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    • The GMM Difference estimator also known

    2018-10-26

    The GMM Difference estimator – also known as the Arellano–Bond estimator – seeks to address the problem of endogeneity with the technique of instrumental variables. This methodology suggests the estimation in two steps. The problem encountered in GMM Difference is that in most cases the error term is correlated with the lagged dependent variable. Considering this, the Arellano–Bover/Blundell–Bond estimator was designed aiming to improve the model: This extension aims to provide more consistent and efficient estimators, showing that the first-difference estimators of Arellano and Bond are biased due to the use of weak instruments or problems with measurement errors (Baltagi, 2001). The GMM System estimator also improves accuracy and reduces the bias in finite samples. The use of these two methods requires to its’ validation the crucial assumption that the instruments are exogenous. To check the validity of the joint moment conditions it is used the difference in Hansen Test for restrictions of over-identification.
    Presentation and discussion of results The results of dynamic models, GMM Difference and GMM System, are exposed simultaneously with the difference in Hansen Test in Table 3. This test makes the comparison between these two models and its null Sirolimus is that the instruments are valid. The variables Spread and Lnopcred, Inadpf and Varlucro were considered endogenous, since the error term may contain variables that affect the rate of profit of banks as well as amount of loans and the default rate and are not included in the theoretical model. For the dynamic model GMM Difference, shown in the second column of Table 3, the number of instruments was 12 and the p-value for the chi2 test was zero, indicating that the model variables have statistical significance and are able to explain in some measure, the dependent variable Spread. The most significant variables were lagged Spread, Selic, Inapf and Rzpib. Inadpf\'s coefficient has a negative value, as is also the case for Rzpib. This shows that the higher the default rate for individuals, the lower the level of banking spreads, as banks tend to realize that the best solution is to facilitate payment, renegotiating the debts of debtors and reducing the spreads charged to facilitate payment and increase the bank\'s revenue. The increase in profits of banks allows them to reduce their spreads to gain market share. Regarding the variable Rzpib, its negative coefficient is consistent with that found by Nakane (2001), which means that Brazilian banks do not behave competitively, but the results indicated that banks are approaching an oligopoly. Observing tests Arellano–Bond AR (1) and AR (2), which seek to show whether there is or not a correlation of the explanatory variables with the residue, it is possible to note that AR (1) takes on a low p-value of 0.011, showing that there is high correlation as AR (2) has a high p-value of 0.275, meaning that there is not a high correlation. These results match what is expected from the results of this model. Analyzing the test Hansen, note that the p-value of the chi2 test obtained a high value (0.083), meaning that the null hypothesis should be rejected, i.e., the instruments are valid and are not correlated with the error term of the difference equation, and the endogeneity bias was discarded. The final model presented herein is the dynamic model GMM System displayed in the third column of Table 3 that, as mentioned earlier, represents an attempt for improving the GMM Difference model in which, in most cases, the error term was correlated with the lagged dependent variable. This model is also more suitable, as it reduces the bias in finite samples as occurs in this case, resulting in more efficient estimators that have a lower variance. The number of instruments of this model was 17 and the p-value for the chi2 test was zero, showing that the null hypothesis should be rejected and that the variables contained in the model are able to explain to some extent the dependent variable Spread. The most significant variables were the lagged variable Spread and Selic, Inadpf and Rzpib. Variables Inadpf and Rzpib continue to present a negative coefficient.