In simple linear regression, where there is only one regressor ( with a constant ), the OLS coefficient estimates have a simple form that is closely related to the correlation coefficient between the covariate and the response.
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Park, on noting a standard recommendation of assuming proportionality between error term variance and the square of the regressor, suggested instead that analysts'assume a structure for the variance of the error term'and suggested one such structure:
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In other words : if both the vector-of-ones ( constant term ) regressor and an exhaustive set of dummies are present, perfect multicollinearity occurs, and the system of equations formed by the regression does not have a unique solution.
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Imbens and Angrist ( 1994 ) demonstrate that the linear IV estimate can be interpreted under weak conditions as a weighted average of local average treatment effects, where the weights depend on the elasticity of the endogenous regressor to changes in the instrumental variables.
25.
Where \ theta is the model's parameter and w are those regressors which are assumed to be error-free ( for example when linear regression contains an intercept, the regressor which corresponds to the constant certainly has no " measurement errors " ).
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