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# Empirical Tests of Equilibrium Models

In the two previous chapters we stressed the fact that the construction of a theory necessitates a simplification of the phenomena under study. To understand and model any process, elements in the real world are simplified or assumed away. While a model based on simple assumptions can always be called into question because of these assumptions, the relevant test of how much damage has been done by the simplification is to examine the relationship between the predictions of the model and observed real-world phenomena. In our case, the relevant test is how well the simple capital asset pricing model (CAPM), or perhaps some other general equilibrium model, describes the behavior of actual capital markets.

The principle is easily stated and intuitively appealing. However, it opens up a new series of problems. Namely, how does one design meaningful empirical tests of a theory? In particular, how can one test the CAPM or any of its numerous variants? In this chapter we review several of the tests of the general equilibrium models that have been presented in the literature. In doing so, we discuss many of the problems encountered in designing these tests. Finally, we discuss fundamental work by Roll (1977) that suggests certain problems with all of the tests of general equilibrium models and opens up the area to further questions.

## THE MODELS—EX ANTE EXPECTATIONS AND EX POST TESTS

Most tests of general equilibrium models deal with either the standard ...