1. Consider the following model Y = Bo+BX+U. We suspect that X is endogenous and propose to use Z as an instrument for X. What assumptions must Z satisfy? In the next questions we focus on the following structural model Y = Bo+BiX+Y1W +...+YW +U where we assume that X is endogenous, W... We are exogenous, and Z... Zg are valid instruments for X. 2. Explain why we have overidentification. 3. Explain how 2SLS uses all of the information from the instruments to estimate the parameters in the structural model. Here you just need to explain the steps for 2SLS. 1. We know that weak instruments can lead to very poor properties for the 2SLS estimator. Explain what is meant by the term 'weak instrument. How does one test for weak instruments? The next two questions relate to the following model. Suppose a firm is interested in implementing a training program to improve the productivity of their employees. A full-scale rollout of the program will be expensive, so to test the efficacy of the program they randomly offer employees to participate in the program. 5. Suppose that T = 1 if employee i is offered to participate and T = 0 if not. Moreover, assume those with high ability think the training is futile and choose not to participate in the program if offered. If we model the effect of the program on productivity using the following model productivity=+PD+U where D; = 1 if employee i participates in the training and D; = 0 if not, then D is endogenous. Why? You may assume that those who are not offered a place cannot receive the training. 6. Explain why 7' is a valid instrument for D. That is, why does instrumental exogeneity hold and why does instru- mental relevance hold?