Methodology, Explanation of GGM, GLS and Endogeneity Analysis - Case Study Example

Methodology, Explanation of GGM, GLS and Endogeneity Analysis Name: Institution: GLS, GMM and Endogeneity Analysis 1. Generalised Least Squares (GLS): Generalized Least Squares (GLS) longitudinal panel regression with robust standard error is carried out to the test of the research hypotheses. GLS is a technique for estimating the unknown parameters in a linear regression model. It is applied when the variances of the observations are unequal or when there is a certain degree of correlation between the observations. Unequal variances may exist due to the presence of outliers and skewness. Therefore, it is preferable to give less weight for observations arising from populations with greater variability than the weight given for observations from populations with smaller variability. It is cloud be better to mentioned that OLS does not make use of the information pertaining to the unequal variability of the dependent variable as it assigns equal weight to each observation (Gujarati, 2003). In addition, the advantage of panel data regression is that it takes the time effect into account. The robust standard error option is applied in order to adjust the GLS parametric test to fit with non-parametric data. Use of GLS to test corporate governance (independent variables) In order to use GLS model to test corporate governance, the main independent variables used include: gender diversity that is measured as a percentage of female directors involved in the board membership. Another independent variable is ethnic diversity that is measured in terms of the number of people from different ethnic backgrounds in the board. Board size is measured in terms of the number of directors in the board in a specific financial year. The variable of return on assets (ROA) is used where it measures the net profit compared with the assets of the company, GNENDISTY which is a variable that measures the percentage of female directors in the board and BOARDCOM that measures the composition of the board by taking into account the number of non-executive directors as a percentage of the board size. 1Alterovitz, G., Benson, R., & Ramoni, M. F. (2009). Automation in proteomics and genomics: An engineering case-based approach. Chichester, West Sussex, U.K: John Wiley. In order to apply the GLS model to determine the relationship between the diversity of the independent variables, the following formula is used: Yit = αo + β1X1it + β2X2it + Cit + µit….where Y is a measure of performance of an organization, α is an intercept coefficient, β is a vector coefficient of the board diversity, X1 is a vector measure of the board diversity and β2 is a vector coefficient of the control variables. Subscripts such as I and t are specific error coefficients relating to firm i in year t. U is the remaining error component. When various independent variables are introduced into the equation, it becomes: Firm performance = αo + α1GENDISTYit + α2ETHDISTYit + α3FRGNDIRit + α4BOARDCOMit + α5BOARDSZit + α6BOARDSZSQit + α7DIROWNRit + α8DIROWNRSQit + α9FAMDIRit Ci + µit…. In the above equation, αo represents the intercept, GNEDSITY measures gender diversity, ETHDISTY measures ethnic diversity, FRGNDIR measures the effect of foreign directors, BOARDCOM is a variable that measures the composition of the board, BOARDSZSQ is a variable that measures the square of board size and DIROWN is a variable that measures the ownership of directors. FAMDIR is a variable that measures the family directorship in the organization and C is a unit specific component or error. µ represents the remaining error component. On disclosure quality (dependent variables) The disclosure of the quality of dependent variables is determined by using the values that have been multiplied by the various coefficients in the equation: Firm performance = αo + α1GENDISTYit + α2ETHDISTYit + α3FRGNDIRit + α4BOARDCOMit + α5BOARDSZit + α6BOARDSZSQit + α7DIROWNRit + α8DIROWNRSQit + α9FAMDIRit Ci + µit…. 2Buliung, R., Dall'erba, S., Gallo, J. ., & Páez, A. (2010). Progress in spatial analysis: Methods and applications. Berlin [u. a.: Springer Berlin. 3McPherson, G., & McPherson, G. (2001). Applying and interpreting statistics: A comprehensive guide. These values are then used to obtain rations that enable understanding of performing loans from non-performing loans. For instance, for performing loans, a ratio of 11.9 or above is required in order to ascertain that a firm is performing well. Financial performance (dependent variables) During the measure of financial performance the main dependent variable used is the Tobin’s Q value that is determined by finding the ratio of the sum of all assets, market value equity minus book value equity minus deferred taxes divided by total assets. Another dependent variable is the Return on Assets (ROA) that is measured by dividing the earnings after tax by total assets. Return on equity is another dependent variable that is measured by dividing the earnings after tax by the total equity. The actual values of the parameters of the formula are obtained by multiplying them with the coefficients in the equation: Yit = αo + β1X1it + β2X2it + Cit + µit after which they are substituted into the formulas. Control variables In order to apply the GLS model effectively to understand corporate governance, a number of control variables can be used. An example of a control variable is sales of the company that is measured in terms of the overall sales in a particular period, turnover that is measured by getting the ratio of net sales to total assets; and Industry dummies. This is achieved by two components are used to separate variance of residuals; these include model error variance, that measures the precision of the true model in predicting the flood quantiles and the error in sampling of flood quantile estimates. During the process of estimating quantiles, a region that contains N gauging stations flood peaks are noted as Q1…..Qn. Each site has a flow that is given as I and it is assumed to be independent and identically distributed. There may be concurrent observations at various sites. The records from each site must be less than 100 years old. The main aim of GLS regression model is to provide an analysis and identification of the best model that facilitates understanding of flood quantiles such as 100-year peak flow at a particular site considering k basin characteristics. The basin characteristics are measured with negligible error. The distribution or error is assumed to be normal and independent with a mean of zero and a variance of σ2. 2. Endogeneity: Endogeneity exists when independent variables are correlated to error terms (e.g. Roberts and Whited, 2011; Li, 2011). Thus, it is comprised of three main elements: omitted variables, simultaneity and measurement error (e.g. Li, 2011; Roberts and Whited, 2011; Brown et al., 2011). Li (2011, p. 9) found omitted variable problems can be mitigated if “unobservable determinants of” independent variables are controlled in the model. Concerning simultaneity, most of the prior literature suggests the use of a simultaneous system of equation (e.g. Farooque et al., 2010; Cornett et al., 2008) or an instrumental variable regression (e.g. Li, 2011; Yu, 2008; Brown et al. 2011). Measurement error, which is defined as the “discrepancy between the true variable of interest and the proxy” (Roberts and Whited, 2011, p. 13) could be mitigated by the use of a valid measurement for a specified proxy. Endogeneity analysis has been identified as an important analysis for estimation of parameters so that consistent estimates can be obtained. The problem of endogeneity arises when deriving discrete models such as probit, logit and nested logit. Endogeneity also arises when the variables under exploration are not independent of factors that have not been observed. Endogeneity analysis ensures this is taken into account so that inconsistent parameters are avoided. An example of an approach used in endogeneity analysis is the maximum-likelihood method. In this method, a ‘new statistical instrument-free strategy is used in estimating endogeneity problem. 4Ries, K. G., Massachusetts., & Geological Survey (U.S.). (1994). Development and application of generalized-least-squares regression models to estimate low-flow duration discharges in Massachusetts. Marlborough, Mass: U.S. Dept. of the Interior, U.S. Geological Survey It involves modelling the joint distribution of the endogenous regressor and the structural error term using a Gaussian copula and density estimates in construction of marginal distribution of the endogenous regressor. Another method that has been used during endogeneity analysis is the BLP approach that deals with endogeneity when discrete choice models are used. It also involves introduction of a social influence variable in a behavioural model that is endogenous. BLP approach is also used in correcting price endogeneity in automobile ownership choice. Endogeneity analysis is also used during estimation of maximum simulated likelihood and instrumental variables. This is where various parameters are estimated using contraction method. When the model has been estimated, the parameters are implemented during linear regression and estimates of factors affecting price are made. Due to the fact that price is endogenous in the repression, instrumental variables can be used. In addition, maximum likelihood aprach can be used during endogeneity analysis. This is where the parameters of the model are determined using simultaneous approach rather than two stages. When various approaches in endogeneity analysis are compared, it is found that BLP approach is the simplest but it has a number of limitations thus, it is not always commonly used. The main components of GMM model include the column vector of empirical moment condition that is determined by a parameter designated as β. The objective function in this model is quadratic and the weighting matrix is important in a situation where there are many moment conditions than parameters to choose as well as illustrating the trade-offs between empirical moments during selection of β. Thus, it observed that GMM has a number of familiarities with estimation methods such as OLS and TSLS. 5Timm, N. H. (2002). Applied multivariate analysis. New York: Springer. 3. Generalized Method of Moments (GMM): (The dynamic difference GMM model) Generalized Method of Moments (GMM) is a dynamic panel approach which takes account of the impact of past disclosures quality on the current one on the section of the effect of corporate governance on disclosure quality. Also, it is applied the same technique for the influence of corporate governance on financial performance. However, the dynamic difference GMM model it was employed for this research. The GMM procedure, as developed by Hansen (1982), provides a non-parametric approach to estimating model parameters. GMM is an appealing approach to modeling the governance–performance relation as it imposes no distributional assumptions on the model specification. As such, GMM standard errors are robust to autocorrelation and heteroskedasticity of unknown form. Under mild regularity conditions, the orthogonality conditions of the population model are specified and the sample analogues set equal to the population moments. The necessary exogeneity assumption required to produce consistent parameter estimates is determined by the choice of instruments outlined in the orthogonality conditions. An appealing aspect of the GMM estimation procedure is that, if a suitable instrument set is implemented in the orthogonality conditions, it is possible to produce estimates that are robust to simultaneity. Moreover, slight transformations of the equation of interest can overcome the biases introduced by unobservable heterogeneity and dynamic endogeneity. Holtz-Eakin et al. (1988) and Arellano and Bond (1991) developed the difference GMM specification for dynamic panel datasets that produces consistent parameter estimates in the presence of endogeneity. These estimates are robust to dynamic endogeneity, firm fixed-effects, endogenous regressors, heteroskedasticity and serial correlation in the innovations of firm performance. A desirable property of the difference GMM is the use of internal instruments that are embedded in the existing dataset, and hence, are readily available to the econometrician. Moreover, all variables are time differenced so that unobservable firm characteristics are eliminated without the necessity for strict exogeneity assumptions, allowing for the inclusion of the lag of the dependent variable on the right-hand side to account for any possible dynamic endogeneity. Well recognized authorities in the field are contributors to the volume and they are based in Australia, Europe and North America. GMM offers a method which is computationally convenient for the estimation of the statistical models parameters on the basis of the data in conditions of population moments (Alterovitz, Benson & Ramoni, 2009). Its structure has made it precisely common in econometrics for the reason that competing economic theories every so often infer that variables of economic live up to diverse collections of population moment conditions. The particular outline of these population moment conditions is dependent on the framework however the generic outline of the GMM estimator is similar in all events. The flexibility of GMM implies that it has been employed in areas which are diverse such as labour economics, environmental economics, agricultural economics, finance and macroeconomics. The extensive use of GMM in econometrics has in cooperation been expedited and motivated through the development of various statistical inference procedures based on the estimators of GMM. Such interpretations sanction scholars, among others, to test the consistency of the data with the population moment conditions (McPherson & McPherson, 2001). Additionally, GMM incorporates other clearly distinguished estimators, for instance maximum likelihood, instrumental variables, and least squares. For this reason, GMM offers a useful context for considering overall facets of inference in addition to estimation in statistics. Furthermore, GMM is turning out to be the predominant language of econometric dialogue. References Alterovitz, G., Benson, R., & Ramoni, M. F. (2009). Automation in proteomics and genomics: An engineering case-based approach. Chichester, West Sussex, U.K: John Wiley. Buliung, R., Dall'erba, S., Gallo, J. ., & Páez, A. (2010). Progress in spatial analysis: Methods and applications. Berlin [u. a.: Springer Berlin. McPherson, G., & McPherson, G. (2001). Applying and interpreting statistics: A comprehensive guide. Ries, K. G., Massachusetts., & Geological Survey (U.S.). (1994). Development and application of generalized-least-squares regression models to estimate low-flow duration discharges in Massachusetts. Marlborough, Mass: U.S. Dept. of the Interior, U.S. Geological Survey. Timm, N. H. (2002). Applied multivariate analysis. New York: Springer. Wooldridge, J. M. (2007). Solutions Manual and Supplementary Materials for Econometric Analysis of Cross Section and Panel Data. 2nd Edition. Read More