A method of extracting marginal density approximations using the multivariate version of the Laplace formula is given and applied to instrumental variable estimators. Some leading exact distributions are derived for the general single equation case which lead to computable formulae and generalize all known results for marginal densities. These results are related to earlier work by Basmann (1963), Kabe (1964) and Phillips (1980b). Some general issues bearing on the current development of small sample theory and its application in empirical work are discussed in the introduction to the paper.
Phillips, Peter C.B., "Marginal Densities of Instrumental Variable Estimators in the General Single Equation Case" (1981). Cowles Foundation Discussion Papers. 845.