In Table 3, column 3 displays the results for the preferred specification. The dependent variable is the daily count of domestic violence per 100,000 people. After controlling for the insured unemployment rate, seasonality, day of the week, holidays, temperature, and time-invariant city fixed effects, for every increase of 0.1 in the average fraction of people who stay home all day, we observe 0.10 additional daily reports of domestic violence per 100,000 people, a 3.22% increase relative to the sample mean.
From Fig. 1, we can see that the rates of staying at home appeared to increase in earnest around March 13 in our sample, where we estimate the fraction of people staying at home all day at 0.230. Setting this as a baseline, the average change in the fraction of people staying at home from March 13 to May 24 is 0.165.Footnote 10 Applying this to the estimated effect of staying at home on domestic violence, we estimate that domestic violence increased by 5.31% during this period. If victims who are trapped at home or economically disadvantaged during shutdowns report to the police less often, this is an underestimate of the true effect of staying at home on domestic violence (Li and Schwartzapfel 2020).
Alternative specifications and robustness checks
In this section, we perform several alternative specifications and robustness checks. First, we use two alternative measures of social distancing, one based on time spent at home and one based on interactions between pinged smartphones in commercial venues. Second, we include leads of the insured unemployment rate. Third, we restrict the analysis to more uniform sets of calls for service and police incident data. Fourth, we cluster errors at the state level. Fifth, we combine cities in the same county into one data unit. Sixth, we include May 25-31 in the sample and add a dummy for this period. Finally, we re-run the main specification excluding one city at a time.
Average time spent at home
To test whether our result holds for a different measure of staying at home, we estimate the average time spent at home using SafeGraph data. SafeGraph calculates the median time spent at home for all pinged devices in a census block group. We take a county-level average of this measure weighted by the sample size of devices in each census block group, and we divide by the minutes in a day to obtain the estimated fraction of time spent at home by county and day. The average fraction of time spent at home in the sample is 0.47, with a standard deviation of 0.10. Column 1 of Table 4 estimates the effect of average time at home instead of the percentage of people at home all day; the results are qualitatively similar to the main specification. Increasing time spent at home statistically significantly increases reports of domestic violence.
Device exposure index
While SafeGraph data measures the degree to which people stay at home, other cell phone tracking data measure different types of social distancing efforts, including the degree to which people congregate in commercial venues. Here we use an alternative measure developed by Couture et al. (2020) called the Device Exposure Index (DEX). DEX comes from PlaceIQ movement data and measures how often people visit the same commercial venues, i.e., how little they are social distancing. Starting on January 20, 2020, DEX takes every smartphone in the sample, notes what commercial venues it visited, and measures how many other smartphones visited the same venue that day. It then averages this value across phones. We use adjusted DEX, which assumes the number of actual devices in the area has not declined over time, to account for smartphone sampling issues. The average of DEX is 111.97, and the standard deviation is 93.31. To increase the ease of interpretation we divide the measure by 100, so the coefficient measures the marginal effect of DEX increasing by 100. We do not find a statistically significant effect of DEX on domestic violence; see column 2 of Table 4.
Delays in unemployment insurance claims mean that we may measure lagged unemployment in a rapidly changing labor market. One way to combat this is to include a one-week lead for unemployment to capture unemployed workers whose claims were delayed. The issue with this specification is that domestic violence can itself influence future unemployment. Column 3 of Table 4 indicates that the main results still hold.
Some data included in the sample are crime data, and other data lack a description of the incident that allows us to identify domestic assaults as opposed to other forms of domestic violence such as child abuse. To ensure that these differences in data sources do not drive the results, we restrict the analysis to data where we can identify domestic assaults. Specifically, we omit Baltimore, Cincinnati, Mesa, Montgomery (AL), Montgomery County (MD), Phoenix, Sacramento, Salt Lake City, San Jose, Santa Monica, Santa Rosa, St. John, and Tucson. In column 1 of Table 5 in the Appendix, we find that the results hold in the more restrictive sample. We then further restrict the sample by excluding crime data, which eliminates Austin, Baton Rouge, Chicago, Denver, Durham, Fayetteville, Kansas City (MO), and Louisville. Column 2 of Table 5 shows that the results still hold.
Errors clustered at the state level
Cities and counties within the same state enacted shelter-in-place orders at different times, and efforts to stay at home varied significantly for different cities in the same state.Footnote 11 That said, there could still be some within-state correlation for staying at home. For that reason, in Column 3 of Table 5 estimate we cluster standard errors at the state level and find that the results remain significant.
Combining cities in the same county
Some cities included in the sample are in one county. Chandler, Gilbert, Mesa and Phoenix are all in Maricopa County, and Santa Monica and Los Angeles are both in Los Angeles County. Here, we combine all cities in the same county into one data unit with a combined population and daily count of crime. The results in column 4 of Table 5 indicate that this does not change the result.
Including the end of May
We exclude May 25–31, 2020 from the sample to avoid confounding issues surrounding contemporary protests over police violence. Here, we include this data in the sample and add a dummy indicating this range of dates. From column 5 of Table 5, we see that the results do not substantially change.
We omit one city at a time from the analysis to ensure the results are not driven by any single city. See Fig. 2 in the Appendix. The coefficient of staying at home remains significant at a 5% level.