X-Efficiency

X-Efficiency in Hospitals and Health Systems

X-efficiency is the kind of efficiency that asks how fully a provider gets output from the staff, equipment and supplies it already has, so X-inefficiency is the extra cost a hospital or practice carries above the lowest cost its inputs and technology allow. Harvey Leibenstein named it in his 1966 paper in the American Economic Review, setting it against allocative efficiency, which concerns how resources are spread across markets and products. He argued that the losses from slack inside organisations were often much larger than the losses from misallocation, a claim that matters in health care because many providers face weak competitive pressure. The idea sits behind payment by fixed prices, hospital benchmarking and the frontier methods health economists use to estimate waste.

Leibenstein's contrast with allocative efficiency

Leibenstein's starting point was that microeconomic theory dealt with allocative efficiency, while empirical studies suggested the gains from better allocation were small. His Table 1 lists estimates of the welfare loss from monopoly and tariffs, among them Harberger's figure of 0.07 per cent of United States national product for 1929. He explained the smallness with Harberger's triangle, the deadweight loss approximated as half the price gap times the quantity gap, scaled by the share of national income in the affected industries. As a share of national income the approximation is as follows.

$$\frac{L}{Y} \approx \frac{1}{2} \, s \, \eta \, d^{2} = \frac{1}{2} \times 0.5 \times 1.5 \times 0.2^{2} = 0.015$$

where $L$ is the welfare loss, $Y$ is national income, $s$ is the share of output produced in monopolised industries, $\eta$ is the price elasticity of demand and $d$ is the proportional excess of the monopoly price over the competitive price. With his deliberately large values (half of output monopolised, a 20 per cent price gap and an elasticity of 1.5) the loss is only 1.5 per cent.

X-efficiency was his name for the non-allocative kind. Motivation was a major element of it but not the only one, so he avoided the term motivation efficiency. Frantz explains that the X stood for an inefficiency of unknown nature. The evidence in the 1966 paper included an Egyptian refinery case and ILO productivity missions, whose simple changes to plant layout, work methods, waste control and payment by results cut unit costs, frequently by more than 25 per cent, without additional capital.

Why given inputs do not fix output

Leibenstein gave four reasons why given inputs cannot be turned into predetermined outputs. Labour contracts are incomplete, not all factors of production are marketed, the production function is not completely specified or known, and interdependence and uncertainty lead competing firms to cooperate tacitly and imitate each other's techniques. Much of the performance expected under a labour contract is left to custom, authority, motivational techniques and individual discretion.

Competitive pressure is one of the forces that decide how much of that discretion turns into slack. Leibenstein concluded that firms and economies work on a production surface well within the outer bound their resources allow, and that where pressure is light people trade the disutility of effort for less pressure and easier relations at work. He also reported that some firms reverted to their old methods once the productivity missions had left, so a gain achieved under scrutiny may not last.

Health care fits this account closely. Clinical work is hard to specify fully in a contract, many hospitals face little local competition, and the payer cannot easily observe effort, the territory of the principal-agent problem. The European Observatory study of health system efficiency edited by Cylus, Papanicolas and Smith states that technical inefficiency arises mainly at provider and practitioner level and may result from inappropriate incentives, weak or constrained management and inadequate information.

Measuring distance from the frontier

Empirical work turns the idea into a distance from a best-practice frontier. In the Observatory study, Hollingsworth defines technical efficiency for a hospital at point C, which uses more labour and capital than hospitals on the frontier to produce the same output, with A the frontier point on the same ray from the origin and B the point on that ray whose cost equals that of the least-cost frontier point Q.

$$TE = \frac{OA}{OC}, \qquad AE = \frac{OB}{OA}$$

where $O$ is the origin of the diagram, $OA$ is the distance to the frontier, $OC$ the distance to the hospital's actual input use, $OB$ the distance to the least-cost level given input prices, $TE$ is technical efficiency and $AE$ is input-side allocative efficiency, the excess cost from using inputs in the wrong proportions. Both ratios lie above 0 and at most 1.

Studies in Leibenstein's tradition report an X-efficiency score on the same scale. Frantz notes that a score of 0.8 means the firm could have used 20 per cent fewer inputs for the same output, and that X-inefficiency is computed either as one minus the score (0.2) or as that shortfall divided by the score (0.25). He puts the average across more than 200 studies in many industries at about 0.8, and his review lists one health study, of primary care facilities in rural Burkina Faso, with an average of 0.86.

Two frontier methods dominate in health. Hollingsworth describes data envelopment analysis as by far the most common, applied over 400 times in health care settings, and stochastic frontier analysis as splitting the usual regression error term into inefficiency and error. He also warns that data envelopment analysis gives only relative efficiency, so a hospital judged efficient is efficient only against the practices observed in its sample.

Worked example with reference costs for one hospital

All figures in this example are illustrative. The Observatory study describes a unit-cost index in which a hospital's case numbers in each diagnosis-related group are multiplied by a national reference cost, often the mean unit cost across comparable institutions, and the result is compared with the hospital's actual costs. Hospital H treats 400 hip replacements with a reference cost of GBP 6,000, 1,500 cataract operations at GBP 900 and 600 heart failure admissions at GBP 3,500, and its actual costs are GBP 6,435,000.

1. Expected cost at reference prices. The expected cost sums cases times reference cost over the three groups.

$$E = \sum_{g} n_g \, r_g = 400 \times 6000 + 1500 \times 900 + 600 \times 3500 = 5850000$$

where $E$ is the expected cost in GBP, $g$ indexes the groups, $n_g$ is the number of cases in group $g$ and $r_g$ is its reference cost.

2. Relative cost index. Dividing actual by expected cost gives 6,435,000 / 5,850,000 = 1.10, so the hospital spends 10 per cent more than an average provider would for the same activity, an excess of GBP 585,000.

3. Remove what management cannot control. A case-mix review finds that the hospital's heart failure patients are sicker than the national average, which justifies GBP 150,000 of extra cost. The adjusted expected cost is GBP 6,000,000 and the unexplained excess is GBP 435,000, enough at the reference cost to fund about 124 further heart failure admissions (435,000 / 3,500).

4. Score against average and against best practice. Against the adjusted average the score is 6,000,000 / 6,435,000 = 0.932. Suppose the best hospitals run 8 per cent below reference cost. The frontier cost is then 6,000,000 × 0.92 = 5,520,000, and the score falls to 5,520,000 / 6,435,000 = 0.858, an X-inefficiency of 0.142 by the first of Frantz's conventions.

5. Interpret the result. The GBP 435,000 is an upper bound on the excess over average practice, since the Observatory study names variation in accounting practice as one reason for apparent variation in unit costs, and part of the gap may be input prices. The comparison with best practice matters too, because a reference cost set at the mean already contains the average provider's slack, and against the frontier the gap is GBP 915,000.

Payment, competition and pressure on hospital costs

Payment design is one of the levers health systems use against X-inefficiency. Shleifer's theory of yardstick competition starts from the point that a franchised monopoly under typical regulation has little incentive to reduce costs, and proposes paying each firm a price based on the costs of identical firms, under which each chooses a socially efficient level of cost reduction. He noted that Medicare's prospective payment of hospitals by diagnosis-related groups is very similar. The same logic runs through activity-based funding.

In England, Lord Carter's 2016 review of operational productivity in non-specialist acute hospitals found significant unwarranted variation across all of the main resource areas. He estimated it as worth GBP 5bn of efficiency opportunity, at least 9 per cent of the GBP 55.6bn spent by those hospitals, and proposed an adjusted treatment cost metric based on reference cost data. The review covers procurement as well as staff and clinical practice, so its figure mixes X-inefficiency with input prices, a limit shared by most benchmarking.

What X-inefficiency means for cost-effectiveness analysis

A cost-effectiveness analysis that prices resource use at national average unit costs inherits the average provider's X-inefficiency, since those costs come from real providers and not from a frontier. The resulting ratio describes value under current delivery and can change as providers become more or less X-efficient.

The NICE manual (PMG36, section 6.3.1) reasons that, given the fixed budget of the NHS, the maximum acceptable ICER is the opportunity cost of programmes displaced by new, more costly technologies. How much health those displaced programmes produce depends partly on how X-efficient they are, so any estimate of that opportunity cost, and of the cost-effectiveness threshold built on it, also reflects the efficiency of existing services. The Observatory study adds that inefficiency anywhere in the system is likely to deny health improvement to patients who might have been treated if resources had been used better.

The idea is neutral between the two normative traditions. Leibenstein made his comparison in the consumer surplus terms of welfare economics, while Brouwer and colleagues describe extra-welfarism as usually judging health care by health outcomes, though health need not be its only object of concern. X-inefficiency shrinks the output of a given budget under either objective, as lost welfare or as lost QALYs.

Boundaries with technical, allocative and productive efficiency

X-efficiency overlaps with technical efficiency without being identical to it. Technical efficiency is a measured distance from a frontier for any reason, while X-efficiency names a cause, the effort, motivation and organisation inside the unit. Leibenstein's allocative efficiency is the market-level allocation behind Harberger's triangle, whereas allocative efficiency in health efficiency studies usually means the mix of services or of inputs, as in the ratio above. Productive efficiency combines the technical and input-mix parts, and some bank studies in Frantz's review report cost efficiency under the X-efficiency label, so the definition behind any reported score needs checking.

Criticisms and common misreadings of X-efficiency

The concept has always been contested. Mefford summarises the neoclassical position that maximising behaviour, full knowledge and competition leave no room for inefficiency, notes that Stigler presented these arguments succinctly in 1976, and records the reply that people may be maximising leisure or other goals, so apparent slack is still utility maximisation. For a payer with a fixed health budget, slack taken as leisure still leaves fewer patients treated.

1. Reading every frontier gap as slack. The Observatory study stresses external influences outside a provider's control, such as the severity of patients' disease, and stochastic frontier models can misstate inefficiency if their assumptions about the error term fail.
2. Treating the average as the frontier. A score against national mean costs understates X-inefficiency, as step 4 of the worked example shows.
3. Assuming one push removes it. Leibenstein's reports of reversion after the productivity missions left suggest that gains need continuing incentives.
4. Confusing the two meanings of allocative. Leibenstein's contrast is with market-level allocation, not with the input mix inside a hospital.

Sources

• Brouwer WBF, Culyer AJ, van Exel NJA, Rutten FFH. Welfarism vs. extra-welfarism. Journal of Health Economics. 2008;27(2):325-338. https://doi.org/10.1016/j.jhealeco.2007.07.003
• Carter of Coles (Lord Carter). Operational productivity and performance in English NHS acute hospitals: unwarranted variations. An independent report for the Department of Health. February 2016. https://www.gov.uk/government/publications/productivity-in-nhs-hospitals
• Cylus J, Papanicolas I, Smith PC, editors. Health system efficiency: how to make measurement matter for policy and management. Health Policy Series 46. European Observatory on Health Systems and Policies; 2016. Chapters 1 and 5 (chapter 5 by Hollingsworth B). https://eurohealthobservatory.who.int/publications/i/health-system-efficiency-how-to-make-measurement-matter-for-policy-and-management-study
• Frantz R. Harvey Leibenstein, and an anomaly called X-Efficiency. Journal of Behavioral Economics for Policy. 2018;2(1):25-31. https://sabeconomics.org/ojs/index.php/jbep/article/view/61
• Leibenstein H. Allocative efficiency vs. "X-efficiency". American Economic Review. 1966;56(3):392-415.
• Mefford R. X-efficiency: economists and managers view it differently. Journal of Behavioral Economics for Policy. 2017;1(2):25-30. https://www.sabeconomics.org/wordpress/wp-content/uploads/JBEP-1-2-4.pdf
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Section 6.3.1. https://www.nice.org.uk/process/pmg36/chapter/committee-recommendations
• Shleifer A. A theory of yardstick competition. RAND Journal of Economics. 1985;16(3):319-327. https://econpapers.repec.org/RePEc:rje:randje:v:16:y:1985:i:autumn:p:319-327