OLS derivation - Class Notes for EC355 Ordinary Least...

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Class Notes for EC355 Ordinary Least Squares and Method of Moments Derivation under the Gauss Markov assumptions Jean Eid Assume that the following hold MLR1 Linearity in the parameter eg. suppose we have y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + ··· + β k x k + u MLR2 Independence of the error term u and random sampling Independence of the error term means that the characteristics of individuals that we do not observe are related to each others. A situation where this could be violated is as follow: Suppose we survey children in Canadian households. Let’s say that we are interested in their educational attainment, and we collect data on grade levels completed, age, and sex. You can imagine a scenario where the more educated the child’s parents are, the higher his or her educational attainment. Suppose we have a lot of brothers and sisters in our data. Since parents’ education which is unobservable (we do not have data on) in our example have an effect on all their children we end up having a situation were some of the unobserved characteristics (i.e. the us) are correlated. We need random sampling to represent the population, otherwise we cannot draw conclusion for the whole population. MLR3 No perfect Collinearity This means that we cannot obtain the values of one independent vari- able by forming linear combinations of some other ones. as an example, suppose we have the following model. y
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OLS derivation - Class Notes for EC355 Ordinary Least...

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