Question about latent variables in Co-integration Regression

Question

I have a question about cointegration regression models as follows: Is it common to have latent variables or regressors with measurement error in the cointegrating regression model? Is it highly motivated? Please provide some examples. Much appreciated!

Answer 1

No, I do not think it is common. Most of the literature on cointegration assumes measurement error away (as do most other models within and outside of time series analysis), even though some typical examples within macroeconomics would clearly qualify as having measurement error. The example given to illustrate the VECM capabilities of the vars package in R is a system of variables containing labor productivity (defined as the log-difference between GDP and employment), the logarithm of employment, the unemployment rate and real wages, defined as the logarithm of the real wage index. None of these variables are measured without error.