While estimating a regression model you found that the explanatory variable is measured with certain error. Specify the model. What are its consequences on the parameters?

In econometrics, when an explanatory variable in a regression model is measured with error, it leads to what is known as measurement error or errors-in-variables (EIV) problem. This issue arises when the observed independent variable does not perfectly reflect the true variable, leading to biased and inconsistent parameter estimates.

Specification of the Model

Consider the standard simple linear regression model:

Yi=β0+β1Xi+uiY_i = \beta_0 + \beta_1 X_i + u_i

where:

• YiY_i is the dependent variable,
• XiX_i is the true (but unobserved) explanatory variable,
• uiu_i is the error term, and
• β0\beta_0 and β1\beta_1 are the parameters to be estimated.

However, suppose XiX_i is not observed directly. Instead, an error-ridden version of it, Xi∗X_i^*, is observed:

Xi∗=Xi+νiX_i^* = X_i + \nu_i

where νi\nu_i is the measurement error, which is assumed to be a random variable with mean zero, i.e., E(νi)=0E(\nu_i) = 0.

Thus, the actual regression model in terms of ___ ___ _______ __________ ____ _________ _________ ______.
____ __________ _____ _________ _______ ____ ___ ______.
__________ _________ __________ _______ __________ _________ __________ _______.
_____ ________ ________ ____ ________.
________ __________ _____ _____ _____ ____ ________ ___.
_________ ___ ___ __________ _______ _____ ____ ___ ______.
______ ________ ____ ______ _______ ______ _____ ____ _____ _________.
__________ _____ ___ _______ _____ _________ _____ ________ ___ ____ __________ ____.
_____ ___ ________ _______ _______ ________ ___.
___ ____ _____ _____ _________ ____ ___ _________ ______ __________ _____ _______.
________ ___ _________ _______ ___ ________ ________ _________ ____ _____ ____.
___ ___ ________ _____ _____ ____ ______.
________ _____ ______ __________ ______ __________.
______ ___ _____ __________ _____ _______ ___.
______ __________ _______ ______ ___ ____ _________ _____.
_____ ______ ________ ____ __________ ___ __________ ___ _______.
_______ _______ __________ _______ _____ ___ ______ ________ _____.
___ ____ _____ ______ _______ _______ ________ ____ _______ ____ ___ _________.
____ __________ ______ _______ ___.
_________ __________ _____ _____ ____ ____ __________.
_____ __________ __________ ____ _________ ______ ____ ________ ____ ___ ___ _________.
______ ________ ____ ___ ___ _______ __________ _________ ___ ______ __________ __________.
______ ______ ____ _________ __________ ______ _________ ____ ______ _______ _____ ____.
___ ____ ____ ___ _________.
___ _________ __________ _________ _____ _______.
_______ ________ ____ ____ ______ ______ __________ ____ _______ ____.
__________ ____ __________ ___ _______ ____ __________ _____ ____ _______.
________ _________ _____ __________ _____.
_________ ________ _______ _______ _________.
_______ ______ _________ ____ _______ ________ _______ _______ _________ _________ ___.
____ ________ __________ _______ _____.
_________ _____ _________ ____ _____ ______.
____ _____ ______ ___ _______ ________ _____ ___ _______ __________.
_____ ___ _____ ________ _______ ___ ________.
__________ ___ ________ __________ _______ ________ __________ __________.
___ ___ ______ ___ ______ ________ _____ _______ ___ __________ _________ ____.
_______ ________ _____ ___ ________ _________ ___.
____ _____ ________ _______ _______ _______ ______.
______ ___ _______ _______ _______.
________ ______ _______ ______ __________ ______ __________ ________ _______.
_________ ___ _________ _______ ____ ______.
_________ __________ __________ ________ _________ ______ ____ _____.
______ ______ _____ ________ _________ ____ __________ ___.
_______ ________ ___ ___ __________.
_______ ___ ________ _____ _______ ________ ________ ____ __________.
______ ________ __________ ______ ______ _____ _____.
__________ ____ __________ ___ _________ ___ __________ ___ _________ ________ _______ ______.
________ ________ ___ ________ _________ _________.
_____ ___ ________ ____ ___ ________ ________.
_____ ______ ___ _______ ___.
________ ___ ____ __________ _______.
______ ________ ___ ____ __________ ____ _________ ___ _____ ____ ______.
__________ __________ ________ ________ ______ ________ __________ ____ __________ ______ __________.
________ __________ ___ _________ _______.
______ _______ ____ ______ _________ ________ _____ _________ ________ ______.
Get Full Answer on WhatsApp