Table 2. Characteristics of selected previous food tax and subsidy modelling papers.

		Price elasticity matrix
Author	Interventions and setting	Number of food groups	Derivation of PE matrix	Cross-PE used?	Constraint or rescaling after PE application?	Health gain findings
Blakely et al (current study)	NZ. SAFA and sugar tax, F&V subsidy.	340 (disaggregated from 23)	Bayesian LAIDs model, 12 hierarchical demand systems. Marshallian conditional PEs.	Yes	Yes; using TFEe	Substantial HALY gains: SAFA tax ≈ sugar tax > F&V subsidy.
Briggs et al (2013) [6]	UK. 20% sugar sweetened drink tax.	12 drinks categories and 5 food categories.	Bayesian AIDs model, 5 hierarchical demand systems. Unconditional within each demand system; conditional across demand systems.	Yes	No	20% SSB tax would result in 1.3% reduction in obesity rates.
Cobiac et al (2017) [9]	Australia. Separate and combined policies such that all policies had <1% impact on total food expenditure. Salt, sugar, saturated fat and SSB taxes: F&V subsidy.	24	NZ PE matrix as used in Ni Mhurchu et al (2015) [4]. UK PE matrix for sensitivity analysis.	Yes, with suppression of statistically non-significant cross-PE.	No	Combined taxes and F&V subsidy > sugar tax > salt tax ≈ SAFA tax. F&V subsidy alone led to health loss. Sensitive to PE matrix used.
Ni Mhurchu et al (2015) [4]	NZ. Sodium and sugar tax. F&V subsidy. Tax on foods contributing to greenhouse gases.	24	Household economic survey data, with prices from food price index	Yes, with theoretical suppression of non-important cross-PE.	No	Sodium tax > sugar tax > F&V subsidy in terms of deaths prevented or postponed.

AIDS = almost ideal demand system. LAIDS = linear AIDS. HALY = health adjusted life year.

Unconditional means that the a change in expenditure was allowed in the assumptions for calculating PE.