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C8D1 - STOCHASTIC REGRESSORS AND ASSUMPTIONS FOR MODEL B...

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1 Until now we have assumed that the explanatory variables in a regression model are nonstochastic, that is, that they do not have random components. We have done this to simplify the analysis of the properties of the regression estimators. Assumptions for Model B B.1 The model is linear in parameters and correctly specified. Y = β 1 + β 2 X 2 + … + β k X k + u B.2 The values of the regressors are drawn randomly from fixed populations B.3 There does not exist an exact linear relationship among the regressors B.4 The disturbance term has zero expectation STOCHASTIC REGRESSORS AND ASSUMPTIONS FOR MODEL B
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2 We will now progress to Model B and the case of stochastic regressors, where the values of the regressors are assumed to be drawn randomly from defined populations. This is a much more realistic framework for regressions with cross-sectional data. Assumptions for Model B B.1 The model is linear in parameters and correctly specified. Y = β 1 + β 2 X 2 + … + β k X k + u B.2 The values of the regressors are drawn randomly from fixed populations B.3 There does not exist an exact linear relationship among the regressors B.4 The disturbance term has zero expectation STOCHASTIC REGRESSORS AND ASSUMPTIONS FOR MODEL B
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3 We will begin by re-stating the regression model assumptions and we will then review the properties of the modified model. Assumptions for Model B B.1 The model is linear in parameters and correctly specified. Y = β 1 + β 2 X 2 + … + β k X k + u B.2 The values of the regressors are drawn randomly from fixed populations B.3 There does not exist an exact linear relationship among the regressors B.4 The disturbance term has zero expectation STOCHASTIC REGRESSORS AND ASSUMPTIONS FOR MODEL B
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4 Assumptions for Model B B.1 The model is linear in parameters and correctly specified. Y = β 1 + β 2 X 2 + … + β k X k + u B.2 The values of the regressors are drawn randomly from fixed populations B.3 There does not exist an exact linear relationship among the regressors B.4 The disturbance term has zero expectation STOCHASTIC REGRESSORS AND ASSUMPTIONS FOR MODEL B Assumption B.1 is the same as A.1.
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5 The values of the regressors in the observations in the sample are drawn randomly from fixed populations with finite means and finite population variances. In Model A we simply assumed that their values were fixed and given, with no further explanation.
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