A Note on Endogeneity Resolution in Regression Models for Comparative Studies

Abstract

We provide a justification for why and when endogeneity will not cause a major bias in the interpretation of the coefficients in a regression model. We give detailed mathematical steps so that our results are instructive to a wide audience. This technique 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. As an illustration of this phenomenon, we look 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. Our results indicate that by looking at the changes in the coefficients, we end up measuring the actual change between the coefficients and hence we are using the correct values to understand how trading costs have altered before and after the event.