Shadow Prices of CO₂ Emissions at U.S. Electric Utilities : A Random-Coefficient, Random-Directional-Vector Directional Output Distance Function Approach

We estimate the shadow prices of CO₂ emissions of electric utilities in the United States over the period from 2001 to 2014, using a random-coefficient, random-directional-vector directional output distance function (DODF) model. The main feature of this model is that both its coefficients and directional vector are allowed to vary across firms, thus allowing different firms to have different production technologies and to follow different growth paths. Our Bayes factor analysis indicates that this model is strongly favored over the commonly-used fixed-coefficient DODF model. Our results obtained from this model suggest that the average annual shadow price of CO₂ emissions ranges from $61.62 to $105.72 (in 2001 dollars) with an average of $83.12. The results also suggest that the firm-specific average shadow price differs significantly across electric utilities. In addition, our estimates of the shadow price of CO₂ emissions show an upward trend for both the sample electric utilities as a whole and the majority of the individual sample electric utilities