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In two-sample Mendelian randomization, any bias from weak instruments (instrumental variables that are not strongly associated with the risk factor) is in the direction of the null [ 17], so the use of large numbers of genetic variants which are valid instrumental variables should not result in causal claims which are false positives.
It should be noted that, in the specifications based on data aggregated at the municipal level, the instrumental variables used pass the "weak instruments" and "Wu-Hausman" tests.
Moreover, the test for weak instruments reveals that they are jointly significant in the probit specification.
The null hypothesis of weak instruments can be rejected at 5%% of distortion.
However, given these weak instruments, the power of the Wu-Hausman test is acknowledged to be poor, and therefore, we proceed to employ an alternative IV strategy that caters for the weak instruments used.
Two exceptions are the variables EDA, where inflation is replaced by the annual growth of M2 to avoid weak instruments.
We also tested for weak instruments by computing the Kleibergen-Paap rk Wald F statistic (van Ours and Stoeldraijer 2011).
As shown by Hahn et al. (2004), Flores-Lagunes (2007), these estimators perform better overall with weak instruments.
The coefficients are statistically significant at 5percentt significant level, confirming the results of the test for weak instruments.
We deal with the endogeneity problem using instrumental variables, and a reduced-form approach is also applied to allow for weak instruments in estimation.
The interpretation of results from models that rely solely on chance variation in peer groups is therefore complicated by bias from weak instruments.
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