Simulation-Based Finite-Sample Inference in Simultaneous Equations

In simultaneous equation (SE) contexts, nuisance parameter, weak instruments and identification problems severely complicate exact and asymptotic tests (except for very specific hypotheses). 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. We extend, to non-Gaussian contexts, the bound given in Dufour (Econometrica, 1997) on the null distribution of the LR criterion, associated with possibly non-linear- hypotheses on the coefficients of one Gaussian structural equation. We also propose a tighter bound which will hold: (i) for the limited information (LI) Gaussian hypothesis considered in Dufour (1997) and for more general, possibly cross-equation restrictions in a non-Gaussian multi-equation SE system. For the specific hypothesis which sets the value of the full vector of endogenous variables coefficients in a limited information framework, we extend the Anderson-Rubin test to the non-Gaussian framework. We also show that Wang and Zivot's (Econometrica, 1998) asymptotic bounds-test may be seen as an asymptotic version of the bound we propose here. In addition, 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 performedSimultaneous Equation, Weak Instruments, Monte Carlo test, Identification

Uncertainty propagation and speculation in projective forecasts of environmental change: a lake-eutrophication example

The issue of whether models developed for current conditions can yield correct predictions when used under changed control, as is often the case in environmental management, is discussed. Two models of different complexity are compared on the basis of performance criteria, but it appears that good performance at the calibration stage does not guarantee correctly predicted behavior. A requirement for the detection of such a failure of the model is that the prediction uncertainty range is known. Two techniques to calculate uncertainty propagation are presented and compared: a stochastic first-order error propagation based on the extended Kalman filter (EKF), and a newly developed and robust Monte Carlo set-membership procedure (MCSM). The procedures are applied to a case study of water quality, generating a projective forecast of the algal dynamics in a lake (Lake Veluwe) in response to management actions that force the system into a different mode of behavior. It is found that the forecast from the more complex model falls within the prediction uncertainty range, but its informative value is low due to large uncertainty bounds. As a substitute for time-consuming revisions of the model, educated speculation about parameter shifts is offered as an alternative approach to account for expected but unmodelled changes in the system