Simulation Based Inference in Simultaneous Equations

Lynda Khalaf

No 1078, Econometric Society World Congress 2000 Contributed Papers from Econometric Society

Abstract: In the context of multivariate regression (MLR) and simultaneous equations (SE), it is well known that commonly employed asymptotic test criteria are seriously biased towards over-rejection. In this paper, we propose exact likelihood based tests for possibly nonlinear hypotheses on the coefficients of SE systems. We discuss a number of bounds tests and Monte Carlo simulation based tests. The latter involves maximizing a randomized p-value function over the relevant nuisance parameter space which is done numerically by using a simulated annealing algorithm. We consider limited and full information models, in which case we introduce a multi-equation Anderson-Rubin-type test. Illustrative Monte Carlo experiments show that: (i) bootstrapping standard instrumental variable (IV) based criteria fails to achieve size control, especially (but not exclusively) under near non-identification conditions, and (ii) the tests based on IV estimates do not appear to be boundedly pivotal and so no size-correction may be feasible. By contrast, likelihood ratio based tests work well in the experiments performed.

Date: 2000-08-01
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