Question 2 A large-landholding farmer outsmarts others by running an experiment to measure the effect of fertilizer application on agricultural yields. She randomly assigns her 400 land plots into two groups. In the first group, she inputs 20 kg/mu of fertilizers, while the other group receives 40 kg/mu of fertilizers. She also keeps other agricultural inputs (water, pesticides, labors) equally between these two groups. Let Yi denote the yields for ith plot, let Xi denote the amount of fertilizer application per unit of land, (Xi=20 or 40), and consider the regression model Yi=β0+β1Xi+μi 1. Explain what the term ui represents. Proposal a potential reason that why different plots might have different values of ui ? (2 point) 2. Is E[ui∣Xi]=0 in this case? Explain why or why not? (1 point) 3. The estimated regression is Yi=300+0.7Xi+μi. (a) Is β1=0.7 an unbiased estimator? (1 point) 5 (b) After you got this estimation, the farmer's assistant tells you that he is concerned that the program may not actually have randomly allocated fertilizer quantity across the 400 plots, and that some cheating may have gone on (he heard that the richest land (land with highest soil quality) were more likely to be put into the more fertilizer group). What concern would this give rise to in your estimation? (1 point) (c) What additional variable (data) would you like to collect to verify whether the assistant's concern is true, and what regression specification would you use these data for to investigate whether his concern is true? (3 points)