  Bayesian hierarchical models are a methodology for aggregation and synthesis
of data from heterogeneous settings, used widely in statistics and other
disciplines. I apply this framework to the evidence from 7 randomized
experiments of expanding access to microcredit to assess the general impact of
the intervention on household outcomes and the heterogeneity in this impact
across sites. The results suggest that the effect of microcredit is likely to
be positive but small relative to control group average levels, and the
possibility of a negative impact cannot be ruled out. By contrast, common
meta-analytic methods that pool all the data without assessing the
heterogeneity misleadingly produce "statistically significant" results in 2 of
the 6 household outcomes. Standard pooling metrics for the studies indicate on
average 60% pooling on the treatment effects, suggesting that the site-specific
effects are reasonably externally valid, and thus informative for each other
and for the general case. The cross-study heterogeneity is almost entirely
generated by heterogeneous effects for the 27% households who previously
operated businesses before microcredit expansion, although this group is likely
to see much larger impacts overall. A Ridge regression procedure to assess the
correlations between site-specific covariates and treatment effects indicates
that the remaining heterogeneity is strongly correlated with differences in
economic variables, but not with differences in study design protocols. The
average interest rate and the average loan size have the strongest correlation
with the treatment effects, and both are negative.
