Leymon 17
ANALYTICAL TOOLS
Time-series cross-section (TSCS) regression was used to analyze the data, but several problems can
arise in this type of analysis (Beck and Katz, 1995; England, Farkas, Kilbourne, and Dou, 1988). Parks
(1967) first developed a generalized least squared (GLS) regression procedure to solve some of the issues
of TSCS data analysis and numerous studies have adopted the method (Beck and Katz, 1995). Park’s
method, however, may understate the standard errors of regression coefficients by as much as 50 to 300
percent, seriously calling into question the use of this estimator. To counter this problem, Beck and Katz
(1995) recommend an approach that uses the Prais-Winston regression with panel corrected standard
errors (PCSE). Prais-Winston regression with PCSE is a variant of ordinary least squared (OLS)
regression and while regular OLS is not particularly useful in TSCS (England et al., 1988), it can be
correctly implemented when used in conjunction with PCSE and first-order autoregressive corrections.
Preliminary analysis in the form of a Hausman test
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revealed that large variations in imprisonment
rates existed from state-to-state. These findings indicate that there is significant unexplained state-to-state
variability in the data that must be controlled for when focusing on changes over time.
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Fixed effects can
be implemented in OLS regression with PCSE by including dummy variables for each state. This serves
to hold constant the unexplained state variation in the models. An OLS model with PCSE and fixed
effects for states will control the state level effects that are stable over time. The most important
advantage of this procedure is that it controls for “unexplained” variation between panels (states). This
procedure can substantially improve the reliability of the results (England, et al., 1988), but it also
removes any cross-sectional effects that might be the focus of a study concerned with differences between
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Because the assumptions of the random error model for panels lies entirely in the statistical application of the method,
the choice between inclusion of unit fixed effects and exclusion of unit fixed effects is not one that can be based on
theoretical grounds. The choice lies solely on statistical grounds and if empirical evidence suggests the assumptions are
violated, the model should always include fixed effects for units.
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If analysis indicates that considerable state to state variation is present than a researcher one of two options, they may
include additional time invariant variables, e.g. dummy codes for regional effects, or they may include “fix effects” for
units that would “washout” unmeasured time-invariant effects. In effect, fixed effects for panels exploits within group
variation by holding constant unexplained between group variations. The estimates achieve an unbiased consistency
even when the random effects assumptions are violated. When the random effects assumptions are violated, which
research suggests are often, the unit fixed-effects model offer significant advantages over the random effects model
(Halaby 2004).
Convention