In this thesis, we propose identification-robust numerical and statistical confidence-set estimation tools for Dynamic Stochastic General Equilibrium [DSGE] models. The first chapter introduces Particle Swarm Optimization [PSO] to econometrics with focus on test inversion and numerical projections. Empirically, the paper analyzes a three-equation New-Keynesian model. In contrast to PSO, the genetic algorithm, simulated annealing and even grid searches converge to local optima that suggest misleading economic decisions on: (i) the nature of the New-Keynesian Phillips Curve [NKPC], (ii) determinacy of monetary policies, and (iii) the persistence of the Taylor rule. Given this evidence and using PSO, the next three chapters introduce new and improved econometric methods for inference on DSGEs. The second chapter documents the sensitivity of the identification of DSGE models to auxiliary assumptions on exogenous shock processes using the identification-robust inference procedure of Dufour, Khalaf and Kichian (2013). We find that adding lagged endogenous variables instead of assuming autoregressive shocks to capture external propagation improves the identification of important parameters, even when the slope of the NKPC is near zero. Also, the asymptotic Likelihood Ratio [LR] test is oversized in small sample, which provides motivation for the third chapter. The third chapter proposes a finite-sample exact confidence-set estimation method using a LR distance measure for DSGEs. We demonstrate that our method has exact size in finite samples, and use it to estimate a canonical three-equation New-Keynesian DSGE model. We find no conclusive evidence that the “pre-Great Moderation" era conforms to a passive monetary policy rule corresponding to an indeterminate model, as argued in the literature. The final chapter extends the method proposed in the third chapter beyond the LR distance measure and approximate Vector Autoregression [VAR] context for DSGE models. We propose to use a VAR with Leads and Lags [VARLL] as the alternative reduced form and estimate the volatility parameters simultaneously together with other parameters. Taken collectively, the results of this thesis suggest that far more attention needs to be paid to numerical precision as test inversion gains popularity in applied econometrics.