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MANKIND QUARTERLY 2023 63:4 699-721
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Prison Populations: The International Mystery
Simon Wright*
Independent Researcher, UK
Emil O.W. Kirkegaard
Ulster Institute for Social Research, London, UK
* Corresponding author: simonwright50392@protonmail.com
At first glance international prison rates, measured by prisoners per
100,000 population, appear to be uncorrelated with national intelligence
and with racial diversity, which contradicts both a priori expectations and
individual level observations that higher intelligence (IQ) generally
reduces criminality, although GDP per capita shows a small positive
correlation. We present a solution to this mystery by first breaking prison
rates into three components: crime rates (proxied by homicide rates),
effectiveness at catching and imprisoning criminals, and sentencing
length. We then employ a path analysis to first estimate the effect of
national IQ and racial diversity on GDP per capita and income inequality.
Finally, we estimate both the direct and indirect association of intelligence
and diversity with our prison rate components. Consistent with previous
literature we find that national IQ increases GDP per capita and reduces
income inequality, whilst racial diversity raises income inequality. GDP per
capita in turn is correlated with lower homicide rates, higher effectiveness
and longer sentencing length, whilst inequality is not significantly
associated with any outcome variable, after controlling for racial diversity.
While the association between national IQ and prison rate components
appears to be entirely indirect, through the channel of national income,
racial diversity is directly associated with higher homicide rates and is
weakly positively correlated with sentencing length. This evidence
suggests that the opposing effects of raising effectiveness and reducing
homicide rates provides an explanation for the lack of correlation between
national IQ and prison rates.
Keywords: Prisoners, Crime, Homicide, Intelligence, GDP, Racial
diversity, Income inequality, Police effectiveness
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Differing national rates of imprisonment are difficult to predict using simple
correlations with factors that should intuitively show associations. For instance,
the prison population of a country is very weakly correlated with its violent crime
rate (Herring & Widra, 2021) (Pearson’s r = .355). National intelligence (IQ) also
fails to predict prison population in a linear way (Figure 1). This lack of simple
correlates provides a mystery for researchers interested in explaining differences
in national prison populations. The failure to find simple robust predictors of prison
populations in countries makes it difficult to explain outliers. This difficulty can be
highlighted with the example of the United States, where a recent paper argued
that the US has an exceptionally large prison population relative to the rest of the
developed world (Lewis & Usmani, 2022).
Figure 1. Intelligence and prison rates. Data from Becker (2019) and UN (2021).
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
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However, the US is not an outlier in terms of prisoners per homicide. It is also
not an outlier in terms of police per 100,000 but its exceptionally high homicide
rate means it has a very low number of police per homicide. Lewis & Usmani
(2022) argue that their measure of severity (prisoners/arrests) shows the US to
be an outlier, however this observation could also be explained by US police being
forced to concentrate on homicides with the highest chances of conviction.
Alternatively, while the US has a very high homicide rate for developed countries,
it is not unusual in the rates of less serious crimes such as robbery (UN, 2021).
Given that the US has a crime distribution abnormally skewed towards homicide,
which carries the longest sentences, it may not be unexpected that they have a
high number of prisoners per arrest. Our analysis aims to address this failure to
identify simple predictors of prison population by decomposing it into the
individual effects of sentencing length, homicide rates, and effectiveness.
Literature review
Theoretical evidence
Theoretical models of criminal behavior do not a priori predict the effect of
GDP per capita on crime. Nations with a high national income present more
opportunities for individuals to earn high wages through legal means, raising the
opportunity cost of crime. However, they simultaneously increase the potential
reward, as victims of criminal behavior have a greater wealth to steal (Fajnzylber
et al., 2002). The effect of income on robbery is likely to spill over into homicide,
through the creation of a criminal class, and through robberies gone wrong. At a
national level, countries with higher incomes are able to spend more on law
enforcement and the justice system, which increases the chances of getting
caught, and hence the deterrent for crime (Fajnzylber et al., 2002).
Unlike GDP, most theoretical arguments point towards inequality having a
positive impact on crime. High levels of income inequality may lead to frustration
and resentment when individuals see wealth around them but have not attained
any themselves (Pare & Felson, 2014). This frustration may be linked to
increased aggression (Berkowitz, 1989). Additionally, high levels of income
inequality raise the potential reward of crime for low-income individuals who can
steal from wealthy households, but lowers the reward for those who are wealthy
already (Fajnzylber et al., 2002). We further suggest that countries with higher
levels of inequality may be perceived as more unjust, which may make individuals
more likely to rationalize committing crime.
Additionally, social heterogeneity theory suggests that inequality may act as
a mediator between ethnic diversity and crime. Societies with high levels of ethnic
diversity may have higher levels of income inequality, which can influence crime
rates for reasons outlined above (de Soysa & Noel, 2020). By contrast, social
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disorganization theory posits a direct impact of ethnic diversity on crime (de
Soysa & Noel, 2020). Different ethnic groups find themselves with different and
competing value systems. This erodes social trust, trust in institutions, and
institutional effectiveness and integrity, which can increase crime rates.
Comparing these two theories generates alternative testable hypotheses. Social
disorganization theory predicts that when economic outcomes for different
ethnicities are similar, then high levels of diversity will still be positively correlated
with crime. On the other hand, social heterogeneity predicts that only in the case
of economic disparity will we find a positive association. One empirical test for
this is to control for income inequality in a regression. If social disorganization
theory is correct then we should still expect to see a positive association between
ethnic diversity and crime, whereas we should expect the association to vanish
in the case of social heterogeneity theory.
Intelligence is likely to directly reduce crime rates at an individual level.
Individuals with a higher IQ are more able to factor in the long-term consequences
of their actions (Ackert et al., 2020). This can keep people from committing crimes
because the rewards of committing a crime are immediate, whilst the potential jail
sentence is more distant (Guay et al., 2005). Additionally, more intelligent people
may be more able to empathize with their potential victims and decide not to
engage in crime (Guay et al., 2005). However, individuals with higher intelligence
may also be more able to avoid police detection, not getting caught and evading
the potential negative consequences of crime (Fajnzylber et al., 2002). This can
reduce the disincentive to commit crime and allow criminals to commit more
crimes before capture. Such an effect would be difficult to detect at an individual
level, as more intelligent criminals are less likely to be captured, and hence would
not be surveyed by the researcher. In this arms race, more intelligent countries
are likely to have more competent police but will also have to capture more
intelligent criminals. At the national level, high intelligence plausibly causes
increased national income and growth (Francis & Kirkegaard, 2022), which may
influence crime rates through the potential channels mentioned above.
Empirical evidence
Previous international literature has typically focused on how economic,
political, and demographic factors affect crime rates. Fajnzylber et al. (2002)
find robust results showing that low income inequality and high economic
growth are associated with low homicide and robbery rates, although the effect
of GNP per capita appears to be non-existent and may even increase robbery
rates. The authors also test the effect of educational attainment, finding it not
to be associated with crime rates. This is relevant for the present analysis as
educational attainment is strongly associated with national intelligence
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
703
(Meisenberg, 2012) and so a failure to find an association with crime suggests
that national IQ’s effect is either non-existent or indirect, through its effect on
economic growth (Francis & Kirkegaard, 2022) and income inequality
(Meisenberg, 2012). However, it should be noted that educational attainment
is more strongly correlated with GDP per capita than with national intelligence
(Meisenberg, 2012), so it is unclear how strong a proxy for intelligence
educational outcome is when controlling for national incomes. By contrast, and
Templer (2009) find that in simple correlations national IQ is negatively
correlated with homicide, rape and serious assault, whilst national income is
only negatively associated with homicide.
Chon, (2011) estimates the effect of population heterogeneity on homicide
rates. The authors find that ethnic and linguistic diversity are associated with
higher homicide rates, as is higher income inequality. GDP per capita meanwhile
shows a negative association with homicide rates. Other demographic variables
such as urbanization and population average age did not have a significant effect.
This is partially supported by de Soysa and Noel (2020), who find a positive
association between ethnic diversity and homicide rates. However, this effect
shows an unexpected negative interaction with income inequality: In societies
with high income inequality, ethnic heterogeneity reduces homicide rates (de
Soysa & Noel, 2020). It should also be noted that these papers use ethnic rather
than racial diversity measures, which are only weakly related (Meisenberg, 2007).
At an individual and local level the vast majority of studies have found that
higher income and higher intelligence are associated with lower chances of
committing a crime (Ellis et al., 2009). However, in the case of poverty the effect
at the regional level is much more ambiguous (Ellis et al., 2009). Additionally,
teasing out the causal effect of poverty on crime is difficult because poverty is
correlated with other factors such as intelligence that appear to affect crime rates.
One approach to finding the causal effects is to analyze the impact of exogenous
shocks on criminality. For instance, Iyer and Topalova (2014) found that in India,
changes in rainfall and trade barriers increased rates of poverty, which in turn
increased crime rates.
One paper to directly model prison rates was D’Amico and Williamson
(2015). Whilst the focus of the paper was the impact of legal origins, they also
model GDP per capita as a control variable. The results were inconsistent.
Depending on the model, GDP per capita moves from negative to positive
associations with overall prison populations.
Research hypotheses
Based on the existing theoretical and empirical evidence we are able to
create several hypotheses. Firstly, GDP per capita will likely be positively
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associated with effectiveness as wealthier countries can afford better policing.
This, combined with other theoretical mechanisms, means we expect homicide to
be negatively associated with GDP per capita. Given that we expect national
intelligence to be positively associated with income, we expect national IQ should
have these same effects indirectly. Additionally national IQ should be directly
negatively associated with homicide rates, whilst its direct association with
effectiveness is ambiguous. Finally, income inequality should mediate the
relationship between racial diversity and income if social disorganization theory
is correct; whilst if social heterogeneity theory is true, there should be a direct
association between racial diversity and homicide.
Data
We start with the theoretical framework that the prison population is equal to
the crime rate multiplied by the proportion of criminals caught (Effectiveness)
multiplied by the average length of stay in prison (Sentencing length):
(1) Prison population = Crime rate * Effectiveness * Sentencing length + ε
When the variables are defined this way, this equation is tautological in the long
run, although year to year fluctuations can cause an error term.
Such a model is unintuitive to estimate with OLS as each variable has a
multiplicative effect on prison population. By taking logarithms of both sides of
this equation, we transform this into a simple linear model:
(2) n( ) = ( ) + () +
(Sentencing length) + ε
This transformation allows for a linear estimation with OLS.
Data for our three components was obtained from the United Nations Office
of Drugs and Crime (UN, 2021) for the years 2000-2021.
Crime rates
We use the homicide rate per 100,000 total population (UN, 2021) as our
proxy for national crime rates. This has the advantage of having a standard
definition across countries and the widest coverage of data. Otherwise, different
countries criminalize different activities and apply different definitions to different
categories of crime. Homicide is not a perfect measure of “crime rate”, but it is the
best proxy available with current data. Poor data quality in low-income countries
such as Nigeria is yet another limitation of our analysis (Vazsonyi et al., 2019).
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
705
Sentencing length
Sentencing length is estimated as the number of prisoners in jail in a given
year divided by the number of new prisoners entering prison. This roughly
corresponds to the average length of prison stay for criminals. For instance, if a
country had 100 criminals in jail, and admitted 10 every year, then this would
mean that the average criminal spends 100/10 = 10 years in jail. Owing to a
scarcity of data on prison intake, this variable had to be averaged across years.
Averaging across multiple years is the same procedure taken by Fajnzylber et al.
(2002) when confronted with data scarcity on police personnel, whilst retaining a
panel structure for other variables. Sentencing length is closely related to the
concept of sentencing harshness, although other factors such as the types of
crime committed in a country also play a role.
Effectiveness
Here we define effectiveness as the prison population divided by the
homicide rate, both obtained from UN (2021). This assumes that crimes other
than homicide vary in tandem with homicide at the country level, and provides a
crude measure for effectiveness to capture criminals. However, this measure of
effectiveness also captures sentencing length because, ceteris paribus, countries
with longer sentences would have more prisoners per capita. We therefore control
for sentencing length in all our regressions. Our simple measure of effectiveness
has a tendency to produce large outliers when the homicide rate of a country
suddenly drops or rises. For instance, Cyprus briefly had 47,679 prisoners per
homicide in 2011, as a result of a near zero homicide rate that year. This is a
violation of OLS assumptions (Hanck et al., 2019, Chapter 4.4). Additionally,
because data availability is scarce for many countries an averaging approach to
removing outliers fails for many countries. For instance, Venezuela and Ecuador
each have only one year of homicide and prison population data in which there
was an exceptionally low 1.5, and exceptionally high 710 prisoners per homicide
respectively. Our approach to solving this was to convert our effectiveness scores
into ranks: ordering from lowest to highest effectiveness, and then transforming
these ranks into z scores. This is analogous to the process used to find
Spearman’s rank correlations, which is more robust to outliers than Pearson’s r
(de Winter et al., 2016; Spearman, 1904).
Other variables
We obtain national IQ (NIQ) data from Becker (2019). This dataset aims to
increase the reliability of other national IQ datasets by supplementing them with
data from international student tests. For a detailed description of this
methodology see Becker and Rindermann (2016) and Rindermann (2007, 2008).
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Meisenberg (2007) provides us with two estimates of racial diversity: racial
diversity based on genes and racial diversity based on IQ. The genes-based
measure weights diversity by genetic distance based on allele frequency
differences between people of different continental origin (defined as where
someone’s ancestors lived in 1500) within a country. Racial diversity based on IQ
is estimated similarly but uses differences in national IQ between countries of
origin instead of genetic distance. This alternative metric provides a robustness
test to our main analysis, although the use of psychometric tests to measure racial
diversity does introduce a possibility of racial bias. We measure income inequality
using the Gini index obtained from World Bank (2021). For years where inequality
estimates aren’t available we impute them using irmi (Head, 2016; Kirkegaard,
2022).
Descriptive statistics are shown in Table 1 and correlations are shown in
Table 2. It is interesting to note that both national IQ and GDP per capita are
similarly correlated with our outcome variables. The best overall predictor of
prison population is racial diversity based on genes.
Table 1. Summary statistics. Effectiveness is the rank order of prisoners per
homicide, transformed into z-scores. 478 observations from 57 countries.
Mean ± SD
median
min
max
range
Year
2010.6 ± 6.2
2011
2000
2021
21
ln(GDP per capita)
9.441 ± 1.187
9.564
5.527
12.023
6.496
National IQ
85 ± 11.8
85.2
60.19
105.29
45.1
Sentencing length
1.173 ± 0.78
1
0.084
3.993
3.908
Effectiveness
0 ± 1
0.004
-1.728
1.728
3.457
Prison population
183.9 ± 146.4
141.4
15.8
1293.8
1278
Racial diversity genes
18.909 ± 27.162
4.7
0
101.3
101.3
Racial diversity IQ
14.481 ± 20.121
4.6
0
84
84
Homicides/100,000
5.797 ± 10.735
1.752
0.001
105.231
105.23
ln(homicide rate)
0.822 ± 1.327
0.561
-6.76
4.656
11.416
ln(prison population)
4.947 ± 0.741
4.951
2.76
7.165
4.405
ln(sentencing length)
-0.069 ± 0.713
0
-2.474
1.384
3.859
Gini index
38.84 ± 8.09
37.684
23.2
64.8
41.6
Table 2. Correlation matrix.
1
2
3
4
5
6
7
8
9
10
11
1.
ln(GDP per
capita)
1
2.
National IQ
0.768
1
3.
Sentencing
length
-0.139
-0.110
1
4.
Effectiveness
0.511
0.513
0.064
1
5.
Prison
population
0.192
-0.005
0.293
0.036
1
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
707
1
2
3
4
5
6
7
8
9
10
11
6.
Racial diversity
genes
0.005
-0.243
0.142
-0.225
0.442
1
7.
Racial diversity
IQ
0.070
-0.174
0.141
-0.214
0.368
0.929
1
8.
Homicides/100
,000
-0.326
-0.471
0.179
-0.577
0.297
0.523
0.522
1
9.
ln(homicide
rate)
-0.492
-0.587
0.212
-0.829
0.381
0.484
0.477
0.754
1
10.
ln(prison
population)
0.285
0.111
0.366
0.064
0.891
0.416
0.406
0.297
0.395
1
11.
ln(sentencing
length)
-0.202
-0.152
0.914
0.016
0.317
0.171
0.138
0.227
0.260
0.420
1
12.
Gini
-0.366
-0.541
0.176
-0.411
0.217
0.541
0.537
0.527
0.562
0.205
0.199
Methods
A key issue associated with interpreting traditional OLS are bad controls
(Cinelli et al., 2021). These occur when introducing further control variables
biases our OLS estimator away from the true effect size. For instance, suppose
that national IQ increases GDP per capita (GDP/c) which in turn reduces homicide
rates, then GDP/c acts as a mediator between IQ and homicide. If we were to
conduct an OLS regression predicting homicide with IQ but controlling for GDP
per capita, then only those effects of IQ on homicide that are not mediated by per
capita GDP will remain and the actual importance of IQ will be underestimated.
Path analysis can address this issue by, for instance, first regressing national
IQ on GDP/c and then estimating the association between IQ, GDP/c, and
homicide rates. The total effect of IQ can then be estimated as the direct effect
plus the indirect effect (the effect of IQ on GDP/c multiplied by the effect of GDP/c
on homicide) (Beaujean, 2014).
Path analysis requires the a priori specification of associations between our
variables (Beaujean, 2014). We first set out the model in Figure 2, and aim to
justify our specification below. In the first layer sit our demographic variables
national IQ and racial diversity, as we believe that they are unlikely to be
influenced by other variables. These are allowed to influence the economic
factors of GDP per capita and income inequality. In the third layer are our three
prison rate components, which are influenced by the socio-economic factors
directly, and by the demographic factors both directly and indirectly through their
influence on socio-economic variables. Finally, because a higher homicide rate is
likely to overwhelm police forces (Borg & Parker, 2001), reducing effectiveness,
and to improve model fit, homicide rates are allowed to influence effectiveness.
To address the concern of autocorrelation in the panel data, we employ
heteroskedasticity and autocorrelation consistent (HAC) standard errors (Hanck
et al., 2019, Chapter 10.4). This analysis was conducted using the lavaan
package in R (Rosseel et al., 2022).
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Figure 2. Path model. Dashed arrow shows an assumed non-causal control, as
outlined in our data section.
We believe that these directions of association are reasonable based on
previous literature. National IQ is strongly and robustly associated with GDP and
GDP growth. Francis & Kirkegaard (2022) have estimated the strength of this
association using both Bayesian model averaging and instrumental variables,
finding that the estimated effect on the steady state of GDP is similar to a simple
bivariate correlation. Finding this using instrumental variables minimizes concern
of reverse causation (GDP improving IQ) which could bias the estimated impact
of IQ on GDP. Evidence for the direction of association between racial diversity
and income inequality is less strong. However (Meisenberg, 2007) has shown
that there is a positive association between them, even after controlling for
several other factors, and the alternative direction of causation: from high income
inequality to high racial diversity, appears implausible because high income
inequality is unlikely to create more racial diversity.
Because of the difficulty in specifying directions of causation we consider two
alternative specifications. The first arises from the question of the direction of
causation between racial diversity and GDP per capita. The current literature
reveals a consistent pattern of racial disparities in IQ within countries, as
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
709
evidenced by empirical investigations conducted across multiple geographical
regions worldwide (Lynn, 2015). A notable implication stemming from this
phenomenon is that countries blessed (or afflicted) with higher levels of racial
heterogeneity may possess a more cognitively gifted “smart fraction” (controlling
for average IQ), which appears to positively influence economic growth
(Rindermann et al., 2009). Alternatively, causation may flow the other way as
countries with higher GDP per capita attract more immigration and therefore
increase racial diversity (Boubtane et al., 2013). We present this alternate
specification of our model in Figure 3, with causation flowing in this latter direction.
Our second alternative specification concerns the direction of causation
between homicide rates and effectiveness. If police effectiveness prevents
criminals from recidivism while in jail, then effectiveness may reduce homicide
rates. Evidence from Italy’s experiment of releasing one third of their prison
population suggests that holding criminals in jail is an effective way to reduce
recidivism and crime rates (Buonanno & Raphael, 2013). This model is presented
in Figure 4. A bidirectional model was considered but rejected as it showed a
poorer model fit and an insignificant (and positive) estimate for the effect of
effectiveness on homicide. To account for potential autocorrelation, all our models
employ heteroskedasticity and autocorrelation consistent (HAC) standard errors
(Hanck et al., 2019, Chapter 10.5).
Figure 3. Alternative specification 1. Dashed arrow shows a non-causal control,
as outlined in our data section.
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Figure 4. Alternative specification 2. Dashed arrow shows a non-causal control,
as outlined in our data section.
Results
Direct effects only
Our main results are presented in Table 3 and Figure 5. Our demographic to
economic estimates mostly show the expected sign and are statistically
significant. Intelligence is positively associated with GDP and negatively
associated with income inequality whilst racial diversity is positively associated
with income inequality.
Table 3. Path analysis. Effectiveness is the rank order of prisoners per homicide,
transformed into z-scores. * p < .05; ** p < .01; *** p < .001 Path coefficients with
HAC standard errors in parentheses. N = 478, clusters (countries) = 57.
Dependent variable
Independent variable
Estimate
Gini index
National IQ
-0.440** (0.155)
Gini index
Racial diversity genes
0.847*** (0.128)
ln(GDP per capita)
National IQ
0.955*** (0.064)
ln(GDP per capita)
Racial diversity genes
0.272*** (0.08)
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
711
Dependent variable
Independent variable
Estimate
Effectiveness
National IQ
-0.110 (0.131)
Effectiveness
Racial diversity genes
0.119 (0.107)
Effectiveness
ln(sentencing length)
0.338*** (0.061)
Effectiveness
Gini index
-0.047 (0.076)
Effectiveness
ln(GDP per capita)
0.240** (0.088)
Effectiveness
ln(homicide rate)
-0.880*** (0.072)
ln(homicide rate)
National IQ
0.075 (0.201)
ln(homicide rate)
Racial diversity genes
0.459** (0.143)
ln(homicide rate)
Gini index
0.161 (0.112)
ln(homicide rate)
ln(GDP per capita)
-0.539*** (0.162)
ln(sentencing length)
National IQ
0.404 (0.285)
ln(sentencing length)
Racial diversity genes
0.630* (0.295)
ln(sentencing length)
Gini index
-0.073 (0.18)
ln(sentencing length)
ln(GDP per capita)
-0.722*** (0.211)
ln(prison population)
Effectiveness
0.744*** (0.107)
ln(prison population)
ln(homicide rate)
0.934*** (0.164)
ln(prison population)
ln(sentencing length)
0.244*** (0.07)
Figure 5. Path analysis, diagram of results shown in Table 3. Coefficients with p
< .05 are shown. Dashed arrow shows a non-causal control, as outlined in our
data section. Path coefficients are shown.
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The direct impacts of the demographic variables on our decomposed prison
rate variables are mostly insignificant. The exceptions to this are that racial
diversity is directly associated positively with homicide rates (supporting
proposition 4) and may be positively associated with sentencing length. This latter
effect is large in magnitude but is only significant at the 5% level. Surprisingly, this
means that national IQ has no significant direct effect on any of our prison
variables, failing to support proposition 2.
Consistent with proposition 1, GDP per capita is associated with low
homicide rates, low sentencing length, and high effectiveness. These effects are
highly statistically significant and of the expected sign. High income inequality, on
the other hand, is not generally significant. Finally, as expected, high homicide
rates are strongly associated with low effectiveness. Using our alternate measure
of racial diversity (based on IQ) in Table 4 and Figure 6 largely doesn’t affect the
results, except that racial diversity based on IQ fails to significantly predict
sentencing length.
Table 4. Path analysis. Effectiveness is the rank order of prisoners per homicide,
transformed into z-scores. *p < .05; ** p < .01; *** p < .001. Path coefficients, with
HAC standard errors in parentheses. N = 478, clusters (countries) = 57.
Dependent variable
Independent variable
Estimate
Gini index
National IQ
-0.505*** (0.152)
Gini index
Racial diversity IQ
0.754*** (0.112)
ln(GDP per capita)
National IQ
0.933*** (0.063)
ln(GDP per capita)
Racial diversity IQ
0.240*** (0.071)
Effectiveness
National IQ
-0.095 (0.139)
Effectiveness
Racial diversity IQ
0.178. (0.1)
Effectiveness
ln(sentencing length)
0.337*** (0.062)
Effectiveness
Gini index
-0.080 (0.07)
Effectiveness
ln(GDP per capita)
0.204* (0.098)
Effectiveness
ln(homicide rate)
-0.890*** (0.072)
ln(homicide rate)
National IQ
0.037 (0.195)
ln(homicide rate)
Racial diversity IQ
0.408** (0.137)
ln(homicide rate)
Gini index
0.156 (0.117)
ln(homicide rate)
ln(GDP per capita)
-0.541*** (0.164)
ln(sentencing length)
National IQ
0.292 (0.279)
ln(sentencing length)
Racial diversity IQ
0.388 (0.276)
ln(sentencing length)
Gini index
0.005 (0.186)
ln(sentencing length)
ln(GDP per capita)
-0.652** (0.203)
ln(prison population)
Effectiveness
0.744*** (0.107)
ln(prison population)
ln(homicide rate)
0.934*** (0.163)
ln(prison population)
ln(sentencing length)
0.244*** (0.07)
Gini index
Gini index
0.317*** (0.055)
ln(GDP per capita)
ln(GDP per capita)
0.140*** (0.03)
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
713
Figure 6. Path analysis, diagram of results shown in Table 4. Coefficients with p
< .05 are shown. Dashed arrow shows a non-causal control, as outlined in our
data section. Path coefficients are indicated.
Total effects
By tracing direct and indirect effects of the demographic factors on the prison
population in our main model it is possible to estimate their total effect sizes.
These overall estimated impacts of our demographic factors are shown in Tables
5 and 6. As expected, national IQ is positively associated with effectiveness and
negatively associated with homicide rates. These two effects cancel each other
out when estimating the total impact of IQ on prison population. For racial diversity
based on genes, there is a highly statistically significant positive impact on
homicide rates, and a weakly significant negative impact on effectiveness,
resulting in a weakly significant positive impact on total prison population. The
estimates have the same sign when IQ measures are used, however the impact
on effectiveness is now insignificant whilst the overall impact on the prison
population is much stronger.
MANKIND QUARTERLY 2023 63:4
714
Table 5. Total estimated effect of demographic variables. Effectiveness is the
rank order of prisoners per homicide, transformed into z-scores. * p < .05; **
p < .01; *** p < .001 Path coefficients, with HAC standard errors in
parentheses. N = 478, clusters (countries) = 57.
Dependent variable
Independent variable
Estimate
ln(homicide rate)
National IQ
-0.511*** (0.118)
Effectiveness
National IQ
0.589*** (0.145)
ln(sentencing length)
National IQ
-0.254 (0.204)
ln(homicide rate)
Racial diversity genes
0.450*** (0.102)
Effectiveness
Racial diversity genes
-0.251* (0.109)
ln(sentencing length)
Racial diversity genes
0.372 (0.237)
ln(prison population)
National IQ
-0.100 (0.102)
ln(prison population)
Racial diversity genes
0.324* (0.128)
Table 6. Total estimated effect of demographic variables. Effectiveness is the
rank order of prisoners per homicide, transformed into z-scores. * p < 0.05; ** p <
0.01; *** p < 0.001 Path coefficients, with HAC standard errors in parentheses. N
= 478, clusters (countries) = 57.
Dependent variable
Independent variable
Estimate
ln(homicide rate)
National IQ
-0.547*** (0.116)
Effectiveness
National IQ
0.622*** (0.146)
ln(sentencing length)
National IQ
-0.320 (0.201)
ln(homicide rate)
Racial diversity IQ
0.396*** (0.095)
Effectiveness
Racial diversity IQ
-0.185 (0.114)
ln(sentencing length)
Racial diversity IQ
0.235 (0.222)
ln(prison population)
National IQ
-0.125 (0.098)
ln(prison population)
Racial diversity IQ
0.289** (0.112)
Alternative specification
The results of our first alternative specification, where GDP per capita
influences genetic diversity, are presented in Table 7. Under this model diversity
positively influences GDP, as expected. However, the large negative coefficient
on IQ appears causally implausible as it implies that countries with a high IQ will
causally generate drastically lower levels of racial diversity. This coefficient
therefore may best be interpreted as a control variable rather than an effect size.
This model also performs much more poorly than our main results based on AIC
information criteria.
Table 7. Path analysis, alternative specification. Effectiveness is the rank order
of prisoners per homicide, transformed into z-scores. * p < .05; ** p < .01; *** p <
.001. Path coefficients, with HAC standard errors in parentheses. N = 478,
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
715
clusters (countries) = 57. HAC standard errors.
Dependent variable
Independent variable
Estimate
Gini index
National IQ
-0.440** (0.155)
Gini index
Racial diversity genes
0.847*** (0.128)
ln(GDP per capita)
National IQ
0.840*** (0.075)
Racial diversity genes
ln(GDP per capita)
0.477** (0.168)
Racial diversity genes
National IQ
-0.822*** (0.201)
Effectiveness
National IQ
-0.110 (0.131)
Effectiveness
Racial diversity genes
0.119 (0.107)
Effectiveness
ln(sentencing length)
0.338*** (0.061)
Effectiveness
Gini index
-0.047 (0.076)
Effectiveness
ln(GDP per capita)
0.240** (0.088)
Effectiveness
ln(homicide rate)
-0.880*** (0.072)
ln(homicide rate)
National IQ
0.075 (0.201)
ln(homicide rate)
Racial diversity genes
0.459** (0.143)
ln(homicide rate)
Gini index
0.161 (0.112)
ln(homicide rate)
ln(GDP per capita)
-0.539*** (0.162)
ln(sentencing length)
National IQ
0.404 (0.285)
ln(sentencing length)
Racial diversity genes
0.630* (0.295)
ln(sentencing length)
Gini index
-0.073 (0.18)
ln(sentencing length)
ln(GDP per capita)
-0.722*** (0.211)
ln(prison population)
Effectiveness
0.744*** (0.107)
ln(prison population)
ln(homicide rate)
0.934*** (0.164)
ln(prison population)
ln(sentencing length)
0.244*** (0.07)
Table 8 presents the results of our second alternative specification, where
effectiveness influences homicide rates. These results are broadly as before,
except effectiveness reduces homicide rates. Interestingly, when controlling for
effectiveness, GDP per capita loses its significance at directly predicting homicide
rates at the 5% level (p = .077). This model performs considerably worse than the
main specification in comparative fit index but remains slightly above the 0.95
threshold needed to be considered a good fit. It performs similarly to the main
specification in terms of AIC.
Table 8. Path analysis, alternative specification. Effectiveness is the rank
order of prisoners per homicide, transformed into z-scores. * p < .05; ** p < .01;
*** p < .001 Path coefficients, with HAC standard errors in parentheses. N =
478, clusters (countries) = 57.
MANKIND QUARTERLY 2023 63:4
716
Dependent variable
Independent variable
Estimate
Gini index
National IQ
-0.44** (0.155)
Gini index
Racial diversity genes
0.847*** (0.128)
ln(GDP per capita)
National IQ
0.955*** (0.064)
ln(GDP per capita)
Racial diversity genes
0.272*** (0.08)
Effectiveness
National IQ
-0.136 (0.226)
Effectiveness
Racial diversity genes
-0.224 (0.159)
Effectiveness
ln(sentencing length)
0.24*** (0.072)
Effectiveness
Gini index
-0.195. (0.115)
Effectiveness
ln(GDP per capita)
0.644*** (0.162)
ln(homicide rate)
National IQ
0.049 (0.147)
ln(homicide rate)
Racial diversity genes
0.412** (0.158)
ln(homicide rate)
Gini index
0.022 (0.079)
ln(homicide rate)
ln(GDP per capita)
-0.233. (0.131)
ln(homicide rate)
Effectiveness
-0.651*** (0.069)
ln(sentencing length)
National IQ
0.404 (0.285)
ln(sentencing length)
Racial diversity genes
0.63* (0.295)
ln(sentencing length)
Gini index
-0.073 (0.180)
ln(sentencing length)
ln(GDP per capita)
-0.722*** (0.211)
ln(prison population)
Effectiveness
0.744*** (0.072)
ln(prison population)
ln(homicide rate)
0.934*** (0.119)
ln(prison population)
ln(sentencing length)
0.244*** (0.045)
Gini index
Gini index
0.323*** (0.055)
Interaction effects
Finally, we test the results found by de Soysa and Noel (2020) of an
interaction effect between income inequality and racial diversity on homicide
rates. These results are presented in Table 9. They do not support a negative
interaction effect.
Table 9. Interaction effect test. Dependent variable: ln(homicide rate), the natural
logarithm of the homicide rate. lnGDPc is the natural logarithm of the real GDP
per capita of a country. Effectiveness is the rank order of prisoners per homicide,
transformed into z-scores. *p < 0.05; ** p < .01; *** p < .001 Path coefficients are
shown, with HAC standard errors in parentheses.
Model 1
Model 2
(Intercept)
0.270* (0.110)
0.220* (0.101)
Racial diversity genes
0.377** (0.134)
Racial diversity IQ
0.327** (0.12)
ln(GDP per capita)
-0.454*** (0.126)
-0.465*** (0.128)
Gini index
0.185 (0.096)
0.176. (0.098)
National IQ
-0.002 (0.137)
-0.019 (0.133)
Diversity * Gini index
0.094 (0.081)
0.127 (0.07)
WRIGHT, S. & KIRKEGAARD, E.O.W. PRISON POPULATIONS
717
Discussion
While most of our results show estimates in line with previous literature and
a priori expectations, there are some exceptions which merit further discussion.
Notable was income inequality’s lack of association with homicide rates, which is
contrary to the results of Fajnzylber et al. (2002), Chon (2011), and Wilkinson and
Pickett (2011). The results of Fajnzylber et al. (2002) could plausibly be explained
as omitted variable bias, as they do not include measures of racial diversity in
their model. However, our contrary results to Chon (2011) are harder to account
for. Tentatively we suggest that the discrepancy may be accounted for by the
difference between ethnic and racial diversity used in Chon (2011) and the
present study respectively. Income inequality correlates more strongly with racial
diversity than with ethnic diversity. This is true both in Meisenberg (2007)
(Pearson’s r of .425, .410 and .180 for racial diversity based on genes, racial
diversity based on IQ, and ethnic diversity respectively) and in the measure of
ethnic diversity used in Chon (2011) (Pearson’s r of .26). This suggests that the
results of Chon (2011) can be explained by omitted variable bias, specifically by
failing to control adequately for racial diversity. The distinction between ethnic and
racial diversity may also account for our contrary results to de Soysa and Noel
(2020).
The most surprising result in our analysis is the failure to find any direct
association between IQ and any of our decomposed prison rates, with the effects
only operating through GDP. Although this is congruent with the results of
Fajnzylber et al. (2002), it is contrary to the results expected from higher IQ
individuals having greater empathy and impulse control. The only theoretical
mechanism as to why this may occur is that criminals in high-IQ countries are
likely to be, on average, more intelligent than those in low-IQ countries and can
therefore effectively evade capture, thus lowering the cost of crime and allowing
criminals to commit more crimes before getting caught. Such an effect would have
to outweigh the effect of a more competent police force in high-IQ countries.
Similarly, higher IQ individuals may be more able to sustain organized crime
gangs, as is seen in South America. Alternatively, low IQ countries may be
underreporting their homicide rates, as appears to be the case in Nigeria
(Vazsonyi et al., 2019).
The direct effect of racial diversity on homicide rates supports the social
disorganization theory of crime, whereby competing value structures are the
cause of higher crime rates, rather than indirect impacts through income
inequality. Social heterogeneity theory, by contrast, only received very weak
support. We can also plausibly hypothesize that countries with higher levels of
racial diversity may have more intelligence inequality, and therefore a less
intelligent and more criminal underclass.
MANKIND QUARTERLY 2023 63:4
718
Limitations
This study has several limitations, primarily due to constraints in data
availability. Firstly, the dataset comprises information from only 57 countries,
which leaves the results with quite low power. Additionally, the limited number of
observations from each country may impact the reliability and robustness of the
results.
Secondly, the scarcity of comprehensive data has necessitated the use of
imperfect proxies for the outcome variables, potentially affecting the accuracy of
the conclusions drawn. In particular, the lack of extensive datasets on annual
homicide convictions hampers the establishment of a more effective proxy for
police effectiveness that is less influenced by the choices of a country’s criminals.
Moreover, the credibility of homicide statistics from developing countries remains
dubious (Vazsonyi et al., 2019). If these countries, which typically exhibit a lower
national average IQ, underreport homicides, the significance of national IQ in the
data may be understated. Such unreliability may also affect prison population
statistics.
Lastly, previous literature has not established the causal direction between
some of our variables, such as GDP and racial diversity. Consequently, the paper
remains agnostic on this relationship by providing two alternative specifications.
Future research may seek to explore these connections more thoroughly,
especially if longitudinal racial diversity data becomes available. Such data would
enable a determination of whether increases in racial diversity precede or
succeed increases in GDP per capita.
Data availability: Data and replication files are available at https://osf.io/3hywt/
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