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    Question

    Which of the following conditions is not necessary for ordinary least squares to be the best unbiased linear estimator (BLUE)? 

    A All errors are normally distributed Correct Answer Incorrect Answer
    B All errors are independent and uncorrelated to each other Correct Answer Incorrect Answer
    C All errors have expectation zero Correct Answer Incorrect Answer
    D All errors have the same variance Correct Answer Incorrect Answer

    Solution

    The Ordinary Least Squares (OLS) method is used to estimate the parameters in a linear regression model. For the OLS estimator to be the Best Linear Unbiased Estimator (BLUE), it must satisfy the Gauss-Markov assumptions. These assumptions are: 1.      Linearity : The relationship between the independent variables and the dependent variable is linear. 2.      Random Sampling : The data is obtained through a random sample of the population. 3.      No Perfect Multicollinearity : There is no perfect multicollinearity between the independent variables. 4.      Zero Conditional Mean : The errors have an expectation of zero given any value of the independent variables. 5.      Homoscedasticity : The errors have constant variance (σ2). 6.      No Autocorrelation : The errors are uncorrelated with each other. Given these assumptions, the condition that is not necessary for OLS to be BLUE is: (a) All errors are normally distributed Normality of the errors is not required for the OLS estimator to be BLUE according to the Gauss-Markov theorem. Normality is only necessary if we want to make specific inference statements (like t-tests and F-tests) or for the errors to follow a normal distribution.  

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