Time Series, Homicide, and the Deterrent Effect of Capital Punishment

Abstract

Erlich [5; 6] presents regression results showing that the U.S. time-series data supports the deterrent effect of capital punishment (the deterrence hypothesis). Other researchers [9; 10; 16] criticize Erlich's findings on a number of grounds-including the possibility of simultaneity bias, and the sensitivity of the results to the choice of sample period, control variables, and functional form. Layson [11] extends Erlich's U.S. sample to the 1936-1977 period and, taking account of these criticisms, concludes that the U.S. time-series evidence provides robust support for the deterrence hypothesis. This paper contributes to the debate on the deterrence hypothesis by analyzing the time-series properties of the homicide rate; the U.S. homicide rate is a nonstationary time series. It is well known that the use of nonstationary series in regression analysis leads to inconsistent coefficient estimators, biases estimators of coefficient standard errors toward zero, and invalidates standard statistical-inference procedures [2; 8; 13; 14; 15; 17; 18]. Nonstationarity may be due to a linear trend (trend nonstationarity) or may be a property of the underlying stochastic process (difference nonstationarity). If the time series is difference nonstationary then use of a linear trend does not correct these problems and may be misleading [13; 14; 15]. We explicitly test for the source of the nonstationarity of the homicide rate, difference or trend nonstationarity, using the tests recently developed by Dickey and Fuller [3; 4; 7]. We find that the homicide rate is difference nonstationary. This implies that the data must be first differenced to achieve stationarity, and that use of a linear trend (as in [5; 6; 9; 10; 11; 16]) is inappropriate. The regression results obtained using the first-differenced, stationary data do not provide robust support for a deterrence effect of capital punishment.