Assessing the sensitivity of annual streamflow to precipitation is challenging due to the complexity of the processes that control the water balance. A low-dimensional model can be useful to interrogate data in regional assessments of a large number of catchments, and can provide insights into the broad similarities and differences between catchments' behaviors. This work assesses the sensitivity to precipitation of total annual streamflow, as well as its slow and fast flow components, within the framework of the Ponce and Shetty water balance model. This framework assumes that there are upper limits on the ability of a catchment to store and evaporate water, and there are minimum threshold amounts of precipitation and wetting (precipitation minus fast flow) needed to initiate fast and slow runoff. The flow elasticities (percent of change in flow per percent of change in annual precipitation) were estimated for 405 catchments in the Model-Parameter Estimation Experiment data set (including an assessment of parameter uncertainty). The elasticity of total discharge was 2.1 on average across the catchments, which is consistent with other studies. The fast component was higher (≈ 2.4) and slow flow was lower (≈ 2.0). Elasticities were highest and most variable in arid areas. The variations in elasticity between sites were shown to be primarily controlled by the two threshold parameters. The thresholds were a high proportion of mean annual precipitation in arid sites where only a small proportion of catchment wetting is released as slow flow. This provides some insight into previous observations that the sensitivity is correlated with climate.