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Engels' pause: Technical change, capital accumulation, and inequality in the british industrial revolution
恩格斯的停顿英国工业革命中的技术变革、资本积累与不平等

Robert C. AllenNuffield College, New Road, Oxford OX1 1NF, UKDepartment of Economics, Oxford University, Manor Road, Oxford OX1 3UQ UK

A R T I C L E I N F O

Article history: 文章历史：

Received 8 February 2008 2008 年 2 月 8 日收到
Available online xxxx 可在线查阅 xxxx

Keywords: 关键词：

British industrial revolution
英国工业革命
Kuznets curve 库兹涅茨曲线
Inequality 不平等
Savings 节约
Investment 投资

Abstract 摘要

A B S T R A C T The paper reviews the macroeconomic data describing the British economy from 1760 to 1913 and shows that it passed through a two stage evolution of inequality. In the first half of the 19th century, the real wage stagnated while output per worker expanded. The profit rate doubled and the share of profits in national income expanded at the expense of labour and land. After the middle of the 19th century, real wages began to grow in line with productivity, and the profit rate and factor shares stabilized. An integrated model of growth and distribution is developed to explain these trends. The model includes an aggregate production function that explains the distribution of income, while a savings function in which savings depended on property income governs accumulation. Simulations with the model show that technical progress was the prime mover behind the industrial revolution. Capital accumulation was a necessary complement. The surge in inequality was intrinsic to the growth process: technical change increased the demand for capital and raised the profit rate and capital's share. The rise in profits, in turn, sustained the industrial revolution by financing the necessary capital accumulation. After the middle of the 19th century, accumulation had caught up with the requirements of technology and wages rose in line with productivity.
A B S T R A C T 本文回顾了描述 1760 年至 1913 年英国经济的宏观经济数据，表明英国经济经历了两个阶段的不平等演变。19 世纪上半叶，实际工资停滞不前，而工人的人均产出却有所增长。利润率翻了一番，利润在国民收入中的份额扩大，牺牲了劳动力和土地。19 世纪中叶以后，实际工资开始与生产率同步增长，利润率和要素份额趋于稳定。我们建立了一个增长与分配的综合模型来解释这些趋势。该模型包括一个解释收入分配的总生产函数，以及一个储蓄取决于财产收入的储蓄函数。该模型的模拟结果表明，技术进步是工业革命的主要推动力。资本积累是必要的补充。不平等的激增是增长过程的内在因素：技术变革增加了对资本的需求，提高了利润率和资本份额。反过来，利润的增加又为必要的资本积累提供了资金，从而支撑了工业革命。19 世纪中叶以后，积累赶上了技术的要求，工资也随着生产率的提高而提高。

( 2009 Elsevier Inc. All rights reserved.
( 2009 Elsevier Inc.保留所有权利。
"Since the Reform Act of 1832 the most important social issue in England has been the condition of the working classes, who form the vast majority of the English people. . What is to become of these propertyless millions who own nothing and consume today what they earned yesterday?... The English middle classes prefer to ignore the distress of the workers and this is particularly true of the industrialists, who grow rich on the misery of the mass of wage earners."
"自1832年《改革法》颁布以来，英国最重要的社会问题就是占英国人民绝大多数的工人阶级的状况。......这些没有财产的千百万人将何去何从，他们一无所有，今天消费的是昨天赚来的钱。......英国的中产阶级宁愿无视工人的苦难，工业家尤其如此，他们依靠广大工薪阶层的苦难发家致富"。
-Friedrich Engels, The Condition of the Working Class in England in 1844, pp. 25-26.
弗里德里希-恩格斯：《1844 年英国工人阶级的状况》，第 25-26 页。
Engels' Condition of the Working Class in England in 1844 (1845) was an early and famous account of unequal development. He describes how the industrial revolution led to massive urbanisation and great increases in output. While per capita income was rising, real wages remained constant, however, so the gains from economic development accrued overwhelmingly to capitalists. The period of constant wages in the midst of rising output per worker was 'Engel's pause'. The pause had a progressive side, however, for the bourgeoisie saved from its growing income, and the ensuing investment drove the economy forward. In this paper, I argue that Engel's description of the industrial revolution was, in many respects, an insightful one.
恩格斯的《1844 年英国工人阶级状况》（1845 年）是早期关于不平等发展的著名论述。他描述了工业革命如何导致大规模城市化和产出的大幅增长。虽然人均收入不断增加，但实际工资却保持不变，因此经济发展的收益绝大部分归资本家所有。在工人人均产出不断提高的同时，工资却保持不变，这就是 "恩格尔的停顿期"。然而，这种停顿也有进步的一面，因为资产阶级从不断增长的收入中节省了资金，随之而来的投资推动了经济的发展。在本文中，我认为恩格尔对工业革命的描述在许多方面都很有见地。
Engels was not alone in his view of British industrialization. Among economists, Ricardo, Malthus, and Marx all believed that real wages would remain constant during capitalist development. They differed, however, in their explanations: Ricardo and Malthus believed that population growth would accelerate in response to any rise in income and ultimately force wages back to subsistence; Marx, on the other hand, believed that technological progress had a labour saving bias that would
恩格斯对英国工业化的看法并非孤见。在经济学家中，李嘉图、马尔萨斯和马克思都认为，在资本主义发展过程中，实际工资将保持不变。不过，他们的解释有所不同：李嘉图和马尔萨斯认为，人口增长会随着收入的增加而加速，并最终迫使工资回到维持生计的水平；而马克思则认为，技术进步具有节约劳动力的倾向，这将使工资保持不变。
eliminate any upward demand pressure on wages even as output per worker surged. In this paper, I offer a model that explains why Engel's pause happened and why it eventually gave way to a more equitable process of growth in which workers gained as well as capitalists. The model allows us to assess the importance of the demographic and technological factors emphasized by the classical economists in their analyses of industrialization.
即使在工人人均产出激增的情况下，也消除了对工资的需求压力。在本文中，我提供了一个模型来解释为什么会出现恩格尔的停顿，以及为什么它最终会让位于一个工人和资本家都获得收益的更加公平的增长过程。通过这个模型，我们可以评估古典经济学家在分析工业化时所强调的人口和技术因素的重要性。
The empirical point of departure is the comparison between the growth of output per worker and the real wage shown by the most widely used measures of these variables (Fig. 1). According to the Crafts-Harley estimates of British GDP, output per worker rose by between 1780 and 1840 . Over the same period, Feinstein's real wage index rose by only . It was only a slight exaggeration to say that the average real wage was constant, and it certainly rose much less than output per worker. This was the period, and the circumstances, described by Engel's in The Condition of the Working Class. In the next 60 years, however, the situation changed. Between 1840 and 1900, output per worker increased by and the real wage by . This was the 'modern' pattern in which labour productivity and wages advance at roughly the same rate, and it emerged in Britain around the time Engel's wrote his famous book.
经验的出发点是比较工人人均产出和实际工资的增长情况，这些变量的最广泛使用的衡量标准显示了工人人均产出和实际工资的增长情况（图 1）。根据 Crafts-Harley 对英国 GDP 的估算，1780-1840 年间工人人均产出增长了 。在同一时期，费恩斯坦的实际工资指数仅上升了 。说平均实际工资保持不变只是略显夸张，它的增长幅度肯定远远低于工人人均产出的增长幅度。这就是恩格尔在《工人阶级状况》中所描述的时期和情况。然而，在接下来的 60 年里，情况发生了变化。从 1840 年到 1900 年，工人的人均产出增加了 ，实际工资增加了 。这就是 "现代 "模式，即劳动生产率和工资以大致相同的速度增长。
The key question is: why did the British economy go through this two phase trajectory of development? Table 1 provides some basic macro data in a growth accounting framework that help specify the question. Between 1760 and 1800, the real wage grew slowly ( per annum) but so did output per worker ( ), capital per worker, and total factor productivity ( ). Between 1800 and 1830, the famous inventions of the industrial revolution came on stream and raised aggregate TFP growth to per year. This technology shock pushed up growth in output per worker to pa but had little impact on capital accumulation or the real wage, which remained constant. This was the heart of Engel's Pause, and the relationship between technology, capital accumulation, and wages is the problematic of this paper. In the next 30 years 1830-1860, TFP growth increased to almost one percent per annum, capital per worker began to grow, and the growth in output per worker rose to pa. The real wage finally began to grow ( pa) but still lagged behind output per worker with most of the shortfall in the beginning of the period. From 1860 to 1900, productivity, capital per worker, and output per worker continued to grow as they had in 1830-1860. In this period, the real wage grew slightly faster than output per worker (1.61% pa versus ). The 'modern' pattern was established.
关键问题是：英国经济为什么会经历这两个阶段的发展轨迹？表 1 提供了增长核算框架下的一些基本宏观数据，有助于说明这一问题。1760 年至 1800 年间，实际工资增长缓慢（ 年），但工人人均产出（ ）、工人人均资本和全要素生产率（ ）也在缓慢增长。1800 至 1830 年间，工业革命中著名的发明相继问世，使全要素生产率的年增长率上升到 。这种技术冲击将工人人均产出增长推高到 pa，但对资本积累或实际工资的影响甚微，两者保持不变。这就是恩格尔暂停的核心，而技术、资本积累和工资之间的关系正是本文的问题所在。在接下来的 30 年（1830-1860 年）中，全要素生产率的年增长率提高到近 1%，工人人均资本开始增长，工人人均产出的增长率上升到 pa。实际工资终于开始增长（ 年），但仍落后于工人人均产出，大部分缺口出现在这一时期的初期。从 1860 年到 1900 年，生产率、工人人均资本和工人人均产出与 1830-1860 年一样继续增长。在此期间，实际工资的增长速度略高于工人人均产出的增长速度（1.61%/年对 ）。现代 "模式已经确立。
Before explaining why the productivity shock of the industrial revolution was accompanied by a lag in real wage growth, we must acknowledge that not everyone shares this characterization of the industrial revolution. There is a long standing, 'optimistic' tradition that maintains that workers did better than Engels and the classical economists thought. The most recent proponent of this view is Clark (2001, 2005, 2007a,b), who believes that the average real wage grew faster than Feinstein contended and who also thinks that GDP grew less rapidly than Crafts and Harley calculated. Putting faster wage growth together with slower output growth implies that 'manual worker's real incomes in the industrial revolution period rose much more than did real output per capita' (Clark, 2001, p. 6). Workers, rather than capitalists, were the winners in the industrial revolution, according to Clark. This is exciting revisionism, but neither Clark's real wage series nor his GDP series are convincing improvements on the existing literature (See Appendix B for more discussion). Consequently, this paper is based largely on the estimates of Feinstein, Crafts, and Harley.
在解释为什么工业革命对生产力的冲击伴随着实际工资增长的滞后之前，我们必须承认，并非所有人都认同工业革命的这一特征。有一种由来已久的 "乐观 "传统认为，工人们的表现比恩格斯和古典经济学家们想象的要好。克拉克（2001、2005、2007a,b）是这一观点的最新支持者，他认为平均实际工资的增长速度比费因斯坦所主张的要快，而且他还认为国内生产总值的增长速度比克拉夫斯和哈雷计算的要低。将较快的工资增长与较慢的产出增长结合起来，意味着 "工业革命时期体力劳动者实际收入的增长远高于实际人均产出的增长"（Clark，2001 年，第 6 页）。克拉克认为，工人而非资本家是工业革命的赢家。这是令人兴奋的修正主义，但克拉克的实际工资系列和国内生产总值系列都不是对现有文献的令人信服的改进（更多讨论见附录 B）。因此，本文主要基于费恩斯坦、克拉夫茨和哈雷的估计。

1. The functional distribution of income
1.收入的功能分配

A complete description of the functional distribution of income in the industrial revolution requires the histories of the prices of labour, land, and capital as well as the shares of national income accruing to each. Figs. 1-3 graph most of these. All
要完整地描述工业革命时期的收入功能分配，就需要了解劳动力、土地和资本的价格历史，以及它们在国民收入中所占的份额。图 1-3 是其中大部分的示意图。所有
Fig. 1. The two phases of the British industrial revolution.
图 1.英国工业革命的两个阶段。
Table 1 表 1
Growth accounting for Great Britain, 1760-1900.
大不列颠的增长核算，1760-1900 年。
Growth of   的增长 Due to growth in 由于
G
0.11 -0.04 +0.19
0.13 -0.19 +0.69
0.37 -0.19 +0.94
0.30 -0.16 +0.89
Note: the table shows growth rates per year for and and the real wage. The entries for and are the contributions of their growth to the growth in , that is the growth rates per year of and multiplied by the factor shares of capital ( 0.35 ) and land ( 0.15 ), respectively.
注：该表显示了 和 以及实际工资的年增长率。 和 的条目是它们的增长对 增长的贡献，即 和 的年增长率分别乘以资本（0.35）和土地（0.15）的要素份额。
values are real returns and real shares measured in the prices of the 1850 s. I consider them in the order in which they were constructed.
这些数值是以 1850 年代的价格衡量的实际收益和实际份额。
Fig. 1 shows the real wage, which grew very little from 1770 to about 1840 and then rose in line with output per worker. The real wage series in Fig. 1 is my revision of Feinstein's estimate of the average nominal earnings of manual workers divided by the cost of living index. I have increased Feinstein's real earnings index by , so that it equals the average earnings of all labour including the self-employed and those receiving salaries. The mark-up appears to have been constant across the industrial revolution and is explained in Appendix A. With a constant mark-up, the problem of explaining constant earnings of manual workers is the same as explaining the average earnings of labour in general.
图 1 显示的是实际工资，从 1770 年到 1840 年左右，实际工资几乎没有增长，然后随着工人人均产出的增加而增长。图 1 中的实际工资序列是我对费因斯坦估计的体力劳动者平均名义收入除以生活费用指数后得出的修正值。我将费恩斯坦的实际收入指数提高了 ，使其等于包括自营职业者和领取工资者在内的所有劳动力的平均收入。在整个工业革命期间， 加价似乎是不变的，附录 A 中对此进行了解释。在加价不变的情况下，解释体力劳动者固定收入的问题与解释一般劳动力的平均收入问题相同。
The real rent of land rose slowly from1760 to the late 19th century (Clark, 2002, p. 303). Pace Ricardo, it does not play a major role in the surges of inequality.
从 1760 年到 19 世纪末，土地的实际租金缓慢上升（Clark，2002 年，第 303 页）。与李嘉图一样，它在不平等的激增中并没有发挥主要作用。
By multiplying the real wage by the occupied population and the real rent by the cultivated land, one obtains the wage bill and total rent. Subtracting these from GDP gives profits, and dividing total wages, rent, and profits by GDP gives shares.
用实际工资乘以居住人口，用实际地租乘以耕地面积，就得出了工资总额和地租总额。从国内生产总值中减去这两项得出利润，再用工资、地租和利润总额除以国内生产总值得出份额。
Before 1860, capital income was primarily the net income of unincorporated enterprises where the owners' labour has been deducted as a cost valued at the earnings of salaried employees. Profits in this context included the return to entrepreneurship as well as the return to capital narrowly defined. Businessmen of the period regarded "profitability as a product of business acumen rather than the return to capital." As a result, business accounts usually distinguished "between interest on capital and the profits of business." (Hudson, 1986, p. 235) While I impute business profits to capital, this interpretation needs to be kept in mind. Capital income also included the return to residential housing and, beginning about 1840, the net income of railways, which were the principal business corporations before the middle of the 19th century. Thereafter, corporate earnings became an increasingly important part of capital income.
1860 年以前，资本收入主要是指非法人企业的净收入，在这些企业中，所有者的劳动已作为成本扣除，其价值与受薪雇员的收入相当。在这种情况下，利润包括创业回报和狭义的资本回报。当时的商人认为，"盈利能力是商业智慧的产物，而不是资本回报"。因此，商业账目通常区分 "资本利息和商业利润"。(赫德森，1986 年，第 235 页）虽然我将商业利润归结为资本，但这一解释需要牢记。资本收入还包括住宅回报，以及大约从 1840 年开始的铁路净收入，铁路在 19 世纪中叶之前是主要的商业公司。此后，公司收益成为资本收入中越来越重要的一部分。
The shares are graphed in Fig. 2. The share of rent in national income declined gradually over the century. The shares of wages and profits exhibited conflicting trends. In the late 18th century, labour's share was about . It declined steadily until the middle of the 19th century to around one half. Then it rose steadily to a peak around 1900 when its value was back to its late 18th century level. Finally, labour's share sagged again in the decade before the First World War. Capital's share moved inversely, more than doubling from a late 18 th century value of to over in the middle of the 19th century. It fluctuated around the level until the First World War.
这些份额的图表见图 2。地租在国民收入中所占的份额在本世纪逐步下降。工资和利润的份额呈现出相互矛盾的趋势。在 18 世纪末，劳动份额约为 。直到 19 世纪中叶，这一份额稳步下降到一半左右。然后稳步上升，到 1900 年左右达到顶峰，其价值恢复到 18 世纪末的水平。最后，劳动份额在第一次世界大战前十年再次下降。资本所占的份额呈反向变化，从18世纪末的 增加到19世纪中期的 ，增加了一倍多。在第一次世界大战之前，资本份额一直在这一水平上下波动。
Fig. 2. Historical factor shares,
图 2 历史要素份额，
Fig. 3. Historical profit rate, .
图 3.历史利润率， 。
These shares are calculated from real values of factor prices and GDP. Nominal values exhibit similar trends. I have revised Deane and Cole's (1969, p. 166) nominal GDP series by replacing their nominal wage series with Feinstein's to value labour. This makes the GDP estimates consistent with the wage estimates. Using these figures, labour's share dropped from in 1801 to in 1841. This was the period of Engel's pause. The distributional shifts we are analysing are not simply due to relative price movements.
这些份额是根据要素价格和国内生产总值的实际值计算得出的。名义价值表现出类似的趋势。我对 Deane 和 Cole（1969 年，第 166 页）的名义国内生产总值序列进行了修订，用费因斯坦的名义工资序列取代了他们的名义工资序列，以对劳动力进行估值。这使得 GDP 估算值与工资估算值保持一致。使用这些数字，劳动力的份额从 1801 年的 下降到 1841 年的 。这就是恩格尔的停顿期。我们所分析的分配变化并不仅仅是相对价格变动造成的。
Finally, one can calculate the gross profit rate by dividing profits as defined above by the capital stock. Fig. 3 shows two ways of doing the calculation. The 'real profit rate' equals real profits (real GDP less the real wage bill and total real rents) divided by Feinstein's real capital stock. The 'nominal profit rate' is the ratio of Deane and Cole's current value estimate of profits (their estimate of property income less the rent of agricultural land) divided by the capital stock valued in the prices of the year in question. The two series agree closely showing again that the trends analysed in this paper appear in both real and nominal series. In both cases, the series show that the profit rate was comparatively low at the end of the 18th century and rose until the middle of the 19th century when it stabilized until the First World War.
最后，我们可以用上述利润除以资本存量来计算毛利率。图 3 显示了两种计算方法。实际利润率 "等于实际利润（实际 GDP 减去实际工资支出和实际租金总额）除以费恩斯坦的实际资本存量。名义利润率 "是 Deane 和 Cole 对利润的现值估算（他们对财产收入的估算减去农业用地租金）除以按当年价格估算的资本存量的比率。这两个数列非常接近，再次表明本文所分析的趋势既出现在实际数列中，也出现在名义数列中。这两个数列都表明，利润率在 18 世纪末相对较低，直到 19 世纪中叶才开始上升，并在第一次世界大战前趋于稳定。
The rate of return to capital rose from near in the late 18 th century to in the early 19 th and surpassed in the middle of the century. Even deducting a few percentage points for depreciation, the return to capital in the 19th century exceeded interest rates by a wide margin. Some confirmation for these rates c. 1800 comes from Harley's (2006) estimates of the return to capital in the cotton industry calculated from business records: they imply a rate of return (net of depreciation) in the range in the late 18th and early 19th centuries. Hudson's (1986, pp. 235-241, 272,277) study of the records of wool and worsted firms reveals profit rates on business capital of in the 1850 s. Business capital was roughly half trade credit and half fixed capital, so the return on the latter was over , which is in line with Fig. 3. A 20th century perspective is provided by Matthews et al. (1982, p. 187-188)) calculations of the profit rate realized by unincorporated businesses in the UK since the 1930s. These profit rates were in the range of with some industries like construction and commerce occasionally realizing returns as high as . Capital invested elsewhere in the economy realized much lower rates of return. This pattern emerged in the first half of the 19th century.
资本回报率从18世纪末的 附近上升到19世纪初的 ，并在本世纪中叶超过了 。即使扣除几个百分点的折旧，19 世纪的资本回报率也远远超过了利率。 Harley（2006）根据商业记录计算出的棉花产业资本回报率在一定程度上证实了 1800 年前的这些回报率：这意味着 18 世纪末和 19 世纪初的回报率（扣除折旧）在 范围内。Hudson (1986, pp. 235-241, 272,277) 对羊毛和精纺公司记录的研究显示，1850 年代商业资本的利润率为 。商业资本大约一半是贸易信贷，一半是固定资本，因此后者的回报率超过 ，这与图 3 一致。Matthews 等人（1982 年，第 187-188 页）对 20 世纪 30 年代以来英国非法人企业实现的利润率进行了计算，提供了 20 世纪的视角。这些利润率在 之间，建筑和商业等一些行业的回报率偶尔会高达 。投资于经济其他领域的资本实现的回报率要低得多。这种模式出现在 19 世纪上半叶。
Figs. 1-3 show the facts that an investigation of growth and distribution in Britain must explain. The figures verify key features of Engels' pause in the first half of the 19th century: the stagnant real wage, the decline in labour's share of the national income, the rise in capital's, and the increase in the gross profit rate. In addition, the improved position of labour after the middle of the 19th century must be explained.
图 1-3 显示了对英国经济增长和分配的调查必须解释的事实。这些数字验证了恩格斯在 19 世纪上半叶停顿的主要特征：实际工资停滞不前、劳动在国民收入中的份额下降、资本份额上升以及毛利率上升。此外，还必须解释 19 世纪中叶以后劳动地位的提高。

2. Explanations not taken
2.未作解释

There are two approaches to explaining these trends. The first attributes them to a series of accidents: bad harvests and the Napoleonic Wars raised agricultural prices in Britain and checked the growth of real wages at the beginning of the 19th century (Mokyr and Savin, 1976). The Corn Laws then kept food prices high until 1846 and prevented wages from rising
有两种方法可以解释这些趋势。第一种方法将其归因于一系列意外事件：歉收和拿破仑战争抬高了英国的农产品价格，抑制了 19 世纪初实际工资的增长（Mokyr 和 Savin，1976 年）。随后的《玉米法》使食品价格一直高居不下，直至 1846 年，并阻止了工资的增长。
(Williamson, 1990). These unfavourable events were reversed after 1870 with the American grain invasion, which lowered wheat prices and led to higher real wages (O'Rourke, 1997; O'Rourke and Williamson, 1999).
(Williamson, 1990）。1870 年后，随着美国粮食入侵，小麦价格下降，实际工资提高，这些不利事件发生了逆转（O'Rourke，1997 年；O'Rourke 和 Williamson，1999 年）。
While these features of the global economy undoubtedly deserve attention, this paper pursues the second approach, which roots the macro trends in a model of the macro economy. In this model, technical change and capital accumulation govern the history of factor prices. It turns out that a simple model of this sort does a good job of explaining wage stagnation followed by wage acceleration. In view of that success, perhaps incidental features like the Corn Laws really were just incidental?
尽管全球经济的这些特点无疑值得关注，但本文采用的是第二种方法，即把宏观趋势植根于宏观经济模型之中。在这个模型中，技术变革和资本积累主导着要素价格的历史。事实证明，这种简单的模型可以很好地解释工资停滞后的工资加速增长。鉴于这种成功，也许像《玉米法》这样的偶然特征真的只是偶然？
The obvious place to start any discussion of Britain's inequality trends is Lewis' (1954) famous model of 'economic development with unlimited supplies of labour,' for it predicts a two phase development process like that shown in Fig. 1. Conceptually, Lewis divided the economy into two sectors: one was peasant agriculture where the population was in surplus, capital was scarce, the marginal product of labour was zero, and income sharing guaranteed subsistence to all. The other was the modern, industrial sector where capital intensive production meant that labour productivity was high. Growth occurred as the modern sector expanded through capital accumulation. Labour to man the new capacity was available from the agricultural sector in infinitely elastic supply at the subsistence wage. This supply condition kept wages in the modern sector at subsistence-pessimism in action! - with the result that profits increased. The increase in profits provided the savings that allowed the modern sector to enlarge. When it was large enough to absorb all the labour surplus, further accumulation meant that wages rose along with productivity. The result was a two stage growth process with rising inequality in the first stage followed by a more equitable growth trajectory in the second.
要讨论英国的不平等趋势，显然要从刘易斯（1954 年）著名的 "劳动力无限供给的经济发展 "模型说起，因为该模型预测了如图 1 所示的两阶段发展过程。从概念上讲，刘易斯将经济划分为两个部门：一个是农民农业部门，那里人口过剩，资本稀缺，劳动的边际产品为零，收入分享保证了所有人的生存。另一个是现代工业部门，资本密集型生产意味着劳动生产率高。随着现代部门通过资本积累不断扩大，出现了增长。农业部门以维持生计的工资无限弹性地供应新产能所需的劳动力。这种供应条件使现代部门的工资保持在维持生计的水平--悲观主义在发挥作用！- 结果，利润增加了。利润的增加提供了储蓄，使现代部门得以扩大。当现代部门的规模足以吸收所有剩余劳动力时，进一步的积累意味着工资随着生产率的提高而提高。结果是出现了两个阶段的增长过程，第一阶段不平等加剧，第二阶段的增长轨迹更加公平。
Although Lewis' model was inspired by the classical economists analysing the British industrial revolution, the emphasis he placed on surplus labour is hard to reconcile with British history. As a general matter, surplus labour in the countryside is difficult to reconcile with a positive wage. In addition, there are particular problems to applying it to the British industrial revolution. British agriculture did not function as source of surplus labour that kept wages down. For one thing it was too small. In 1801 only of the work force was in agriculture (Deane and Cole, 1969, p. 142) compared to the that characterized the less developed countries Lewis was describing. Moreover, contrary to Marx, the parliament enclosures did not drive workers from the land; indeed, the poor law (through the Speenhamland system) paid men to stay in the countryside and reduced rural-urban migration. Finally, while real wages were stagnant in industrializing Britain, they stagnated at a high level when seen internationally: real wages in 18th century Britain and the Low Countries were higher than anywhere else in Eurasia (Allen, 2001). This does not square with Lewis' scenario. We need another approach.
尽管刘易斯的模型受到了分析英国工业革命的古典经济学家的启发，但他对剩余劳动力的强调却很难与英国历史相吻合。一般来说，农村剩余劳动力很难与正工资相协调。此外，将其应用于英国工业革命也存在特殊问题。英国农业并没有成为压低工资的剩余劳动力来源。首先，它的规模太小。1801 年，只有 的劳动力从事农业生产（Deane 和 Cole，1969 年，第 142 页），而刘易斯所描述的欠发达国家的劳动力则达到了 。此外，与马克思的观点相反，议会圈地并没有把工人从土地上赶走；事实上，穷人法（通过斯皮纳姆地制度）向留在农村的男子支付了报酬，减少了农村人口向城市的迁移。最后，虽然在工业化的英国，实际工资停滞不前，但从国际上看，实际工资停滞在一个较高的水平：18 世纪英国和低地国家的实际工资高于欧亚大陆的其他地方（Allen，2001 年）。这与刘易斯的设想不符。我们需要另一种方法。

3. A model of growth and income distribution
3.增长和收入分配模式

We can avoid the implausibilities of the Lewis model with an integrated model of growth and distribution. This model is a Solow (1956) one sector growth model in which savings are a function of property income rather than total income. Profits as a source of savings is one of Lewis's themes, and it is more revealing than his ideas about surplus labour, for the connection between technical progress, savings, and capital accumulation turns out to be fundamental to explaining the advent and cessation of Engel's pause. Suitably calibrated, this modification of the Solow model closely tracks the growth and inequality history of the industrial revolution. Simulations from 1760 to 1913 reproduce the two phases of rising and then constant inequality that Lewis delineated. Finally, the model allows us to probe the causes of inequality more deeply. While the classical economists all expected the real wage to remain constant, they disagreed about the reason: Malthus and Ricardo emphasized the growth of population, while Marx emphasized the labour saving bias of technical change. We can establish the importance of these explanations by simulating the integrated model.
我们可以用一个增长和分配的综合模型来避免刘易斯模型的不靠谱之处。该模型是索洛（1956 年）的单部门增长模型，其中储蓄是财产收入而非总收入的函数。作为储蓄来源的利润是刘易斯的主题之一，这比他关于剩余劳动的观点更有启发性，因为技术进步、储蓄和资本积累之间的联系对于解释恩格尔停顿的出现和停止是至关重要的。经过适当的校准，索洛模型的这一修改密切追踪了工业革命的增长和不平等历史。从 1760 年到 1913 年的模拟再现了刘易斯所描述的不平等先上升后持续的两个阶段。最后，该模型允许我们更深入地探究不平等的原因。尽管古典经济学家们都期望实际工资保持不变，但他们对原因的看法却不尽相同：马尔萨斯和李嘉图强调的是人口增长，而马克思强调的是技术变革的劳动节约偏向。我们可以通过模拟综合模型来确定这些解释的重要性。
Unlike the standard Solow model, the model proposed here does integrate growth and income distribution. Output and factor prices are determined by neoclassical production function and its marginal products. Savings depends on property income and, thus, on the distribution of income, which, therefore, also feeds back on the growth rate. I begin with the three equations that comprise the heart of the Solow (1956) growth model:
与标准索洛模型不同，本文提出的模型将增长与收入分配结合起来。 产出和要素价格由新古典生产函数及其边际产品决定。储蓄取决于财产收入，因而也取决于收入分配，因此也会反作用于增长率。我首先介绍构成索洛（1956 年）增长模型核心的三个方程：



The first is a neoclassical production function in which GDP depends on the aggregate workforce , capital stock , and land area . The measurement of these variables was defined previously and is discussed in detail in Appendix A. Land is not normally included in a Solow model but is added here due to its importance in the British economy during the industrial revolution. A is an index of labour augmenting technical change. Technical change of this sort is necessary for a continuous rise in per capita income and the real wage, but it also paradoxically represents Marx's view of labour displacing technical change. In the simulations A plays both roles.
第一个是新古典生产函数，其中 GDP 取决于总劳动力 、资本存量 和土地面积 。这些变量的测量方法已在前面进行了定义，并在附录 A 中进行了详细讨论。土地通常不包括在索洛模型中，但由于其在工业革命时期英国经济中的重要性，在此加入了土地。A 是劳动力增强技术变革指数。这种技术变革是人均收入和实际工资持续增长的必要条件，但它也自相矛盾地代表了马克思关于劳动取代技术变革的观点。在模拟中，A 同时扮演着这两种角色。
One input that Eq. (1) does not include is human capital. It is not explicitly represented because human capital accumulation was not an important feature of the industrial revolution. There was little increase in literacy or schooling rates. In this context, the constancy of relative earnings across occupations indicates a lack of rising demand for human capital. Britain before 1860 looks like a good example of Galor and Moav's (2006) picture of an early industrializer where the demand for physical capital was increasing more vigorously than the demand for human capital. Expenditures on education were also much less than those on physical capital. For these reasons, the accumulation of human capital is not explicitly modelled and labour is treated as having an unchanging amount of human capital (Mitch, 2004).
公式(1)没有包括的一项投入是人力资本。之所以没有明确体现，是因为人力资本积累并不是工业革命的重要特征。识字率或入学率几乎没有提高。在这种情况下，不同职业的相对收入不变，表明对人力资本的需求没有增加。1860 年以前的英国是 Galor 和 Moav（2006 年）所描绘的早期工业化国家的一个很好的例子，在那里，对物质资本的需求比对人力资本的需求增长得更快。教育支出也远远低于物质资本支出。由于这些原因，人力资本的积累没有被明确地模拟出来，劳动力被视为拥有不变数量的人力资本（Mitch，2004 年）。
Physical capital accumulation, however, is modelled, and the second equation defines the evolution of the stock. The stock in one year equals the stock in the previous year plus gross investment (I) and minus depreciation (at the rate ) of the previous year's capital stock.
然而，物质资本积累是模型化的，第二个等式定义了存量的变化。一年的存量等于前一年的存量加上投资总额（I），再减去前一年资本存量的折旧（折旧率 ）。
The third equation is the savings or investment function according to which investment is a constant fraction (s) of national income. Eq. (3) is the very simple Keynesian specification that Solow used. In some simulations, I will use it to set the economy-wide savings rate. However, Eq. (3) is not descriptive of industrializing Britain where all saving was done by landlords and capitalists. This idea is incorporated into the model with a savings function along the lines of Kalecki (1942) and Kaldor (1956):
第三个等式是储蓄或投资函数，根据该函数，投资是国民收入的一个恒定部分（s）。公式 (3) 是索洛所使用的非常简单的凯恩斯规范。在某些模拟中，我会用它来设定整个经济的储蓄率。然而，公式（3）并不能描述工业化时期的英国，在那里，所有的储蓄都是由地主和资本家完成的。在模型中，我们按照 Kalecki（1942 年）和 Kaldor（1956 年）的思路将这一想法与储蓄函数结合起来：
In this specification, capitalists and landowners do all the savings since is the propensity to saving out of profits and is the share of profits in national income. Likewise, is the propensity to saving out of rents and is the share of rents. The economy-wide savings rate depends on the distribution of income. With Eq. (4), accumulation and income distribution are interdependent and cannot be analysed separately. In other words, one cannot first ask why income grew and then ask how the benefits of growth were distributed. Each process influenced the other.
在这种情况下，资本家和土地所有者进行所有的储蓄，因为 是用利润进行储蓄的倾向， 是利润在国民收入中所占的份额。同样， 是用租金储蓄的倾向， 是租金所占的份额。整个经济的储蓄率 取决于收入的分配。根据公式（4），积累和收入分配是相互依存的，不能分开分析。换句话说，我们不能先问收入增长的原因，然后再问增长的收益是如何分配的。每个过程都相互影响。
Usually, a growth model also includes an equation specifying the growth in the work force or population (assumed to be proportional) at some exogenous rate. Since the model is being applied here to past events, the work force is simply taken to be its historical time series. There was some variation in the fraction of the population that was employed. I will ignore that, however, in this paper and use the terms output per worker and per capita income interchangeably.
通常情况下，增长模型还包括一个方程，规定劳动力或人口（假定成比例）以某种外生率 增长。由于该模型适用于过去的事件，因此劳动力被简单地视为其历史时间序列。就业人口的比例存在一些变化。不过，在本文中我将忽略这一点，并交替使用工人人均产出和人均收入这两个术语。
Three more equations model the distribution of income explicitly. The derivatives of Eq. (1) with respect to , and are the marginal products of labour, capital, and land, and imply the trajectories of the real wage, return to capital, and rent of land. These factor prices can also be expressed as proportions of the average products of the inputs:
还有三个方程明确地模拟了收入分配。公式 (1) 关于 和 的导数是劳动、资本和土地的边际产品，意味着实际工资、资本回报和土地租金的轨迹。这些要素价格也可以表示为投入品平均产品的比例：
Here , and are the real wage, profit rate, and rent of land. are the shares of labour, capital, and land in national income, as previously noted.
这里的 和 是实际工资、利润率和地租。如前所述， 是劳动、资本和土地在国民收入中所占的份额。
A production function must be specified to apply the model to historical data. The Cobb-Douglas is commonly used, and, indeed, I used a Cobb-Douglas for trial simulations and to determine a provisional trajectory for productivity growth. The function is:
要将模型应用于历史数据，必须指定一个生产函数。柯布-道格拉斯函数是常用的函数，事实上，我也使用柯布-道格拉斯函数进行了模拟试验，并确定了生产率增长的临时轨迹。该函数为
where are positive fractions that sum to one when there is constant returns to scale, as will be assumed. is a scaling parameter. With a Cobb-Douglas technology, can be factored out as which is the conventional, Hicks neutral, total factory productivity index. In addition, in competitive equilibrium, the exponents , and equal the shares of national income accruing to the factors , and ). These shares are constants. They can be calculated from the national accounts of one year; in other words, the model can be calibrated from a single data point.
其中， 为正分数，在规模收益不变的情况下，其总和为 1。 是规模参数。在科布-道格拉斯技术条件下， 可以分解为 ，即传统的、希克斯中性的工厂总生产率指数。此外，在竞争均衡状态下，指数 和 等于要素 和 在国民收入中所占的份额。）这些份额是常数。它们可以从一年的国民账户中计算出来；换句话说，模型可以从一个数据点进行校准。
Ultimately, however, the Cobb-Douglas is not satisfactory for understanding inequality since the essence of the matter is that the shares were not constant. Economists have proposed more general functions that relax that restriction. The simplest is the CES (constant elasticity of substitution). It is not general enough, however, for it requires that the elasticities of substitution between all pairs of inputs be equal (although not necessarily equal to one). Instead, I have used the translog production function. It is the natural generalization of the Cobb-Douglas. With the translog, all shares can vary as can all of the pair-wise elasticities of substitution. The translog is usually written in logarithmic form:
然而，科布-道格拉斯法最终还是无法令人满意地理解不平等问题，因为问题的本质在于份额并非恒定不变。经济学家们提出了放宽这一限制的更一般的函数。最简单的是 CES（恒定替代弹性）。但它不够通用，因为它要求所有投入对之间的替代弹性相等（尽管不一定等于 1）。相反，我使用了转化生产函数。 它是对柯布-道格拉斯生产函数的自然概括。使用 translog，所有份额都可以变化，所有成对的替代弹性也可以变化。平移生产函数通常用对数形式表示：
Fig. 4. Savings propensity out of property income.
图 4.财产收入的储蓄倾向。
subject to the adding up conditions , and . When all of the , the translog function reduces to the Cobb-Douglas.
和 。当所有条件 都满足时，translog 函数就简化为柯布-道格拉斯函数。
Logarithmic differentiation of the translog function gives share equations that imply trajectories of factor prices in accord with Eqs. (5)-(7):
对translog函数进行对数微分，可得到份额方程，其中隐含的要素价格轨迹与公式(5)-(7)一致：
These equations are the basis for calibrating the model, as we will see.
这些方程是校准模型的基础，我们将会看到。

4. Savings and production function calibration
4.储蓄和生产函数校准

The savings and production functions are central to the growth model, and each must be estimated. Were there sufficient data, this could be done econometrically, but data are too limited for that. Instead they are calibrated.
储蓄和生产函数是增长模型的核心，必须对其进行估算。如果有足够的数据，可以通过计量经济学方法进行估算，但数据太有限，无法做到这一点。因此，必须对它们进行校准。
There are two variants of the savings function. In the case of (Eq. (2)), is determined by dividing real gross investment by real GDP. The ratio rises gradually from about in 1760 to in the 1830 s and 1840 s. It sags to about in the 1850s.
储蓄函数有两种变式。在 （公式(2)）的情况下， 由实际投资总额除以实际 GDP 决定。该比率从 1760 年的 逐渐上升到 1830 年代和 1840 年代的 。
The alternative savings function is the Kalecki function