The Deterrent Effect of Capital Punishment Barbora Kolomazn´ıkov´a Charles University in Prague

Abstract Does capital punishment deter murder rates? Although there have been many empirical papers examining the issues, the answer is still not clear. The results vary from research to research. In this paper, I try to prove that there is not any deterrent effect of death penalty. I have collected panel data on 38 U.S. states from period 2000-2013. First, I compare different graphs and figures to find an evidence in recent movements and trends in murder rates and number of executions. Second, I condact a panel-data regression analysis to find an empirical evidence of no deterrent effect. After estimation of econometric model, I interpret and sum up the results and based on these findings I come to a conclusion, that there is not any deterrence.

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Introduction Death penalty (or capital punishment) is nowadays legal in 32 U.S. states. In the end of 2014 there were

3 035 inmates waiting in death row1 . 1 394 people were executed in the U.S. since the capital punishment reinstatement in 1976 (after five years lasting moratorium imposed by Supreme Court). The only industrialised and democratic country with legal capital punishment besides the United States is Japan (with 1 execution per 15 809 458 people).2 History of capital punishment is dated to the beginning of recorded history. One of the earliest mentions about death penalty can be found in the Code of Hammurabi or in the Torah (Jewish Law). Crimes punishable with execution consisted of murders, kidnappings, blasphemy or magic. It was also very common to torture the victim before carrying out execution. The reason for this was to obtain more information about committed crime or just to make the punishment worse. In some countries is this practise still in use. America’s use of death penalty was mostly influenced by Great Britain. When Britons came to the new world, they brought their laws along with them. Death penalty laws varied from colony to colony. Under these laws, denying the “true God” or striking someone’s parents were crimes punishable by death. The first documented 1 Death 2 CNN

row is a place in prison where prisoners are waiting for executions. International. edition.cnn.com: Death Penalty Fast Facts. [online]. 9.1.2015 [Accessed 2015-01-14]. Available from:

http://edition.cnn.com/2013/07/19/us/death-penalty-fast-facts/

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execution on territory of the United States is dated to 1608. British captain was sentenced to death because of spying for Spanish government. At the end of 18th century the first abolitionists’ movements took place. The main goal was to abolish death penalty or at least make the list of crimes punishable by death shorter. Large impact on these efforts had the essay On crimes and punishment by Cesare Beccaria (1767), in which he argued against the appropriateness of executions and their wrong justification. Nowadays, capital punishment is one of the most controversial issues discussed in the U.S. (and in the world as well). There are a lot of arguments against this practise, considering religious, moral or costs aspects. Because of problem of arbitrariness and capricious sentencing, in 1972 the Supreme Court imposed a moratorium on executions and therefore voided 40 statutes of death penalty. The moratorium was in effect to 1976. The most important argument of defenders of capital punishment is its deterrent effect on murder rates. There have been many studies, surveys and other empirical work with the aim to prove or deny this assumed effect of death penalty. Interestingly, each work provides different results. The aim of this work is to show that there is no detterent effect of executions carried out in the U.S. in period 2000-2013. First of all, I discuss in next section some trends in recent evolution of murder rates and executions. In section 3, I review two empirical papers about the deterrence issue and state my own model, which is based on one of the papers. Section 4 is devoted to description of data I used to estimate empirical model. Finally, section 5 discuss estismation method as well as a set of tests that have been used to correctly specify the model. There are also presented and interpreted results of panel-data regression analysis. Conclusion and summary of findings are placed in section 6.

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Deterrence and Capital Punishment In this section I would like to discuss some evidences of no deterrent effect of capital punishment on murder

rates in U.S. states in period 2000-2013. In next sections, I supplement this claims with regression analysis by estimating econometric model. As I have mentioned earlier, there has been a lot of empricial work done, but providing different results. Therefore, it can be difficult to conclude, if there is any deterrence. But first of all, let’s have a look at some annual data and graphs, which can shed some light upon this issue. If we look at Figure 2.1 (in Appendix), we can see that murder rate is on decline from 1990 onwards. But what is more important, average murder rate in non-death penalty states is lower than in death penalty states. Of course, this can be caused by national differences between each state. Therefore, it is convincing to compare neighbouring states, which are assumed to be very similar. Figure 2.2 compares 2008 murder rates in 4 death penalty states (Missouri, Connecticut, Illinois, Virginia) with their non-death penalty neighbours (Iowa, Massachussetts, Wisconsin and West Virginia, respectively). It is obvious that murder rates in former four states are higher that in the later ones. Moreover, if we compare the directions of movements in murder

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rates (Figure 2.1) and in number of executions (Figure 2.3), we can see that both are falling in period 2000-2013 (that is, their movements have the same direction). Hence, we definitely cannot claim that executions lower murder rates. It can be considered as one part of evidence against capital punishment’s deterrent effect. As can be seen from Figure 2.3, number of executions is declining since 1999. This trend might indicate declining popularity of death penalty. This claim supports recent Pew Research Center survey conducted in 20133 . While in 1996, 78 % of Americans were in favour of capital punishment, by 2013, this support had dropped to 55 %. Table 2.1 lists 10 U.S. states with the highest murder rates in year 2013. The highlighted ones are nondeath penalty states. So there are only three non-death penalty states and seven with legal capital punishment. Besides, out of these three, two of them had capital punishment law in period 2000-2013. If there was any deterrent effect, the murder rates of death penalty states would have not been so high.

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Empirical Model In the first part of this section, I review two econometric papers which focus on deterrent effect issue.

Secondly, I describe the model which will be used to estimate the effect of executions on murder rates. The first paper considering deterrent effect of capital punishment was The deterrent effect of capital punishment: a question of life and death by Isaac Ehrlich (1975). In this work, Ehrlich has shown that one execution would, on average, deter eight murders. He used 1933-1967 data to estimate a murder rate equation by instrumental variables. Later, there were other papers supporting Ehrlich’s findings, but using different set of data or different estimation methods, so the results might be considered to be fairly robust. It is not surprising, that there were a huge wave of criticism after presentation of Ehrlich’s results. Many people were (and still are) unwilling to accept the possibility of death penalty efficiency. Therefore, there were many papers directly attacking Ehrlich’s work and trying to disapprove his conclusions. Criticism targets different aspects of econometric work conducted by Ehrlich. For example, omitted variables or wrongly included variables, serial correlation, measurement error, functional form and inadequate sample. My model is based on a model from The deterrent effect of capital punishment: Evidence from a “Judicial experiment” by Hashem Dezhbakhsh and Joanna M. Shepherd (2003). In this paper, Dezhbakhsh and Shepherd used panel data, where cross-section units are U.S. states and time period is from 1960 to 2000. They included both death penalty and non-death penalty states. Besides examination of deterrent effect of capital punishment, they also estimated the effect of death penalty suspension imposed by the Supreme Court in 1972 (to 1976). They found significant deterrent effect, as well as significant effect of death penalty moratorium. 77 additional regressions were done to check the robustness of their results. Moreover, other control variables were included in the basic regression: per capita real income, unemployment rate, police employment, percent minority, percent 3

Pew Research. www.pewforum.org: Religion & Public Life Project. [online]. 28.3.2014 [Accessed 2015-01-14]. Available from:

http://www.pewforum.org/2014/03/28/shrinking-majority-of-americans-support-death-penalty/

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15-19 years old and percent 20-24 years old. Estimation method used was fixed effect method for panel data. Despite the similarity of model I use here and model used by Dezhbakhsh and Shepherd, my target is exactly the opposite. I want to show that there is not any deterrent effect. There are also other differences. I use more recent data (2000-2013) and only from states with death penalty. I made this decission, because many critics of deterrent effect argued that significant proofs of deterrence are reached only after including non-death penalty states in the samples (this can be the case of Dezhbakhsh and Shepherd). Moreover, in period 2000-2013 there was not any moratorium on national level. So I examine only the effect of executions on murder rates. Basic model of the interest is stated as murderrateit = β0 + β1 executionsit + β2 executionsi,t−1 + otherf actorsit + ai + uit where β0 , β1 and β2 are parameters to estimate and ai is an unobserved (or fixed) effect. Unobserved effect contains state specifics that are constant over time, such as state’s location in the U.S., historical reasons for high murder rates etc. I assume that these can be correlated with number of executions. Therefore, fixed effects estimation method will be used to estimate the underlying model. Other assumptions, such as no serial correlation or heteroskedasticity, will be examined. Detailed description of the method and estimation is provided in section 5.

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Revision of Data I use annual data on 38 U.S. states with death penalty law in effect between 2000 and 2013. Six states out of

this 38 abolished death penalty law during the period of interest. Nevertheless, I have decided to include them in the sample. The summary of executions and murder rates by states (alphabetically) can be seen in Table 4.1. The absolute “winner” in executions is Texas (with 309 executions between 2000-2013) and Louisiana among average murder rates (11,9) in 2000-2013. Summary statistics of dependent and explanatory variables can be seen in attached STATA log-file. Table 4.2 provides description of variables. I have chosen the variables, which are, in my opinion, most important in explaining murder rates. I admit that other variables can be included (such as detailed percentage division of minorities in the U.S. population or detailed age division) to better capture the effect, but the variables, that I have chosen, would serve my purpose well enough. As I have stated earlier, we are interested in murder rates (mrate), that is our dependent variable. Murder rate is number of murder per 100 000 inhabitants. Data were collected from annual crime reports of Federal Bureau of Investigation (FBI). Variable of our interest is number of executions (exec). Data comes from Death Penalty Information Center, where can be find other detailed information, such as information about inmates in death row, information about victims, statistics of death penalty and non-death penalty states and also many discussions and articles about death penalty deterrent effect.

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Employ denotes the number of law enforcement employees. This includes police officers as well as employees of security agencies. Range of values is quite wide: from 511 as minimum to maximum 123 506. Data were get from annual crime reports of FBI. Unemployment rate (unemp) is another important variable in explaining murder rates. Data provides U.S. Bureau of Labor Statistics. Gross national income per capita (GNI prc) is gross national income divided by total population. Unfortunately, I was not able to get data on state-level, so I have used national-level one. These can be obtained from U.S. Bureau of Economic Analysis. Arrest rate (arrate) is number of people arrested per 100 000 inhabitans. Like other crime data, number of people arrested comes from annual crime reports of FBI. Arrest rate was then computed using relevant population data. Percentage of minority (perc minor ) is percent of black, hispanic, asian and other minorities among population. Data were collected from U.S. Census Bureau. From the same source come data on population aged 25-29 (age25 29 ). It was difficult to find all data for each state, so I again use the national-level data.

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Estimation and Results I have decided to use fixed effects estimation. The decision is based on result of Hausman test, which compares

fixed and random effects estimates. The test produced p-value equal to zero in three decimal places, which indicates that the key random effects assumption (E(ai | X) = 0) is violated. Then I performed heteroskedasticity test, Pasaran cross-sectional dependence test and serial correlation test4 and concluded that it is appropriate to use some version of robust standard errors. There are two options - cluster-robust standard errors and DriscollKraay standard errors. Choosing standard errors does not affect estimated coefficients, only their t-statistics. Because Pasaran test rejected cross-sectional dependence, it seems that there is no reason to use Driscoll-Kraay, which is used especially to correct for cross-sectional dependence. But using Driscoll-Kraay allows to include variable age25 29 into the regression. If I use cluster-robust SE, including age25 29 is not allowed by STATA. In Appendix, I report both standard errors. The only important difference (except of the presence of age25 29 in the regression) is t-statistic on perc minor. It is significant using Driscoll-Kraay and insignificant using clusterrobust SE. But this changes nothing on the results and conclusions. Moreover, I added year dummies into the regression (their joint significance can be easily tested by using an F test). I do not report them in Table 5.1 just for brevity. GNI prc and employ were very close to random walk process (with ρ > 0, 9) and that is why I included them in first differences into the regression. I also included first lags of exec, lmrate and arrate, because they were assumed to have long-run effect on murder rates (or, in case of exec, its lag is assumed to have no effect 4 all

tests can be seen in STATA log-file

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on murder rates). lmrate denotes log of murder rates. I want to point out that estimating about 40 different regressions with different functional forms produced coefficients on exec (and its lag), which were statistically insignificant every time. This finding can serve as test of robustness of the model. It is also important to state that strict exogeneity assumption is really difficult one. It is almost imposible to completely assure its fulfillment. Nevertheless, I assume that this assumption hold. Assumptions about homoskedasticity and no serial correlation were violated, but Driscoll-Kraay standard errors have been used to correct for this. All test statistics and p-values should be asymptotically valid. Table 5.1 shows the results for the model. Both exec and its lag are statistically insignificant (even at 30% level). Therefore we can conclude that in period 2000-2013 there is not any deterrent effect of capital punishment on murder rates. Interestingly, exec has positive sign (what is exactly the oposite of deterrence). Maybe it is not so strange – if we look again at Figure 2.1 and Figure 2.3, both murder rates and number of executions were falling in period 2000-2013 (so they have the same direction or sign). Number of law enforcement employees as well as per capita GNI are statistically insignificant. In case of GNI, the reason could be national-level nature of the data. At least, it has got an expected negative sign. On the other hand, demploy is insignificant and with unexpected sign. One can argue that number of law enforcement employees is jointly determined with murder rates, so simultaneous equations model would be appropriate. But our goal is not to estimate the effect of law enforcement employees. Dropping it out of the regression does not make much difference in the results. Other variables are statistically significant at 5% level (perc minor at 10% using Driscoll-Kraay SE and insignificant using cluster-robust SE). The interpretation of coefficient on unemp is really interesting. It has got negative sign, which means that increasing unemployment rate leads to decreasing murder rate: %∆mrate =

100.(−0, 0292405)∆unemp

= −2, 92405.∆unemp So if unemployment rate rises by 1 percent, murder rate will be about 2,9 percent lower.5 Although the direction of the effect is unexpected, it is common in many empirical papers.6 This phenomenon does not have economic (or rational) explanation. Arrest rate have contemporaneous positive effect on murder rate, which si certainly something that one would not expect. Maybe it is because arrest rate is measure of criminal activity in given year. Then it is 5 more

accurate is %∆mrate

6 CAMERON,

=

100.(e−0,0292405 − 1)∆unemp

=

−2, 88171331.∆unemp

Samuel. A review of the econometric evidence on the effects of capital punishment. The Journal of Socio-Economics,

1994, 23.1: 197-214.

6

natural to assume that as criminal activity rises, murder rate will be higher. On the other hand, lag of arrest rate has negative sign. In this case, arrest rate can be a measure of police force efficiency (that means the ability of police to catch criminals). If police efficiency grows, murder rate falls. Effect of percentage of minorities can be computed in the same way as the effect of unemployment rate, that is %∆mrate = =

100.(0, 0171908)∆perc minor 1, 71908.∆perc minor

If there is 10% more minorities in the U.S. (which is quite possible, because number of minority population is still growing), murder rate will be about 17% higher.7 That is not a small effect. Percentage of population aged 25-29 has also significant effect.8 We can write %∆mrate = =

100.(0, 1316474)∆age25 29 13, 16474.∆age25 29

Two percent increase in population between 25 and 29 years old rises murder rate about 26%.9 It will be more descriptive to use detailed variales for population’s distribution according to age, but using only this one serves our purpose well enough. The most significant variable, and also with large practical effect, is lag of murder rate. If we look at Table 5.1, we can immediatelly see that 10% higher last year’s murder rate indicates about 28,6% higher current murder rate. That is definitely not a negligible effect.

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Conclusion The primary goal was to show that number of executions has no deterrent effect on murder rates. This

has been done in section 2 by discussing different graphs and trends, and then in section 5 by estimating an empirical model. The results, discussed in previous section, provide important evidence that supports stated 7 more

accurate is %∆mrate

8 Only

=

100.(e0,0171908 − 1)∆perc minor

=

1, 733941217.∆perc minor

when using Driscoll-Kraay SE. If I use cluster-robust SE, age25 29 will be omitted because of presence of constant, which

cannot be suppresed. (age25 29 has got really small variance) 9 more accurate is %∆mrate

=

100.(e0,1316474 − 1)∆age25 29

=

14, 07060354.∆age25 29

7

hypothesis. Both number of executions as well as its lag are statistically insignificant in conducted panel-data regression analysis. Despite of finding an evidence of no deterrent effect, there are still many empirical papers that prove the exact opposite. Maybe the results presented here would have been different, if more control variables were used. Or if time series instead of panel data were used. It is really difficult to say, what makes the difference. Interesting analysis of this issue provides Samuel Cameron in A review of the economic evidence on the effects of capital punishment.10 He came to conclusion that including non-death penalty states into sample is the key feature of proving a presence of deterrence. This can be a subject of further analysis: to compare results when using death penalty states only and using sample uncluding all U.S. states. Analysis provided here does not answer a question, if capital punishment should be in use. Other relevant factors and arguments have to be weighted to determine the optimal use of death penalty. It is very complex topic, which cannot be handled using only econometrics analysis.

10 CAMERON,

Samuel. A review of the econometric evidence on the effects of capital punishment. The Journal of Socio-Economics,

1994, 23.1: 197-214.

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References CAMERON, Samuel. A review of the econometric evidence on the effects of capital punishment. The Journal of Socio-Economics, 1994, 23.1: 197-214. CNN International. edition.cnn.com: Death Penalty Fast Facts. [online]. 9.1.2015 [Accessed 2015-01-14]. Available from: http://edition.cnn.com/2013/07/19/us/death-penalty-fast-facts/ c Death Penalty Information Center. www.deathpenaltyinfo.org. [online]. 2015 [Accessed 2015-01-14]. Available from: www.deathpenaltyinfo.org DEZHBAKHSH, Hashem; SHEPHERD, Joanna M. The deterrent effect of capital punishment: evidence from a “judicial experiment”. Economic Inquiry, 2006, 44.3: 512-535. EHRLICH, Isaac. The Deterrent Effect of Capital Punishment: A Question of Life and Death. The American Economic Review, 1975, 65.3: 397-417. c The Federal Bureau of Investigation. www.fbi.gov: Crime Statistics. [online]. 2015 [Accessed 2015-01-14]. Available from: http://www.fbi.gov/stats-services/crimestats Pew Research. www.pewforum.org: Religion & Public Life Project. [online]. 28.3.2014 [Accessed 2015-01-14]. Available from: http://www.pewforum.org/2014/03/28/shrinking-majority-of-americans-support-death-penalty/ c U.S. Bureau of Economic Analysis. www.bea.gov. [online]. 2015 [Accessed 2015-01-14]. Available from: www.bea.gov c U.S. Census Bureau. www.census.gov. [online]. 2015 [Accessed 2015-01-14]. Available from: www.census.gov c U.S. Bureau of Labor Statistics. www.bls.gov. [online]. 2015 [Accesed 2015-01-14]. Available from: www.bls.gov

Appendix Figure 2.1: Murder rates in states with and without the death penalty

source: http://www.amnestyusa.org/our-work/issues/death-penalty/us-death-penalty-facts/the-death-penalty-and-deterrence

Figure 2.2: Comparison of murder rates in neighbouring states

source: http://www.deathpenaltyinfo.org/deterrence-states-without-death-penalty-have-had-consistently-lower-murder-rates

Figure 2.3: Number of executions in time

source: http://www.deathpenaltyinfo.org/executions-year

Table 2.1: List of 10 U.S. states with the highest murder rates in 2013 U.S. states

Murder rates in 2013

1. Louisiana

10,8

2. Alabama

7,2

3. Mississippi

6,5

4. Maryland

6,4

5. Michigan

6,4

6. South Carolina

6,2

7. Missouri

6,1

8. New Mexico

6

9. Nevada

5,8

10. Georgia

5,6

source: http://www.deathpenaltyinfo.org/murder-rates-nationally-and-state

Table 4.1: Summary of U.S. death penalty states in 2000-2013 U.S. states

number of executions in 2000-2013

average murder rates in 2000-2013

Alabama

37

7,2

Arizona

17

6,8

Arkansas

6

6

California

6

6

Colorado

0

3,4

Connecticut (2012)

1

3,1

Delaware

6

4,3

Florida

37

5,5

Georgia

30

6,6

Idaho

2

2,1

Illinois (2011)

0

6,4

Indiana

13

5,4

Kansas

0

4

Kentucky

1

4,5

Louisiana

3

11,9

Maryland (2013)

2

8,4

Mississippi

17

7,9

Missouri

29

6,4

Montana

1

2,5

Nebraska

0

3

Nevada

4

7

New Hampshire

0

1,2

New Jersey (2007)

0

4,3

New Mexico (2009)

1

7,2

New York (2007)

0

4,4

North Carolina

28

5,9

Ohio

51

4,4

Oklahoma

89

5,5

Oregon

0

2,2

Pennsylvania

0

5,3

South Carolina

19

6,9

South Dakota

3

2,1

Tennessee

6

6,5

Texas

309

5,5

Utah

1

2

Virginia

37

4,9

Washington

2

2,9

0

2,4

Wyoming

Years in parentheses denote years of abolishing capital punishment law

Table 4.2: Description of variables Variables

Description

mrate

Murder rate, number of people murdered per 100 000 inhabitants

exec

Number of executions

employ

Number of law enforcement employees

unemp

Unemployment rate

GNI prc

Gross national income per capita

arrate

Arrest rate, number of people arrested per 100 000 inhabitants

perc minor

Percentage of minorities in the population

age25 29

Percentage of population aged 25-29

Table 5.1: Murder rate regression results; U.S. states’ panel data (2000-2013) Dependent variable: lmrate Independent variables exec

Coefficients estimates .0031483 (1.06)*** [1.12]***

lagexec

.0002884 (0.14)*** [0.06]***

demploy

1.87e-06 (1.11)*** [1.21]***

unemp

-.0292405 (-3.45)* [-2.61]*

dGN I prc

-6.60e-06 (-0.62)*** [-0.54]***

arrate

.0000253 (2.35)* [2.16]*

lagarrate

-.0000247 (-2.49)* [-2.10]*

perc minor

.0171908 (2.06)** [0.68]***

age25 29

.1316474 (5.94)* omitted

laglmrate

.2862916 (7.51)* [3.00]*

year dummy variables

...

Observations

494

within R2

.2173

t-statistics, using Driscoll-Kraay SE, are in parentheses t-statistics, using cluster-robust SE, are in brackets variable age25 29 is omitted when using cluster-robust SE * denotes statistical significance at 5% level ** denotes statistical significance at 10% level *** denotes statistical insignificance