Taking a New Look at Empirical Models of Adoption: Average Treatment Effect Estimation of Adoption Rates and their Determinants

This paper shows that the observed sample adoption rate does not consistently estimate the population adoption rate even if the sample is random. It is proved that instead the sample adoption rate is a consistent estimate of the population joint exposure and adoption rate, which does not inform about adoption per se. Likewise, it is shown that a model of adoption with observed adoption outcome as dependent variable and where exposure to the technology is not observed and controlled for cannot yield consistent estimates of the determinants of adoption. Such model can at best provide consistent estimates of the effects of the included explanatory variables on joint exposure and adoption. Even for that to be possible, the model must be explicitly specified as a model of determinants of joint exposure and adoption and not as a model of determinants of adoption alone. The paper uses the counterfactual outcomes framework to show that the true population adoption rate corresponds to what is defined in the modern treatment effect literature as the average treatment effect (ATE), which measures the effect or impact of a "treatment" on a person randomly selected in the population. In the adoption context, a "treatment" corresponds to exposure to the technology. Another quantity that is also the subject of attention in the treatment effect literature is the average treatment effect on the treated, which measures the effect of treatment in the treated subpopulation and corresponds in the adoption context to the adoption rate among those exposed to the technology. The paper uses the ATE estimation framework to derive consistent nonparametric and parametric estimators of population adoption rates and their determinants and applies the results to consistently estimate the population adoption rates and determinants of the NERICA (New Rice for Africa) rice varieties in Cote d'ivoire.