"Economic and Health Impacts of Social Distancing Policies
during the Coronavirus Pandemic"
  with Hunt Allcott, Levi Boxell, Jacob Conway, Billy Ferguson, Matthew Gentzkow
Full paper available here
As the coronavirus moved through the US, Americans began "social distancing" to slow the spread of the virus. State and local governments implemented business closing and shelter-in-place (SIP) orders to encourage residents to remain at home. We study the impact that these orders have on social distancing, spending and employment, and spread of the virus. 
We use cell phone location data to measure visits to points of interest (POIs) such as shops, parks, hospitals, and other locations. The figure below shows POI visits as a percentage of visits in the first week of February.
POI visits were reduced to about 1/3 of their normal level by the end of March—even in counties that did not have a shelter-in-place order until April. This begs the question: what portion of the total reduction in POI visits, employment and spending, and spread of the virus is attributable to the causal effect of shelter-in-place policies? We study this question in an event-study framework by comparing counties with stay-at-home orders to those that never received orders or those that received orders later or earlier. 
The presence of "pre-trends" implies that counties about to receive a SIP had already begun reducing their POI visits more than untreated (or later treated) counties. However, the discrete jump the day after the SIP order is implemented suggests the orders reduced POI visits by about 15% relative to their "pre-order" level.
Next, we use a SIRD (susceptible, infectious, recovered, diseased) epidemiological model to derive reduced form estimating equations that allow us to study the impact of the SIP orders on the "contact rate." The contact rate is an important parameter in the SIRD model that governs the rate at which infected people infect susceptible people.  
The estimates are noisy but consistently hover slightly below 0 suggesting that SIP orders reduce the contact rate by approximately 5%.
Finally, we turn to economic outcomes to estimate the impact that the SIP orders have on spending and employment. 
Similar to the social distancing and virus outcomes, we see small percentage reductions in spending and employment right after the SIP order is implemented.  
With all this evidence on the table, can we say what fraction of the total reduction in these outcomes (distancing, virus spread, and economic) is attributable to the SIP orders? On one hand, we know the SIP orders reduced POI visits by about 15% from their "pre-order" level, but, on the other hand, our first figure showed that POI visits were already greatly reduced by the end of March when most SIP orders were issued. So, if this 15% impact is off an already greatly reduced visit level, the total portion of the reduction in visits attributable to the SIP might be low. 
We estimate the fraction of the total change in each of our outcomes that is attributable to the government orders using the treatment effects estimated from the event studies. If, for instance, the SIP orders were only responsible for 10% of the reduction in POI visits but 50% of the reduction in employment, we might be concerned that SIP orders impose a large economic cost for a small reduction in interactions. 
Our estimates imply that the SIP orders are responsible for less than 20% of the total reduction in POI visits, total wages paid, and employment that occurred between February and April. The mandatory business closing orders account for a slightly larger share of the reduction in wages and employment.
We repeat this analysis for the contact rate parameter and check for robustness by varying the other key parameters in the SIRD model.
Similar to the economic and social distancing outcomes, the SIP orders account for approximately 20% of the total reduction in the contact rate.
Taken together, our estimates suggest that the ratio of health benefits to economic impacts is similar for the social distancing induced by policy and the largely voluntary social distancing that preceded it.