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In social science field (particularly Finance and Operations Management), we usually need to prove or disprove hypotheses of the type: X are positively associated with Y. One of the typical method to quantitatively assess this association is regression analysis (i.e. $Y = a_0 + a_1X + \epsilon$ where $\epsilon$ is some error term. The goal is to try estimating $a_0$ and $a_1$ based on some input data and OLS or 2-stage Least Squares, and conduct t-test to measure whether the estimator is statistically significant at a pre-specified significance level (the consensus is 5%)). However, since the goal is to find out whether the association exists and its direction, should we care about potential issues like endogeneity or omitted variables bias? I meant, even when we know that in those cases the estimators given by OLS would give biased and/or inconsistent, don't we only care about the sign of the estimator in order to make the conclusion on association? Same question as above, but in the context of causality.

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