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
• Background
• Research objectives
• Methodology
• Results
• Discussion
Background• 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
How best to design a fiscal policy improving households’ allocation of goods in terms of nutrient adequacy
to recommendations?
Objective
Identify the optimal price conditions improving
households’ diet quality.
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 modelRamsey's model (1927)
IpVVMax ,. s.c.
i
ii xtR
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 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.
kkk
k
ept 1
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.
IpVVMax ,.
s.c.
i
iiobj xqualiquali
i
ii xtR
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.
k
k
kkk
k
pquali
ept
211
22
Optimal taxation modelSystem of simultaneous equations
,,,,, ** txpequaliftk
• The maximization program results in a system of equations where each optimal price variation, tk, :
• Solving this sytem requires to estimate a complete food demand system.
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.
Methodology – Demand model A conditionally linear system
• Selection of the Almost Ideal Demand System model (Deaton and Muellbauer, 1980):
• Iterated Least Square Estimator (Blundell and Robin, 1999).
iij
n
jijii PMpw
)ln(lnln1
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.
Methodology - Nutrient adequacy indicators
• MAR:
• LIM:
• SAIN:
10011
n
j jRNI
nutri
nMAR ij
i
100
10011
i
n
j
ENER
RNI
nutri
nSAIN j
ij
i
10050
_
22_
315331
ii
i
sugarAddfatSatNaLIM i
Nutrient adequacy indicatorsMAR - Mean adequacy ratio
The MAR for a 100g of food i:
The MAR for a food basket:
n
jij
n
j j
iji NAR
nRNINutri
nMAR
11
11
p
iii
n
jij
p
iiP MARxNARxnMAR
11 1
1
Nutrient adequacy indicatorsLIM – Score des composés à limiter
The LIM for a 100g o food i:
The LIM for a food basket:
n
jij
ijijiji LAR
nsugarAddedfatSatNa
LIM1
150_
22_
315331
p
iii
n
jij
p
iiP LIMxLARxnLIM
11 1
1
Nutrient adequacy indicatorsSAIN – Score d’adéquation individuel aux recommandations nutritionnelles
The SAIN for a 100g of food i:
The SAIN for a food basket:
n
j i
iji ENER
NARnSAIN
1
1
p
iii
Pi
n
j P
ijp
iiP SAINxENER
ENERENERNARxnSAIN
11 1
1
Results – Price elasticty of demand
Uncompensated own-price elasticities
• Statistically significant.
• Negatives.
• Low and inelastic.
• Within usual range.
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
• 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
• 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
Welfare losses homogeneously spread over all income groups.
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.
Appendices
Use of the Lagragian Method to obtain a system of n+2 linear and non-linear equations and n+2 unknowns.
j i i
jijij
jjj R
px
ettxt )0(
)0(
,)0( ...
0..2
2.2
1, )0()0(
)0(
,)0(
)0(
,)0(
)0(
,
ki i
kiki
i k
ikii
i k
ikii x
pxet
pxet
pxequalik
I
IpV c
,
j jjj
i i
jijij xqualiobj
px
etquali 0...%.. )0()0(
)0(
,
with
Methodology – Optimal taxation (2)
Methodology – Optimal taxation (3)
i k
ikiii k
ikiik pxet
pxeMARxk )0(
)0(,)0(
)0(,* .2
2.21,
• Using the Lagrangian method:
I
IpV c
,with
• And assuming a differentiable demand function:
ii i
kikkk tpxexxk ., )0(
)0(,
)0(*
Methodology – Optimal taxation (4)
i
cii IpxMARMARMax ,.
s.c. i
cii CostIpxt ),(
• Increasing the MAR objective until the other constraints collapse is equivalent to:
• Maximisation Program:
Methodology – Optimal taxation (5)
IpVVMax c ,.
s.c.
• Maximisation Program:
i
cii ObjectIpxMAR .),(
i
cii CostIpxt ),(
)0(%.40, kk ptk
