Estimating Economic Relationships under Measurement Error: An Application to the Productivity of US Manufacturing

We propose an approach to the problem of measurement errors that evokes long established but rarely used results about the identifiability of the error-in variables (EIV) models. Our approach uses the dynamic structure of the true series and measurement errors to identify the parameters of interest. The dynamics of the underlying time series are introduced into the model using a structural time series approach and the identification of the parameters of interest is achieved by a simple property of the multivariate normal distribution. This modeling framework has several advantages. The first is the possibility of incorporating more flexible components of the time series being studied, such as trends, cycles, and seasonality. The second is that the model allows for a non-zero correlation between the measurement errors of the variables involved in the structural relationship. The third is that using a multivariate normal distribution to derive the structural relationship between variables allows for the time-variation in the relationship, i.e., in both slope and intercept parameters. We prove two results to show our estimator can identify the structural parameters, provide a simulation exercise and an empirical illustration using data from the Bureau of Labor Statistics to compare our findings to those recently presented in Diewert and Fox (2008), where they raise the issue of severe measurement error and the endogeneity of inputs and outputs