last assignment econ2206 S1 2014
In the given function, respond is a binary function, which is dependant on the other explanatory variable which aligns with the requirement of the linear probability model (LPM). This is an extention to the zero conditional mean condition which assumes that E(ul(resplast),(avggift),(propresp),(mailsyear))=0 and hence allow for E(ylx) to omit the error term producing P(respond = 1lx)= β(0)+ β(1) resplast+ β(2)avggift+ β(3)propresp+ β(4)mailyear. This allows the interpretation of β(1) to be the degree at which the change of resplast have on the change in the probability for respond=1 under ceteris Paribas.
Let the measurement error term of the dependant variable be defined as e(0)=y(true)-y(observe). Under the assumption that MLR 1-4 holds for the original model, we can substitute in to the regression model to produce equation respond(true)= β(0)+ β(1)resplast+ β(2)avggift+ β(3)propresp+ β(4)mailyear+u+e(0). Given that there are no correlation with the explanatory variables, OLS estimators βs will remain constant and unbiased. This is an extension of MLR 3(zero conditional mean) which suggests that the error term u has no correlation to the βs and hence can infer that likewise ‘e’ has zero conditional mean making the OLS estimators consistent and unbiased. If we consider that e(0) does not satisfy zero conditional mean then only β0 will be biased.
In this case we will define the additive error as e(4)=mailsyear(observed)-mailsyear(true). Considering that MLR1-4 holds in the model, we can include the error term into the regression model producing the function, respond = β(0)+ β(1)resplast+ β(2)avggift+ β(3)propresp+ β(4)mailyear+u- β(4)e(4). It is given that Cov(mailsyear(true),e(1))=0, so under the classical errors-in-variables (CEV), it suggests correlation between the error term e(1) and observed mailsyear will be Cov(mailsyear,e(1)) = E(mailsyear,e(4)) = E(mailsyear(true),e(4))+ E(e(4)^2) = 0+σ²(e(4))= σ²(e(4)). We then consider the covariance of (mailsyear,
Let the measurement error term of the dependant variable be defined as e(0)=y(true)-y(observe). Under the assumption that MLR 1-4 holds for the original model, we can substitute in to the regression model to produce equation respond(true)= β(0)+ β(1)resplast+ β(2)avggift+ β(3)propresp+ β(4)mailyear+u+e(0). Given that there are no correlation with the explanatory variables, OLS estimators βs will remain constant and unbiased. This is an extension of MLR 3(zero conditional mean) which suggests that the error term u has no correlation to the βs and hence can infer that likewise ‘e’ has zero conditional mean making the OLS estimators consistent and unbiased. If we consider that e(0) does not satisfy zero conditional mean then only β0 will be biased.
In this case we will define the additive error as e(4)=mailsyear(observed)-mailsyear(true). Considering that MLR1-4 holds in the model, we can include the error term into the regression model producing the function, respond = β(0)+ β(1)resplast+ β(2)avggift+ β(3)propresp+ β(4)mailyear+u- β(4)e(4). It is given that Cov(mailsyear(true),e(1))=0, so under the classical errors-in-variables (CEV), it suggests correlation between the error term e(1) and observed mailsyear will be Cov(mailsyear,e(1)) = E(mailsyear,e(4)) = E(mailsyear(true),e(4))+ E(e(4)^2) = 0+σ²(e(4))= σ²(e(4)). We then consider the covariance of (mailsyear,