Leymon 18
states rather than changes within states.
15
Additionally, in this analysis the variation of interest is the
variation over time and it was decided not to include fixed effects for years (period effects) in this
analysis. When the researcher is interested in the pattern of change over time in the predictors, then the
fixed-effects approach for the panels without the inclusion of fixed effects for time sacrifices little
(Halaby 2004).
16
In addition to the desire to leave the year-to-year variation in the analysis intact,
including dummy variables for years may lead to large colinearity with the logarithmic growth curve
codes for guidelines, which are also time-varying covariates.
17
For each of the analyses, Prais-Winston regression with panel-corrected standard errors with fixed
effects for states and AR1 controls for autocorrelation was used to predict imprisonment rates in all fifty
states and across 30 years (for the total imprisonment rate) of data. All models included two logarithmic
growth curve variables to assess the independent effect of presumptive and voluntary guidelines. Other
models included some combination of the number of arrests for violent crimes per 1000, the number of
drug crime arrests per 1000, the number of inmates returned to prison for parole violation per 1000, the
number of new commitments to prison per 1000, the percent black, the percent Hispanic, the percent
white, the poverty rate, and the unemployment rate. These variables were used to predict the dependent
variables of total prison population per 1000, black prison population per 1000 black, white prison
population per 1000 white, Hispanic prison population per 1000 Hispanic, and ratios of black to white
imprisonment rates and Hispanic to white imprisonment rates.
RESULTS
ANALYSIS OF BLACK, WHITE, AND HISPANIC INCARCERATION RATES
Table 1 reports findings based on the separate analysis of the black, white, and Hispanic
15
An important advantage in this analysis is that fixed effects for states will control for any regional differences that may
be present. For example, research has shown that the south has higher rates of imprisonment and the analysis will
control this difference and remove its effect from the results.
16
When fixed effects for both units and time are included, the substantive interpretation of the coefficients becomes a
measure of the panels deviation from the grand mean of the panels that are stable over time. This is because the time
invariant explanatory variables, in this case the dummy variables for units, can interact with time trends or periods and
what is left are terms that show the effect of time varying explanatory variables on the dependent variable. While the
inclusions of fixed effects for units is entirely statistical, the choice of inclusion of fixed effects for time is one that is solely
theoretical (Halaby 2004).
17
Additionally, each state has almost complete autonomy over their imprisonment rates and its changes will be a
reflection of change over time (within panels), but “explaining” the uncontrolled variation over time may result in a
misspecification of state effects.
Convention