This paper advances a structural inter-temporal model of labour supply that is able to simulate the dynamics of labour supply in a continuous setting and addresses two main drawbacks of most existing models. The first limitation is the inability to incorporate individual heterogeneity as every agent is sharing the same parameters of the utility function. The second one is the strong assumption that individuals make decisions in a world of perfect certainty. Essentially, this paper offers an extension of marginal-utility-of-wealth-constant labour supply functions known as “Frisch functions” under certainty and uncertainty with homogenous and heterogeneous preferences. The lifetime models based on the fixed effect vector decomposition yield the most stable simulation results, under both certain and uncertain future wage assumptions. Due to its improved accuracy and stability, this lifetime labour supply model is particularly suitable for enhancing the performance of the life cycle simulation models, thus providing a better reference for policymaking.