In a recent working paper, economists Thomas Buchmueller and Colleen Cary find that one particular kind of restriction does reduce opioid misuse among Medicare beneficiaries:

The misuse of prescription opioids has become a serious epidemic in the US. In response, states have implemented Prescription Drug Monitoring Programs (PDMPs), which record a patient’s opioid prescribing history. While few providers participated in early systems, states have recently begun to require providers to access the PDMP under certain circumstances. We find that “must access” PDMPs significantly reduce measures of misuse in Medicare Part D.

Yet, they also find

no statistically significant effect [of must access PDMP’s] on a key medical outcome: opioid poisoning incidents.

How is this possible?

The simplest explanation is that, despite all the hype, prescription opioids are not that dangerous, even in heavy doses, when used under medical supervision. Instead, most poisonings reflect use of diverted prescription opioids, or black market opioids like heroin, that users obtain when doctors cut them off from prescription opioids. These alternate sources may be adulterated, of higher dosage than the user realized, or consumed with other drugs that generate adverse reactions.

Under this interpretation, restrictions on opioid prescribing might even increase opioid poisonings.