Nutrition

Question 1

In the equation below, what does “v” represent? income today =v x (productivity today) = v x f(nutrition today)

Answer 1

Your income today is a function of your ability to earn income today. This is determined by how productive you can be, given by the second term on the right hand side of the equation (since it is a function of how nourished you are today) and how much you can earn for your labor. “v” represents how much can earn for each unit of labor, the piece wage.

Question 2

True or False. The capacity curve (and the wage) generates a mapping between your income yesterday and your income today.

Answer 2

True, your income in one period affects your nutrition and thus determines your productivity in the following period. This in turn determines your income in the following period and so on. Thus, income yesterday is linked to your income today and income today is linked to your income tomorrow

Question 3

How many steady states are there in the figure below? (Excluding (0,0))

Answer 3

One. There is only one intersection in the curve shown. Thus, those who start off very poor converge on the single point while even for those who start off relatively richer (and further up the curve), the returns to investing in education are so low that they invariably slide down the capacity curve and converge on the single intersection point.

Question 4

How many stable steady states are there in the figure below?

Answer 4

Two. Although there are three steady states (the three points at which the capacity curve intersects with the 45-degree line) shown in this graph, only two of them are stable steady states. Trajectories that initiate immediately to the left and immediately to the right of a stable steady state tend to converge to the same point. With an unstable steady state, such as the one that occurs where the capacity curve cuts the 45-degree line from below, if you start above the steady state, you move up the capacity curve to a higher stable steady state while if you start below you move down the capacity curve to a lower stable steady state.

Question 5

In the graph from the previous question (reproduced below), do people starting off at y0 versus y0” end up at the same, or different, stable steady states?

Answer 5

Different. Those starting at y0 will slide down the capacity curve to the stable steady state to the left of y0 while those starting at y0” will move up the curve to the stable steady state at the top right of the graph.

Question 6

In order to have a poverty trap, the capacity curve which links today’s income to tomorrow’s income must intersect the 45-degree line from above.

Answer 6

False. In order to have a poverty trap, the capacity curve must intersect the 45-degree line from below since an unstable steady state is created in that situation. All trajectories originating below the intersection on the capacity curve will converge to a lower steady state, thus creating the conditions for a poverty trap.

Question 7

If f is a function linking nutrition today to income tomorrow (the capacity curve) and g is a function linking income today to nutrition today. That is, y_t+1= f(n_t) and n_t=g(y_t). f ‘ and g ‘ are the first derivatives of the two functions, then a poverty trap will emerge if:

Answer 7

f ‘g’ > 1

The curve linking income today and income tomorrow is given by f o g. That is y_t+1= f o g(y_t​). For there to be a poverty trap, this composite curve needs to intersect the 45 degree line from below. That is, the slope . Since , this simply translates to as Professor Duflo notes in the video.

Question 8

Let (f’/f)g be the elasticity of income tomorrow with regards to nutrition and let (g’/g)y be the elasticity of nutrition with regards to income. Then, to see a poverty trap based on the mechanism that insufficient nutrition lowers productivity and that wages need to thus be enough to sustain a certain level of nutrition, we need:

Answer 8

(f’/f)g * (g’/g)y > 1

As you can see, it is the product of two elasticities. Thus, when the product of these two elasticities is greater than 1, a poverty trap will emerge.

Question 9

If the elasticity of calorie consumption with regards to income is greater than 1, what does a 10 percent increase in income lead to?

Answer 9

An increase in calorie consumption that is greater than 10 percent.

Question 10

True or False: One implication of the capacity curve model of nutrition and productivity sketched out in this lecture is that different members of the population can have different elasticities of nutrition with regards to income.

Answer 10

True. The underlying return to investing in calories will be different for different people, depending on where on the capacity curve they lie. Thus, investing in more nutrition may not be worthwhile for the poorest people since they are caught in a poverty trap and are unable to get to a point where the returns to investing in nutrition are very high, while people just above the poorest might have the highest returns to investing in nutrition. The latter will have a higher elasticity of nutrition with regards to income.

Question 11

True or False. In the study from India by Deaton and Dreze, the researchers measure the elasticity of nutrition with regards to income by looking at changes in household calorie consumption with respect to changes in household per capita income.

Answer 11

False. The Deaton and Dreze study uses household per capita expenditure as a measure of household income in calculating the income elasticity of nutrition since expenditure is a more accurate measure of how much income households have to spend on nutrition rather than actual income.

Question 12

Professor Duflo mentions the difficulty of measuring income as one reason for looking at the elasticity of nutrition with regards to expenditure instead of with regards to income. What is another reason that she mentions?

Answer 12

a. Income varies a lot over time.
b. Households try to smooth expenditures and consumption by borrowing and saving.
c. Expenditure is more stable than income and a better measure of permanent income.

Question 13

In the graph below, what does the slope of each of the lines give us?

Answer 13

The expenditure elasticity of calorie consumption. Since both household expenditure and household calorie consumption have been transformed onto a log scale, the slope of the line gives us the percentage change in calorie consumption (on the y-axis) with respect to a percentage change in expenditure (on the x-axis.) This is simply the expenditure elasticity of calorie consumption.

Question 14

If expenditure is used as a proxy for household income, the graph below tells us that:

Answer 14

Over time, households at a given expenditure level consume fewer calories.

Households at higher expenditure consume more calories.

We see the Engel curves shift to the right over time for both urban and rural samples. Thus, over time, households at a given expenditure level consume fewer calories. However, we see that moving along a curve at a given point in time, households at higher expenditure level consume more calories.

Question 15

If we were to estimate the expenditure elasticity of calorie consumption in the graph below by comparing across households at a given moment in time, we would find the elasticity to be:

Answer 15

Positive. Each curve represents the relationship between household expenditure and household calorie consumption at a given point in time. Thus, if we were to compare just across households, the elasticity would simply be given by the slope of each line, which is positive in every case (since the lines are upward sloping.)

Question 16

If we were to estimate the expenditure elasticity of calorie consumption in the graph below by looking at what happens as households become richer over time, we would find the elasticity to be:

Answer 16

Uncertain. Over time, household become richer, so they travel up the expenditure curve, and all else equal they consume more calories. But at the same time the engel curves shift to the right, and that makes them consume less. Depending on which force dominates they may end up eating more or less.

Question 17

True or False. The cross-sectional relationship depicted in the graph below captures the causal effect of expenditure on calorie consumption.

Answer 17

False. There might be other factors the make poorer people fundamentally different from richer people; at the very least, as the graph shows, they likely consume fewer calories to begin with. Thus, the cross-sectional relationship captures not just the causal relationship of expenditure, but any number of differences between rich and poor people that might explain why the latter end up eating less.

Question 18

Say we have an outcome Y that we measure for individuals in our sample, who can fall in one of two binary conditions: treated or not treated. If ex ante, each individual i has two potential outcomes Yi(0) if not treated and Yi(1) if treated, then Yi(1) – Yi(0) is:

Answer 18

The treatment effect for individual i. The expression Yi(1) - Yi(0) simply tells us the difference in the outcome Y for individual i when treated versus when not treated. Thus, this is the treatment effect for individual i.

Question 19

True or False. Rubin causal model. We can never observe the treatment effect for a specific individual i.

Answer 19

True. Say we have an outcome Y that we measure for individuals in our sample, who can fall in one of two binary conditions: treated or not treated. Ex ante, each individual i has two potential outcomes Yi(0) if not treated and Yi(1) if treated. However, in the real world, only one of these outcomes is realized since individuals cannot be both treated and not treated; thus, we can never actually observe the treatment effect for each individual, we can only hope to infer it from estimates of the treatment effect for a group of individuals.

Question 20

Let Yi denote an outcome that we measure for individual i, with Yi(0) denoting potential outcomes if untreated and Yi(1) denoting potential outcomes if treated. Wi denote a binary treatment for individual i, which is 1 for treated and 0 for untreated/control. Then, E[Yi(0) | Wi=1] denotes:

Answer 20

The potential outcome if untreated for treated individuals. Since Wi=1, we are dealing with individuals who are actually treated here and Yi(0) indicates that we are dealing with potential outcomes if untreated.

Question 21

What is E[Yi(1) – Yi(0) | Wi=1]

Answer 21

Average treatment on the treated.

Question 22

Under random assignment, what is E[Yi(0) | Wi=1] – E[Yi(0) | Wi=0]?

Answer 22

0

The term E[Yi(0) | Wi=1] – E[Yi(0) | Wi=0] is simply the difference in the potential outcome (if untreated) of the treated and untreated populations i.e. the selection effect. Since random assignment produces treatment and control populations that are similar on average, these differences average out to 0 and thus, there is no bias/selection effect introduced from selection into the treatment or control group.

Question 23

What comparison allowed the researchers in the GiveDirectly evaluation to identify spillover effects of the cash transfer intervention?

Answer 23

Outcomes for untreated households in the treatment villages versus outcomes for households in the control villages. Any spillovers from the GiveDirectly program would have shown up for untreated households in the treatment villages since these spillovers would have come from treated households in those same villages. In order to measure the magnitude of these effects, the researchers compared the outcomes for these untreated households to the outcomes for untreated households that would not have received any spillovers i.e. households in the control villages.

Question 24

True or False. As income rises, you may start spending more on more expensive calories. Thus, the price per calorie increases at the same time as the number of calories consumed. This means that the elasticity of food expenditure is an upwards biased estimate of the income elasticity of calories consumed.

Answer 24

True. We see in the Give Directly evaluation that the income elasticity of expenditures on meat and fish is higher than the corresponding elasticity for expenditures on fruit and vegetables. The former are typically more expensive, indicating that people tend to substitute towards more expensive calories as they get richer. Thus, total expenditures on food may increase by a greater proportion than total calories consumed.

Question 25

A one-time increase in child nutrition can:

Answer 25

Shift a child’s location on the capacity curve and shift a child’s capacity curve.

Question 26

The graph below, comparing log labor earnings for children receiving a deworming treatment versus in the control group, shows a positive impact of the treatment on labor earnings.

Note: here both “treatment” and “control” groups went through the deworming program, the difference is that those in the treatment group did so earlier.

Answer 26

True. The distribution of log earnings in the graph has shifted to the right for the treatment group, indicating that average earnings increased for children in the treatment group compared to those in the control group.

Question 27

The Miguel and Kremer evaluation of the deworming program in Kenya demonstrated:

Answer 27

a. Increases in school participation in the short run
b. Increases in labor earnings in the long run
c. High benefit-cost ratio