Making Good Inferences from Bad Data

Errors in variables can seriously distort inference when they are not taken into account explicitly. Coefficient values, their significance, and whether some explanatory variables should instead be used as instruments are largely a matter of interpretation unless further information is available. Higher moments of the observable variables impose restrictions that allow testing for identification and specification and estimating the parameters of the standard errors-in-variables model. The argument is developed partly through examples illustrating the points. Errors in variables can seriously distort inference when they are not taken into account explicitly. Coefficient values, their significance, and whether some explanatory variables should instead be used as instruments are largely a matter of interpretation unless further information is available. Higher moments of the observable variables impose restrictions that allow testing for identification and specification and estimating the parameters of the standard errors-in-variables model. The argument is developed partly through examples illustrating the points.