Two Models of Measurements and the Investment Accelerator

This paper describes two models of an agency that is collecting and reporting observations on a dynamical linear stochastic economy. The first is a "classical" model, with the agency reporting data that are the sum of a vector of "true" variables and a vector of measurement errors that are orthogonal to the true variables. The second is a model of an agency that uses an optimal filtering method to construct least-squares estimates of the true variables. These two models of the reporting agency imply different likelihood functions. A model of the investment accelerator is used as an example to illustrate the differing implications of the models.