Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![1. Consider the following regression model
y = x3 + u.
(1)
Let 3 denote the Ordinary Least Squares (OLS) estimator of B. The so-called Gauss-
Markov assumptions are:
• MLR.1: The true model in the population is given by (1).
• MLR.2: We have a random sample of n observations {(ri, Yi), i = 1, 2, .., n}
following the population model in (1).
....
• MLR.3: No one explanatory variable can be written as a linear combination of the
remaining explanatory variables that is, there is no perfectcollinearity.
• MLR.4: In the population, the error u has an expected value of zero given any values
of the explanatory variables, that is Elu|x] = 0.
• MLR.5: In the population, the error u has the same variance given any values of the
explanatory variables, that is Var[u|x] = o? , an unknown finite, positive constant.
In the following scenarios, state whether B is an unbiased and consistent estimator of 3,
and provide a brief justification for your answer in each case - but no formal mathematical
derivations are required:
(b)
MLR.2 does not. (Word limit: 100 words)
Assumptions MLR.1, MLR.3, MLR.4 and MLR.5 hold but Assumption](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0aa778ed-f124-4220-858b-6e3fee5e0b77%2Fd6a77913-6e08-42d6-a90e-3d5ef6b11a5e%2Fonb4gkn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the following regression model
y = x3 + u.
(1)
Let 3 denote the Ordinary Least Squares (OLS) estimator of B. The so-called Gauss-
Markov assumptions are:
• MLR.1: The true model in the population is given by (1).
• MLR.2: We have a random sample of n observations {(ri, Yi), i = 1, 2, .., n}
following the population model in (1).
....
• MLR.3: No one explanatory variable can be written as a linear combination of the
remaining explanatory variables that is, there is no perfectcollinearity.
• MLR.4: In the population, the error u has an expected value of zero given any values
of the explanatory variables, that is Elu|x] = 0.
• MLR.5: In the population, the error u has the same variance given any values of the
explanatory variables, that is Var[u|x] = o? , an unknown finite, positive constant.
In the following scenarios, state whether B is an unbiased and consistent estimator of 3,
and provide a brief justification for your answer in each case - but no formal mathematical
derivations are required:
(b)
MLR.2 does not. (Word limit: 100 words)
Assumptions MLR.1, MLR.3, MLR.4 and MLR.5 hold but Assumption
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