Question

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. 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 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

Answer 1

5. The causal effect can be obtained by OLS estimators as the change in the log og wages is nothing but the return on the wages and can be obtained by the linear regression equation as given. So, the parameter $\beta_1$ gives us the value we seek.

6. The assumptions here would be that we need a large dataset. So we need many responses based on wage and education so that the results we obtain are conclusive enough. Also, we need people with the same work experience, location and position when they are working because the wage is a factor of the location, position of the person and work experience too.

7. The validity for a large dataset is by rule of thumb to be more than 30. However, the larger the dataset the better the results.

To check for similarity in other parameters, we must choose people working in the same region and having the same work experience to compare across the dataset.

8. A weak instrument is one which does not have a strong correlation with the independent variable.

So to identify a weak instrument we must be sure theoretically that one influences the other and the correlation of the two must be weak.

For weak instruments, we can check by the Cragg Donald statistic and the Anderson and Rubin test