Revisiting Energy Subsidy Calculations: A Focus on Saudi Arabia

The implicit nature of many energy subsidies has led to disagreements over what defines a ‘subsidy’ while making it difficult to estimate their indirect fiscal cost. Most energy subsidies in Saudi Arabia are implicit, leading to forgone government revenue. Using a comprehensive dataset, we estimate energy subsidies in Saudi Arabia for ten fuels and electricity for the 2007–2018 period. We begin by applying the price-gap method, then introduce a formulation that better captures the for-gone revenues from maintaining a subsidy, accounting for the domestic demand response to the removal of the subsidy, which in turn frees up exports that can reduce the international market price. Our method shows that the magnitude of Saudi Arabia’s implicit energy subsidies may be overestimated. For instance, we find that the crude oil subsidy can fall from $8.6 billion (the price-gap estimate) to as low as $3.3 billion in 2018.


INTRODUCTION
Saudi Arabia is the world's leading exporter of oil, a member of the Group of 20 (G20), and one of the largest energy consumers in the Middle East.BP (2020) estimated the Kingdom's primary energy consumption in 2019 to exceed 260 million tonnes of oil equivalent (Mtoe), consisting almost exclusively of crude oil and natural gas.As a result, it is also one of the largest emitters of carbon dioxide (CO 2 ) in the region, releasing 580 million tonnes in 2019 (BP, 2020).Shown in Figure 1, Saudi Arabia's primary energy consumption has been partially driven by economic development and population growth.Domestic energy pricing policy has also influenced the Kingdom's energy use.For decades, Saudi Arabia has generally set domestic fuel prices below international market levels.This policy has helped support households' needs for basic energy services while also supporting the growth of nascent industries.Nevertheless, low energy prices have discouraged investment in energy efficiency and, as Matar et al (2015) show, stymied the efficient allocation of energy in the Kingdom.Starting in 2016, the Saudi government began to reform its domestic energy pricing policy in response to the undesired effects of low energy prices.These changes came under the wider banner of Saudi Vision 2030 (SV2030, 2016), a blueprint for social and economic reform.
The International Monetary Fund (IMF, 2013) rightly noted the difficultly of capturing the fiscal cost of low energy prices in oil exporters such as Saudi Arabia, in which the "subsidies provided by low energy prices are often implicit."This is because in countries like Saudi Arabia, there is often no expenditure by the government to support low energy prices.Instead, the low energy prices lead to forgone revenues for the government.In this vein, this paper examines subsidy definitions, focusing on implicit subsidies in oil-exporting countries.The IMF (2013) also listed "lack of information regarding the magnitude and shortcomings of subsidies" at the top of their list of barriers to energy price reform.This paper addresses this barrier to Saudi energy price reform by comprehensively estimating energy subsidies in Saudi Arabia, by fuel and over time.
We initially use the price-gap method to calculate energy subsidies by measuring the gap between the domestic price and a reference price for each energy product (Koplow, 2009).The reference price depends on how a 'subsidy' is defined.This method has been applied for Saudi Arabia by Alyousef and Stevens (2011), Coady et al (2019), and the International Energy Agency (IEA, 2020).Its appeal stems from its simplicity.
The price-gap method, however, does have some drawbacks.It misses out on key effects like the impact of potential price reform on domestic demand and international market prices.Also, Koplow (2009) discussed how there are subsidies that do not influence market prices and are therefore neglected by the price-gap method.For instance, governments may subsidize the production process of an energy product that is then sold domestically at the international market price.Although the price gap would be zero in this case, those subsidy costs are still incurred.Since the price gap method misses such subsidies, Koplow (2009) argues that it understates global fossil fuel subsides.
Focusing on the measurement of implicit subsidies, we propose a generalization to the price-gap method that incorporates the responses of domestic demand and international markets to the removal of a subsidy.Our approach addresses these two drawbacks to the price-gap method, but it is not designed to capture subsidies that do not influence market prices.It also retains elements of the price-gap method's simplicity.We showcase the proposed method for Saudi Arabia, comparing results across both methods.Our results reveal that the crude oil subsidy in Saudi Arabia in 2018 can fall from 8.6 billion United States (U.S.) dollars ($) to as low as $3.3 billion, depending on elasticity assumptions.The diesel subsidy can drop from $10.7 billion to as low as $4.4 billion, while the gasoline subsidy can fall from $4.3 billion to as low as $2.0 billion.These relatively smaller estimates stem from the domestic and international market responses to the removal of the subsidy.The remainder of this paper is structured as follows.Section 2 of this paper provides a background on Saudi energy policy to support our estimations of Saudi energy subsidies.Section 3 reviews the literature, covering different subsidy definitions and previous estimates of energy subsidies for the Kingdom.Section 4 presents the methods and data.Section 5 discusses the results, and Section 6 concludes.

AN OVERVIEW OF SAUDI ENERGY POLICY
Energy prices have been regulated by the Saudi government for decades.As noted in Saudi Arabia's accession to the World Trade Organization (WTO) (2005), energy price regulation is used to "secure the needs and welfare of consumers and preserve important social interests of the Kingdom." Low feedstock prices, for example, helped the Saudi Basic Industries Company (SABIC) establish itself as a major player in the global petrochemicals industry.In the absence of a local market, prices for domestic supplies of natural gas and ethane had to be increased to make investments in production and processing worthwhile.The current natural gas price of $1.25 per million British thermal units (MMBtu) still falls short of the domestic marginal value of its demand (given the prevailing domestic supply) when fuel prices are deregulated (Matar and Anwer, 2017). 1ow fuel prices have also supported households' needs for essential services such as air conditioning and mobility.For example, Saudi Arabia set the price of Arab Light crude at a nominal $4.24 per barrel ($/barrel) for decades, which, along with the low natural gas price, allowed the local electricity regulator to charge low electricity prices to households, schools, mosques, and commercial centers.Also, the Kingdom introduced a more inexpensive grade of gasoline in 2007, priced at a fixed 0.45 Saudi Arabian Riyals per liter, or roughly $0.45 per gallon.
However, low domestic energy prices have discouraged investment in energy efficiency for conversion and end-use sectors.For instance, the Saudi Electricity Company (SEC, 2020a) reported that the average national thermal efficiency for power generation in 2015 was 36.2%, compared to 42.1% globally (Enerdata, 2020).Low energy efficiency at the conversion stage has been compounded by low energy efficiency at the end-use stage.Domestic levels of energy efficiency for appliances such as air conditioners also appear to have lagged global averages (Alyousef and Varnham, 2010).The same applies to the fuel economy of passenger cars.To improve end-use energy efficiency, the Saudi Energy Efficiency Center (SEEC) has implemented mandatory thermal insulation for new buildings, minimum energy performance standards for air conditioners, energy efficiency labeling for automobiles and appliances, and fuel economy standards.
Since late 2015, the Saudi government has worked to reform energy prices to more closely reflect costs of production or international market prices for three primary reasons.First, higher energy prices would improve its fiscal position by raising government revenues, which have faltered due to a prolonged fall in the international oil price since late 2014.Second, energy price reform can increase the economic efficiency of using domestic resources, allowing supply and demand to balance with minimal external intervention.Third, energy price reform contributes to reducing domestic fossil fuel consumption.
Table 1 summarizes the evolution of domestic energy prices in Saudi Arabia between 1990 and 2018.While the 1990s and 2000s saw a few price changes, the key reforms occurred in 2016 and 2018.In January 2016, the Saudi government raised all fuel prices, and in January 2018, it implemented additional increases focused on the end-use of energy, particularly household consumption.Household electricity tariffs for the first 2 megawatt-hours (MWh) per month rose from 1.33 to 4.80 U.S. cents per kilowatt-hour (kWh) (Alghamdi, 2019).The government also raised gasoline prices substantially in 2016 and again in 2018, after which it linked them to international market prices and started adjusting them each month.
In 2018, the government also introduced the Citizen's Account, a cash transfer scheme that supports lower-income households in an environment of higher prices (FBP, 2018).It has been rec- ognized that low administered energy prices are inefficient at supporting lower-income households, since higher-income households capture a larger share of this support given their higher energy consumption habits (FBP, 2018).Combining energy price reform with the Citizen's Account makes for a much more efficient use of government funds to support lower-income households.Only Saudi citizens qualify for cash transfers from the Citizen's Account, unlike past subsidy schemes, and payments vary according to the beneficiary's household size and income, up to a cut-off point.

Subsidy Definitions and Their Implications on Measurement
Despite their prevalence, subsidies are difficult to define (WTO, 2006). 2 The Oxford English Dictionary and Merriam-Webster offer linguistic definitions of subsidies, both of which emphasize the transfer or grant of money by the state.The System of National Accounts (SNA, 2008) presents an accounting definition that only captures producer subsidies.As stated in the SNA (2008), "subsidies are not payable to final consumers; current transfers that governments make directly to households as consumers are treated as social benefits." The WTO, with 164 members (WTO, 2020a), offers a legal definition of subsidies that is arguably the most widely accepted.WTO Members agree to the definition in Article 1 of the WTO's (1994) Agreement on Subsidies and Countervailing Measures (ASCM).This definition states that a subsidy exists if there is both a financial contribution by the government and a benefit is conferred (WTO, 2020b).The ASCM also requires a subsidy to be specific, as stated in Article 2. Despite providing an internationally agreed upon definition, the WTO (2006) emphasized in a separate report the difficulty of defining subsidies.
Given our focus on energy subsidies, we present their definition according to different organizations, underscoring the variation in definitions (see Table 2). 3The Organisation for Economic Co-operation and Development (OECD, ND) defines fossil fuel subsidies around budgetary expenditures only, excluding forgone revenues.The Organization of the Petroleum Exporting Countries (OPEC) defines energy subsidies with respect to costs of production only, not international market prices, thereby excluding forgone revenues as well (IEA et al, 2010).The International Energy Agency (IEA, 2006) provides a comprehensive definition of energy subsidies that incorporates forgone revenues, while the International Monetary Fund (IMF, 2020a) provides several definitions, distinguishing between consumer and producer energy subsidies and distinguishing the former between "pre-tax" and "post-tax". 4he concept of efficient pricing is at the center of any textbook economics definition of subsidies (Coady et al, 2015;Bhattacharyya 2019).In economic theory, a good's efficient price, also known as its competitive equilibrium price, is achieved when its marginal production cost is equal to its marginal value of demand, yielding efficient resource allocation (Anderton, 2000;Dewees, 2001).When a good is traded internationally and has multiple producers, the efficient price is equal to the marginal producer's cost of supply to meet the demanded quantity at the margin.In economics, an energy subsidy therefore exists when the price of an energy product is below its efficient price.Efficient pricing can also be extended to encompass externalities such as air pollution and greenhouse gas emissions (Steenblik, 2003;Coady et al, 2015).When a good such as crude oil generates externalities, its efficient price requires a Pigovian tax that corrects for them.Therefore, in economics a subsidy can be defined to exist if the price of an energy product is below an efficient price that includes the costs of externalities.The IMF (2020a) includes externalities in its definition of post-tax energy subsidies.
The variation in definitions has major implications on the measurement of subsidies, particularly in fuel-exporting countries.For example, definitions that specify domestic production cost as the reference price or exclude forgone revenue result in a subsidy close or equal to zero for crude oil in Saudi Arabia, which sells oil domestically at a price around its lifting cost plus capital depreciation, but well above the lifting cost alone (Saudi Aramco, 2019).In contrast, definitions in which the reference price is the international market price will produce large crude oil subsidies.

IMF
"Pre-tax consumer subsidies exist when energy consumers pay prices that are below the costs incurred to supply them with this energy.For internationally traded energy products, like natural gas and petroleum products, the supply cost used to calculate subsidies is the international price adjusted for distribution and transportation costs." Yes Domestic crude oil prices are set below international market levels.

IMF
"Post-tax consumer subsidies exist if consumer prices for energy are below supply costs plus the efficient levels of taxation." Since "energy products contribute to local pollution, traffic congestion and accidents, and global warming-efficient taxation requires that the price of energy … reflect these adverse effects on society."Yes Domestic crude oil prices are set below international market levels and there are no carbon or pollution taxes.
The terms 'explicit' and 'implicit' have been used to mitigate some of the inconsistencies around subsidy definitions (Krane et al, 2020).Explicit refers to subsidies that rely on government transfers.Conversely, implicit subsidies are those that require no government spending but lead to forgone revenues.Implicit subsidies have also been referred to as "opportunity cost subsidies" (Moerenhout and Irschlinger, 2020).
We choose to adopt in this paper an economic definition of subsidies that is consistent with the IEA's definition and the IMF's definition of pre-tax energy subsidies, focusing primarily on implicit subsidies and excluding externalities.

The Opportunity Cost of Selling Energy Domestically at Lower Prices
For oil-exporting countries such as Saudi Arabia, the economic concept of opportunity cost plays a central role when defining and measuring subsidies.Opportunity cost refers to the value attributed to forgoing an alternative course of action over the one chosen.For example, the opportunity cost of selling crude oil domestically at a low price that is above production costs is the value that could have been obtained from selling it domestically or exporting it at the international market price.
When measuring subsidies, it is often assumed that the international market price is the opportunity cost of traded fuels in oil-exporting countries (Davis, 2017), although this may not necessarily be the case.Karanfil and Pierru (2021) discuss the issue of determining the appropriate opportunity cost for crude oil in Saudi Arabia.They show that market imperfections alter estimates.For example, Saudi Arabia is the world's leading exporter of oil, and the 'small economy' assumption that its exports will not influence international oil prices does not hold.Furthermore, the authors estimate that the opportunity cost of a barrel of oil in Saudi Arabia varies between 31% and 84% of the international oil price.Other constraints, such as restrictions on crude oil production levels, can further alter the opportunity cost of a barrel of oil in Saudi Arabia.The key takeaway is that the opportunity cost of oil is lower than its international market price.

Previous Estimates of Energy Subsidies
There are only a handful of estimates for energy subsidies in Saudi Arabia, mostly as part of aggregated global estimates that include the Kingdom.Clements et al (2014) estimated global pre-tax energy subsidies to be $492 billion in 2011, while Coady et al (2019) valued them at $296 billion in 2017.In both estimates, producer subsidies accounted for only a fraction of the total.Taylor (2020) found global fossil fuel subsidies to be at least $447 billion in 2017.The IEA (2020) had them at 335 billion 2019$ in 2017, while the IMF (2020b) estimated them at $295 billion in the same year.In most of these estimates, Middle Eastern countries such as Saudi Arabia were among the largest energy subsidizers, along with larger countries such as China, Russia, and India.
For Saudi Arabia alone, several wide-ranging estimates of energy subsidies exist, and none cover all major energy products.The IMF (2020b) estimated Saudi fossil fuel subsidies at $28 billion in 2017, while the IEA (2020) estimated them at 41 billion 2019$ in the same year.Taylor (2020) also estimated fossil fuel subsidies in Saudi Arabia, finding them to be roughly 45 billion 2018$ in 2017.According to these three studies, energy subsidies in Saudi Arabia would account for roughly 10% of the global total.
A few studies have focused on calculating energy subsidies for specific fuels in Saudi Arabia.For individual refined oil products, Alyousef and Stevens (2011) compared domestic prices to production costs in the 2000s.The costs were derived using a simplified oil refining model.For natural gas, they used an average-cost estimate that factors in the use of associated and non-associated gas.As a result, they found Saudi Arabia did not explicitly subsidize those fuels.For electricity, Alyousef and Stevens (2011) alternatively used an average marginal cost 5 estimate of 9.92 cents/ kWh as the reference price and found around $13.3 billion of electricity subsidies in 2010.They did not provide subsidy estimates for crude oil used directly or natural gas liquids (NGLs).Charles et al (2014) estimated gasoline and diesel subsidies, the latter for the transport sector only, to be $14 billion and $13 billion, respectively, in 2011.Davis (2017) found gasoline and diesel subsidies in Saudi Arabia to be almost $20 billion in 2014. 6 While there are a handful of estimates for Saudi Arabia, one of the largest economies in the Middle East, there is no comprehensive analysis that tracks Saudi energy subsidies over time for all the major energy products.Moreover, all these studies used the price-gap method, which may not realistically capture the implicit fiscal cost of energy subsidies in Saudi Arabia.The remainder of this paper aims to fill these gaps.

The Price-Gap Method for Calculating Energy Subsidies
The price-gap approach is used to measure the gap between the domestic energy price and a reference price.The price gap G f for each energy product f is calculated using the following equation (Koplow, 2009): Where is the initial reference price (i.e., the international market price for traded energy products and the domestic marginal cost of production for the non-traded ones) and f dom P is the domestic energy price for each energy product f.
Multiplying an energy product's price gap by the initial domestic demand quantity consumed f Q produces an estimate for the subsidy f S .
( ) We use the term 'initial' when describing both the reference price and the domestic quantity consumed because both variables should change following energy price reform.The price gap method does not account for this. 5. Alyousef and Stevens (2011) did not provide a source for their domestic marginal cost value.It is well above recent estimates for Saudi Arabia using the low fuel prices and the power generation fleet in 2015 (Matar and Anwer, 2017).
6. Other studies explored the welfare impacts of energy price/subsidy reform for Saudi Arabia.For example, Gonand et al ( 2019) used a dynamic macroeconomic model to quantify the intertemporal impacts, finding that energy price reform improves the intertemporal welfare of households.Aldubyan and Gasim (2021) quantified the changes in deadweight loss and external costs due to gasoline and electricity price reforms using a partial equilibrium analysis, finding the reforms to be welfare enhancing.Soummane et al (2022) used a dynamic simulation model to quantify the economy-wide macroeconomic impacts of full energy subsidy reform, finding that they protect Saudi Arabia's budget outlook against a future downturn in oil prices.These studies did not discuss the magnitude of energy subsidies in Saudi Arabia.

A Generalized Method for Calculating Implicit Energy Subsidies
A large share of fossil fuel subsidies in Saudi Arabia is implicit.Its magnitude reflects the forgone revenue, or implicit fiscal cost, that the government faces by not selling the fuel at higher international prices.
Quantifying the forgone revenue from maintaining energy subsidies is nuanced.For example, removing crude oil subsidies in Saudi Arabia would reduce domestic crude oil demand to below its pre-reform level, freeing up crude oil that could be exported instead.Additional exports would depress the international oil price, thus reducing the reformed domestic crude oil price, which is now directly linked to the international price.The updated domestic crude oil price would alter domestic demand and exports again-a process that would repeat until a new equilibrium is reached.Moreover, Saudi Arabia may choose to stockpile fuel or keep crude oil underground.Changes to domestic crude oil demand and the international oil price can be respectively estimated using a price elasticity for domestic crude oil demand and a price elasticity for the global demand for Saudi crude oil exports. 7The price-gap method ignores these important responses.
In Equation ( 2), we could replace with the new international market price after subsidy reform, f ref P , to obtain an improved subsidy measure.Shown by Equation (3),  f S demonstrates that the forgone revenue from maintaining a subsidy should be measured by comparing the difference between the revenue obtained by selling the quantity f ini Q at the new reference price (after allowing it to adjust to additional exports) minus the revenue from selling it domestically at the pre-reform domestic price.

 ( )
However, Equation (3) does not account for the loss in revenue on the initial level of exports following subsidy removal.This revenue loss stems from the export price falling from It is important to account for this revenue loss if the magnitude of the subsidy is to fully capture the forgone revenue.
We therefore introduce a formulation for obtaining a more realistic estimate of the implicit subsidy on traded fuels, f S , as shown by Equation (4).f S accounts for the changes in domestic and export revenues, and whether the government decides to export the saved fuel.

(
) ( ) The first term on the right-hand side of Equation ( 4) represents the additional revenue from selling the new domestic quantity consumed and the additionally exported quantity at P ref f .The variable f Q is the new consumption quantity after the subsidy on fuel f has been lifted.Thus, ( ) is the domestically saved fuel that could be exported.f µ is a policy decision parameter that charac- terizes how much of the quantity saved domestically is exported; it varies from 0 to 1.
The second term on the right-hand side represents the loss in export revenue on the initial quantity of exports, as the export price drops from (the initial market price) to P ref f (the new market price) because of the additional exports.E ini f is the initial exported quantity.Lastly, the third term on the right-hand side represents the initial revenue from selling the initial quantity of fuel consumed domestically at the pre-reform domestic price, f dom P .
7. Additional Saudi crude oil or refined products on the market may affect the demands for other crude oil grades as global refineries re-optimize their processes.Changes in the consumption of refined products alone may also affect the opportunity cost of crude oil, even if its domestic price, and hence domestic consumption, is unchanged.
The definition of f µ plays a key role in estimating forgone revenue.On one extreme, 0 f µ = means that fuel saved domestically is not exported and thus there is no change in the international price (i.e., P ref f = P iniref f ). 8 On the other, 1 f µ = indicates that all the fuel saved is exported and thus it would have the largest impact on international prices.A country may choose any value in between depending on geopolitical and policy-driven criteria.OPEC quotas may influence the value of f µ .However, since the quotas are placed on production, a decrease in domestic consumption following subsidy removal should allow for higher exports in the short run.In addition, as Ansari (2017) points out, Saudi Arabia is not likely to cut production unilaterally.A multi-lateral agreement to jointly cut production would be needed for Saudi Arabia to lower its exports.At least in the short run, we expect f µ to be equal or close to unity.We use Equation ( 4) to generate forgone revenue estimates for Saudi Arabia that vary with three factors: the domestic demand elasticity, the global demand elasticity for Saudi exports, and the policymakers' decision to not export fuel that is saved domestically.Our generalized method for calculating implicit subsidies requires an estimate of two variables: domestic demand quantity after subsidy removal and the new international market price after it adjusts to additional exports.
We solve Equations ( 5) and ( 6) for each year independently to obtain the new domestic demand quantity and reference price following subsidy removal.Equations ( 5) and ( 6) represent discrete formulations of price elasticities, which are often referred to as arc elasticities.As noted by Morrill (1983), there are several formulations for the arc elasticity, and the choice of formulation often depends on "priorities or preferences".Arc elasticities are preferably used when price changes are small (Allen and Lerner, 1934).We present our results using a range of elasticity values to emphasize that the arc elasticities may be variable, accommodating the large price changes that subsidy removal could bring. 9We also should not be restricted to a single elasticity value because of the potential bias between the arc and point elasticities for large price changes (see Appendix A for more details).By using these elasticity equations, we assume that demand outside Saudi Arabia remains unchanged.Hence, Equations ( 5) and ( 6) yield a partial equilibrium.

(
) ( ) ε d f is the short-run own-price elasticity of domestic demand, defined as the percentage change in domestic fuel demand over the percentage change in fuel price.ε E f is the short-run global price elasticity for additional Saudi fuel exports, defined as the percentage change in Saudi fuel exports over the percentage change in the international fuel price.Therefore, 1 / ε E f reflects how responsive the international price is to additional Saudi exports; ε E f approaches zero as price responsiveness increases.
Solving the system of Equations ( 5) and ( 6) gives symbolic solutions for f Q and P ref f , which can then be plugged into Equation (4).Equation (7a) shows the solution for f Q , with the parameters 8.If domestic demand for a fuel were to fall to zero following subsidy removal, and policymakers decided against increasing exports, such that . This negative subsidy value indicates that in this extreme scenario the removal of the subsidy does not lead to higher revenues but instead leads to a loss in revenues, at least in the short run.
9. In other words, these equations do not presume a certain form for the demand functions.
f α and f β , given by Equations ( 7b) and (7c), defined for simplification purposes.The ratio f f α β equals unity only when the domestic price equals the initial reference price (i.e., when no subsidy exists).The solution relates f Q to only the elasticities and the initial prices and quantities. Where, Equations ( 8a) and (8b) show the solution for P ref f .The ratio f f σ β equates to 1 when either ε d f equals 0, the domestic price equals the initial reference price, or f µ is 0. Where, Plugging Equations (7a) and (8a) into Equation (4) yields Equation ( 9), which relates the subsidy to the initial quantities and prices and the two elasticities. 10Equation ( 9) collapses to Equation (2) (the price-gap equation) if ε d f = 0.If one assumes all the domestically saved quantities are exported, Equation ( 9) can be simplified to Equation (10).
1 1 To reiterate, our formulation allows us to calculate the implicit subsidy for any traded fuel in an oil-exporting country such as Saudi Arabia, while allowing the international fuel price and domestic quantity consumed to change following the removal of the subsidy.This results in a more realistic subsidy estimate.
10.The values of f Q and ε df should be inspected before using Equation ( 9).For a huge percentage increase in the domestic price following subsidy removal and an (implausibly) large arc elasticity, it is possible to obtain negative values for f Q .However, as shown in Appendix A, for huge percentage increases in domestic prices, the arc elasticity will be small, as its curve approaches a horizontal asymptote as the point elasticity approaches infinity.If a plausible range of values for the arc elasticity is used, there should be no issues with regards to the values of f Q .

Oil and Secondary Oil Products
We obtain crude oil consumption data from the IEA (2020).In our calculation of crude oil subsides, we only include the quantities of crude oil that are burned directly and not refined.We also use IEA (2020) consumption data for gasoline, jet fuel, heavy fuel oil, diesel, and liquefied petroleum gas (LPG).For naphtha consumption, we use data from the Saudi Arabian Monetary Authority11 (SAMA, 2020).We exclude the consumption of oil products by the oil and gas industry.We also ignore jet fuel and heavy fuel oil used for international aviation and marine bunkering, respectively.Figure 2 shows the quantities of crude oil (for direct burn) and secondary oil products consumed in Saudi Arabia.For diesel, we disaggregate demand data by sector, allowing us to distinguish between consumption by transport, power, and industry.This is critical because domestic diesel prices vary across these three sectors.
Since the IEA demand data does not distinguish between different gasoline grades, we use data from Saudi Aramco (2016a) to break down the gasoline quantities into the two grades sold in the Kingdom, gasoline with research octane numbers (RON) of 91 and 95.Using Saudi Aramco (2016a) data, we set the share of 91 RON to be two-thirds of the total between 2007 and 2015, three-fourths in 2016 and 2017, and nine-tenths in 2018.The share of 91 RON gasoline generally increased following each wave of gasoline price reform.
We obtain the domestic prices of crude oil, gasoline, diesel, heavy fuel oil, jet fuel and kerosene, and LPG by combining data from WTO (2005), Aleqt (2015), Matar et al (2015), Council of Ministers Decision No. 95, andSPA (2017).The prices of these energy products remained fixed from 2007 until the first wave of energy price reform at the end of 2015.The second wave of energy price reform in 2018 resulted in further price increases to a smaller subset of these fuels.We obtain the domestic price of naphtha, which is equal to the Saudi export price (WTO, 2005), from the General Authority for Statistics (GAStat) (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019).
We use the Arab Light price from SAMA (2020) as the reference price for crude oil.For gasoline, diesel, jet fuel, LPG, and naphtha, we use the Saudi export prices for these products, which we obtained from GAStat (2008GAStat ( -2019)).However, because Saudi Arabia did not consistently trade heavy fuel oil during the 2007 to 2018 period, we combine GAStat's data with annual percentage changes in the wholesale price of residual fuel oil in the U.S. from the Energy Information Agency (EIA, 2020).

Natural Gas and Natural Gas Liquids
Quantities consumed of natural gas and NGLs, shown in Figure 3, are obtained from Saudi Aramco (2012( , 2014( , 2016( , 2018( , 2019( ), GAStat (2008( -2019)), and SAMA (2020).The specific NGLs we look at are ethane, propane, and butane, all of which are used in the petrochemicals sector as feedstock to directly make olefins and polymers.Since Saudi Aramco only lists the overall sales of those NGLs, we used GAStat trade statistics to derive how much propane and butane were consumed domestically.We obtain domestic prices of natural gas and NGLs through 2015 from the WTO (2005) and HSBC (2015).The Council of Ministers Decision No. 95 provides domestic prices since 2016.While the domestic prices of natural gas and ethane are fixed, propane and butane are sold at a discount to the export price from the Ras Tanura terminal on the east coast of Saudi Arabia.
Since Saudi Arabia does not trade natural gas and ethane internationally, global market prices lack relevance.Instead, we use the short-run marginal costs of domestic production as the efficient reference prices.Alyousef and Stevens (2011) cite 4.0 $/MMBtu as the marginal cost for producing conventional non-associated gas in Saudi Arabia.We add 0.5 $/MMBtu to the natural gas marginal production cost to account for the further processing required to produce ethane.Conversely, Saudi Arabia does trade propane and butane, allowing us to acquire their reference prices from the annual export statistics released by GAStat (2008GAStat ( -2019)).

Electricity
Ideally, we would like to compare the marginal costs of electricity production to the domestic electricity prices paid by consumers to estimate electricity subsidies.Due to data limitations, we use the average annual cost for electricity service in Saudi Arabia as the reference price.Electricity service costs comprise generation, transmission, distribution, consumption of capital, and capital expenditure for a given year.Since the calculated electricity service costs embed the subsidies on fuels used for power generation, the electricity subsidy we compute is the incremental subsidy for electricity only.To calculate this, we measure the gap between the average annual electricity service cost and the average annual price that electricity consumers paid.

Additional Data Requirements for Our Proposed Method
Our proposed method for calculating implicit subsidies requires three additional sets of data: the initial exports of each fuel and the two price elasticities.We obtain the former from SAMA (2020) and GAStat (2008GAStat ( -2019)).
For the price elasticities, the range of values we use for ε d f and ε E f are displayed in Table 3. ε d f is estimated to range from a hypothetical unresponsive consumer base (ε d f = 0) to a value consistent with recent point elasticity estimates for gasoline (Atalla et al, 2018;Mikayilov et al, 2020;Aldubyan and Gasim, 2021).The range for ε E f is selected based on the values estimated by Karanfil and Pierru (2021) and the conclusions of Blazquez et al (2017); the latter of whom found that international oil prices in the short run may be somewhat sticky.We incorporate a range of values because demand elasticities may vary with the marginal quantity of a fuel exported or demanded domestically.et al (2020), Karanfil and Pierru (2021), and Aldubyan and Gasim (2021).

Magnitude of Energy Subsidies in Saudi Arabia Using the Price-Gap Method
Table 4 lists our estimates of Saudi energy subsidies in 2019$ for crude oil and oil products, natural gas, NGLs, and electricity using the price-gap method.The subsidies shown are implicit12 for oil products and explicit for natural gas, ethane, and electricity. 13The majority of energy subsidies in Saudi Arabia are thus implicit, representing forgone revenue and requiring no government expenditure.In Section 5.1, any mention of dollars refers to 2019$.We use the Arab Light price deflator to normalize for inflation.Total annual energy subsidies grew from $42.3 billion in 2007 to a peak of $85.0 billion in 2012 then fell to $46.6 billion in 2018.In 2012, total energy subsidies represented 12% of real GDP, versus 6% in 2018.
Crude oil and oil product subsidies grew between 2009 and 2014 due to both higher international oil prices and growth in domestic consumption quantities.They decreased sharply between 2015 and 2018, as international oil prices fell and the government implemented two waves of energy price reform in 2016 and 2018.
Crude oil subsidies climbed from $4.5 billion in 2007 to a peak of $19.3 billion in 2012 before falling to $8.4 billion by 2018.Although domestic crude oil prices did not change between 2007 and 2012, subsidies rose fourfold, driven by greater domestic consumption and the near doubling of the international oil price.From 2015 onward, crude oil subsidies decreased because of a fall in the international oil price and energy price reform.
Diesel subsidies accounted for the largest share of total energy subsidies for most of the 2007-2018 period.However, this share declined from 36% in 2008 to 24% in 2019 due to the first wave of price reform and diesel displacement in the electric power sector.14 Diesel subsidies reached a peak of $28.1 billion in 2012, roughly a third of total energy subsidies that year, before falling to $11.3 billion by 2018.Gasoline subsidies rose from $6.7 billion in 2007 to a peak of $13.9 billion in 2014, before falling to $4.3 billion in 2018.Energy price reform affected gasoline subsidies more than those of the other fuels examined.
Electricity is the only energy product that saw its subsidy eliminated following the 2018 wave of reform.Electricity subsidies grew from $1.1 billion in 2007 to a peak of $3.8 billion in 2016 before falling to zero in 2018.The peak magnitude occurred in 2016, following the first wave of energy price reform, in which the prices of fuels consumed by the power sector, such as natural gas, increased more than the electricity tariffs.This led to a larger gap between electricity costs and tariffs and thus a larger subsidy.
Fuel oil subsidies grew from $5.9 billion in 2007 to a peak of $10.6 billion in 2014, before decreasing slightly to $9.9 billion by 2018.Despite the increase in fuel oil prices since the first wave of reform, the share of fuel oil subsidies in total energy subsidies rose from under 11% to over 21% between 2015 and 2018, due to considerable growth in the quantity consumed by the power sector.Kerosene subsidies for domestic aviation and LPG subsidies for the residential sector accounted for very small shares of total energy subsidies in Saudi Arabia.Natural gas subsidies climbed from $6.9 billion in 2007 to a peak of $10.2 billion in 2015, just before the implementation of the first wave of energy price reform, then fell to $8.8 billion by 2018.Given steadily rising domestic supply and our use of a fixed production cost as the reference price for the entire 2007-2018 period, the fall in natural gas subsidies from 2016 onward was entirely driven by energy price reform.Ethane subsidies, which hovered between $1-2 billion, followed a very similar trend to natural gas.NGL subsidies fluctuated between $1-3.5 billion, tracking international fuel prices closely during the 2007-2018 period.
The magnitude of total energy subsidies appears to be dependent on the international oil price, as shown in Figure 4, although the two series appear to have decoupled in 2018 following the second wave of energy price reform.In 2016, international oil prices fell while Saudi Arabia implemented the first wave of energy price reform, making it difficult to disentangle both effects.To highlight the impact of energy price reform on total energy subsidies, Table 5 illustrates our estimates while holding reference prices for each energy product fixed at their 2010 levels, eliminating the effects of fluctuating international fuel prices.By holding reference prices fixed, we show that energy price reform caused total fossil fuel subsidies to fall from a peak of $80.7 billion in 2015 to $51.6 billion in 2018.
We also compare our price-gap estimates to those of the IEA (2020) and IMF (2020b).Although we incorporate more fuels, our estimates of total energy subsidies ($48.5 billion for 2017) fall somewhat close to theirs (US$41.2 billion by the IEA and US$28.1 billion by the IMF for the same year).The estimates differ not only because we include all major fuels, but also because we disagree on the reference price used to measure subsidies on natural gas.Since Saudi Arabia does not trade natural gas internationally, we opt for the marginal cost of production as the reference price.For electricity, we also differ from the IEA and IMF by only estimating the incremental subsidy.Furthermore, we find data input irregularities in the IMF calculations to be a source of discrepancy.A detailed comparison of the price-gap estimates can be found in Appendix B. Note: electricity subsidies are excluded because both the prices and shares of the input fuels varied substantially.

Magnitude of Implicit Energy Subsidies in Saudi Arabia Using Our Proposed Method
This section presents the subsidy estimates using our proposed method.We assume that all the saved fuel is exported.Using Equation (10), we estimate implicit energy subsidies for crude oil, gasoline, and diesel in 2018.Those three fuels are chosen because they are traded internationally and they account for a sizeable share of total energy subsidies in Saudi Arabia.The estimates for f d ε = 0 correspond to the simple price-gap estimates.When the price elasticity of domestic demand equals zero, no additional fuel is freed up for export, so domestic demand and the international market price remain unchanged.As the domestic price elasticity increases, removing the subsidy reduces domestic demand, raising exports.Higher exports then result in a lower reference price, with its responsiveness to additional exports increasing as f E ε moves from -10 to -1.4, thus yielding a lower domestic reformed price.Because of these effects, the magnitude of the implicit subsidy, or the forgone revenue, is lower than the estimates we showed previously using the price-gap method.
Figures 5 to 7 show that implicit crude oil, gasoline, and diesel subsidies for Saudi Arabia may be greatly overestimated using the price-gap method.They reveal how sensitive the magnitudes of implicit fuel subsidies are to the price elasticities.The results in Figures 5 to 7 assume that any domestically saved fuel due to subsidy reform is exported (i.e., 1 µ = ).Results for when 1 µ < are shown in Appendix C. * Due to the large gap between domestic and international crude oil prices, the crude oil subsidy curve is limited to a maximum d ε of -0.08.In the 2018 case for crude oil, d ε = -0.08 is equivalent to a point elasticity of -0.6 estimated using a constant elasticity demand function (as explained in Appendix A).The crude oil subsidy can fall from $8.6 billion (the price-gap estimate) to as low as $3.3 billion, depending on the elasticity assumptions.The diesel subsidy can drop from $10.7 billion to as low as $4.4 billion, while the gasoline subsidy can fall from $4.3 billion to as low as $2.0 billion.The curves slope downward because, depending on the elasticities, subsidy reform reduces the reference price and export revenues to a point where the government gains substantially less additional revenues by removing the domestic subsidy.Our results are aligned with the findings of Blazquez et al (2020), who show that when additional exports are unlocked by a domestic policy that saves oil, thereby depressing the international price, the potential welfare gains from such domestic policies are reduced.The slopes of the curves in Figures 5 to 7 also depend on the initial gap between the pre-reform domestic price and the initial reference price.This explains why our method finds a relatively smaller reduction in the gasoline subsidy than that of crude oil, for which the initial gap is much larger.
Furthermore, we estimate the incremental change in the forgone revenue as a result of raising the 2018 domestic price by 1%.We take crude oil as an example.Applying Equation (10) (i.e., when µ is unity), we subtract the forgone revenue estimation shown in Figure 5 from the one esti- mated for a case where the domestic price is 1% higher.In both instances, all other parameters are fixed to their 2018 levels.Table 6 shows the changes in forgone revenue for ranges of d ε and E ε .At 0 d ε = , which is the conventional price-gap assumption, a 1% increase in the domestic price would lead to a $9 million reduction (or, -0.10%) in the implicit subsidy, or forgone revenue.At 0.02 , some crude oil is saved domestically and exported following a 1% increase in the domestic price.Depending on E ε , the additional exports will have a varying impact on export and domestic rev- enues.If 0.02 and 8 E ε = − , the international oil price is sticky and therefore the additional exports do not reduce the international export price substantially.In this case, a 1% increase in the domestic price would lead to a $6.3 million reduction (or, -0.07%) in the subsidy.With a more responsive international oil price ( 5) E ε = − , a 1% increase in the domestic price would only lead to a $4.8 million reduction (or, -0.06%) in the subsidy.With an even more responsive oil price ( 2) E ε = − , a 1% increase in the domestic price can counterintuitively increase the subsidy by $1.4 million (or, +0.02%). 15These results underscore the importance of accounting for such market responses when calculating the impact of domestic price changes on subsidy calculations.
15. Assuming very responsive domestic and international markets, we find that an incremental 1% increase in the domestic price can increase the magnitude of the subsidy.However, the impacts of further incremental 1% increases decline, eventually becoming negative.In other words, eventually the incremental 1% increases in the domestic price will reduce the magnitude of the subsidy.

CONCLUSION
The debate surrounding global fossil fuel subsidies has become more contentious due to climate change, with disagreements over how to define and measure subsidies, particularly implicit ones.We contributed by discussing the disparate definitions of a 'subsidy' and methods for accurately measuring implicit subsidies, which reflect forgone revenues, before applying the methods to Saudi Arabia.
Using the conventional price-gap method, we provided comprehensive estimates for Saudi energy subsidies from 2007 to 2018, based on exhaustive price and quantity data.This period encompasses rapid socio-economic growth and two waves of energy price reform.Our results revealed that energy subsidies peaked in 2012 at 85 billion 2019$.Crude oil, diesel, and gasoline constituted 70% of the 2012 total.In 2016, as oil markets were in decline and the first wave of energy price reform kicked in, the total subsidy declined to 39 billion 2019$.The second wave of reforms in 2018 mainly reduced electricity and gasoline subsidies, although the total subsidy increased to 47 billion 2019$ due to some recovery in international oil prices.
The price-gap method, however, does not account for the effects of subsidy removal on domestic consumption quantities, fuel exports, and international market prices.Therefore, we proposed a generalization to the price-gap method to account for these market responses to subsidy removal, focusing on implicit subsidies (forgone revenue).If domestic demand is not responsive to higher domestic prices, our method collapses to the simple price-gap equation.Our method eliminates some of the strong assumptions that are made when using the price-gap method, although it does assume that only Saudi Arabia's additional exports are considered with no demand response from any other country-a partial equilibrium assumption.
Using our proposed method, we demonstrated that the magnitude of total subsidies in oil exporters such as Saudi Arabia, in which a large share of subsidies represents forgone revenues, may be considerably lower than the value estimated by the simple price-gap method.For instance, the implicit crude oil subsidy in 2018 amounted to $8.6 billion using the price-gap method.If the short-run domestic price elasticity of crude oil demand is -0.06 and Saudi Arabia exported all the domestically saved crude oil, the subsidy is estimated to be around $4.6 billion, 46% smaller than the price-gap estimate.We presented our subsidy calculations across a range of elasticity values, illustrating how the implicit subsidy decreases as the elasticities increase in magnitude.Our analysis also revealed that if Saudi Arabia were to export less than the domestic quantity saved following subsidy removal, the implicit subsidy would have a steeper downward slope as the elasticities increase.
Our method can provide more accurate estimates of implicit energy subsidies in oil-exporting countries, contributing to the recognition of their national circumstances and fostering a more effective global dialogue on energy subsidy reform, which is a key policy tool for tackling climate change.Given that our method requires little additional data, there is potential for applying it to calculate implicit energy subsidies for other fossil fuel-exporting countries.

Figure A1: The relationship between the point and arc elasticities given different percentage changes in prices.
Source: authors' calculations.

APPENDIX B: COMPARISON OF PRICE-GAP ESTIMATES
We compare our price-gap estimates to the IEA (2020) and IMF (2020b), who have also estimated Saudi energy subsidies using the price-gap approach.Their latest data begin in 2010.The IMF (2020b) data end in 2017, while the IEA data goes up to 2018, as do our estimates.Figures B1 to B6 compare the values we obtain with their estimates.The IMF (2020b) estimates both pre-tax and post-tax subsidies, as it has defined them.We make use of the IMF's pre-tax values for our comparison given that we exclude externalities from our calculations.The IEA (2020) defines energy subsidies similarly, and classifies them into three categories: natural gas, oil, and electricity.It is not clear what fuels they consider for 'oil'.The IMF (2020b) provides more detail, stating that they consider gasoline, diesel, and kerosene only.The IMF therefore excludes heavy fuel oil, an important fuel in Saudi Arabia.The IMF also does not compute the subsidy for crude oil, which is burned directly in Saudi Arabia.Unlike the IEA (2020), the IMF (2020b) reports publicly the supply costs and consumer prices used in its estimates.
The fact that both organizations consider different sets of fuels in their estimates should produce discrepancies between them.That said, as Figure B1 displays, the total subsidy amounts are all in the same ballpark.Although they are similar, the components comprising total fossil fuel subsidies appear to vary greatly.Figures B3 to B5 show the subsidy estimates for refined oil products.Since the IEA (2020) does not clarify the constituents of its oil subsidy estimate, we only compare the IMF's with our own.Subsidy estimates for those three refined products, for which the IMF reports values, are well-correlated and consistent.Kerosene estimates are almost exactly the same.
Our estimates for electricity subsidies are not as high as both the IEA and IMF (see Figure B6).The IMF's electricity service costs and prices are generally much higher than the values ECRA (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018) reports.The IMF's electricity supply cost in 2011, for example, is 13 U.S. cents per kWh, and the electricity price is 6 U.S. cents per kWh.The average cost of electricity supply was below 4 U.S. cents per kWh and the average electricity price was 3.76 U.S. cents per kWh that year.

APPENDIX C: THE EFFECT OF VARYING µ ON IMPLICIT ENERGY SUBSIDIES
In Section 4.2 we revealed our method for estimating implicit energy subsidies in an oil-exporter such as Saudi Arabia.We introduced the parameter , f t µ for each fuel f , which reflects the share of domestic fuel savings following subsidy removal that is exported., f t µ varies between 0 (no additional exports) and 1 (all domestically saved fuel exported), and it depends on geopolitical and policy-driven criteria.In Section 5.2 we presented our estimates of implicit energy subsidies in Saudi Arabia for , 1 f t µ = = 1. Figure C1 shows specifically the crude oil subsidy in Saudi Arabia in 2018 when 1 = .
We also show the crude oil subsidy in Saudi Arabia in 2018 for two other values of µ.
Using Equation (9), Figure C2 illustrates how the magnitude of the crude oil subsidy changes when 0.5 µ = .It demonstrates that the surface becomes more downward sloping.In other words, forgone revenues from maintaining the subsidy fall faster when half of the saved crude oil is not exported and therefore does not contribute to forgone revenues.When μ = , the surface becomes even more downward sloping, as shown in Figure C3, because 90% of the saved crude oil following subsidy removal is not exported and thus does not contribute to the forgone revenues from maintaining a subsidy.
We alluded to the behavior of Equation ( 9) at certain values of µ in Section 4.2 and this Appendix.Here, we explore the behavior of Equation ( 9) for ranges of µ and d E ε ε .Taking crude oil as an example, Figure C4 shows a plane that is experiencing a downward force at 0.1

Figure 2 :
Figure 2: Domestic use of crude oil and oil products from 2007 to 2018.Sources: Authors' calculations using data from IEA and SAMA.

Figure 3 :
Figure 3: Domestic use of natural gas and NGLs from 2007 until 2018.Sources: Authors' calculations using data from Saudi Aramco and GAStat.

Figure 4 :
Figure 4: Saudi energy subsidies versus the price of Arab Light from 2007 to 2018.(2019$ values)

Figure 5 :
Figure 5: The forgone revenue from maintaining the crude oil subsidy for a range of ε d and ε E in 2018*

Figure 6 :
Figure 6: The forgone revenue from maintaining the gasoline subsidy for a range of ε d and ε E in 2018.

Figure 7 :
Figure 7: The forgone revenue from maintaining the diesel subsidy for a range of ε d and ε E in 2018.

Figure B1 :
Figure B1: Comparison of total energy subsidies estimates in Saudi Arabia.

Figure B2 :
Figure B2: Comparison of natural gas subsidy estimates in Saudi Arabia.

Figure B3 :
Figure B3: Comparison of gasoline subsidy estimates in Saudi Arabia.

Figure B4 :
Figure B4: Comparison of diesel subsidy estimates for Saudi Arabia.

Figure B5 :
Figure B5: Comparison of kerosene subsidy estimates for Saudi Arabia.

Figure B6 :
Figure B6: Comparison of electricity subsidy estimates for Saudi Arabia.
e., additional exports are not allowed).As a function of d E ε ε , the plane exhibits an increasingly steeper negative slope as µ approaches zero.All the other parameters in Equation (9) are fixed to the Saudi case in 2018.

Figure C1 :
Figure C1: The forgone revenue from maintaining the crude oil subsidy for a range of d ε and E ε in 2018 when

Figure C2 :
Figure C2: The forgone revenue from maintaining the crude oil subsidy for a range of d ε and E ε in 2018 when

Figure C3 :
Figure C3: The forgone revenue from maintaining the crude oil subsidy for a range of d ε and E ε in 2018 when

Figure C4 :
Figure C4: The forgone revenue from maintaining the crude oil subsidy for a range of / d E ε ε and µ in 2018.