as one moves through the panel, whereas the Anderson and Hsiao type estimators uses only ∆yi,t-2 to

instrument ∆yi,t-1. The set of valid instruments change depending upon the assumption

concerning the correlation between Xikt and ɛit. It is suggested that the valid instruments for

period t for the equation in first differences will be Zit = (yi,…., yi,t-2, Xik1,…, Xik,t-1) under the

assumption that ɛit. is serially uncorrelated, and Xikt is predetermined. That is ,E(Xikt ɛis) ≠ 0 for

all t,s then all X’s are valid instruments. In this case Zit become (yit,…., yis, Xik1,…, XikT) where s=

1,….T-2.