Inflation prediction guides decisions on interest rates, investments, and wages, playing a key role in economic stability. Yet accurate forecasting is challenging due to dynamic factors and the layered structure of the Consumer Price Index, which organizes goods and services into multiple categories. We propose the Bi-directional Hierarchical Recurrent Neural Network (BiHRNN) model to address these challenges by leveraging the hierarchical structure to enable bidirectional information flow between levels. Informative constraints on the RNN parameters enhance predictive accuracy at all levels without the inefficiencies of a unified model. We validated BiHRNN on inflation datasets from the United States, Canada, and Norway by training, tuning hyperparameters, and experimenting with various loss functions. Our results demonstrate that BiHRNN significantly outperforms traditional RNN models, with its bidirectional architecture playing a pivotal role in achieving improved forecasting accuracy.