Determinants of Murder Rates in the United States
MurderRates.RdCross-section data on states in 1950.
Usage
data("MurderRates")Format
A data frame containing 44 observations on 8 variables.
- rate
Murder rate per 100,000 (FBI estimate, 1950).
- convictions
Number of convictions divided by number of murders in 1950.
- executions
Average number of executions during 1946–1950 divided by convictions in 1950.
- time
Median time served (in months) of convicted murderers released in 1951.
- income
Median family income in 1949 (in 1,000 USD).
- lfp
Labor force participation rate in 1950 (in percent).
- noncauc
Proportion of population that is non-Caucasian in 1950.
- southern
Factor indicating region.
References
Maddala, G.S. (2001). Introduction to Econometrics, 3rd ed. New York: John Wiley.
McManus, W.S. (1985). Estimates of the Deterrent Effect of Capital Punishment: The Importance of the Researcher's Prior Beliefs. Journal of Political Economy, 93, 417–425.
Stokes, H. (2004). On the Advantage of Using Two or More Econometric Software Systems to Solve the Same Problem. Journal of Economic and Social Measurement, 29, 307–320.
Examples
data("MurderRates")
## Maddala (2001, pp. 331)
fm_lm <- lm(rate ~ . + I(executions > 0), data = MurderRates)
summary(fm_lm)
#>
#> Call:
#> lm(formula = rate ~ . + I(executions > 0), data = MurderRates)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -4.5306 -1.1247 -0.2501 0.8773 6.3045
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -8.497374 10.421497 -0.815 0.4204
#> convictions -3.696766 2.675976 -1.381 0.1759
#> executions -3.566994 6.593152 -0.541 0.5919
#> time -0.017940 0.006836 -2.624 0.0128 *
#> income -4.094888 1.778390 -2.303 0.0274 *
#> lfp 0.399650 0.219809 1.818 0.0776 .
#> noncauc 6.444205 5.493819 1.173 0.2487
#> southernyes 2.540775 1.315494 1.931 0.0616 .
#> I(executions > 0)TRUE 2.598009 1.231312 2.110 0.0421 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 2.349 on 35 degrees of freedom
#> Multiple R-squared: 0.7746, Adjusted R-squared: 0.723
#> F-statistic: 15.03 on 8 and 35 DF, p-value: 2.859e-09
#>
model <- I(executions > 0) ~ time + income + noncauc + lfp + southern
fm_lpm <- lm(model, data = MurderRates)
summary(fm_lpm)
#>
#> Call:
#> lm(formula = model, data = MurderRates)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.70536 -0.26992 0.09636 0.27047 0.50990
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.9929477 1.3260699 1.503 0.14113
#> time 0.0014615 0.0009978 1.465 0.15122
#> income 0.6577319 0.2404256 2.736 0.00941 **
#> noncauc 1.9882407 0.7595481 2.618 0.01264 *
#> lfp -0.0545619 0.0282569 -1.931 0.06098 .
#> southernyes 0.3433565 0.1892451 1.814 0.07753 .
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.3533 on 38 degrees of freedom
#> Multiple R-squared: 0.3376, Adjusted R-squared: 0.2504
#> F-statistic: 3.873 on 5 and 38 DF, p-value: 0.0062
#>
## Binomial models. Note: southern coefficient
fm_logit <- glm(model, data = MurderRates, family = binomial)
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(fm_logit)
#>
#> Call:
#> glm(formula = model, family = binomial, data = MurderRates)
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 10.99326 20.77336 0.529 0.5967
#> time 0.01943 0.01040 1.868 0.0617 .
#> income 10.61013 5.65409 1.877 0.0606 .
#> noncauc 70.98785 36.41181 1.950 0.0512 .
#> lfp -0.66763 0.47668 -1.401 0.1613
#> southernyes 17.33126 2872.17069 0.006 0.9952
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 44.584 on 43 degrees of freedom
#> Residual deviance: 17.465 on 38 degrees of freedom
#> AIC: 29.465
#>
#> Number of Fisher Scoring iterations: 19
#>
fm_logit2 <- glm(model, data = MurderRates, family = binomial,
control = list(epsilon = 1e-15, maxit = 50, trace = FALSE))
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(fm_logit2)
#>
#> Call:
#> glm(formula = model, family = binomial, data = MurderRates, control = list(epsilon = 1e-15,
#> maxit = 50, trace = FALSE))
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.099e+01 2.077e+01 0.529 0.5967
#> time 1.943e-02 1.040e-02 1.868 0.0617 .
#> income 1.061e+01 5.654e+00 1.877 0.0606 .
#> noncauc 7.099e+01 3.641e+01 1.950 0.0512 .
#> lfp -6.676e-01 4.767e-01 -1.401 0.1613
#> southernyes 3.133e+01 1.733e+07 0.000 1.0000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 44.584 on 43 degrees of freedom
#> Residual deviance: 17.465 on 38 degrees of freedom
#> AIC: 29.465
#>
#> Number of Fisher Scoring iterations: 33
#>
fm_probit <- glm(model, data = MurderRates, family = binomial(link = "probit"))
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(fm_probit)
#>
#> Call:
#> glm(formula = model, family = binomial(link = "probit"), data = MurderRates)
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 6.91551 11.34891 0.609 0.5423
#> time 0.01131 0.00567 1.995 0.0460 *
#> income 6.46112 3.10937 2.078 0.0377 *
#> noncauc 42.49827 19.62469 2.166 0.0303 *
#> lfp -0.40929 0.26523 -1.543 0.1228
#> southernyes 5.46462 551.39841 0.010 0.9921
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 44.584 on 43 degrees of freedom
#> Residual deviance: 17.281 on 38 degrees of freedom
#> AIC: 29.281
#>
#> Number of Fisher Scoring iterations: 19
#>
fm_probit2 <- glm(model, data = MurderRates , family = binomial(link = "probit"),
control = list(epsilon = 1e-15, maxit = 50, trace = FALSE))
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(fm_probit2)
#>
#> Call:
#> glm(formula = model, family = binomial(link = "probit"), data = MurderRates,
#> control = list(epsilon = 1e-15, maxit = 50, trace = FALSE))
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 6.916e+00 1.135e+01 0.609 0.5423
#> time 1.131e-02 5.670e-03 1.995 0.0460 *
#> income 6.461e+00 3.109e+00 2.078 0.0377 *
#> noncauc 4.250e+01 1.962e+01 2.166 0.0303 *
#> lfp -4.093e-01 2.652e-01 -1.543 0.1228
#> southernyes 7.881e+00 1.253e+06 0.000 1.0000
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 44.584 on 43 degrees of freedom
#> Residual deviance: 17.281 on 38 degrees of freedom
#> AIC: 29.281
#>
#> Number of Fisher Scoring iterations: 35
#>
## Explanation: quasi-complete separation
with(MurderRates, table(executions > 0, southern))
#> southern
#> no yes
#> FALSE 9 0
#> TRUE 20 15