Saturday, March 27, 2010

Getting even on crack vs. powder

Boston Globe editorial "Getting even on crack vs. powder" (March 27th, 2010) discusses a possible gap between legal penalties for possession of crack cocaine and possession of powdered cocaine. It discusses the penalties between the two, and how there was a "100-to-1" penalty for holding crack. Corrections sees the matter as slightly more nuanced than the Globe allows.

The political wheels have begun to turn on correcting the imbalance in sentencing those who possess crack and powder cocaine, but more attention is necessary. Under current law, a person caught with five grams of crack gets the same five-year mandatory prison sentence as someone possessing 500 grams of powder. The 100-to-1 crack-to-powder ratio was enacted at a time that crack was thought to be far more addictive than powder and would spark unprecedented crime waves. Studies long ago disproved both notions, but the law remains on the books, and its burden falls disproportionately on black defendants. More than 80 percent of those incarcerated for possession of crack are black.

We noted in a previous post that addictive substances such as crack cocaine were a technological advancement on cocaine. It allowed for small cheap, unobtrusive, mass distribution in a way cocaine did not, a point lifted from Roland Fryer, Paul Heaton, Steven Levitt, and Kevin Murphy’s 2005 NBER working paper “Measuring the Impact of Crack Cocaine.” It is not immediately clear whether or not this phenomenally destructive drug would have been as prevalent as it was were cocaine itself not illegal. On the one hand, cocaine is an input into crack cocaine production. On the other hand, cocaine is a substitute to crack cocaine itself, one whose competitive availability is likely increased much more than crack cocaine’s, in light of crack’s popularity being in part due to cocaine’s inefficient illegal distribution system.

Crack cocaine is a technological advancement on cocaine--distribution is made easier. Therefore, it may make sense to "tax" it at a higher rate, if one catches individuals who deal in it much less often. That is, if one is caught half as often with crack cocaine, then a doubling of the sentence may "equalize" the penalties between the two crimes, an objective the Globe seems to pursue.

Corrections might further add that the law-race discrepancy may have less to do with politician racism than it might have to do with endogenous selection into drug markets. Let us imagine that individuals have three choices: to work for wages in the "above ground" economy (legal), to work selling powdered cocaine (powder), and to work selling crack cocaine (crack). Every job choice has two wages that are taken as a bundle--the average wage per hour and the expected years in prison one receives. A fortiori, assume wages are the same between the two groups.

Finally, imagine that while the wages of both whites and blacks are the same, blacks lose less from prison (as we shall see, a more reasonable assumption is that their outside wages are different). Let us say that a "conversion factor" between years in prison and wage is $2/year for whites and $1/year for blacks.

Then we display our hypothetical wages graphically below (click to enlarge):

In this case, we should see blacks specializing in crack, even though the sentence is higher, while whites split between legal work and powdered cocaine. The law itself caused blacks to enter into crack, rather than attempting to punish them unfairly. It's not clear whether or not sentencing caused racial segregation of this particular crime or discrimination by politicians caused the disparity in sentencing.

Finally and briefly, we might view this slightly differently and come up with an even more interesting result. Imagine that blacks and whites are two agents producing one of three goods--legal work, powdered cocaine, or crack cocaine. Each individual has an endowment of two inputs--money, and sentencing time. In this assumption, blacks have a larger endowment of the input "sentencing time," so they specialize in the good that is relatively more intensive in sentencing time. If we eliminate the disparity, then the rents they were accruing because they held more of a relatively rarer input go away--blacks could be made worse off if we eliminate the disparity by Stolper-Samuelson Theorem (note that eliminating the disparity essentially floods the market with an infinite amount of "sentencing time" and returns to possessing it become zero). Stolper-Samuelson gives the idea behind why an unskilled worker in a country such as the U.S. may have their standard of living harmed by international trade because they are much less rare an input.

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