of energy type is necessary since the subsidies vary across energy sources. Furthermore, electricity subsidies are netted out of carbon subsidies. kk To calculate the fossil fuel subsidy (or negative carbon tax) per energy source, we use IEA data (for the period 2010 to 2019) and IMF data (for 2007 to 2009) on the total amount of subsidies paid for each of the three energy sources and electricity. Subsidies for electricity are described in more detail below. We use data on the total amount of emissions from each fuel type. Fossil fuel subsidies for energy type divided by total emissions from energy type provides the subsidies for energy type per ton of CO2. The kk data for 1980 to 2006 are calculated using the average share of subsidies in the world market price. kk ii The taxed quantities are the energy sources in ktoe. In order to obtain the tax per ktoe we need a conversion coefficient, denoted as . It will be in units of tons of CO2 per kiloton of oil equivalent (t/ktoe). Following (Carrara and Marangoni 2017), we obtain the following values: = 2.26 , = αα<sup>kk</sup> tt 1.75 , = 1.34 and = 0 . αα<sup>EECCbbEE</sup> kkttCCEE αα<sup>CCiiEE</sup> tt tt tt kkttCCEE αα<sup>EEbbff</sup> kkttCCEE αα<sup>rrEECC</sup> kkttCCEE

# _3.2.1.2 Constructing the energy variables used in PAKMod_

Because we want to track the carbon and other GHG emissions associated with energy production from different sources, the model needs to account for energy volumes both in terms of physical quantities as well as the more traditional national accounting volumes derived from base-year values and market or factor-price deflators. We construct the national account equivalent variables in the model using the data above.

Energy prices and the valuation of energy value added is complicated by the mechanisms by which fuels are subsidized in Pakistan. Historically, crude oil and natural gas are purchased by the government in international markets at market prices ( ), and then sold to firms at a lower fixed cost. The final domestic market price at which firms are allowed to sell products is also fixed by the government. This UUSSDD kk,tt PP implicit subsidy to consumers is represented in the model as a negative carbon tax. In the model, the nominal market value of each fuel type produced is given by �. CCKK UUSSDD kk kk kk where is the amount paid by the firm when purchasing the energy source , and kk,tt kk,tt tt kk,tt tt represents the physical quantity produced (and sold) in kilotons of oil equivalent (ktoe). The remainder of the expression CCKK YY<sup>�</sup> = QQ ∗FFXX �PP ∗ββ + ττ ∗αα kk,tt kk,tt YY<sup>�</sup> QQ reflects the market price of energy in local currency and is the product of the exchange rate and the international market price in USD in barrels, or cubic meters multiplied by a conversion factor (which converts the USD price per commodity unit (say Barrel) to a USD price per ktoe). The final expression ββ<sup>kk</sup> reduces (or increases) the international price by the amount of the implicit subsidy (or carbon tax). Where the carbon tax /subsidy rate ( ) is in USD per ktoe of CO2. where converts the commodity quantity into ktoe of carbon. kk kk tt ττ αα 24