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We use a stochastic dynamic framework to compare price collars (price ceilings and floors) in a cap-and-trade system. Sources of uncertainty include shocks to baseline emissions, affectingcorresponding abatement costs, and shocks to the supply of offsets. We consider a continuum between soft collars, which have a limited volume of additional emission allowances (a reserve) available at theprice ceiling, and hard collars, which provide an unlimited supply of additional allowances, thereby preventing allowance prices from exceeding the price ceiling. For all cases considered, we set the price floors and ceiling such that the expected cumulative emissions net of offsets are equal to the cumulative allowances. Consequently, increasing the size of the allowance reserve requires higher price ceilings and floors, and a lower probability of reaching the ceiling. Across most parameter values examined, we find that increasing the size of the allowance reserve leads to lower expected net present values of compliance costs, although the differences are not large. However, when offset supply shocks are highly persistent and exhibit strong (negative) correlation with baseline emission shocks, hard collars deliver noticeably lower expected costs, though with a wider range of emission outcomes than the soft collars.