When the frontier is drawn by the poorest countries: comparison-set sensitivity in health system efficiency rankings

Abstract Background Cross-country league tables of health system efficiency rank countries and are used to argue that one institutional form outperforms another. A country’s score depends on the comparator set. We ask how much of a ranking that choice produces, and what survives when it is made explicit and second-stage inference uses methods suited to bounded DEA scores. Methods Input-oriented data envelopment analysis (DEA) was applied to a 2019 cross-section of 70 countries with complete data on four health inputs and one output (life expectancy at birth). Countries were scored against a pooled frontier, an income-group frontier, and a DEA meta-frontier with a technology gap ratio. Bias-corrected scores and confidence intervals came from a non-parametric bootstrap that resampled the decision-making units (B = 1000 replications). Leave-one-out and order-m estimates tested whether the pooled frontier was anchored by one or two observations. Second-stage inference used the Papke-Wooldridge fractional response model and a parametric truncated regression in the Simar-Wilson framework (B = 1000) on three dependent variables (pooled VRS, within-group CRS, meta-frontier TGR), n = 58. Results Two of 70 countries defined the pooled CRS frontier (Gambia, Papua New Guinea). China scored 0.158 against pooled CRS (34th of 70) and 0.997 against pooled VRS (25th of 70; 23 of 70 countries sit on the VRS frontier with score = 1.000, so China is close to the VRS frontier). Within its upper-middle-income group it scored 0.491 (14th of 17), with a technology gap ratio of 0.322. Removing both frontier countries together moved China’s CRS score to 0.169 (rank 33 of 68) while leaving the country ordering nearly intact (Spearman rho = 0.993). The out-of-pocket share was not associated with efficiency on any of the three primary dependent variables (all p > 0.30). System-type coefficients did not reverse sign under VRS, and their 95% confidence intervals included zero on the TGR dependent variable; marginal VRS associations in one control set did not survive the other control set. The United States market-based coefficient was negative in direction but imprecise in the bounded-outcome model. Common support was poor (mean GDP per capita US$4813 vs. US$58842 across fragmented and national-health-service groups). Conclusions Comparison-set sensitivity is the main result. The out-of-pocket association and system-type effects reported in earlier pooled-CRS work do not survive methodologically appropriate re-estimation; they reflect that a pooled CRS frontier spanning all income groups is defined by the lowest-spending countries. China’s financing projections are exploratory.