19 type definitions in many countries. There are many differences between these studies and all we can say is that the hypothesis of heterogeneous effects of inequality on growth finds support in their study but not here.

Another issue that needs to be highlighted here is the evident instability of coefficient estimates and regression diagnostics to minor changes in the estimation procedures. It does appear, at least in our data sets, that GMM methods in particular are very sensitive to the myriad of choices that need to be made by the researcher. Simple changes not only move coefficient estimates around, but also render instrument sets invalid or uninformative in many instances. Although we have diligently combed the latest literature on GMM estimation techniques and closely adhered to the recommendations regarding robustness checks and detailed reporting in Roodman (2009a), examining our results does not suggest that these econometric techniques are reliable strategies in addressing the question at hand.

Similar (or more serious) data and econometric issues have also affected previous studies, and the instability of results between the three “phases” of the empirical cross-country literature reviewed in Section 2 smacks of the same lack of robustness that we have encountered in our two country samples. A review of that literature suggests that, in retrospect, perhaps each individual researcher drew firmer conclusions from his or her own particular study than later appears warranted. We are not confident that the latest crop of papers - including Ostry et al. (2014), that relies on the SWIID data from Solt (2000) - will prove to be immune from this trend. The lack of robustness in our own study may reflect additional factors, such as unusually large measurement error in the inequality of opportunity variable, but it also arises from data and methodological problems that have plagued the literature at large. One conclusion we draw from our null results is that considerable circumspection is in order when interpreting findings from any single cross-country study of the relationship between inequality and growth.

If the best available cross-country data sets and the best available econometric techniques do not appear suitable to answering this important question that has been the subject of considerable debate recently, then what is? Taking advantage of case studies and natural experiments may be one such promising avenue. Every time policymakers target certain interventions to disadvantaged groups, they attempt to reduce future inequality of opportunity: anti-discrimination laws against minorities; early childhood interventions for certain ethnic groups; schooling and mentoring programs for adolescent girls; interventions that give voice and increase the participation of oppressed groups are all examples of such interventions. To the extent that such interventions cause strong changes in measurable inequality of opportunity (and satisfy exclusion restrictions), they can be used as instruments to study the relationship between inequality of opportunity and subsequent growth. In cases where one country, or one region/state/district within a country, implemented a novel policy or program with plausible effects on reducing inequality of opportunity, recent causal inference methods, such as synthetic controls (Abadie, Diamond, and Hainmueller, 2010), can be utilized. One could even imagine long-term randomized controlled trials. Natural experiments and other causal inference methods relying on interesting cases around the world may end up providing more fruitful avenues for studying this important question than using cross-country regressions.