Instrumental Models and Indirect Encompassing

Methods of indirect, simulation-based inference for nested and nonnested hypotheses are developed. The methods make use of instrumental models and are applicable in cases where likelihood-based inference is numerically unfeasible. The asymptotic normality of an indirect Wald vector is shown and the implicit null hypotheses of the proposed tests are characterized as generalizations of the standard encompassing hypothesis. Some of the tests generalize well-known instrumental variable methods and Hausman-Wu specification tests.