An alternative instrument for private school competition
Empirical studies estimating the effect of private school competition on student outcomes commonly use the share of Catholics in the local population as an instrument for private school competition. I show that this is not a valid instrument since it is endogenous to private school competition and suggest using instead the local share of Catholics in the population in 1890 and its squared term. These instruments are very strong and are also exogenous to both student achievements and private school competition. I further show that using the current Catholic share as an instrument results in seriously flawed estimates of the effect of private school competition on math test scores and on educational attainment, to the extent that significant positive effects of private school competition on these outcome measures do not hold when the historical Catholic share in 1890 is used as an alternative instrument. The historical Catholic share in 1890 can also be applied to estimate the treatment effect of Catholic schools.
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