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
Iyer et al. (2012) "The Power of Political Voice: Women's Political Representation and Crime in India”

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

https://doi.org/10.1093/restud/rdt013
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
Sekhri and Storeygard (2014) "Dowry deaths: Response to weather variability in India”

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

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

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

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

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

https://www.aeaweb.org/articles?id=10.1257/pol.20150299
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
. @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/
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
Lindo et al. (2018) "College Party Culture and Sexual Assault”

https://www.aeaweb.org/articles?id=10.1257/app.20160031
. @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
. @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
Card and Dahl (2011) "Family Violence and Football: The Effect of Unexpected Emotional Cues on Violent Behavior”

https://doi.org/10.1093/qje/qjr001
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
Carrell and Hoekstra (2010) "Externalities in the Classroom: How Children Exposed to Domestic Violence Affect Everyone's Kids”

https://www.aeaweb.org/articles?id=10.1257/app.2.1.211
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
Aizer and Dal Bó (2009) "Love, hate and murder: Commitment devices in violent relationships”

https://doi.org/10.1016/j.jpubeco.2008.09.011
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
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
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
Anderson & Genicot (2015) "Suicide and property rights in India”

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

http://www.nber.org/papers/w21901 
. @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
Carrell and Hoekstra (2012) "Family Business or Social Problem? The Cost of Unreported Domestic Violence"

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

https://www.aeaweb.org/articles?id=10.1257/089533003769204399
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 
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 
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
Ana Tur-Prats (2018)
"Family Types and Intimate-Partner Violence: A Historical Perspective"

https://doi.org/10.1162/rest_a_00784
. @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
. @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
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
. @causalinf, DeAngelo, & Tripp. 2019. "Craigslist Reduced Violence Against Women"

http://scunning.com/craigslist110.pdf
. @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
Seetha Menon. 2020. "The effect of marital endowments on domestic violence in India"

https://doi.org/10.1016/j.jdeveco.2019.102413
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
. @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
. @RadhaKIyengar. 2019. "Corrigendum to 'Does the certainty of arrest reduce domestic violence? Evidence from mandatory and recommended arrest laws'"

https://doi.org/10.1016/j.jpubeco.2019.104098
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
. @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
Tianshu Li, @sonalSpandya, & Sheetal Sekhri. 2020. "Repelling Rape: Foreign Direct Investment Empowers Women"

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