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 model
Ramsey'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.
Max
.V
Vp,I
s.c.
Rti xi
i
Optimal taxation model
Inverse 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.
tk 

1





p

e
k
 kk
Optimal taxation model
Application 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.
Max
.V
Vp,I
s.c.
Rti xi
i
obj
quali

quali

ix
i
i
Optimal taxation model
A 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.





1


t
quali

2
1
k
k


 





p
2
e
2
p
k
kk

  k
Optimal taxation model
System of simultaneous equations
• The maximization program results in a system of
equations where each optimal price variation, tk, :


*
*
t

f
quali
,
e
,
p
,
x
,
t
,
k
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
•
Selection of the Almost Ideal Demand System
model (Deaton and Muellbauer, 1980):
 
n

w


ln
p

(ln
M

ln
P
)


i
i
ij
j
i
i
j

1
•
Iterated Least Square Estimator (Blundell
and Robin, 1999).
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:


1nnutri
ij
MAR


100
 
i
n
j
1RNI

j




Add
_
suga


Sat
_
fat
Na
1
i
i
i

LIM




10


i


3
3153
2250








1n nutri
ij

100
 
nj
1RNI

j 


SAIN


100
i
ENER
i
Nutrient adequacy indicators
MAR - Mean adequacy ratio
The MAR for a 100g of food i:
n
n
Nutri
1
ij 1
MAR

NAR


i
ij
n
RNI
n
j

1
j

1
j
The MAR for a food basket:
np
p
1 x
MAR
P

i
NAR
ij

x
i
MAR
i



n
j

1
i

1
i

1
Nutrient adequacy indicators
LIM – Score des composés à limiter
The LIM for a 100g o food i:
n
Na
Sat
_
fat
Adde
_
sug


1
1
ij
ij
ij


LIM




LA

i 
ij

3
3153
22
50
n
j

1


The LIM for a food basket:
np
p
1 x
LIM
P

i
LAR
ij

x
i
LIM
i



n
j

1
i

1
i

1
Nutrient adequacy indicators
SAIN – Score d’adéquation individuel aux recommandations nutritionnelles
The SAIN for a 100g of food i:
n
ij
1 NAR
SAIN
i
nj
i
1ENER
The SAIN for a food basket:
p
n
p
ij
NAR
ENER
i
1x
SAIN
P

i

x
i
SAIN
i



n
ENER
P
ENER
P
j

1
i

1
i

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.
Conclusion
Results 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
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.









(
0
)
(
0
)
(
0
)






x
x
x
1
2
0
)
i
i
k (







k
, 
quali
.
e

t
.
e

t
.
e

x

0
i
i
,
k
i
i
,
k
i
k
,
i
k
(
0
)
(
0
)
(
0
)






2
p

2
p
p
i
i
i
k
k
i






(
0
)
x


j
(
0
)




quali
.
t
.
e

obj
.%
.
quali
.
x

0



j
i
j
,
i(
j
j
0
)

p
j
i
j
i


(
0
)
x
j
(
0
)
t
.
x

t
.
t
.
e

R


j j
j
i j
,
i (
0
)
p
j
j
i
i
with
Vpc,I
I

Methodology – Optimal taxation (3)
• Using the Lagrangian method:


 x

x

1

2

k
,

x

MAR
.
e

t
.
e









2



2
p

  p

*
k
i
(
0
)
i
i
i
,
k
(
0
)
k
with
(
0
)
i
i
i
,
k
(
0
)
k
i
Vpc,I
I

• And assuming a differentiable demand function:
(
0
)
x
(
0
)
k
*

k
,

x

x
e
k
,
i
.
t
i
k
k

(
0
)
p
i
i
Methodology – Optimal taxation (4)
• Increasing the MAR objective until the other
constraints collapse is equivalent to:
• Maximisation Program:


Max
.
MAR

MAR
i
x
i
p
c
,
I

i
s.c.
tx(p,I)
Cost

i i
i
c
Methodology – Optimal taxation (5)
• Maximisation Program:
pc,I
Max
.V
V
s.c.
MAR
x
(
p
,I
)

Object
.

ii c
i
tx(p,I)
Cost

i i
c
i
(0
)

k
,
tk
40
%.
p
k