Does Capital Punishment Have a Deterrence Effect on the Murder Rate? Issues and Evidence

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1 Does Capal Punishmen Have a Deerrence Effec on he Murder Rae? Issues and Evidence Seven S. Cuellar, Ph.D.* Deparmen of Economics Sonoma Sae Universy 181 Eas Coai Avenue Rohner Park, CA 998 () -5 Kyle Buehring Sonoma Sae Universy 181 Eas Coai Avenue Rohner Park, CA 998 () -5 Absrac This paper uses a cross secion of sae level daa pooled from 19- o analyze deerren effec of capal punishmen on he murder rae. Using a fixed effecs model and correcing for endogeney, we find a negaive and significan deerren effec of capal punishmen on sae level murder raes. These findings are robus o specificaion and mehodological changes. Key words: Pooled Cross Secion Time Series Daa; Insrumenal Variable Regression. *Denoes conac auhor. The auhors would like o hank paricipans a Sonoma Sae Universy s Deparmen of Economics Seminar Series for helpful commens. We would also like o hank Sonoma Sae Universy s School of Business and Economics for funding his research.

2 I. INTRODUCTION Ever since he seminal aricle by Isaac Ehrlich in 195, in which he auhor shows ha he deah penaly exers a deerren effec on homicides, he quesions surrounding he effec of capal punishmens on he murder rae has cenered on issues of economeric mehod, model specificaion and variable inclusion. More recenly, a series of sudies by Dezhbakhsh, Rubin and Shepherd (), Mocan and Gings (), Kaz, Lev and Shusorovich () and Shepherd (5) have reigned he debae by showing ha capal punishmen does have a negaive effec on he murder rae. Donohue and Wolfers () dispue he deerren effec of hese sudies and argue ha resuls are sensive o economeric mehod, model specificaion, and variable inclusion. While Mocan and Gings () respond o Donohue and Wolfers () in a spired defense of heir resuls, he debae coninues. II. DATA The daa used for his sudy consis of he annual number of murders per 1, people for each sae in each year from 19-. The execuion daa is number of execuions per year for each sae from 19-. The demographic daa was consruced from he March Curren Populaion Survey for each sae in each year from 19-.

3 Annual Muder Rae Per 1, Year 8 1 Annual Number of Execuions Annual Murder Rae Per 1, Annual Execuions III. THEORETIC MODEL The model we propose is ha he criminal acivy, he murder rae in his paper, responds o changes in he cos of engaging in ha behavior. While he deah penaly represens he ulimae price paid for criminal acivy, he probabily of being caugh, conviced and execued remains relaively low. Raher han speculae on he naure in which hese probabilies are calculaed, we use he number of execuions per year in each sae as he deerren. However, o accoun for he fac ha he deerren effec of he number of execuions may have differen affecs a differen levels, we include he square of he number of execuions o accoun for any non-linear affecs of execuions.

4 IV. SIMPLE MODEL Consider firs he simple single equaion model of he form: MurderRae = β + β Exec. + β Texas _ Exec + β Texas _ Exec β Exec. + β Unem. + β Year + β Sae + u β DC + β Texas Where: Murder Rae is he murder rae per 1, in sae i and year j. Execuions is he number of execuions in sae i and year j. Execuions is he square of execuions. Unemployed is he unemploymen rae in sae i and year j and is used o conrol for macroeconomic condions in each sae and year. Police is a variable represening he dollar amoun of police expendures in sae i and year j. The Disric of Columbia is an oulier in he murder rae and Texas is an oulier in execuions so we include dummy variables for each. Year is a variables used o represen year level fixed effecs. Sae is a variable used o represen he sae level fixed effecs.

5 As hypohesized, he affec of he number of execuions on he murder rae is non-linear wh he coefficien on he number of execuions being posive and he coefficien on he number of execuions squared negaive, boh are significan a he 1%. Alhough hese are very preliminary resuls, here does appear o be a hreshold effec in which afer approximaely six execuions, he deah penaly exers a deerren effec on he murder rae. While he resuls are ineresing, is obvious ha, his simple model suffers from a variey of economeric afflicions. To begin wh, is clear ha here is simulaney among he murder rae, he number of execuions and police expendures. We address hese issues in he nex secion. V. SIMULTANEOUS EQUATIONS MODEL To accoun for endogeniey among he murder rae, he number of execuions and police expendures we consruc he following sysem of equaions: (1) () () MurderRae = β + β Exec. + β Texas + β Texas _ Exec + β Texas _ Exec Execuions + α Police 5 8 = α PoliceExpendures + γ % Black 1 + β Exec. 9 + α1murderrae + α Re + α DC + α Texas + v 5 = γ + γ MurderRae. + γ + γ Texas + γ Year + ω 1 + β Unem. + β Year + u 1 publican + γ Burglary + α Correcions 5 + γ Assaul. + β DC + α Police

6 OLS Models Fixed Effecs Models IV Models w/fixed Effecs Model 1 Model Model Model Model 5 Model Model Murder Murder Murder Murder Murder Murder Murder Rae Rae Rae Rae Rae Rae Rae Number of Execuions (1.98)* (.91) (.8)** (8.1)** (.5) (.)** (1.) Number of Execuions (5.1)** (5.9)** (.9) (.1)** (1.58) Unemploymen (.)** (.1)** (.9)** (.)** (.)** -.5 (.1)** Police Expendures (.8) (5.1)** (5.1)** (8.1)** (.)** Police Expendures (11.)** (.)** (.)** (.)** (.8)** DC (.91)** (.19)** (.)** Texas (.85)** (.)** (.5)** Texas Execuions (5.1)** (5.9)** (1.5) (5.5)** (1.8) Texas Execuions (5.1)** (5.9)** (.) (.)** (1.59) Consan (.)** (.)** (.9)** (.)** (.) (.)** (1.55) Observaions R-squared Absolue value of -saisics in parenheses. * significan a 5% level; ** significan a 1% level Deerren Effec None None 5.** 5.98** None.85** 5.1

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