Regarding that paper, I'm not so sure about this. Moody and Marvell use lagged dependent variables with fixed effects, which are known to be inconsistent. You have to use the Arrelano and Bond estimator if you're wanting to explore the dynamics with fixed effects like that.
The paper also uses the Fryer, et al. crack index, which is good to see. Fryer, et al. mention that application on the last paragraph of the original paper (as well as to use it to re-examine the abortion-crime hypothesis).
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