# Tax method

The tax method is based on Weitzman (2013) or Weitzman (2014). He advocates that it would be easier for countries to negotiate a global carbon price, since agreeing on one number would reduce the negatiations and countries would benefit directly from the tax revenues. Given a total budget, we look for a 2014 carbon price that reduces the forecasted emissions until 2050.

To get the amount of excess emissions (EE), we have to forecast the regional and global cumulative emissions from 2011 to 2050. For simplicity we assume emissions will remain constant at 2014 levels (E2014,i), although we could use more complicated forecasts. Thus, the regional cummulative emissions are given by:

E_{2015-2050,i} = \sum_{2015}^{2050}E_{2014,i}

This allows us to get global excess emissions (EE):

EE = \sum_i E_{2015-2050,i} - Z^\text{rem}_\text{scaled}, \qquad (1)

where Z^\text{rem}_\text{scaled} is the remaining re-scaled budget as described in General settings.

Mathematically, we are looking for the price that is able to reduce emissions in each country to avoid the excess emissions. For this, we have to find a proxy for energy costs in all countries. A readily available proxy would be fuel costs, Pi (either gasoline or diesel). If we then assume that the long run price elasticity of demand, ε, is constant across countries, we can calculate how much the demand would reduce when we increase the price. Accordingly emissions would go down by the same percentage. Therefore,

EE = \sum_i \frac{ E_{2015-2050,i} \cdot \epsilon \cdot \tau}{P_i}, \qquad (2)

where τ is the price increase or the global tax. We chose ε = 0.8 in line with Hausman and Newey (1995) and Kilian and Murphy (2013). Solving for τ we obtain:

\tau = \frac{EE}{\sum_i E_{2015-2050,i}\cdot \epsilon/P_i}

Using equations (1) and (2) and knowing that by construction \displaystyle Z = \sum_i Z_i the country budgets are given by

Z_i = E_{2015-2050,i} \cdot \left(1-\frac{\tau}{P_i}\epsilon\right)