Question

Question l 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: A 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. 2. What are the two averages that Ana can observe in her data?« 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)e How large is the selection bias? (provide a number)e Are the 1,000 households where no one migrated a good counterfactual for the 1,000 households where someone migrated? Why?4 7. 8.

Answer 1

1. The two averages Ana can observe in her data are-

i) the average income of the 1000 households where no one migrated

ii)the average income of the 1000 households where someone migrated

2. Ana would like to have the average income of the 1000 households where someone migrated and the average potential income of the 1000 households where someone migrated had they not migrated.

3. To check the selection bias, Ana requires the average potential income of the 1000 households where someone migrated had they not migrated and the true average income of the 1000 households where no one migrated.

4. $\small E\left [ Y1i\mid \ Di=1]$ = The average income of household i given that someone from that household has migrated

$\small E\left [ Y0i\mid \ Di=1]$ = The average potential income of household i had someone not migrated from that household given that someone from that household has actually migrated.

5. Naive ATE= 42,000 CFA- 30,000 CFA= 12,000 CFA

This doesn't take into account the selection bias and simply subtracts the average incomes of those who didn't migrate from the average incomes of those who did migrate.

6. The true causal impact is $\small E\left [ Y1i\mid \ Di=1]$ minus $\small E\left [ Y0i\mid \ Di=1]$

which implies the ATE is 42,000 CFA-33,000CFA = 9,000 CFA

7. Selection Bias is $\small E\left [ Y0i\mid \ Di=1]$ minus $\small E\left [ Y0i\mid \ Di=0]$

33,000 CFA-30,000 CFA=3,000 CFA

8. No, because this ignores the selection bias. It cannot be said that the average difference in incomes between these two household groups is solely due to migration. A number of other external factors could be at play therefore, it is not a valid counterfactual.