Question Two [25 marks] A. Suppose the relationship between consumption expenditures and household income of a...

 

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Question Two [25 marks] A. Suppose the relationship between consumption expenditures and household income of a representative sample of households in Ghana is specified as, Y=B₁ + B₂X₁ + ₁, where i refers to household i, and i=1,2,..., n It is believed that while low income households have similar and less flexible consumption habits, high income households have rather flexible and varied consumption habits. The consumption pattern so described corresponds to a situation where at least one of the fundamental assumptions to the Classical Linear Regression Model is violated, Identify that or those of the fundamental hypotheses that are systematically violated. Indicate the consequences of the violation of those fundamental hypotheses on the ordinary least squares estimation of the specified model. (iii). Suggest an alternative estimation approach which corrects for the identified violation. B. We have production data for 22 firms, from which the following summary statistics are derived, 72 y=20, (-)² = 100,= 10, (x₁ - x)² = 60, (x-x)(y-7) = 30 where y = In output and x = labour hours input (1) Compute the least squares estimates of a and ß in the model, y=a+Bx+e (ii) Estimate the output elasticity of labour (iii) Test the hypothesis that B = 1. (iv) Form a 95% confidence interval for o², the variance of E. Note: x² = 9.5908 0.025,20 = 34.1696 and x² i=1 0.975,20 Page 3 of 3 Question Two [25 marks] A. Suppose the relationship between consumption expenditures and household income of a representative sample of households in Ghana is specified as, Y=B₁ + B₂X₁ + ₁, where i refers to household i, and i=1,2,..., n It is believed that while low income households have similar and less flexible consumption habits, high income households have rather flexible and varied consumption habits. The consumption pattern so described corresponds to a situation where at least one of the fundamental assumptions to the Classical Linear Regression Model is violated, Identify that or those of the fundamental hypotheses that are systematically violated. Indicate the consequences of the violation of those fundamental hypotheses on the ordinary least squares estimation of the specified model. (iii). Suggest an alternative estimation approach which corrects for the identified violation. B. We have production data for 22 firms, from which the following summary statistics are derived, 72 y=20, (-)² = 100,= 10, (x₁ - x)² = 60, (x-x)(y-7) = 30 where y = In output and x = labour hours input (1) Compute the least squares estimates of a and ß in the model, y=a+Bx+e (ii) Estimate the output elasticity of labour (iii) Test the hypothesis that B = 1. (iv) Form a 95% confidence interval for o², the variance of E. Note: x² = 9.5908 0.025,20 = 34.1696 and x² i=1 0.975,20 Page 3 of 3

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