effectiveness of vaccinations differs by gender, for example, this may break down. One clue that this is probably not the case comes from earlier work that I have done (Oster, 2008), which shows that differences in vaccination rates by gender explain about 30% of the gender differences in mortality in childhood. This suggests that, empirically, girls do suffer significantly from lack of vaccination.
Ultimately, however, the best way to see whether the changes in vaccinations map into non-monotonicities in mortality is to look in the data. Ideally, we would like to have a relatively long time-series in which child mortality by gender is observed. These type of data are not generally available. It is possible, however, to create a short time series using retrospective reports on child mortality in the two survey waves of the NFHS. I consider the mortality outcomes for children born between five and ten years before each survey year (1992 and 1998). This effectively creates a time series of child death rates from 1982 through 1993. The outcome of interest is death between 18 months and five years. I do not consider very early life mortality, since it will be generally unaffected by investments like vaccinations.
The theory would suggest that, to the extent that the cost of vaccinations decreased over this period, the gender imbalance in mortality should go up in areas where the initial level of vaccination was low, and down in areas where the initial level of vaccination was high. Obviously, if we had a very long time series, it would be possible to look for non-monotonic changes within a given area over time. With such a short time series, however, it is necessary to use cross-sectional variations in initial levels. I use state-level variation in vaccination levels as the initial condition, and estimate the following equation:
+ β 1 ( g i r l i s ) + β 2 ( g i r l i s × b i r t h d a t e i s × v a c c i n e s 9 2 s )
+ β 3
(girlis × birthdateis × vaccines92
where i indexes the individual and s indexes the state of residence, and vaccines92s is the level of vaccination in that state in 1992. The controls here (X s) include standard demographics plus all of the appropriate interactions between gender, birthdate and vaccinations so we can consistently estimate the triple interactions. As in the earlier regressions, if there is a non-monotonicity in i n e q u a l i t y h e r e , w e e x p e c t t o s e e t h a t β 2 > 0 a n d β 3 < 0 . T h a t i s , i n e q u a l i t y i s i n c r e a s i n g o v e r t i in areas that start with low levels of vaccines, but decreasing in areas that start with high levels of vaccines. m e
One important wrinkle in this analysis lies in the fact that, as stated above, this should a link between vaccination and lower mortality.