This paper studies dynamic panel data linear models that allow multiplicative and additive heterogeneity in a short panel context by allowing both the coefficients and intercept to be individual-specific. I show that the model is not point-identified and yet partially identified, and I characterize the sharp identified sets of the mean, variance, and distribution of the partial effect distribution. The characterization applies to both discrete and continuous data. A computationally feasible estimation and inference procedure is proposed, based on a fast and exact global polynomial optimization algorithm. The method is applied to study lifecycle earnings and consumption dynamics in U.S. households in the Panel Study of Income Dynamics (PSID) dataset. Results suggest large heterogeneity in earnings persistence and earnings elasticity of consumption, and a strong correlation between the two. Calibration of the lifecycle model suggests that heterogeneity in asset-related factors, such as interest or discount rates, is required to describe real-world consumption and savings behaviors accurately.