Signature
B = beta * g_econ
| Inputs | Definition | Unit |
|---|---|---|
beta | Percentage growth in real health spending associated with each 1 per cent of growth in economy-wide labour productivity; 0.48 in the OECD estimate used by the OBR in 2024 | none |
g_econ | Projected annual growth in economy-wide labour productivity, entered in per cent (1.5 for 1.5 per cent) | per cent a year |
B | Contribution of the Baumol effect to annual real growth in health spending | percentage points a year |
|---|
Function
Baumol unbalanced growth relative cost and labour allocation function
Maps output per hour, or its annual growth, in health care and in the rest of the economy to the labour cost of a unit of health care relative to a unit of other output, and to the share of working hours that health care needs when the mix of outputs is held fixed. With a common wage in both sectors the wage cancels, so the relative cost depends only on relative productivity. A related top-down form, used in UK fiscal projections, turns economy-wide productivity growth into an allowance for real health spending growth.
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Implementations
Excel
Baumol component of health spending growth in one cell
With the coefficient in a cell named BaumolCoef and projected productivity growth in per cent in EconProdGrowth, Excel returns the Baumol component in percentage points a year.
=BaumolCoef*EconProdGrowth
Assumptions
Constant Baumol coefficient across the projection
The coefficient is applied unchanged in each projection year, in the OBR's 2024 projection every year beyond 2028-29. A coefficient of 0 corresponds to health care productivity growing in line with the whole economy, and a coefficient of 1 to each 1 per cent of economy-wide productivity growth being matched by real health spending growth but not by health output.
Baumol component as one part of other cost pressures
B is one component of a top-down allowance. In the OBR's 2024 decomposition the other cost pressures total 1 percentage point a year, of which 0.72 points come from the Baumol effect, 0.15 from chronic conditions and a 0.13 point residual that may partly reflect technology, and they are applied to current health spending only.
Worked examples
OBR 2024 Baumol component at a coefficient of 0.48
With economy-wide productivity growth averaging 1.5 per cent a year and the OECD coefficient of 0.48, the Baumol effect adds 0.72 percentage points a year to real health spending growth, as in the OBR's 2024 baseline.
beta = 0.48; g_econ = 1.5; B = 0.72
OBR lower productivity variant with a coefficient of 1
In the OBR's lower productivity variant the coefficient is 1, so the Baumol component equals productivity growth, 1.5 percentage points a year. In that variant health spending reached 20.1 per cent of GDP in 2073-74, against a baseline of 14.5 per cent.
beta = 1; g_econ = 1.5; B = 1.5
OBR higher productivity variant with a coefficient of zero
In the OBR's higher productivity variant the coefficient is 0 and the Baumol component disappears. Health spending then reached 10.7 per cent of GDP by the end of the projection.
beta = 0; g_econ = 1.5; B = 0
Common errors
Adding a full technology driver on top of the Baumol component
The OBR assumes that most spending growth from new technology is already captured by a mixture of its Baumol and income effects, leaving only a small residual of 0.13 percentage points. Adding a separate full technology driver to B and the income effect counts much of the same growth twice.
Reading the Baumol component as a change in the GDP share
B is a contribution to the annual growth rate of real health spending, not a change in health spending as a share of GDP. The 0.72 points in the OBR baseline are one input to a projection in which the share of GDP depends also on demography, incomes and GDP growth.
Sources
OBR Baumol coefficient applied to economy-wide productivity growth
Office for Budget Responsibility. Fiscal risks and sustainability (CP 1142). London: OBR; September 2024. Chapter 3. Paragraphs 3.25 to 3.28, which apply the OECD Baumol coefficient of 0.48 to economy-wide productivity growth averaging 1.5 per cent a year to give 0.72 percentage points, paragraph 3.34 on technology, and paragraphs 3.39 and 3.40 on the variants with coefficients of 0 and 1.
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