  This paper investigates the consumption and risk taking decision of an
economic agent with partial irreversibility of consumption decision by
formalizing the theory proposed by Duesenberry (1949). The optimal policies
exhibit a type of the (s, S) policy: there are two wealth thresholds within
which consumption stays constant. Consumption increases or decreases at the
thresholds and after the adjustment new thresholds are set. The share of risky
investment in the agent's total investment is inversely U-shaped within the (s,
S) band, which generates time-varying risk aversion that can fluctuate widely
over time. This property can explain puzzles and questions on asset pricing and
households' portfolio choices, e.g., why aggregate consumption is so smooth
whereas the high equity premium is high and the equity return has high
volatility, why the risky share is so low whereas the estimated risk aversion
by the micro-level data is small, and whether and when an increase in wealth
has an impact on the risky share. Also, the partial irreversibility model can
explain both the excess sensitivity and the excess smoothness of consumption.
