Econometrics for Corporate Social Responsibility

Question: Describe about panel data- fixed and random effects. Answaer: The methodology advocates the other aspects that contributes to the paper. The methodology applied in paper is panel data, which includes both temporal heterogeneity and the individual heterogeneity. The former allows controlling the macro economic effects whereas the latter allows controlling the individualistic characteristics of the firms (Hsiao, 2014). Moreover, the methodology used considers the dynamic performance of firms. However, review studied the firm performance and its effect of CSR based on cross sectional data. On the other hand, panel data has been taken to elaborate the association between CSR and firm performance to solve the problem of inherent endogeneity so that the results obtained are robust as well as consistent in nature (Madorran Christina, 2016). However, CSR and firm performance have received much consideration in the literature. Panel data has been carried out in the study to test the hypothesis on the methodology that allows taking into account both the temporal as well as unobservable individual heterogeneity. However, individual heterogeneity at one point becomes difficult to study the firm level features that directly affect the controlled firm value (Kessler, 2014). This technique not only provides a complete information regarding the testing of hypothesis but also allows the stated facets to be taken into account. The outcomes obtained are more pertinent than the cross sectional data used in the literature. Nevertheless, one-period lagged performance has been used in order to include the dynamic performance indicators to measure the persistence level of performance of the parameter. CSR is an indicator of the firm i in t-1 years. The lag has been introduced in the model because CSR efforts do not immediately affect the firm performance rather the result is reviewed later. The choice of methodology has been performed to achieve the significant objectives based on the efficiency of the results. However, panel data applied in this context has been incorporated due to four reasons. Firstly, it includes dynamic characteristics of the variables in the underlined analysis. Secondly, the times effects has been used as a variable of the year to introduce undetected individual effect in the individual heterogeneity. Hansen Over identification Test - The dynamic model can be estimated based on two generalized step of moments that not only provide an efficient yet consistent estimator but also addresses the impending endogeneity in the model. The instruments in lags in independent variable are considered from t 1 whereas the lags in dependent variable are considered from t 2 (O'Neill Hanrahan, 2016). However, Hansens instruments validates the statistic results through the over identification chi square distribution. The test involves degrees of freedom that are equal to the number of over-identifying limitations. Nonetheless, in order to remove the individual effects it is important that individual effects be associated with the remaining variables based on the first differences of the variables (Corredor Goi, 2011). Error Correction Procedure by Windmei - On the other hand, the model estimation for error correction is carried out on the small samples. The correlation in error terms m1 and m2 is for serial correlation in order of 1 and 2 respectively that has been calculated using fist differences in the residuals. These tests are asymptotically distributed as N (0, 1) under the statement of no serial correlation in null hypothesis and m2 is calculated following Arellano (Roodman, 2015). Wald Statistics On the other hand, the coefficients offer the Walds statistic based on z1 and z2. z1 statistic is used for shared significance of the model whereas z2 is used for shared significance of the time dummies. However, both the statistics just like Windmei Error Collection Procedure, the statistics are normally distributed as under null hypothesis as a chi square of no joint significance. However, all these statistics are executed using STATA, statistical tool (Hernndez-Cnovas, Mnguez-Vera Snchez-Vidal, 2014). Alternatively, the other way of evaluating a longitudinal or cross sectional data is with the help of pooled OLS regression treats the regression of y on x using controlled variables. However, it ignores the structure followed by the panel data such that the pooled regression omits the invariant unobserved variables from the study. Hence, it is important that all the unobserved variables be controlled for the probable influence by the generalized least square random effect regression model (GLS-RE). GLS-RE regression with OLS assumes to have no correlation between explanatory variables as well as error terms but it takes into consideration unobserved variables that will not only be constant over time but also will vary between companies while others may not be just constant between companies but might vary over time (Hagen Waldeck, 2014). However, as stated, it is observed that GLS-RE ought to violate the auto regression correlation of the least square. Comparatively, GLS-RE regression is appropriate to control the influence of the time-constant variables that often face the problem of serial correlation in the error term. The assumptions that hold efficient in the given nature of the data such that it follows the order to analyse the use of RE estimator. The error term e is a composite error terms that comprises of both time-varying (mit) as well as time-constant (ai) firm specific variable such that e as ai mit are uncorrelated through time. The unobserved effects (mit) and idiosyncratic errors (ai) are assumed to be uncorrelated with independent variables across all time periods (strict exogeneity) The unobserved as well as observed variables are randomly drawn from the certain distribution. Furthermore, in order to ensure the assumption, the researcher has forecasted the residuals with the predict command to plot a histogram of r for visual analysis. However, to ensure the results validity as well as clarity, the test of Shapiro-Wilk W-test had been conducted. The W statistics in the test specifies normality if the value of W is close or equal to one given that the null hypothesis states that r is normally distributed. The results and null hypothesis will not be rejected if the p value comes greater than 0.05 (Hanusz, Tarasinska Zielinski, 2016) The validity of the results can further be proven by other tests. Tests like Breusch-Pagan Lagrange multiplier (LM) is needed to check the validity of random-effect estimator. This test has been designed not only to check the efficiency and validity of the RE models but has also been designed to test the efficiency in conducting unobserved heterogeneity. In this particular test, the square of the residuals (error term) are regressed on the independent variables. The null hypothesis for the particular tests states that the variance across the regression equation is zero (Ho: 0; no substantial dissimilarity across units) (Baltagi, Feng Kao, 2012). Moreover, if the test failed to reject the null hypothesis then RE model will be considered not suitable for the evaluation. Conversely, the test assumes to favor Random Effect Estimator if test is significant at 1% confidence level. The regression in LM tests are run according to the standard error that will spontaneously modify all standard errors as well as p-values looking for any possible problem of outliers, heteroskedasticity and other irregularities and lately mend the rationality of the results. As dependent variable helps in acknowledging the financial performance of the firm. As a result, the factors are controlled thoroughly such that it does not affect the financial performance. However, those variables are included that not only affect the financial performance of the firms but also controls the unobservable with fixed combination effects like firm, year and industry. The econometric specification will be discussed in the following section below. To choose a multivariate statistical method, the research starts form the OLS (Ordinary Least Square) specification in which firstly, the firms performance will be specified (Performit) as a function that is linear in nature with vector X of explanatory/ independent variables from time t of the firm i additional to the error term uit. As provided by the panel structure of the data, the major possibility arises that all the error terms will be correlated with firms over time. This kind of serial correlation paves way to spurious regression results (Wooldridge, 2015). To deal with serial correlation the model will now turn into a dynamic longitudinal model. This model will incorporate lags in linear autoregressive dynamics of dependent variable as regressor to encompass performance for within-firm persistence. Explicitly, to incorporate lag of one-year in the dependent variable then the within-firm AR (1) process will be followed in every specification. The within-firm serial correlations addresses the dynamics of AR(1) such that there is probability that error term (ei) across time will not be independent. However, any effect related to time-dependence that is not included in X will incorporated in the error term. However, the earlier researches have studied that there are many macro-economic factors that are linked with performance constituting of changes in systemic, government policy as well as macro-economic shocks. There is a need to measure all these effects with the corresponding time componenet so that it can be considered in the error term (eit). As a result, this methodical component will lead to correlation in the error terms that will violate the assumptions of OLS. Theoretically, the decomposition of error term (eit) into fixed time effects vector such that it will be labelled as Zt where Zt will symbolize dummy variables of the year with v.i.t as vector term and i.i.d as normal error terms with mean equal to zero. The equation will represent the eit decomposition (Bai Wang, 2015). As a final point, there is still a strong possibility that vector term (v.i.t) will not be independent of within industries or firms. This states that due to any occurrence if these firms operate in a different manner methodically due to transient factors that are long term in nature then there will be unobserved heterogeneity. However, to correct this, the fixed effects will come into play in industry/ firm according to the specifications (Ertur Musolesi, 2012). However, the final economic specification can be summarized based on within-firm AR (1) dynamics, fixed industry/ firm and fixed effects in year to control the features that are not restrained by other variables that might associate with the performance of the firm (Huang, 2013). This possible benefit of the approach is that it not only controls for unobserved heterogeneity without measuring the source of heterogeneity but also eliminates bias and provides strong estimates is statistical results. The possible drawback of this approach is that it is difficult to specify as well as identify different individual factors that will affect the dependent variable. Nevertheless, the goal is to not to test these effects or control the effects then the tradeoff will be accepted. The concerns relating to unobserved heterogeneity and autocorrelation are associated with panel data. However, to solve these issues, standard techniques are applied. Initially, Hausman test was conducted to provide a proper estimation method but the results depicted correlation issue between regressors and error (Marvel Pitts, 2014). Nonetheless, to solve this issue, firm fixed effects models were suggested over the random effects model for statistical evaluation. However, to test the validity as well as the efficiency of the findings, the outcomes reported were associated and compared to the random effects model results. As a result, the results obtained were lower from the perspective of random effect model based on the magnitude, significance levels as well as largely consistent coefficients. Therefore, the reported estimates are considered conservative using the fixed effects model. However, with any further correction in the potential autocorrelation might lead to biased param eter estimates in time series data and might vary over time to control the effects that assumes to be constant across firms and by adding year dummy variables, a time fixed effects was also incorporated. References Bai, J., Wang, P. (2015). Econometric Analysis of Large Factor Models. Baltagi, B. H., Feng, Q., Kao, C. (2012). A Lagrange Multiplier test for cross-sectional dependence in a fixed effects panel data model.Journal of Econometrics,170(1), 164-177. 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