Domestic violence, sexual assault, sexual harassment, and stalking are very difficult for economists to study because of data quality. Survey evidence suggests that such offenses are typically not reported.
This means admin data are (likely) a selected sample of the full stock of offenses. It also means that interventions aimed at reducing the incidence of such offenses may increase reporting substantially, making it tough to measure impacts on underlying behavior.
That said, there is *some* research in economics on these topics. This Twitter thread will keep track of this research, for my own and others’ reference.
Aizer (2010) "The Gender Wage Gap and Domestic Violence”

https://www.aeaweb.org/articles?id=10.1257/aer.100.4.1847">https://www.aeaweb.org/articles...
Iyer et al. (2012) "The Power of Political Voice: Women& #39;s Political Representation and Crime in India”

https://www.aeaweb.org/articles?id=10.1257/app.4.4.165">https://www.aeaweb.org/articles...
Bhuller et al. (2013) "Broadband Internet: An Information Superhighway to Sex Crime?”

https://doi.org/10.1093/restud/rdt013">https://doi.org/10.1093/r...
Bobonis et al. (2013) "Public Transfers and Domestic Violence: The Roles of Private Information and Spousal Control”

https://www.aeaweb.org/articles?id=10.1257/pol.5.1.179">https://www.aeaweb.org/articles...
Sekhri and Storeygard (2014) "Dowry deaths: Response to weather variability in India”

https://doi.org/10.1016/j.jdeveco.2014.09.001">https://doi.org/10.1016/j...
Cesur and Sabia (2016) "When War Comes Home: The Effect of Combat Service on Domestic Violence”

https://doi.org/10.1162/REST_a_00541">https://doi.org/10.1162/R...
Raissian (2016) "Hold Your Fire: Did the 1996 Federal Gun Control Act Expansion Reduce Domestic Homicides?”

https://doi.org/10.1002/pam.21857">https://doi.org/10.1002/p...
Brassiolo (2016) "Domestic Violence and Divorce Law: When Divorce Threats Become Credible”

https://www.journals.uchicago.edu/doi/abs/10.1086/683666">https://www.journals.uchicago.edu/doi/abs/1...
Anderberg et al. (2016) "Unemployment and Domestic Violence: Theory and Evidence”

https://doi.org/10.1111/ecoj.12246">https://doi.org/10.1111/e...
Bisschop et al. (2017) "Street Prostitution Zones and Crime”

https://www.aeaweb.org/articles?id=10.1257/pol.20150299">https://www.aeaweb.org/articles...
La Mattina (2017) "Civil conflict, domestic violence and intra-household bargaining in post-genocide Rwanda”

https://doi.org/10.1016/j.jdeveco.2016.08.001">https://doi.org/10.1016/j...
. @causalinf and Shah (2017) "Decriminalizing Indoor Prostitution: Implications for Sexual Violence and Public Health”

http://www.restud.com/paper/decriminalizing-indoor-prostitution-implications-for-sexual-violence-and-public-health/">https://www.restud.com/paper/dec...
Knepper (2017) "When the Shadow Is the Substance: Judge Gender and the Outcomes of Workplace Sex Discrimination Cases”

https://www.journals.uchicago.edu/doi/abs/10.1086/696150">https://www.journals.uchicago.edu/doi/abs/1...
Lindo et al. (2018) "College Party Culture and Sexual Assault”

https://www.aeaweb.org/articles?id=10.1257/app.20160031">https://www.aeaweb.org/articles...
. @g_borker (2018) "Safety First: Perceived Risk of Street Harassment and Educational Choices of Women"

https://www.dropbox.com/s/09hrk6nah4f80t0/Borker_JMP.pdf?dl=0">https://www.dropbox.com/s/09hrk6n...
. @BetseyStevenson and @JustinWolfers (2006) "Bargaining in the Shadow of the Law: Divorce Laws and Family Distress”

https://doi.org/10.1093/qje/121.1.267">https://doi.org/10.1093/q...
Card and Dahl (2011) "Family Violence and Football: The Effect of Unexpected Emotional Cues on Violent Behavior”

https://doi.org/10.1093/qje/qjr001">https://doi.org/10.1093/q...
Carrell, Hoekstra, and @EliraKuka (2017) "The Long-Run Effects of Disruptive Peers"

http://elirakuka.weebly.com/uploads/1/0/0/6/10064254/chk.2017.07.20.pdf">https://elirakuka.weebly.com/uploads/1...
Carrell and Hoekstra (2010) "Externalities in the Classroom: How Children Exposed to Domestic Violence Affect Everyone& #39;s Kids”

https://www.aeaweb.org/articles?id=10.1257/app.2.1.211">https://www.aeaweb.org/articles...
Miller and Segal (2016) "Do Female Officers Improve Law Enforcement Quality? Effects on Crime Reporting and Domestic Violence”

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2335990">https://papers.ssrn.com/sol3/pape...
Aizer and Dal Bó (2009) "Love, hate and murder: Commitment devices in violent relationships”

https://doi.org/10.1016/j.jpubeco.2008.09.011">https://doi.org/10.1016/j...
Iyengar (2009) "Does the certainty of arrest reduce domestic violence? Evidence from mandatory and recommended arrest laws”

https://doi.org/10.1016/j.jpubeco.2008.09.006">https://doi.org/10.1016/j...
Aizer (2011) "Poverty, Violence, and Health: The Impact of Domestic Violence During Pregnancy on Newborn Health"

http://jhr.uwpress.org/content/46/3/518.abstract">https://jhr.uwpress.org/content/4...
Bloch and Rao (2002) “Terror as a Bargaining Instrument: A Case Study of Dowry Violence in Rural India”

https://www.aeaweb.org/articles?id=10.1257/00028280260344588">https://www.aeaweb.org/articles...
Anderson & Genicot (2015) "Suicide and property rights in India”

https://doi.org/10.1016/j.jdeveco.2014.11.004">https://doi.org/10.1016/j...
Alesina, Brioschi, & La Ferrara (2016) “Violence Against Women: A Cross-cultural Analysis for Africa”

http://www.nber.org/papers/w21901 ">https://www.nber.org/papers/w2...
. @Thomas_S_Dee (2003) "Until Death Do You Part: The Effects of Unilateral Divorce on Spousal Homicides”

https://doi.org/10.1093/ei/41.1.163">https://doi.org/10.1093/e...
Carrell and Hoekstra (2012) "Family Business or Social Problem? The Cost of Unreported Domestic Violence"

https://doi.org/10.1002/pam.21650">https://doi.org/10.1002/p...
Basu (2003) "The Economics and Law of Sexual Harassment in the Workplace”

https://www.aeaweb.org/articles?id=10.1257/089533003769204399">https://www.aeaweb.org/articles...
Lindo, @dave_marcotte, Palmer, & Swensen (2018) "Any Press is Good Press? The Unanticipated Effects of Title IX Investigations on University Outcomes"

http://www.nber.org/papers/w24852 ">https://www.nber.org/papers/w2...
Currie, @Econ_Mike, & @maya_rossin (2018) "Violence while in Utero: The Impact of Assaults During Pregnancy on Birth Outcomes"

http://www.nber.org/papers/w24802 ">https://www.nber.org/papers/w2...
Roy, Hidrobo, Hoddinott, and Ahmed. (2018) "Transfers, Behavior Change Communication, and Intimate Partner Violence: Post-Program Evidence from Rural Bangladesh”

https://doi.org/10.1162/rest_a_00791">https://doi.org/10.1162/r...
Ana Tur-Prats (2018)
"Family Types and Intimate-Partner Violence: A Historical Perspective"

https://doi.org/10.1162/rest_a_00784">https://doi.org/10.1162/r...
. @AnnaBindler & @nadineketel (2019)
"Scaring or scarring? Labour market effects of criminal victimisation"

https://gupea.ub.gu.se/bitstream/2077/58594/1/gupea_2077_58594_1.pdf">https://gupea.ub.gu.se/bitstream...
. @RiccardoCiacci & @micasviatschi (2018) "The Effect of Adult Entertainment Establishments on Sex Crime: Evidence from New York City"

http://www.micaelasviatschi.com/wp-content/uploads/2018/07/sex_cr_17_7_18.pdf">https://www.micaelasviatschi.com/wp-conten...
Guadalupe Kavanaugh, @micasviatschi, & Iva Trako. 2019. "Female Officers, Gender Violence and Human Capital: Evidence from All-Women’s Justice Centers in Peru"

http://www.micaelasviatschi.com/wp-content/uploads/2019/02/Peru_paper_working25.pdf">https://www.micaelasviatschi.com/wp-conten...
. @causalinf, DeAngelo, & Tripp. 2019. "Craigslist Reduced Violence Against Women"

http://scunning.com/craigslist110.pdf">https://scunning.com/craigslis...
. @NWPapageorge, Pauley, Cohen, Wilson, Hamilton, & Pollak. 2019. "Health, Human Capital and Domestic Violence"

http://jhr.uwpress.org/content/early/2019/11/07/jhr.56.4.1115-7543R5.abstract">https://jhr.uwpress.org/content/e...
Seetha Menon. 2020. "The effect of marital endowments on domestic violence in India"

https://doi.org/10.1016/j.jdeveco.2019.102413">https://doi.org/10.1016/j...
Rachel Heath, Melissa Hidrobo, & Shalini Roy. Forthcoming. "Cash transfers, polygamy, and intimate partner violence: Experimental evidence from Mali"

https://doi.org/10.1016/j.jdeveco.2019.102410">https://doi.org/10.1016/j...
. @YooMiChin1 & @causalinf. 2019. "Revisiting the effect of warrantless domestic violence arrest laws on intimate partner homicides"

https://doi.org/10.1016/j.jpubeco.2019.104072">https://doi.org/10.1016/j...
. @RadhaKIyengar. 2019. "Corrigendum to & #39;Does the certainty of arrest reduce domestic violence? Evidence from mandatory and recommended arrest laws& #39;"

https://doi.org/10.1016/j.jpubeco.2019.104098">https://doi.org/10.1016/j...
. @RadhaKIyengar. 2019. "Corrigendum to & #39;Does the certainty of arrest reduce domestic violence? Evidence from mandatory and recommended arrest laws& #39;" https://doi.org/10.1016/j...
. @RadhaKIyengar. 2019. "Corrigendum to & #39;Does the certainty of arrest reduce domestic violence? Evidence from mandatory and recommended arrest laws& #39;" https://doi.org/10.1016/j...
Muchow & Amuedo-Dorantes. 2020. "Immigration enforcement awareness and community engagement with police: Evidence from domestic violence calls in Los Angeles"

https://doi.org/10.1016/j.jue.2020.103253">https://doi.org/10.1016/j...
. @emilycleslie & @1rileywilson. 2020. "Sheltering in Place and Domestic Violence: Evidence from Calls for Service during COVID-19"

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3600646">https://papers.ssrn.com/sol3/pape...
Tianshu Li, @sonalSpandya, & Sheetal Sekhri. 2020. "Repelling Rape: Foreign Direct Investment Empowers Women"

https://uva.theopenscholar.com/files/sonal-pandya/files/fdi_rapeindia.pdf">https://uva.theopenscholar.com/files/son...
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