In Ghana and many African countries, demand for non-life insurance remains strikingly low, even in South Africa, which dominates the continent’s insurance market. This is particularly perplexing given that many non-life insurance products, such as motor insurance, are legally mandated. This study aims to investigate the determinants of non-life insurance demand in Ghana. It utilizes a robust set of regularization methods—specifically Ridge, Least Absolute Shrinkage and Selection Operator (LASSO), and Elastic net—moving beyond traditional least squares and conventional dimension reduction techniques. The study uses data that span from 1995 to 2022. The findings indicate that the two most important determinants of non-life insurance demand in Ghana are income and economic freedom driven by government expenditure. Furthermore, the study reveals that the most parsimonious model produced by the LASSO algorithm is the most reliable. Based on these insights, we recommend that the government implement economic policies that promote job creation, wage growth, and entrepreneurship to enhance disposable income. Additionally, increasing expenditure on public goods and services—such as roads, utilities, healthcare, education, security, and social intervention programs—would alleviate financial burdens on individuals and businesses, making insurance more affordable and attractive.