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 + ____ _________ __________ _____ ___ ______ ___ ____ _________ _______ ______ _____.
________ ____ __________ __________ _______ ________ ____ __________ ___ ____ _____ ____.
__________ ______ _____ ______ ______ ________ ________ ____.
___ _______ ________ ______ ___ __________.
____ ________ _______ ________ ___.
____ _____ ____ __________ ________ ______ _________ ____ ____ ___ ___.
____ ___ ____ ____ ________ _________ ____ _________ ____ __________ _________.
_______ _________ ___ ____ ___ ______ ___ ______ _______ _________ ____ ____.
___ _____ __________ ________ ____ _________.
________ _______ ________ __________ ________.
_____ ________ _________ ____ _______ _______ ___ ______ _________ __________ ____.
__________ ______ ________ _______ ______ ______ _________.
____ ________ ___ ____ _________ ____ ____ _______.
_____ ____ ____ _______ ________ _____ _______ ________.
________ _________ _____ _____ ___.
_______ ____ _____ ________ _______ ____.
______ __________ ___ ___ _________.
________ ________ ___ __________ _______ ______ __________ __________.
___ _____ ________ ____ ____ ___ _________ _____ ___ ______.
___ __________ _________ ________ _________ _________ ____ ________ __________ ________.
__________ ______ ____ _______ _________ ________ ____ ____ _______ ___ ____ _____.
___ ________ _______ _________ ___ _______ _________ _________ _____ _______.
_________ _________ ________ ____ _____ ____ _________ _______ _________ _____ __________ ________.
____ _________ _______ _______ _________ ____.
__________ _____ ____ __________ ___ _______.
________ ________ ____ ________ ______ _______ ________.
________ __________ ___ ____ ____ _______ ____ ___ ____ __________ _______ ____.
_______ _____ _____ _________ _____ ____ __________ ________.
_____ ___ _____ __________ ___ ___ ________ ______ _________.
_______ _______ ______ ________ ____.
____ ____ __________ _________ ______ ______ ____ _____ ____ _________.
___ _________ __________ ___ ___ _________ ___ _________ _____ _______ __________.
______ _______ _________ __________ ________.
_______ _______ _____ _____ _____ __________ ___ ______ _____ _________ __________.
_________ ___ _______ _________ ____ ______ ___ ________ ______ _____ _______.
_______ _____ ________ ____ ____.
_________ ________ __________ _______ ________ _____ ___.
_____ _______ ______ _________ _______ __________ _____ _____ _____ __________.
________ _______ __________ _____ ____ ______.
____ ______ ____ ______ _______ ______ ___ ____ ___ _____ _________.
_______ _______ ________ ____ ____ _________ _____.
______ ______ ______ _______ __________ __________.
_____ ____ ______ ______ _______ _______ _________ _____ _________ _________ ________.
_______ _________ ____ __________ _________ _________ ___.
_______ __________ ____ ________ ____ ______ _________ ___ ___ _________.
_______ _____ ________ ____ __________ ____ _______ __________.
____ ______ ___ __________ _______ _______ _________ _____ ______ ____ _______.
__________ _________ __________ __________ _______ ____ ___.
______ ______ ___ ________ _______ ____.
__________ ____ _____ ____ _______ ______ _________ ____ ________ __________ __________ __________.
____ _______ __________ ___ __________ ________ ________ ________ ____ _________ ______ ________.
_________ ____ __________ ______ ___ _____ ______ ___ ______ __________ _______.
___ ___ ___ __________ _________.
_____ ________ __________ __________ __________ _________ _________ ______ _________.
______ ______ _________ ______ ______ __________ _____ _____ __________ _______ _______.
______ ____ __________ _____.
Get Full Answer on WhatsApp