There’s some confusion about what Sam Peltzman said/found in his work on automobile safety discussed in the comments to this post .
Peltzman argued that mandatory safety devices such as seat belts reduced the probability of harm to the driver if the car crashed. That in turn would encourage people to drive more recklessly. The effect on the number of deaths was an empirical question. Which effect would be larger—the harm from the increase in the number of accidents or the reduction in harm when an accident occurred?
Holding other factors constant that might change the number of accidents (and this is never easy but he did the best he could with the data at hand), Sam found that mandatory seat belts did indeed cause more accidents. But this effect was roughly the same as the effect in the opposite direction, that accidents were less harmful. So the net number of fatalities of drivers was unaffected by the law. Sam found some evidence that the effect of the law might be to reduce driver fatalities. Unfortunately, because drivers were more reckless, there were more accidents involving pedestrians and cyclists. So their death rate due to cars increased. Total deaths were unchanged.
You may find this intuitive or unintuitive. You can challenge the empirical analysis. But at the time, the findings were shocking (and distasteful) to the safety community and to academics who had confidently predicted that safety regulations would produce dramatic significant reductions in driver deaths. These engineering predictions ignored any possible behavioral response by drivers. Whether Sam measured these behavioral responses accurately is always an open question. But his insight that people respond to incentives is always a very good place to start.
The second issue that came up in our podcast  was airbags. In general, airbags have the same effect as seatbelts—they reduce the likelihood of injury and death from an accident which in turn increases reckless driving and the number of accidents. But in the early days of airbags, they could kill you, especially if you were a small person or a child. That led to some tragic deaths of kids in the passenger seat and small women in the driver seat. That in turn led to the government changing the requirements on the speed and force of the airbag deployment. Sam pointed out in the podcast that this is one of the problems that can arise when a national standard is mandated. Unlike the case where a car company might try something like this and learn from its mistake or a state might impose such a regulation, here everyone was forced to provide airbags, and the deaths from a badly designed regulation were magnified.
I encourage readers to read Sam’s original article. Unfortunately, the only online copy I can find is at JStor .