A common practice in macroeconomics is to assess the validity of general equilibrium models by first deriving their implications for population moments and then comparing population moments with observed sample moments. Generally the population moments are not explicit functions of model parameters, and so computational experiments are used to establish the link between parameters and moments. In most cases the general equilibrium models are intended to describe certain population moments (for example, means) but not others (for example, variances). The comparison of population moments with observed sample moments is informal, a process that has been termed calibration by some economists and ocular econometrics by others.
This paper provides a formal probability framework within which this approach to inference can be studied. There are two principle results. First, if general equilibrium models are taken as predictive for sample moments, then the formal econometrics of model evaluation and comparison are straightforward. The fact that the models describe only a subset of moments presents no obstacles, and the formal econometrics yield as a byproduct substantial insights into the workings of models. Second, if general equilibrium models are taken to establish implications for population moments but not sample moments, then there is no link to reality because population moments are unobserved. Under this assumption, atheoretical macroeconomic models that link population and sample moments can be introduced coherently into the formal econometrics of model evaluation and comparison. The result is a framework that unifies general equilibrium models (theory without measurement) and atheoretical econometrics (measurement without theory).
The paper illustrates these using some models of the equity premium.