Consider a linear model with an explanatory variable that may be endogenous. We have random sample to estimate the causal relationship between the explained and explanatory variable using an nstrument that satisfies the conditions of exogeneity and relevance. a. With the information available, derive an expression for the slope parameter of the model in terms of the covari- ances of the instrumental variable with the explained and explanatory variable (70%). From this expression. provide a consistent estimator of the slope parameter of the model (30%). b. Explain how the two-stage least squares estimator of the slope is obtained (50%), and show that the estimator obtained is algebraically identical to the estimator obtained in a. (50%). c. Express the parameters of the structural form in terms of the parameters of the reduced forms of the explained and explanatory variable (50%). From the relation obtained, obtain a consistent estimator of the slope parameter of the model (10%), and show that it is identical to the estimator in b. (40%).