Maize holds a special place in the lives of many Mozambicans. However, it is con

Question

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 denoted Y. 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 observed Y for both groups in tons per hectare.

The students used these measures of Y to 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.

Q. 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).

D. 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).

Explanation / Answer

A. The two samples can be combined to get the yield as:

Y = Y_Sofala + D(Y_Manica - Y_Sofala)

When D=0, we get Y=Y_Sofala and when D=1, we get Y=Y_Manica

Seelction bias = E(Y|D=0) - E(Y|D=1), i.e. the difference in means when the sample is from Sofala and Manica

B. The two main terms are the expected value of yield when the sample is from Manica and the expected value of the yield when the sa,ple is from Sofala.

C. Selection bias would exist when E(Y|D=0) is not equal to E(Y|D=1).
They may differ in absolute terms so we need to check they are statistically equal or not.
H0: E(Y|D=0) = E(Y|D=1)
H1: E(Y|D=0) not equal to E(Y|D=1)

D. We expect the drought tolerant maize variety to give better yield than the normal variety. Hence we expect the Average Treatment Effect, defined as the difference between average yield of Sofala and Manica to be negative.

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