Some Consequences of Using "Measurement Error Shocks" When Estimating Time Series Models

In a number of time times models there are I(1) variables that appear in data sets in
differenced from. This note shows that an emerging practice of assuming that observed
data relates to model variables through the use of "measurement error shocks" when
estimating these models can imply that there is a lack of co-integration between model
and data variables, and also between data variables themselves. An analysis is provided
of what the nature of the measurement error would need to be if it was desired to
reproduce the same co-integration information as seen in the data. Sometimes this
adjustment can be complex. It is very unlikely that measurement error can be described
properly with the white noise shocks that are commonly used for measurement error.