pq2_2 - 1 X i + 2 D i + 3 X i D i + u i The variable X is a...

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Econ 410 - Fall 2006 Practice Questions for the Second Midterm - Part II 1. Consider the following model: Y i = β 0 + β 1 X i + u i Assume that all the least squares assumptions hold. You know that the error term is heteroskedastic, in particular you know that Var ( u i | X i )= ( αX i ) 2 where α is a constant. You want to change the model so that the error term is homoskedastic, so you decide to divide all variables by p Var ( u i | X i )= αX i and you obtain the following model: Y i α = β 0 α X i + β 1 α + u i α which is equivalent to: Y i = β 0 X i + β 1 + u i In this model, Y i = Y i X i ,X i = 1 X i and u i = u i X i . (a) Does the conditional mean assumption hold in this new model? (b) Is the error term u i homoskedastic? (c) What if u i was actually homoskedastic, i.e. Var ( u i | X i )= α 2 ? Would the error term u i be homoskedastic in this case? 2. Consider the following nonlinear regression model: Y i = β 0 +
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Unformatted text preview: 1 X i + 2 D i + 3 X i D i + u i The variable X is a continuous variable, while D is a binary variable. Assume that all the least squares assumptions hold. (a) What is the expected change in Y when X changes and D = 1 ? What is the expected change in Y when X is changed and D = 0 ? (b) What are the conditions under which the expected change in Y when X is changed and D = 1 equal to the expected change in Y when X is changed and D = 0? (c) Write the population regression function when D = 1 and the popu-lation regression function when D = 0 . (d) What are the conditions under which the population regression func-tion when D = 1 is equal to the population regression function when D = 0? 1...
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