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overview - ECON2206/ECON3290 Week 12 Overview Dr Rachida...

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ECON2206/ECON3290: Week 12 Overview Dr. Rachida Ouysse School of Economics UNSW ECON2206/ECON3290
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Overview of this course material We discussed estimation issues under a set of model assumptions. The benchmark model: linear regression under Gauss Markov assumptions: The population model for the conditional mean of y i given x i : E ( y i | x i ) = m ( x i ) is assumed to be linear in x i : y i = x 0 i β + i (1) = β 0 + β 1 x i 1 + β 2 x i 2 + · · · + β k x ik + i (2)
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Overview of this course material Assumption 1 : Linearity in β : if not correct we have model misspecification. Can still have nonlinearity with respect to x i . Possible to test for misspecification: RESET test. (See W. Ch. 9): First estimate y = β 0 + β 1 x 1 + β 2 x 2 + · · · + β k x k + μ, (3) get b y and then test in the augmented model y = β 0 + β 1 x 1 + β 2 x 2 + · · · + β k x k + δ 1 b y 2 + δ 2 b y 3 + μ, (4) the null hypothesis H 0 : δ 1 = δ 2 = 0 Under the null RESET is distributed as an F 2 , n - k - 3 .
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Overview of this course material Assumption 2: Random Sampling We have a random sample of n observations, { ( x i 1 , x i 2 , · · · , x ik , y i ) : i = 1 , 2 , · · · , n } , following the population model in equation (2). Nonrandom sampling causes OLS estimator to be biased and inconsistent.
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When does the non random sampling fail? Sampling from a truncated population induces systematic bias due to non random sampling. Censoring systematically assigns a fixed value to a nontrivial proportion of the population: therefore nonrandom! Selection bias: when dealing with choice variables. Example years ability and years of schoolins. More able people may systematically choose higher level of education. Studies of return to education that uses a wage equation are affected with such bias.
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