# Does the death penalty reduce crime?

It happens every now and then that something goes wrong with an execution, and there is some debate about the death penalty. The result – as usually in politics – is that nothing changes. But now that this topic was all over the news again some time ago, I decided to see what the data says.

This post attempts to answer whether the death penalty has a deterrent effect. Can it reduce crime?

The main idea here is to see whether the possibility of the death penalty has a significant (negative) effect on crime. Specifically, I will estimate regressions of the form

${Crime}_i = \alpha {CP}_i + \beta \textbf{X}_i + \epsilon_i$

where Crime refers to some measure of the violent crime rate, CP is some measure of the extent of capital punishment, and X is a vector of control variables.

I use three alternative measures of crime. First, there is simply the violent crime rate (per 100,000 inhabitants) for each state in 2011. Second, there is the percentage change in this crime rate from 1976 to 2011. Third, the absolute change in this crime rate over the same period. The year 1976 is chosen because it was then that capital punishment was reintroduced in many states. The idea with the second and third variables would be to see whether crime decreased more in states that allow capital punishment.

To measure capital punishment, I use five variables. The number of executions since 1976 (total and per capita), the number of current death row inmates (total and per capita), and a dummy variable indicating whether capital punishment is legal in the state in question.

Finally, the control variables include the gross state product (GSP) per capita (which is like the GDP for states), the poverty rate, population density, and in some cases population, the percentage of gun owners, and the percentage of African Americans in a given state. This last one can be useful because the poverty rate is somewhat correlated (0.19-0.36) with capital punishment, but the percentage of African Americans is not (0.05-0.26). Yet states with more African Americans tend to have higher poverty (correlation: 0.49). So using this variable instead of the poverty rate can reduce multicollinearity while perhaps still capturing the effects of poverty.

Another variable that may come to mind is the incarceration rate. Unfortunately but not surprisingly, the incarceration rate is highly correlated with capital punishment (0.35-0.64). That is, states that embrace the death penalty more, tend to have higher incarceration rates. So this variable cannot really be added to the regression without causing multicollinearity problems. Still, I tried it in some specifications. Its presence does not change the main results of the analysis.

The thing to look out for then in these regressions is the sign and significance of alpha, that is the coefficient of capital punishment. If capital punishment is in any way related to the violent crime rate, then alpha should be significantly different from 0. If in particular the death penalty reduces crime by deterrence, then alpha should be negative.

As a visual check, the figure below illustrates current death row inmates per capita vs. the violent crime rate. Click to enlarge.

First, I ran some basic OLS regressions of the form shown above. Various combinations of violent crime measures, capital punishment measures, and controls were tried. The general picture is that poverty is the variable that seems to be highly significant in most specifications with an expected positive sign. Capital punishment in most cases is not significant. When it is, its coefficient happens to have a positive sign, which is not what a deterrent effect would indicate as discussed above.

Nevertheless, we might have a problem of double causality. It might be that states with higher crime rates simply “have to” execute more people. So it would be ideal to find an instrumental variable (IV) to get rid of this endogeneity problem.

Thus secondly, I try an IV specification. To get an IV, we need something that correlates with capital punishment measures but not with crime rates. I collected/constructed several measures of how conservative and/or Republican a state is. This should be sufficient. It turns out, however, that these measures of conservativeness are not so much correlated with capital punishment. The best one I could find is simply the percentage of registered Republican voters, which is a decent (though far from excellent) instrument for the dummy indicating whether the death penalty is legal in a state.

In the IV specification I use GSP per capita and the poverty rate as controls. These seemed to be the best controls in the OLS specifications. To characterize the quality of the IV, note that regressing the dummy of the legal status on the IV and the controls shows that the IV is highly significant (p < 0.001) with a t-statistic of 4.886. Running the same specification as a logit regression produces a z-statistic of 2.984 (p < 0.01). Regressing measures of crime directly on the IV and the controls shows that the IV is not significant (but then again, neither is the original variable), and it has a negative sign.

Then running two-stage least squares shows that capital punishment’s coefficient has a negative sign. However, it is not significantly different from 0. The p-value is around 0.29. Poverty is highly significant in the IV specification as well (p < 0.001), GSP per capita isn’t.

Using another (similarly strong) IV does not change the results. Using other controls, or different dependent variables (as specified above) has no effect either.

While it may be somewhat arguable whether the IV is strong enough, I think the conclusion is consistent throughout the models: capital punishment does not seem to have an effect on crime. In any case, even if causality is not satisfactorily established in the above regressions for the tastes of some, it seems that there is no relationship between violent crime and capital punishment as alpha is insignificant in most specifications.

In sum, it seems that the death penalty does not have a significant deterrent effect. This seems logical from a behavioral point of view. I mean the crimes you can get the capital punishment for are not really things rational people commit. These people are not likely to do an implicit cost-benefit analysis in their heads before committing a crime in my opinion. It seems the American public shares this opinion, as 64% believe the death penalty is not a good deterrent. In any case, these results are based on a rather simple analysis. So a more in-depth study with better IVs, and perhaps concentrating more on the changes in crime rates over time would be necessary to finalize the verdict. But the preliminary results to me suggest that the death penalty is not a deterrent.

IVs tried include: % registered Republicans, ratio of % registered Republicans to % registered Democrats, % conservatives, ratio of % conservatives to % liberals. Finally, using the table here: how many of the eight possible offices/elections Republicans control/won in each state.