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Our methodology integrates simulation estimation methods using auxiliary statistics with Monte Carlo test principles. Results cover deep parameters and impulse responses. Auxiliary statistics include coefficients of linear and nonlinear vector autoregressions and local projections. Proposed procedures are illustrated through laboratory experiments and an empirical application on a nonlinear real business cycle model. In simulations, we study size, power, and the trade\u2010off between robustness and insensitivity to misspecification. 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