Case II - Effect Does Exist
3.6 Multivariate Statistics
3.6.4 Extreme Bounds Analysis
studies), Finnish studies, very large or small locations, studies which check the reliability of vari-ables with correlations, use the probability and severity of punishment (and the celerity) by offi-cials or friends and family in surveys, as well as estimates which are not corrected for simultaneity.
The opposite effect can be found when Canadian data is studied, when “other” public data bases are used, when the studied individuals have almost all been convicted before, when authors do not check representativeness, when closed or mixed questions are used in a pretest, when the exoge-nous variables is metric or measured in differences, when the deterrence variable relates to prison sentences or recidivism, and, finally, covariates relating to poverty and welfare are implemented.
Last but not least, the technical influence of the sample size and the size of the studied population (which strongly correlates with the sample size) have to be mentioned.
When the results are compared with the bivariate analysis in section 3.5, noteworthy changes are: German authors, when controlling for other effects, are now correlated with less support of the deterrence theory, while studies from Alex R. Piquero are now associated with more support in the larger set (table 3.49). The impact of many variables, which measure deterrence in surveys and appeared to be associated with less support insection 3.5is now reversed. The coefficients of the covariates age, marital status and the social class switch their signs. Curiously, the correlation between the studied offenses and the resulting (normalized) t-values are rather incompatible with those fromtable 3.43.
• A Cumulative Distribution Function (CDF) Test (A): a variable is considered important, if the 1% and 99% quantiles share the same sign.
• A strong sign test (B): the influence of a variable is considered important, if all of its t-values are of the same sign.
• An extreme CDF-Test (C): a variable is considered important, if the 99% confidence inter-vals around the minimum and maximum of a variable do not include zero.
• To compare EBA with other methods which select only a few variables (about 50 variables), we add an absurd test (D), which includes a variable only if a(1−7.342·10−51)% confi-dence interval around the mean does not include zero.
Since every variable is included in at least 128777 regressions47, there are still several variables which pass test D easily. There is no specific ordering of the tests except that any variable which passes test B also passed test A. Even a variable which passes the most restrictive test D may not pass test C if the distribution of the variable’s t-values has rather long tails. However, we should not be too impressed by the results, reminding the advice given byLovell(1983): “it is ironic that the data mining procedure that is most likely to produce regression results that appear impressive in terms of the customary criteria is also likely to be the most misleading in terms of what it asserts about the underlying process generating the data under study.”
However, we do not use EBA to find any underlying model structure but to find variables which seem to have a stable influence in regard to the results a study provides. For reasons of robustness, we may not want to include variables with very asymmetrical tails, which might indicate an un-stable distribution. Therefore, by calculating two stability coefficients, we exclude those variables X, which do not satisfy either
(X99%−X)/(X−X1%)∈[0.75,1.25]or(X/X50%)∈[0.99,1.01], whereasXy%is they%-quantile of the distribution of variable X.
Although EBA is often used in economics (e.g.,Levine and Renelt(1992);Sala-I-Martin(1997) or Bartley et al. (1998)) and also in deterrence studies (e.g., McManus (1985) or McAleer and Veall(1989)), it has several disadvantages. First, computing the statistics of all Nk
combinations is, in practice, computationally impossible for even smallkifN is large. Our own implementation in STATA (Statacorp LP,2005) requires one gigabyte of data per 3.6 million regressions and has a runtime of O(Nk). Therefore, the largestk possible is three, resulting in 515−53
=21978620 regressions generating about 6GB of data, requiring about one week of calculation on a 4.2GHz Athlon X2 using only one core (k=4 would result in 2785 million regressions, taking 127x more time to run and would generate about 1TB of data; it is unlikely that an optimized version of the al-gorithm would make this feasible). Second, the vote-counting problem (Hedges and Olkin,1985)
47This is the number of observations on which the interpretation of each variable is based.
might increase the difficulty of interpreting the distributions, because errors of the second type increase with the number of observations (in this case combinations). Third, it is an unresolved problem whether the calculated t-values should be weighted, e.g., with the ML of the respective model (Sala-I-Martin, 1997). Weighting can improve the quality of the conclusions (minimizing the influence of obviously improper models) or dampen them (since all models, whether they have a high ML or not, will most likely suffer severely from omitted variable bias).
Results from EBA could be further analyzed by applying a Response Surface Analysis (RSA), as sketched byFlorax and de Groot(2002). However, this is not done here due to computational constraints (in combination with an EBA, the algorithm has a runtime ofO(Nk+1)). Instead, we apply a simple check for tail characteristics using the stability coefficients described above.
While interpreting the results, displayed in table 3.51, we have to keep in mind that all vari-ables are accompanied by seven other varivari-ables of which five appear in every regression. Thus, the linear effects of the year of publication, the journal as media of publication, the overall in-fluence of the user tr (i.e., the study was recorded in Darmstadt) and the number of observations are already taken care of. The reported statistics refer to the t-values across the regressions of all three-dimensional (unordered) subsets of the remaining variables. Negative values indicate that a variable enhances the compliance with the deterrence hypothesis (i.e., the null hypothesis is discarded with larger confidence) as it increases (e.g., when the dummy variable is one). Positive values indicate the reverse, while values near zero imply that a variable is not a significant determi-nant in a study about general deterrence. We have to keep in mind that a variable, which is almost never significant (e.g., most of its absolute t-values are below 1.96), but is negative (or positive) in all cases, still indicates that it may have a strong influence on the (normalized) t-values. For reasons of parsimony, we only display those variables which pass at least two tests (244 variables are not shown).
Table 3.51: Multivariate analysis - extreme bounds analysis
Variable var A B C D mean sd min 1% 50% 99% max
Study: publication, number 83.3 1 1 0 0 1.70 0.17 0.22 1.10 1.72 2.18 3.07
Study: publication, year 100.0 1 1 0 0−1.46 0.14 −2.49−1.87−1.46−1.07−0.31
Study: measuring points 97.4 1 1 1 0−1.50 0.13 −2.36−1.88−1.50−1.06−0.44
Study: size of first realized sample 58.8 1 1 1 1−4.10 0.06 −4.64−4.31−4.10−3.91−3.63 Study: rate of return of second sample 0.9 1 1 1 1−1.61 0.08 −2.36−1.93−1.61−1.31−0.45 Study: error and plausibility checks 31.4 1 1 1 0−0.80 0.11 −1.46−1.13−0.78−0.56−0.30
Study: tests of significance 9.4 1 1 1 1−2.21 0.13 −3.58−2.55−2.21−1.87−1.54
Study: number of bivariate estimates 32.4 1 1 1 0 1.86 0.14 0.83 1.40 1.85 2.34 2.90
Study: user, mw 1.4 1 1 1 1 1.28 0.07 0.92 1.10 1.27 1.55 1.83
Study: publication, miscellaneous type 3.3 1 1 1 0 0.78 0.07 0.30 0.58 0.78 0.95 1.15
Study: publication, book 1.5 1 1 1 0−0.52 0.06 −0.87−0.68−0.52−0.35−0.17
Study: author, Steven D. Levitt 1.7 1 1 1 1 1.63 0.09 0.95 1.41 1.62 1.99 2.52
Study: author, Simon Hakim 1.0 1 1 1 1−1.35 0.07 −2.26−1.52−1.35−1.17−0.91
continued on the next page. . .
. . . last page oftable 3.51continued
Variable var A B C D mean sd min 1% 50% 99% max
Study: author, Daniel S. Nagin 1.3 1 1 1 1 1.30 0.08 0.52 1.01 1.29 1.55 1.80
Study: author, Raymond Paternoster 2.4 1 1 0 0−1.31 0.17 −2.50−1.76−1.33−0.80−0.09
Study: author, Isaac Ehrlich 1.0 1 1 1 1−3.73 0.21 −5.43−4.19−3.74−2.85−1.80
Study: author, Harold G. Grasmick 1.6 1 1 1 0−2.15 0.17 −4.94−2.52−2.16−1.80−1.45
Study: author, Laurence H. Ross 1.0 1 1 0 0−0.79 0.06 −1.34−0.94−0.80−0.59−0.05
Study: journal, Economic Inquiry 1.4 1 1 1 1−1.23 0.04 −2.02−1.38−1.23−1.10−0.68
Study: journal, Criminal Justice 2.2 1 1 1 1 2.53 0.12 1.25 2.23 2.53 2.88 3.15
Study: journal, Law and Economics 2.8 1 1 1 1−1.58 0.08 −2.13−1.79−1.57−1.35−0.86 Study: journal, American Economic Review 2.0 1 1 0 0−1.66 0.15 −3.09−2.19−1.66−1.25−0.35
Study: journal, Social Forces 2.2 1 1 1 0−2.39 0.18 −3.75−2.91−2.39−1.78−0.80
Study: journal, American Journal of Economics and Sociology 1.7 1 1 1 1 0.96 0.06 0.43 0.74 0.96 1.10 1.52 Study: journal, Review of Economics and Statistics 1.6 1 1 1 1−1.12 0.06 −1.45−1.27−1.13−0.92−0.53
Study: journal, Crime and Delinquency 1.1 1 1 0 0 2.01 0.17 0.37 1.52 2.01 2.65 3.80
Study: journal, Quantitative Criminology 1.4 1 1 0 1 0.89 0.06 0.14 0.71 0.90 1.01 1.24 Study: journal, Southern Economic Journal 1.3 1 1 0 0 1.57 0.14 0.29 1.21 1.58 1.98 2.91 Study: journal, Social Science Quarterly 2.2 1 1 1 0−2.22 0.16 −3.29−2.65−2.21−1.74−0.49
Study: journal, Legal Studies 2.0 1 1 1 1−1.24 0.08 −1.82−1.51−1.24−0.98−0.66
Study: publication, USA 21.9 1 1 1 1−1.79 0.11 −2.49−2.12−1.79−1.47−0.70
Study: publication, Netherlands 2.6 1 1 1 1 2.55 0.09 1.73 2.34 2.54 2.85 3.42
Study: author, Canada 5.2 1 1 0 1 3.09 0.20 0.47 2.41 3.11 3.42 3.82
Study: author, Switzerland 1.0 1 1 1 1 3.04 0.16 2.25 2.69 3.01 3.70 4.53
Study: author, Sweden 0.9 1 1 1 1 2.48 0.11 1.58 2.17 2.49 2.78 3.29
Study: author, psychology 4.2 1 1 1 1−3.31 0.16 −4.24−3.59−3.34−2.61−1.66
Study: publication, economics 36.0 1 1 1 1−1.80 0.11 −2.47−2.07−1.80−1.37−0.64
Study: publication, criminology 20.4 1 1 1 1 3.92 0.12 2.93 3.51 3.92 4.21 4.61
Study: institute, law 3.9 1 1 1 0−1.04 0.08 −1.68−1.24−1.04−0.78−0.38
Study: institute, miscellaneous 14.9 1 1 1 1 3.25 0.13 1.94 2.86 3.24 3.65 4.12
Study: cross section 23.2 1 1 1 0 1.61 0.16 0.68 1.21 1.62 2.36 3.14
Study: experiment (field, institutional initiative) 1.6 1 1 1 1−1.65 0.09 −2.06−1.83−1.66−1.19−0.80 Study: first population, United Kingdom 5.0 1 1 1 1−1.29 0.07 −1.93−1.57−1.29−1.13−0.93
Study: first population, Canada 4.3 1 1 1 1 3.87 0.21 1.35 2.91 3.90 4.28 5.10
Study: first population, Finland 0.9 1 1 0 0−4.97 0.61−12.25−6.31−4.93−3.72−0.54 Study: first population, Australia 1.7 1 1 0 0−1.06 0.12 −2.67−1.56−1.05−0.75−0.05
Study: first population, other country 6.2 1 1 0 0 0.79 0.08 0.22 0.57 0.78 1.03 1.90
Study: sample base, second population, complete country 2.4 1 1 0 1−2.05 0.13 −2.88−2.29−2.07−1.43−0.30 Study: sample unit, first population, states 21.9 1 1 1 1 2.80 0.13 2.10 2.43 2.81 3.22 3.62 Study: sample individuals, second population, students 0.5 1 1 1 0−3.41 0.25 −7.68−3.99−3.44−2.42−1.16
Study: sample of extreme groups 0.5 1 1 0 0 1.37 0.16 0.14 0.97 1.36 1.96 3.72
Study: complete sample 9.8 1 1 1 1−1.21 0.06 −1.63−1.37−1.21−1.06−0.85
Study: miscellaneous public data base 40.1 1 1 1 0 1.26 0.13 0.37 0.83 1.28 1.62 2.55
Study: income above average 0.6 1 1 0 0−0.80 0.09 −1.94−1.13−0.80−0.57−0.16
Study: upper class over-represented 0.6 1 1 0 0−0.80 0.09 −1.94−1.13−0.80−0.57−0.16 Study: main location>500000 inhabitants 3.5 1 1 1 1−1.32 0.05 −1.72−1.45−1.32−1.18−0.99 Study: main location 100000-500000 inhabitants 1.4 1 1 0 0 0.33 0.05 0.02 0.20 0.32 0.49 0.86
continued on the next page. . .
. . . last page oftable 3.51continued
Variable var A B C D mean sd min 1% 50% 99% max
Study: mixed location 0.5 1 1 0 0 0.55 0.06 0.03 0.38 0.55 0.72 1.14
Study: does not check representativeness 26.9 1 1 1 1 2.46 0.12 1.73 2.15 2.44 2.83 3.32 Study: conditions for significance check fulfilled 49.2 1 1 0 0 0.80 0.09 0.09 0.54 0.80 1.06 1.46
Estimate: number of used covariates 74.1 1 1 0 0 1.03 0.10 0.21 0.68 1.04 1.29 1.67
Estimate: deterrence is focus-variable 14.8 1 1 1 1−1.38 0.08 −1.99−1.63−1.39−1.16−0.63
Estimate: deterrence is a covariates 14.8 1 1 1 1 1.38 0.08 0.63 1.16 1.39 1.63 1.99
Estimate: sub-sample of males 1.4 1 1 1 0 1.74 0.12 0.94 1.39 1.75 2.10 2.60
Estimate: sub-sample of youths 1.3 1 1 1 1−1.03 0.04 −1.31−1.12−1.03−0.94−0.37
Estimate: sub-sample of urban area 0.2 1 1 1 0 1.40 0.13 0.37 0.99 1.40 1.81 2.73
Estimate: sub-sample with high detection probability 0.3 1 1 1 1−2.10 0.11 −3.01−2.48−2.10−1.73−1.34 Estimate: exogenous, index multiplicative 1.9 1 1 1 1 1.09 0.06 0.20 0.93 1.08 1.28 1.52 Estimate: exogenous, index miscellaneous 0.8 1 1 0 0 1.41 0.16 0.03 0.92 1.42 2.09 2.96 Estimate: exogenous, index items unprocessed 2.8 1 1 1 1 1.20 0.07 0.38 1.00 1.19 1.45 1.85
Estimate: study type, death penalty 8.2 1 1 1 1 3.23 0.15 2.16 2.77 3.25 3.60 5.31
Estimate: exogenous, crime data, arrest rate 9.5 1 1 1 1−3.02 0.13 −3.94−3.43−3.00−2.68−2.00 Estimate: exogenous, crime data, conviction rate 3.9 1 1 1 1−1.56 0.06 −1.90−1.72−1.55−1.42−1.10 Estimate: exogenous, crime data, incarceration rate 0.6 1 1 0 0 0.67 0.08 0.08 0.46 0.68 0.93 1.37 Estimate: exogenous, crime data, mean sentence length (sentenced) 2.0 1 1 1 0 1.83 0.15 0.91 1.48 1.84 2.59 3.27 Estimate: exogenous, crime data, mean sentence length (served) 1.7 1 1 0 0 1.65 0.18 0.04 1.08 1.67 2.13 2.87 Estimate: exogenous, crime data, police expenditures 4.0 1 1 1 1 1.82 0.08 1.30 1.61 1.82 2.10 2.76 Estimate: exogenous, crime data, police strength 7.9 1 1 1 1 3.09 0.08 2.62 2.88 3.09 3.33 3.89
Estimate: exogenous, crime data, other 8.5 1 1 1 0 0.62 0.07 0.20 0.43 0.63 0.80 1.50
Estimate: exogenous, crime data, probability dummy (regime shift) 3.5 1 1 1 0−2.72 0.23 −5.05−3.28−2.73−2.01−0.70 Estimate: exogenous, crime data, severity dummy (regime shift) 3.6 1 1 1 1−1.55 0.08 −2.28−1.78−1.55−1.30−1.00 Estimate: exogenous, crime data, incarceration per crime 0.9 1 1 1 1−2.06 0.12 −3.32−2.46−2.05−1.62−1.08 Estimate: exogenous, crime data, convicted per crime 0.6 1 1 1 1−2.40 0.10 −3.51−2.69−2.39−2.16−1.39 Estimate: exogenous, survey, type of punishment 0.3 1 1 1 0 1.41 0.11 0.58 1.13 1.40 1.79 2.39 Estimate: exogenous, survey, probability of other kind of punishment 0.4 1 1 0 0 2.32 0.24 0.34 1.50 2.33 3.06 4.26 Estimate: exogenous, survey, probability of detection by friends or family 0.2 1 1 1 1−2.74 0.18 −4.07−3.23−2.76−2.12−1.45 Estimate: exogenous, survey, probability of punishment by friends or family 1.6 1 1 1 1−3.44 0.20 −4.71−4.00−3.46−2.78−2.05 Estimate: exogenous, survey, severity of punishment by friends or family 1.0 1 1 0 0 1.53 0.19 0.44 0.99 1.52 2.13 2.96 Estimate: exogenous, survey, probability of detection by others 0.4 1 1 1 1 1.43 0.05 0.92 1.26 1.42 1.63 1.88 Estimate: exogenous, survey, probability of punishment by others 0.9 1 1 1 0 1.37 0.15 0.52 0.95 1.35 1.87 2.67 Estimate: exogenous, survey, severity of punishment by others 0.4 1 1 1 1 1.30 0.04 0.86 1.18 1.29 1.44 1.62 Estimate: exogenous, survey, time between offense and clearance 0.1 1 1 1 0−1.09 0.09 −1.86−1.43−1.08−0.87−0.61
Estimate: exogenous, in differences 3.1 1 1 1 1 2.33 0.13 1.36 2.03 2.34 2.80 4.14
Estimate: endogenous, number of convicted 0.3 1 1 0 0 1.61 0.17 0.20 1.09 1.63 2.09 5.04 Estimate: endogenous, probability of delinquency of fictitious offense
(sur-veyed is delinquent)
1.2 1 1 0 0 1.60 0.20 0.26 1.01 1.59 2.15 3.09
Estimate: endogenous and exogenous relate not to the same offense 6.3 1 1 1 1 1.96 0.12 1.34 1.66 1.96 2.35 4.20
Estimate: crime category, other 1.5 1 1 1 0 2.13 0.17 0.55 1.72 2.12 2.84 3.73
Estimate: offense, manslaughter 1.2 1 1 0 0 0.72 0.10 0.05 0.42 0.72 1.14 1.87
Estimate: offense, negligent assault 1.8 1 1 0 0 0.80 0.10 0.25 0.55 0.80 1.14 1.86
Estimate: offense, burglary 12.2 1 1 1 0 1.36 0.09 0.62 1.05 1.36 1.62 1.95
continued on the next page. . .
. . . last page oftable 3.51continued
Variable var A B C D mean sd min 1% 50% 99% max
Estimate: offense, drug possession (soft) 0.7 1 1 1 0 1.38 0.11 0.59 1.12 1.37 1.82 2.51 Estimate: offense, drug possession (hard) 0.5 1 1 1 1−1.26 0.03 −1.85−1.40−1.26−1.21−0.98
Estimate: offense, sexual assault 0.5 1 1 1 0 1.40 0.10 0.53 1.11 1.41 1.72 2.44
Estimate: offense, embezzlement 0.1 1 1 1 1−1.62 0.09 −3.01−1.96−1.62−1.37−1.02
Estimate: offense, other crimes 8.1 1 1 0 0 1.10 0.10 0.09 0.85 1.11 1.41 1.80
Estimate: offense, crime rate (general) 6.2 1 1 1 0 1.15 0.09 0.54 0.88 1.17 1.36 1.67
Estimate: offense, vehicle theft 8.5 1 1 1 0 1.32 0.09 0.59 1.04 1.32 1.56 1.86
Estimate: offense, environmental crimes, Violations of prescriptive limits 2.3 1 1 1 1 1.47 0.07 0.72 1.25 1.47 1.71 2.10 Estimate: violent characteristics 15.1 1 1 1 0−1.40 0.10 −2.36−1.66−1.40−1.13−0.38
Estimate: endogenous, metric category 20.0 1 1 0 0 2.27 0.19 0.07 1.68 2.28 2.76 3.29
Estimate: endogenous, interval category 4.1 1 1 0 0 1.19 0.17 0.25 0.75 1.18 1.75 2.85 Estimate: endogenous, binary category 9.6 1 1 1 1−2.15 0.11 −2.71−2.40−2.16−1.82−0.62 Estimate: endogenous, other transformation 7.8 1 1 1 1−1.20 0.06 −1.76−1.42−1.20−1.08−0.38 Estimate: endogenous and exogenous relate to the same time 28.0 1 1 0 0−0.98 0.12 −1.97−1.29−0.99−0.62−0.05 Estimate: endogenous occurs before exogenous (lagged endogenous) 1.3 1 1 1 1 2.05 0.07 1.25 1.86 2.05 2.27 2.55
Estimate: covariate, sex 14.3 1 1 0 0−0.57 0.09 −1.29−0.87−0.57−0.32−0.04
Estimate: covariate, nationality 3.3 1 1 1 1 2.73 0.12 1.94 2.41 2.74 3.09 3.80
Estimate: covariate, profession 0.4 1 1 0 0 0.83 0.09 0.11 0.51 0.84 1.06 1.77
Estimate: covariate, social integration 1.5 1 1 1 0 2.05 0.17 0.64 1.52 2.04 2.59 3.28
Estimate: covariate, religion 1.7 1 1 1 0 1.31 0.12 0.39 0.96 1.31 1.66 2.23
Estimate: covariate, drug usage 1.3 1 1 1 1−0.88 0.06 −1.30−1.12−0.88−0.75−0.59
Estimate: covariate, previous convictions 1.6 1 1 1 1 2.93 0.18 1.65 2.32 2.93 3.50 4.18 Estimate: covariate, personal characteristics 3.0 1 1 1 1−1.51 0.05 −1.90−1.66−1.51−1.33−1.01 Estimate: covariate, fixed effects (spatial) 10.0 1 1 1 1−1.74 0.09 −2.71−2.12−1.73−1.54−1.29
Estimate: covariate, random effects 1.0 1 1 1 1 2.48 0.11 1.30 2.07 2.50 2.77 3.29
Estimate: covariate, other 35.8 1 1 1 0 2.08 0.17 0.88 1.53 2.11 2.58 3.09
Estimate: covariate, time trend 5.4 1 1 0 0 1.60 0.15 0.30 1.16 1.62 1.97 2.77
Estimate: covariate, poverty, welfare 6.4 1 1 1 1 3.25 0.10 2.37 2.94 3.26 3.51 3.95
Estimate: covariate, urbanity 8.2 1 1 1 0 1.92 0.15 1.15 1.60 1.92 2.57 3.99
Estimate: covariate, GDP 1.4 1 1 1 0−1.04 0.07 −1.72−1.24−1.03−0.85−0.47
Estimate: covariate, population (-growth) 11.5 1 1 1 0 1.43 0.11 0.57 1.10 1.44 1.76 2.21 Estimate: covariate, alcohol (consumption) 1.7 1 1 1 1 2.41 0.12 1.47 2.06 2.42 2.69 3.39
Estimate: covariate, labor force 2.5 1 1 1 1−1.65 0.10 −2.41−1.94−1.64−1.38−0.77
Estimate: covariate, risk propensity 0.8 1 1 1 0 4.67 0.33 2.51 3.53 4.68 5.85 7.37
Estimate: no correction for simultaneity 19.3 1 1 1 1−2.09 0.12 −3.08−2.44−2.11−1.76−0.58 Estimate: correction for simultaneity (with methodology) 9.1 1 1 1 1 2.13 0.12 0.68 1.87 2.14 2.49 3.20
Estimate: weighted model 6.8 1 1 1 1 1.13 0.06 0.56 0.98 1.12 1.32 1.69
Estimate: unweighted model 6.8 1 1 1 1−1.13 0.06 −1.69−1.32−1.12−0.98−0.56
Estimate: bivariate method, bivariate regression 0.6 1 1 1 1−2.70 0.12 −3.26−2.96−2.71−2.25−1.72 Estimate: bivariate method, correlation 9.5 1 1 1 1 2.43 0.16 1.21 2.00 2.43 2.84 3.82 Estimate: bivariate method, point biserial correlation 0.4 1 1 1 0−1.33 0.12 −2.80−1.88−1.34−1.04−0.64
Estimate: bivariate method,ρ 0.5 1 1 1 0−1.38 0.15 −3.01−2.05−1.37−1.03−0.43
Estimate: bivariate method, t-test for independent samples 0.5 1 1 1 1−1.57 0.07 −3.16−1.77−1.56−1.40−1.24
Estimate: bivariate method,τ 0.9 1 1 1 1−2.42 0.13 −3.33−2.79−2.42−2.08−1.29
continued on the next page. . .
. . . last page oftable 3.51continued
Variable var A B C D mean sd min 1% 50% 99% max
Estimate: multivariate method, OLS 24.2 1 1 1 0 1.83 0.15 0.48 1.35 1.85 2.27 3.01
Estimate: multivariate method, GMM 0.8 1 1 1 1 3.06 0.20 0.79 2.40 3.09 3.61 4.42
Estimate: multivariate method, other ML method 1.1 1 1 1 0 2.77 0.20 0.73 2.11 2.80 3.49 4.34 Estimate: multivariate method, GLS 1.7 1 1 1 1−3.20 0.14 −3.91−3.55−3.21−2.62−2.07 Estimate: multivariate method, VAR 0.6 1 1 1 0−1.05 0.10 −2.19−1.35−1.04−0.74−0.44
Estimate: test of significance 5.5 1 1 1 0 0.95 0.08 0.37 0.78 0.95 1.15 2.17
Estimate: no test of significance 5.5 1 1 1 0−0.95 0.08 −2.17−1.15−0.95−0.78−0.37 Estimate: square root of sample size for negative values 79.2 1 1 1 1−3.38 0.07 −4.35−3.67−3.37−3.26−3.04 Estimate: square root of sample size for positive values 82.5 1 1 1 1 6.21 0.07 5.76 6.06 6.20 6.44 6.98
A, B, C and D correspond to the four tests of significance described insubsection 3.6.4. The columnvarrefers to the variation of a variable (i.e., the percentage of valid observations); the maximum variation for dummy variables is fifty percent. All other values are properties of the distribution of the t-values in the regressions. For reasons of parsimony we report only those variables in this table, which pass more than one test; 244 variables which only pass test A or are not considered stable are not shown (in fact, only 114 out of 515 variables do not pass test A).
The reference category for dummies is usually the opposite property or, in the case of multiple categories, the missing values.
end of thetable 3.51
The results concerning the countries of the authors are, at large, compatible with the bivariate analysis insection 3.5. Canadian, Australian, Swedish and authors from Switzerland have more positive t-values, while authors from the U.S., UK and Finland48 have more negative t-values.
The results for the author-variables, which pass at least one of the tests, are also in line with table 3.36with the exception of Nagin, who has now a positive effect on the (normalized) t-values and Marvell who has a negative effect.
Surprisingly, the only disciplines of the authors to pass the tests are psychology and miscella-neous; the direction of their influences are as expected (table 3.30 seemed to suggest that being an economist, sociologist or criminologist would also be important). Nevertheless, these effects are found in the characteristics of the publisher and the institutional background of the authors.
Authors from an economic or law institution present more negative results, while authors with a criminological or miscellaneous background seem to have the opposite effect. The same applies to the type of the publisher.
Looking at the specific journals delivers a more diversified picture: while all significant crim-inological journals have rather positive values, economical, sociological and other journals can be found on both sides. The number of selected journal shows no obvious tendency towards a specific discipline.
It is also noteworthy that journals are associated with rather positive (normalized) t-values, while books and working papers are associated with a negative effect. Assuming that a publication bias is, if at all, more present for studies published in journals, this would imply that the results are
48In fact, only Matti Vir´en comes from Finland.
slightly biased towards zero. However, recalling table 3.24casts some doubts on this reasoning because analytical evidence indicates a publication bias for books and working papers but not for journal articles.
Those studies which examine Canadian data, use cross sections, employ a miscellaneous pub-lic data base, present large numbers of bivariate estimates or study the states of a nation, stand out and have a positive effect on the (normalized) t-values. The opposite effect is found among studies which employ complete samples, experiments, data from the United Kingdom, Australia or Germany, use data from large cities, report checks of significance or checks for plausibility and errors.
Looking at the implemented covariates, the results of table 3.45 are largely replicated. Con-trolling for spatial fixed effects, labor force, GDP, drug usage and personal characteristics imply more negative (normalized) t-values. Only the latter does not comply with the results from the ANOVA. Smaller (i.e., more positive) effects are found when religion, population, urbanity, social integration, alcohol consumption, random effects, nationality, previous convictions, poverty and time trends are controlled for. Again, only the latter does not conform with the ANOVA.
There are only a few studied crimes which have a significant influence on the outcome of an es-timate. Of those with a negative influence, no one passes more than one test. Malicious mischief, speeding, severe larceny and drunk driving are compatible with the results fromtable 3.43but pass only the first test, while general drug related crimes have a negative effect (opposite to the results from the ANOVA). Among the crimes with a positive effect, all are in line with the results from the ANOVA and the following crimes pass more than one test: burglary, general crime rate, environ-mental offenses, manslaughter, negligent assault, other crimes and vehicle theft. Environenviron-mental offenses stand out by passing all four tests while the effect is ambiguous in the ANOVA.
The results of the variables which measure deterrence comply withtable 3.42. Especially the arrest and conviction rate and the regime shift dummies have a negative effect and pass three or four tests. A positive effect is found among the sentence lengths and police related deterrence variables. Among the implemented methods, the usage of correlations, OLS and 2SLS have a very prominent positive effect on the (normalized) t-values, while ARIMA- and GLS-methods imply more negative values. These are more or less in line withtable 3.48.
It is also interesting to note that exogenous variables in binary form are negatively associated, while metric variables and those measuring intervals have a positive (normalized) impact on t-values. More negative (normalized) t-values are found when simultaneity is not accounted for, the model is not weighted, deterrence is the focus of a study, a sample of youths is studied, the exogenous variables are transformed in another form (than log or differences) or a violent crime is studied. A positive effect is found when the deterrent variable and the endogenous variable do not relate to the same offense, the number of included covariates increases, simultaneity is methodologically accounted for, the deterrence variable is measured in differences or the study is about the death penalty. The most significant variable is the square root of the sample size, diversified by the sign of the t-values. This relationship indicates the existence of an effect and is
described insection 3.4.