Problem 1: Consider the following econometric model for primary schools: yavgscore=0+1xexpend+2xpovrate+u, where the average score of a standardized performance test ( yavgscore) is explained by the expenditures in education per student (xexpend) and the poverty rate (xpovrate) of the children in the school. However, in the recorded data set of the single school districts, only observations for the score of students who passed the test and the expenditures per student are available. The poverty rate is not observed individually. Thus, one could only estimate 1 as ~1 in the reduced model: yavgscore=~0+~1xexpend+v (a) Which sign do you expect for the unknown parameter 2 in the original regression model (1)? (b) What is your guess about the correlation of xexpend and xpovrate ? (c) Calculate the possible bias of ~1 and discuss your findings. (d) Repeat the short simulation study from Problem 1(b) of Exercise 2 for the given task. Note that model (1) is now assumed to be the true model in the population, but model (2) is estimated for which the zero conditional mean assumption is violated.1 Problem 1: Consider the following econometric model for primary schools: yavgscore=0+1xexpend+2xpovrate+u, where the average score of a standardized performance test ( yavgscore) is explained by the expenditures in education per student (xexpend) and the poverty rate (xpovrate) of the children in the school. However, in the recorded data set of the single school districts, only observations for the score of students who passed the test and the expenditures per student are available. The poverty rate is not observed individually. Thus, one could only estimate 1 as ~1 in the reduced model: yavgscore=~0+~1xexpend+v (a) Which sign do you expect for the unknown parameter 2 in the original regression model (1)? (b) What is your guess about the correlation of xexpend and xpovrate ? (c) Calculate the possible bias of ~1 and discuss your findings. (d) Repeat the short simulation study from Problem 1(b) of Exercise 2 for the given task. Note that model (1) is now assumed to be the true model in the population, but model (2) is estimated for which the zero conditional mean assumption is violated.1