Methodological Critique of OLS in Recent Abortion/Crime Papers

Although admittedly a bit technical, for an exceptionally important methodological critique of a series of recent papers exploring the relation between abortion and crime rates, see Numerical Analysis in Least Squares Regression With an Application to the Abortion-Crime Debate. In it, Bill Anderson (Cornell) and Marty Wells (Cornell) take up limitations with OLS that are especially salient to social science in general and empirical legal scholarship in particular.  From the abstract:

"The more ill-conditioned the data are, the more sensitive the computed solution is to perturbations in the data, and the more unstable the computed solutions are. Condition numbers can also be used to signal the presence of solution degrading collinearity in regression problems. We apply the various numerical analysis tools and model diagnostics to the abortion-crime debate, and show the regression analysis used in various papers addressing the abortion-crime debate can not be trusted."