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宏观经济学所有的专业词汇英文缩写及其翻译accounting 会计accounting cost 会计成本accounting profit 会计利润adverse selection 逆向选择allocation 配置allocation of resources 资源配置allocative efficiency 配置效率antitrust legislation 反托拉斯法arc elasticity 弧弹性Arrow's impossibility theorem 阿罗不可能定理Assumption 假设asymetric information 非对称性信息average 平均average cost 平均成本average cost pricing 平均成本定价法average fixed cost 平均固定成本average product of capital 资本平均产量average product of labour 劳动平均产量average revenue 平均收益average total cost 平均总成本average variable cost 平均可变成本Bbarriers to entry 进入壁垒base year 基年bilateral monopoly 双边垄断benefit 收益black market 黑市bliss point 极乐点boundary point 边界点break even point 收支相抵点budget 预算budget constraint 预算约束budget line 预算线budget set 预算集Ccapital 资本capital stock 资本存量capital output ratio 资本产出比率capitalism 资本主义cardinal utility theory 基数效用论cartel 卡特尔ceteris puribus assumption “其他条件不变”的假设ceteris puribus demand curve 其他因素不变的需求曲线Chamberlin model 张伯伦模型change in demand 需求变化change in quantity demanded 需求量变化change in quantity supplied 供给量变化change in supply 供给变化choice 选择closed set 闭集Coase theorem 科斯定理Cobb—Douglas production function 柯布--道格拉斯生产函数cobweb model 蛛网模型collective bargaining 集体协议工资collusion 合谋command economy 指令经济commodity 商品commodity combination 商品组合commodity market 商品市场commodity space 商品空间common property 公用财产comparative static analysis 比较静态分析compensated budget line 补偿预算线compensated demand function 补偿需求函数compensation principles 补偿原则compensating variation in income 收入补偿变量competition 竞争competitive market 竞争性市场complement goods 互补品complete information 完全信息completeness 完备性condition for efficiency in exchange 交换的最优条件condition for efficiency in production 生产的最优条件concave 凹concave function 凹函数concave preference 凹偏好consistence 一致性constant cost industry 成本不变产业constant returns to scale 规模报酬不变constraints 约束consumer 消费者consumer behavior 消费者行为consumer choice 消费者选择consumer equilibrium 消费者均衡consumer optimization 消费者优化consumer preference 消费者偏好consumer surplus 消费者剩余consumer theory 消费者理论consumption 消费consumption bundle 消费束consumption combination 消费组合consumption possibility curve 消费可能曲线consumption possibility frontier 消费可能性前沿consumption set 消费集consumption space 消费空间continuity 连续性continuous function 连续函数contract curve 契约曲线convex 凸convex function 凸函数convex preference 凸偏好convex set 凸集corporatlon 公司cost 成本cost benefit analysis 成本收益分cost function 成本函数cost minimization 成本极小化Cournot equilihrium 古诺均衡Cournot model 古诺模型Cross—price elasticity 交叉价格弹性Ddead—weights loss 重负损失decreasing cost industry 成本递减产业decreasing returns to scale 规模报酬递减deduction 演绎法demand 需求demand curve 需求曲线demand elasticity 需求弹性demand function 需求函数demand price 需求价格demand schedule 需求表depreciation 折旧derivative 导数derive demand 派生需求difference equation 差分方程differential equation 微分方程differentiated good 差异商品differentiated oligoply 差异寡头diminishing marginal substitution 边际替代率递减diminishing marginal return 收益递减diminishing marginal utility 边际效用递减direct approach 直接法direct taxes 直接税discounting 贴税、折扣diseconomies of scale 规模不经济disequilibrium 非均衡distribution 分配division of labour 劳动分工distribution theory of marginal productivity 边际生产率分配论duoupoly 双头垄断、双寡duality 对偶durable goods 耐用品dynamic analysis 动态分析dynamic models 动态模型EEconomic agents 经济行为者economic cost 经济成本economic efficiency 经济效率economic goods 经济物品economic man 经济人economic mode 经济模型economic profit 经济利润economic region of production 生产的经济区域economic regulation 经济调节economic rent 经济租金exchange 交换economics 经济学exchange efficiency 交换效率economy 经济exchange contract curve 交换契约曲线economy of scale 规模经济Edgeworth box diagram 埃奇沃思图exclusion 排斥性、排他性Edgeworth contract curve 埃奇沃思契约线Edgeworth model 埃奇沃思模型efficiency 效率，效益efficiency parameter 效率参数elasticity 弹性elasticity of substitution 替代弹性endogenous variable 内生变量endowment 禀赋endowment of resources 资源禀赋Engel curve 恩格尔曲线entrepreneur 企业家entrepreneurship 企业家才能entry barriers 进入壁垒entry/exit decision 进出决策envolope curve 包络线equilibrium 均衡equilibrium condition 均衡条件equilibrium price 均衡价格equilibrium quantity 均衡产量eqity 公平equivalent variation in income 收入等价变量excess—capacity theorem 过度生产能力定理excess supply 过度供给exchange 交换exchange contract curve 交换契约曲线exclusion 排斥性、排他性exclusion principle 排他性原则existence 存在性existence of general equilibrium 总体均衡的存在性exogenous variables 外生变量expansion paths 扩展径expectation 期望expected utility 期望效用expected value 期望值expenditure 支出explicit cost 显性成本external benefit 外部收益external cost 外部成本external economy 外部经济external diseconomy 外部不经济externalities 外部性FFactor 要素factor demand 要素需求factor market 要素市场factors of production 生产要素factor substitution 要素替代factor supply 要素供给fallacy of composition 合成谬误final goods 最终产品firm 企业firms’demand curve for labor 企业劳动需求曲线firm supply curve 企业供给曲线first-degree price discrimination 第一级价格歧视first—order condition 一阶条件fixed costs 固定成本fixed input 固定投入fixed proportions production function 固定比例的生产函数flow 流量fluctuation 波动for whom to produce 为谁生产free entry 自由进入free goods 自由品，免费品free mobility of resources 资源自由流动free rider 搭便车，免费搭车function 函数future value 未来值Ggame theory 对策论、博弈论general equilibrium 总体均衡general goods 一般商品Giffen goods 吉芬晶收入补偿需求曲线Giffen's Paradox 吉芬之谜Gini coefficient 吉尼系数goldenrule 黄金规则goods 货物government failure 政府失败government regulation 政府调控grand utility possibility curve 总效用可能曲线grand utility possibility frontier 总效用可能前沿Hheterogeneous product 异质产品Hicks—kaldor welfare criterion 希克斯一卡尔多福利标准homogeneity 齐次性homogeneous demand function 齐次需求函数homogeneous product 同质产品homogeneous production function 齐次生产函数horizontal summation 水平和household 家庭how to produce 如何生产human capital 人力资本hypothesis 假说Iidentity 恒等式imperfect competion 不完全竞争implicitcost 隐性成本income 收入income compensated demand curveincome constraint 收入约束income consumption curve 收入消费曲线income distribution 收入分配income effect 收入效应income elasticity of demand 需求收入弹性increasing cost industry 成本递增产业increasing returns to scale 规模报酬递增inefficiency 缺乏效率index number 指数indifference 无差异indifference curve 无差异曲线indifference map 无差异族indifference relation 无差异关系indifference set 无差异集indirect approach 间接法individual analysis 个量分析individual demand curve 个人需求曲线individual demand function 个人需求函数induced variable 引致变量induction 归纳法industry 产业industry equilibrium 产业均衡industry supply curve 产业供给曲线inelastic 缺乏弹性的inferior goods 劣品inflection point 拐点information 信息information cost 信息成本initial condition 初始条件initial endowment 初始禀赋innovation 创新input 投入input—output 投入—产出institution 制度institutional economics 制度经济学insurance 保险intercept 截距interest 利息interest rate 利息率intermediate goods 中间产品internatization of externalities 外部性内部化invention 发明inverse demand function 逆需求函数investment 投资invisible hand 看不见的手isocost line 等成本线，isoprofit curve 等利润曲线isoquant curve 等产量曲线isoquant map 等产量族Kkinded—demand curve 弯折的需求曲线Llabour 劳动labour demand 劳动需求labour supply 劳动供给labour theory of value 劳动价值论labour unions 工会laissez faire 自由放任Lagrangian function 拉格朗日函数Lagrangian multiplier 拉格朗乘数，land 土地law 法则law of demand and supply 供需法law of diminishing marginal utility 边际效用递减法则law of diminishing marginal rate of substitution 边际替代率递减法则law of diminishing marginal rate of technical substitution 边际技术替代率law of increasing cost 成本递增法则law of one price 单一价格法则leader—follower model 领导者--跟随者模型least—cost combination of inputs 最低成本的投入组合leisure 闲暇Leontief production function 列昂节夫生产函数licenses 许可证linear demand function 线性需求函数linear homogeneity 线性齐次性linear homogeneous production function 线性齐次生产函数long run长期long run average cost 长期平均成本long run equilibrium 长期均衡long run industry supply curve 长期产业供给曲线long run marginal cost 长期边际成本long run total cost 长期总成本Lorenz curve 洛伦兹曲线loss minimization 损失极小化1ump sum tax 一次性征税luxury 奢侈品Mmacroeconomics 宏观经济学marginal 边际的marginal benefit 边际收益marginal cost 边际成本marginal cost pricing 边际成本定价marginal cost of factor 边际要素成本marginal period 市场期marginal physical productivity 实际实物生产率marginal product 边际产量marginal product of capital 资本的边际产量marginal product of 1abour 劳动的边际产量marginal productivity 边际生产率marginal rate of substitution 边替代率marginal rate of transformation 边际转换率marginal returns 边际回报marginal revenue 边际收益marginal revenue product 边际收益产品marginal revolution 边际革命marginal social benefit 社会边际收益marginal social cost 社会边际成本marginal utility 边际效用marginal value products 边际价值产品market 市场market clearance 市场结清，市场洗清market demand 市场需求market economy 市场经济market equilibrium 市场均衡market failure 市场失败market mechanism 市场机制market structure 市场结构market separation 市场分割market regulation 市场调节market share 市场份额markup pricing 加减定价法Marshallian demand function 马歇尔需求函数maximization 极大化microeconomics 微观经济学minimum wage 最低工资misallocation of resources 资源误置mixed economy 混合经济model 模型money 货币monopolistic competition 垄断竞争monopolistic exploitation 垄断剥削monopoly 垄断，卖方垄断monopoly equilibrium 垄断均衡monopoly pricing 垄断定价monopoly regulation 垄断调控monopoly rents 垄断租金monopsony 买方垄断NNash equilibrium 纳什均衡Natural monopoly 自然垄断Natural resources 自然资源Necessary condition 必要条件necessities 必需品net demand 净需求nonconvex preference 非凸性偏好nonconvexity 非凸性nonexclusion 非排斥性nonlinear pricing 非线性定价nonrivalry 非对抗性nonprice competition 非价格竞争nonsatiation 非饱和性non--zero—sum game 非零和对策normal goods 正常品normal profit 正常利润normative economics 规范经济学Oobjective function 目标函数oligopoly 寡头垄断oligopoly market 寡头市场oligopoly model 寡头模型opportunity cost 机会成本optimal choice 最佳选择optimal consumption bundle 消费束perfect elasticity 完全有弹性optimal resource allocation 最佳资源配置optimal scale 最佳规模optimal solution 最优解optimization 优化ordering of optimization(social) preference (社会)偏好排序ordinal utility 序数效用ordinary goods 一般品output 产量、产出output elasticity 产出弹性output maximization 产出极大化Pparameter 参数Pareto criterion 帕累托标准Pareto efficiency 帕累托效率Pareto improvement 帕累托改进Pareto optimality 帕累托优化Pareto set 帕累托集partial derivative 偏导数partial equilibrium 局部均衡patent 专利pay off matrix 收益矩阵、支付矩阵perceived demand curve 感觉到的需求曲线perfect competition 完全竞争perfect complement 完全互补品perfect monopoly 完全垄断perfect price discrimination 完全价格歧视perfect substitution 完全替代品perfect inelasticity 完全无弹性perfectly elastic 完全有弹性perfectly inelastic 完全无弹性plant size 工厂规模point elasticity 点弹性positive economics 实证经济学post Hoc Fallacy 后此谬误prediction 预测preference 偏好preference relation 偏好关系present value 现值price 价格price adjustment model 价格调整模型price ceiling 最高限价price consumption curve 价格费曲线price control 价格管制price difference 价格差别price discrimination 价格歧视price elasticity of demand 需求价格弹性price elasticity of supply 供给价格弹性price floor 最低限价price maker 价格制定者price rigidity 价格刚性price seeker 价格搜求者price taker 价格接受者price tax 从价税private benefit 私人收益principal—agent issues 委托--代理问题private cost 私人成本private goods 私人用品private property 私人财产producer equilibrium 生产者均衡producer theory 生产者理论product 产品product transformation curve 产品转换曲线product differentiation 产品差异product group 产品集团production 生产production contract curve 生产契约曲线production efficiency 生产效率production function 生产函数production possibility curve 生产可能性曲线productivity 生产率productivity of capital 资本生产率productivity of labor 劳动生产率profit 利润profit function 利润函数profit maximization 利润极大化property rights 产权property rights economics 产权经济学proposition 定理proportional demand curve 成比例的需求曲线public benefits 公共收益public choice 公共选择public goods 公共商品pure competition 纯粹竞争rivalry 对抗性、竞争pure exchange 纯交换pure monopoly 纯粹垄断Qquantity—adjustment model 数量调整模型quantity tax 从量税quasi—rent 准租金Rrate of product transformation 产品转换率rationality 理性reaction function 反应函数regulation 调节，调控relative price 相对价格rent 租金rent control 规模报酬rent seeking 寻租rent seeking economics 寻租经济学resource 资源resource allocation 资源配置returns 报酬、回报returns to scale 规模报酬revealed preference 显示性偏好revenue 收益revenue curve 收益曲线revenue function 收益函数revenue maximization 收益极大化ridge line 脊线risk 风险Ssatiation 饱和，满足saving 储蓄scarcity 稀缺性law of scarcity 稀缺法则second—degree price discrimination 二级价格歧视second derivative --阶导数second—order condition 二阶条件service 劳务set 集shadow prices 影子价格short—run 短期short—run cost curve 短期成本曲线short—run equilibrium 短期均衡short—run supply curve 短期供给曲线shut down decision 关闭决策shortage 短缺shut down point 关闭点single price monopoly 单一定价垄断slope 斜率social benefit 社会收益social cost 社会成本social indifference curve 社会无差异曲线social preference 社会偏好social security 社会保障social welfare function 社会福利函数socialism 社会主义solution 解space 空间stability 稳定性stable equilibrium 稳定的均衡Stackelberg model 斯塔克尔贝格模型static analysis 静态分析stock 存量stock market 股票市场strategy 策略subsidy 津贴substitutes 替代品substitution effect 替代效应substitution parameter 替代参数sufficient condition 充分条件supply 供给supply curve 供给曲线supply function 供给函数supply schedule 供给表Sweezy model 斯威齐模型symmetry 对称性symmetry of information 信息对称Ttangency 相切taste 兴致technical efficiency 技术效率technological constraints 技术约束technological progress 技术进步technology 技术third—degree price discrimination 第三级价格歧视total cost 总成本total effect 总效应total expenditure 总支出total fixed cost 总固定成本total product 总产量total revenue 总收益total utility 总效用total variable cost 总可变成本traditional economy 传统经济transitivity 传递性transaction cost 交易费用Uuncertainty 不确定性uniqueness 唯一性unit elasticity 单位弹性unstable equilibrium 不稳定均衡utility 效用utility function 效用函数utility index 效用指数utility maximization 效用极大化utility possibility curve 效用可能性曲线utility possibility frontier 效用可能性前沿VValue 价值value judge 价值判断value of marginal product 边际产量价值variable cost 可变成本variable input 可变投入variables 变量vector 向量visible hand 看得见的手vulgur economics 庸俗经济学Wwage 工资wage rate 工资率Walras general equilibrium 瓦尔拉斯总体均衡Walras's law 瓦尔拉斯法则Wants 需要Welfare criterion 福利标准Welfare economics 福利经学Welfare loss triangle 福利损失三角形welfare maximization 福利极大化Zzero cost 零成本zero elasticity 零弹性zero homogeneity 零阶齐次性zero economic profit 零利润回答：2010-02-16 22:16。
Equilibrium，competitive竞争均衡见竟争均衡（competitive equilibrium）。
Equilibrium，general⼀般均衡见⼀般均衡分析（general－equilibrium analysis） Equilibrium，macroeconomic宏观经济均衡意愿总需求等于意愿总供给的GDP⽔平。
在均衡时，意愿的消费（C），政府⽀出（G），投资（I）和净出⼝（X）的总量正好等于在当前价格⽔平下企业所愿意出售的总量。
Equimarginal principle等边际法则决定收⼊在不同消费品之间分配的法则。
消费者可按此法则选择消费组合，使花费在所有商品和服务上的每⼀美元的边际效⽤都相等，就能保证消费者所获得的效⽤化。
Exchange rate汇率见外汇汇率（foreign exchange rate） Exchange－rate system汇率制度国家之间进⾏⽀付时所依据的⼀组规则、安排和制度。
历最重要的汇率制度是⾦本位制、布雷顿森林体系和现在的浮动汇率制。
Excise tax vs.sales tax消费税和销售税消费税是对某种或某组商品，如酒和烟草的购买所课征的税。
销售税是对除少数特定商品（如⾷品）以外的所有商品所课征的税。
Exclusion principle排他原则私⼈品区别于公共品的⼀种性质。
当⽣产者将⼀种商品卖给A后，若能很容易地将B、C、D 等⼈排除在该商品益处享⽤过程之外，则排他原则就在发⽣作⽤，该商品也因此是⼀项私⼈品。
若不能轻易地把其他⼈排除在分享过程之外，如公共卫⽣或国防，则我们称该商品具有公共品的特征。
Exogenous vs.induced variables外⽣变量和引致变量外⽣变量是那些由经济体系以外的因素来决定的变量。
与外⽣变量相对应的是引致变量，后者是由经济体系的内在运⾏所决定的。
例如，天⽓变化是外⽣变量，⽽消费的变化则常常由收⼊变动所引致。
经济评价基本术语英汉对照（精选五篇）第一篇：经济评价基本术语英汉对照汉英对照经济评价基本术语备择方案AlternativeOpen 备选方案Option备选方案价值 Option Value备选方案评估 OptionAppraisal标准换算系数 Standard Conversion Factor , SCF补贴 Subsidy 不变价格 Constant Price不可外贸货物 Non-Tradable Goods财务补贴 Financial Subsidy 环境卫生 Environment Sanitation 换算系数 Conversion Factor汇率溢价 Foreign Exchange Premium 或有估价法 Contingent Valuation Method , CVM 货币的时间价值 Time Value of Money机会成本 Opportunity Cost 基准收益率 Hurdle Cut-Off Rate 计算单位 Numeraire加权平均资金成本 Weighted Average Cost of Capital , 年金价值 Annuities Value平均增量财务费用 Average Incremental Financial Cost , AIFC 平均增量成本 Average Incremental Cost , AIC平均增量经济费用Average Incremental Economic Cost , AIEC 评估 Appraisal 评价 Evaluation项目框架 Project Rramework 项目周期 Project Cycle 消费者剩余 Consumer Surplus 效果费用比 Effectiveness Cost Ratio 需求曲线 Demand Price 需求曲线 Demand Curve要求回报率Required Rate of Return, RRR 意愿调差评估法Contingent Valuation 隐含价值法Hedonic Method 财务分析Financial Analysis 财务价格 Financial Price财务净现值 Financial Net Present Value , FNPV 财务可持续性Financial Sustainability财务内部收益率 Financial Internal Rate of Return , FIRR 财务效益 Financial Benefit财务效益费用分析Financial Benefit –Cost Analysis 残值Residual Value偿债备付率Debt Service Coverage Ratio , DSCR 陈诉偏好Stated Preference 成本回收Cost Recovery成本有效性分析Cost Effectiveness Analysis 出口评价Export Parity Price到岸价格Cost , Insurance & Freight , C.I.F 等价年度费用Equivalent Annual Cost非外贸产出和收入Non-Traded Output and Input非外贸货物Non-Traded Goods 费用效果比 Cost Effectiveness Ratio 费用效果分析 Cost Effectiveness Analysis , CEA 费用效益分析Cost Benefit Analysis , CBA 分配分析 Distribution Analysis 福利费用 Welfare Cost福利效益 Welfare Benefit公共产品 Public Goods 供给价Supply Price官方汇率 Official Exchange Rate , OER规模经济 Economies of Scale 国民收入平减指数 GDP Deflator耗减补偿 Depletion Premium 核算单位 Unit of Account环境估价Environment Valuation 环境可持续性Environment SustainabilityWACC价格扭曲Price Distortion价格指数Price Index 交叉补贴CrossProject 无形的 Intangible息税前利润 Earnings Before Interest and Tax , EBIT 显示偏好Revealed Preference 现存价值 Existence Value现金流出（量）Cash Outflow , CO 现金流（量）Cash Flow , CF 现金流入（量）Cash Inflow , CI 现值 Present Value , PV 相对价格作用Relative Price effect 项目备选方案Project Option盈亏价值法 Break – Even Point 影响陈述 Impact Statement影子工作率 Shadow Wage Rate , SWR影子工资系数Shadow Wage Rate Factor , SWRF 影子汇率Shadow Exchange Rate影子汇率系数Shadow Exchange Rate Factor ,SERF 影子价格Shadow Price有项目WithToEquity 资本化价值 Capitalized Value 资本金 Equity资本金净利润率 Return On Equity , ROE 资产负债率 Liability On Asset Ratio , LOAR 资金成本 Resource Cost资金的财务机会成本Financial Opportunity Cost of Capital , FOCC资金的经济机会成本 Economic Opportunity Cost of Capital , EOCC资源成本 Resource Cost总投资收益率 Return On Investment , ROI最低可接受收益率Minimum Acceptable Rate of Return , MARR第二篇：地质年代术语英汉对照stratum 地层stratigraphic correlation 地层对比horizon 层位key bed 标志层barren bed 哑层lacuna 缺失hiatus 间断continuity 连续discontinuity 不连续conformity 整合unconformity 不整合angular unconformity 角度不整合para-unconformity平行不整合geochronologic unit 地质年代单位eon 宙era 代period 纪epoch 世stage 期chron 时chronostratigraphic unit 年代地层单位eonothem 宇erathem 界system 系series 统stage 阶chronozone 时带biostratigraphic unit 生物地层单位biostratigraphic zone 生物地层带lithostratigraphic unit 岩石地层单位group 群formation 组member 段bed 层geochronologic scale 地质年代表Phaneozoic Eon(Eonothem)显生宙（宇）Cainozoic Era(Erathem)新生代（界）Cenozoic Era(Erathem)新生代（界）Quaternary Period(System)第四纪（系）Holocene Epoch(Series)全新世（统）Pleistocene Epoch(Series)更新世（统）Tertiary Period(System)第三纪（系）Neogene Period(System)新第三纪（系）Pliocene Epoch(Series)上新世（统）Miocene Epoch(Series)中新世（统）Paleogene Period(System)老第三纪（系）Oligocene Epoch(Series)渐新世（统）Eocene Epoch(Series)始新世（统）Paleocene Epoch(Series)古新世（统）Mesozoic Era(Erathem)中生代（界）Cretaceous Period(System)白垩纪（系）Jurassic Period(System)侏罗纪（系）triassic Period(System)三叠纪（系）Palaeozoic Era(Erathem)古生代（界）Permian Period(System)二叠纪（系）Carboniferous Period(System)石炭纪（系）DevonianPeriod(System)泥盆纪（系）Silurian Period(System)志留纪（系）Ordovician Period(System)奥陶纪（系）Cambrian Period(System)寒武纪（系）Cryptozoic Eon(Eonothem)隐生宙（宇）Proterozoic Eon(Eonothem)元古宙（宇）Neoproterozoic Era(Erathem)新元古代（界）Sinian Period(System 震旦纪（系）Mesoproterozoic Era(Erathem)中元古代（界）Palaeoproterozoic Era(Erathem)古元古代（界）Archaean Eon(Eonothem)太古宙（宇）Precambrian 前寒武纪第三篇：会计术语英汉对照会计名词术语英汉对照（仅供参考，欢迎指正和补充）account title 会计科目，账户名称 account 账户accounting circle 会计循环accounting entity assumption 会计主体假设accounting period assumption 会计分期假设accounting process 会计流程accounting report 会计报告 accounts payable 应付账款accounts receivable turnover ratio 应收账款周转率accounts receivable 应收账款accrual-basis accounting 应计制会计，权责发生制会计accrued accounting 应计制会计 accrued revenues 应计收入accumulated depreciation 累计折旧 adjusting entries 调整分录administrative expenses 管理费用 advances 预付款aging schedule 账龄分析表allowance for doubtful accounts 坏账准备allowance for returns 备抵销售退回 asset 资产average collection period平均收款期 bad debts expense 坏账费用 balance sheet 资产负债表 bank account 银行存款bank reconciliation银行存款余额调节 bank statement 银行对账单book of original entry 原始分录簿book value 账面价值bookkeeping 簿记business document 业务凭证 calendar year 日历carrying value 账面价值，现存价值cash(net)realizable value 可变现净值 cash advance 预付现金cash count sheet 现金盘点表cash disbursement 现金支出cash discount 现金折扣 cash inflows 现金流入 cash outflows 现金流出 cash over or shot 现金溢缺cash payments journal 现金支出分录簿 cash receipt 现金收入cash receipts journal 现金收入分录簿 cash refund 现金折扣cash register receipt 收款机收据（收银条）cash 现金cash-basis accounting 现金制会计，收付实现制会计 cashier 收银员，出纳chart of accounts 会计科目表 check register 支票登记簿 check 支票claim 索取权、求偿权 claimer 索取者、求偿权人classified balance sheet 分类资产负债表 closing entries 结账分录 closing the book 结账 common stock 普通股 comparability 可比性compensating balances 补偿性余额，补偿性最低存款额compound entry 复合分录conceptual framework 概念框架conservatism 稳健性consistency 一致性contra asset account 资产对销账户，资产备抵账户contra-revenue account 收入抵消账户 corporation 公司correcting entries 更正分录 cost of goods sold 销货成本 cost principle 成本计价原则 credibility 可靠性credit balance 贷方余额 credit(s)贷，贷方current assets 流动资产 current liability 流动负债 current ratio 流动比率current replacement cost 现行重置成本 dealership 代理商debit balance 借方余额 debit(s)借，借方debt to total assets ratio 资产负债率 debt(s)债务decision usefulness 决策有用性 deferrals 递延项目deposit slip 存款单 deposit ticket 存款单deposits in transit 在途存款depreciation expense 折旧费用dishonor(note)拒绝承兑（票据）dividend 股利double-entry system 复式记账法 due date 到期due from sb.应收某人 due from sb.应收某人earnings per share 每股盈余economic entity assumption 经济主体假设 economic event 经济事项electronic funds transfer 电子资金转账 ending balance 期末余额 endorsement 背书 enter 登记 expense 费用expired cost 已耗成本factor 客账经纪商，代理商faithful representation 忠实表述，如实反映 feedback value 反馈价值Financial Accounting Standards Board(FASB)（美国）财务会计准则委员会financial statements 财务报表 finished goods 产成品first-in, first-out(FIFO)先进先出法fiscal year 会计，财政FOB destination 目的地交货 FOB shipping point 寄发地交货 FOB 离岸价格For Deposit Only 仅限转账 freight cost 运费general journal 普通分录簿Generally Accepted Accounting Standards(GAAP)公认会计准则going concern assumption 持续经营假设going-concern assumption 持续经营假设 grace period宽限期 gross profit 毛利guaranteed debt 担保债券 honor(note)承兑（票据）imprest system 定额备用金制度 income from operations 营业利润 income sheet 利润表income summary 损益汇总income tax 所得税intangible assets 无形资产 interim period 中期International Accounting Standards Board(IASB)国际会计准则委员会 inventory count 存货盘点，盘存inventory summary sheets 库存汇总表 inventory turnover 存货周转率 investor 投资者journal 分录簿，日记账journalize 登分录簿，记日记账last-in, first-out(LIFO)后进先出法 lease liability 租赁负债 ledger 分类账 liability 负债liquidity 流动性，变现能力long-term investment 长期投资long-term liability 长期负债lower of cost or market 成本与市价孰低法 market value 市场价值matching principle 匹配原则 materiality 重要性merchandise inventory 库存商品 miscellaneous expense 杂费monetary measurement assumption货币计量假设 monetary unit assumption 货币单位假设 money down 现金，现款 mortgage 抵押借款 net assets 净资产 net income 净收益 neutral 中立性nominal account 虚账户 note payable 应付票据 note(s)附注obligations 承付款项 on account 赊账on demand 见票即付operating expenses 营业费用 operating income 营业利润other expenses and losses 其他费用和损失other revenues and gains 其他收入和利得 outstanding checks 未兑现支票 owed to sb.应付、亏欠某人 paid-in capital 投入资本partnership 合伙企业，合伙制 past-due 逾期，过期未付periodic inventory system 定期盘存制 permanent account 永久性账户perpetual inventory system 永续盘存制 petty cash fund 小额现金基金 postdated check 未到期支票 posting 过账predictive value预测价值 prepaid expenses 预付费用 prepaid insurance 预付保险profit margin percentage 销售利润率profitability 盈利能力promissory note 本票proprietorship 独资企业，业主制purchase invoice 购货发票purchases journal 购货分录簿 raw meterials 原材料 real account 实账户 relevance 相关性 reliability 可靠性remittance advice 汇款通知restrictive endorsement 限制性背书 retailer 零售商retained earnings statement 留存盈余表 retained earnings 留存盈余 return on assets 总资产收益率return on equity 权益收益率，净资产收益率revenue recognition principle 收入确认原则 revenue 收入reversing entries 转会分录 ring up 把款项（金额）记入 sale on credit 赊销，信用销售 sales discount 销售折扣 sales journal 销货分录簿sales return and allowance 销售退回和折让sales slip 销售单scrap value 残值Securities and Exchange Commission(SEC)（美国）证券交易委员会selling expenses 销售费用 service revenue 服务收入 simple entry 简单分录 solvency 偿债能力source document 原始凭证 special journal 特种分录簿specific identification 个别认定法，个别计价法statement of cash flows 现金流量表stockholders’ equity 股东权益 subsidiary ledger 明细分类账 supplies（日常）用品 taxes payable 应付税费temporary account 暂时性账户three-column form of account 三栏式账户time period assumption 会计分期假设 treasurer 财务主管，出纳 trial balance 试算平衡 uncollectable(s)坏账uncollected account expense 坏账费用 unearned revenue 预收收入，未实现收入 unexpired cost 未耗成本 unexpired cost 未耗用成本 verifiable 可核性，可验证性 voucher register 付款凭单登记簿voucher system 付款凭单制度wage payable 应付职工薪酬wholesaler 批发商work in process 在产品work sheet 工作底稿working capital 营运资本 working paper 工作底稿 write-off 冲销第四篇：英汉对照计量经济学术语计量经济学术语A 校正R2（Adjusted R-Squared）：多元回归分析中拟合优度的量度，在估计误差的方差时对添加的解释变量用一个自由度来调整。
泰尔指数分析我国卫生资源地区分布公平性泰尔指数的运用可以避免采用基尼系数时由于指数缺陷而产生的偏差,更为准确地衡量我国卫生资源地区分布的公平性。
本文首先使用泰尔指数从地区内部和地区之间两个方面分解我国不公平性产生的途径,然后综合两种途径对我国卫生资源地区分布的不公平性进行测算。
研究发现我国卫生资源地区间分布的公平性有所改善,而地区内部的不公平程度却有加剧的倾向,使得总体公平性的改善不明显;卫生硬件资源分布的公平性要优于软件资源。
标签：卫生资源公平性泰尔指数一、前言作为社会公平基本内容之一,卫生资源分布的公平意味着每一位社会成员拥有相同的机会获得医疗卫生服务,其直接体现社会公平,并对构建和谐社会产生重要的影响。
通过进行卫生服务资源公平性的研究,可以指导卫生资源合理配置,发现并保护弱势群体,进而促进建立卫生服务公平的动态监测与反馈机制等。
国内对卫生资源分布公平性已有一些研究,但是大部分研究文章停留在描述性分析的层面上,没有根据公平性指标对其进行量化。
部分研究采用了洛伦兹曲线(Lorenz Curve)和基尼系数(Gini Coefficient)来评价我国卫生资源分布的公平性,但是由于这两种测算方法存在着内在缺陷,分析结果往往与实际情况不完全相符。
本文通过泰尔(Theil)指数的运用,试图克服基尼指数分析的缺陷,较为深入地分析我国卫生服务资源的公平性。
文中所用到的全国各省地级市人口和卫生资源的数据资料来源于国家统计局国民经济综合统计司编写的《中国区域经济统计年鉴》2002、2004、2006和2008年卷。
二、研究方法与结果1.研究方法的说明关于公平性分析的指标,国外有一些文献采用公平性指数对卫生服务公平性进行分析。
Wagstaff 等(1991) 利用集中指数法衡量保健费用和健康状况分布的不公平性。
Doorslaer等(1994) 提出了一种使用各种患病率指标衡量健康不公平性的方法。
Gerdtham 等(1996) 用集中指数法衡量健康状况的不公平性。
泰尔指数ev-概述说明以及解释1.引言文章1.1 概述：泰尔指数ev是一种常用的经济学指标，用于衡量一个国家或地区的财富或收入分配的不平等程度。
它是由意大利统计学家科雷多·泰尔（Corrado Gini）在1912年提出的。
泰尔指数通过计算财富或收入分布的不平等程度，可以帮助我们了解一个社会的公平性和社会经济发展的程度。
泰尔指数的值范围在0到1之间，值越接近0，表示财富或收入分配越均衡；而值越接近1，表示财富或收入分配越不平衡。
当泰尔指数为0时，意味着所有人的财富或收入都完全相同；当泰尔指数为1时，表明一个个体拥有了全部的财富或收入，而其他人没有任何财富或收入。
泰尔指数的计算方法相对简单，可以通过对个体财富或收入进行排序后，根据累计百分比计算得出。
具体来说，我们可以将财富或收入按照从小到大的顺序排序，然后计算累计百分比，最后根据泰尔指数的公式进行计算。
泰尔指数在各个领域都有广泛的应用。
在经济学领域，泰尔指数可以帮助研究者了解经济的公平性和稳定性情况，为制定经济政策提供参考。
在社会学领域，泰尔指数可以帮助我们了解财富或收入分配对社会的影响，揭示社会阶层和社会不平等问题。
在发展经济学领域，泰尔指数可以帮助我们比较不同国家或地区之间的财富或收入分配情况，从而进行国际比较和分析。
总而言之，泰尔指数ev作为一种重要的经济学指标，对于了解一个国家或地区的财富或收入分配的不平等情况具有重要意义。
通过计算泰尔指数，我们可以更好地了解社会经济的公平性和稳定性，为制定相关政策提供支持。
在未来，泰尔指数的应用领域还有待进一步拓展和研究，以更好地服务于社会经济的发展与进步。
1.2 文章结构文章结构部分的内容:文章分为引言、正文和结论三大部分。
引言部分主要包括概述、文章结构和目的。
在概述部分，将对泰尔指数进行简要介绍，包括其定义、计算方法和应用领域等基本信息。
在文章结构部分，将详细说明本篇文章的整体结构安排，以便读者能够清晰地了解文章的组织框架。
对测量不平等的泰尔指数和基尼系数比较作者：刘续棵来源：《经济研究导刊》2014年第07期摘要：测量收入不平等以及研究贫困问题主要采用的两种方法就是利用基尼系数和泰尔指数。
基尼系数的计算本身存在三种最为常用的区别，而泰尔指数在组内组间分解上更优于基尼系数，但是由于其计算收入转移上的敏感性，使得其与基尼系数相比更可能高估不平等。
通过对比这两种计算方法，可以对不同的微观数据采用不同的方法。
关键词：基尼系数；泰尔系数；收入不平等中图分类号：F0 文献标志码：A 文章编号：1673-291X（2014）07-0012-03一、基尼系数的测量就衡量收入不平等而言，我们最为常用的方式就是使用基尼系数进行衡量。
从1921年基尼系数（Gini，1921）第一次出现到现在已经有八十年的历史（Xu，Kuan，2004），对基尼系数的研究和分析已经形成一套很成熟的方法和并积累了大量相关的文献。
在对基尼系数论述的的文献历史中，Anand （1983）和Chakravarty （1990）对包括基尼系数在内的不平等测量方法进行了全面的调查，Lambert （1989），以及Atkinson and Bourguignon （2000）也对利用基尼系数衡量收入不平等以及贫困问题提供了全面的参考文献。
对于基尼系数的发展历程及文献综述回顾可以参见Kuan Xu（2004），其根据以往的文献对基尼系数的产生和发展进行了一次全面的梳理，同时对基尼系数的解释，社会福利效应以及收入分解都做了详细的介绍。
在Kuan Xu（2004）的文章中，基尼系数定义为用来衡量收入、消费以及财产分配差异的指标。
对基尼系数的测量主要有三种方法：几何法、协方差法以及矩阵法。
（一）几何法对于几何法而言，主要是根据洛伦兹曲线来对基尼系数进行几何描述，其初始公式为：A：是洛伦兹曲线与完全平等曲线（45度线）之间的区域面积B：是洛伦兹曲线以下的区域面积以人口的累积百分比由低到高作为横坐标，由收入的累计百分比由低到高作为纵坐标。
苹果iPod Shuffle 营销分析在美国人的生活中，iPod突然变得无所不在。
当你身处麦迪逊大街，看到几乎每一个街区都有人戴着白色耳机；当你走进健身房，发现几乎每个人都戴着它；而当你坐在校园的长凳上，也会发出会心的微笑——学生们都在用iPod。
iPod，已成为联结人们的纽带。
将近3/4的美国人的口袋里揣着iPod，是什么神奇的力量，让这么多美国人对小小的iPod一见钟情，百用不厌，爱不释手呢？1.1政策背景 (5)1.1.1宏观政策背景 (5)1.1.2 政府促进和鼓励技术创新的政策 (5)1.2经济背景 (6)1.2.1经济发展状况 (6)1.2.2收入情况 (6)1.3社会人文背景 (7)1.3.1人口规模分析 (7)1.3.1.1美国人口 (7)1.3.1.2美国的移民 (8)1.3.1.3美国种族 (8)1.3.2年龄结构 (9)1.3.3性别比例 (9)1.3.4教育 (9)1.3.5社会文化 (9)1.4技术背景 (10)1.5环境因素 (11)1.6 法律背景 (11)第二部分美国消费者分析 (13)2.1不同社会阶层的消费态度 (13)2.2不同地区的消费能力 (14)2.3不同学的教育程度消费能力 (15)2.4不同职业的消费能力 (15)2.5不同种族的消费能力---亚裔成美国最富有族群 (16)2.6不同年龄的消费能力与消费观念 (17)2.6.1 X-一代 (17)2.6.2 Y-一代 (17)2.6.3 Tweens 一代 (18)2.7不同性别的收入与消费特性 (18)2.8季节对美国消费的影响 (19)第三部分美国MP3市场分析 (20)3.1 美国MP3概况 (20)3.1.1价格与存储媒介 (20)3.1.2音质与行业背景 (21)3.1.3版权与压缩格式 (21)3.1.4使用与下载方式 (22)3.1.5宽频内容大行其道对MP3市场的影响 (22)3.2美国MP3 市场发展规模 (22)3.2.1美国MP3市场销售总量 (22)3.2.2美国MP3消费人群 (24)3.2.3产品结构 (25)3.2.4产品价格结构 (25)3.2.5品牌市场结构 (25)3.2.6销售渠道结构 (26)3.3美国MP3市场特点 (27)3.3.1市场规模迅速扩大，厂商分化为两大阵营 (27)3.3.2大容量，高兼容性成为未来产品市场发展的方向 (27)3.3.3闪存供货紧张妨碍了全球闪存型MP3播放机市场的发展 (27)3.3.4 MP3播放机厂商介入线上音乐市场产业链日趋规范 (28)第四部分 iPod Shuffle 营销策略 (29)4.1 iPod 品牌建设 (29)4.1.1苹果的由来 (29)4.1.2苹果公司的企业文化 (29)4.1.3企业品牌形象 (30)4.1.4 iPod 品牌策略 (30)4.1.5 强势的品牌需要优越的产品品质 (30)4.1.5.1产品创意 (30)4.1.5.2产品设计 (30)4.1.5.3产品策略 (31)4.2 iPod 市场分析 (31)4.2.1.1性别细分 (31)4.2.1.2 年龄细分 (32)4.2.1.3 教育程度细分 (32)4.2.1.4 职业细分 (33)4.2.1.5根据产品特性细分 (33)4.2.2 iPod 目标市场 (35)4.2.3 iPod 市场差异化定位 (36)4.2.3.1水平层次差异化 (36)4.2.3.2垂直层次的差异化 (36)4.2.4市场优势劣势机会和威胁分析 (37)4.2.4.1 iPod MP3的优势和机会 (38)4.2.4.2 iPod MP3的劣势和威胁 (39)4.3 iPod Shuffle 营销计划 (40)4.3.1 iPod Shuffle产品 (40)4.3.1.1目标市场 (40)4.3.1.2市场定位 (40)4.3.1.3 产品介绍 (40)4.3.1.4产品策略 (41)4.3.1.5产品包装 (42)4.3.2价格 (42)4.3.2.1分析竞争者的产品与价格 (42)4.3.2.1.1主要竞争对手分析： (42)4.3.2.2 iPod Shuffle 价格策略 (44)4.3.3 渠道建设 (44)4.3.4营销策略 (45)4.3.4.1文化营销 (45)4.3.4.2产品营销 (46)4.3.4.3服务营销 (47)4.3.4.4联合营销 (47)4.3.4.5体验营销 (48)4.3.4.5广告营销 (49)4.3.5 促销手段 (49)4.3.5.1新品发布会 (49)4.3.5.2以旧换新 (49)4.3.5.3圣诞节，感恩节打折促销 (50)4.3.5.4校园促销活动 (50)4.3.6财务方面 (50)第一部分美国市场环境分析1.1政策背景1.1.1宏观政策背景美国有着良好的经济体制兼有资本主义和混合经济的特征。
㊃卫生服务评价㊃十三五 期间我国卫生人力资源配置现状及公平性分析高祺阳1, 刘丽丽1, 周恭伟2ʌ基金项目ɔ 国家重点研发计划项目(2018Y F C 1311701);国家重点研发计划项目(2016Y F C 0901705)ʌ作者单位ɔ 1宁夏医科大学,宁夏银川,7500042国家卫生健康委统计信息中心,北京,100810ʌ通信作者ɔ 周恭伟,E -m a i l :z h o u g w@n h c .go v .c n ʌ摘要ɔ 目的 了解 十三五 期间我国卫生人力资源配置现状,并分析其配置的公平性,为我国卫生人力资源的合理配置提供建议㊂方法 根据统计年鉴数据,通过描述性统计㊁卫生资源集聚度方法分析 十三五 期间我国31个省㊁自治区和直辖市及东中西部地区卫生人力资源配置的公平性㊂结果 2016-2020年我国卫生人力资源总体呈现增长趋势,但依旧存在机构间㊁区域间以及城乡间分配不均衡㊂机构层面,医院的人力资源总量持续高于基层医疗卫生机构,卫生技术人员占比逐年提高㊂地区层面,东部地区千人口执业(助理)医师数㊁千人口注册护士数㊁千人口药师(士)数均高于中西部地区㊂其中,绝对数值相差最大的是2019年千人口执业(助理)医师数,城乡差距为0.48㊂城乡层面,城市每千人口卫生技术人员㊁执业(助理)医师㊁注册护士数始终高于农村,各项指标均在农村数量的2倍以上㊂卫生人力资源配置公平性存出明显的区域差异,东部地区的集聚度值大于中㊁西部地区㊂各省份比较发现,东部地区中上海的各类卫生技术人员集聚度最高,中部地区中河南各类卫生技术人员集聚度最高,而西部地区中重庆卫生技术人员集聚度最高㊂结论 十三五 期间我国卫生人力资源配置存在机构间㊁区域间以及城乡间分配不均衡的问题,且我国卫生人力资源按人口配置的公平性优于按地理配置的公平性㊂政府应兼顾地理和人口等多方面因素,缩小卫生人力资源配置地区差异,均衡卫生人力资源配置,优化卫生人力资源按地理配置的公平性㊂ʌ关键词ɔ 卫生人力资源; 卫生资源集聚度; 公平性ʌ中图分类号ɔ R 197.1 ʌ文献标志码ɔ A D O I :10.3969/j.i s s n .1673-5625.2024.02.024R e s e a r c ho nt h eC u r r e n tS i t u a t i o na n d F a i r n e s so fC h i n a 's H e a l t h H u m a n R e s o u r c e A l l o c a t i o nd u r i n gt h e "13t hF i v e -Y e a rP l a n "P e r i o d G A O Q i y a n g *,L I U L i l i ,Z H O U G o n g w e i .*N i n g x i aM e d i c a lU n i v e r s i t y ,Y i n c h u a n ,750004,C h i n a ʌA b s t r a c t ɔ O b je c t i v e T h e a i mof t h i s s t u d y i s t og a i na nu n d e r s t a n d i n g o f th e c u r r e n t s t a t u so f h e a l t hh u m a nr e -s o u r c e a l l o c a ti o n i n C h i n a d u r i n g t h e 13t h F i v e -Y e a r P l a n p e r i o d ,a n d t o a n a l y z e t h e e q u i t y of s u c h a l l o c a t i o n .F u r t h e r m o r e ,t h i s r e s e a r c ha i m s t o p r o v i d e r e c o m m e n d a t i o n s f o r t h e r a t i o n a l d i s t r i b u t i o no f h e a l t hh u m a n r e s o u r c e si n C h i n a .M e t h o d s T h i s s t u d y e m p l o y e d d e s c r i p t i v e s t a t i s t i c a l a n a l ys i s t o a s s e s s t h e p r e s e n t s i t u a t i o n .A d d i t i o n a l l y ,h e a l t h r e s o u r c e c o n c e n t r a t i o nm e t h o d sw e r e u t i l i z e d t o a n a l y z e t h e e q u i t y of h e a l t hh u m a n r e -s o u r c e a l l o c a t i o na c r o s st h e31p r o v i n c e s ,a u t o n o m o u sr eg i o n s ,m u n i c i p a l i t i e s ,a s w e l la sth ee a s t e r n ,c e n t r a l ,a n d w e s t e r n r e gi o n s o f C h i n a d u r i n g t h e 13t hF i v e -Y e a r P l a n p e r i o d .R e s u l t s T h e f i n d i n g s i n d i c a t e d a n o v e r a l l i n c r e a s i n gt r e n d i nh e a l t hh u m a n r e s o u r c e s d u r i n g t h e p e r i o d f r o m2016t o 2020.H o w e v e r ,s i g n i f i c a n t d i s pa r i t i e s i nd i s t r ib u t i o n p e r s i s t e d a m o n g d i f f e r e n t i n s t i t u t i o n s ,r e gi o n s ,a n du r b a na n d r u r a l a r e a s .A t t h e i n s t i t u t i o n a l l e v e l ,t h e r ew a s a c o n -s i s t e n t i m b a l a n c e i n t h e a l l o c a t i o n o f h u m a n r e s o u r c e s ,w i t hh o s p i t a l s h a v i n g a h i g h e rw o r k f o r c e c o m p a r e d t o p r i m a r y h e a l t h c a r e i n s t i t u t i o n s .T h e p r o p o r t i o no fh e a l t ht e c h n i c a l s t a f fh a ds h o w nas t e a d y ri s eo v e r t h e y e a r s .F r o mar e -g i o n a l p e r s p e c t i v e ,t h e e a s t e r n r e g i o n e x h i b i t e dh i g h e r n u m b e r s o f p r a c t i c i n g (a s s i s t a n t )p h y s i c i a n s ,r e gi s t e r e dn u r s e s ,a n d p h a r m a c i s t s p e r t h o u s a n d p o p u l a t i o n c o m p a r e d t o t h e c e n t r a l a n dw e s t e r n r e g i o n s .N o t a b l y ,t h e l a r ge s t d if f e r e n c e i na b s o l u t en u m b e r sw a s o b s e r v e d i n 2019,w h e r e t h e s h o r t ag e o f p r a c t i c i n g (a s s i s t a n t )ph y si c i a n s p e r t h o u s a n d p o p u -l a t i o nb e t w e e nu r b a na n dr u r a l a r e a sr e a c h e d0.48.F u r t h e r m o r e ,u r b a na r e a sc o n s i s t e n t l y m a i n t a i n e ds i g n i f i c a n t l yh i g h e r n u m b e r s o f h e a l t h t e c h n i c i a n s ,p r a c t i c i n g (a s s i s t a n t )p h y s i c i a n s ,a n d r e g i s t e r e dn u r s e s p e r t h o u s a n d p o pu l a t i o n c o m p a r e d t o r u r a l a r e a s ,w i t h t h e f o r m e r c o n s i s t e n t l y e x c e e d i n g t h e l a t t e r b y m o r e t h a nd o u b l e .I n t e r m s o f e q u i t yi n t h e a l l o c a t i o no f h e a l t hh u m a nr e s o u r c e s ,s i g n i f i c a n t r e g i o n a l d i s p a r i t i e sw e r eo b s e r v e df r o m b o t h g e o g r a ph i c a l a n d d e m o g r a p h i c p e r s p e c t i v e s ,w i t h c o n c e n t r a t i o n v a l u e s c o n s i s t e n t l y h i g h e r i n t h eE a s t e r n r e g i o n c o m pa r e d t o t h e c e n t r a l a n dw e s t e r n r e g i o n s .A m o n g t h e p r o v i n c e s ,S h a n g h a i i n t h e e a s t e r n r e g i o n e x h ib i t e d t h e h i g h e s tc o n c e n t r a t i o n o f v a r i -832中国社会医学杂志2024年4月第41卷第2期 C h i n e s e J o u r n a l o f S o c i a lM e d i c i n e ,A pr i l 2024,V o l .41,N o .2o u s c a t e g o r i e s o f h e a l t h t e c h n i c a l s t a f f,w h i l eH e n a n i nt h ec e n t r a l r e g i o na n dC h o n g q i n g i nt h ew e s t e r nr e g i o nd e-m o n s t r a t e d t h e h i g h e s t c o n c e n t r a t i o n o f h e a l t h t e c h n i c a l s t a f f.C o n c l u s i o n T h i s s t u d y r e v e a l s u n e q u a l d i s t r i b u t i o n o fh e a l t hh u m a n r e s o u r c e s a c r o s s i n s t i t u t i o n s,r e g i o n s,a n du r b a na n d r u r a l a r e a s d u r i n g t h e13t hF i v e-Y e a rP l a n p e r i o di nC h i n a.T h e f i n d i n g s h i g h l i g h t t h e s u p e r i o r i t y o f e q u i t y b a s e do nd e m o g r a p h i c c o n s i d e r a t i o n s r a t h e r t h a n g e o g r a p h i c a l c o n s i d e r a t i o n s i n t h e a l l o c a t i o no fh e a l t hh u m a nr e s o u r c e s.I no r d e r t oa d d r e s s t h e s ed i s p a r i t i e sa n da c h i e v eam o r e b a l a n c e dd i s t r i b u t i o no fh e a l t hh u m a nr e s o u r c e s,i t i sr e c o m m e n d e dt h a t t h e g o v e r n m e n t t a k e i n t oa c c o u n tv a r i o u s f a c t o r s,i n c l u d i n gp o p u l a t i o na n d g e o g r a p h y,a n do p t i m i z e t h e g e o g r a p h i c a l l o c a t i o no f h e a l t hh u m a n r e s o u r c e s.ʌK e y w o r d sɔ H e a l t hh u m a n r e s o u r c e s; H e a l t h r e s o u r c e a g g l o m e r a t i o n; E q u i t y卫生人力资源是指在一定时间和一定区域范围内存在于卫生行业内部的具有一定专业技能的各类卫生工作者数量和质量的总和,是卫生资源中最重要的资源,是保障人民健康和促进社会生产活动的最基本最重要的资源[1]㊂其配置的公平性㊁合理性直接反映出居民健康的平等程度,对于卫生服务质量的提升和卫生事业健康持续发展具有重要作用[2]㊂因此,本文以 十三五 时期为时间节点,运用卫生资源集聚度分析 十三五 期间我国卫生人力资源配置公平性,总结其配置的特点及存在的问题,为进一步优化我国卫生人力资源配置㊁推动全民健康目标的实现提供可行性建议策略㊂1资料与方法1.1资料来源本文所涉及的卫生技术人员㊁执业(助理)医师㊁注册护士㊁药师(士)㊁技师(士)㊁每千人口执业(助理)医师㊁每千人口注册护士数据均来源于2016-2017年‘中国卫生和计划生育统计年鉴“㊁2018-2021年‘中国卫生健康统计年鉴“㊂各地区及总人口数来源于‘中国统计年鉴“;各地区地理面积来自人民政府网国情部分;不同区域划分根据国家统计局地区分组标准将我国31个省㊁自治区和直辖市分为东㊁中㊁西部三个区域㊂1.2研究方法当前,国内外用于评价卫生资源配置公平性的方法主要有基尼系数㊁泰尔指数㊁集中指数㊁集聚度等,本研究中采用集聚度指标来评价卫生人力资源配置的公平性㊂集聚度指一个区域的卫生资源相对于整体的卫生资源集聚程度的指标,反映了资源在不同维度下的配置集中情况,包括卫生资源集聚度(h e a l t hr e s o u r c ea g g l o m e r a t i o nd e g r e e,H A R D)和人口集聚度(p o p u l a t i o na g g l o m e r a t i o nd e g r e e, P A D)[3]㊂本研究利用E x c e l2021录入数据,计算各地区卫生资源集聚度和人口集聚度值㊂1.2.1卫生资源集聚度地理配置公平性用卫生资源集聚度表示,计算公式:H A R D i=(H R i/A i)/ (H R n/A n)㊂H A R D i表示某区域i的卫生资源集聚度,H R i 表示某区域i拥有的卫生资源数量,H R n表示全国拥有的卫生资源总量㊂A i表示某区域i的地理面积,A n表示全国地理面积㊂其中H A R D i>1代表该地区拥有的卫生资源按地理面积配置过剩;H A R D i<1代表该地区拥有的卫生资源按地理面积配置不足;H A R D i=1则代表该地区卫生资源按地理面积配置绝对公平㊂1.2.2人口集聚度人口配置公平性用卫生资源集聚度与人口集聚度的比值(H A R D i/P A D i)表示,计算公式:P A D i=(P i/A i)/(P n/A n)㊂P A D i表示某区域i的人口集聚度,P i表示某区域i拥有的人口数量,P n表示全国拥有的人口总量㊂A i表示某区域i的地理面积,A n表示全国地理面积㊂其中H A R D i/P A D i>1代表该地区拥有的卫生资源量相对于该地区人口过剩;H A R D i/ P A D i<1代表该地区拥有的卫生资源量相对于该地区人口不足;H A R D i/P A D i=1则代表该地区拥有的卫生资源按人口配置处于绝对公平状态㊂2结果2.1我国卫生人力资源配置现状2.1.1卫生人力资源机构配置现状 十三五 期间,我国医院㊁基层医疗卫生机构包括卫生技术人员在内的人员数量呈现逐年增长趋势㊂在卫生人员总量上,医院始终高于基层医疗卫生机构,且此差距逐年加大,截至2020年我国医院人员总数已经超过基层机构43万余人㊂卫生技术人员数量方面,医院高于基层医疗卫生机构,2016-2019年差距逐年加大,2020年该差距有所回落㊂见表1㊂人力资源配置结构方面,我国医院㊁基层医疗卫生机构卫生技术人员占比逐年提高,医院卫生技术人员占比由2016年的82.77%提高至2020年的83.52%,基层医疗卫生机构卫生技术人员占比也由2016年的63.93%提高至2020年的71.98%,尽管基层医疗机构该指标始终低于医院,但已将差距由18.84%缩小至11.54%㊂ 十三五 期间,我国医院㊁基层卫生机构各类卫生技术人员数量增速基本呈现 先加快后放缓 的态势,通过增长率横向对比可知,2019年㊁2020年基层医疗卫生机构各类卫生技术人员增长率均超过医院同期水平㊂见表2㊂932中国社会医学杂志2024年4月第41卷第2期 C h i n e s e J o u r n a l o f S o c i a lM e d i c i n e,A p r i l2024,V o l.41,N o.2表1 十三五 期间我国医院㊁基层医疗卫生机构人员数量情况年份医院医院人员数/人卫生技术人员数/人卫生技术人员占比/%基层医疗卫生机构基层医疗卫生机构人员数/人卫生技术人员数/人卫生技术人员占比/%20166542137541506682.773682561235443063.9320176976524578471282.923826234250517465.4720187375273612920183.103964744268298367.6720197782171648749783.364160571292099970.2120208111981677476483.524339745312395571.98表2 十三五 期间我国医院㊁基层医疗卫生机构卫生技术人员结构情况年份执业(助理)医师医院人数/人增长率/%基层医疗卫生机构人数/人增长率/%注册护士医院人数/人增长率/%基层医疗卫生机构人数/人增长率/%201618034626.5411454083.9526133678.556957817.60201719325307.1612136075.9528224468.0076920610.55201820535276.2613051087.5430208137.0385237710.81201921742645.88143661910.0832379877.1996037412.67202022825744.9815363816.9433884454.65105742010.11年份药师(士)医院人数/人增长率/%基层医疗卫生机构人数/人增长率/%技师(士)医院人数/人增长率/%基层医疗卫生机构人数/人增长率/%20162787304.611380602.652915536.44928845.4220172878373.271424823.203101916.39993076.9220182976383.411468273.053261745.151055906.3320193075703.341520203.543444615.611131547.1620203150912.451570013.283585974.101185154.742.1.2 卫生人力资源区域配置状况十三五 期间我国东㊁中㊁西各区域各类卫生技术人员每千人口均数有所变化:2016-2020年我国不同区域每千人拥有各类卫生技术人员数均逐年增加,东㊁中㊁西部与国家平均水平折线随着时间变化有 集中-离散-集中 的趋势㊂东部地区千人口执业(助理)医师数㊁千人口注册护士数㊁千人口药师(士)数均高于中西部地区㊂其中,绝对数值相差最大的是千人口执业(助理)医师数,2019年东部地区千人口执业(助理)医师数比中部地区高0.48,约高出当年中部地区千人口执业(助理)医师数的18.90%㊂见图1㊂图1 十三五 期间卫生技术人员每千人口数量的变化趋势42中国社会医学杂志2024年4月第41卷第2期 C h i n e s e J o u r n a l o f S o c i a lM e d i c i n e ,A pr i l 2024,V o l .41,N o .22.1.3卫生人力资源城乡配置情况2016-2020年,我国城乡每千人口卫生技术人员[包括执业(助理)医师㊁注册护士]数均呈现增长态势,但城市每千人口卫生技术人员㊁执业(助理)医师㊁注册护士数始终高于农村,农村与城市差距有所缩小但极其有限,城市各项指标均在农村数量的2倍以上㊂截止2020年底,我国城市地区每千人口执业(助理)医师数为4.3,农村地区为2.1,相差2.2;我国城市地区每千人口注册护士数为5.4,农村地区2.1,相差3.3㊂见表3㊂表3 十三五 期间我国城乡每千人口卫生技术人员数量情况年份每千人口卫生技术人员/人城市农村每千人口执业(助理)医师/人城市农村每千人口注册护士/人城市农村201610.44.13.81.64.71.5 201710.94.34.01.75.01.6 201810.94.64.01.85.11.8 201911.15.04.12.05.22.0 202011.55.24.32.15.42.12.2卫生人力资源配置公平性2.2.1我国东㊁中㊁西部不同区域间卫生人力资源集聚度结果2016-2020年我国卫生人力资源配置公平性呈现明显的区域差异㊂地理配置公平性方面:我国东部执业(助理)医师㊁注册护士㊁药师(士)㊁技师(士)的卫生资源集聚度值始终大于中部㊁西部地区,并且其值均在3.7以上,中部地区1.5以上㊂总体而言,东部㊁中部地区的卫生资源集聚度值大于西部地区,我国东㊁中㊁西部地区卫生人力资源集聚度差距较大;人口配置公平性方面:2016-2020年期间执业(助理)医师㊁注册护士㊁药师(士)㊁技师(士)的H A R D与P A D的比值大小虽存在差距,但差距较小㊂这表明,基于地理和人口,我国卫生人力资源配置公平性均存在区域差异,但我国卫生人力资源人口配置公平性优于地理配置公平性㊂见表4㊂表4我国东㊁中㊁西部地区卫生人力资源集聚度地区P A D执业(助理)医师H A R D比值注册护士HA R D比值药师(士)HA R D比值技师(士)H A R D比值2016年东部3.784.011.063.921.044.201.123.821.02中部1.771.730.981.700.961.620.901.750.97西部0.380.350.920.370.970.360.950.381.01 2017年东部3.794.031.063.901.034.221.123.821.01中部1.761.710.971.670.951.590.881.720.96西部0.380.350.920.381.000.360.960.391.03 2018年东部3.804.071.073.911.034.211.123.791.00中部1.751.690.971.660.951.570.871.710.95西部0.380.350.920.381.000.370.970.401.05 2019年东部3.814.071.073.841.014.221.113.760.99中部1.751.670.951.680.961.540.861.690.94西部0.380.360.950.391.030.370.980.411.07 2020年东部3.834.041.053.810.994.211.083.740.96中部1.731.690.981.690.981.540.901.700.99西部0.380.360.950.391.030.370.990.411.082.2.2我国各省份卫生人力资源集聚度结果研究结果显示,地理配置公平性方面:东部地区上海的执业(助理)医师集聚度(29.12)㊁注册护士集聚度(31.32)㊁药师(士)集聚度(32.55)㊁技师(士)集聚度(32.93)远高于东部其他省份,为全国最高㊂中部地区河南的各类卫生技术人员集聚度均明显大于其他省份,将近于同为中部地区黑龙江的7~9倍㊂西部地区中重庆四项指标集聚度值分别是西藏的127倍㊁271倍㊁116倍和123倍㊂这表明在我国同一区域内不同省份间的卫生人力资源配置公平性存在显著差异;人口配置公平性方面:各省份指标的H A R D与P A D比值亦存在差异,但其差异相对较小㊂其中,东部地区H A R D与P A D比值小于1的省份最少,西部地区中H A R D与P A D比值142中国社会医学杂志2024年4月第41卷第2期 C h i n e s e J o u r n a l o f S o c i a lM e d i c i n e,A p r i l2024,V o l.41,N o.2小于1的省份最多,这表明西部地区各省份普遍存在卫生人力资源相对于人口不足的现象㊂见表5㊂表52020年我国不同省份卫生人力资源集聚度地区P A D执业(助理)医师H A R D比值注册护士HA R D比值药师(士)HA R D比值技师(士)H A R D比值东部北京9.0915.461.7014.691.6217.881.9714.911.64福建2.332.050.882.060.882.551.092.110.91广东4.784.010.844.260.894.801.003.720.78海南1.941.800.932.031.051.860.961.860.96河北2.713.011.112.190.812.050.752.280.84江苏5.636.151.095.861.046.151.095.550.98辽宁1.992.041.022.001.001.810.911.950.98山东4.525.071.124.751.054.701.044.380.97上海26.7429.121.0931.321.1732.551.2232.931.23天津8.049.861.237.420.9210.991.379.401.17浙江4.325.041.164.681.085.981.384.621.07中部安徽2.982.770.932.760.922.310.782.640.89河南4.063.900.963.720.923.430.854.221.04黑龙江0.480.501.040.460.960.470.990.491.02湖北2.122.020.962.201.041.950.922.020.96湖南2.142.110.992.271.061.970.921.980.92吉林0.881.071.221.041.190.901.030.941.08江西1.851.480.801.580.861.830.991.911.04山西1.531.641.081.521.001.370.901.551.02西部甘肃0.380.330.880.370.970.320.850.391.03广西1.441.240.871.441.001.651.141.461.02贵州1.491.300.871.531.021.160.771.681.13内蒙古0.140.161.160.141.040.181.330.151.07宁夏0.740.791.070.801.080.951.280.771.04青海0.060.061.070.061.000.071.210.071.33陕西1.311.301.001.541.181.551.181.971.50四川1.181.140.971.201.021.140.971.181.00西藏0.020.020.890.010.560.020.840.020.82新疆0.110.100.930.100.940.100.920.121.11云南0.820.730.900.901.100.650.800.821.01重庆2.652.540.962.711.022.330.882.470.933讨论本研究结果显示,就我国卫生人力资源配置现状而言,存在机构间㊁区域间以及城乡间分配不均衡的问题,这与苏彬彬等[4]㊁朱文鹏和肖月[5]的研究结果一致㊂且我国卫生人力资源按人口配置的公平性优于按地理配置的公平性㊂3.1医疗机构间卫生人力资源配置不均衡自2015年我国实施分级诊疗政策以来,我国医疗服务体系在基层首诊㊁双向转诊㊁急慢分治㊁上下联动机制的有效运转下, 十三五 期间我国基层卫生人力资源配置得到了较大的改善㊂2016-2020年,我国基层医疗卫生机构卫生技术人员数量占比呈明显增长趋势,基层卫生人力队伍不断壮大㊂但客观上医疗机构间卫生人力资源配置仍然不均衡,尤其在我国基层医疗卫生机构约占95%,主要承担着基层群众的基本医疗和基本公共卫生服务,在改善和保障人民健康方面发挥着举足轻重的作用㊂如果长期未能有效改善卫生人力资源的机构间配置差异,将会影响居民健康的公平及可及性,不利于居民健康水平的提升㊂3.2区域间卫生人力资源配置不均衡十三五 期间,我国不断深化医药卫生服务体系改革,优化卫生资源配置,逐步缩小卫生人力资源配置区域差异,但综合来看我国卫生人力资源配置仍然存在显著的区域差异,需进一步优化区域配置㊂2016-2020年我国东部㊁中部㊁西部不同区域卫生人力增加明显㊂一方面,我国各区域每千人口各类卫生技术人员数量逐年增加,但中西部地区水平较低,而东部地区水平高于全国平均水平;另一方面,随着国家加大对西部地区的开发,各项优惠福利政策开始向西部地区倾斜,西部地区的卫生人力资源有了明显的增长,十三五以来,西部地区每千人口注册护士数逐年超过中部地区,接近于全国242中国社会医学杂志2024年4月第41卷第2期 C h i n e s e J o u r n a l o f S o c i a lM e d i c i n e,A p r i l2024,V o l.41,N o.2平均水平,但仍存在区域配置差异㊂3.3城乡间卫生人力资源配置不均衡随着2016年‘ 健康中国2030 规划纲要“的颁布,明确要以农村和基层为重点,逐步缩小城乡间居民基本健康服务和健康水平的差异,推动卫生服务均等化㊂ 十三五 期间,政府加大了对农村地区卫生资源配置的倾斜力度,不断推进统筹城乡发展,我国城乡间的卫生人力资源配置差异有所改善,但仍存在一定差距,这种差距的长期存在不利于我国实现全民健康的目标㊂3.4卫生人力资源按地理面积配置的公平性较弱分析结果显示,我国卫生人力资源按人口配置的公平性优于按地理配置的公平性㊂就地理配置公平性而言,我国各区域以及各省份间卫生人力资源集聚度的差异远大于按人口配置㊂其原因可能主要有两点,首先,在我国卫生资源配置规划的制定中,主要以人口因素为主,地理环境以及其他因素所占的比重较小[6];其次, 十三五 期间我国西部地区经济发展水平提高,居民生活水平提升,卫生服务需求也发生了很大变化,而在卫生人力资源配置的过程中未能及时考虑到这些因素[7]㊂3.5对策与建议3.5.1合理规划布局,均衡卫生人力资源配置建议推广学习 三明医改 经验,建立医院驻乡驻村制度,组建相关专家与医院高年资主管护师等技术指导团队分流到基层,补充基层卫生人力[8];其次,针对区域间配置不均衡现状,建议西部地区借助国家优惠政策,加强与东部㊁中部地区的联系,制定合理卫生人才政策,提升薪酬待遇水平,一方面主动吸引卫生人力到西部,另一方面,接收东部㊁中部地区相对过剩人员,缓解不均衡问题;同时,也应高度重视城乡间配置不均衡的问题,在职称㊁待遇㊁职称晋升等方面给予大学生村医政策倾斜,督促相应高校做好定向医生培养工作,从源头上有效缓解城乡卫生人力资源配置不均衡的问题㊂3.5.2改善我国区域间与区域内卫生人力资源配置公平性差异建议积极发挥政府宏观调控作用㊂一方面,应注重区域协调作用,整合各省份卫生人力资源,做到各省份统筹发展,形成一个有效的卫生资源整合共享圈,进而合理配置卫生人力资源[9];另一方面,深入落实区域医疗卫生服务体系规划建设,优化卫生人力资源,引导不同区域㊁不同省份的相关医疗机构建立目标明确㊁权责清晰的分工协作机制,推动医疗资源合理配置和纵向流动[10]㊂其次,积极探索紧密型医共体的构建,促使各区域医联体成为集利益㊁责任㊁发展㊁服务以及管理为一体的共同体,推进区域卫生人力资源共享,提升区域内卫生人力资源的流动性,进而优化其配置的公平性㊂3.5.3优化我国卫生人力资源按地理面积配置的公平性为进一步优化我国卫生人力资源按地理面积配置的公平性,建议相关部门在制定政策时兼顾地理与人口等众多因素,具体问题具体分析,诸如在地广人稀的西部地区,提高地理因素的比重,运用互联网等信息技术,结合实际,制定相应的配置标准,同时在标准实施过程中加强监督,提升我国卫生人力资源按地理面积配置的公平性[11]㊂参考文献[1]许龄木,汪哲名,朱航榉.江苏省卫生人力资源配置的公平性及预测研究[J].现代预防医学,2021,48(21):3915-3919;3939.[2]朱泉同,高山.基于组合预测模型的江苏省卫生人力资源需求预测探讨[J].中国卫生统计,2020,37(6):862-865.[3]袁素维,危凤卿,刘雯薇,等.利用集聚度评价卫生资源配置公平性的方法学探讨[J].中国医院管理,2015,35(2):3-5.[4]苏彬彬,刘尚君,卢彦君,等.基于集聚度的我国基层卫生人力资源配置评价研究[J].中国卫生政策研究,2021,14(4):49-54.[5]朱文鹏,肖月.新医改以来我国卫生人力资源配置公平性研究[J].中国卫生经济,2020,39(2):51-54.[6]李丽清,赵玉兰,周绪,等.我国卫生人力资源配置现状及其公平性分析[J].中国卫生经济,2020,39(11):44-48.[7]王狄佳,陈丹镝,杨先碧,等.我国西部地区基层卫生人力资源配置公平性研究[J].现代预防医学,2019,46(11):1986-1989.[8]詹积富.三明医改:一场倒逼的改革 我所经历的三明医改[J].中国医院院长,2018,2018(23):50-55.[9]刘璐,谭巍.2014-2018年我国卫生人力资源配置公平性研究[J].中国社会医学杂志,2022,39(3):352-355.[10]王志昊,徐宁,郎颖. 十三五 期间宁夏卫生资源配置公平性研究[J].中国药物经济学,2022,17(2):18-23.[11]张文天,孔凡悦,王权,等.我国卫生资源配置公平性现状及 十四五 期间公平性预测研究[J].中国卫生事业管理,2022,39(3):161-165;207.(收稿时间2023-08-31)(本文编辑杨婷婷)342中国社会医学杂志2024年4月第41卷第2期 C h i n e s e J o u r n a l o f S o c i a lM e d i c i n e,A p r i l2024,V o l.41,N o.2。
基尼系数是国际上用来衡量收入分配差异状况的一个重要分析指标。
基尼系数国际上通常把0.4作为收入分配贫富差距的“警戒线”，认为0.4-0.6为“差距偏大”，0.6以上为“高度不平均”。
基尼系数低于0.2表示收入绝对平均，0.2-0.3表示比较平均，0.3-0.4表示相对合理，0.4-0.5表示收入差距较大，0.6以上表示收入差距悬殊.
巴西目前仍有1627万赤贫人口，占全国人口的8.5%
巴西2010年判断收入分配公平程度的基尼系数为0.5304，是自1960年有该项统计以来的最低值，表明巴西贫富差距明显缩小。
(GNI and GNI per capital) /data?qterm=income&os=0
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The Theoretical Basics of Popular Inequality MeasuresTravis Hale, University of Texas Inequality ProjectThis document explores several inequality measures used broadly in the literature, with a special emphasis on how to compute Theil’s T statistic. Inequality is related to several mathematical concepts, including dispersion, skewness, and variance. As a result, there are many ways to measure inequality, which itself arises from various social and physical phenomena. While this is not an exhaustive discussion of inequality measures, it does deal with several of the most popular statistics. Several examples are included that pertain to inequality of salaries within two fictional companies – Universal Widget and Worldwide Widget – but all of the inequality measures discussed apply to a broad set of research questions. The salary schedules for the example problems are below, followed by discussions of range, range ratios, the McLoone Index, the coefficient of variation, and the Gini Coefficient. Following these brief introductions is an extended description of Theil’s T statistic.RangePerhaps the simplest measure of dispersion, the range merely calculates the difference between the highest and lowest observations of a particular variable of interest. Strengths of the range include its mathematical simplicity and ease of understanding. However, it is a very limited measure. The range only uses two observations from the overall set, it does not weight observations by important underlying characteristics (like the population of a state, the experience of an employee, etc.), and it is sensitive to inflationary pressures. In the case of a company, the range between the salaries of the highest and lowest paid employees may not give much information. For Universal Widget, the range in salaries is $982,000 ($1,000,000 - $18,000), while for Worldwide Widget the range is $4,985,000 ($5,000,000 - $15,000). Does this mean that Worldwide Widget has a much more unequal wage structure than Universal Widget? Not without further evidence.Range RatiosTo find the range ratio for a certain variable, divide the value at a certain percentile (usually above the median) by the value at a lower percentile (usually below the median). One range ratio often used in the study of inequality in educational expenditures is the Federal Range Ratio, which divides the difference between the revenue for the student at the 95th percentile and the 5th percentile by the revenue for the student at the 95th percentile.1 Another popular range ratio is the inter-quartile range ratio. Subtracting the observation at the 25th percentile by the observation at the 75th percentile results in a quantity known as the inter-quartile range, and dividing the observation at the 75th percentile by the 25th percentile calculates the inter-quartile range ratio. Range ratioscan measure all sorts of inequalities and the percentiles can be constructed in any manner.A range ratio can take on any value between one and infinity, and smaller values reflect lower inequality.Using the example data, one can compute a 90:10 range ratio for the two widget companies. For Universal Widget, the 90th percentile falls at a salary of $60,000 and the 10th percentile is $25,000. Thus, the 90:10 range ratio is $60,000/$25,000 or 2.4. For Worldwide Widget, the 90th percentile falls at a salary of $35,000 and the 10th percentile is $30,000. Therefore, the 90:10 range ratio is $35,000/$30,000 or 1.17. Given this information, Worldwide Widget has a more equal pay structure, the opposite conclusion gleaned from the range.Range ratios are easy to understand and simple to compute. They can directly compares the “haves” - observations at the 90th percentile or elsewhere above the median value - with the “have-nots” - observations at the 10th percentile or elsewhere below the median, without being sensitive to outliers at the very top or very bottom of the distribution. However, like the range, range ratios only look at two distinct data points, throwing away the great majority of the data. Because of this significant limitation, researchers often employ more sophisticated inequality measures.McLoone IndexThe McLoone Index is another example of a measure that compares one part of a distribution to another. However, the McLoone Index takes a much larger proportion of the data into account. It compares how much of a resource is concentrated in the bottom half of a distribution to the median amount. To compute the McLoone Index value, divide the sum of all of the observations at or below the median level by the product ofthe number of observations at or below the median level and the value of the median level. Values of the McLoone Index are bound below by zero - if the lower half of the distribution receives none of the resource - and above by one - if there are no observations below the median. The latter case would occur if the lowest value is shared by at least half of the observations. Unlike most inequality measures, a higher value for the McLoone Index describes a more equitable distribution.For example, the Universal Widget Company has 400 employees. The median salary value is approximately that of the 200th least compensated employee. That employee is an Equipment Operator who makes $25,000. The McLoone Index is the ratio of the actual salaries of the least paid half of the Universal Widget workforce to the counterfactual denominator of $25,000 * 200 = 5,000,000. Thus the McLoone Index for Universal Widget equals (7*18,000 + 10*22,000 + 183*25,000) / 5,000,000 or .9842. Parallel computations reveal that Worldwide Widget has a McLoone Index valueof .9595. This leads to a conclusion that Universal has a more equal pay structure.The McLoone Index is relatively easy to understand, and might be an appropriate measure if researchers are primarily interested in the bottom of a distribution. If the median observation reflects an “adequate” level, th en the McLoone Index gives some sense of how the bottom half of the distribution is doing compared the middle. However, the McLoone Index has some potentially objectionable properties. First, it does not use all information, throwing away the observations above the median. Certainly there is a substantial difference between a distribution where the higher values lie just above the median and one where some observations lie far beyond the median. The McLoone Index compares reality with a counterfactual model, so the researcher may be asked tojustify the comparison of reality to an alternative where the entire bottom half of the distribution shares the median value. While the McLoone Index has thus far been concerned primarily with school finance inequality measurement, there are similar measures with broader application, and there is no reason that the McLoone Index itself could not be applied to other phenomena.The Coefficient of VariationThe coefficient of variation is simply the standard deviation of a variable divided by the mean.2 Graphically, the coefficient of variation describes the peakedness of a unimodal frequency distribution. For a dataset that is closely bunched around the mean, the peak will be high, and the coefficient of variation small. Data that is more dispersed will have a shorter peak and a higher coefficient of variation. Ceteris paribus, the smaller the coefficient of variation, the more equitable the distribution.The first step in computing coefficients of variation for the sample data is to find the mean and standard deviation of each set. This is fairly easy to do with statistics software, or a spreadsheet program such as Microsoft Excel. Universal Widget has an average salary of $36,452.50 and a standard deviation of 52,630.52. Worldwide Widget has an average salary of $38,773.08 and a standard deviation of 138,990.96. This leads to coefficients of variation of 1.44 and 3.58 for Universal and Worldwide, respectively, concluding that Universal has the more equitable salary structure.The coefficient of variation has some attractive properties. If group data is used, but weighted by population size, small outlying observations do not skew the distribution greatly. Individuals with even a limited statistical background are likely to be familiar with the standard deviation and sample mean, making the coefficient of variation easy to explain to a non-technical audience. Furthermore, by construction, inflation does not affect the coefficient of variation. A disadvantage of the measure is that, theoretically, the coefficient of variation can take any value between zero and infinity, and there is no universal standard that defines a reasonable value of the measure for particular phenomena.The Gini CoefficientThe Gini coefficient derives from the Lorenz Curve. To plot a Lorenz curve, rank the observations from lowest to highest on the variable of interest, and then plot the cumulative proportion of the population on the X-axis and the cumulative proportion of the variable of interest on the Y-axis.3 The Gini coefficient compares this cumulative frequency and size curve to the uniform distribution that represents equality. In thegraphical depiction below, a diagonal line represents perfect equality, and the greater the deviation of the Lorenz curve from this line, the greater the inequality. The Gini coefficient is double the area between the equality diagonal and the Lorenz curve, bounded below by zero (perfect equality) and above by one (the case when a single member of the population holds all of a resource).There are several ways to compute the Gini coefficient for a dataset. Researchers who are comfortable with Calculus and spreadsheet analysis and have a large amount of data that results in smooth plots can estimate a high order polynomial for the Lorenz Curve (Microsoft Excel will add up to a 6th degree polynomial as a trend line for an XY graph), and then take an appropriate integral to compute the size of the shaded area. Likewise, other estimation techniques, such as the method of rectangles, the method of trapezoids, or Monte Carlo integration will provide reasonable estimates. Another way tocompute the Gini is directly from an algebraic formula. Given that the data is ordered from smallest to largest values of the variable of interest, the formula is:12(21)'n ii i n x G n μ=--=∑, where i is the individual’s rank order number, n is thenumber of total individuals, x’i is the individual’s variable value, and μ is the population average.4To compute the Gini coefficients for the sample data, it is easiest to organize the data such that each individual is given his or her own record (such that the salaryschedule for Universal Widget has 400 rows, one for each employee). After splitting the data in this manner, it is fairly straightforward to apply the formula above. For Universal Widget, the Gini coefficient is 0.279625369, while for Worldwide Widget, the Gini coefficient is 0.227509252.The Gini coefficient is a full-information measure, looking at all parts of thedistribution. It is probably the most well-known and broadly used measure of inequality used in economic literature. The Gini coefficient facilitates direct comparison of two populations, regardless of their sizes. In other words, with the Gini coefficient one can directly compare the inequality in a classroom to the inequality in a country. While the actual computation of the Gini coefficient may include taking an integral or using a slightly complex formula, the visual description is elegant and easy to understand. The Gini coefficient does suffer from the lack of a true zero, and the need for a context.While a distributional policy, like giving everyone below the poverty line $1,000, has real implications, the repercussions of a 5% reduction of the Gini coefficient are much less clear.Theil’s T StatisticThe inequality measures discussed above are each appropriate in certain circumstances. The rationale for preferring Theil’s T statistic is not that there is som e inherent flaw in the other measures, but that Theil’s T has a more flexible structure that often makes it more appropriate. If a researcher always had access to complete, individual level data for the population of interest, then measures like the coefficient of variation or the Gini coefficient would usually be sufficient for describing inequality. However, in practice, individual data is rarely available, and researchers are asked to make due with aggregated data. Returning to the example problem illustrates the point. What if the Universal Widget salary schedule did not reflect the exact salary for each employee but the average salary over each job category? It would be possible to compute values for the coefficient of variation or the Gini coefficient under the assumption that each employee receives exactly the average salary, but the results would only give an upper or lower bound of each inequality measure, because variance within each job category will contribute to total inequality. For most practical data, data that has some degree of aggregation or an underlying hierarchy (e.g. cities within regions within nations), Theil’s T statistic is often a more appropriate and theoretically sound tool.5 The following formulae give the algebra behind Th eil’s T statistic. While these particular equations use income as the variable of interest, Theil’s T can address any number of quantifiable phenomena. When household data is available, Theil’s T statistic is6:]1[where n is the number of individuals in the population, y p is the income of the person indexed by p , and μy is the population’s average income. If every individual has exactly the same income, T will be zero; this represents perfect equality and is the minimum value of Theil’s T. If one individual has all of the income, T will equal ln n ; this represents utmost inequality and is the maximum value of Theil’s T statistic.If members of a population can be classified into mutually exclusive and completely exhaustive gro ups, then Theil’s T statistic is made up of two components, the between group element (T’g ) and the within group element (T w g ).[2]T = T’g + T w gWhen aggregated data is available instead of individual data, T’g can be used as a lower bound for the pop ulation’s value of Theil’s T statistic. The between group element of Theil’s T can be written as:]3[where i indexes the groups, p i is the population of group i , P is the total population, y i is the average income in group i , and μ is the average income across the entire population. T’g is bounded above by ln (P/p i (min)), the natural logarithm of the total population∑=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎪⎪⎭⎫ ⎝⎛⎪⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛=np y p y p yy n T 1ln **1μμ∑=⎭⎬⎫⎩⎨⎧⎪⎪⎭⎫ ⎝⎛⎪⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛=mi ii i g y y P p T 1ln **'μμdivided by the size of the smallest group. This value is attained when the smallest group holds all the resource. When data is hierarchically nested (i.e. every municipality is in a province and each province is in a country) Theil’s T statistic must increase or stay the same as the level of aggregation becomes smaller (i.e. T population ≥T’g (district) ≥T’g (county) ≥T’g (region)). Theil’s T statistic for the population equals the limit of the between group Theil component as the number of groups approaches the size of the population.Because the central purpose of this document is t o show how to use Theil’s T statistic, the examples relating to its use will be a little more involved.Example 1: Construct Theil’s T statistic for Universal Widget and Worldwide Widget with the data as given.A.First, consider Universal Widget. To follow along in Excel, open the spreadsheet “Example Problems with Theil’s T Statistic” and select the worksheet “Theil Example1A”. Since individual level data is available, Equation 1 is rele vant. The first step is to sum the number of employees and the total payroll and to divide total payroll by the number of employees to get the average salary. Next, compute the salary/average salary quotient for each salary level. Then, take the natural logarithm of the same quotient. An individual’s “Theil element” is the contribution that he or she makes to Theil’s T statistic. This value is computed as [1/n]*[salary/average salary]*[ln(salary/average salary)]. After computing the Theil elements for each job position, multiply by the number of employees in the position. Adding up these values yields the Theil Index, which in the case of Universal Widget is 0.28615395.B. To compute Theil’s T statistic for Worldwide Widget, follow the exact same st eps as in Part A. The computations can be found in the Excel spreadsheet “ExampleProblems with Theil’s T Statistic” under the worksheet “Theil Example 1B”. The result is a Theil’s T Statisti c value of 0.463162658.Analysis: Computing values for Theil’s T statistic is a relatively simple process of plugging values into a formula. The real concern is to make some conclusion about inequality. Is it possible to conclude that Worldwide Widget has a more unequal salary structure than Universal Widget because Worldwide has a higher value of Theil’s T statistic? Not necessarily. As discussed above, with individual data, the value of Theil’s T statistic is bounded by ln (n), so while Universal Widget has an upper bound of ln(400) = 5.991464547, Worldwide Widget has an upper bound ln(1300) = 7.170119543. Because Worldwide Widget has more employees, ceteris paribus it will have a greater value of Theil’s T statistic (in fact if the companies had identical Theil’s T statistic values, one could conclude that the larger company had less inequality). Generally speaking, values of Theil’s T statistic need a context to make sense. Given that last year’s Theil’s T statistic for salaries at Universal Widget was .1000, the Theil’s T statistic for salaries at Worldwide Widget was .5000, and both companies had workforces of similar size to their current levels, one could conclude that salary inequality increased at Universal and decreased at Worldwide over the last year. Knowing only this year’s information and that the two companies have significantly different sized workforces, it is difficult to make many substantive conclusions. If only one year’s worth of data is available, then another inequality measure, such as the Gini coefficient or coefficient of variation may be more appropriate.Example 2: What is the interpretation of Theil’s T statistic if the salary schedules given represent the average salary across positions, not the exact salaries?In other words, for Universal Widget, the 7 members of the Custodial Staff have an average salary of $18,000 per year, but this may fluctuate among individuals. Analysis: Looking at Equation 2, Theil’s T statistic is composed of a between group part and within group part. Under the assumptions of this problem statement, there is no way to compute the within group component, because there is no knowledge of individual salaries, only average salaries. However, it is possible to compute the between group component and note that this is the lower bound for total inequality. For this task, the proper mathematical relation is Equation 3, which by no accident bears a striking resemblance to Equation 1. Because the salary figures are the same, the numerical values of T heil’s T statistic do not change for either company, but the interpretation does. Now 0.28615395 represents the between group component of Theil’s T statistic for Universal Widget and the lower bound of total inequality. The spreadsheet analysis for both Universal and Worldwide can be found in the Excel Spreadsheet “Example Problems with Theil’s T Statistic” under the worksheets “Theil Example 2A” and “Theil Example 2B.” Notice how the column headings change, which changes the underlying interpretation of the calculations.Example 3:Consider the following data:Unlike examples 1A and 1B, employees draw different salaries based on both their level of seniority (entry, mid, senior) and their job position. Example 3 resumes the assumption from the first example that the data represents exact salary information for each individual.Given this new data, what is the Theil Index for Universal Widget?Answer: There are several ways to do this problem, and four solutions are worked out in the spreadsheet. The first solution (Theil Example 3A) starts by computing the within-group inequality for each job position (custodial staff, engineers, etc.). A Theil component is computed for each experience level within each job position, the summation of which gives within group inequality. However, before concluding how much the job position inequality contributes to total company-wide inequality, we must re-weight by the proportion of salaries within the job position. (In other words, inequality within the equipment operator group takes on greater weight than among the custodial staff, because 70% of workers operate equipment while less than 2% perform custodial services.) Computing the Theil Index in this manner helps us to parse total inequality into within-group and between-group components. The total value of the Theil Index is now 0.12860521, of which 0.124275081 is between-group inequality and0.004330129. The substantive lesson here is that the difference in average salaries between job positions causes the vast majority of the inequality, and the differences among seniority levels within job positions contribute very little to total inequality.Theil Example 3B calculates total inequality by comparing each job position-experience level combination to the average salary. The value of the total Theil Index is the same, but this method does not naturally parse the Index into within-group andbetween-group portions. Full enumeration - Theil Example 3C makes each employee a separate record, which, yet again, leads to the same value for the total Theil Index, but does not calculate the within group and between group portions.Alternative approach – compute the Theil Index by experience level instead of job positionAdvantages and Disadvantages of the Theil IndexThe principle disadvantage of the Theil index is that its values are not always comparable across different units (such as nations). If the number and sizes of groups differ, then limit of the index will differ. On the other hand, the Theil index has less stringent data requirements – group data is often easier to come by than individual survey data – and Theil index values can tell a rich story about inequality over different levels of aggregation…1 Given that all observations are ordered from lowest to highest, a percentile is merely the observation that is a certain portion away from the lowest value. If a company had 200 employees and listed their salaries from lowest to highest, the 5th percentile would be found at the 10th lowest observation (.05 * 200 = 10) and the 95th percentile would be found at the 190th lowest observation (or the 10th highest depending on your perspective; .95 * 200 = 190.) The median is the 50th percentile, or middle value.2The standard deviation is defined asNS=where X is the sample average and some texts substitute N for N –3For more information on Lorenz Curves, see the entry in Eric Weisstein’s World of Mathematics,/.Christian Damgaard, “Lorenz Curve.” Online. Available: /LorenzCurve.html. Accessed : 20 June 2003.4For a more complete treatment on the Gini Coefficient, see the entry in Eric Weisstein’s World of Mathematics, /.Christian Damgaard, “Gini coefficient.” Online. Available:/GiniCoefficient.html. Accessed : 20 June 2003.5 Pedro Conceição and Pedro Ferreira provide a much more detailed analysis of these issues in their UTIP working paper “The Young Person’s Guide to the Theil Index: Suggesting Intuitive Interpretations and Exploring Analytical Applications.”Pe dro Conceição and Pedro Ferreira, “The Young Person’s Guide to the Theil Index: Suggesting Intuitive Interpretations and Exploring Analytical Applications.” UTIP Working Paper Number 14. Online. Available: . Accessed: 20 June 2003.6Equations 1, 2, and 3 closely follow: Pedro Conceição, James K. Galbraith, and Peter Bradford; “The Theil Index in Sequences of Nested and Hierarchic Grouping Structures: Implications for the Measurement of Inequality through Time, with Data Aggregated at Different Levels of Industrial Classification,” Eastern Economic Journal, Volume 27 (2000), Pages 61 – 74.。
泰尔指数和基尼系数的不同
泰尔指数和基尼系数是反映一个国家或地区收入分配不均的常用指标。
虽然两个指标都可以用于评估贫富差距，但它们之间的计算方式和含义有所不同。
泰尔指数是一种衡量收入不平等的方法，它根据不同收入群体的收入份额来计算。
具体来说，泰尔指数是最富裕的20%家庭收入占总收入的百分比与最穷困的20%家庭收入占总收入的百分比之差的一半。
如果这个差值越大，则泰尔指数越高，表明贫富差距越大。
而基尼系数则是另外一种测量收入不平等的方法，它是相对于每个人平均收入而言的。
基尼系数的范围在0到1之间，其中0表示完全平等，1表示完全不平等。
在这种计算方式下，基尼系数的计算与泰尔指数类似，但是不再仅仅考虑最富裕和最贫困的20%人口，而是将所有人口分成若干收入群体，然后根据每个群体在总收入中所占的比例来计算基尼系数。
总体来说，这两种指标的计算方式不同，但它们都可以用来评估一个国家或地区中收入分配是否公平。
在实际应用中，研究人员和政策制定者通常会综合使用这些指标来获得更准确的衡量结果，并采取措施来减少贫富差距的不平等。
stata 泰尔指数-回复Stata 泰尔指数概述泰尔指数（Theil index）是一种衡量收入或财富的不平等程度的统计指标，经常被用来描述一个经济体中不同个体或群体之间的收入分配差异。
它是由经济学家Horst Theil于1967年提出的，也被称为Theil-T指数。
在实际应用中，Stata是一个非常流行的统计软件，被广泛用于计量经济学、社会科学等领域的数据分析。
泰尔指数的计算方式泰尔指数的计算方式有多种，常见的有两种：Theil T指数和Theil L指数。
其中，T指数是一个输入位阶比奥编程相关的指数，用来衡量泰尔不等度，而L指数是以连续性变量作为输入的指数，它是基于信息熵和基尼系数的计算方法。
在Stata中，可以使用“ineqdeco”命令来计算泰尔指数。
该命令是由StataCorp开发的，它通过最大熵原理来尽可能准确地估计泰尔指数。
以下是在Stata中计算泰尔指数的具体步骤：步骤1：导入数据首先，我们需要将要分析的数据导入Stata。
可以使用Stata的“import”命令将数据从外部文件导入到Stata中。
例如，如果数据保存在名为“data.csv”的CSV文件中，可以使用以下命令导入数据：import delimited "data.csv", clear步骤2：生成变量接下来，我们需要使用Stata的“generate”命令生成所需的变量。
对于泰尔指数的计算，我们需要生成两个变量：一个变量表示个体的收入或财富水平，另一个变量表示个体的权重。
例如，假设我们的数据集中有一个名为“income”的变量表示收入，以及一个名为“weight”的变量表示个体的权重。
我们可以使用以下命令生成这两个变量：generate income = .replace income = <Income Value> if <Condition>generate weight = .replace weight = <Weight Value> if <Condition>请将<Income Value>和<Weight Value>替换为相应的具体数值，以及<Condition>替换为收入和权重的条件。
数字普惠金融对收入机会不平等的门限研究一、研究背景随着全球经济的快速发展，数字普惠金融已经成为推动经济增长和社会进步的重要力量。
数字普惠金融的发展过程中，收入机会不平等问题日益凸显。
收入机会不平等不仅影响社会公平和稳定，还可能阻碍数字普惠金融的可持续发展。
研究数字普惠金融对收入机会不平等的影响具有重要的理论和现实意义。
在过去的研究中，学者们普遍关注数字普惠金融对贫困人口的影响，以及如何通过数字普惠金融提高贫困人口的金融素养和金融服务可及性。
这些研究往往忽略了数字普惠金融对非贫困人口的影响，以及数字普惠金融在不同收入阶层之间的分布不均现象。
现有研究对于数字普惠金融与收入机会不平等之间的关系尚未形成明确的认识。
本研究旨在探讨数字普惠金融对收入机会不平等的门限效应，以期为政策制定者提供有益的参考。
本研究将从以下几个方面展开：首先，通过收集和整理相关数据，分析数字普惠金融在不同收入阶层之间的分布情况；其次，从理论层面探讨数字普惠金融对收入机会不平等的影响机制；根据研究结果，提出针对性的政策建议，以促进数字普惠金融在减少收入机会不平等方面发挥更大的作用。
1. 数字普惠金融的概念和发展现状随着互联网技术的快速发展，数字普惠金融作为一种新型的金融服务模式，已经在世界范围内得到了广泛的关注和应用。
数字普惠金融是指利用互联网、大数据、人工智能等技术手段，为广大人民群众提供便捷、高效、低成本的金融服务，以满足其多样化的金融需求，促进社会经济的发展。
全球范围内数字普惠金融的发展呈现出以下几个特点：首先，数字普惠金融已经成为各国政府关注的重点领域，许多国家纷纷出台相关政策和措施，推动数字普惠金融的发展。
数字普惠金融已经在全球范围内取得了显著的成果，许多发展中国家和地区的金融服务水平得到了显著提高，为当地经济社会发展创造了良好的条件。
数字普惠金融的发展也面临着一些挑战，如信息安全、数据隐私保护等问题，需要各国政府、企业和社会各界共同努力，加强监管和技术创新，推动数字普惠金融的健康发展。
Measuring inequality:the Gini Index 1Math 128–Fall 2005Introduction Most people would agree that “good things,”such as money income,should be more or less equally distributed.In practice,of course,good thingsare not evenly distributed,and so it’s useful to have a numerical measure of inequality.We might,for instance,watch such a measure over several years to decide whether equity is increasing or decreasing.The Gini Index (GI)is such a measure.It is widely used used by economists to measure and compare income equality in various countries,or in a given country over time.A GI of 0.00corresponds to perfect equality—everyone has exactly the same income.A GI of 1.00corresponds to perfect in equality—one person gets all the income and everyone else gets nothing.No real-world society has perfect income equality (or complete inequality),and there are good political,moral,and economic arguments to be had about how much income equality is “best”in a given society.Calculating the Gini Index mathematically does not settle these arguments—the disagreements are philo-sophical,not just mathematical.But knowing the Gini Index can lend some quantitative weight to the discussion.GI information is easy to find on the Web.Here,for instance,are some rough GI data on family income in various countries,culled from the CIA World Factbook.(The GI is reported here as a percent ,ranging from 0to 100.)Denmark24.7Russia 39.9Japan24.9China 40.0Sweden25.0United States 40.8Kazakhstan35.4Honduras 56.3Portugal35.6Brazil 60.7Ireland 35.9Sierra Leone 62.9The Lorenz curve The GI is defined in terms of the so-called Lorenz curve ,or Lorenz function ,which we’ll denote by L (x ).The Lorenz function is defined as follows:If 0≤x ≤1,then L (x )is the fraction of all income received by the lowest-paid fraction x of the population.Observe:•L (0.31)=0.23means that the “poorest”31%of the population receive 23%of the income;•L (1/2)=1/3means that the poorest half of the population get one-third of the income.•None of the expressions L (−23),L (1.2),and L (0.3)=213makes good sense.(Do you see why not?)•For every income distribution,we have L (0)=0and L (1)=1.The Lorenz curve is the graph of the Lorenz function.Note that,in a perfectly egalitarian system,we would have L (x )=x for all x (1/2of the people would have 1/2of the income,and so on)and so the Lorenz curve is just the 45-degree line y =x .Defining the Gini Index The Gini Index can be defined in several ways.Here is a definition in calculus language:The Gini Index is twice the area between the Lorenz curve and the line y =x .In symbols:GI =2 10(x −L (x ))dx (The factor 2may seem 1Some ideas here come from Bruce Teague,North Carolina School of Science and Mathematics.1equationand deciles In real-world situations we can’t know L(x) for every possible fraction x.What is often available(and tabulated by governments)is information on income quintiles and(sometimes)income deciles.For quintiles,a population is divided into equal-sized fifths,ranging from the poorestfifth to the richestfifth.(For deciles the population is divided into tenths.) For example,the following table shows such data for two different years in the US:Share of income(percent)by quintileYear poorest second third fourth richest1968 4.211.117.524.442.81992 3.89.415.824.246.9The data in each row can be used tofind several values of the Lorenz function for a given year.For1968, we have L(0.2)=.042,L(0.4)=.042+.111=.153,and L(0.8)=.042+.111+.175+.244=.572.This process lets usfind six values of L(x):L(0)=0,L(0.2),L(0.4),L(0.6),L(0.8),and L(1)=1.By “connecting the dots”between these values we can approximate the full Lorenz curve,and use the result to “see”the area that defines the GI.We can also use the function values and the trapezoid rule to estimate 1(x−L(x))dx,which appears in the GI.the integralOn the Web Here are two Web sources;“googling”willfind many more./~dhenwood/Gini_supplement.html /hhes/income/histinc/ie3.html ProblemsDo as many as you can manage from among the following problems;some are open-ended or non-mathematical.1.Is equal distribution of income the“best”policy for a society?Why or why not?2.Explain briefly in money language why,for every Lorenz curve,(i)L(0)=0;(ii)L(1)=1;(iii)L(x)≤x,for all x;(iv)L(x)is an increasing function.13.Explain why the alternative formula GI=1−2L(x)dx can also be used to calculate the GI.4.Suppose we know L(0)=0,L(0.2),L(0.4),L(0.6),L(0.8),and L(1)=1for a particular population.Give a formula for using the trapezoid rule to estimate the GI.(Use some sigma notation.)5.Calculate the GIs for the two years1968and1992for which quintile data are given above.(Use yourformula from the preceding problem.)In which year was there“more inequality”?6.A powerful genie(genie...get it?)grants a wish and doubles everybody’s income.How does this affectthe GI?7.Another genie,not to be outdone,adds$1million to everybody’s income.How does this affect the GI?8.Suppose we have income decile information,and therefore know L(0)=0,L(0.1),L(0.2),...,L(0.9),and L(1)=1for a particular population.Give a formula for using the trapezoid rule to estimate the GI.(Use sigma notation.)9.For which positive numbers n could L(x)=x n possibly be a Lorenz function?For such values of n,what is the GI?What happens as n gets very large?10.Mother Hubbard’s ten children receive weekly allowances(in dollars)of1,1,1,2,2,4,4,5,8,10.Calcu-late a reasonable GI for the Hubbard children.(Use deciles.)211.Suppose that10people have incomes i1,i2,i3,...,i10,listed in increasing order.How would youmimic the GI formula above(which involves an integral)to calculate the GI for this small group? ment on the table above that shows the family income GIs for various countries.Do low-GIcountries have something in common?Do high-GI countries?13.Some politicians assert that income inequality has been increasing in recent years.Do the data and GIcalculations support this claim?(See /hhes/income/histinc/ie3.html.)If so,can you suggest any reasons?14.Do rich countries usually have higher(or lower)GIs than poor countries,or is there no clear pattern?Look on the Web for data to support your claim.15.The GI is based on the idea that,in some sense,the“perfect”income distribution has Lorenz functionL(x)=x.Suppose that for some reason we decide to consider a distribution with Lorenz function L(x)=x2as“perfect.”Then,we might measure“imperfection”using a new,improved quantity,sayIGI(for Improved Gini Index),defined by IGI=1x2−L(x)2dx.(The square in the integrandlets us forget about the sign of any difference.)(a)Comment on this notion of perfection,and on the IGI formula.Is either reasonable?(b)Calculate the IGI for the two years1968and1992discussed above.In which year was there more“imperfection”?3。
