Accurately forecasting central bank policy decisions, particularly those of the Federal Open Market Committee(FOMC) has become increasingly important amid heightened economic uncertainty. While prior studies have used monetary policy texts to predict rate changes, most rely on static classification models that overlook the deliberative nature of policymaking. This study proposes a novel framework that structurally imitates the FOMC's collective decision-making process by modeling multiple large language models(LLMs) as interacting agents. Each agent begins with a distinct initial belief and produces a prediction based on both qualitative policy texts and quantitative macroeconomic indicators. Through iterative rounds, agents revise their predictions by observing the outputs of others, simulating deliberation and consensus formation. To enhance interpretability, we introduce a latent variable representing each agent's underlying belief(e.g., hawkish or dovish), and we theoretically demonstrate how this belief mediates the perception of input information and interaction dynamics. Empirical results show that this debate-based approach significantly outperforms standard LLMs-based baselines in prediction accuracy. Furthermore, the explicit modeling of beliefs provides insights into how individual perspectives and social influence shape collective policy forecasts.