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[31]Alfonso Arpaia,Esther Pérez,and Karl Pichelmann,“Understanding Labour Income Share Dynamics in Europe,” European Economy Economic Papers 379 (2009),European Commission,Brussels,quote p. 2。他们还表示“劳动比重不仅在过去30年里下降,还可能因为资本积累和高技能劳动力在就业总人口中的比重上升而在未来持续下降”。
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[32]Lawrence H. Summers,“Economic Possibilities for Our Children,” The 2013 Martin Feldstein Lecture,NBER Reporter 4 (2013): 1-6。我们用K 1表示资本的第一个用途,用K 2表示资本的第二个用途,这样总量生产函数变成F(K 1,AL + B K 2),其中A和B取决于技术水平。Autor、Katzand Kearney在“The Polarization of the U.S. Labor Market”中采用的任务法也探讨了(从事常规任务时)机器人作为劳动力的完美替代品的案例。
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[33]如果(1/A)个工人对生产的贡献等同于(1/B)个机器人,那么工人工资与回报率之比低于A/B时,生产中就不会采用机器人。工人工资与回报率之比等于A/B时,生产中会同时使用机器人和工人。
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[34]Carl Benedikt Frey and Michael Osborne,“The Future of Employment: How Susceptible Are Jobs to Computerisation?” Oxford Martin School Working Paper (2013),http://www.oxfordmartin.ox.ac.uk/downloads/academic/The_Future_of_Employment.pdf.
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[35]James E. Meade,Efficiency,Equality and the Ownership of Property (London: Allen and Unwin,1964).
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[36]Paul Samuelson,“Review,”Economic Journal 75 (1965): 804-806,quote p. 805.
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[37]Michael Kalecki,“Class Struggle and the Distribution of National Income,” Kyklos 24 (1971): 1-9,quote p. 3.
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[38]这个分析将工资谈判模式(在这个模式里,工会对就业产生影响)与Avinash Dixit和Joseph Stiglitz的垄断竞争模式结合了起来,关于垄断竞争模式,请参见Avinash Dixit and Joseph Stiglitz,“Monopolistic Competition and Optimum Product Diversity,” American Economic Review 67 (1977): 297-308。
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[39]John K. Galbraith,American Capitalism: The Concept of Countervailing Power (London: Hamish Hamilton,1952).
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[40]Office for National Statistics,Ownership of UK Quoted Shares,2012 (London: Office for National Statistics,2013),Table 1.
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[41]Andrea Brandolini,“Nonlinear Dynamics,Entitlement Rules,and the Cyclical Behaviour of the Personal Income Distribution,” Centre for Economic Performance Discussion Paper 84,London School of Economics,July 1992.
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[42]和关于异质性行为人的宏观经济学文献一样,请参见Vincenzo Quadrini and José-Victor Rios-Rull,“Inequality in Macroeconomics,” in Anthony B. Atkinson and Franois Bourguignon,eds.,Handbook of Income Distribution,vol. 2B (Amsterdam: Elsevier,2015),1229-1302.
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[43]U.S. Census Bureau,Educational Attainment in the United States: 2013,Table 1: “Educational Attainment of the Population 18 Years and Over.”
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[44]World Bank,Data on labour force with tertiary education: http://data.worldbank.org/indicator/SL.TLF.TERT.ZS.
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[45]这些计算假设收入分配的上尾表现出帕累托分布。帕累托分布是由Vilfredo Pareto于19世纪末首次提出的,它的数学形式是:收入为Y及以上的人群比重与Y -α成一定比例,其中α为帕累托系数。帕累托分布的特性是Y以上的平均收入等于α/(α-1) Y。英国的帕累托系数从1977年的4.5左右下降到2003年的2.8(数据来源:Anthony B. Atkinson and Sarah Voitchovsky,“The Distribution of Top Earnings in the UK since the Second World War,” Economica 78 (2011): 440-459),这些数值是本书计算相关数字的基础。譬如,α=4.5时得出Y以上的平均收入为4.5/3.5 (= 1.29)乘以Y。从收入的前十分之一进入前百分之一,收入需要上升10 1/α倍。
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[46]Jacob S. Hacker and Paul Pierson,“Winner-Take-All Politics: Public Policy,Political Organization,and the Precipitous Rise of Top In comes in the United States,” Politics and Society 38 (2010): 152-204.
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[47]See Atkinson,The Changing Distribution of Earnings in OECD Countries,Ch. 4.
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[48]Anthony B. Atkinson,“The Distribution of Top Incomes in the United Kingdom 1908-2000,” in A. B. Atkinson and Thomas Piketty,eds.,Top Incomes: A Global Perspective (Oxford: Oxford University Press,2010),82-140,Figure 4.11。
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[49]Thomas Piketty and Emmanuel Saez,“Income and Wage Inequality in the United States,1913-2002,” in Atkinson and Piketty,Top Incomes,quote p. 153.
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[50]Jon Bakija,Adam Cole,and Bradley T. Heim,“Jobs and Income Growth of Top Earners and the Causes of Changing Income Inequality: Evidence from U.S. Tax Return Data,” Williams College Department of Economics Working Paper,2010-22 (revised 2012).
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[51]Alfred Marshall,Principles of Economics,8th ed. (London: Macmillan,1920).
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[52]Thomas Lemieux,W. Bentley MacLeod,and Daniel Parent,“Performance Pay and Wage Inequality,” Quarterly Journal of Economics 124 (2009): 1-49.
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[53]Hacker and Pierson,“Winner-Take-All Politics,” p. 203.
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[54]Hacker and Pierson,“Winner-Take-All Politics,” p. 192.
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[55]Facundo Alvaredo,Anthony B. Atkinson,Thomas Piketty,and Emmanuel Saez,“The Top 1 Per Cent in International and Historical Perspective,”Journal of Economic Perspectives 27 (2013): 3-20,表1。美国的数据来源于Christoph Lakner,“Wages,Capital and Top Incomes: The Factor Income Composition of Top Incomes in the USA,1960-2005,” forthcoming。Rolf Aaberge,Anthony B. Atkinson,Sebastian Knigs和Christoph Lakner还对比了美国数据和挪威数据,请参见Rolf Aaberge,Anthony B. Atkinson,Sebastian Knigs and Christoph Lakner,“Wages,Capital and Top In comes,” forthcoming。劳动收入的定义为工资、养老金与2/3营业(自营)收入之和。
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