Climate change and global warming are significantly affected by carbon emissions that arise from the burning of fossil fuels, specifically coal, oil, and gas. Accurate prices are essential for the purposes of measuring, capturing, storing, and trading in carbon emissions at regional, national, and international levels, especially as carbon emissions can be taxed appropriately when the price is known and widely accepted. This paper uses a novel Capital (K), Labor (L), Energy (E) and Materials (M) (or KLEM) production function approach to calculate the latent carbon emission prices, where carbon emission is the output and capital (K), labor (L), energy (E) (or electricity), and materials (M) are the inputs for the production process. The variables K, L, and M are essentially fixed on a daily or monthly basis, whereas E can be changed more frequently, such as daily or monthly, so that changes in carbon emissions depend on changes in E. If prices are assumed to depend on the average cost pricing, the prices of carbon emissions and energy may be approximated by an energy production model with a constant factor of proportionality, so that carbon emission prices are a function of energy prices. Using this novel modeling approach, this paper estimates the carbon emission prices for Japan using seasonally adjusted and unadjusted monthly data on the volumes of carbon emissions and energy, as well as energy prices, from December 2008 to April 2018. The econometric models show that, as sources of electricity, the logarithms of coal and oil, though not Liquefied Natural Gas (LNG,) are statistically significant in explaining the logarithm of carbon emissions, with oil being more significant than coal. The models generally displayed a high power in predicting the latent prices of carbon emissions. The usefulness of the empirical findings suggest that the methodology can also be applied for other countries where carbon emission prices are latent.
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