Consumption dynamics with law of small numbers

We propose an intertemporal consumption-saving model by exploring the implications of the Law of Small Numbers (LSN), a belief heuristic stating that any sample realization of a population should be representative of the population. First, the existence of the LSN reduces the precautionary savings demand. More importantly, we show that the LSN belief structure provides an alternative explanation for two fundamental anomalies in consumption theory: (1) excess sensitivity by showing that past changes in income predict future changes in consumption; and (2) excess smoothness by lowering consumption volatility and generating the empirical magnitude.