Structural Regression Model with Measurement Errors under Exchangeability Conditions

A structural regression model with measurement errors is proposed to study the impact of measurement errors on estimating the average treatment effect under exchangeability conditions. Without other additional conditions, the average treatment effect is still identified even though most of the population parameters could not be identified. If the distribution of the covariate measurement errors in the exposed group is the same as that under control, it will only have some influence on the preciseness of estimating the average treatment effect.