## _wp13185 ## Source details **Canonical URL:** [_wp13185](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13185.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13185.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13185.pdf.json) --- ### I. Introduction: context and objectives - China achieved rapid poverty reduction since reform and opening up, but experienced rising inequality. - Paper objective: investigate factors behind inequality across households and between provinces using the Shapley decomposition technique. - Core observation: inequality may be an inevitable by-product of China’s investment- and export-led growth model emphasizing manufacturing, capital, and coastal/urban development. - Core channels identified: - Capital stock supported manufacturing growth to meet export demand. - Low wages due largely to a large labor dividend. - Geographic advantages of the East coast that attracted trade and foreign direct investment. - Linkage made to global drivers of inequality: globalization, skill-biased technological change, declining bargaining power of workers. ### II. Stylized trends in poverty and inequality - Poverty reduction magnitudes: - In 1981, nearly 85 percent of China’s population lived on less than $1.25 a day. - By 2008, this proportion had fallen to 13 percent. - Growth lifted more than 500 million people out of poverty within a single generation. - China remained home to almost 175 million people living in extreme poverty. - Inequality magnitudes and trends: - World Bank estimates: Gini index increased from 29 percent in 1981 to over 42 percent in 2005. - Official estimates report a Gini index of over 47 (with a noted downtick since 2009). - Household-level Gini (CHNS): around 38 percent in 1991; 49 percent in 2009. - Example study: Gini of 0.61 in 2010 (China Household Finance Survey Center of Chengdu’s Southwestern University of Finance and Economics). - Rural-urban income gap: - Reached a ratio of more than 3:1 since 1998; the ratio has fallen somewhat since 2009 but remains above three. - Comparator range for other Asian economies: 1.3‒1.8. - Regional example: average incomes in Guangdong were two and a half times those in Gansu in 2012. ### III. Empirical findings on drivers of inequality - Household-level determinants (most important factors identified): - Location - Education - Access to health insurance - Labor market variables: sector of employment and enterprise size - Provincial-level determinants of per capita income divergence: - Relative level of capital-intensity - Public spending - Financial access - Privatization - Urbanization - Quantitative household-level findings (CHNS, ~4,000 households in nine provinces): - Income-generation explanatory variables: Education (schooling years of family head), Age (and Age2), Health (health insurance dummy), Manager (managerial position), Scale (working in a big organization), Sector (agricultural or not), Coast (coastal province dummy), Urban (urban locality dummy). - Estimated return example: in 2009, an additional year of schooling for the family head increases household income by around 6 percent. - Shapley decomposition (Gini): education accounts for almost one-quarter of the explained variation in incomes by the latest period; disparities in employee seniority and enterprise size account for almost one-fifth; location effects (urban and coast) remain strong. - Household Gini rose from around 38 percent in 1991 to 49 percent in 2009. - Provincial-level findings (NBS data, 1987–2009; 22 provinces, four autonomous regions, three municipalities): - Provincial income-generation variables: per capita capital input (Capital), trade/GDP ratio (Openness), proportion of labor in nonstate enterprises (Privatization), proportion nonagricultural population (Urbanization), per capita government expenditure (Public spending), per capita bank lending (Financial Access), Central and West location dummies (Location). - OLS results: capital intensity, public spending, financial access and urbanization generally have strong positive influence on provincial per capita incomes; openness has ambiguous/smaller effects and contributed negatively during the global crisis; location effects favor coastal provinces. - Shapley decomposition (Gini) for the latest period: financial access, urbanization, and privatization emerged as the three most important contributors, accounting for more than 85 percent of the observed divergence in provincial incomes in the latest period. - Public spending role shifted: from contributing to interprovincial inequality in the late 1980s/early 1990s to detracting from it since 2000, coinciding with the “Go-West” policy. ### IV. Liquidity, investment, and asset-price channel - Definition and context: - Excess liquidity defined as when total liquidity (total stock of financial instruments held by the nonfinancial sector) exceeds total productive capacity of the economy (Han and Lee, 2012). - Observed and comparative magnitudes: - In the United States, excess liquidity peaked in 2007 at about 20 percent above productive capacity; subsequent adjustment led to US$3.8 trillion more public debt by 2010. - In China, excess liquidity is currently about the same level as the U.S. peak in 2007. - Effects and mechanisms: - If credit expansion does not translate into productive capital stock, prices increase due to excess demand; asset holders using leverage gain, wage earners and non-asset holders lose. - Episodes of liquidity expansion in China associated with equity and property price increases that outpaced wage growth. - Rapid expansion of total social financing in 2012 supported property price increases despite excess supply of completed property relative to sold floor space. - Ample liquidity facilitated investments in some noncoastal provinces that became less efficient and wasteful, generating more corporate profit with limited spillover to household incomes. - Financial allocation and distributional consequences: - Financial controls transferred resources from households to the corporate sector, and from SMEs to large corporates. - Estimated burden of financing over-investment borne by households: close to 4 percent of GDP per year. - SMEs face higher price of capital due to funding priority given to larger corporations. - Risks from deteriorating investment efficiency: - Excess capacity erosion and capital depreciation can result in nonperforming loans (NPLs) that must be absorbed by financial asset holders or taxpayers; leveraged actors can gain at the expense of general households. ### V. Methodology: variable construction and Shapley value procedure - Household-level variable construction (CHNS): - Household Income: Per capita household income. - Education: Schooling years of the family head. - Age: Age of the family head (linear and quadratic forms included). - Health: Health = 1 if family head has health insurance; otherwise Health = 0. - Manager: Manager = 1 if family head works as a manager; otherwise Manager = 0. - Scale: Scale = 1 if family head works in a big organization (more than 20 employees); otherwise Scale = 0. - Coast: Coast = 1 if family lives in a coastal province (Jiangsu or Shandong); otherwise Coast = 0. - Urban: Urban = 1 if family lives in urban area; otherwise Urban = 0. - Sector: Sector = 1 if family head works in agricultural sector; otherwise Sector = 0. - Provincial-level variable construction (1987–2009): - Income: Weighted average of urban and rural per capita incomes, with nonagricultural and agricultural population shares as weights. - Capital: Capital stock data estimated by Zhang (2008) using the perpetual stock method. - Public Spending: Per capita government expenditure. - Openness: Trade/GDP ratio. - Privatization: Proportion of workers and staff in nonstate-owned entities. - Urbanization: Proportion of nonagricultural population in the total. - Financial Access: Per capita bank loan. - Location: Regional Effects (Central and West dummies; Chongqing and Sichuan treated as a single jurisdiction; Tibet dropped). - Shapley value procedure: - Purpose: decompose income inequality indicator I into additive contributions from a set K of explanatory factors while satisfying symmetry and exact conditions. - Implementation steps: - Enumerate all N! permutations of factor orderings. - For each ranking, compute incremental (rank-based) contributions. - Average marginal contributions across all permutations to obtain Shapley contributions, thereby satisfying both symmetry and exactness. - Inequality measures considered: Gini index, mean log deviation (GE0), Theil Index (GE1), Atkinson index (ATK, ε = 0.5), coefficient of variation (CV). Main text results based on Gini. - Data sources and notes: - Provincial analysis relies mostly on the China Statistical Yearbook (NBS, various years). - Capital stock uses Zhang (2008) estimates following Zhang, Wu, and Zhang (2004). ### VI. Key empirical magnitudes (preserved exactly) - Household-level Gini (CHNS): around 38 percent in 1991; 49 percent in 2009. - Example study Gini: 0.61 in 2010. - Rural-urban income gap: ratio of more than 3:1 (fell somewhat since 2009 but remains above three). - Comparator rural-urban ratio for other Asian economies: 1.3‒1.8. - Guangdong incomes = two and a half times Gansu in 2012. - U.S. excess liquidity peak: about 20 percent above productive capacity in 2007. - U.S. public debt increase: US$3.8 trillion more public debt by 2010. - Household burden estimate from over-investment financing: close to 4 percent of GDP per year. - Public social protection spending in China: 5.7 percent of GDP. - Fiscal spending on education and health: rose from 18 to 21 percent of total expenditure in the last five years (as of the source). - Combined employee and employer social security contributions: generally top 40 percent of wages. - Labor share of national income: fell from an estimated 50 percent in early 1990s to around 40 by mid 2000s. - Employment elasticity of growth: fell from 0.44 to 0.28 between 1991 and 2011. ### VII. Policy recommendations (preserved phrasing and priorities) - Maintain prudent monetary and credit policies. - Implement a more progressive fiscal tax and expenditure system. - Consider more progressive taxes; broaden tax base; improve progressivity given that indirect taxes account for three-quarters of tax revenue in China (compared to less than one-third in advanced economies). - Increase public spending on health and education. - Continued emphasis warranted given rising skill premia and increasing returns to human capital. - Expand and better target social protection. - Consider conditional cash transfer programs and targeted social expenditures to reach vulnerable households (AsDB finds current programs do not reach around one-third of the poor). - Reduce regressive social security contributions: - Reduce highly regressive combined employee and employer contributions (top 40 percent of wages) and compensate lost revenue through budget transfers while ensuring pension system sustainability. - Labor market and distributional policies: - Raise labor incomes and assist vulnerable workers via tighter labor markets, financial sector liberalization, increases in minimum wages, rural employment schemes, reducing labor market duality, hukou reform, and worker training/skills upgrading. - Competition and structural reform: - Continue deregulation and reforms to increase competition, especially in services. - Monetary and financial sector policy: - Monetary policy should pay attention to the stock of liquidity and asset prices; avoid excessive liquidity expansion that raises asset prices disproportionately to wages. - Financial sector liberalization and improved regulation to allocate resources efficiently, reduce asymmetric information and transaction costs, and expand access to financial services for poor and small entrepreneurs. - Improve access to finance for households and SMEs, including in rural areas. - Develop financial instruments (e.g., insurance products) to help vulnerable households adjust to shocks. - Alignment and implementation notes: - Recommendations align with the 12th Five Year Plan directions and recent World Bank and Asian Development Bank recommendations. - The income distribution plan approved by the State Council identifies reform priorities including minimum wage increases, improving the tax system, and strengthening social security; implementation remains the key challenge. - Demographic trends (rising wages) may also support a transition to a more equal society. *Source: _wp13185 (selected pages of the IMF working paper).* ### References ............................................................................................................. ### _wp13185 - References ### I. Introduction: context and objectives - China achieved rapid poverty reduction since reform and opening up, but experienced rising inequality. - The paper investigates factors behind inequality across households and between provinces using the Shapley decomposition technique. - Key observation: inequality may be an inevitable by-product of China’s investment- and export-led growth model, which emphasized manufacturing, capital, and coastal/urban development. - Core channels identified: - Capital stock supported manufacturing growth to meet export demand. - Low wages due largely to a large labor dividend. - Geographic advantages of the East coast that attracted trade and foreign direct investment. - The paper connects these structural features to global drivers of inequality (globalization, skill-biased technological change, declining bargaining power of workers). ### II. Stylized trends in poverty and inequality - Poverty reduction: - In 1981, nearly 85 percent of China’s population lived on less than $1.25 a day. - By 2008, this proportion had fallen to 13 percent. - Growth was “highly pro-poor,” lifting more than 500 million people out of poverty within a single generation. - China remained home to almost 175 million people living in extreme poverty. - Inequality trends: - World Bank estimates: Gini index increased from 29 percent in 1981 to over 42 percent in 2005. - Official estimates report a Gini index of over 47 (with a noted downtick since 2009). ### III. Empirical findings on drivers of inequality - Household-level determinants (most important factors): - Location - Education - Access to health insurance - Labor market variables: sector of employment and enterprise size - Provincial-level determinants of per capita income divergence: - Relative level of capital-intensity - Public spending - Financial access - Privatization - Urbanization - Role of public sector: - Public spending can dampen geographic disparities; evidence cited from the “Go-West” policy of 2000. - Liquidity, investment, and asset-price channel: - Rapid growth in liquidity increasingly used to power investment may have exacerbated inequality in the last decade. - As investment became relatively less efficient and more reliant on credit expansion, property prices climbed and strained affordability. - Asset price inflation widened wealth gaps, further differentiating incomes of the rich and poor. ### IV. Policy recommendations - Maintain prudent monetary and credit policies. - Implement a more progressive fiscal tax and expenditure system. - Increase public spending on health and education. - Continue deregulation and reforms to increase competition. - Adopt measures to raise labor incomes and assist vulnerable workers. - Improve access to finance for households and SMEs, including in rural areas. - These recommendations align with the 12th Five Year Plan directions and recent World Bank and Asian Development Bank recommendations. - Note: The income distribution plan approved by the State Council identifies reform priorities including minimum wage increases, improving the tax system, and strengthening social security; implementation remains the key challenge. - Demographic trends (rising wages) may also support a transition to a more equal society. ### V. Paper structure and scope - Sections II and III review related literature and trends in poverty and inequality. - Section IV conceptualizes links between growth model, liquidity, and inequality. - Section V empirically tests effects on household and provincial inequality and concludes with policy recommendations. *Source: _wp13185 - References (selected pages of the IMF working paper).* ### 2012. Many unofficial estimates are even higher. ### _wp13185 - 2012. Many unofficial estimates are even higher. ### Trends in inequality and poverty - Wage inequality and capital incomes (property and entrepreneurial incomes) have increased sharply; capital incomes were virtually insignificant in China prior to reforms. - Those in the bottom quintile have seen smaller rises in living standards; their share of overall incomes has fallen. - Spatial disparities account for more than half of overall inequality in China (AsDB, 2012). - Rural-urban income gap: - Reached a ratio of more than 3:1 since 1998; the ratio has fallen somewhat since 2009 but remains above three. - For most other Asian economies, the ratio falls between 1.3‒1.8 (Eastwood and Lipton, 2004). - Regional example: average incomes in Guangdong were two and a half times those in Gansu in 2012. - Household-level inequality (CHNS sample): Gini increased from around 38 percent in 1991 to 49 percent in 2009. - Asset-price and liquidity episodes: - In the United States, excess liquidity peaked in 2007 at about 20 percent above productive capacity; subsequent adjustment led to US$3.8 trillion more public debt by 2010. - In China, excess liquidity is currently about the same level as the U.S. peak in 2007. - Public social spending: - Public expenditure on health, pensions, and other forms of social protection amounts to 5.7 percent of GDP in China. - Fiscal spending on education and health has risen from 18 to 21 percent of total expenditure in the last five years (as of the source). ### Links between China’s growth model and inequality - Core features of the growth model: - Investment-induced capacity growth, largely in manufacturing, with strong utilization following WTO accession in 2001. - Large labor dividend and influx of young and migrant workers suppressed wages relative to corporate profits. - Favoring capital over labor benefited the corporate sector more than workers; less of growth flowed to household income. - Spatial and policy drivers: - East coast developed first due to trade, FDI, geography, and preferential policies, propagating regional income gaps. - Hukou system limited migrant access to social services. - Larger corporations benefited from better and cheaper access to financing under the state-led banking system. - Labor and sectoral channels: - Rising skill premia increased returns to education and managerial skills. - Manufacturing paid more than agriculture because of productivity differences. - Corporate and large-enterprise advantages increased relative incomes of those connected to firms and assets. ### The role of excess liquidity and financial allocation - Definition: an excess arises if total liquidity (total stock of financial instruments held by the nonfinancial sector) exceeds the total productive capacity of the economy (Han and Lee, 2012). - Effects of excess liquidity: - If credit expansion does not translate into productive capital stock, prices increase due to excess demand; asset holders using leverage gain, wage earners and non-asset holders lose. - In China, episodes of liquidity expansion were associated with equity and property price increases that outpaced wage growth. - Rapid expansion of total social financing in 2012 supported property price increases despite excess supply of completed property relative to sold floor space. - Ample liquidity facilitated investments in some noncoastal provinces that became less efficient and wasteful, generating more corporate profit with limited spillover to household incomes. - Financial controls and transfers: - Through financial controls, resources are transferred from households to the corporate sector, and from SMEs to large corporates. - Estimated burden of financing over-investment borne by households: close to 4 percent of GDP per year. - SMEs face higher price of capital due to funding priority given to larger corporations. - Risks if investment efficiency deteriorates: - Excess capacity erosion and capital depreciation can result in nonperforming loans (NPLs) that must be absorbed by financial asset holders or taxpayers; leveraged actors can gain at the expense of general households. ### Empirical evidence — household and provincial analyses - Methodology: - Used Shapley value decomposition (Shorrocks, 2012) to obtain additive contributions of factors to total inequality. - Inequality measures considered: Gini index, mean log deviation (GE0), Theil Index (GE1), Atkinson index (ATK, ε = 0.5), coefficient of variation (CV). Main text results based on Gini. - Household-level findings (CHNS; sample covers around 4,000 households in nine provinces): - Income-generation model explanatory variables: Education (schooling years of family head), Age (and Age2), Health (health insurance dummy), Manager (managerial position), Scale (working in a big organization), Sector (agricultural or not), Coast (coastal province dummy), Urban (urban locality dummy). - Estimated returns (example): in 2009, an additional year of schooling for the family head increases household income by around 6 percent. - Decomposition (Gini): education is the most important contributor, accounting for almost one-quarter of the explained variation in incomes by the latest period; age remains important but its contribution has fallen; disparities in employee seniority and enterprise size account for almost one-fifth of explained inequality; location effects (urban and coast) remain strong. - Quantitative trend: household Gini rose from around 38 percent in 1991 to 49 percent in 2009. - Provincial-level findings (NBS data, 1987–2009): - Provincial income-generation variables: per capita capital input (Capital), trade/GDP ratio (Openness), proportion of labor in nonstate enterprises (Privatization), proportion nonagricultural population (Urbanization), per capita government expenditure (Public spending), per capita bank lending (Financial Access), Central and West location dummies (Location). - OLS estimates: capital intensity, public spending, financial access and urbanization generally have strong positive influence on provincial per capita incomes; openness has ambiguous/smaller effects and contributed negatively during the global crisis; location effects favor coastal provinces. - Decomposition (Gini) for latest period: financial access, urbanization, and privatization emerged as the three most important contributors, accounting for more than 85 percent of the observed divergence in provincial incomes in the latest period. - Public spending shifted over time: from contributing to interprovincial inequality in late 1980s/early 1990s to detracting from it since 2000, coinciding with the Go-West policy that diverted resources to inland provinces. - Labor share and employment elasticity: - Labor share fell from an estimated 50 percent during the early 1990s to around 40 by the mid 2000s. - Employment elasticity of growth between 1991 and 2011 fell from 0.44 to 0.28 in China. ### Key empirical magnitudes and exact figures preserved from the source - Gini estimates and changes: - Household-level Gini (CHNS): around 38 percent in 1991; 49 percent in 2009. - Example study: Gini of 0.61 in 2010 (China Household Finance Survey Center of Chengdu’s Southwestern University of Finance and Economics). - Rural-urban income gap: ratio of more than 3:1 (fell somewhat since 2009 but remains above three); comparator range for other Asian economies: 1.3‒1.8. - Regional income example: Guangdong incomes = two and a half times Gansu in 2012. - U.S. excess liquidity peak: about 20 percent above productive capacity in 2007; US$3.8 trillion more public debt by 2010. - Household burden estimate: close to 4 percent of GDP per year borne by households due to financing of over-investment. - Public social protection spending in China: 5.7 percent of GDP. - Fiscal spending on education and health: rose from 18 to 21 percent of total expenditure in the last five years (as of the source). - Combined employee and employer social security contributions: generally top 40 percent of wages. - Labor share of national income: fell from an estimated 50 percent in early 1990s to around 40 by mid 2000s. - Employment elasticity: fell from 0.44 to 0.28 between 1991 and 2011. ### Policy implications and recommendations - Fiscal and tax policy: - Consider more progressive taxes; broaden tax base; improve progressivity given that indirect taxes account for three-quarters of tax revenue in China (compared to less than one-third in advanced economies). - Use redistributive fiscal policy to raise transfers and target vulnerable households. - Public spending and social protection: - Increase public spending on education and health; continued emphasis warranted given rising skill premia and increasing returns to human capital. - Expand and better target social protection; consider conditional cash transfer programs and targeted social expenditures to reach vulnerable households (AsDB finds current programs do not reach around one-third of the poor). - Address intergovernmental fiscal relations: sub-provincial spending is high while local levels often lack revenue sources, leading to unequal provision of services. - Social security reform: - Reduce highly regressive combined employee and employer contributions (top 40 percent of wages) and compensate lost revenue through budget transfers while ensuring pension system sustainability. - Labor market and distributional policies: - Lower capital-intensity and boost labor share of income via tighter labor markets, financial sector liberalization, increases in minimum wages, rural employment schemes, reducing labor market duality, hukou reform, and worker training/skills upgrading. - Competition and structural reform: - Increase competition and deregulation, especially in services, to unleash productivity and bridge regional disparities. - Monetary and financial sector policy: - Monetary policy should pay attention to the stock of liquidity and asset prices; avoid excessive liquidity expansion that raises asset prices disproportionately to wages. - Financial sector liberalization and improved regulation to allocate resources efficiently, reduce asymmetric information and transaction costs, and expand access to financial services for poor and small entrepreneurs. - Develop financial instruments (e.g., insurance products) to help vulnerable households adjust to shocks. *Source: _wp13185 - 2012. Many unofficial estimates are even higher.* ### 2009. We follow the following methods to construct the variables we need: ### _wp13185 - 2009. We follow the following methods to construct the variables we need: ### Household-level variable construction - Household Income: Per capita household income. - Education: Schooling years of the family head. - Age: Age of the family head. We include both linear and quadratic form of age to capture life-cycle effects. - Health: If the family head has health insurance, Health = 1; if not, Health = 0. - Manager: If the family head works as a manager, Manager = 1; if not, Manager = 0. - Scale: If the family head works in a big organization (more than 20 employees working for the organization), Scale = 1; if not, Scale = 0. - Coast: If the family lives in a coastal province (Jiangsu or Shandong), Coast = 1; if not, Coast = 0. - Urban: If the family lives in urban area, Urban = 1; if not, Urban = 0. - Sector: If the family head works in agricultural sector, Sector = 1; if not, Sector = 0. ### Provincial-level variable construction (22 provinces, four autonomous regions, three municipalities; period 1987–2009) - Data sources and coverage notes: - The dataset covers 22 provinces, four autonomous regions and three municipalities over the period 1987–2009. - Footnote 20: Our approach is based on Wan, Lu, and Chen (2007) but with a different time period and set of explanatory variables. - Footnote 21: As is standard in the literature that uses provincial data in China, we drop Tibet because of a large number of missing observations. - Footnote 22: Chongqing (which was separated from the latter in 1997) and Sichuan are treated as a single jurisdiction. - Variables and construction methods: - Income: Weighted average of urban and rural per capita incomes, with nonagricultural and agricultural population shares as weights. - Capital: Using capital stock data estimated by Zhang (2008), which adopted the perpetual stock method, following the methodology in Zhang, Wu, and Zhang (2004). - Public Spending: Per capita government expenditure. - Openness: Trade/GDP ratio. - Privatization: Proportion of workers and staff in nonstate-owned entities. - Urbanization: Proportion of nonagricultural population in the total. - Financial Access: Per capita bank loan. - Location: Regional Effects. ### Empirical method: Shapley Value Procedure - Purpose: Decompose income inequality indicator I into contributions from a set K of explanatory factors. - Setup (as in source): - Let K be a set of explanatory factors, which jointly determine income inequality indicator I (IFK = ) (equation numbering appears in source). - Desiderata for decomposition coefficients C_k: - Symmetric condition: kC should not depend on the way in which the factors in K are ranked. - Exact condition: the contributions must sum to I (the source states the exact condition in equation form). - Alternative definitions and their limitations: - Define kC as F(K) − F(K\{k}) (notation in source). This satisfies the symmetric condition but not the exact condition. - Rank-based incremental contributions (source notation using sequences and superscripts). This satisfies the exact condition but violates symmetry. - Shapley value procedure (as described in source): - Step 1: Find all possible ways of ranking the factors in K. If there are N dimensions in K, the total number of possibilities will be N! (source footnote). - Step 2: For each ranking, compute the incremental contribution n_kC using the rank-based method. - Step 3: The Shapley contribution of factor k is the average of all n_kC across all permutations: - The source states this averaging formula in the form: (1/N!) sum over σ∈Σ of C_k(F,σ) (equation-like representation in the source), which satisfies both the symmetric and exact conditions. ### Key methodological notes - The provincial analysis relies mostly on the China Statistical Yearbook (NBS, various years). - Capital stock uses Zhang (2008) estimates applying the perpetual inventory method and methodology in Zhang, Wu, and Zhang (2004). - The Shapley value procedure is implemented by enumerating all permutations of factor orderings and averaging marginal contributions to ensure both symmetry and exact decomposition. *Source: _wp13185 - 2009. We follow the following methods to construct the variables we need.* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13185.pdf_