Estimating the Impact of Energy Price Reform on Saudi Arabian Intergenerational Welfare using the MEGIR-SA Model

This paper investigates the intergenerational welfare impact of raising administered retail energy prices in Saudi Arabia, an example of an oil-exporting country with a fast growing population. To achieve this, we develop a dynamic model with overlapping generations (called MEGIR-SA), which we believe is the first empirical application of its type to be developed for an oil-exporting country. The model is used to analyze the effects of the increase in some Saudi administered energy prices implemented at the end of December 2015. In particular, the model analyzes how these price increases might affect the welfare of Saudis through a direct increase in energy expenditures, an indirect rise in Saudi public income stemming from a lower domestic demand for oil that fosters oil exports at a given level of domestic oil production, and a direct increase of the turnover of the energy sector. The two latter effects can be redistributed by the Saudi public authorities to private agents through higher current public spending and/or public investment. The analysis suggests that the increase in end-user energy prices results in a net overall favorable effect on the intertemporal welfare of all households. This mirrors the impact on the income of private agents of the surplus in public oil income associated with lower domestic consumption of oil products and recycled to private agents. Moreover, it is shown that the additional oil income associated with the increase in domestic energy prices tends to be relatively more beneficial to future generations if it is recycled through public investment. This is reinforced if the future price of oil remains relatively low. In a possible future situation of declining oil prices and domestic production, a policy that would help meet the Saudi Arabian objectives may consist of gradually increasing the fraction of the additional oil income that is recycled through public capital spending.

Justification of the introduction of parameter in the private agents' utility function: with total factor productivity gains and a Harrod-neutral technological progress, the optimal level of consumption increases over time. Without parameter , the contribution of consumption to the instantaneous utility would be all the higher as the individual would be older and/or born further in the future. To cope with this problem, Auerbach and Kotlikoff (1987) consider that the only solution is to use a parameter of relative preference for leisure that changes over time, i.e., increases with age at the rate of the technological progress. This is done here by using such parameter, which allows for stabilizing the relative contributions to utility of consumption and leisure over time in a context of a strictly positive technological progress. This setting can be traced back to Broer et al. (1994). On the problems arising with intertemporal utilities and technological progress, see Arrow (1973).
As concerns the parameter which links the age of a cohort to its productivity, we use a quadratic function: = .
. Miles, 1999). The model only deals with the effects of the public finances and the productivity of labor and capital for Saudi households and their welfare. In the model, non-Saudis only provide their labor force in the production function (the labor force in the production function includes Saudis and non-Saudis as well). It is assumed that non-Saudis send all their savings abroad and accordingly do not contribute, at least significantly, to the accumulation of productive capital in the KSA. This is rather in line with the specificities of the context of Saudi Arabia. It is assumed that remittances sent back to the KSA by Saudis living in foreign countries are negligible at the aggregate scale.

Energy module
In MEGIR-SA, there are fewer items in the energy mix of GCC countries than in Gonand and Jouvet (2015) for western countries. The model encapsulates demand for crude oil, refined products, natural gas and electricity, but not for coal, hydro, photovoltaics, nuclear, biomass, or wind. We The a <, , weighting coefficients used to compute the weighted energy prices (q <, ) are computed using observable data of consumption from past periods. For future periods, they are frozen at their level in the latest published data available: whereas the model takes account of interfuel substitution effects (see below), it does not model possible substitution effects between subcategories of energy products, for which data about elasticities are not easily available.
Since end-user prices of energy are set by the government, this version of MEGIR-SA does not model -as Gonand and Jouvet (2015) do -the real supply price at year t of the product j of energy i, or the cost of transport and distribution and/or refinery for the different energy products for natural gas and oil, or the taxes paid by an end-user of a product j of energy i at year t, the more so since there are no such taxes in the KSA.
Regulated prices of electricity: as from 2000 -when a specific royal decree was signed -we use a calibration procedure, because the tariffs become progressive and we lacked some precise data about the structure of consumption for households. In this context, we rely on the dynamics of the tariffs for households consuming close to 1.8 MWh/month. To obtain a realistic level for the average price of electricity for households over the last 15 years, we multiply this tariff by a constant of calibration to obtain an average price received by the power suppliers of SAR 0.141/kWh, which is as listed in ECRA (2014).
Derivation of the energy mix between oil, natural gas and electricity: using a CES function and knowing the levels of D ? @ A, B , D @ A, B , of the endogenous annual variations of E , provided by the general production function of the economy, along with the retail energy prices q <, 's and the exogenous elasticity of substitution between D ? @ A, and D @ A, , the variables D ? @ A, and D @ A, can be derived. This operation is iterated for each year over the whole period of simulation of the model to obtain all D ? @ A, 's and D @ A, 's for future years. The method is then used to split, at any year in the future, each D ? @ A, into D ?<@, and D C, .
Formally, one derives the demand for electricity as: and q , is the end-use price of oil products and q B, is the enduse price of natural gas in the KSA. In such a framework, the dynamics of the energy mix depends largely on the changes in the relative prices of oil, natural gas, and electricity. The more the relative price of one source of energy increases, the more its relative demand declines.
We assume that the structure of production of electricity from oil, crude or refined products, , where Eff @, , , i j stands for the thermal efficiency, in percent, of producing power from oil. Thus defined, the demand for oil in the power sector is influenced by the level of activity in the country, through D @ A, or through any other variable that modifies the intertemporal general equilibrium of model, such as demographics, policies, etc. The overall energy efficiency index, the total demand for energy and the elasticity of substitution between physical capital and energy are dealt with in the section covering the production function.

Production function
In the expression of ! , ∆ corresponds to the average optimal working time in t. Thus ∆ l corresponds to the total number of hours worked, and m n ∆ l is the labor supply expressed as the sum of efficient hours worked in t, or, as an equivalent, the optimal total flow of efficient labor in a year t -i.e., the optimal total labor supply brought by Saudis and expatriates. The Saudi labor supply is partially endogenous, insofar as ∆ is endogenous.
As mentioned in the section on the model's energy module, the variable o is the main input for a nest of CES functions allowing for computing the relative importance in the future of each component of the energy mix -i.e., D ?<@, , D C, and D @ A, , depending on changes in their relative prices (computing using the p q, 's) and exogenous public policy for some renewables. Thus the energy mix derives, through the total energy demand, from total activity in general equilibrium and from changes in energy prices which trigger changes in the relative demands for oil, natural gas, coal, electricity, and renewables. Accordingly, the modeling allows for a) energy prices to influence the total demand for energy, and b) total energy demand, along with energy prices, to define in turn the demand for different energy vectors.

Saudi public finances
The other public revenues ( where m n ∆ l is the total efficient labor force and • #‚#q <, B − q <, B , * D †,2016 ƒ, " <…B is the initial, permanent surplus of public income in real terms which stems from the one-off permanent increase in retail Saudi energy prices as decided in 2016, that benefits the public energy sector and feeds into the "other revenues" (r ? i C, ) of the Saudi government.
This model delivers simulations over several decades into the future, during which the populations of the GCC countries will probably experience aging. This will impact the financial situation of public PAYG schemes. The model considers this phenomenon by modeling a PAYG system that is financed by social contributions ‡ ,ˆ that are proportional to gross labor income 5 .
The full pension Φ , is itself proportional to past labor income, depends on the age of the individual and on the age at which an individual is entitled to obtain a full pension. The pension of the average representative individual is flat over time -i.e., not wage indexed -but is adjusted each year by the change in the number of pensioners in each cohort. In all scenarios, the future imbalances of the PAYG regime, caused by demographic aging, are covered by a rise in ‡ ,ˆ.

Parameterization
Oil and energy sector: unless otherwise stated, the domestic production of crude oil P ?<@,Š‹{, is set exogenously in the model by authorities close to its current level, i.e., 10.6 MMbbl/d in the future.
The elasticity of substitution between oil and natural gas is 0.3 in the model. For future periods, we assume that the USD/SAR exchange rate remains constant at its current levels. The thermal efficiency of producing electricity from fossil fuels is constant at 35 percent.
Demographics: all matrices are first computed with five-year age groups, then linearly interpolated to obtain annual data. Total population data come from the World Bank. For the labor force projection, our research uses participation rates by age group and by gender as computed by the International Labor Organization. We checked that this method of computing is compatible with data provided by the World Bank relating to the KSA labor force. In figures for the employed population, we use employment rates by age group and gender provided by the International Labor Organization. We checked that this method of computing is compatible with data provided by the IMF relating to the employed population in the KSA. The structure of each matrix by age group is assumed to remain constant after 2050, with only the levels increasing at a rate set at +2 %%every five years -i.e., close to +0.4 % per year after 2050, slightly above demographic growth rates currently experienced by most western countries.
OLG framework/households' program: the households' psychological discount rate OE is set at 2 %per annum, in line with much of the empirical literature (Gourinchas and Parker, 2002). Parameter • -the preference for leisure relative to consumption -is set to 0.25, in line with empirical literature.
The elasticity of substitution between consumption and leisure in the instantaneous utility function (1/ Ž) is equal to unity to avoid a temporal trend in the conditions for the optimal working time (see Auerbach and Kotlikoff, 1987, p.35 (2013) rely on a log function, thus with an intertemporal substitution elasticity tending asymptotically to 1. Our assumption is the mean between the values used by these two latter papers.
Production function: the elasticity of substitution between capital and labor is set at 0.8. A wide but still inconclusive body of empirical literature has attempted to estimate the elasticity of substitution between capital and labor in the CES production function. On average, these studies suggest a value close to unity.
The elasticity of substitution between energy and capital (• ) is 0.4. Hogan and Manne (1977) have suggested that the elasticity of substitution between energy and capital in a CES function could be proxied by the price elasticity of energy demand, which is easier to assess. It is generally agreed that physical capital and energy can be partial substitutes, especially in the long run.
The weighting parameter (a) in the CES production function with energy is set at 0.1. In the CES nest, ' refers to aggregate production in volume, and thus takes account of intermediate consumption (here, ' ). Accordingly, the weighting parameter (a) should not be computed as the share of the value added of the energy sector in GDP but, preferably, as the share of intermediate consumption in energy items, as a fraction of private non-oil GDP. In developed countries, this yields around 10 percent, a figure relatively stable over time.
The weighting parameter " in the K-L production function is set at 0.3. In models incorporating a depreciation rate (Börsch-Supan et al., 2003), the value for this parameter is usually higher, e.g.,  The average effective age of retirement is set at 61 years. The level of the average replacement rate is computed as the ratio of pensions received per capita over gross wages received per capita. It is set at 100 %on Saudi data (OECD, 2015).
Calibration and numerical convergence of the model: as in Gonand and Jouvet (2015), and contrary to other studies, the model is not calibrated on some technical parameters -e.g., relative aversion to risk -so as to produce broadly observed

ANNEX 2: IMPACT OF A CHANGE IN SAUDI OIL EXPORTS ON THE INTERNATIONAL OIL PRICE AND ASSOCIATED SIMULATIONS. Background
As explained in the main text, given the very long-run analysis undertaken for this research we assume that a change in Saudi oil exports would not impact on the international oil price; in other words, we assume that the elasticity of the international price with respect to Saudi oil exports is zero. However, there are several reasons to question the zero-elasticity assumption, at least in the short run. 4 Many theoretical models of the world oil market view OPEC and/or Saudi Arabia as a dominant firm leader facing a downward-sloping excess demand curve (i.e., world demand minus fringe supply) of oil (cf. Huppmann and Holz, 2012). Moreover, events suggest that in the past OPEC managed to raise (lower) oil prices by limiting (increasing) its production and lowered the price of oil by increasing its production (Yergin, 2012). Furthermore, several studies have concluded when OPEC's spare capacity is low (high) oil prices tend to be more (less) volatile  suggesting that OPEC face a downward sloping demand curve so that any decrease (increase) in oil exports by Saudi Arabia/OPEC would increase (decrease) the international oil price. In which case, a change in Saudi oil exports would impact the international price. That said, there is some evidence to suggest otherwise such as Killian (2009) and Killian and Hicks (2013), which suggests that an oil supply shock does not necessarily trigger a sizeable and long-lasting impact on the international price of oil.
Therefore, although we assume that the elasticity of the international price with respect to Saudi oil exports is zero, given our focus on the very long-run, we felt it would be prudent to check the sensitivity of this assumption given the discussion above. The following sections of Annex 1 details the estimation of the key elasticity and the impact of using this has on the model simulation results.

Conceptual model
Oil prices, like any other prices, can be analyzed using a supply-demand framework (see, Kilian, 2008;Aastveity et al., 2012). Several previous studies modeled oil prices using an augmented supply-demand framework, in which other variables of interest are included in the analysis. For example, in addition to oil supply and demand fundamentals, Wang and Sun (2017) included wars and political tensions, economic policy uncertainty, Kilian and Lee (2014) and Kaufmann (2011) 4 We are grateful for an anonymous referee for urging us to consider these issues more than we did initially. added oil inventories, Liu et al. (2016) considered derivative market speculation, Chen et al. (2016) used political risk and speculation. Additionally, Fan and Xu (2011) assess the impact of the price of gold, among other explanatory variables, on the price of oil. The idea being that gold and oil can be alternatives for each other in international commodity markets. Bataa and Park (2017) examined the separate effect of the USA shale oil production, their variable of interest, alongside global oil production and aggregate demand on the oil price. Our framework, outlined below, is similar to theirs but our variable of interest is Saudi oil exports rather than Saudi oil production. Additionally, we include the prices of natural gas and coal into the analysis inspired by Brown and Yucel (2008), Bachmeir and Griffin (2006), Zamani (2016), Zellou and Cuddington (2012), Villar and Joutz (2006), Asche et al. (2006), and Hartley et al. (2007), who show that the prices of oil and natural gas move together in the long-run.
Therefore, to estimate the key elasticity we used the following specification in the empirical testing and estimation.
Definitions of the variables are given Table A2.1 with all variables entered in Equation (A2.1) in natural logarithm form and hence expressed in lower case. Given this, the coefficients • < represent the elasticities to be estimated econometrically, in particular • B is the elasticity of the real international oil price with respect to Saudi oil exports. § is the error term. Equation (A2.1) expresses the real price of Arabian light (opar) as a function of Saudi crude oil exports (oxs), world oil demand (ocw), world oil supply excluding Saudi exports (opw) and the real price of the substitutive goods, i.e., natural gas (npwr) and coal (cpwr).
We also estimate and test Equation (A2.2), in which both the demand-and supply-sides are represented by the world GDP (also defined in Table A2.1).
Where again all variables are in natural logarithms so the coefficients ¨< represent the elasticities to be estimated econometrically, with in particular intercept ¨ and ª is the error term.

Data and methodology
We use annual time series data over the period 1980-2017 in the empirical analysis. Table A2.1 documents the variables, their notation, description and sources. Cointegration and error correction modeling methodology is employed for the empirical testing and estimation. We first check integration properties of the data, applying the Augmented Dickey-Fuller (ADF, Dickey and Fuller, 1981) unit root test to check stationarity of our variables. As a robustness check, we also use ADF test with structural breaks developed by Perron (1989), Perron and Vogelsang (1992a, 1992b, and Vogelsang and Perron (1998). The Autoregressive Distributed Lags Bounds Testing (ARDLBT) method is employed to test for the existence of the cointegration and estimate the long-run relationship between our variables. The ARDLBT method is selected because it outperforms its counterparts and yields more consistent results in small samples (Pesaran and Shin, 1999;Pesaran et al., 2001). To have robust interferences about the cointegration properties of the variables, we use small sample bias correction in the ARDLBT by applying Narayan (2005) critical values.

Results of the Empirical Analysis.
All the variables are found to be non-stationary in their log-level and stationary in the first difference of their log-level. In other words, the variables follow the integrated order of one, I(1) process. The unit root test results are not reported here and the details are available from the authors under request. The maximum lag order is set to three and the Schwarz information criterion is preferred to pick up the optimal lag length (see Pesaran and Shin, 1999;Pesaran et al., 2001) (1) and (2). Notes: opar is the dependent variable in the estimations; ± ‹™ , ± {«™¬ , ± ¬-®« , ± ²² ¦ ± ³ denote F statistics to test the null hypotheses of no serial correlation, no autoregressive conditioned heteroscedasticity, no heteroscedasticity in the residuals and no functional form mis-specification and no cointegration in the Wald test, respectively; °' -indicates the Jarque-Bera statistic to test the null hypotheses of normal distribution of the residuals. " denotes SoA coefficient; * indicates that sample statistic is greater than upper bound of the critical value of Pesaran et al. (2001) at the 1% significance level in the given combination of the regressors and Intercept is included in the long-run equation. A and B indicate that sample statistic is greater than upper bound of the critical value of Narayan (2005) at the 1% and 5% significance levels, respectively in the given combination of the regressors, number of observations and Intercept is included in the long-run equation. Coef. and Prob. mean coefficient and its probability. Constant is omitted for simplicity; Estimation period: 1983-2017.

Discussion of the Results
We find a cointegrated relationship between the Arabian light oil price and its determinants in both specifications even after applying the small sample bias correction, which is consistent with our a-priori expectations that the relationship between the real oil price and its determinants is in line with the supply-demand framework. The numerical results of the relationships are given in Table A2 (11.2%) in 2014. They further discuss that Saudi was the number one oil exporter in the world by holding 17% of the total world crude oil exports in 2015 and produced 12.7% of the total world crude oil including lease condensate during 2010-2014.
Given our main interest in this indicative econometric analysis is to ascertain what the impact of a change on Saudi crude oil exports might have on the real price, we do not discuss in detail the impacts of the other explanatory variables here. However, it is worth mentioning that they also have economically expected, and statistically significant effects and findings are consistent with those of the earlier studies mentioned above.
Our estimates of the elasticity of the real oil price to Saudi oil exports of somewhere between -0.43% and -0.47% stems from an econometric analysis using data over the relatively recent past. The very long run elasticity however might well be lower. For example, Blazquez et al. (2018), using an analytical relationship parametrized on real Saudi data, suggest a value of -0.3. Thus we feel it is prudent to assume a value -0.5 as an alternative to that in the main text, which assumes that this key elasticity is to zero. The results of the alternative model simulations are therefore discussed below.
Alternative results for the MEGIR-SA model Compared to the scenarios with a zero elasticity of the price of oil to Saudi exports, the declining profile of the price of oil over time in all scenarios entails an upward impact on the price of oil when this elasticity is set at -0.5. In scenarios B, the intertemporal profile of Saudi oil exports declines relatively slowly at least up to the 2040s: thus the effect of endogenizing the price of oil builds up progressively and begins to materialize significantly in the 2040s. In scenarios C, the decline of future Saudi oil exports is steeper, and so the upward effect on oil prices is stronger. This effect accounts for the fact that the impact of the reform on the households' intertemporal welfare is slightly higher when the elasticity is -0.5 rather than 0.
Compared to the no-reform, baseline scenario A, the upward impact of the Saudi oil exports stemming from higher administered energy prices on the domestic market (scenarios B and C) triggers a downward influence on the price of oil when the elasticity is assumed to be -0.5. This impact kicks in from the implementation of the reform onwards. For scenarios B, this effect accounts for the fact that the impact of the reform on the households' intertemporal welfare is slightly lower when the elasticity is -0,5 rather than 0.