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Abstract:: Behavioral studies have revealed the sub-additive discounting pattern, which is at odds with the prevailing hyperbolic discounting framework that explains intertemporal choices. In this study, we demonstrate that completely and partially sophisticated individuals who are aware of their shifting preferences over time may exhibit sub-additive discounting behaviors. More importantly, these behaviors are not determined by whether an individual has hyperbolic time preferences or not. Instead, we show that the choices of reference points and partial projection bias may be the underlying drivers of the observed sub-additive discounting. Keywords: Hyperbolic discounting, Non-hyperbolic discounting, Sub-additive discounting, Projection bias, Reference point, JEL classification: D81, D90