Question 2 [20 = 5+5+5+5 ] A researcher has access to so called panel data on companies. This means that he/she has information on characteristics of specific companies for a certain time period. The company is indicated by the index i and time by the index t. The researcher uses a linear model with one explanatory variable and a constant: Vit = a + Baie + (i + Eit) = a + Brie + eit i = 1,..,N; t = 1,.., T. The error term el consists of two elements: an error term that differs across companies but is constant in time and an error term exe that differs both across companies and in time. The following holds: Ecclxx) = 0, Elewit) = 0, E( max) = 0, var(it) = 0, var(n) = o7. cit is not correlated with the other errors in the model for all i and t and ni is not correlated with the other errors in the model for all i and t. a). Which of the listed assumptions relating to the error term is crucial in proving that the ordinary least squares estimator is unbiased and consistent? b). Is the error term eit homoskedastic? Show this by a calculation. c). Is there autocorrelation present in the model? Show this by a calculation d). What is the consequence of the presence of heteroskedasticity and/or autocorrelation for the quality of the ordinary least squares estimator? Question 2 [20 = 5+5+5+5 ] A researcher has access to so called panel data on companies. This means that he/she has information on characteristics of specific companies for a certain time period. The company is indicated by the index i and time by the index t. The researcher uses a linear model with one explanatory variable and a constant: Vit = a + Baie + (i + Eit) = a + Brie + eit i = 1,..,N; t = 1,.., T. The error term el consists of two elements: an error term that differs across companies but is constant in time and an error term exe that differs both across companies and in time. The following holds: Ecclxx) = 0, Elewit) = 0, E( max) = 0, var(it) = 0, var(n) = o7. cit is not correlated with the other errors in the model for all i and t and ni is not correlated with the other errors in the model for all i and t. a). Which of the listed assumptions relating to the error term is crucial in proving that the ordinary least squares estimator is unbiased and consistent? b). Is the error term eit homoskedastic? Show this by a calculation. c). Is there autocorrelation present in the model? Show this by a calculation d). What is the consequence of the presence of heteroskedasticity and/or autocorrelation for the quality of the ordinary least squares estimator