This is a question that can be answered empirically but doing so is challenging. While cross-country comparisons are feasible for comparing public and private health care provisions, often there are many other differences between health care systems across country. Within any given country, there is significant selection bias in terms of who receives public vs. private care. Moreover, most research focuses on public vs. private financing of health care (e.g., Medicare Advantage vs. Medicare FFS), but less so whether the providers are public employees or not.
To answer this question, a paper by Frakes, Gruber, and Justicz (2023) examines data on obstetrical care within the Military Health System (MHS) using Military Health System Data Repository data. The authors summarize MHS as follows:
The MHS is a $50 billion per year program that provides care to active duty military, their dependents, and military retirees, covering over 9 million eligible individuals. Crucially, MHS
beneficiaries have access to government-owned and run facilities on military bases, as well as private providers that are contracted to the military through an insurance company. Care is split roughly equally between the two sources; 49 percent of outpatient encounters and more than 67 percent of hospitalizations for MHS beneficiaries take place with private providers.
The authors claim that base transfers are a source of exogenous variation in access to public vs. private health care because on- vs. off-base provision of health care is likely to vary by base depending on the capacity and services offered. Moreover, the authors further limit the sample to mothers who give birth at least twice and move between the births. The identification strategy follows once from Finkelstein, Gentzkow, and Williams (2016) is a difference-in-difference approach:
…we compare mothers who move, but both before and after the move do (or do not) have a military hospital nearby, to mothers who move and who see a change in their nearby access to military hospitals
Using this approach, the authors get the following results:
…we find highly significant outcomes for both comparisons for all measures of complications, suggesting lower rates of complications when deliveries are off base. The impacts are sizeable, with the rate of severe complication being less than two-thirds as large for those who move away from an MTF hospital rather than staying near an MTF hospital, and almost one-third lower for those who stay away from an MTF hospital rather than moving close to one. We do not find any significant impact on infant mortality, although this is partly due to imprecision;
the estimates imply a large reduction in both 28-day and 1-year infant mortality for those moving away from an MTF hospital. And we see a large and significant reduction in unplanned readmissions for those who move away from an MTF hospital or those who stay away from an MTF hospital.
However, private provision (off-base) do have higher rates of C-sections, longer length of stay, and more diagnostics. Is the extra care worth it?
These sizeable outcome results imply that the delivery of care off base is cost effective. For example, the average amount allowed for C-section versus non-C-section deliveries off base is $2,422.39 (in 2020 dollars). Multiplied by the increased rate of C-sections, this is $70.25 per admission. At the same time, the average readmission cost for our sample is $15,563. A 0.5 percent reduction in readmissions therefore saves $78.26 per delivery—larger than the costs of increased utilization. This ignores any additional health benefits from fewer complications and any cost savings related to lower rates of hospitalization for the child after the delivery.
The paper is interesting throughout and you can view the full manuscript here.