Understanding the factors that might reduce violent crimes can be used to direct resources to fight criminal activity. Violent crimes in a state can be affected by the percentage of the population in prison, legislation to reduce prison overcrowding, unemployment, concentration of police, per capita income, racial composition, percentage of residents living in a inner city and the age stratification of the population within a state. In this post we are interested in how increasing the percentage of people in prison affects the crime rate. Intuitively putting more criminals in prison should reduce the crime rate. Specifically, this post will focus on estimating the elasticity of the crime rate relative to the prison population. If the measure is elastic then the crime rate is very responsive to incarceration rates, otherwise violent crime would be non-responsive to incarceration rates in a state.
Using panel data from all 50 states and the District of Columbia over a period of 13 years this post estimated a fixed effect instrumental variable regression model. The simultaneous equations part of this model comes from the fact that crime rates and incarceration rates can be determined simultaneously as two separate regressions. In order to deal with this econometric issue, a binary variable indicating whether or not legislation to reduce prison overcrowding passed the state legilature on a given year will be used as an IV for prison population.
Using the results from the estimate above we can see that the crime rate is responsive to the incarceration rate as evidence by by the -1.51 coefficient on the lpris variable. According to this estimate, increasing the prison population by 10% would reduce the crime rate by about 15%. Depending on the cost of such a policy, implicit or explicit, one can say that violent crime rates are highly responsive to the percentage of the population behind bars.