Debasri Mukherjee

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn about this separating hyperplane. Exact likelihood or least squares methods to estimate the thresholding parameter involve an indicator function which make them difficult to optimize and are, therefore, often tackled by using a surrogate loss that uses a smooth approximation to the indicator. In this paper, we demonstrate that the resulting estimator is asymptotically normal with a near optimal rate of convergence: n−1 up to a log factor, in both classification and regression thresholding models. This is substantially faster than the currently established convergence rates of smoothed estimators for similar models in the statistics and econometrics literatures. We also present a real-data application of our approach to an environmental data set where CO2 emission is explained in terms of a separating hyperplane defined through per-capita GDP and urban agglomeration.

The present article uses semiparametric regression to capture the impact of foreign-aid given for health purposes on the Infant Mortality Rate (IMR) of poor developing countries, after controlling for other covariates. We also investigate whether education (general awareness) helps lower IMR directly or helps improve effectiveness of health-aid in reducing IMR. In addition, the study investigates whether various disaggregated components of health-aid (for example, aid that goes for infectious disease control or nutrition) help lower IMR. We find that although adult education (awareness) always lowers IMR, the overall effect of health-aid remains insignificant. Our conclusion is robust to various disaggregated components of health-aid as well. We also check if health-aid has improved prenatal care for expecting mothers but our conclusion regarding the overall ineffectiveness of aid remains unchanged. Interestingly, we find that total health-aid as well as nutrition aid may lower IMR only after education exceeds a threshold level – a new angle that has not been explicitly explored before. We also find interesting role of education in making the aid more effective for prenatal care. Our semiparametric nonlinear estimation strategy helps us unravel certain interesting thresholds and facts which cannot be captured in a linear parametric estimation framework.

The relationship between foreign aid and economic growth has been the subject of much controversy. A recent theme suggesting that aid promotes growth, but only in a good policy environment has ratcheted up that debate. In this paper, we assess the importance of policy and aid in generating growth when the aid, policy, and growth relationship is nonlinear. This allows us to examine the varying effects of aid and policy in different data segments, which we do without imposing any particular structure on the underlying relationship. We find that policy is an important determinant of growth. We also find partial corroboration of the view that aid is growth enhancing in a good policy environment, and some evidence of diminishing returns to aid. These findings suggest that nonlinearities if not appropriately addressed fail to capture the detailed underlying dynamics and thereby mask some key features of the aid‐policy‐growth relationship.