Ch 2 Solutions to Slr
Solutions, Chapter 2/HL
ANSWERS TO CHAPTER 2 The Simple Regression Model
Econometrics Economics of Innovation and Growth
A = Problems B = Examples (from chapter 2) C = Cumputer Exercises
1
Solutions, Chapter 2/HL
A: Problems
2.1 Let kids denote the number of children born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is kids = β 0 + β1educ + u where u is the unobserved error. (i) (ii) What kind of factors are contained in u? Are these likely to be correlated with level of education? Will a simple regression analysis uncover ceteris paribus effects of education on fertility? Explain.
(i) Income, age, and family background (such as number of siblings) are just a few possibilities. It seems that each of these could be correlated with years of education. (Income and education are probably positively correlated; age and education may be negatively correlated because women in more recent cohorts have, on average, more education; and number of siblings and education are probably negatively correlated.) (ii) Not if the factors we listed in part (i) are correlated with educ. Because we would like to hold these factors fixed, they are part of the error term. But if u is correlated with educ then E(u|educ) ≠ 0, and so SLR.3 fails. --------------------------------------------------------------------------------------------------------------2.2 In the simple linear regression model y=β0+β1x + u, suppose that E(u) ≠ 0. Letting α0=e(u), show that the model can always be rewritten with the same slope, but new intercept and error, where the new error has a zero expected value. Answers In the equation y = β0 + β1x + u, add and subtract α0 from the right hand side to get y = (α0 + β0) + β1x + (u − α0). Call the new error e = u − α0, so that E(e) = 0. The new intercept is α0 + β0, but the slope is still β1.
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Solutions, Chapter 2/HL 2.3 The following table contains the ATC
ANSWERS TO CHAPTER 2 The Simple Regression Model
Econometrics Economics of Innovation and Growth
A = Problems B = Examples (from chapter 2) C = Cumputer Exercises
1
Solutions, Chapter 2/HL
A: Problems
2.1 Let kids denote the number of children born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is kids = β 0 + β1educ + u where u is the unobserved error. (i) (ii) What kind of factors are contained in u? Are these likely to be correlated with level of education? Will a simple regression analysis uncover ceteris paribus effects of education on fertility? Explain.
(i) Income, age, and family background (such as number of siblings) are just a few possibilities. It seems that each of these could be correlated with years of education. (Income and education are probably positively correlated; age and education may be negatively correlated because women in more recent cohorts have, on average, more education; and number of siblings and education are probably negatively correlated.) (ii) Not if the factors we listed in part (i) are correlated with educ. Because we would like to hold these factors fixed, they are part of the error term. But if u is correlated with educ then E(u|educ) ≠ 0, and so SLR.3 fails. --------------------------------------------------------------------------------------------------------------2.2 In the simple linear regression model y=β0+β1x + u, suppose that E(u) ≠ 0. Letting α0=e(u), show that the model can always be rewritten with the same slope, but new intercept and error, where the new error has a zero expected value. Answers In the equation y = β0 + β1x + u, add and subtract α0 from the right hand side to get y = (α0 + β0) + β1x + (u − α0). Call the new error e = u − α0, so that E(e) = 0. The new intercept is α0 + β0, but the slope is still β1.
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2
Solutions, Chapter 2/HL 2.3 The following table contains the ATC