Reading Freakonomics for the second time I was rather surprised at the lack of statistical evidence I missed during my first reading. The authors Levitt and Dubner merely present a continues stream of anecdotal numbers they introduce as fake statistics, for any actual statistics related to their models they merely mention studies (often which they themselves did). With that in mind I was rather looking forward to reading their actual research and not a watered down version. However this was disappointing, DL used the same technique of presenting a multitude of numbers (not statistics and mostly trends) in establishing not just a correlation between crime and abortion but a casual relation. I was quite glad to read Foote and Goetz rework DL’s regression work; most apparent to me was the omitted variable biases both regressions DL used and also the discontinuity between DL’s regressions that FG only mentioned.

Without doing any regressions myself I would side with FG and the other literature they site as agreeing with them (Sailer, Joyce, Lott and Whitley) that DL’s work is flawed and only shows signs of correlation and in no way causality. DL overlooking the obvious correlation between high crime and high abortion rates, while only looking at a lack of relationship in the trends of crime and abortion rates. They base their causality claims on this. However I find it odd that one would check for a correlation in rates before averages (and not in averages at all), it is merely counter intuitive especially given the plethora of numbers they use in claiming causality. I am much more inclined to believe that they checked for a correlation in average rates of abortion and crime and then neglected the high and significant coefficient because it didn’t fit within their theory of causality. This makes them potential frauds, although no explicit evidence of this exists.

Additionally, I thought the blatant contradiction of the results from their two regressions indicative of fraudulently presenting their findings as significant and casual. The first cross-state regression showed evidence of correlation between abortion and crime rates, while the second regression only shows that states with more abortions (and also more crime to begin with) experienced a sharper relative drop compared to average states. However there was not a significant correlation between crime rates and abortion rates in the regressions done on individual states, this more than anything should have altered DL to potential problems in their regressions.

That said about FG’s and the other literatures critique of DL I had some additional critiques of DL’s work. I felt the critiques of DL operate within the framework DL set out to stringently, mostly be using the same effective abortion measure, a simple summation of all previous abortion rates times a measure of arrest rate for that age group. What this does is potentially introduce a bias for a particular cohort being more violent that another in addition to assuming that the effect of abortion is constant in the propensity to commit a crime over the entire life of a criminal. This might be why DL and FG didn’t run any regressions with data past 1997. What I really want see, in establishing causality is stabilization in the crime rate after 1998, the abortion rate stabilizing in 1980, this follows directly from DL’s theory that abortion has a lagged effect on crime rates of roughly 18 years. In order to demonstrate this and the establishment of a steady state crime rate influenced by abortion rates a new effective abortion term needs to be established; one that demonstrates a constant correlation between criminality and age (this term will need to be raised to a power because of the drop off in criminality rates as age increases) and one that corrects for estimated coefficient between crime and lagged abortion rates. Replacing the summation used by DL and others with an integral yields a differential equation able to find a steady state component in the crime rate if it is truly related to the abortion rate, producing a test for causality. Figure 1 in DL’s paper indicates a very stable steady state in the abortion rate between 1980 and 1990 making this test possible.

Where a_{i} is the population of cohort i, X(i,t) is a measure of the criminality of age group i at time t and A(i,t) is a measure of the abortion rate of age group i at time i (time of birth). A(i,t) is also a function of time since the abortion rate is not constant over 1973-1980 (although this could be inputted directly into a similar model assuming like DL that abortions and criminality have no common factors across time).