The law of diminishing marginal returns in health insurance: evidence on child health outcomes from Pakistan’s Sehat Sahulat program

Background: Child malnutrition remains a serious public health challenge in Pakistan. The national health insurance initiative, the Sehat Sahulat Program (SSP), aims to improve access to health care for low-income families. This study examines whether the effectiveness of SSP follows the Law of Diminishing Marginal Returns (LDMR), whereby the marginal health benefits of insurance are greatest for the poorest households and decline with increasing wealth. Methods: We analyzed data on 4,499 children under 5 years of age in the Pakistan Demographic and Health Survey 2017-18. To address endogeneity and wealth-based heterogeneity, we employed an IV-Probit model and an IV-Quantile Regression (IV-QR) across wealth quintiles, using community-level internet access and distance to the nearest health facility as instrumental variables. Logistic regression was applied as a baseline model. Results: Analysis reveals a strong gradient in the effectiveness of SSP program. Insurance coverage is associated with reduced stunting and marked declines in diarrhea rates among the poorest households. These benefits have diminished in the overall distribution of wealth and have become statistically insignificant for the richest quintile. Econometric tests have confirmed a clear pattern of declining marginal returns. Conclusion: The Sehat Sahulat project is a very effective tool for reducing malnutrition among poor children in Pakistan. The observed pattern of diminishing returns suggests that SSP provides the greatest health benefits to the poorest households. These findings support a pro-poor targeting strategy in Pakistan to maximize the program's impact within resource constraints.