Piecewise smooth approximation of bottom–up abatement cost curves

Top–down models usually include piecewise-smooth functions to describe marginal cost curves, while bottom–up models use step function curves. When a bottom–up cost curve is available, we can explicitly represent this curve with a top–down model in order to replicate its shape instead of using arbitrary assumptions. We propose several methods to approximate a piecewise function from a step function using constant elasticity of substitution technologies. Specifically, we consider a pollution abatement sector and calibrate the parameters of the abatement function in order to allow proper assessment of the economic effects of an environmental policy. Our methodology can be applied to any sector characterized by decreasing returns to scale technologies. We conclude that the elasticities of substitution need not be estimated only on the basis of historical data, but can be precisely calibrated on the basis of engineering estimates of technology potential.