Despite their impressive performance, large language models (LLMs) such as ChatGPT are known to pose important risks. One such set of risks arises from misplaced confidence, whether over-confidence or under-confidence, that the models have in their inference. While the former is well studied, the latter is not, leading to an asymmetry in understanding the comprehensive risk of the model based on misplaced confidence. In this paper, we address this asymmetry by defining two types of risk (decision and composite risk), and proposing an experimental framework consisting of a two-level inference architecture and appropriate metrics for measuring such risks in both discriminative and generative LLMs. The first level relies on a decision rule that determines whether the underlying language model should abstain from inference. The second level (which applies if the model does not abstain) is the model's inference. Detailed experiments on four natural language commonsense reasoning datasets using both an open-source ensemble-based RoBERTa model and ChatGPT, demonstrate the practical utility of the evaluation framework. For example, our results show that our framework can get an LLM to confidently respond to an extra 20.1% of low-risk inference tasks that other methods might misclassify as high-risk, and skip 19.8% of high-risk tasks, which would have been answered incorrectly.