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 Optimal Taxation and Food Policy: Impacts of Food Taxes on Nutrient Intakes

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 Optimal Taxation and Food Policy: Impacts of Food Taxes on Nutrient Intakes. New Directions in Welfare – OECD, Paris – July 2011. Thomas Allen (University of Perpignan, CIHEAM/IAMM-MOISA and INRA-ALISS) Olivier Allais (INRA-ALISS) Véronique Nichèle (INRA-ALISS)

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 Optimal Taxation and Food Policy: Impacts of Food Taxes

on Nutrient Intakes

New Directions in Welfare – OECD, Paris – July 2011

Thomas Allen (University of Perpignan, CIHEAM/IAMM-MOISA and INRA-ALISS)

Olivier Allais (INRA-ALISS)

Véronique Nichèle (INRA-ALISS)

Martine Padilla (CIHEAM/IAMM-MOISA)

outline of the presentation
Outline of the presentation
  • Background
  • Research objectives
  • Methodology
  • Results
  • Discussion

Increase in the prevalence of obesity and overweight in France since 1990 (Obépi, 2009);

Higher risk of illnesses for which nutrition is an essential determinant, among the low-income groups (InVS, 2006)

Nutrient-rich food are associated with higher diet costs and energy-dense food with lower costs (Darmon et al., 2007);

Public Health authorities’ questioning and academic discussion on the prospect of potential « fat taxes ».

research question
Research Question

How best to design a fiscal policy improving households’ allocation of goods in terms of nutrient adequacy to recommendations?


Identify the optimal price conditions improving households’ diet quality.

review of the litterature
Review of the Litterature
  • Food consumption economics : Estimation of a food demand system to capture price elasticities (Deaton et al.)
  • Health studies : Definition of the public health question and tools of analysis (Drewnowski et al.)
  • Public economics: Modelisation of the optimal taxation conditions (Ramsey,Murty et al.)
optimal taxation model ramsey s model 1927
Optimal taxation modelRamsey's model (1927)
  • Taxes' objective: Raise funds.
  • Planner's ojective: Maximise social welfare under the constraint that tax revenue covers a given level of public expenditure.


optimal taxation model inverse elasticity rule
Optimal taxation modelInverse elasticity rule

Ramsey rule: The reduction in demand for each good, caused by the tax system, should be proportional for each good.

Inverse elasticity rule: Optimal tax rates on each good should be inversely proportional to the good’s own–price elasticity of demand.

optimal taxation model application to a nutritional policy objective
Optimal taxation modelApplication to a nutritional policy objective

Taxes' objective:Transforming consumption behaviours.

Planner's objectif: Maximise social welfare under the constraint that the overall diet quality of consumers' food basket reach a minimum level in terms of nutrient adequacy to recommendations.


optimal taxation model a nutritional quality price ratio
Optimal taxation modelA nutritional quality/price ratio

Optimal financing criteria : The optimal tax rates, for each good, are decreasing functions of their own-price elasticity of demand.

Optimal adequation criteria: The optimal tax rates, for each good, are decreasing functions of their « nutritional quality/ price » ratio.

optimal taxation model system of simultaneous equations
Optimal taxation modelSystem of simultaneous equations
  • The maximization program results in a system of equations where each optimal price variation, tk, :

Where quali, p and x are vectors of the diet quality indicators, initial prices and quantities associated with each good and e the own and cross price elasticities.

  • Solving this sytem requires to estimate a complete food demand system.
methodology demand model a conditionally linear system
Methodology – Demand modelA conditionally linear system

Selection of the Almost Ideal Demand System model (Deaton and Muellbauer, 1980):

Iterated Least Square Estimator (Blundell and Robin, 1999).

methodology pseudo panel data
Methodology – Pseudo-Panel Data
  • A panel of scanner data:

- 156 periods: 1996-2007

- 8 cohorts: Date of birth/Social status

- 27 food groups

  • Group agregation:

Homogenous categories in terms of nutritional content (fruits/vegetables fresh/processed, snacks/already prepared meals, vegetable/animal fat, salty/sugary fat).

  • Price construction:

24 clusters of price according to Localisation/Social status.

nutrient adequacy indicators mar mean adequacy ratio
Nutrient adequacy indicatorsMAR - Mean adequacy ratio

The MAR for a 100g of food i:

The MAR for a food basket:

nutrient adequacy indicators lim score des compos s limiter
Nutrient adequacy indicatorsLIM – Score des composés à limiter

The LIM for a 100g o food i:

The LIM for a food basket:

nutrient adequacy indicators sain score d ad quation individuel aux recommandations nutritionnelles
Nutrient adequacy indicatorsSAIN – Score d’adéquation individuel aux recommandations nutritionnelles

The SAIN for a 100g of food i:

The SAIN for a food basket:

results price elasticty of demand
Results – Price elasticty of demand

Uncompensated own-price elasticities

  • Statistically significant.
  • Negatives.
  • Low and inelastic.
  • Within usual range.
simulations optimal taxation mar
Simulations – Optimal taxation MAR
  • Goods to tax: Fish, meat, poultry, deli meat, snacks, sugar, animal fat, beverages
  • Goods to subsidize: Fruits and vegetables, yoghurt, milk, cereals and starches, potatoes, vegetable fat and salty snacks
simulations optimal taxation lim
Simulations – Optimal taxation LIM
  • Goods to tax: Fruits and soft drinks, deli meat, snacks, mixed dishes, dairy products, cereals and starches, vegetable and animal fat, sweets and salty snacks.
  • Goods to subsidize: Fish, meat, poultry, vegetables, potatoes, water coffee and tea and alcoholic beverages.
simulations optimal taxation sain
Simulations – Optimal taxation SAIN
  • Improvements once calorie intakes are taken into consideration:
  • Mixed dishes are to be taxed; water to be subsidized.
  • Meat are more heavily taxed; fruits and vegetables more heavily subsidized.
fiscal incidence
Fiscal incidence

Welfare losses homogeneously spread over all income groups.

conclusion results and policy implications
ConclusionResults and policy implications

Theoretical result: A « diet quality/price » ratio and an augmented inverse elasticity rule;

Empirical results: Mixed evidence supporting food taxation:

- Low price elasticities and high tax rates;

- Weak convergence on food groups to tax/ subsidize accross nutrient adequacy indicators.


Methodology – Optimal taxation (2)

Use of the Lagragian Method to obtain a system of n+2 linear and non-linear equations and n+2 unknowns.


methodology optimal taxation 3
Methodology – Optimal taxation (3)
  • Using the Lagrangian method:


  • And assuming a differentiable demand function:
methodology optimal taxation 4
Methodology – Optimal taxation (4)
  • Increasing the MAR objective until the other constraints collapse is equivalent to:
  • Maximisation Program:


methodology optimal taxation 5
Methodology – Optimal taxation (5)
  • Maximisation Program: