Evaluating Real Business Cycle Models: the Data Transformation Problem

There are many methods used for evaluating and comparing models found in the Real Business Cycle (RBC) literature. One major problem faced is how to transform the data into a form acceptable to the model being evaluated, the most commonly used being a filter such as Hodrick-Prescott. Models are evaluated by comparing the filtered data that are observed with filtered data that are simulated. A number of authors have criticised the use of the Hodrick-Prescott filter for distorting the data, leading to other suggestions. This paper formally compares and evaluates competing methods for transforming the observed data using a likelihood-based approach. The paper also describes a method for transforming the data directly to a form that is similar to that predicted by a model. Thus a direct evaluation of a model with the data can be obtained. Since the method of comparison is likelihood based, the competing methods are compared across the full dimension of the observed data. However, a problem with likelihood-based methods for evaluating RBC models is that the likelihood of a RBC model's generating the observed data is practically zero. The observed data have a strong trend while the model may generate data that are stationary around a steady-state value. The problem is to transform the data so the likelihood of a RBC model generating the transformed data is non-zero and the transformed data maintain the essential characteristics of the observed data. Markov chain Monte Carlo methods are used to transform the observed data into a form that is "recognisable" to a RBC model but still maintains the essential characteristics of the observed data. For example, suppose one believes that the essential characteristics of the observed data are captured in the output of the Hodrick-Prescott filter. The method developed in this paper shows how one can transform the observed data so that it is recognisable by a RBC model and has the same characteristics as the raw data. That is, the output of the Hodrick-Prescott filter of the transformed and raw data are the same, but the transformed data are now in a form that is "recognisable" to the model. This allows the use of likelihood-based methods for evaluating the model. This paper examines various methods of defining the essential characteristics of the raw data. It shows how a likelihood-based method can be used to evaluate the performance of the RBC model relative to "matching" these essential characteristics. The paper also shows how parameter uncertainty can be incorporated into the problem of model evaluation through the use of prior information. It is shown that calibrating a model with some uncertainty can affect the evaluation significantly.