THE ECONOMIC COST OF FUEL PRICE SUBSIDIES IN GHANA By Roland Oduro Ofori A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Agricultural, Food and Resource Economics - Master of Science 2015 i ABSTRACT THE ECONOMIC COST OF FUEL PRICE SUBSIDIES IN GHANA By Roland Oduro Ofori I adapt the Harberger formula for deadweight loss to develop approximations for the deadweight loss created by multiple fuel price subsidies. I also estimate the own - price , cross - price , and income elasticit ies of demand for gasoline and diesel in Africa. I use data on fuel prices and sales in combination with my formulas and e lasticity estimates to calculate the deadweight loss of fuel price subsidies in Ghana from 2009 to 2014. I show that the average efficiency cost of the gasoline and diesel price subsid ies in Ghana is 0.8% of fuel price subsidy transfers . This result stress es the futility of basing subsidy reforms on economic efficiency losses, which are relatively small due to very inelastic ener gy demand , and the need for such reforms to be motivated by the poor - targeting of subsidies to low - income households and the impact of subsidies on government debt - financing . iii ACKNOWLEDGMENTS I express my deepest appreciation to the MasterCard Foundation Scholars Program at Michigan S tate University for providing me with comprehensive financial support. I feel honored to be part of th is prestigious p rogram . Second, I thank my major advisor, Dr. Soren Anderson, for being an inspirational mentor, a great teacher, and a friend. I have learn ed a lot from him as a researcher . I also thank my other committee members, Dr. John Hoehn and Dr. Mark Skidmore , for their helpful comments. iv TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ......................... vi LIST OF FIGURES ................................ ................................ ................................ ...................... vii CHAPTER 1 - INTRODUCTION ................................ ................................ ................................ .. 1 1.1 Background and Rationale ................................ ................................ ................................ .... 1 1.2 Fuel Consumption in Ghana ................................ ................................ ................................ .. 3 1.3 Fuel Subsidies in Ghana ................................ ................................ ................................ ...... 11 CHAPTER 2 - THEORY OF DEADWEIGHT LOSS ................................ ................................ . 17 2.1 Introduction ................................ ................................ ................................ ......................... 17 2.2 Fuel Externalities ................................ ................................ ................................ ................. 18 2.3 Harberger Formula and Deadweight Loss from Taxation ................................ .................. 20 2.4 Adapting the Harberger Formula to Price Subsidies ................................ ........................... 22 CHAPTER 3 - FUEL DEMAND ELASTICITIES ................................ ................................ ...... 29 3.1 Model Specification ................................ ................................ ................................ ............ 29 3.2 Sources of Data ................................ ................................ ................................ ................... 30 3.3 Endo geneity and Instrumental Variables ................................ ................................ ............ 30 3.4 Estimation and Results ................................ ................................ ................................ ........ 32 3.5 Comparing Elasticity Estimates ................................ ................................ .......................... 37 CHAPTER 4 - COST OF FUEL PRICE SUBSIDIES ................................ ................................ . 41 4.1 Introduction ................................ ................................ ................................ ......................... 41 4.2 Simple M ethod ................................ ................................ ................................ .................... 41 4.3 General Equilibrium Method ................................ ................................ .............................. 44 4.4 Sensitivity Analysis ................................ ................................ ................................ ............. 46 CHAPTER 5 - CONCLUSION ................................ ................................ ................................ .... 48 APPENDICES ................................ ................................ ................................ .............................. 49 Appendix 1 - Deadweight Loss Formula ................................ ................................ .................. 50 Appendix 2 - Proof of Deadweight Loss Formula ................................ ................................ .... 51 v Appendix 3 - Countries and Summary Statistics ................................ ................................ ...... 52 Appendix 4 - Exchange Rates ................................ ................................ ................................ ... 53 Appendix 5 - Test for Endogeneity of Prices ................................ ................................ ............ 54 Appendix 6 - Tests for Heteroskedasticity and Autocorrelation ................................ ............... 61 Appendix 7 - Stata Outputs for Model Estimation ................................ ................................ .... 63 Appendix 8 - Test for the Significance of Long - Run Coefficients ................................ ........... 71 REFERENCES ................................ ................................ ................................ ............................. 75 vi LIST OF TABLES Table 1.1 Distribution of Fuel Price Subsidies Across Income Groups in Ghana (%) ................. 15 Table 3.1 Results of Model 1 ................................ ................................ ................................ ........ 33 Table 3.2 Results of Model 2 ................................ ................................ ................................ ........ 35 Table 3.3 Long - run Demand Elasticity Estimates for Gasoline and Di esel ................................ . 39 Table 3.4 Long - run Demand Elasticity Estimates for Kerosene and LPG ................................ ... 40 Table 4.1 Economic Cost of Gasoline Price Subsidies in Ghana ................................ ................. 42 Table 4.2 Economic Cost of Diesel Price Subsidies in Ghana ................................ ..................... 42 Table 4.3 Economic Cost of Kerosene Price Subsidies in Ghana ................................ ................ 43 Table 4.4 Economic Cost of LPG Price Subsidies in Ghana ................................ ........................ 43 Table 4.5 Economic Cost of Gasoline and Diesel Price Subsidies in Ghana ............................... 45 Table 4.6 Economic Cost of Gasoline and Diesel Price Subsidies in Ghana ............................... 45 Table 4.7 Economic Cost of Gasoline and Diesel Price Subsidies in Ghana ............................... 46 Table 4.8 Economic Cost of Gasoline and Diesel Price Subsidies in Ghana ............................... 47 Table 3.5 African Countries by Region ................................ ................................ ........................ 52 Table 3.6 Summary Statistics of Variables ................................ ................................ ................... 52 Table 3.7 Description of Variables in Model ................................ ................................ ................ 54 vii LIST OF FIGURES Figure 1.1 Fuel Consumption and Real GDP in Ghana, 1986 - 2012 ................................ .............. 4 Figure 1.2 Shares of Fuel Consumption in Ghana, 1986 - 2012 ................................ ....................... 6 Figure 1.3 Trends in Gasoline Consumption and Retail Prices in Ghana ................................ ...... 7 Figure 1.4 Annual Log - changes in Gasoline Consumption and Retail Prices in Ghana ................ 7 Figure 1.5 Trends in Diesel Consumption and Retail Prices in Ghana ................................ .......... 8 Figure 1.6 Annual Log - changes in Diesel Consumption and Retail Prices in Ghana .................... 8 Figure 1.7 Trends in Kerosene Consumption and Retail Prices in Ghana ................................ ...... 9 Figure 1.8 Annual Log - changes in Kerosene Consumption and Retail Prices in Ghana ............... 9 Figure 1.9 Trends in LPG Consumption and Retail Prices in Ghana ................................ ........... 10 Figure 1.10 Annual Log - changes in LPG Consumption and Retail Prices in Ghana ................... 10 Figure 1.11 Gasoline Prices and Subsidies in Ghana, 2009 - 2014 ................................ ................ 13 Figure 1.12 Diesel Prices and Su bsidies in Ghana, 2009 - 2014 ................................ .................... 13 Figure 1.13 Kerosene Prices and Subsidies in Ghana, 2009 - 2014 ................................ ............... 14 Figure 1.14 LPG Prices and Subsidies in Ghana, 2009 - 2014 ................................ ....................... 14 Figure 2.1 Private Deadweight Loss and Subsidy ................................ ................................ ........ 18 Figure 2.2 Social Deadweight Loss and Subsidy ................................ ................................ .......... 19 Figure 2.3 Simple Harberger Triangle ................................ ................................ .......................... 22 Figure 2.4 DWL of Gasoline Price Subsidy ................................ ................................ ................. 24 viii Figure 2.5 DWL of Sequential Gasoline and Diesel Sub sidies ................................ .................... 26 Figure 2.6 DWL of Simult aneous Gasoline and Diesel Subsidies ................................ ............... 28 Figure 3.1 Exchange Rates in Selected African Countries ................................ ........................... 53 Figure 3.2 Instrument Relevance Test for Gasoline Price (1) ................................ ...................... 55 Figure 3.3 Instrument Relevance Test for Gasoline Price (2) ................................ ...................... 56 Figure 3.4 Instrument Relevance Test for Diesel Price (1) ................................ .......................... 57 Figure 3.5 Instrument Relevance Test for Diesel Price (2) ................................ .......................... 58 Figure 3.6 Fixed Effects Results for Gasoline Model (1) ................................ ............................. 63 Figure 3.7 Fixed Effects Results for Diesel Model (1) ................................ ................................ . 64 Figure 3.8 First Difference Results for Gasoline Model (1) ................................ ......................... 65 Figure 3.9 First Difference Results for Di esel Model (1) ................................ ............................. 66 Figure 3.10 Fixed Effects Results for Gasoline Model (2) ................................ ........................... 67 Figure 3.11 Fixed Effects Results for Diesel Model (2) ................................ ............................... 68 Figure 3.12 First Difference Results for Gasoline Model (2) ................................ ....................... 69 Figure 3.13 First Difference Results for Diesel Model (2) ................................ ........................... 70 1 CHAPTER 1 - INTRODUCTION 1.1 Background and Rationale In recent years, Ghana has recorded commendable developments. According to the Ministry of real Gross Domestic Product ( GDP ) grew at a record 15 % in 2011. In addition , the country discovered crude oil in commercial qu antities in 2007, and began producing oil in 2010. The government of Ghana has been equally faced with c hallenges of inadequate revenue generation and over - spending. Sources of such challenges include the implementation of the new public sector salary policy, Single Spine Pay Policy , in 2010 and the subsidization of refined petroleum products . E xpenditure on compensation of employees was 74.4 % of tax revenue for the first three quarters of 2013 (MOF). With a budget deficit of 12 .1% of G DP in 2012, and a total public debt of about 49% of GDP in August 2013 (MOF), Ghana is surely facing fiscal difficulties . E xplicit fuel subsidies to the Tema Oil Refinery (TOR) and oil distributors reached 2.2 % of GDP in 2004 (Coady et al, 2006). According to the African Development Bank (2012), fuel consumption subsidies in Ghana amounted to US $ 276 million in 2011. The g overnment spent US $ 85 million on fuel subsidies in the second quarter of 2014 (IMANI Ghana, 2015). The budgetary cost of fuel subsidies in Ghana ha s been increasing partly as a result of the depreciation of the Ghana C edi (GHS) against the United States Dollar (US$) . The GHS - US$ exchange rate increased from 0.16:1 in 1996 to 1.95:1 in 2013, with an average of 0.92:1 over the period. With an estimate of US$ 410 billion in total expenditure globally on fuel subsidies in 2010, subsidy 2 reform s are necessary since subsidies deprive economies of scarce resources ( African Development Bank , 2012) . To save government the cost of prov iding fuel price subsidies , and to allow for a more effective use of public funds, the government of Ghana took a bold step to implement the politically unfriendly decision of fuel price deregulation on July 1, 2015. This means the government will no longer determine fuel prices and provide subsidies for gasoline, diesel, kerosene, and liquefied petroleum gas (LPG) . Bulk Distribution Companies (BDCs) and Oil Marketing Companies (OMCs) set their own pri ces based on an agreed pricing formula . Conversely, residual fuel oil and premix fuel, which are consumed by industrial plants and fishing boats , respectively, are still being subsidized, and their prices are set by the government. Whether the government will be able to sustain the deregulation is an open question . Political promises during national elections and oil price hikes may lead to pressure from political opponents, interest groups, and civil societies to force the governmen t to return to the subsidization of fuel prices in the near future. Thus, e valuating the cost of fuel price subsidies in Ghana is important , as the government reinforces its resolve to permanently abolish fuel subsidies to enable more prudent use of public funds to address critical expenditures in health, education, and infrastructure . T he goal of this research is to estimate the economic cost of fuel price subsidies in Ghana. First, I estimate the own - price, cross - price, and income elasticities for gasoline and diesel demand in Africa. Second, I extend the comprehensive Harberger formula to approximate the deadweight 3 loss associated with fuel price subsidies in Ghana from 2009 to 2014. Naively ignoring th e impact of cross - price effect s on deadweight loss , the total cost of fuel price subsidies for gasoline and diesel is GH S 2 6 . 38 million (US$ 15.40 million) from 2009 to 2014 , with a cost of GHS 4. 4 0 million (US$ 2.57 million) per year. Accounting for cross - price effects , however, the total cost of fuel price subsidies f or gasoline and diesel falls almost by half to GHS 13 . 61 million (US$ 8.27 million) from 2009 to 2014, with an annual cost of GHS 2. 27 million (US$ 1.38 million) . A gasoline subsidy, by inducing consumers to choose gasoline over diesel, partially mitigates the distortion caused by a diesel subsidy, and vice versa. Thus, the combined deadweight loss of the two subsidies together is significantly less when accounting fo r these cross - price substitution effects. On average, the cost of fuel price subsidies for gasoline and diesel in Ghana is less than 1 % of subsidy transfers by the government. I also show that changes in the absolute magnitude of demand elasticities result s in a proportional change in the size of calculated deadweight loss. Chapter 1 continues with a review of fuel consumption and subsidies in Ghana. After presenting the theory of deadweight loss in Chapter 2, Chapter 3 follows with the estimation of fuel demand elasticities for the African region using a panel data model . Chapter 4 follows with the calculation of the economic cost of fuel price subsidies for gasoline, diesel, kerosene, and LPG in Ghana from 2009 to 2014. Chapter 5 concludes with a summary and agenda for future research. 1.2 Fuel Consumption in Ghana Refined petroleum product consumption in Ghana has been on the rise over the past three decades. According to data from l consumption for gasoline, diesel, kerosene, and LPG was 12,000 barrels per day (bbl/d) in 1986. 4 With a yearly average consumption of 29,000 bbl/d and a growth rate of about 8 %, total consumption for these fuels increased to 70,000 bbl/d in 2012 . N atural gas consumption increased from 0.1 billion cubic meters (bcm) in 2010 to 0.4 bcm in 2012 . Coal consumption in 2013 was 30,000 metric tons. Real GDP has also been on the increase at an increasing rate year - on - year over the same period, with a record database, real GDP increased from US$ 4.58 billion to US$ 18.52 billion, with an average growth rate of 6% per year from 1986 to 2012. Figure 1.1 shows the trend in fuel consumpti on and real GDP over the period in Ghana. Figure 1.1 Fuel Consumption and Real GDP in Ghana, 1986 - 2012 0 2 4 6 8 10 12 14 16 18 20 0 20 40 60 80 100 120 140 160 Real GDP in billion 2005 US$ Consumption in petajoules Gasoline Diesel Kerosene LPG Real GDP 5 The relation between fuel consumption and real GDP in Ghana is no surprise since various studies have shown that there is a strong relationship between energy consumption and economic growth . Abaidoo ( 2011 ) used the Granger - c ausality test to show the exist ence of a unidirectional causal relationship running from GDP growth to energy consumption in Ghana, finding that a 1% increase in GDP indu ces approximately a 2% growth in electric energy consumption . Adom (2011) , using the Granger - c ausality test , also reveal ed the existence of unidirectional causality running from economic growth to electricity consumption in Ghana. Bildirici ( 2012) estimated the causal relationship bet wee n electricity consumption and economic growth with Markov Switching Vector Auto Regression and Markov Switching Granger Causality metho ds for several emerging countries ( Brunei, Cameron, C รด te d'Ivoire, Nigeria, South Africa, Togo and Zimbab we) and provided evidence of bi - directional Granger - c ausality bet ween GDP and electricity consumption. Bartleet and Gounder ( 2010 ) showed Granger - causality from real GDP to energy consumption in New Zealand . Trends in the composition of fuel consumption in Ghana have changed over the years. Starting in 1986, gasoline accounted for the largest share at 40%, followed by diesel at 38%, kerosene at 20%, and LPG at 2%. In 2012, diesel accounted for the largest sha re at 57%, followed by gasoline at 33%, LPG at 9%, and kerosene at 1%. According to the Nationa l Petroleum Authority (NPA), the higher demand for diesel is driven mostly by the industrial sector, but gasoline dominates the transportation sector in terms of consumption. As income increases, households tend to use more LPG and less kerosene as cooking fuels. Also, some commercial drivers have found the use LPG to be cheaper than gasoline and diesel in some parts of the country ( Biscoff et al, 2012). These 6 dyn amics have led to an increase in LPG consumption at the expense of kerosene during the period. Figure 1.2 shows the shares of fuel consumption from 1986 to 2012. Figure 1.2 Shares of Fuel Consumption in Ghana, 1986 - 2012 Data from the National Petroleum Authority (NPA) shows an upward trend in retail prices for all four fuels from 1989 to 2012. The retail prices, which are largely driven by international crude oil prices , exchange rates , and subsidies , have been increasing over the period. Trend s and annual log - changes (variations ) in retail prices and the consumption for each fuel are displayed in Figures 1.3 to 1. 10 . Notice that annual quantity changes and annual price changes often move in opposite directions. Below, I use this variation (and similar variation from other African countries) to estimate demand elasticities. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Gasoline Diesel Kerosene LPG 7 Figure 1.3 Trends in Gasoline Consumption and Retail Prices in Ghana Figure 1. 4 Annual L og - change s in Gasoline Consumption and Retail Prices in Ghana - 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 Price in Ghana Pesewas/liter Consumption in petajoules Gasoline Consumption Gasoline Retail Prices -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Gasoline Consumption Gasoline Retail Prices 8 Figure 1. 5 Trend s in Diesel Consumption and Retail Prices in Ghana Figure 1. 6 Annual L og - changes in Diesel Consumption and Retail Prices in Ghana - 20 40 60 80 100 120 140 160 180 200 0 10 20 30 40 50 60 70 80 90 Price in Ghana Pesewas/liter Consumption in petajoules Diesel Consumption Diesel Retail Prices -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Diesel Consumption Diesel Retail Prices 9 Figure 1. 7 Trends in Kerosene Consumption and Retail Prices in Ghana Figure 1. 8 Annual L og - changes in Kerosene Consumption and Retail Prices in Ghana - 20 40 60 80 100 120 0 2 4 6 8 10 12 14 16 Price in Ghana Pesewas/liter Consumption in petajoules Kerosene Consumption Kerosene Retail Prices -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Kerosene Consumption Kerosene Retail Prices 10 Figure 1. 9 Trends in LPG Consumption and Retail Prices in Ghana Figure 1. 10 Annual L og - changes in LPG Consumption and Retail Prices in Ghana - 20 40 60 80 100 120 140 0 2 4 6 8 10 12 14 16 Price in Ghana Pesewas/kilogram Consumption in petaajoules LPG Consumption LPG Retail Prices -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 LPG Consumption LPG Retail Prices 11 1.3 Fuel Subsidies in Ghana According to the Energy Center at the Kwame Nkrumah University of Science and Technology (KNUST), the government introduced the automatic price setting mechanism in 2001 . The mechanism was designed to reduce the subsidy burden on government by adjusting do mestic retail prices of refined petroleum products to reflect changes in international oil prices, and to relieve the Tema Oil Refinery (TOR) of its accumulating debts due to fuel subsidies over the years. However, there was pressure on government to abolish the automatic adjustment due to high global oil prices in 2002. In 2003, the mechanism was re - introduced and the adjust ment resulted in about a 90% increase in fuel prices and an 8.5% decline in real income (KNUST) . The mechanism was abandoned in 2004 following public pressure and fuel subsidies amounted to 2.2% of GDP ( Cooke et al, 2014) . F uel prices increased significant ly in mid - 2009, early 2011 , 2012, and 2013 ( Cooke et al, 2014) . The removal of fuel subsidies largely occurred in February 2013 when prices of gasoline , diesel, kerosene, LPG, marine diesel, and residual fuel oil increased by 15 % to 50% , with th e exception of p remix fuel which remain ed subsidized. G radual increases occurred in 2013 which saw the price of gasoline increasing by almost 30% in total from G hana Pesewas (GH p ) 170.80 per liter at the beginning to the market rate of GHp 222 per liter later in the year (Cooke et al, 2014) . On July 1, 2015, fuel prices for all refined petroleum products , except premix fuel and residual fuel oil , were abolished. Prior to the removal of fuel price subsidies in July 2015, the National Petroleum Authority (NPA) negotiate d with refined petrol eum product import e rs , distributors , and marketers to determine the full - pass - through prices for the products, usually every two weeks. The full - pass - through price, or 12 the price at which the full cost of the product is passed ont o the consumer , constitutes international refined petroleum product price, the cost of shipment, margins for suppliers, distributors, and marketers, and taxes and levies . The full - pass - through pr ice represents the marginal cost of fuel. The government provides fuel price subsidies to help lessen the impact of increases in international fuel prices on consumers. The retail price of fuel products in Ghana is the full - pass - through price minus the sub sidy. Occasionally, the government decides to maintain the existing retail prices of fuel when international fuel prices fall , leading to a net tax on fuel. By doing so, the government generates some revenue to defray the budgetary cost of providing fuel price subsidies. Figures 1. 11 to 1.1 4 show the trend s in retail prices, full - pass - through prices, and price subsidies in Ghana from 2009 to 2014. Since there is no explicit data on the amount of fuel price subsid ies provided per unit of fuel , I calculate the amount of subsidy per unit of fuel as the positive difference between the full - pass - through and retail prices. 13 Figure 1. 11 Gasoline Prices and Subsidies in Ghana, 2 009 - 2014 Figure 1. 12 Diesel Prices and Subsidies in Ghana, 2009 - 2014 -100 -50 0 50 100 150 200 250 300 350 02-Jan-09 02-Jan-10 02-Jan-11 02-Jan-12 02-Jan-13 02-Jan-14 GH Pesewas/liter Retail Price Full - Pass - Through Price Subsidy -50 0 50 100 150 200 250 300 350 02-Jan-09 02-Jan-10 02-Jan-11 02-Jan-12 02-Jan-13 02-Jan-14 GH Pesewas/liter Retail Price Full - Pass - Through Price Subsidy 14 Figure 1. 13 Kerosene Prices and Subsidies in Ghana, 2009 - 2014 Figure 1.1 4 LPG Prices and Subsidies in Ghana, 2009 - 2014 -50 0 50 100 150 200 250 300 350 02-Jan-09 02-Jan-10 02-Jan-11 02-Jan-12 02-Jan-13 02-Jan-14 GH Pesewas/liter Retail Price Full - Pass - Through Price Subsidy -100 -50 0 50 100 150 200 250 300 350 02-Jan-09 02-Jan-10 02-Jan-11 02-Jan-12 02-Jan-13 02-Jan-14 GH Pesewas per Liter Retail Price Full - Pass - Through Price Subsidy 15 High - income households benefit more from fuel subsidies since their consumption of fuel is the highest among income groups , hence f uel price subsidies have largely failed to meet distributional goals since they benefit the rich more than the poor ( Cooke et al , 2014) . The richest consumption quintile receives more than 4 4 % of fuel subsidies for gasoline, kerosene, and LPG , while the poorest quintile receives less than 8 % o f these subsidies in Africa (Granado et al, 2010). In Ghana, the richest quintile of the population overall received GHS 15.86 per capita from fuel price subsidies , almost 78% , while the poorest received just GHS 2.23 per capita, less than 3% , in a year ( Cooke et al , 2014) . Looking at particular fuels, t he richest quintile received about 92.8% of gasoline, 96.5% of diesel, and 85.5% of LPG subsidies, while the poor est quinti le received less than 1% of subsidies for these fuels ( Cooke et al , 2014) . Although one might expect poor households to benefit most from kerosene subsidies , since poor households use a lot of kerosene, th is is not the case. The poorest quintile received about 10.7% of kerosene subsidies while about 36.4% went to the richest quintile, as shown in Table 1.1 ( Cooke et al , 2014) . Table 1.1 Distribution of Fuel Price Subsidies Across I ncome Groups in Ghana (%) Subsidies Income Quintile 1 2 3 4 5 Gasoline 0.9 0 1.35 1.62 3.35 92.78 Diesel 0.12 0.63 1.45 1.33 96.46 LPG 0.16 0.69 2.17 11.43 85.55 Kerosene 10.69 13.88 18.06 20.96 36.42 Total 2.97 4.14 5.83 9.27 77.8 0 1 - Poorest, 5 - Richest. Source: Cooke et al ( 2014 ) . 16 Studies have also shown that the phasing - out of fuel subsidies and the scaling - up of social protection programs could be a cost - effective and more sustainable way of protecting the poor against fuel price increases, reducing income inequality and poverty in developing countries. A study by Cooke et al . ( 2014 ) revealed that e xpanding the cash transfer program ( Livelihood Empo w erment Against Poverty ), which provides direct cash transfers to the poor , could entirely reverse the n egative impact of fuel price increases arising from fuel subsidy reform on poor households. 17 CHAPTER 2 - THEORY OF DEADWEIGHT LOSS 2.1 Introduction Deadweight loss, or excess burden, is the loss of economic efficiency. Deadweight loss can occur consumption differs from the marginal social benefit. In other w ords, deadweight loss can occur when equilibrium is not Pareto optimal . Deadweight loss may arise as a result of taxes, subsidies, monopoly pricing, or externalities. Rational consumers are expected to increase consumption of fuel when the price is set bel ow private marginal cost, as a result of a price subsidy. By consuming up to a point where marginal cost exceeds marginal willingness - to - pay, deadweight loss is created in the market. Fuel s ubsidies create deadweight loss by reducing the equilibrium prices. Since fuel price subsid ies are transfer s from the government to consumers, the economic cost involved in providing such transfers is the deadweight loss created. Deadweight loss is then considered as an economic cost to soc iety. According to Davis (2014 ), t he total amount of deadweight loss created in a market depends on the elasticities of demand and supply . The more elastic demand and supply are , the larger the deadweight loss created by a price subsidy (Davis, 201 4 ). Figure 2.1 below illustrates a free market for a fuel product in a small open economy with a constant marginal cost . Producers sell at private marginal cost, P 1 , and consumers are willing to buy Q 1 , as they desire based on their demand schedule. When the g overnment provides a price subsidy for the product, the price falls from P 1 to P 2 , and consumers can now afford extra units of the product beyond the amount they are willing to purchase at private marginal cost. They increase 18 consumption from Q 1 to Q 2 , cre ating excess demand beyond the efficient level, Q 1 . The area ABC is the deadweight loss created by the subsidy. Following Davis (201 4 ) , I can estimate t he private deadweight loss associated with a fuel price subsidy in a given year by first calculating the area of the rectangle P 1 BCP 2 in Figure 2.1 , and then subtracting off the area under the demand curve from P 2 to P 1 . The resulting difference (area ABC), is the private deadweight loss caused the subsidy (Appendix 1). 2.2 Fuel Externalities The consumption of refined petroleum products presents ind irect damages to the consumers, the environment , and the economy as a whole. First of all, the exploration, production, storage , and transportation of crude oil, together with consumption of petroleum products downstream, impact negatively on the natural h abitat of plants and animals both on land and at sea. Exhaust and Price Quantity Figure 2.1 Private Deadweight Loss and Subsidy Private Marginal Cost, P 1 Subsidized Price, P 2 Q 1 Q 2 Demand Private Deadweight Loss A B C 19 pollutants from combustion engines and factories also contaminate the air with harmful gases , such as carbon dioxide, and particulates (i.e., dust), that contribute to climate change and res ult in poor health and respiratory consequences. In addition, the use of fuel is also associated with road accidents , which increase the toll of death and injuries, as well as noise pollution and road ernalities . additional cost to society beyond private marginal cost. Social deadweight loss , or total efficiency cost, associated with the increase in fuel consumption as a result of subsidy is, however, not just the private deadweight loss, area ABC, but also includes the additional deadweight loss, area EABF, caused by externalities. Hence, the social deadweight loss is represented by area ECF. There are s tudies that estimate the size of externalities associated with the consumption of fuels such as gasoline and diesel. Such studies quantify and monetize these indirect costs that society incurs through the consumption of petroleum products. They estimate th e marginal external Price Quantity Figure 2.2 Social Deadweight Loss and Subsidy Private Marginal Cost, P 1 Subsidized Price, P 2 Q 1 Q 2 Social Cost, P 3 Demand Additional Deadweight Loss due to Externalities/Marginal Damage Private Deadweight Loss (without Externalities) A B C D A F Q 3 E 20 damage of both local and global externalities , such as air pollution and the associated health risks, as well as climate change. These estimates also account for the cost of road accidents, injuries, traffic congestion, road maintenance , and noise pollution. One such stud y estimated the marginal external damages to be US$ 1.11 per gallon in the United States (Parry et al, 2007). Although estimating the externalities associated with fuel consumption in Ghana is important, it is not the pr imary focus of this study. As economic agents, consumers of a product consider not only the price of the product, but also the price s of related products in making consumption decisions , especially in the long - run . Hence, a price subsidy provided for a p roduct may influence not just the consumption of the product, but also related products. In the same manner, price subsidies provided for related products will also influence the consumption of the product in question. As a result, an estimate of deadweigh t loss will require a general equilibrium approach that accounts for the impact of cross - price effects of related products. 2.3 Harberger Formula and Deadweight Loss from Tax ation According to Hines Jr . (1999), Arnold C. Harberger proposed the triang u l ar method of estimating deadweight loss, and applied the method to estimate excess burden, or deadweight loss, arising from income taxes in the United States. Deadweight loss triangles became on subsequent research ( Hines Jr ., 1999). According to Goulde r and Williams III (2003) , the comprehensive Harberger formula, which is a linear approximation of excess burden, is given by: 21 where EB is the excess burden or deadweight loss caused by t he impos ition of a tax on good , represents respective quantities demanded , is a related good, and is the tax. The term represents the deadweight loss created by in market , and the term represents the reduction in deadweight loss created by in other related markets due to the presence of pre - existing taxes in these other markets. That is, for example, a tax on good w ould not create as much deadweight loss as you might otherwise expect, if it reduces the deadweight loss due to a tax on a close substitute good . Under the assumptions un derlying the formula, the tax rate represents marginal distortionary cost or the discrepancy between marginal social value and marginal social cost ( Goulde r and Williams III 2003) . Since it is often difficult to obtain all the cross - price effects for all possible related goods, researchers rarely use the comprehensive Harberger formula. Instead, the simple formula which ignores the cross - price effects is mostly used ( Goulde r and Williams III, 2003) . The simple Harberger formula is written as : The simple Harberger formula assumes that or for all . Under the assumption of a constant marginal cost curve, I illustrate the simple Harberger triangle in Figure 2.3 . 22 2.4 Adapting the Harberger Formula to Price Subsidies By adapting t he comprehensive Harberger formula to fuel price subsidies , I derive estimates for the deadweight loss associated with gasoline and diesel price subsidies . In S cenario 1, a subsidy is provided for only one product. In S cenario 2, multiple s ubsid ies are provided for gasoline and diesel in a sequential order (gasoline first, then diesel or vice versa) . In S cenario 3, multiple subsidies are provided for gasoline and diesel simultaneously . For simplicity, I make the following assumptions; (1) consume the price of substitute fuel types holding other factor ( such as income ) constant , (2) consumers face no barrier to switch between fuels, (3) all consumers respond negatively to ch anges in own price and positively to changes in cross price at all times (since these are substitute goods) , (4) P 1 + t k B Q 1 Q 2 Demand Quantity Private Marginal Cost, P 1 Simple Harberger Triangle/Excess Burden A C Price Figure 2.3 Simple Harberger Triangle 23 changes in price arising from non - tax sources , a nd (5) con s ta nt marginal cost curves for gasoline and diesel supply , since Ghana is a small open economy where majority of petroleum products are imported and consumers take prices as given . Scenario 1: A price subsidy is provided to gasoline consumers (Figure 2.4). The subsidy for gasoline will induce consumers to increase demand of gasoline from Qg1 to Qg2, while demand for diesel falls from Qd1 to Qd2 as the demand curve for diesel shifts inwards from D1 to D2 . The subsidy creates a distorti on in only the gasoline market. The deadweight loss (area ABC) can be estimated as : w here is quantity demand ed for gasoline, and is fuel price subsidy for gasoline , is the price of gasoline , , and is the own - price elasticity of gasoline demand. This formula is equivalent to the simple Harberger formula. 24 Scenario 2 : A price subsidy is provided first to the gasoline consumer, then to the diesel consumer (Figure 2.5). This scenario is equivalent to providing a diesel price subsidy in the presence of a pre - existing gasoline subsidy ( continuing from S cenario 1) . When a diesel price subsidy is introduced, a deadweight loss (area ABC) will be created in the diesel market, as consumption of diesel increases from Qd1 to Qd2. Since gasoline consumers will find diesel relatively cheaper, consumption of gasoline will d ecrease from Qg1 to Qg2 as the gasoline demand curve shifts inward from G 1 to G 2. The initial deadweight loss created by the pre - existing price subsidy for gasoline will be reduced by area EBCD. Figure 2.4 DWL of Gasoline Price Subsidy Gasoline Market Diesel Market Price Private Marginal Cost, Pd1 D2 D1 Qd2 Qd1 Quantity Price Private Marginal Cost, Pg1 G1 A B Subsidized Price, Pg2 C Quantity Qg1 Qg2 25 Thus, I can extend the Harberger formula to estimate the total deadweight loss created by the sequential provision of gasoline and diesel price subsidies as: where is diesel price subsidy, is the price of diesel, is quantity demand ed for diesel, , , is the incremental deadweight loss created by the diesel subsidy in the diesel market, represents the amount of reduction in the pre - existing deadweight loss in the gasoline market c aused by the cross - price effect of the diesel subsidy , is own - price elasticity of diesel demand, and is the cross - price elasticity of gasoline demand. Alternatively, I can start with a diesel subsidy, then introduce a gasoline subsidy. In that case, t he estimate for deadweight loss will be: 26 where , and is the cross - price elasticity of diesel demand. Since the sequential order ing of the provision of subsidies in Scenario 2 is different for and , the estimates are not the same in general due to the path - dependence problem (Just, Hueth, and Schmitz, 2004). Scenario 3: G asoline and diesel price subsidies are provided simultaneously to consumers (Figure 2.6). T he initial deadweight loss, area ABC, in each market will be created as prices fall and consumption increases . As consumers respond to cross - price effects between the two markets, however, the demand curves will shift inwards and consumers in each market will reduce consumption simultaneously. The reduction in quantity demand ed of each product will cause a reduction in the initial deadweight lo ss from area ABC to area AED in each market . Following Figure 2.5 DWL of Sequential Gasoline and Diesel Subsidies Price Private Marginal Cost, Pg1 G2 G1 A B Subsidized Price, Pg2 C Quantity Qg2 Qg1 Gasoline Market Diesel Market D E Price Private Marginal Cost, Pd1 D1 A B Subsidized Price, Pd2 C Quantity Qd1 Qd2 27 Parry et al (2014) , I calculate the net change in consumption in each market caused by the own - price and cross - price effects of the simultaneous subsid ies. I then use the quantity changes and the subsidies in each market to estimate deadweight loss using the conventional (triang u lar) method . The total deadweight loss created in both markets by the simultaneous provision of gasoline and diesel price subsi dies is approximated as: where and are the net quantity changes in the gasoline and diesel markets, respectively, resulting from the provision of price subsidies for both products at the same time. 28 In Appendix 2, I show that the approximation for deadweight loss in Scenario 3 is equal to the average of the two estimates in Scenario 2. All the extended formulas in Scenarios 2 and 3 are valid general equilibrium approximations for the deadweight loss associated with multiple price subsid ies for substitute products. Figure 2.6 DWL of Simultaneous Gasoline and Diesel Subsidies Price Private Ma rginal Cost, Pg1 G2 G1 A Subsidized Price, Pg2 Quantity Gasoline Market Diesel Market C B Qg1 Qg3 Qg2 D E Price Private Marginal Cost, Pd1 D2 D1 A Subsidized Price, Pd2 Quantity C B Qd1 Qd3 Qd2 D E 29 CHAPTER 3 - FUEL DEMAND ELASTICITIES 3.1 Model Specification I use two linear panel data model s to estimate price and income elasticities of demand for gasoline and diesel in Africa. I specify quantity demanded as a function of t he price of the fuel, the price of the substitute fuel, and income. I specify Model 1 in natural logs as: where is fuel consumption for country in year , is the real price of the fuel, is the real price of the substitute fuel, and is real income. and are vectors of year and country dummies. The terms and are the coefficients and is the error term. I specify another model in natural logs, Model 2, which is the same as Model 1 but with time lags: , where and are the coefficients and is the error term. For each fuel, I estimate both models to obtain their respective coefficients , which are the demand elasticities for own - price, cross - price, and income. In Model 1, the coefficients are both the short - run and long - run estimates. In Model 2, the coefficients for variables in time are the short - run estimates, while the sum of the coefficients for variables in time and are the 30 long - run estimates. I estimate each demand model with f ixed e ffects and f irst d ifference estimators using Stata (13.1). 3. 2 Sources of Data I create a panel consisting of annual data on twenty seven African countries (Appendix 3 ) spanning 1998 to 2010 with one year intervals. Data on gasoline and diesel consumption in k ilo t ons of oil equivalent , nominal retail prices for gasoline and diesel in US$ per liter, real GDP in 20 05 US$ , database. I use GDP as a proxy for income. I follow Liu (2004) t o obtain real prices in 2010 US Dollars . I first convert US $ nominal prices into respective country currencies using equivalent rates in each year , then covert t o real respective country currency values using respective CPI. F inally , I convert back to 2010 US $ using 2010 US $ exchange rates. Data on kerosene and LPG consumption and prices are not available for mo st of the countries in the panel so these fuels are excluded from the analysis . S ummary statistics for all the variables are shown in Appendix 3 . 3.3 Endogeneity and Instrument al Variable s Although gasoline and diesel prices are sometimes found to be endogenous, I have reasons to ex pect prices to be exo genous in my model. Most of the African countries in my panel are small open economies. As a result, consumers in these countries take prices as given. According to data onsumption of gasoline in Africa totaled 894 thousand bar rels per day (bbl/d), while that of the United States reached 8 , 682 thousand bbl/d in 2012. T he local 31 currencies o f most of the African countries , on average, depreciate against the US$ because as net importer s , their demand for the US$ often exceeds suppl y (Appendix 4) . Finally, fuel price subsidies are provided to consumers to minimize the effects of increases i n international oil prices and exchange rates on domestic retail prices. Hence, domestic retail prices for petroleum products in Africa are less influenced by the interaction of deman d and supply. With these characteristics in mind, I do not expect prices to be endogenous. To expl ore this issue, I run tests to examine the end ogeneity of prices in my model. Some studies use instruments such as the prices of related fuel products, regional dummy variables , and average fuel price in neighboring countries or locations [Dahl (1979), Manzan and Zerom (2010), Liu (201 4 )]. One potential instrument, given the nature of fuel pricing in Africa, is changes in fuel price subsidies, but such data are not available for most of the countries in my panel. Another good instrument is the average prices of fuel in neighboring countries . The average fuel price in neighboring countries is a valid and strong instrument since governments in African countries take into account fuel prices in neighboring countries when making pricing decisions to avoid fuel smuggling. Hence, I expect prices in nei ghboring countries to be correlate d with local prices in each country (instrument relevance) , but uncorrelated with fuel consumption residual s (instrument exogeneity) . I first test the instrument relevance assumption. I run regression s to test if the coefficient on the potential instrument is significantly different from zero (Appendix 5). The results show that the average price in neighboring countries is a statistically significant predictor of diesel price, but not so for gasoline pr ice . I then use average fuel price in neighboring countries as an instrument to run 32 endogeneity tests , and I am unable to reject the null hypothesis that gasoline and diesel prices are e xoge nous (Appendix 5 ) . 3.4 Estimation and Results I conduct a test for heteroskedasticity and autocorrelation for both models, and the results confirmed the presence of heteroskedasticity and autocorrelation in the error term (Appendix 6 ) . Thus, I use cl ustered s tandard errors in my estimation to correct for heteroskedasticity and autocorrelation . Details of the estimation procedures are contained in Appendix 7. Table 3. 1 shows results for the fixed effects and first difference estimates of Model 1 . Gasoline: The fixed effec ts estimates for the gasoline model are larger in magnitude t han the first difference estimates, but both models yield the expected signs for all coefficients . For instance, in both the fixed effects and first difference models, the estimates for own - price elasticity ( - 0.34 and - 0.13) are negative , while the estimates for cross - price elasticity (0.19 and 0.08) and income elasticity (0.44 and 0.16) are both positive respectively . Estimated s tandard errors are high, except that of the fixed effects estimate f or the income elasticity . The fixed effects and first difference estimates for the income elasticity are significant at 1% and 5% respectively. Diesel: All of the fixed effects estimates for the diesel model have the expected signs, but the first differe nce estimates all have the wrong signs. As Table 3.1 shows , the estimate for own - price elasticity ( - 0.22) is negative, while the estimates for cross - price elasticity (0.14) and income elasticity ( 0.19) are both positive for the fixed effects model. However, the own - price elasticity (0.0 5 ) estimate is positive, while the cross - price elasticity ( - 0.1 1 ) and income elasticity ( - 0.1 7 ) 33 estimates are both negative for the first difference model. Also, all of the fixed effects e stimates are larger in magnitude than the first difference estimates. However, standard errors for all of the estimates are high, and none of the estimates are statistically significant. Table 3.1 Results of Model 1 Fixed Effects First Difference Gasoline Diesel Gasoline Diesel Price of Gasoline - 0.34 0.14 - 0 .13 - 0.1 1 (0.36) (0.50) (0. 15 ) (0.1 3 ) Price of Diesel 0.19 - 0.22 0.0 8 0. 0 5 (0.28) (0.46) (0.1 2 ) (0.1 2 ) Income 0.44 * ** 0.19 0. 16** - 0. 1 7 (0.08) (0.15) (0.0 8 ) (0.2 6 ) Year Effects Yes Yes Yes Yes R - squared 0. 51 0. 37 0.1 1 0.0 9 Observations 181 181 153 153 C lustered Standard Errors in parenthes e s. Sign ificance: * **1%, **5%, *10%. Table 3. 2 shows the estimation results for Model 2 using fixed effects and first difference estimators. Gasoline: All of the fixed effects and first difference estimates have the expected signs . As Table 3.2 shows, a ll of the fixed effects estimates are larger in magnitude than the first difference estimates for both the short - run and long - run coefficients , and all of the long - run estimates are 34 larger in magnitude than the short - run estimates, except the cross - price elasticity estimates . In both the fixed effects and first difference models, t he short - run estimates for own - price elasticity ( - 0.24 and - 0. 15 ) are negative, while the short - run estimates for cro ss - price elasticity (0.10 and 0. 1 0 ) and income elasticity (0.24 and 0. 1 7 ) are both positive , r espectively . The long - run estimates for own - price elasticity ( - 0.38 and - 0.29) are negative, but the long - run estimates for cross - price elasticity (0.15 and 0.19) and income elasticity (0. 48 and 0. 3 6) are positive, in both the fixed effects and first difference models , respectively. The fixed effects and first difference estimates for both the short - run and long - run income elastici ties have low standard errors and are statistically significant at 1% (Appendix 8) . Conversely , the rest of the estimates have high standard errors and are not statistically significan t. Diesel: Most of the fixed effect s estimates and few of the first difference estimates have the expected signs . Likewise, most of the fixed effects estimates are larger in magnitude than the first difference estimates. A ll of the fixed effects and first difference e stimates, except the first difference short - run estimate for income, have high standard errors . Table 3.2 shows that the short - run estimates for income elasticity (0.22 and 0.16) are positive, and the long - run estimates for income elasticity (0.31 and 0.14) are also positive in both the fixed effects and first difference models , respectively. The first difference sh ort - run and the fixed effects long - run estimates for income elasticity are statistically significant at 10% and 5% , respectively , but the rest of the estimates are not (Appendix 8). 35 Table 3.2 Results of Model 2 Fixed Effects First Difference Gasoline Diesel Gasoline Diesel Price of Gasoline - 0.24 - 0.01 - 0.1 5 - 0. 09 (0.34) (0.37) (0.21) (0. 20 ) Lag, Price of Gasoline - 0.15 0.10 - 0.13 0. 08 (0.24) (0.48) (0. 19 ) (0. 32 ) Price of Diesel 0.10 - 0.11 0. 10 0. 04 (0.26) (0.33) (0.1 7 ) (0.1 6 ) Lag, Price of Diesel 0.05 - 0.14 0. 09 - 0.0 3 (0.21) (0.53) (0. 17 ) ( 0. 32 ) Income 0.24 * ** 0.22 0. 17 * ** 0. 16* (0.08) (0.11) (0.0 6 ) (0.0 9 ) Lag, Income 0.24 * ** 0.08 0. 19* ** - 0. 01 (0.08) (0.09) (0.0 7 ) (0. 09 ) Long - run, Price of Gasoline - 0.38 0.09 - 0.29 - 0.01 [ 0.49 ] [ 0.91 ] [0.4 7 ] [ 0.98 ] Long - run, Price of Diesel 0.15 - 0.26 0.19 0.01 [ 0.73 ] [ 0.76 ] [ 0.56 ] [ 0.9 9 ] Long - run, Income 0.48 0.31 0.36 0.14 [ 0.00 ] [ 0.03 ] [ 0.00 ] [ 0.2 6 ] Year Dummies Yes Yes Yes Yes R - squared 0. 51 0. 34 0.1 8 0. 0 5 Observations 154 154 127 127 C lustered Standard Errors in parenthes e s. P - values for test of null hypothesis that long - run estimates are zero in square brackets. Significance: ***1%, **5%, and *10%. 36 The fixed effects and first difference estimat es for Models 1 and 2 are not substantially different for the gasoline model coefficients in terms of signs and statistical significance . But it is evident that in general the fixed effect estimator provides better estimates for the diesel model coefficients in Model 1 than the rest of the estimates in terms the signs. For the diesel model coefficients , all of the fixed effects estimate s for Model 1 have the correct signs, but all of the first difference estimates for Model 1 have the wrong signs (Table 3.1). Also, some of the coefficient estimates in Model 2 have wrong signs for the diesel estimates (Table 3. 2 ) . For consistency, I prefer the fixed effects estimates to the first difference estimates, and Model 1 to Model 2 , for the long - run gasoline and diesel demand elasticities. My preferred long - run own - price, cross - price, and income elasticity estimates for gasoline demand ( - 0.34, 0.19, 0.44) and diesel demand ( - 0.22, 0.14. 0.19), respectively, are all inelastic. Although by thems elves , all of my estimates , except income elasticity for gasoline demand, are not statistically significant, they are reasonable in term s of magnitude and sign if I compare them to other estimates in the literature (Table 3.3 and 3.4). My estimates reveal that a 1% increase in the real price of gasoline will lead to a 0.34% reduction in gasoline consumption, and a 1% increase in the real price of diesel will lead to 0.22% reduction in diesel consumption in Africa, holding other factor s c onstant. Since gasoline and diesel are substitutes, a 1% increase in the real price of diesel will induce a 0.19% increase in gasoline consumption, while a 1% increase in the real price of gasoline will cause a 0.14% increase in diesel consumption in Afric a , all else equal. Also, a 1% increase in the real income of consumers will induce a 0.44% increase in gasoline consumption, while a 1% increase in the real income of 37 consumers will induce a 0.19% increase in diesel consumption in Africa , all else equal. M y income elasticit y estimates confirm that gasoline and diesel are normal goods. 3.5 Comparing Elasticity Estimates There is wide variation in the literature on estimates for fuel demand elasticities in different parts of the world. This is no surprise, however, as socioeconomic factors differ, and researchers adopt different estimation techniques to address specific kn owledge gaps. Liu (2004) noted the discernible divergence among the estimates of energy demand elasticities from empirical studies as a result of the differences in modeling methodologies and data sets applied in these studies . Nonetheless, since such es timates are expected to provide insights and inform energy policy, achieving realistic estimates should be a priority. One guiding principle should be the fact that, consumers in low - income economies have lower willingness - to - pay compared to consumers in t he high - income economies, and hence the former should be more price responsive. As a region dominated by low - income economies, I expect fuel demand elasticities, on the average, to be more elastic in African countries, such as Ghana, than in high income co untries like the United States. My estimates for gasoline and diesel demand elasticities are not substantially different from other recent estimates ( Table 3.3 and 3.4 ). I have not found any estimate for cross - price elasticity of demand for any type of petroleum product. Dahl (2012) conducted a study that revealed that estimates for own - price elasticities of gasoline and diesel in African countries ranged from - 0.09 to - 0.33 and - 0.13 to - 0.46 , respectively, while 38 that of income ranged from 0.54 to 1.65 for gasoline and 1.19 to 1.46 for diesel. Using a structural time - series model , Abdullahi (2014) found long - run own - price elasticit y estimates for gasoline demand ( - 0.23 ) , diesel demand ( - 0.30 ) , kerosene demand ( - 0.20 ) , LPG demand ( - 0.58 ), and fuel oil demand ( - 0.18 ) in Nigeria to be inelastic. Mensah (2014) estimated long - run demand elasticities for LPG in Ghana. He reported long - run estimates using an autoregressive distributed lag model ( - 0.28 , 0.4 5 , 5. 89 ) and a partial adjustment model ( - 0.2 8 , 0.55 , 5.62 ) for own - price, income, and rate - of - urbanization elasticities respectively . Boshoff (2012) , in comparing own - price and income elasticity estimates for gasoline demand in South Africa, found using an autoregress ive distributed lag model that elasticity estim ates using short sample periods ( - 0 . 59 and 0. 82 ) are higher than estimates using long sample periods ( - 0.44 and 0. 67 ) . Akinboade, Ziramba, and Kumo (2008) estimated own - price and income elasticities of - 0 .47 and 0.36 , respectively , for gasoline demand in South Africa , also with an autoregressive distributed lag b ound s co - integration approach . Gebreegziabher et al. (2010) estimated own price elasticity of demand for kerosene as - 0.66 for E thiopia using a n almost - ideal demand system approach . In Asia, Koshal et al. (1999) estimate d a long - run own - price elasticity of demand for kerosene in Indonesia to be - 0.17 with a time - series model. Lim et al . (2012) estimated - 0.547 and 1.478 as long - run own - price and income elasticities , respectively , for diesel demand in Korea. Lin and Zeng (201 3 ) estimate d the intermediate - run own - price elasticity of gasoline demand ( - 0.497 to - 0.196 ) and income elasticity ( 1.01 to 1.05 ) for China. Finally, Liu (201 4 ) estimated own - price and income elasticities of gasoline demand for various s tates in the United States. Her estimates range from - 0.013 ( Illinois ) to - 0.235 ( West Virginia ) for 39 own - price elasticity , and 0.017 ( Illinois ) to 0.172 ( West Virginia ) for income elasticity , using a semi - parametric smooth coeffi cient model. In their study, Hughes , Knittel , and Sperling ( 2008 ) discuss evidence of a shift in the demand elasticity for gasoline in the United States as they estimate short - run own - price elasticities of - 0.21 to - 0.34 f rom 1975 to 1980, and - 0.034 to - 0.077 from 2001 to 2006 (Tables 3.3 and 3.4). Table 3.3 Long - run Demand Elasticity Estimates for Gasoline and Diesel Own - Price Elasticity Income Elasticity Gasoline Diesel Gasoline Diesel C ount ry / R e g io n Source - 0.34 - 0.22 0.44 0.19 Africa This study - 0.09 to - 0.33 - 0.13 to - 0.46 0.54 to 1.65 1.19 to 1.46 Africa Dahl, 2012 - 0.23 - 0.30 Nigeria Abdullahi, 2014 - 0.44 0.67 S . Africa Boshoff, 2012 - 0.47 0.36 S . Africa Akinboade et al, 2008 - 0.20 to - 0.50 a 1.01 to 1.05 China Lin and Zeng, 2012 - 0.55 1.48 Korea Lim et al, 2012 - 0.01 to - 0.24 0.02 to 0.17 USA Liu, 2011 - 0.03 to - 0.08 b USA Hughes et al, 2006 a. Intermediate - run. b. Short - run. 40 Table 3. 4 Long - run Demand Elasticity Estimates for Kerosene and LPG Own - Price Elasticity Kerosene LPG Country Source - 0.20 - 0.58 Nigeria Abdullahi, 2014 - 0.28 Ghana Mensah, 2014 - 0.66 Ethiopia Gebreegziabher et al, 2010 - 0.17 Indonesia Koshal et al, 1999 41 CHAPTER 4 - COST OF FUEL PRICE SUBSIDIES 4.1 Introduction I use my long - run own - price and cross - price elasticity estimates for gasoline ( - 0.34 and 0.19) and diesel ( - 0.22 and 0.14) in Table 3. 1 , long - run own - price e lasticity estimates for kerosene ( - 0.20 ) and LPG ( - 0.58) for Nigeria by Abdullahi (2014) , and fuel consumption and price data from the National Petroleum Authority (NPA) to estimate the deadweight loss associated with fuel price subsidies in Ghana. 4. 2 Simple Method I calculate the deadweight loss associated with fuel price subsidies using the adapted simple Harberger formula , . The average subsidies per liter (or per kilogram for LPG) for gasoline, diesel, kerosene, and LPG during 2009 to 2014 are GHS 0.13 , GHS 0.10 , GHS 0.48 , and GHS 0.37 , respectively. Under the assumption that cross - price effects are insignificant , or zero , the cost of fuel price subsidies for gasoline, diesel, kerosene and LPG from 2009 to 2014 in each market are shown in Tables 4.1 to 4.4. The total deadweight loss, or economic cost , associated with subsidies for these fuels is GHS 109 . 45 million for the period 2009 to 2014 , with an annual total cost of GHS 18.24 million for all four fuels. As the Tables below show, t he annual economic costs of fuel price subsidies in Ghana are GHS 2. 93 million for gasoline , GHS 1.4 7 million for diesel , GHS 2 . 03 million for kerosene , and GHS 11.81 million for LPG. 42 Table 4.1 Economic Cost of Gasoline Price Subsidies in Ghana Year Subsidy a Quantity Consumed b Deadweight Loss c 2009 0.17 929.47 4.51 2010 0.04 997.34 0.21 2011 0.13 1083.23 2.07 2012 0.27 1332.52 9.29 2013 0.08 1450.53 0.84 2014 0.09 1522.24 0.65 Average 0.13 1219.22 2.93 a. Ghana Cedis per liter. b. Million liters. c . M illion Ghana Cedis . Table 4.2 Economic Cost of Diesel Price Subsidies in Ghana Year Subsidy a Quantity Consumed b Deadweight Loss c 2009 0.00 1326.95 0.00 2010 0.03 1212.82 0.09 2011 0.12 1343.60 1.32 2012 0.25 1569.38 6.21 2013 0.06 1663.53 0.30 2014 0.12 1649.81 0.88 Average 0.10 1461.02 1.47 a. Ghana Cedis per liter. b. Million liters. c . M illion Ghana Cedis . 43 Table 4.3 Economic Cost of Kerosene Price Subsidies in Ghana Year Subsidy a Quantity Consumed b Deadweight Loss c 2009 0.04 110.50 0.02 2010 0.15 61.09 0.15 2011 0.64 77.31 3.43 2012 1.01 56.61 6.39 2013 0.89 34.47 2.20 2014 0.18 11.50 0.01 Average 0.48 58.58 2.03 a. Ghana Cedis per liter. b. Million liters. c . M illion Ghana Cedis . Table 4.4 Economic Cost of LPG Price Subsidies in Ghana Year Subsidy a Quantity Consumed b Deadweight Loss c 2009 0.16 220.60 2.38 2010 0.36 177.19 8.15 2011 0.66 214.43 25.72 2012 0.74 268.49 32.39 2013 0.24 251.76 2.11 2014 0.07 237.25 0.13 Average 0.37 228.29 11.81 a. Ghana Cedis per kilogram. b. Million liters. c . M illion Ghana Cedis . 44 4. 3 General Equilibrium Method Using the three general equilibrium formulas for estimating deadweight loss created by multiple fuel price subsidies in Scenarios 2 and 3 above, I calculate the economic cost of gasoline and diesel price subsidies in Ghana from 2009 to 2014 . T he results confirm that the approximat ion in Scenario 3 (simultaneous subsidies) is equal to the average of the two approximations in Scenario 2 (sequential subsidies) . Hence, I show only one results (Scenario 3) in Table 4. 5 . T he estimates show that accounting for cross - price effects under the general equilibrium approach reduces t he cost of fuel price subsidies for gasoline and diesel almost by half. In particular , the total cost falls from GH S 2 6 . 38 million (US$ 15.40 million) to GHS 1 3 . 61 million (US$ 8.27 million) during 2009 to 2014 , while the annual cost falls from GHS 4. 40 million (US$ 2.57 million) to GHS 2. 27 million (US$ 1.38 million) . Table 4. 6 expresses the deadweight loss of the fuel price subsidy total expenditure on fuel price subsidies . The ratio varies from a high of 2.81% in 2009 to a low of 0.19% in 2010. On average, the annual cost of the fuel price subsidy in Ghana is 0.8% of the subsidy expenditure. 45 Table 4. 5 Economic Cost of Gasoline and Diesel Price Subsidies in Ghana Yea r Simple Method (mm GHS) Gen. Equilibrium Method (mm GHS) Ratio Gen. Equilibrium Method (mm US $) 2009 4.51 4.47 0.99 3.17 2010 0.30 0.14 0.46 0.10 2011 3.39 1.42 0.42 0.94 2012 15.51 6.42 0.41 3.58 2013 1.14 0.54 0.47 0.28 2014 1.53 0.62 0.41 0.21 Average 4.40 2.27 0.53 1.38 Figures in million GHS and million US$. Simple Method is from Table s 4.1 and 4.2. General E quilibrium Method is Scenario 3. Table 4. 6 Economic Cost of Gasoline and Diesel Price Subsidies in Ghana Year Subsidy Cost (million GHS) Subsidy Expenditure (million GHS) Ratio 2009 4.47 159.00 2.81% 2010 0.14 72.14 0.19% 2011 1.42 298.42 0.48% 2012 6.42 744.52 0.86% 2013 0.54 217.84 0.25% 2014 0.62 327.91 0.19% Average 2.27 303.31 0.80% 46 4.4 Sensitivity Analysis To help understand the sensitivity of the deadweight loss created by the fuel price subsidy in Ghana to the assumed demand elasticities , Tables 4. 7 and 4. 8 show estimates of deadweight loss with different elasticities. I increase my own - price and cross - pri ce elasticity estimate s for gasoline ( - 0.34 , 0.19) and diesel ( - 0.22, 0.14) by 50% in Table 4.7 and 100% in Table 4. 8 . T he results below show that a n increase in the size of the elasticities results in a proportional increase in the size of the de adweight loss. That is, my main estimate imply that the average cost of gasoline and diesel price subsidies is GHS 2.27 million (Table 4.6) . The average cost increase s by 50% to GHS 3.40 million (Table 4.7) and 100% to GHS 4.54 million (Table 4.8) when I increase the elasticity estimates by 50% and 100%, respectively . Table 4. 7 Economic Cost of Gasoline and Diesel Price Subsidies in Ghana Year Subsidy Cost (million GHS) Subsidy Expenditure (million GHS) Ratio 2009 6.70 159.00 4.21% 2010 0.21 72.14 0.29% 2011 2.13 298.42 0.71% 2012 9.64 744.52 1.29% 2013 0.81 217.84 0.37% 2014 0.93 327.91 0.28% Average 3.40 303.31 1.19% General Equilibrium Method is Scenario 3. O wn - price and cross - price elasticit ies for gasoline ( - 0.51, 0.29) and diesel ( - 0.33, 0.21). 47 Table 4. 8 Economic Cost of Gasoline and Diesel Price Subsidies in Ghana Year Subsidy Cost (million GHS) Subsidy Expenditure (million GHS) Ratio 2009 8.93 159.00 5.62% 2010 0.28 72.14 0.38% 2011 2.84 298.42 0.95% 2012 12.85 744.52 1.73% 2013 1.08 217.84 0.50% 2014 1.24 327.91 0.38% Average 4.54 303.31 1.59% General Equilibrium Method is Scenario 3. O wn - price and cross - price elasticit ies for gasoline ( - 0.68, 0.38) and diesel ( - 0.44, 0.28). 48 CHAPTER 5 - CONCLUSION I adapt the Harberger triangle for excess burden to approximate the size of the deadweight loss associated with fuel price subsidies for gasoline and diesel in Ghana from 2009 to 2014. I find that the deadweight loss ( e fficiency or economic cost) from energy subsidies are quite small due to inelastic energy demand. I also find that naively ignoring cross - price effects between energy markets nearly doubles the size of the deadweight loss associated with gasoline and diesel price subsidies in Ghana , all else equal. My preferred estimate s imply, on average, that for every Ghana Cedi of government revenue spent on gasoline and diesel price subsidies, an efficiency cost of 0.8% is created. Th ese findings indicate that subsidy reforms would be better motivated by their poor targeting of poor households and impact on debt - financing, rather than their efficiency losses. Although my estimates for gasoline and diesel demand elasticities are not statistically significant, they are consistent with other estimates in the literature. In the future, it would be worthwhile to estimate the own - price and cross - price elasticities for all fuel types in Ghana. Such estimates are vital since they wil l help expand the general equilibrium analysis and estimation of deadweight loss to include other fuels , such as LPG, which is increasingly used as a transportation fuel in Ghana. 49 APPENDICES 50 Appendix 1 - Deadweight Loss Formula Following Davis (2013), I can estimate the deadweight loss using a constant price elasticity demand function, . is the quantity of fuel consumed, is the price of fuel, and is the long - run price elasticity of demand, and is a scale parameter. Deadweight loss (DWL) associated with a fuel price subsidy can be approximated as : 51 Appendix 2 - Proof o f D eadweight Loss Formula 52 Appendix 3 - Countries and Summary Statistic s Table 3.5 African Countries by Region Northern Western Eastern Southern Central Algeria Benin Eritrea Botswana Angola Egypt Ethiopia Namibia Cameroon Libya Ghana Kenya South Africa Congo Morocco Nigeria Mozambique Congo, DR Sudan Senegal Tanzania Gabon Tunisia Togo Zambia Zimbabwe Table 3.6 Summary Statistics of Variables Variables Obs. Mean Std. Dev. Min. Max. Gasoline consumption 1 188 985.35 1898.03 5.00 8155.00 Diesel consumption 1 188 1041.21 1582.12 11.00 6557.00 Real p rice of g asoline 2 183 0.67 0.39 0.02 2.28 Average real price of gasoline in three neighboring countries 2 189 0.59 0.27 0.16 1.37 Real p rice of diesel 2 183 0.55 0.34 0.02 1.43 Average real price of diesel in three neighboring countries 2 189 0.50 0.27 0.12 1.20 Real GDP (Billion 2005 US$) 184 32.19 52.45 0.57 348.39 1. Kilotons of oil equivalent. 2. 2010 US$ per liter. 53 Appendix 4 - Exchange Rates The graph below exhibits an upward trend in exchange rates in local currency to US $ for ten African countries. The graph shows that, for the period 1996 to 2014, the local currencies of the countries depreciated, on average, against the US $ . Figure 3.1 Exchange Rates in Selected Africa n Countries Note: E xchange rates have been indexed with 1996 as the base year (1.0) . 1.0 3.0 5.0 7.0 9.0 11.0 13.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Ghana and Nigeria All Others Algeria Egypt Ethiopia Kenya Tanzania Namibia Botswana South Africa Ghana Nigeria 54 A ppendix 5 - Test for Endogeneity of Prices Table 3.7 Description of Variables in Model Variables Description of variables lngas Log of gasoline consumption lndiz Log of diesel consumption lnpg Log of real price of gasoline lnpgiv L og of real average price of gasoline in neighboring countries lnpd Log of real price of diesel lnpdiv Log of real average price of diesel in neighboring countries lngdp Log of real GDP To test the instrument relevance assumption for the instrument variable (IV) of average price in three neighboring countries, I run the following regression s . For each fuel, I run two regressions : (1) price against IV, and (2) price against all exogenous variable s including the IV. The results of the regressions are shown in Figures 3.2 to 3.5 below, and indicate that the average price of fuel in neighboring countries is a statistically significant predictor of the price o f diesel, but not so for the price of gasol ine. 55 Figure 3.2 Instrument Relevance Test for Gasoline Price (1) 56 Figure 3.3 Instrument Relevance Test for Gasoline Price (2) 57 Figure 3.4 Instrument Relevance Test for Diesel Price (1) 58 Figure 3.5 Instrument Relevance Test for Diesel Price (2) For each model, I run 2SLS IV regressions with average fuel price in neighboring co untries as instrument for local price . I then run the Durbin and Wu - Hausman procedures to test if gasoline and diesel prices are endogenous. The results below show that prices are not endogenous (i.e., I am unable to reject the null hypothesis that the prices are exogenous) . 59 1. Test for E ndogenous G asoline P rice in Gasoline Model ivregress 2sls lngas lnpd lngdp _Iyear_* _Icountry_* (lnpg=lnpgiv ), cluster(country) estat endogenous Tests of endogeneity Ho: variables are exogenous Robust regression F(1,26) = .185633 (p = 0.6701) (Adjusted for 27 clusters in country) 2. Test for E ndogenous D iesel P rice in Gasoline Model ivregress 2sls lngas lnpg lngdp _Iyear_* _Icountry_* (lnpd=lnpdiv ), cluster(country) estat endogenous Tests of endogeneity Ho: variables are exogenous Robust regression F(1,26) = .101343 (p = 0.7528) (Adjusted for 27 clusters in country) 60 3. Test for E ndogenous G asoline price in Diesel Model ivregress 2sls lndiz lnpd lngdp _Iyear_* _Icountry_* (lnpg=lnpgiv ), cluster(country) estat endogenous Tests of endogeneity Ho: variables are exogenous Robust regression F(1,26) = 1.35525 (p = 0.2549) (Ad justed for 27 clusters in country) 4. Test for E ndogenous D iesel P rice in Diesel Model ivregress 2sls lndiz lnpg lngdp _Iyear_* _Icountry_* (lnpd=lnpdiv ), cluster(country) estat endogenous Tests of endogeneity Ho: variables are exogenous Robust regre ssion F(1,26) = 1.09551 (p = 0.3049) (Adjusted for 27 clusters in country) 61 Appendix 6 - Tests for Heteroskedasticity and Autocorrelation 1. Test for Heteroskedasticity in Gasoline Model reg lngas lnpg lnpd lngdp _Iyear_* _Icountry_* hettest Breusch - Pagan / Cook - Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of lngas chi2(1) = 20.55 Prob > chi2 = 0.0000 2. Test for Heteroskedasticity in Diesel Model reg lndiz lnpg lnpd lngdp _Iyear_* _Icountry_* hettest Breusch - Pagan / Cook - Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of lndiz chi2(1) = 27.00 Prob > chi2 = 0.0000 62 3. Test for first - order Autocorrelation in Gasoline Model xtserial lngas lnpg lnpd lngdp _Iyear_* _Icountry_* Wooldridge test for autocorrelation in panel data H0: no first - order autocorrelation F( 1, 26) = 5.570 Prob > F = 0.0261 4. Test for first - order Autocorrelation in Diesel Model xtserial lndiz lnpg lnpd lngdp _Iyear_* _Icountry_* Wooldridge test for autocorrelation in panel data H0: no first - order autocorrelation F( 1, 26) = 35.057 Prob > F = 0.0 000 6 3 Appendix 7 - Stata Outputs for Model Estimation Figure 3. 6 Fixed E ffects R esults for Gasoline Model (1) xtreg lngas lnpg lnpd lngdp _Iyear_* , i(cid) fe cluster(country) 64 Figure 3. 7 Fixed E ffects R esults for Diesel Model (1) xtreg lndiz lnpg lnpd lngdp _Iyear_* , i(cid) fe cluster(country) 65 Figure 3. 8 First D ifference Resu lts for Gasoline Model (1) reg D.lngas D.lnpg D.lnpd D.lngdp _Iyear_* , cluster(country) 66 Figure 3. 9 First D ifference R esults for Diesel Model (1) reg D.ln diz D.lnpg D.lnpd D.lngdp _Iyear_* , cluster(country) 67 Figure 3. 10 Fixed E ffects R esults for Gasoline Model (2) xtreg lngas lnpg l.lnpg lnpd l.lnpd lngdp l.lngdp _Iyear_* , i(cid) fe cluster(country) 68 Figure 3. 11 Fixed E ffects R esults for Diesel Model (2) xtreg lndiz lnpg l.lnpg lnpd l.lnpd lngdp l.lngdp _Iyear_* , i(cid) fe cluster(country) 69 Figure 3. 12 First D ifference R esults for Gasoline Model (2) reg D.lngas D.lnpg D.L.lnpg D.lnpd D.L.lnpd D.lngdp D.L.lngdp _Iyear_* , cluster(country ) 70 Figure 3. 13 First D ifference R esults for Diesel Model (2) reg D.lndiz D.lnpg D.L.lnpg D.lnpd D.L.lnpd D.lngdp D.L.lngdp _Iyear_* , cluster(country) 71 Appendix 8 - Test for the Significance of Long - Run Coefficients A. Test for Significance of Long - run Fixed E ffects Coefficients for Gasoline Model (2) xtreg lngas lnpg l.lnpg lnpd l.lnpd lngdp l.lngdp _Iyear_* , i(cid) fe cluster(country) 1. Long - run own - price coefficient: test lnpg+l.lnpg=0 ( 1) lnpg + L.lnpg = 0 F( 1, 26) = 0.49 Prob > F = 0.4922 2. Long - run cross - price coefficient: test lnpd+l.lnpd=0 ( 1) lnpd + L.lnpd = 0 F( 1, 26) = 0.12 Prob > F = 0.7280 3. Long - run income coefficient: test lngdp+l.lngdp=0 ( 1) lngdp + L.lngdp = 0 F( 1, 26) = 27.05 Prob > F = 0.0000 72 B. Test for Significance of Long - run Fixed E ffects Coefficients for Diesel Model (2) xtreg lndiz lnpg l.lnpg lnpd l.lnpd lngdp l.lngdp _Iyear_* , i(cid) fe cluster(countr y) 4. Long - run cross - price coefficient: test lnpg+l.lnpg=0 ( 1) lnpg + L.lnpg = 0 F( 1, 26) = 0.01 Prob > F = 0.9123 5. Long - run own - price coefficient: test lnpd+l.lnpd=0 ( 1) lnpd + L.lnpd = 0 F( 1, 26) = 0.10 Prob > F = 0.7572 6. Long - run income coefficient: test lngdp+l.lngdp=0 ( 1) lngdp + L.lngdp = 0 F( 1, 26) = 5.05 Prob > F = 0.0334 73 C. Test for Significance of Long - run First D ifference Coefficients for Gasoli ne Model (2) reg D.lngas D.lnpg D.L.lnpg D.lnpd D.L.lnpd D.lngdp D.L.lngdp _Iyear_* , cluster(country) 7. Long - run own - price coefficient: test d.lnpg+d.l.lnpg=0 ( 1) D.lnpg + LD.lnpg = 0 F( 1, 26) = 0.54 Prob > F = 0.4679 8. Long - run cross - price coefficient: test d.lnpd+d.l.lnpd=0 ( 1) D.lnpd + LD.lnpd = 0 F( 1, 26) = 0.34 Prob > F = 0.5642 9. Long - run income coefficient: test d.lngdp+d.l.lngdp=0 ( 1) D.lngdp + LD.lngdp = 0 F( 1, 26) = 20.02 Prob > F = 0.0001 74 D. Test for Significance of Long - run First D ifference Coefficients for Diesel Model (2) reg D.lndiz D.lnpg D.L.lnpg D.lnpd D.L.lnpd D.lngdp D.L.lngdp _Iyear_* , cluster(country) 10. Long - run cross - p rice coefficient: test d.lnpg+d.l.lnpg=0 ( 1) D.lnpg + LD.lnpg = 0 F( 1, 26) = 0.00 Prob > F = 0.9797 11. 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