always missing. To estimate the law’s effect, one must have a way of “filling in” the missing observation.
The discussion of this problem can be streamlined considerably by using mathematical notation. Let i index locations (possibly counties) and t index time periods (possibly years). Let denote the crime rate that county i would have in year t with a right-to-carry law in effect. Let denote the crime rate that county i would have in year t without such a law. Then the effect of the law on the crime rate is defined as under the assumption that all other factors affecting crime are the same with or without the law. The fundamental measurement problem is that one can observe either (if the law is in effect in county i and year t) or (if the law is not in effect in county i and year t) but not both. Therefore, Δit can never be observed.
One possible solution to this problem consists of replacing the unobservable Δit by the difference between the crime rates after and before adoption of a right-to-carry law (in other words, carrying out a before-and-after study). For example, suppose that county i (or county i’s state) adopts a right-to-carry law in year s. Then one can observe whenever t < s and whenever t > s. Thus, one might consider measuring the effect of the law by (for example) (the crime rate a year after adoption minus the crime rate a year before adoption). However, this approach has several serious difficulties.
First, factors that affect crime other than adoption of a right-to-carry law may change between years s – 1 and s + 1. For example, economic conditions, levels of police activity, or conditions in drug markets may change. If this happens, then measures the combined effect of all of the changes that took place, not the effect of the right-to-carry law alone. Second, can give a misleading indication of the effect of the law’s adoption even if no other relevant factors change. For example, suppose that crime increases each year before the law’s adoption and decreases at the same rate each year after adoption (Figure C-1). Then , indicating no change in crime levels, even though the trend in crime reversed in the year of adoption of the right-to-carry law. Taking the difference between multiyear averages of crime levels after and before adoption of the law would give a similarly misleading indication. This has been pointed out by Lott (2000:135) in his response to Black and Nagin (1998). As a third example, right-to-carry laws might be enacted in response to crime waves that would peak and decrease even without the laws. If this happens, then might reflect mainly the dynamics of crime waves rather than the effects of right-to-carry laws.
Finally, the states that have right-to-carry laws in effect in a given year may be systematically different from the states that do not have these laws in effect. Indeed, Lott (2000:119) found that in his data, “states adopting