Aggregating Distributional Treatment Effects: A Bayesian Hierarchical Analysis of the Microcredit Literature (Job Market Paper)
Abstract: This paper develops methods to aggregate evidence on distributional treatment effects from multiple studies conducted in different settings, and applies them to the microcredit literature. Several randomized trials of expanding access to microcredit found substantial effects on the tails of household outcome distributions, but the extent to which these findings generalize to future settings was not known. Aggregating the evidence on sets of quantile effects poses additional challenges relative to average effects because distributional effects must imply monotonic quantiles and pass information across quantiles. Using a Bayesian hierarchical framework, I develop new models to aggregate distributional effects and assess their generalizability. For continuous outcome variables, the methodological challenges are addressed by applying transforms to the unknown parameters. For partially discrete variables such as business profits, I use contextual economic knowledge to build tailored parametric aggregation models. I find generalizable evidence that microcredit has negligible impact on the distribution of various household outcomes below the 75th percentile, but above this point there is no generalizable prediction. Thus, while microcredit typically does not lead to worse outcomes at the group level, there is no generalizable evidence on whether it improves group outcomes. Households with previous business experience account for the majority of the impact and see large increases in the right tail of the consumption distribution.
Understanding the Average Impact of Microcredit Expansions: A Bayesian Hierarchical Analysis of 7 Randomised Experiments
Abstract: I perform a Bayesian hierarchical analysis of the evidence from 7 randomized trials of microcredit to assess the general impact on household outcomes and the heterogeneity in this impact across sites. Across all outcomes, the results suggest that the average effect of microcredit is positive but small relative to control group average levels, with a reasonably high chance of effectively zero impact. Standard pooling metrics for the studies indicate on average 60% pooling on the treatment effects, suggesting that the site-specific effects have substantial external validity. The cross-study heterogeneity is almost entirely generated by heterogeneous effects for the 27% households who previously operated businesses before microcredit expansion, and impacts on this group appear to be much larger 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.
Fast robustness quantification with variational Bayes (2016 ICML Workshop on #Data4Good: Machine Learning in Social Good Applications, New York, NY) with Ryan Giordano, Tamara Broderick, Jonathan Huggins, Michael Jordan
Abstract: Bayesian hierarchical models are increasingly popular in economics. When using hierarchical models, it is useful not only to calculate posterior expectations, but also to measure the robustness of these expectations to reasonable alternative prior choices. We use variational Bayes and linear response methods to provide fast, accurate posterior means and robustness measures with an application to measuring the effectiveness of microcredit in the developing world.
Vitamin A Supplements and Child Mortality: Resolving a Controversy in Meta-analysis (Paper completed but embargoed, draft available by email)
Competing Lending Platforms, Endogenous Reputation, and Fragility in Microcredit Markets (Joint with Peter Bardsley) (submitted)
Abstract: This paper shows that market fragility and mass default can arise in microcredit markets as a result of the strategic interaction between a microlender using a reputation-based mechanism and a traditional lender using physical collateral. In our model, borrowers solve a dynamic programming problem which induces an endogenous equilibrium distribution of reputational capital. Because the quality of each lender's pool of borrowers is affected by both lenders' interest rates, lender reaction curves are non-monotonic and discontinuous. This can result in knife edge equilibria and mass default on the microlender precipitated by minor parametric perturbations. Fragility is exacerbated by borrower screening and sovereign risk, but ameliorated when microlenders have social welfare goals. Our results highlight the importance of studying the entire credit market rather than microfinance in isolation.
Research in Progress
Combining Experimental and Observational Studies in Meta-Analysis: Leveraging Experimental Structures to Eliminate Selection Bias (Joint with Michael Gechter)
Competition and Welfare in Microcredit Markets: A Structural Bayesian Hierarchical Approach (Joint with Shoshana Vasserman)
A Multifaceted Approach to Poverty Alleviation in Six Countries: A Bayesian Hierarchical Analysis of the Graduation Program (Joint with Andrew Gelman, Dean Karlan, Shira Mitchell and Chris Udry)