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- holds whenever there is an intercept, it means the error term is zero, on average.
- No perfect multicollinearity and all Xs must exhibit some variation (MLR)
- *No perfect linear relationship between the Xs
- *The higher the variation in independent variables, the lower the variance of estimators. To increase variation, increase the sample size.
- Conditional independence assumption
- If this holds, there is no selection effect. (observed effect = causal effect)
- Zero serial correlation in the errors
- homoskedasticity, or constant conditional variance of the residual term
- errors are normally distributed with a mean zero and constant variance.
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Suppose one is interested in measuring the impact of participation in preschool between ages 0 and 3 (Pi a dummy variable which takes value 1 if an individual ever participated in preschool between the ages of O and 3, and which takes value O otherwise) on mathematics test scores measured at age 12 (Mi). Therefore, one could think of running the following regression:
- In a given dataset where we observe M and P for a cross section of individuals, should we expect P and u to be uncorrelated? Explain your answer. Should we expect the OLS estimate of β to be unbiased? Explain. [6 points]
- What is the expression of the estimator for βif you use the procedure you described in part 2 of this question. Is it unbiased? If yes, show why. If not, show the expression for the [6 points]
- Suppose now that compliance with the lottery was perfect, which means that every child offered a place accepted it, and none of the children rejected in the public sector ever enrolled in preschool. Would you be able to get an unbiased estimate of β estimating the model in part 1 of this question? Why, or why not? [5 points]
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