**Nutrition and Productivity**

Bhijit Banerjee

Department of Economics, M.I.T.

1 A simple theory of nutrition and productivity

The capacity curve (ﬁg1)

• The capacity curve: It relates income and work capacity
(productivity)

Higher income → better nutrition.

Better nutrition: ﬁrst used by the body for the basic
metabolism. Then only it translates in higher capacity.

As a result, the work capacity is convex, and it intersects
the 45 degree line from below.

The Piece-wage schedule (ﬁg2)

• The piece wage schedule

— The amount of income you get for each task you perform

3

—: v1 >v ∗ >v

—There is a wage v ∗ at which the body ”breaks even” → it creates a
discontinuity in the labor supply.

Discontinuous labor supply
(ﬁg3)

• The individual labor supply jumps

• We can now draw the aggregate labor supply.

Equilibrium (ﬁg3)

• Introduce a labor demand curve.

• What happens if the labor supply cross the labor demand in
the gap?

• There is involuntary unemployment Deﬁnition= A person is
involuntarily unemployed if he cannot ﬁnd employment in a market which does
employ a person very similar to him and if the latter person, by virtue of his
employment in this market is distinctly better oﬀ than him.

• The vicious circle is complete: low wage leads to reduced
work capacity, which closes access to employment.

1.1 The eﬀect of non-labor
income (ﬁg4)

• In what direction do assets move the capacity curve?

• Who is more likely to be employed: the rich or the poor?

• Who earns a larger wage income if both are employed?

The vicious circle of
inequality: the functioning of the labor market magniﬁes assets inequality.

1.2 The eﬀect of
redistributing wealth

• Imagine individuals are ranked by land holding (ﬁg 5)

• m have no land.

Who will work (ﬁg6)

Deﬁnition: Minimum wage such
that an individual can or want to work.

• Capacity curve and labor supply.

• what is the minimum wage at which someone can work?

• Labor supply for capacity to work: the minimum wage necessary
decreases with wealth

•

• Willingness to work and labor supply

• The willingness to work is smaller for richer people

• Labor supply for willingness to work: the minimum wage
necessary increases with wealth.

Labor Supply (ﬁg7)

• Combine the two: labor supply.

• How does redistributing land frm the rich to the poor aﬀect labor supply

• what happens to wages, production.

1.3 Dynamics

• Assume now that work capacity today is a function of last
period’s nutrition:

work capacity t = f(nt−1),f0
> 0

• To simplify the analysis, let us assume away all the labor
market issues—everyone works on his own and gets an income equal to his work
capacity. Furthermore nutrition is an increasing function of income.

• Therefore

nt = g (workcapacityt)= g(f(nt−1)).

Implications

• Poverty trap (ﬁg10).

• Reinforces
the lack of a equity-eﬃciency
trade-oﬀ

• What if poor people could enter into long term employment
contracts?

• What
would be the eﬀect
of providing free meals?

• What
would be the eﬀect
of providing access to credit?

• What
would be the eﬀect
of an employment guarantee scheme?

• How much does an improvement in a household’s income increase
investments in human capital?

1.4 Looking at the evidence

• Observe that the model, in order to generate a poverty trap,
requires that over a range, the f(g(•)) curve intersects the 45 degree line
from below.

• A poverty trap will emerge if f0g> 1. Let’s denote income
by y and do some algebra:

0

0 0

gf0 gf

0

f0 g = gf0 ∗ = g ∗ y ∗ (1)

gf gy

0

The expressions ff 0 g and gy
are called“elasticities”.

g

• On the 45 degree line, f = y. Expression 1 tells us that there
can be a nutrition-based poverty trap only if the product of the elasticity’s
of the income-nutrition and nutrition-productivity relationships is greater
than 1. It gives us a clear empirical fact to look for.

1.5 A Methodological aside: investigating the relationship between two
variables

• Say we are interested in the relationship between

log (income) and log (calories).

• We start with a data set (say, data from India), which will look like two columns (two variables),
with one observation of income and one observation of log(calories) for a
sample of individuals (for example: 200 individuals).

• The ﬁrst thing we could do: plot the data. We put log(income)
on the x axis and log(calories) on the y axis.

• Suppose we want to summarize the shape of this graph:

• The most ﬂexible way is the “non-parametric regression”: we
try to trace the function g(.)which best captures the variation in the data. We
want to ﬁnd g such that

ln(calories)=ˆg(ln(income))
+ˆ²

Where E(ˆ²)=0. ˆ² is called
the residual of our regression. gˆ(ln(income)) is the predicted value of
ln(calories)

• We are not going to go into the details of how we ﬁnd this
function ˆg(.). There are several methods, of which the “kernel” regression is
the most commonly used.

• The most economical form is to run a linear regression: we
restrict the function ˆg(.)to be a linear function of log (expenditure per
capita). That is, we try to ﬁnd the line that represent the best the cloud of
points.

• Note that these are all just ways to describe the data.

• It is not because we have decided to run this particular
regression that we have uncovered the true causal relationship between income
and nutrition.

• For example, what would I ﬁnd if I were to run a regression of
the number of sick people on the number of doctor in an area? How should I
interpret it?

• Often, we assume that the data has been generated byamodel of
the form:

ln(calories)= βˆ+ˆα
ln(income)) +ˆ²,

where E(ˆ²)=0.

ln(calories)= β + α
ln(income)+ ²,

where ² is some error term,
with E(²| ln(income)) = 0 and then, the linear regression will uncover our best
estimates of α and β (notice that the hats are gone above the parameters).

• In this case we assume that log(expenditures per capita)
causes log(calories per capita). In this course, we will see many instances
(for example today!) where this is not the right model to assume, and how to
deal with that.

1.6 The relationship between income and nutrition: The “conventional
wisdom” and its problems

• “Conventional wisdom”: more income leads to more income spent
on food and to better nutrition. In the data: strong correlation between income
and food expenditures.

• Note:
if you regress food expenditures on total expenditures, the coeﬃcient is less than
one. What does the relationship between the share of expenditure spent on food
and total expenditure?

• This is called Engel’s law: As household income increases,
the share spent on food decreases.

Problems with ﬁguring out how
much income aﬀects
nutrition

1. Reverse causality

2. Common causes

3. Measurement problem (1):
Food expenditures are not correctly measured.

• Meals taken outside th household and given to people.

• Who tends to eat out?

• Who tends to feed people?

• In what direction does that bias the relationship between
income and actual nutrition if you do not observe meals taken out and given to
people but only total expenditure on food?

•

4. Measurement problem (2)

• Food waste

• Who tends to waste more?

• In what direction does that bias the relationship between
income and actual nutrition if you do not observe waste but only total
expenditures on food?

•

5. Measurement problem (3):

• Even if expenditures were correctly measured, they do not
give a correct representation of quality. As people get richer, they buy better
tasting food.

• How does it bias α?

1.7 Income and nutrients in Maharastra, India

Based on Deaton and
Subramanian (JPE, 1996)

D-S deal with some
measurement issues

• Meals taken in and given out. The data set includes the
number of meals taken out, meals given to people, meals taken at home: they
correct for this.

• Quality: They start with 149 food items that the households
have consumed in the past 30 days. Items are very precise (ex: several
categories of rice are included). They use a conversion table to calculate how
many calories are provided by each item.

• Cannot ﬁx Waste and Endogeneity

D-S take a Non-parametric approach
In addition, their work not only examines the average relationship, but also
the entire shape of the relationship between income and nutrition: Do we
observe the non-linearity which forms the basis of the Dasgupta-Ray model we
studied in lecture 2?

To do so, they run
non-parametric regressions:

ln(calories)=
g(ln(expenditure)) + ²

They try to estimate the
shape of the function g(.).

D-S Results:

• The relationship between expenditure and calories

• Figure2: More expenditures → better nutrition.

• Figure 3: Elasticity: derivative of the curve in ﬁgure 2. It
is declining with expenditures (the curve is concave), but not very fast.

• The relationship between quality and expenditures

• An indicator of quality: price paid per calorie.

• Figure 4: Log of price per calorie increases with
expenditures.

• Figure 5: Elasticity is fairly constant with expenditures.

1.8 Conclusion

• There is a fairly strong relationship.

• However there is also a lot of substitution towards quality
even at low incomes.

• Not surprsing given that they calculate that 2000 calories
cost about 4% of the average daily wage.

• The elasticity is nowhere close to 1....

2 The relationship between nutrition and productivity

Is there evidence that this
relationship is very steep?

• There is experimental evidence that better-fed workers are
more productive at physical tasks. Example: 302 anemic rubber tree tapper in Indonesia. Half were allocated to a treatment group who was
given iron supplement, half were allocated to a placebo. After 60 days, the
treatment group had lower anemia, higher capacity, and higher productivity than
the placebo group.

• In the early 1990s, the Indonesian government experimented
with an increase in health care prices: they increased the prices in a set of
(randomly chosen) pilot locations. The consequences were: people were less
likely to participate in the labor market in the pilot areas. Those who
participated earned less.

• However the elasticity of the productivity-nutrition relationship
is below one... The product will not be above one: a study of the relationship
between farm productivity and calorie consumption in Burkina Faso (Strauss 1986) ﬁnds an elasticity of 0.34, 0.49 for
the poorest.

3 Conclusion: Should we abandon DasGupta and Ray?

• This exercise has shown us that this very clever and
appealing model is not a literal description of the reality: the relationship
between calories and nutrition is not steep enough to generate a poverty trap
by itself: the product of the two elasticities is around 0.09, which is far
from one!!

• However, the model forces us to think about how the nexus
between human capital and income can lead to a vicious circle: this circle may
be found in contexts other than the health and productivity nexus.

•

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