Measurement Models for Time Series Analysis: Estimating Dynamic Linear Errors-in-Variables Models

Abstract

This article uses state space modeling and Kalman filtering to estimate a dynamic linear errors-in-variables model with random measurement error in both the dependent and independent variables. I begin with a general description of the dynamic errors-in-variables model, translate it into state space form, and show how it can be estimated via the Kalman filter. I report the results of a simulation in which the amount of random measurement error is varied, to demonstrate the importance of estimating measurement error models and the superiority that Kalman filtering has over regression. I use the model in a substantive example to examine the effects of public opinion regarding nuclear power on the enforcement decisions of the Nuclear Regulatory Commission. I then estimate a dynamic linear errors-in-variables model using multiple indicators for the latent variables and compare simulations of this model to the single indicator model. Finally, I provide substantive examples which examine the effect of people's economic expectations on their approval of the president and their approval of government more generally.