Migration plays an important role in development and as a strategy for poverty reduction. Burkina Faso, whose conditions for agriculture are far from favorable, has a long history of migratory movement, and migration within West Africa has long taken place in response to drought and low agricultural productivity. In recent decades, migration to destinations outside the African continent and in particular to Western Europe has become more important for migrants from Burkina Faso. el
Migration affects the household in three ways:
1. When a household member migrates, the household loses labor.
2. Migration often results in remittances.
3. Migration implies a reduction in household size for consumption.
A critical question is what happens to the welfare of rural households when they engage in migration. When households lose labor, it may be harder for them to participate in and generate income from other activities such as agriculture. Remittances may partly compensate for these negative effects. In addition, a reduction in household size means less consumption pressure on the household.
ANA, a famous theoretical economist, is trying to estimate the causal impact of migration on household income Ana took a random sample of 1,000 households where a household member has migrated and another random sample of 1,000 households where no household member has migrated. 4 In Ana's final report she estimates the naive Average Treatment Effect (ATE) on the Treated of the program by subtracting the average income of the 1,000 households where no one migrated from the average income of the 1,000 households where someone migrated.1 4'
For the rest of this question, use the following information:
The average income of the 1,000 households where no one migrated is 30,000 CFA
The average potential income of the 1,000 households where no one migrated had they migrated is 35,000 CFA
The average income of the 1,000 households where someone migrated is 42,000 CFA
The average potential income of the 1,000 households where someone migrated had not they migrated is 33,000 CFA .
1. . What are the two averages that Ana can observe in her data?«
2. What are the two averages that Ana would like to have to estimate the true Average Treatment Effect on the Treated?
3. What are the two averages that Ana would like to have to check if there is selection bias?
Now, let Y denote income and D denote migration status (i.e. 1 if individual migrated and 0 otherwise). And, remember that: ATETRUE +Selection Bias+
4. What are the equivalents of E Yii 1] and E [YoilD 1] in words, respectively?
For expositional purposes, in the reminder of this document we will refer to the average treatment effect (ATE) on the treated as ATE.
5. What is Ana's estimate of the naive Average Treatment Effect on the Treated3(provide a number)
6. What is the true causal impact of migrating on the income of households where someone migrated? (providea number)
7 How large is the selection bias? (provide a number)
8 Are the 1,000 households where no one migrated a good counterfactual for the 1,000 households where someone migrated? Why?