A Tale of Two Comparisons, Before and After or This and That : A Case Study and Step By Step Guide for Endogeneity Resolution in Regression Models

We demonstrate the use of comparative studies to resolve endogeneity issues. We provide a simple way to statistically test the corresponding condition which can help to ascertain that endogeneity is not posing any issues in a regression analysis. We give a step by step guide that can be illustrative to anyone looking to mitigate, or completely remove, the effects of endogeneity by designing appropriate quantitative models for their research problems.Our approach provides a justification for why and when endogeneity will not cause a major bias in the interpretation of the coefficients in a regression model. This technique, of conducting econometric analysis, can be a viable alternative or even used alongside the instrumental variable method. We show that when performing any comparative study, it is possible to measure the true change in the coefficients under a broad set of conditions. This happens as long as the co-variance structure among the explanatory variables and the co-variance between the error term and the explanatory variables are comparable within the same system at different time periods or across multiple systems at the same point in time. To illustrate this phenomenon, we have conducted a numerical case study. We have looked at the effect of the tick size changes on the TOPIX 100 index names made by the Tokyo Stock Exchange on Jan-14-2014 and Jul-22-2014. This event is an example of financial services marketing. Our results indicate that by looking at the changes in the coefficients, we end up measuring the actual change between the coefficients. Hence we are able to understand more precisely how trading costs are affected by this event and gauge the efficacy of this marketing initiative