Product attribute value identification (PAVI) involves automatically identifying attributes and their values from product information, enabling features like product search, recommendation, and comparison. Existing methods primarily rely on fine-tuning pre-trained language models, such as BART and T5, which require extensive task-specific training data and struggle to generalize to new attributes. This paper explores large language models (LLMs), such as LLaMA and Mistral, as data-efficient and robust alternatives for PAVI. We propose various strategies: comparing one-step and two-step prompt-based approaches in zero-shot settings and utilizing parametric and non-parametric knowledge through in-context learning examples. We also introduce a dense demonstration retriever based on a pre-trained T5 model and perform instruction fine-tuning to explicitly train LLMs on task-specific instructions. Extensive experiments on two product benchmarks show that our two-step approach significantly improves performance in zero-shot settings, and instruction fine-tuning further boosts performance when using training data, demonstrating the practical benefits of using LLMs for PAVI.