Problem Set #4: RISK TAKING, INSURANCE MARKETS and IMPACT EVALUATION Cristina, Oscar and Javier are maize farmers in the village of Girasol. They each have zero wealth (W=0), so their consumption is...

Problem Set #4: RISK TAKING, INSURANCE MARKETS and IMPACT

EVALUATION

Cristina, Oscar

and Javier are maize farmers in the village of Girasol. They each have zero wealth (W=0), so their

consumption is equal to the income they earn from their economic activity. Each of them must choose one (and only one)

of the following three activities:

·

Activity

1: Full time farming with hybrid maize: Hybrid maize has two important characteristics. First, it is labor intensive. To get the full benefit of hybrid maize, a farmer

should work full time (7 days per week) on their farm. Second, hybrid maize is risky, because it is

vulnerable to a combination of weather and pests. If a farmer works full time, she has a 50%

probability of having a GOOD harvest and earning income of $280 and a 50% chance

of having a BAD harvest and earning only $40.

·

Activity

2: Full time farming with traditional maize. Traditional maize varieties are also labor

intensive, however traditional maize is very well adapted to local weather

conditions and thus has no risk. If a

farmer works full time she will earns $140 with certainty.

·

Activity

3: Part-time farming with hybrid maize: In this third

activity, the farmer plants hybrid maize and works Monday through Thursday on

her farm managing the hybrid maize, and she works Friday through Sunday as a

construction worker in a nearby city.

Since she is not able to work full-time on the farm, it is more likely

that she suffers damages from pests or bad weather. Specifically, the probability of having a

GOOD maize harvest and earning $280 drops to 25%, while the probability of

having a BAD harvest and earning only $40 increases to 75%. The individualalso earns $40 with certainty as a construction worker (i.e., she

earns $40 in addition to her farm income under both a GOOD and a BAD harvest).

1.

What

is the expected value of consumption for each activity (3 points)?

Activity 1:

Activity 2:

Activity 3:

2.

Cristina,

Oscar and Javier view risk differently.

This is reflected in the differences in their utility functions, which

are listed below. Using those utility

functions, compute the certainty equivalent (CE), the risk premium (RP) and

expected utility (EU) associated with each of the three activities for each

individual. Report your answers in Table

1 below (9 points).

·

Cristina: .0/msohtmlclip1/01/clip_image002.png”>

·

Oscar: .0/msohtmlclip1/01/clip_image004.png”>

·

Javier: .0/msohtmlclip1/01/clip_image006.png”>

Table 1.

Certainty Equivalent, Risk Premium and Expected Utility for 3 Activities

Activity 1

Activity 2

Activity 3

EU Cristina

CE Cristina

RP Cristina

EU Oscar

CE Oscar

RP Oscar

EU Javier

CE Javier

RP Javier

3.

Which

activity will be chosen by each individual (3 points)?

Cristina chooses:

Oscar chooses:

Javier chooses:

4.

Which

type of risk preferences describe each individual (3 points)? (Risk Neutral,

Risk Averse, or Risk Loving?)

Cristina is:

Oscar is:

Javier is:

5.

Assume

that the three farmers start with the same level of wealth. In this environment would you expect wealth inequality

to remain the same, increase or decrease over time? Explain your answer (2 points).

The government is

interested in supporting higher adoption rates of hybrid maize and asks Yaxi,

the CEO of “Take a Chen-ce on Me” Insurance Company to offer crop insurance to

hybrid maize farmers. Yaxi conducts a market analysis and decides to offer

conventional crop insurance contracts tofull time hybrid maize farmers (Activity 1). She is not interested in offering insurance

to part-time hybrid maize farmers. The

contracts are straightforward. At the

beginning of the season, farmers pay a premium of $120. At the end of the season, Yaxi pays farmers

an indemnity payment of $240 if the farmer had a BAD harvest. If the farmer had a GOOD harvest, Yaxi doesn’t

pay the farmer anything. For questions 6-10,

assume that Yaxi has perfect information about the farmer’s activity

choice. In other words, if a farmer buys

her insurance, Yaxi is able to enforce a contract that requires the farmer to

choose full-time hybrid maize farming.

6.

What

is the expected value of Yaxi’s profit from an insurance contract? (Yaxi’s profit is just the premium she

collects from the farmer minus the indemnity payment she makes to the farmer) (2

points).

7.

What

is the expected value of consumption for an individual who chooses full-time hybrid

maize farming (Activity 1) with Yaxi’s insurance contract (3 points)?

8.

What

is the expected utility associated with full-time hybrid maize farming with an

insurance contract for each individual (3 points)?

9.

Now

assume that each individual can choose between the four available activities:

Activity 1 with Insurance, Activity 1 without Insurance, Activity 2, and

Activity 3. Which activity will each individual choose (3 points)?

·

Cristina

·

Oscar

·

Javier

10. In this environment of perfect information

based insurance, would you expect wealth inequality to remain the same,

increase or decrease over time? Explain

your answer. Compare your answer here

to your answer to question 5 (3 points).

Now let’s make a

more realistic assumption about information.

Assume that Yaxican observe whether a farmer plants

hybrid maize, but shecannot observe how much time the

farmer spends working on her fields. This means that a farmer who plants hybrid

maize may purchase the insurance contract and then choose to either farm full

time or farm part time. An individual

who plants traditional maize cannot purchase an insurance contract.

11. Which activity will be chosen by each

individual now (3 points)? (Activity 1 with Insurance, Activity 1 without

Insurance, Activity 2, Activity 3 with Insurance, or Activity 3 without

Insurance)

12. What is Yaxi expected profit? Will she be willing to offer the insurance

contract (3 points)? Why or why not? (what type of problem does Yaxi face)?

../downloads/mozambique-map-black-and-white.gif” src=”file:///C:/Users/Pals/AppData/Local/Temp/OICE_84C66147-A4B8-4C2A-B5AD-15ED6EA715FD.0/msohtmlclip1/01/clip_image008.jpg”>

Maize holds a special place in the lives of

many Mozambicans. However, it is concerning how low agricultural yields are for

maize producers in the drought-prone Manica province where a lot of farmers

practice subsistence farming. To address this problem, a project to increase

agricultural production and raise farm productivity was designed by a group of

UC Davis students. The project consisted of providing a new variety of a

drought tolerant maize seed to a random sample of farmers located in Manica,

which was specifically targeted because it is drought prone.

To evaluate the impact of this program, the

students want to estimate the causal impact of the drought tolerant maize

variety on agricultural yields denotedY.

First, they drew a random sample of 1,000 households that received the drought

tolerant maize seed in Manica to serve as the treated group (D=1). At the same time, they drew another

random sample of 1,000 households in the neighboring Sofala province who were

not part of the program to serve as the control group (D=0). Via surveys, the students observedYfor both groups in tons per hectare.

The students used these measures ofYto estimate the Average Treatment

Effect of the program by subtracting the average yield of the 1,000 households in

Sofala from the average yield of the 1,000 households in Manica.

13. At this point, the students reach out to

you to ask for your guidance. Help the team understand Selection Bias by:

a. Providing an equation that defines

Selection Bias using notation from the Potential Outcome Framework that we

developed in class (4 points).

b. Writing a sentence that defines the two

main terms in your equation (4 points).

c. Giving a careful and clear, but brief

explanation of when selection bias would exist (i.e., when it would not be

equal to zero) (4 points).

14. Without any further information, do you

expect selection bias in the students’ estimate of the Average Treatment Effect

to be zero, negative or positive?

Explain your answer (4 points).

For the rest of

this question, use the table below. These average yields measured in tons of

maize per hectare presume that you know all the counterfactual values of this

outcome variable (e.g., you know.0/msohtmlclip1/01/clip_image010.png”>,

which is what the average yield for drought tolerant maizewould have been for those who did not adopt drought tolerant maize)

Table 1

.0/msohtmlclip1/01/clip_image012.png”>

.0/msohtmlclip1/01/clip_image014.png”>

.0/msohtmlclip1/01/clip_image016.png”>

5.2

1.4

.0/msohtmlclip1/01/clip_image018.png”>

5.5

2.5

15. Which of the numbers in the table above can

be measured by the researchers based on their survey data (2 points)?

16. Based on this table, what is the students’ estimate

of the Average Treatment Effect (4 points)?

17. How large is the selection bias (provide a

number) (4 points)?

What is the true

causal impact of the program onY?

(i.e., what is the true Average Treatment Effect?) (4