Chapter 1 examines computational methods for solving continuous-time macroeconomic models, comparing grid-based methods enhanced by high-performance computing (HPC) and grid-free ap- proaches using deep learning. While HPC improves grid-based methods’ performance, I show how Amdahl’s Law constrains their scalability. Deep learning methods, particularly the Deep Galerkin Method, offer an alternative that better handles high-dimensional problems by avoiding the curse of dimensionality. In the subsequent chapters, my co-authors and I provide implementation frame- works for both approaches in solving Hamilton-Jacobi-Bellman equations and demonstrate their applications in macroeconomic and climate economics models. In chapter 2, using firm-level data, I document five empirical facts that reveal a misalignment between high ESG scores and actual environmental performance. To explain these facts, I develop a novel general equilibrium model with distorted learning. The model quantifies the economic and environmental costs of greenwashing. Key findings include: (1) firms can take up to three times as long to reduce emissions compared to scenarios with perfect information; (2) even after a decade, economies with significant greenwashing exhibit emissions that are 0.01 gigatons (0.1% of total US emissions) higher and are 9% less green than in scenarios with perfect information; and (3) greenwashing can increase social cost of carbon by up to $18 billion due to delayed emission reductions. In chapter 3, my co-authors (Lars Hansen, Michael Barnett, William Brock, and Ruimeng Hu) and I develop a neural-network-based computational algorithm that incorporates pseudo-states variables to derive accurate global solutions to high-dimensional, non-linear, dynamic models with jumps and uncertainty aversion. We use this algorithm to study optimal carbon-neutral transition policy in response to climate change, a setting where endogenous nonlinearities from model uncertainty and jump processes are first-order considerations. Our social planner places substantial value on investment in R&D and green capital, though the significant “social pay-off” of green technological innovation means only R&D investment is significantly augmented by uncertainty concerns, even with uncertainty concerns about jumps in the severity of climate change damages.