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

Received 8 February 2008 2008 年 2 月 8 日收到
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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

( 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。

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。

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。

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。

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。

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 (Eq. (4)). This function is preferred since household budgets from the industrial revolution indicate that, on average, workers did not save (Horrell and Humphries, 1992; Horrell, 1996). All of the savings, therefore, came from landlords and capitalists.
另一个储蓄函数是卡莱基函数 （公式 (4)）。由于工业革命时期的家庭预算表明，工人平均没有储蓄（Horrell 和 Humphries，1992 年；Horrell，1996 年），因此该函数更受青睐。因此，所有储蓄都来自地主和资本家。

Fig. 4 shows the ratio of savings to their income. Use is made of the identity that savings equals investment, and of Feinstein's estimates of the latter. There is some suggestion that the savings rate out of property income rose in the 1760s and 1770 s, but thereafter there was no trend. Regression of the savings rate on the shares of profits and rents in national income for the period 1770-1913 showed a small difference between landlords and capitalists:
图 4 显示了储蓄与收入的比率。图中使用了储蓄等于投资这一特性，以及费恩斯坦对后者的估计。 有迹象表明，财产收入中的储蓄率在 17 世纪 60 年代和 70 年代有所上升，但此后没有趋势。1770-1913 年间，储蓄率与利润和租金在国民收入中所占份额的回归显示，地主和资本家之间的差异很小：

The coefficients had estimated standards errors of 0.013 and 0.004 , respectively. In this model, capitalists saved a higher proportion of income than landlords. I used this equation for most simulations except that I lowered the coefficient of savings by capitalists to 0.14 in the 1760 s and 0.16 in the 1770 s. This improved the simulations in those years and creates a small exogenous component to the rise in savings in 1780. The increase in savings in later years remains dependent on changes in the distribution of income.
系数的估计标准误差分别为 0.013 和 0.004。在这个模型中，资本家储蓄占收入的比例高于地主。除了将 1760 年代和 1770 年代的资本家储蓄系数分别降低到 0.14 和 0.16 之外，我在大多数模拟中都使用了这一方程。后期储蓄的增加仍然取决于收入分配的变化。

Table 2 表 2
Translog coefficients. Translog 系数

The parameters of the translog function must also be determined. While the parameters of the Cobb-Douglas function can be calculated from the factor shares at one point in time, the translog requires two sets of factor shares. If the adding up conditions and are imposed on Eqs. (10)-(12), one gets:
还必须确定平移函数的参数。柯布-道格拉斯函数的参数可以根据某一时点的要素份额计算出来，而平移函数则需要两组要素份额。 如果在公式（10）-（12）中加入 和 条件 ，就可以得到：

If the values for the three shares and the corresponding , and are substituted into these three equations for two years, then one obtains six equations in the six unknown parameters , and . These can be solved by inverting the matrix and premultiplying the share vector with it. The remaining parameters can be calculated from the imposed conditions.
如果将三个份额的值以及相应的 和 代入这三个方程中的两年，那么就会得到六个未知参数 和 的六个方程。将矩阵倒置并与份额向量相乘即可求解。其余参数可根据施加条件计算得出。

A complication is that the parameters depend on , and depends on the parameters, so values must be obtained by iterating from one to the other. In reality, the dependence of the parameters on is not very great and vice versa, so that finding a consistent solution is not difficult. The parameters and were estimated in the following stages. First, I set the factor share values at , and in 1770 and , and 0.10 in 1860 . These values were typical of those years. Second, a trial set of values of the labour augmenting technological change parameter was computed by assuming a Cobb-Douglas technology (Eq. (8)). A was set equal to one in 1770 and subsequent values were computed for the later years during the industrial revolution for which GDP has been estimated (1801, 1830, and 1860) as well as 1875,1896 , and 1913 , which divide the late 19 th century in a conventional manner. Third, the 1770 and 1860 values of were substituted into the six share equations for those two years, and a set of values of the translog parameters was then computed. Fourth, the now calibrated translog production function was used to compute GDP in 1801, 1831, and so forth up to 1913. These computed values were not equal to the actual values since the values of had been computed with a different production function. The values of were changed, so that computed GDP equalled actual GDP. The adjustments were made period by period, i.e., the growth in A between 1770 and 1801 was altered, so that the computed and actual GDP were equal in 1801 . This was repeated for 1830,1860 , and so forth to 1913. Fifth, with the new values of in 1770 and 1860, the six share equations were again solve for a new set of translog parameters as in stage three just described. The cycle of computing values of and the translog parameters was repeated until estimation errors of GDP were eliminated. This only took a few iterations. The estimated rate of labour augmenting technical change increased from per year in to in 1801-1830 and, finally, to from 1831 to 1896 when it slumped to until 1913. No distributional information between 1770 and 1860 was used to calibrate the model, so its ability to replicate Engel's pause (as we will see) is independent verification of the model rather than an artefact of its construction.
一个复杂的问题是，参数取决于 ，而 又取决于参数，因此必须通过从一个参数到另一个参数的迭代来获取数值。实际上，参数与 的关系并不大，反之亦然，因此找到一致的解并不困难。参数和 的估算分以下几个阶段进行。首先，我将 1770 年的要素份额值设为 和 ，将 1860 年的要素份额值设为 和 0.10。这些数值是这些年份的典型值。其次，假定采用柯布-道格拉斯技术（公式 (8)），计算了一组劳动力增加技术变化参数 的试验值。A 在 1770 年被设为 1，随后的数值是在工业革命期间的后期年份（1801、1830 和 1860 年）以及 1875、1896 和 1913 年计算得出的，这些年份以传统方式划分了 19 世纪晚期。第三，将 1770 年和 1860 年的 值代入这两年的六个份额方程中，然后计算出一组平移参数值。第四，使用现在校准过的转化生产函数计算 1801 年、1831 年的国内生产总值，以此类推，直到 1913 年。由于 的值是用不同的生产函数计算出来的，因此这些计算值并不等于实际值。对 的值进行了修改，使计算出的国内生产总值与实际国内生产总值相等。调整是逐期进行的，即改变 1770 年至 1801 年 A 的增长，使计算的国内生产总值与 1801 年的实际国内生产总值相等。1830 年、1860 年和 1913 年也是如此。 第五，利用 1770 年和 1860 年 的新值，再次求解六个份额方程，以获得一组新的平移参数，如上述第三阶段。计算 值和平移参数的循环重复进行，直到消除国内生产总值的估计误差。这只需要几次反复。劳动力增加技术变化的估计速率从 的每年 增加到 1801-1830 年的 ，最后从 1831 年增加到 1896 年的 ，随后下滑到 直到 1913 年。1770 年至 1860 年期间的分布信息没有被用来校准模型，因此，它复制恩格尔停顿的能力（我们将看到）是对模型的独立验证，而不是模型构建的产物。

The estimated translog parameter values are shown in Table 2. Their economic significance lies in their implications for elasticities of substitution - in particular, for the elasticity of substitution between labour and capital. In this case, it was close to zero and that plays an important role in explaining both economic growth and the two phase history of inequality.
表 2 列出了估计的转换参数值。它们的经济意义在于对替代弹性的影响，特别是对劳动力和资本之间的替代弹性的影响。在这种情况下，该弹性接近零，这在解释经济增长和不平等的两阶段历史方面发挥了重要作用。

Fig. 5 shows the labour-capital isoquant for the translog function in 1810 and, for comparison, a Cobb-Douglas isoquant through the same input combination. The Cobb-Douglas has an elasticity of substitution equal to one for all input pairs. In the
图 5 显示了 1810 年 translog 函数的劳动-资本等量关系，以及相同投入组合的柯布-道格拉斯等量关系，以作比较。 在所有投入组合中，柯布-道格拉斯的替代弹性都等于 1。在

Fig. 5. Translog and Cobb-Douglas isoquants, 1810 .
图 5.Translog 和 Cobb-Douglas 等差数，1810 年。
figure, the Cobb-Douglas isoquant is quite flat, while the translog is closer to the right angle of a Leontief fixed proportions technology. The elasticity of substitution between capital and labour was estimated by trial and improvement to be approximately 0.2 in 1810. Berndt (1976) claimed a value of one for twentieth century America, but some older and many recent investigators have concluded that the elasticity of substitution was considerably lower - in some cases as low as (Acemoglu, 2003; Antràs, 2004; David and van de Klundert, 1965; Lucas, 1969; McAdam and Willman, 2006). The production function of industrializing Britain used here is consistent with this line of research.
从图中可以看出，柯布-道格拉斯等差数列非常平缓，而平移等差数列更接近于列昂惕夫固定比例技术的直角。1810 年，通过试验和改进，估计资本和劳动力之间的替代弹性约为 0.2。 Berndt（1976 年）声称 20 世纪美国的替代弹性值为 1，但一些较早的研究者和许多最近的研究者都认为替代弹性要低得多--在某些情况下甚至低至 （Acemoglu，2003 年；Antràs，2004 年；David 和 van de Klundert，1965 年；Lucas，1969 年；McAdam 和 Willman，2006 年）。本文使用的工业化英国的生产函数与这一研究思路一致。

The low elasticity of substitution between capital and labour reflected two important features of industrializing Britain. First, much of the investment was in social overhead capital (Feinstein, 1988, p. 431), and that did not admit much substitutability between capital and labour. The population was expanding, and industrialization meant urbanization. Each new job, in other words, required a large dollop of housing and infrastructure. The British industrial revolution was done on the cheap, so far as this kind of investment was concerned (Williamson, 1990), so these dollops were as small as possible and did not admit much substitutability with labour. As Britain was industrializing, capital was required in fixed proportion to labour, and that is what the low elasticity of substitution picks up. Later, when the urban structure was stabilized, the substitution of capital for labour at the plant level influenced the aggregate statistics more, and estimated elasticities of substitution were greater.
资本与劳动力之间的低替代弹性反映了英国工业化的两个重要特征。首先，大部分投资用于社会间接资本（Feinstein，1988 年，第 431 页），这就不允许资本和劳动力之间有太大的替代性。人口不断膨胀，工业化意味着城市化。换句话说，每个新的工作岗位都需要大量的住房和基础设施。就此类投资而言，英国的工业革命是以低成本完成的（Williamson，1990 年），因此这些投资规模尽可能小，与劳动力之间的替代性不强。在英国工业化的过程中，资本与劳动力的需求成固定比例，这就是低替代弹性的原因。后来，当城市结构趋于稳定时，工厂一级的资本对劳动力的替代对总体统计数据的影响更大，估计的替代弹性也更大。

Second, for many industries during the industrial revolution, there was little scope to substitute capital for labour even at the plant level. The implements of production in many industries were the same around the world irrespective of relative factor prices. In the 1760 s, cloth was woven on similar looms in England where wages were high and in India where they were low (Broadberry and Gupta, 2006a,b). The creation of mechanized technology during the industrial revolution meant that the scope for factor substitution broadened. By the late 19th century, weaving was done by power looms in Britain and America and by handlooms in the third world, while everyone had used hand looms a century before. However, the implication of the slow rate of aggregate TFP growth shown in Table 1 is that this modernization (and with it the increase in the elasticity of substitution) was confined to only a few 'revolutionized' industries (Crafts, 1985a; Crafts and Harley, 1992). Throughout the industrial revolution, the opportunities to substitute capital for labour in most branches of the economy were limited, and that is reflected in the low elasticity of substitution between capital and labour.
其次，在工业革命期间，对许多行业来说，即使在工厂一级，也几乎没有用资本替代劳动力的余地。许多行业的生产工具在世界各地都是一样的，与相对要素价格无关。1760 年代，在工资高的英国和工资低的印度，都是用类似的织布机织布（Broadberry and Gupta, 2006a,b）。工业革命期间机械化技术的出现意味着要素替代的范围扩大了。到 19 世纪末，英国和美国使用动力织布机织布，第三世界使用手摇织布机织布，而在一个世纪前，所有人都使用手摇织布机。然而，表 1 所示的全要素生产率总增长率缓慢的含义是，这种现代化（以及随之而来的替代弹性的增加）仅局限于少数 "革命化 "的行业（Crafts，1985a；Crafts and Harley，1992）。在整个工业革命期间，大多数经济部门用资本替代劳动力的机会是有限的，这反映在资本与劳动力之间的低替代弹性上。

The low elasticity of substitution has an important implication for growth: Under this circumstance, both capital and productivity (i.e., effective labour) must increase in tandem for growth to occur. More capital without more productivity scarcely raises output. Likewise, productivity growth without capital accumulation fails to increase production. Without both technical progress and the capital accumulation to match it, there was no economic growth.
低替代弹性对经济增长具有重要影响：在这种情况下，资本和生产率（即有效劳动力）必须同步增长，才能实现增长。只有更多的资本而没有更高的生产率，就很难提高产出。同样，没有资本积累的生产率增长也无法提高产量。没有技术进步和与之相匹配的资本积累，就没有经济增长。

To see how well the model performs, we need to simulate it with historical values for the exogenous variables to check that the simulated values of the endogenous variables track their historical counterparts. GDP, of course, is tracked very closely since the rates of technical progress and the production function parameters were chosen to ensure that. The history of
为了了解模型的运行情况，我们需要用外生变量的历史值对其进行模拟，以检查内生变量的 模拟值是否与历史值一致。当然，由于技术进步率和生产函数参数的选择是为了确保这一点，因此国内生产总值的跟踪非常密切。国内生产总值的历史

Fig. 6. Simulating Britain's two stage development trajectory.
图 6.模拟英国两个阶段的发展轨迹。
the other endogenous variables provide a better test of the model. The most fundamental question is whether the model replicates the two phase pattern of British history.
其他内生变量对模型进行了更好的检验。最根本的问题是该模型是否复制了英国历史的两阶段模式。

Fig. 6 compares the actual and simulated values of output per worker and the real wage from 1770 to 1913 . The trajectories of both are accurately mapped. The simulated wage rate shows the two phases of British history clearly, and the timing of shift from the first to the second - which was not imposed in the estimation - is accurately replicated. The model passes this fundamental test.
图 6 比较了 1770 年至 1913 年工人人均产值和实际工资的实际值和模拟值。两者的轨迹都被准确地描绘出来。模拟工资率清晰地显示了英国历史的两个阶段，并且准确地复制了从第一个阶段向第二个阶段转变的时间--这在估算中并没有强加。模型通过了这一基本检验。

The model also replicates the history of the other factor prices. The simulated profit rate reproduces the step pattern of the historical series (whether measured with real or nominal variables) - the comparatively low returns of the 18th century, the doubling between 1800 and 1840, and then stability to the First World War (Fig. 7). Real land rents rose slowly from 1770 to the 'great depression' (1873-1896) when they stabilised and then slumped (Fig. 8). This pattern is also captured.
该模型还复制了其他要素价格的历史。模拟利润率再现了历史序列的阶梯模式（无论是用实际变量还是名义变量衡量）--18 世纪相对较低的回报率、1800 年至 1840 年间的翻倍，以及到第一次世界大战前的稳定（图 7）。实际地租从 1770 年开始缓慢上升，到 "大萧条"（1873-1896 年）期间趋于稳定，然后下滑（图 8）。图 8 也反映了这一模式。

Finally, the model captures the history of the factor shares (Fig. 9). The decline of labour's share during the first half of the 19th century is reproduced as is the increase later. The declining share of income accruing to land is very accurately reproduced, as is the history of capital's share. Like the profit rate, it went through three phases - a low level in the 18th century, a doubling in the first half of the 19th century, and then stability until World War I. The model was calibrated with shares for 1770 and 1860, so it is no surprise that they are reproduced. However, the timing of the movements between 1770 and 1860 were not imposed, and so the correspondence between actual and predicted values is evidence in favour of the model. The
最后，模型反映了要素份额的历史（图 9）。模型再现了 19 世纪上半叶劳动份额的下降和后来的上升。土地收入份额的下降与资本份额的历史一样得到了非常准确的再现。与利润率一样，它也经历了三个阶段--18 世纪的低水平、19 世纪上半叶的翻倍以及直到第一次世界大战前的稳定。然而，1770 年和 1860 年之间的变动时间并不是强加的，因此实际值和预测值之间的对应关系是支持模型的证据。模型

Fig. 7. Actual and simulated profit rates, 1770-1913
图 7.1770-1913 年实际利润率和模拟利润率

Fig. 8. Actual and simulated land rent, 1770-1913.
图 8.1770-1913 年实际地租和模拟地租。

Fig. 9. Actual and simulated shares, .
图 9.实际份额和模拟份额， 。
broad correspondence between predictions and historical trends between 1860 and the First World I is further confirmation of the model. This period provides a distinctly 'out of sample’ test.
1860 年至第一次世界大战期间的预测与历史趋势之间的广泛对应进一步证实了这一模型。这一时期提供了明显的 "样本外 "检验。

While the model replicates the broad distribution patterns after 1860, the forecast errors were certainly larger than previously. This is not surprising since the model was calibrated over the period 1770-1860 when the British economy was comparatively closed. It became much more open after the middle of the 19th century with the repeal of the Corn Laws and Navigation Acts and the construction of a global system of railways and steamships. The 'grain invasion' of the late 19th century depressed British agriculture and rents (O'Rourke, 1997). In addition, the opportunities for foreign investment increased dramatically, and millions of Brits moved to North America and Australasia. Growing openness meant that international factors played a much more dramatic role in growth and income distribution in Britain (O'Rourke and Williamson, 2005). Since none of this is included in the model, it is not surprising that it does not track distributional shares as well as it did pre-1860. What is even more surprising, however, is that it works as well as it does. The implication is that technical progress and capital accumulation continued to play important roles in determining output and wages in Britain: cheap American food, in other words, was not the decisive reason that the real wage rose after 1870.
虽然模型复制了 1860 年后的广泛分布模式，但预测误差肯定比以前大。这并不奇怪，因为该模型是在 1770-1860 年期间校准的，当时英国经济相对封闭。19 世纪中叶以后，随着《玉米法》和《航海法》的废除以及全球铁路和轮船系统的建设，英国经济变得更加开放。19 世纪末的 "谷物入侵 "抑制了英国农业和租金（O'Rourke，1997 年）。此外，外国投资的机会急剧增加，数百万英国人移居北美和澳大拉西亚。日益开放意味着国际因素在英国的经济增长和收入分配中发挥了更为显著的作用（O'Rourke 和 Williamson，2005 年）。由于这些因素都没有包括在模型中，因此模型不能像 1860 年前那样很好地跟踪分配份额也就不足为奇了。然而，更令人吃惊的是，该模型竟能如此有效。这意味着技术进步和资本积累在决定英国的产出和工资方面继续发挥着重要作用：换句话说，廉价的美国食品并不是 1870 年后实际工资上升的决定性原因。

Fig. 10. Actual and simulated investment rates, .
图 10.实际投资率和模拟投资率， 。

Why did Britain exhibit the two stage inequality history that Lewis highlighted? It was not for the reason he advanced, namely, the disappearance of surplus labour. Rather, balance was restored between the accumulation of capital and the growth of productivity.
为什么英国会出现刘易斯所强调的两个阶段的不平等历史？这并不是因为他提出的原因，即剩余劳动力的消失。相反，资本积累和生产力增长之间恢复了平衡。

The first stage of rising inequality was precipitated by the acceleration of technical progress after 1800 in conjunction with the low elasticity of substitution between capital and labour in the aggregate production function. With technical progress specified as labour augmenting, a higher rate of technical progress was like more rapid population growth: it reduced the ratio of capital to augmented labour. A lower capital-labour ratio implied a higher marginal product of capital. With an elasticity of substitution less than one, the higher marginal product of capital translated into a higher share of capital in national income - as Fig. 9 shows. Inequality increased and the real wage stagnated.
1800 年后，技术进步加速，加之总生产函数中资本与劳动力之间的替代弹性较低，促使第一阶段的不平等加剧。由于技术进步是以增加劳动为目的的，因此技术进步的速度越快，人口增长就越快：资本与增加劳动的比率就越低。较低的资本-劳动比率意味着较高的资本边际产品。在替代弹性小于 1 的情况下，较高的资本边际产品转化为较高的资本在国民收入中的份额--如图 9 所示。不平等加剧，实际工资停滞不前。

The first stage contained the seeds of its own undoing, however. As the share of profits increased, the economy-wide savings rate rose since capitalists saved a constant share of their income. As a result, capital accumulation accelerated. This is shown in Fig. 10, which compares actual and simulated investment rates for 1770-1860. The general rise in investment that took place is replicated by the model. Eventually, enough capital was accumulated to correspond to the requirements of higher productivity. Once steady state growth was achieved, so capital grew as rapidly as augmented labour, productivity growth boosted the real wage as well as GDP per worker. This change occurred in the middle of the 19th century. Britain shifted from Lewis' first stage to his second.
然而，第一阶段包含了其自身失败的种子。随着利润份额的增加，整个经济的储蓄率也随之上升，因为资本家的储蓄占其收入的比例是不变的。因此，资本积累加速。图 10 比较了 1770-1860 年的实际投资率和模拟投资率。模型复制了投资的普遍增长。 最终，积累的资本足以满足更高的生产率要求。一旦实现了稳态增长，资本的增长速度与劳动力的增长速度一样快，生产率的增长就会提高实际工资以及工人的人均国内生产总值。这一变化发生在 19 世纪中期。英国从刘易斯的第一阶段转向第二阶段。

The transition from the first stage to the second, which occurred around the time of the publication of the Communist Manifesto (1848), provides a wry commentary on Marx's expectations. The acceleration of productivity growth did, indeed, shift income from workers to capitalists, as he expected. The result, however, was not continually increasing immiseration, for the capitalists invested a portion of their extra income and the increase in the capital stock eventually allowed rising productivity to be manifest as rising real wages. History did, indeed, exhibit a stage pattern of evolution, but the stage of flat real wages was followed by the most sustained rise in real wages ever seen - not by socialist revolution. The integrated growth model captures the logic of history.
从第一阶段向第二阶段的过渡发生在《共产党宣言》（1848 年）发表前后，这为马克思的预期提供了一个诙谐的注解。生产力的加速增长确实如他所预期的那样，将收入从工人转移到了资本家手中。然而，其结果并不是不断加剧的不自由，因为资本家将其额外收入的一部分进行了投资，资本存量的增加最终使生产率的提高表现为实际工资的提高。历史确实呈现出阶段性的演变模式，但在实际工资持平的阶段之后，实际工资出现了有史以来最持续的上涨，而不是社会主义革命。综合增长模式抓住了历史的逻辑。

The classical economists shared a common expectation that capital accumulation and technical progress would not trickle down to the working class as rising wages, but they disagreed about the reason for wage stagnation. Marx thought that a high rate of labour augmenting technical progress would reduce labour demand and keep wages from rising. Malthus, on the other hand, accepted that technical progress would increase the demand for labour but believed this would be offset by an increase in the population. We can explore these conjectures by simulating the model with different rates of productivity growth and population growth.
古典经济学家们有一个共同的期望，即资本积累和技术进步不会以工资上涨的形式惠及工人阶级，但他们对工资停滞不前的原因存在分歧。马克思认为，技术进步带来的高劳动生产率会减少劳动力需求，从而使工资不涨。另一方面，马尔萨斯承认技术进步会增加对劳动力的需求，但认为这将被人口的增加所抵消。我们可以通过模拟不同生产率增长率和人口增长率的模型来探讨这些猜想。

To explore Marx's view, we can simulate the economy holding the rate of productivity growth at at pre-industrial level. In that case, there was no economic growth and no change in inequality. Rising productivity was a necessary condition for rising inequality-indeed, for anything at all to happen.
为了探讨马克思的观点，我们可以模拟将生产力增长率保持在工业化前水平的经济。在这种情况下，经济没有增长，不平等也没有改变。生产率的提高是不平等现象加剧的必要条件--事实上，是任何事情发生的必要条件。

Fig. 11. Simulated GDP/head and the real wage with no population growth.
图 11.无人口增长情况下的模拟人均 GDP 和实际工资。

The result is more interesting if we simulate the industrial revolution and eliminate the population explosion that accompanied it. Fig. 11 shows the trajectories of output per worker and the real wage from 1770 to 1860 . Both trend upward, and there is little lag of wages behind output after the increase in productivity growth in 1801. Engel's pause in real wage growth is eliminated. The simulated shares change very little. Without the burden of equipping an expanding population, the increased demand for capital induced by rising productivity could be met without a marked shift of income to property owners. Consequently, population growth was a necessary condition for stationary real wages: Engels' pause looks like Malthus' dismal science come true.
如果我们模拟工业革命并剔除伴随工业革命而来的人口爆炸，结果会更加有趣。图 11 显示了 1770 年至 1860 年工人人均产出和实际工资的变化轨迹。两者都呈上升趋势，而且在 1801 年生产率增长之后，工资几乎没有落后于产出。恩格尔的实际工资增长停顿现象消失了。模拟份额变化很小。如果没有为不断扩大的人口提供装备的负担，生产力的提高所引起的对资本需求的增加就可以得到满足，而不会使财产所有者的收入发生明显的转移。因此，人口增长是实际工资保持稳定的必要条件：恩格斯的停顿看起来就像是马尔萨斯的悲观科学成真了。

History was more complicated, however. While population growth was a necessary condition for rising inequality, it was not sufficient. This is shown by the experience of Britain after 1860 when real wages rose in line with population even though population was growing as rapidly as in the first half of the 19th century. Population growth and technical progress were both necessary for an increase in inequality, but their impact was mediate by the adjustments to the capital stock that are at the core of the integrated growth model. Only by considering the feedbacks in the model can the evolution of output and wages be understood. Malthus and Marx are not enough.
然而，历史更为复杂。虽然人口增长是不平等加剧的必要条件，但并不是充分条件。1860 年后英国的经验就证明了这一点，当时，尽管人口增长速度与 19 世纪上半叶一样快，但实际工资却与人口增长同步。人口增长和技术进步都是不平等加剧的必要条件，但它们的影响受到资本存量调整的调节，而资本存量调整是综合增长模型的核心。只有考虑到模型中的反馈，才能理解产出和工资的演变。马尔萨斯和马克思是不够的。

The analysis of this paper changes the emphasis in our understanding of the industrial revolution. Three general revisions stand out. First, inequality rose substantially in the first four decades of the 19th century. The share of capital income expanded at the expense of both land and labour income. The average real wage stagnated, while the rate of profit doubled. Second, these trends can be explained without reference to contingent events like the Napoleonic Wars or the settlement of the American West. The main trends can be explained with a simple macroeconomic model. Third, that macro model implies that the explanation of growth cannot be separated from the discussion of inequality since each influenced the other. In the first instance, it was the acceleration of productivity growth that led to the rise in inequality. Reciprocally, it was the rising share of profits that induced the savings that met the demand for capital and allowed output to expand. Moreover, these two general points are interconnected: the production function parameters that make capital accumulation and technical progress complements in the growth analysis are implied by the change in the factor shares between 1770 and 1860 .
本文的分析改变了我们对工业革命理解的重点。其中有三处总体修正非常突出。首先，在 19 世纪的前 40 年，不平等现象大幅增加。资本收入份额的扩大牺牲了土地和劳动收入。平均实际工资停滞不前，而利润率却翻了一番。其次，这些趋势的解释无需参考拿破仑战争或美国西部定居等偶然事件。主要趋势可以用一个简单的宏观经济模型来解释。第三，这一宏观模型意味着，对增长的解释不能与对不平等的讨论分开，因为两者相互影响。首先，是生产率的加速增长导致了不平等的加剧。反过来说，正是利润份额的上升诱发了储蓄，从而满足了对资本的需求，使产出得以扩大。此外，这两点是相互关联的：在增长分析中，使资本积累和技术进步互为补充的生产函数参数是由 1770 年至 1860 年间要素份额的变化所暗示的。

With these general considerations in mind, we can outline the story of the industrial revolution as follows: the prime mover was technical progress beginning with the famous inventions of the 18 th century including mechanical spinning, coke smelting, iron puddling, and the steam engine. It was only after 1800 that the revolutionized industries were large enough to affect the national economy. Their impact was reinforced by a supporting boost from rising agricultural productivity and further inventions like the power loom, the railroad, and the application of steam power more generally (Crafts, 2004). The adoption of these inventions led to a rise in demand for capital - for cities, housing, and infrastructure as well as for plant and equipment. Consequently, the rate of return rose and pushed up the share of profits in national income. With more income, capitalists saved more, but the response was limited, the capital-labour ratio rose only modestly, the urban environment suffered as cities were built on the cheap, and the purchasing power of wages stagnated (Williamson, 1990). Real wages rising in line with the growth of labour productivity was not a viable option since income had to shift in favour of property owners in order for their savings to rise enough to allow the economy to take advantage of the new productivity raising methods. Hence, the upward leap in inequality.
考虑到这些一般性因素，我们可以将工业革命的来龙去脉概述如下：从 18 世纪的著名发明（包括机械纺纱、焦炭冶炼、炼铁和蒸汽机）开始，技术进步成为工业革命的主要推动力。直到 1800 年以后，这些革命性的工业才发展到足以影响国民经济的规模。农业生产率的提高以及动力织布机、铁路等进一步发明和蒸汽动力的广泛应用，进一步推动了这些产业的发展（Crafts，2004 年）。这些发明的采用导致了对资本需求的上升--对城市、住房、基础设施以及厂房和设备的需求。因此，回报率上升，并推高了利润在国民收入中的比重。由于收入增加，资本家储蓄增加，但反应有限，资本-劳动比率仅略有上升，城市环境因廉价建设而受到影响，工资的购买力停滞不前（Williamson，1990 年）。随着劳动生产率的提高而提高实际工资并不是一个可行的选择，因为收入必须向财产所有者倾斜，才能使他们的储蓄增加到足以使经济利用新的提高生产率的方法。因此，不平等现象急剧上升。

The rise in inequality, however, had ramifications that made it self-extinguishing. The increase in profits induced enough capital formation by the middle of the 19th century for the economy to realize a balanced growth path with
然而，不平等现象的加剧所带来的后果却使其自生自灭。到 19 世纪中叶，利润的增长诱发了足够多的资本形成，使经济实现了平衡增长的道路。
capital and augmented labour growing at the same rate. Under this condition, the real wage grew in line with productivity. The European grain invasion and the chance to move to Australia, Canada, or the USA also boosted the real wage. They were not of fundamental importance, however: The burden of the integrated growth model is that productivity growth and capital accumulation were principally responsible for the rise in working class living standards after 1850, just as they had been responsible for their stagnation in the first half of the 19th century. Even sustained, rapid population growth was not enough to prevent labour incomes from rising once the accumulation conditions were right.
资本和增加的劳动力以同样的速度增长。在这种情况下，实际工资与生产率同步增长。欧洲谷物入侵以及移居澳大利亚、加拿大或美国的机会也提高了实际工资。然而，它们并不具有根本重要性：综合增长模式的重担在于，生产率增长和资本积累是 1850 年后工人阶级生活水平提高的主要原因，正如它们是 19 世纪上半叶工人阶级生活水平停滞不前的原因一样。一旦积累条件成熟，即使人口持续快速增长也不足以阻止劳动收入的提高。

An early version of this paper was presented to the TARGET economic history conference at St Antony's College, Oxford in October, 2004, and I thank those present for their feedback. Peter Temin commented incisively on several drafts of the paper, for which I am very grateful. I thank Paul David for suggesting that I make savings a function of property income. I am also grateful to Tony Atkinson and Andrew Glyn for their encouragement and suggestions. I would also like to thank Victoria Annable, Stan Engerman, Marcel Fafchamps, Tim Guinnane, Knick Harley, David Hendry, Brett House, Jane Humphreys, Ian Keay, Peter Lindert, Jim Malcolmson, Natalia Mora-Sitja, Tommy Murphy, Patrick O’Brien, Fraser Thompson, David Vines, and Gaston Yalonetzky for helpful discussions and comments on earlier drafts. This research has been funded by the Canadian SSHRCC Team for Advanced Research on Globalization, Education, and Technology and by the US NSF Global Prices and Incomes History Group. I am grateful for that support.
本文的早期版本曾于 2004 年 10 月在牛津大学圣安东尼学院举行的 TARGET 经济史会议上发表，我感谢与会者的反馈意见。彼得-特明（Peter Temin）对本文的几稿提出了精辟的意见，对此我深表感谢。我感谢保罗-戴维建议我将储蓄作为财产收入的函数。我还要感谢托尼-阿特金森（Tony Atkinson）和安德鲁-格林（Andrew Glyn）的鼓励和建议。我还要感谢 Victoria Annable、Stan Engerman、Marcel Fafchamps、Tim Guinnane、Knick Harley、David Hendry、Brett House、Jane Humphreys、Ian Keay、Peter Lindert、Jim Malcolmson、Natalia Mora-Sitja、Tommy Murphy、Patrick O'Brien、Fraser Thompson、David Vines 和 Gaston Yalonetzky，感谢他们对我之前的草稿进行了有益的讨论并提出了宝贵意见。本研究得到了加拿大 SSHRCC 全球化、教育和技术高级研究小组以及美国国家科学基金会全球物价和收入历史小组的资助。我对这些支持表示感谢。

We know much more about economic growth during the industrial revolution than was known 50 years ago thanks to the efforts of several generations of economic historians. Key variables, however, have only been established for benchmark years; in particular, Crafts has estimated real GDP only for 1760, 1780, 1801, 1831, and 1860. The small number of observations precludes the econometric estimation of important relationships and requires calibrating the model instead. Also different series use different benchmark years. To bring them into conformity and to simplify simulations, all series were annualized by interpolating missing values. As a result, the series are artificially smoothed but capture the main trends. Real values are measured in the prices of 1850-1860 or particular years in the decade as available. The price level did not change greatly in this period. All values apply to Great Britain unless otherwise noted.
在几代经济史学家的努力下，我们对工业革命时期经济增长的了解比 50 年前要多得多。然而，关键变量只确定了基准年份；特别是，卡夫卡只估算了 1760 年、1780 年、1801 年、1831 年和 1860 年的实际国内生产总值。由于观测数据较少，因此无法对重要关系进行计量经济学估算，而需要对模型进行校准。此外，不同的序列使用不同的基准年。为了使它们保持一致并简化模拟，所有序列都通过对缺失值进行内插法进行了年化处理。因此，这些序列被人为地平滑了，但仍能捕捉到主要趋势。实际值以 1850-1860 年或该十年中特定年份的价格（如有）来衡量。这一时期的价格水平变化不大。除非另有说明，所有数值均适用于大不列颠。

Based on Deane and Cole’s work, Feinstein (1978, p. 84) reckoned GDP in 1830 at million and in 1860 at million (both in 1851-1860 prices). Crafts and Harley have been continuously improving the measurement of British GDP for earlier years (Crafts, 1985; Crafts and Harley, 1992; Harley, 1993), and I have extrapolated Feinstein's 1830 estimate backwards using the Crafts and Harley (1992, p. 715) real output index. This gives real GDP estimates for the benchmark years just noted. GDP was extrapolated to 1913 using Feinstein's (1972, pp. T118-T119) index of real British GDP.
根据 Deane 和 Cole 的研究，Feinstein（1978 年，第 84 页）计算出 1830 年的国内生产总值为 百万，1860 年为 百万（均按 1851-1860 年价格计算）。Crafts 和 Harley 一直在不断改进英国早期国内生产总值的测量方法（Crafts, 1985; Crafts and Harley, 1992; Harley, 1993），我使用 Crafts 和 Harley（1992 年，第 715 页）的实际产出指数向后推算了费恩斯坦 1830 年的估计值。这样就得出了上述基准年份的实际 GDP 估计值。利用费恩斯坦（1972 年，第 T118 至 T119 页）的英国实际 GDP 指数将 GDP 推断至 1913 年。

The inputs were measured as follows:
输入的测量方法如下
Land - acreage of arable, meadow, and improved pasture (commons are excluded). Allen (1994, p. 104, 2005) presents benchmark estimates for England and Wales. Following McCulloch (1847, vol. I, pp. 554-555, 566-567)), these have been increased by to include Scotland.
土地--耕地、草地和改良牧场的面积（不包括公地）。Allen（1994 年，第 104 页，2005 年）提出了英格兰和威尔士的基准估算值。根据 McCulloch（1847 年，第 I 卷，第 554-555 页，第 566-567 页），这些数字增加了 ，以包括苏格兰。
Labour - for 1801, 1811, and continuing at ten year intervals, Deane and Cole's (1969, p. 143) estimates of the occupied population were used. The occupied population for 1760 was estimated by applying the 1801 ratio to the population. Voth (2001) has argued that the working year lengthened in this period. I have not tried to adjust the data for this change, so some of the rise in productivity that I report may be due to greater work intensity.
劳动力--1801 年、1811 年及以后每隔 10 年，使用 Deane 和 Cole（1969 年，第 143 页）对居住人口的估计。1760 年的在业人口是根据 1801 年的人口比例估算的。Voth (2001) 认为这一时期的工作年延长了。我没有尝试根据这一变化调整数据，因此我所报告的生产率的提高可能是由于工作强度的提高。
Capital (and real gross investment) - Feinstein (1988, p. 441) presents average annual gross investment by decade from 1760 to 1860 for Great Britain. The magnitudes are expressed in the prices of the 1850 s . He also estimated the capital stock in the same prices at decade intervals by Eq. (3). To annualize the data, I assumed that real gross investment in each year equalled the average for its decade. I reconstructed the capital stock year by year with Eq. (3). With the annualized data, a depreciation rate of per year gives a capital stock series that matches Feinstein's almost exactly at decennial intervals. Therefore, was used in subsequent simulations.
资本（和实际投资总额）--Feinstein（1988 年，第 441 页）介绍了大不列颠从 1760 年到 1860 年各十年的年平均投资总额。他还用公式（3）估算了每十年以相同价格计算的资本存量。为了使数据年度化，我假设每年的实际投资总额等于其十年的平均值。根据公式（3），我逐年重建了资本存量。根据年度化数据， 年折旧率得出的资本存量序列与费恩斯坦的十年间隔几乎完全吻合。因此，在随后的模拟中使用了 。

The British capital stock from 1861 to 1913 was calculated as the capital stock in the previous year less depreciation at plus real gross investment. The latter was worked out by multiplying real GDP by the UK investment rate. This investment was the ratio of real gross investment for the UK to real GDP for the UK. These were calculated from Feinstein's (1988, pp. 427-428, 470-471) current value investment series, his investment deflator, and his real GDP series given in Feinstein, 1978, p. 84). See also 6 .
1861 年至 1913 年英国资本存量的计算方法是：前一年的资本存量减去 的折旧，再加上实际投资总额。后者的计算方法是实际 GDP 乘以英国投资率。该投资是英国实际投资总额与英国实际 GDP 的比率。这些数据是根据费恩斯坦（1988 年，第 427-428 页、第 470-471 页）的现值投资系列、投资平减指数以及费恩斯坦 1978 年第 84 页中的实际 GDP 系列计算得出的。）另见 6 .

Real rent of land - the history of rent has been the subject of considerable controversy, but the Norton and Gilbert (1889), Allen (1992), and Clark (2002) series agree reasonably well for this period, as does the Turner et al. (1997) series after 1800. Clark's (2002, p. 303) series inclusive of taxes and rents is used here.
实际地租--地租的历史一直是颇有争议的问题，但 Norton 和 Gilbert（1889 年）、Allen（1992 年）和 Clark（2002 年）的系列在这一时期的数据相当吻合，1800 年后 Turner 等人（1997 年）的系列也是如此。这里使用的是 Clark（2002 年，第 303 页）的系列，包括税收和租金。

Real profit rate - calculated as profits divided by the capital stock where profits are computed residually as real GDP minus real wages and salaries minus real land rents.
实际利润率--计算方法是利润除以资本存量，其中利润的计算方法是实际国内生产总值减去实际工资和薪金再减去实际地租。

1770-1882: Nominal earnings and retail price index from Feinstein (1998, pp. 652-653). For 1770-1860, the revision of the consumer price index in Allen (2007) was used instead of Feinstein's orginal deflator. The difference is not great.
1770-1882:名义收入和零售物价指数来自 Feinstein（1998 年，第 652-653 页）。对于 1770-1860 年，使用的是 Allen（2007 年）对消费物价指数的修订，而不是 Feinstein 最初的平减指数。两者差别不大。
1882-1913: Average weekly earnings and retail prices from Feinstein (1972, p. T140).
1882-1913:每周平均收入和零售价格来自 Feinstein（1972 年，第 T140 页）。

The available data, which are far from perfect, indicate that the average return to all labour in the industrial revolution was a constant mark-up over the earnings of manual workers. Deane and Cole (1969, p. 167) thought that the self-employed earned more than the average manual labourer, while Matthews et al. (1982, pp. 167, 170) assumed that the salaried and self-employed earned 2.0-2.6 times the earnings of manual labourers just before the First World War.
现有的数据远非完美，但这些数据表明，工业革命时期所有劳动的平均回报都比体力劳动者的收入高。Deane 和 Cole（1969 年，第 167 页）认为，自营职业者的收入 高于普通体力劳动者，而 Matthews 等人（1982 年，第 167 和 170 页）则假定，在第一次世界大战之前，受薪者和自营职业者的收入是体力劳动者收入的 2.0-2.6 倍。

To investigate the mark-up, begin with 1856 for which Matthews et al. (1982, p. 164) found that wages were of GNP, salaries were , and the labour income of the self-employed was . Assuming that the salaried and self-employed made 1.75 times the earnings of manual workers implies that of the workforce were salaried or self-employed and that total labour income was more than the return to labour when it was valued at the manual labourer's earnings. This premium reflects both the earnings premium of the salaried and self-employed and the share of the labour force they comprised.
马修斯等人（1982 年，第 164 页）发现，在 1856 年，工资占国民生产总值的 ，薪金占 ，自营职业者的劳动收入占 。假定受薪者和自营职业者的收入是体力劳动者收入的 1.75 倍，这意味着 的劳动力是受薪者或自营职业者，劳动总收入比按体力劳动者收入估算的劳动回报率高 。这一溢价既反映了受薪者和自营职业者的收入溢价，也反映了他们在劳动力中所占的比例。

How did these ratios vary during the industrial revolution? At one time, Williamson (1985) had argued that the earnings of high income earners rose with respect to manual labourers during the industrial revolution, but this position was criticized by Jackson (1987), who established the current orthodoxy that relative earnings were constant. What about the structure of the labour force? Accepting Jackson's findings and assuming that the proportions of salaried and self-employed individuals in the work force remained constant, we can calculate the average return to labour by increasing the earnings of manual labourers by . We can check these assumptions for 1801 , for instance, by calculating the number of salaried employees and self-employed as of the occupied population, i.e. 759 thousand people. This figure can be compared to the numbers of people in these categories in Colquhoun's (1806) social table for England and Wales in 1801 (Lindert and Williamson, 1982). The comparison must make allowance for Scotland. Interpreted this way, Colquhoun's figures imply that there were 786 thousand salaried and self-employed people working in Britain in 1801. They were engaged as professionals, civil servants, teachers, merchants, shopkeepers, publicans, manufacturers, farmers, military officers, engineers, and so forth. This is far from an exact science, but there is sufficient correspondence to accept a stable division of the work force between manual workers, on the one hand, and the salaried and self-employed, on the other.
这些比率在工业革命期间有何变化？威廉姆森（Williamson，1985 年）曾一度认为，在工业革命期间，相对于体力劳动者而言，高收入者的收入增加了，但这一观点受到了杰克逊（Jackson，1987 年）的批评，他确立了目前的正统观点，即相对收入是不变的。劳动力结构如何？接受杰克逊的研究结果，并假设劳动力中受薪人员和自营职业者的比例保持不变，我们可以通过将体力劳动者的收入提高 来计算劳动力的平均回报率。例如，我们可以通过计算受薪雇员和自营职业者占就业人口的 （即 75.9 万人）来验证 1801 年的这些假设。这个数字可以与 Colquhoun（1806 年）的 1801 年英格兰和威尔士社会表（Lindert 和 Williamson，1982 年）中这些类别的人数进行比较。比较时必须考虑苏格兰的情况。按此解释，科尔昆的数字意味着 1801 年英国有 78.6 万名受薪者和自营职业者。他们的职业包括专业人士、公务员、教师、商人、店主、公职人员、制造商、农民、军官、工程师等等。这远不是一门精确的科学，但有足够的对应关系来接受劳动力在体力劳动者与受薪者和自营职业者之间的稳定划分。

Factor shares - computed by dividing real factor earnings by real GDP.
要素份额 - 用实际要素收益除以实际 GDP 计算得出。

While Clark's work has raised some important issues, this paper is based on the more established view. So far as wages are concerned, Clark's novel conclusions derive from a new consumer price index. Some of the component series are improvements over those used by Feinstein, but some of Clark's changes degrade the index. A new index based on the best of both is much closer to Feinstein's than to Clark's (Allen, 2007). Moreover, even if Clark's index were used in this paper, the conclusions would be attenuated but not overturned since Clark's index, too, shows a pause in the growth in real wages in the industrial revolution (Fig. 1-Clark). The implied shares and profit rates move similarly to those reported in the text, although the shift against labour is attenuated during the industrial revolution. Indeed, the model can be recalibrated with those data, and it works almost as well as the version reported in this paper. Fig. 1-Clark also shows simulated GDP per worker and the real wage using Clark's real wage and recalibrating the production function accordingly. Clark's work on wages is not enough, therefore, to establish his conclusion that workers were the principal gainers in the industrial revolution nor to suggest a different analysis of its causes.
虽然克拉克的研究提出了一些重要问题，但本文是以更成熟的观点为基础的。就工资而言，克拉克的新结论源自一个新的消费价格指数。与费恩斯坦所使用的指数相比，克拉克指数的某些构成序列有所改进，但克拉克指数的某些变化却降低了指数的质量。基于两者优点的新指数更接近于费恩斯坦的指数，而不是克拉克的指数（Allen，2007 年）。此外，即使本文使用克拉克指数，结论也会有所削弱，但不会被推翻，因为克拉克指数也显示出工业革命时期实际工资增长的停顿（图 1-克拉克）。隐含的份额和利润率的变化与文中报告的类似，尽管在工业革命期间不利于劳动力的转变有所减弱。事实上，该模型可以根据这些数据进行重新校准，其效果与本文报告的版本几乎一样好。图 1-Clark 还显示了使用 Clark 的实际工资并相应地重新校准生产函数后模拟的工人人均 GDP 和实际工资。 因此，克拉克关于工资的研究不足以确立他关于工人是工业革命主要受益者的结论，也不足以对工业革命的原因提出不同的分析。

Fig. 1-Clark. The two phases of the British industrial revolution.
图 1-Clark.英国工业革命的两个阶段。

To reach that conclusion one must reduce the growth in national income so wages grow faster than profits. Thus, the second pillar of Clark's reinterpretation is his calculation of nominal GDP, which increases less rapidly than Deane and Cole's estimates. Clark's nominal GDP is the sum of factor earnings. He estimates employment and the average wage, the area of cultivated land and the average rent, and various series of capital magnitudes and corresponding rates of rate. Deane and Cole had also estimated labour income from employment and wages, but had estimated property income from the income tax returns. Clark accepts Deane and Cole's GDP for the middle of the 19th century. Their property income and GDP for mid-century was larger than Clark's total, so he scaled up his series for earlier years by the same proportion to account for the income he had not been able to measure. This was primarily entrepreneurial income. Clark's procedure produces a much larger figure for nominal GDP in 1801 than Deane and Cole had calculated from employment, wages, and the tax on property income. Clark decides that Deane and Cole had underestimate property income and GDP in 1801 since he contends that tax evasion was higher than they thought. His reason for this conclusion is that his estimates of land and house rents (derived from the Charity Commission returns) implied a higher tax base than the income tax assessments reported.
要得出这一结论，就必须降低国民收入的增长速度，使工资增长快于利润增长。因此，克拉克重新解释的第二个支柱是他对名义 GDP 的计算，名义 GDP 的增长速度低于迪恩和科尔的估计。克拉克的名义 GDP 是要素收入的总和。他估算了就业和平均工资、耕地面积和平均地租，以及各种系列的资本规模和相应的比率。迪恩和科尔也从就业和工资中估算出劳动收入，但他们是从所得税申报表中估算出财产收入。Clark 接受了 Deane 和 Cole 的 19 世纪中期国内生产总值。他们在本世纪中叶的财产收入和国内生产总值大于克拉克的总数，因此他按同样的比例放大了他早年的数据系列，以考虑到他未能测算的收入。这主要是企业收入。克拉克的计算方法得出的 1801 年名义 GDP 数字比迪恩和科尔根据就业、工资和财产收入税计算出的数字要大得多。克拉克认为迪恩和科尔低估了 1801 年的财产收入和国内生产总值，因为他认为逃税现象比他们想象的要严重。他得出这一结论的原因是，他对土地和房屋租金的估算（根据慈善委员会的报表得出）意味着税基高于所得税评估报告。

I prefer old estimates to Clark's for several reasons. First, so far as 1801 income was concerned, Deane and Cole were very conscious of the problem of tax evasion and considered the matter closely for the various schedules of the income tax. Their work builds on a long tradition of research in this issue, which cannot be lightly set aside. Clark's only reason for doing so is his calculation of the taxable value of land and property, which he found to be greater than that in the tax returns. The problem with Clark's argument, however, is that his data are derived from the returns to the Charity Commission and relate to new lettings, as he himself has indicated (Clark, 2002, pp. 381-383). In a time of inflation like the Napoleonic period, rents were rising, so the return on new lettings exceeded the average rent on all property (Clark, 2001, p. 22). Indeed, this is clear in comparing Clark's index of the rent of houses 1770-1860 and Feinstein's. While Clark's was based on new lettings, Feinstein's was based on the total assessed value of property. The two series agree in showing virtually the same inflation between 1770 and 1860. Clark's, however, inflates first, and leads Feinstein's by a large margin c. 1800. Clark's calculations of the tax base from Charity Commission data are, thus, too high at the critical period, and so his arguments about under assessment are not sustained.
与克拉克的估计相比，我更倾向于旧的估计，原因有以下几点。首先，就 1801 年的收入而言，迪恩和科尔非常关注逃税问题，并对所得税的各个附表进行了仔细研究。他们的工作建立在对这一问题的长期研究传统之上，不能轻易搁置。克拉克这样做的唯一理由是他对土地和财产应税价值的计算，他发现这一价值高于报税表中的价值。然而，克拉克论证的问题在于，他的数据来源于向慈善委员会提交的申报表，并且与新的租赁有关，正如他自己所指出的那样（Clark, 2002, pp.381-383）。在拿破仑时期这样一个通货膨胀的时代，租金不断上涨，因此新出租房产的回报率超过了所有房产的平均租金（Clark, 2001, p.22）。事实上，比较克拉克的 1770-1860 年房屋租金指数和费恩斯坦的指数就可以清楚地看到这一点。克拉克的指数基于新出租房屋，而费恩斯坦的指数则基于房产的总评估价值。这两个指数一致显示，1770 年至 1860 年间的通货膨胀率几乎相同。然而，克拉克的通货膨胀率最高，并在 1800 年左右大幅领先于费恩斯坦的通货膨胀率。因此，克拉克根据慈善委员会的数据计算出的税基在关键时期过高，所以他关于评估不足的论点是站不住脚的。

Second, again with respect to 1801, the introduction of the income tax led several contemporaries to estimate the national income at the turn of the century (Deane, 1956), pp. 339-341), and their figures imply totals of million (Beeke’s) and million (Bell's). Colquhoun (1806) estimated English national income based on the results of the 1801 census as million if it is scaled up to include Scotland. These estimates corroborate Deane and Cole’s ( million) while calling Clark's into question. These contemporaries estimate the rental value of housing at the lower values used by Deane and Cole and Feinstein rather than at the higher values implied by the new leases of Charity lands. The lower values are consistent with the assessments in the income tax. There is no reason to prefer Clark's estimate over these.
其次，还是关于 1801 年，所得税的引入导致几位同时代的学者对世纪之交的国民收入进行了估算（Deane, 1956)，第 339-341 页），他们的数字意味着总额为 百万（Beeke's）和 百万（Bell's）。Colquhoun（1806 年）根据 1801 年人口普查的结果估计英国国民收入为 百万，如果将苏格兰包括在内的话。这些估算证实了 Deane 和 Cole 的估算（ 百万），同时对 Clark 的估算提出了质疑。这些同时代的人按照 Deane 和 Cole 以及 Feinstein 使用的较低价值来估算房屋租赁价值，而不是按照慈善机构土地新租约所暗示的较高价值来估算。较低的价值与所得税的评估是一致的。没有理由更倾向于克拉克的估算。

Third, since Clark's nominal GDP series grows slowly, it implies very slowly growing real GDP when he deflates it. "Output per person increased by only from 1760 to compared to Craft's estimate of a gain" (Clark, 2001, p. 33). Clark's conclusion can only be accepted if we accept his view on the income tax in the Napoleonic Wars - a view we believe is unsustainable. Craft's conclusion, on the other hand, is based on aggregating all of the available output data for the British economy estimates. This appears a sounder basis of proceeding.
第三，由于克拉克的名义 GDP 序列增长缓慢，当他对其进行缩减时，这意味着实际 GDP 的增长非常缓慢。"从 1760 年到 年，人均产出只增加了 ，而克拉夫特估计的增幅为 "（Clark, 2001, p.33）。只有接受克拉克关于拿破仑战争期间所得税的观点，我们才能接受他的结论--我们认为这种观点是站不住脚的。另一方面，克拉夫特的结论是基于对英国经济估计的所有可用产出数据的汇总。 这似乎是一个更可靠的基础。

Fourth, we can assess the reliability of the rival national income series by working out their implications for productivity growth and comparing them to alternative measures. The Crafts series, which we use here, of course imply more rapid TFP growth than Clark's. Both are done by comparing real output growth to the growth of land, labour, and capital, and there is no great disagreement about the measurement of the inputs. In contrast, Antràs and Voth (2003) have measured TFP growth in a dual framework comparing product prices to input prices. Their procedure corroborates Crafts' estimates rather than Clark's.
第四，我们可以通过计算竞争对手的国民收入序列对生产率增长的影响，并将其与其他衡量标准进行比较，来评估这些序列的可靠性。我们在此使用的 Crafts 系列当然意味着全要素生产率的增长比克拉克系列更快。两者都是通过将实际产出增长与土地、劳动力和资本的增长进行比较而得出的，在投入的衡量方面没有太大的分歧。与此相反，Antràs 和 Voth（2003 年）通过比较产品价格和投入价格的双重框架来衡量全要素生产率的增长。他们的方法证实了 Crafts 的估计，而不是 Clark 的估计。

Fifth, another implication of Clark's estimates is that all of the productivity growth in the industrial revolution was confined to textiles. Studies of iron, canals, shipping, and agriculture, however, have shown that there was productivity growth outside the textile sector, and this is compatible with the Crafts-Harley view of advance (Crafts, 1985, p. 86; Harley, 1993). Indeed, the principal challenge to this view is Temin's (1997) argument from trade data that productivity growth occurred in other industries was well. These results raise the possibility that real output grew more rapidly than Crafts believed rather than less rapidly as Clark maintains.
第五，克拉克估计的另一个含义是，工业革命中所有的生产力增长都局限于纺织业。然而，对钢铁、运河、航运和农业的研究表明，在纺织业之外，生产率也在增长，这与克拉夫斯-哈雷的进步观点是一致的（Crafts, 1985, p. 86; Harley, 1993）。事实上，对这一观点的主要质疑是 Temin（1997 年）根据贸易数据提出的观点，即其他行业的生产率也出现了增长。这些结果提出了一种可能性，即实际产出的增长速度比克拉夫斯所认为的要快，而不是像克拉克所认为的要慢。

Abramovitz, Moses, David, Paul, 2001. American Macroeconomic Growth: From Exploitation of Natural Resource Abundance to Knowledge-Driven Development, Stanford Institute of Economic Policy Research, SIEPR Discussion Paper 01-005.
Abramovitz, Moses, David, Paul, 2001.American Macroeconomic Growth：From Exploitation of Natural Resource Abundance to Knowledge-Driven Development, Stanford Institute of Economic Policy Research, SIEPR Discussion Paper 01-005.
Acemoglu, Daron K., 2003. Labor- and capital-augmenting technical change. Journal of the European Economic Association 1, 1-37
Acemoglu, Daron K., 2003.Labor- and capital-augmenting technical change.欧洲经济协会期刊》1，1-37
Allen, Robert C., 1992. Enclosure and the Yeoman. Clarendon Press, Oxford.
Allen、Robert C.，1992 年。Enclosure and the Yeoman.牛津克拉伦登出版社。
Allen, Robert C., 1994. Agriculture during the industrial revolution. In: Floud, R., McCloskey, D. (Eds.), The Economic History of Britain since 1700, vol. I. 1700-1860, Cambridge University Press, Cambridge, pp. 96-122.
Allen, Robert C., 1994.工业革命时期的农业。In：Floud, R., McCloskey, D. (Eds.), The Economic History of Britain since 1700, vol. I. 1700-1860, Cambridge University Press, Cambridge, pp.
Allen, Robert C., 2001. The great divergence in European wages and prices from the middle ages to the first world war. Explorations in Economic History 38 , .
Allen, Robert C., 2001.The great divergence in European wages and prices from the middle ages to the first world war.Explorations in Economic History 38 , .
Allen, Robert C., 2005. English and Welsh agriculture, 1300-1850: output, inputs, and income.
Allen, Robert C., 2005.英国和威尔士农业，1300-1850 年：产出、投入和收入。
Allen, Robert C., 2007. Pessimism Preserved: Real Wages in the British Industrial Revolution. Oxford University, Department of Economics, Working Paper 314 .
《艾伦、罗伯特-C.，2007 年。Pessimism Preserved：英国工业革命中的实际工资》。牛津大学经济系，工作论文 314 .
Antràs, Pol, 2004. Is the US aggregate production function Cobb-Douglas? New estimates of the elasticity of substitution. Contributions to Macroeconomics 4 .
Antràs, Pol, 2004.美国总生产函数是柯布-道格拉斯函数吗？替代弹性的新估算.宏观经济学贡献 4 .
Antràs, Pol, Voth, Joachim, 2003. Productivity growth and factor prices during the British Industrial Revolution. Explorations in Economic History 40 , 52-77. Berndt, Ernst, 1976. Reconciling alternative estimates of the elasticity of substitution. Review of Economics and Statistics 58, 59-68.
Antràs, Pol, Voth, Joachim, 2003.英国工业革命时期的生产力增长与要素价格》。Explorations in Economic History 40 , 52-77.Berndt, Ernst, 1976.Reconciling alternative estimates of the elasticity of substitution.Review of Economics and Statistics 58, 59-68.
Broadberrry, Stephen, Földvári, Péter, van Leeuwen, Bas, 2006. British economic growth and the business cycle, 1700-1850
Broadberrry, Stephen, Földvári, Péter, van Leeuwen, Bas, 2006.英国经济增长与商业周期，1700-1850 年
Broadberry, Stephen, Gupta, Bishnupriya, 2006a. The early modern great divergence: wages, prices and economic development in Europe and Asia, 15001800. Economic History Review 59, 2-31
Broadberry, Stephen, Gupta, Bishnupriya, 2006a.The early modern great divergence: wages, prices and economic development in Europe and Asia, 15001800.Economic History Review 59, 2-31

Broadberry, Stephen, Gupta, Bishnupriya, 2006b. Wages, Induced Innovation and the Great Divergence: Lancashire, India and Shifting Competitive Advantage in Cotton Textiles, 1700-1850, revised version CEPR discussion paper 5183.
Broadberry, Stephen, Gupta, Bishnupriya, 2006b.Wages, Induced Innovation and the Great Divergence：Wages, Induced Innovation and the Great Divergence: Lancashire, India and Shifting Competitive Advantage in Cotton Textiles, 1700-1850, revised version CEPR discussion paper 5183.
Christensen, L., Jorgenson, D., Lau, L., 1971. Conjugate duality and the transcendantal logarithmic production function. Econometrica 39 (4-6), 255-256.
Christensen, L., Jorgenson, D., Lau, L., 1971.Conjugate duality and the transcendantal logarithmic production function.Econometrica 39 (4-6), 255-256.
Clark, Gregory, 2001. The secret history of the industrial revolution.
Clark, Gregory, 2001.工业革命秘史》。
Clark, Gregory, 2002. Land rental values and the agrarian economy: England and Wales, 1500-1914. European Review of Economic History 6, 281-308.
Clark, Gregory, 2002.土地租值与农业经济：英格兰和威尔士，1500-1914 年。European Review of Economic History 6, 281-308.
Clark, Gregory, 2005. The condition of the working class in England, 1209-2004. Journal of Political Economy 113, 1307-1340.
Clark, Gregory, 2005.英格兰工人阶级的状况，1209-2004 年。Journal of Political Economy 113, 1307-1340.
Clark, Gregory, 2007a. What made Britannia great? How much of the rise of Britain to world dominance by 1850 does the Industrial Revolution explain. In: Hatton, Tim, O'Rourke, Kevin, Taylor, Alan (Eds.), Comparative Economic History: Essays in Honor of Jeffrey Williamson. MIT Press, Cambridge, pp. 3357.
Clark, Gregory, 2007a.不列颠因何而伟大？工业革命在多大程度上解释了英国在 1850 年崛起为世界霸主的原因。In：Hatton, Tim, O'Rourke, Kevin, Taylor, Alan (Eds.), Comparative Economic History：杰弗里-威廉姆森纪念文集》。麻省理工学院出版社，剑桥，第 3357 页。

Clark, G., 2007b. A Farewell to Alms: A Brief Economic History of the World. Princeton University Press, Princeton.
Clark, G., 2007b.A Farewell to Alms：世界经济简史》。普林斯顿大学出版社，普林斯顿。
Colquhoun, P., 1806. A Treatise on Indigence. J. Hatchford, London.
Colquhoun, P., 1806.贫困论》。J. Hatchford，伦敦。
Crafts, N.F.R., 1985a. British Economic Growth during the Industrial Revolution. Clarendon Press, Oxford.
Crafts, N.F.R., 1985a.工业革命时期的英国经济增长》。Clarendon Press, Oxford.
Crafts, N.F.R., 1985b. English workers' real wages during the industrial revolution: some remaining problems. Journal of Economic History 45, 139-144
Crafts, N.F.R., 1985b.English workers' real wages during the industrial revolution: some remaining problems.Journal of Economic History 45, 139-144
Crafts, N.F.R., 2004. Steam as a general purpose technology: a new growth accounting perspective. Economic Journal 114, 338-351.
Crafts, N.F.R., 2004.蒸汽作为通用技术：新增长会计视角》。Economic Journal 114, 338-351.
Crafts, N.F.R., Harley, C. Knick, 1992. Output growth and the industrial revolution: a restatement of the Crafts-Harley view. Economic History Review 45 (second series), 703-730.
Crafts, N.F.R., Harley, C. Knick, 1992.Output growth and the industrial revolution: a restatement of the Crafts-Harley view.Economic History Review 45 (second series), 703-730.
David, Paul, 1978. Lecture Notes on the US Growth in the Nineteenth Century: Simulating 'The Grand Traverse' and 'The Cantabridgian Synthesis', The University of Cambridge, Lent Term. Available from: pad@stanford.edu.
David, Paul, 1978.关于十九世纪美国增长的讲座笔记：Simulating 'The Grand Traverse' and 'The Cantabridgian Synthesis', The University of Cambridge, Lent Term.可查阅：pad@stanford.edu。
David, Paul A., van de Klundert, 1965. Biased efficiency growth and capital-labor substitution in the US, 1899-1960. American Economic Review 55, 357393 .
David, Paul A., van de Klundert, 1965.美国有偏差的效率增长与资本-劳动替代，1899-1960 年》（Biased efficiency growth and capital-labor substitution in the US, 1899-1960.American Economic Review 55, 357393 .
Deane, P., 1956. Contemporary estimates of national income in the first half of the nineteenth century. Economic History Review 8 (new series), . Deane, P., Cole, W.A., 1969. British Economic Growth, 1688-1959, second ed. Cambridge University Press, Cambridge
Deane, P., 1956.19 世纪上半叶国民收入的当代估算。Economic History Review 8 (new series), .Deane, P., Cole, W.A., 1969.British Economic Growth, 1688-1959, second ed. Cambridge University Press, Cambridge.剑桥大学出版社，剑桥
Diewert, W.E., 1976. Exact and superlative index numbers. Journal of Econometrics 4, 115-145.
Diewert, W.E., 1976.Exact and superlative index numbers.Journal of Econometrics 4, 115-145.
Engels, Frederick, 1845. In: Henderson, W.O., Chaloner, W.H. (Eds.), The Condition of the Working Class in England, Basil Blackwell, Oxford, 1958.
恩格斯，弗雷德里克，1845 年。In：Henderson, W.O., Chaloner, W.H. (Eds.), The Condition of the Working Class in England, Basil Blackwell, Oxford, 1958.
Feinstein, Charles H., 1972. National Income, Expenditure, and Output in the United Kingdom, 1856-1965. Cambridge University Press, Cambridge.
Feinstein, Charles H., 1972.National Income, Expenditure, and Output in the United Kingdom, 1856-1965.剑桥大学出版社，剑桥。
Feinstein, Charles H., 1978. Capital formation in Great Britain. In: Mathias, P., Postan, M.M. (Eds.), Cambridge Economic History of Europe, The Industrial Economies: Capital, Labour, and Enterprise, Part I, Britain, France, Germany, and Scandinavia, vol. VII. Cambridge University Press, Cambridge.
Feinstein, Charles H., 1978.大不列颠的资本形成。In：Mathias, P., Postan, M.M. (Eds.), Cambridge Economic History of Europe, The Industrial Economies：资本、劳动和企业》，第一部分，英国、法国、德国和斯堪的纳维亚，第七卷。剑桥大学出版社，剑桥。
Feinstein, Charles H., 1988. Sources and methods of estimation for domestic reproducible fixed assets, stocks and works in progress, overseas assets, and land. In: Feinstein, Charles H., Pollard, Sidney (Eds.), Studies in Capital Formation in the United Kingdom, 1750-1920. Clarendon Press, Oxford, pp. 258471.
Feinstein, Charles H., 1988.国内可复制固定资产、存货和在建工程、海外资产及土地的来源和估算方法。In：Feinstein, Charles H., Pollard, Sidney (Eds.), Studies in Capital Formation in the United Kingdom, 1750-1920.Clarendon Press, Oxford, pp.

Feinstein, Charles H., 1998a. Wage-earnings in Great Britain during the industrial revolution. In: Begg, Iain, Henry, S.G.B. (Eds.), Applied Economics and Public Policy. Cambridge University Press, Cambridge, pp. 181-208.
Feinstein, Charles H., 1998a.工业革命时期大不列颠的工资收入。In：Begg, Iain, Henry, S.G.B. (Eds.), Applied Economics and Public Policy.Cambridge University Press, Cambridge, pp.
Feinstein, Charles H., 1998b. Pessimism Perpetuated: real wages and the standard of living in Britain during and after the industrial revolution. Journal of Economic History 58, 625-658.
Feinstein, Charles H., 1998b.Pessimism Perpetuated: real wages and the standard of living in Britain during and after the industrial revolution.Journal of Economic History 58, 625-658.
Galor, Oded, Moav, Omer, 2006. Das Human-Kapital: a theory of the demise of the class structure. Review of Economic Studies 73, 85-117.
Galor, Oded, Moav, Omer, 2006.Das Human-Kapital: a theory of the demise of the class structure.Review of Economic Studies 73, 85-117.
Goldin, Claudia, Katz, Lawrence F., 1998. The origins of technology-skill complementarity. Quarterly Journal of Economics 113, 693-732.
Goldin, Claudia, Katz, Lawrence F., 1998.The origins of technology-skill complementarity.Quarterly Journal of Economics 113, 693-732.
Harley, C. Knick, 1993. Reassessing the industrial revolution: a macro view. In: Mokyr, Joel (Ed.), The British Industrial Revolution: An Economic Perspective. Westview Press, Boulder, pp. 171-226.
Harley, C. Knick, 1993.Reassessing the industrial revolution: a macro view.In：Mokyr, Joel (Ed.), The British Industrial Revolution：An Economic Perspective.Westview Press, Boulder, pp.
Harley, C. Knick, 2006. Cotton textiles and the industrial revolution: competing models and evidence of prices and profits.
Harley, C. Knick, 2006.棉纺织品与工业革命：价格与利润的竞争模式与证据》，《棉纺织品与工业革命：价格与利润的竞争模式与证据》，《棉纺织品》，2006 年。
Horrell, Sara, 1996. Home demand and British industrialisation. Journal of Economic History 56, 561-604.
Horrell, Sara, 1996.国内需求与英国工业化》。经济史杂志》第 56 期，561-604 页。
Horrell, Sara, Humphries, Jane, 1992. Old questions, new data, and alternative perspectives: families' living standards in the industrial revolution. Journal of Economic History 52, 849-880.
Horrell, Sara, Humphries, Jane, 1992.Old questions, new data, and alternative perspectives: families' living standards in the industrial revolution.Journal of Economic History 52, 849-880.

Hudson, Pat, 1986. The Genesis of Industrial Capital: A Study of the West Riding Wool Textile Industry, c. 1750-1850. Cambridge University Press, Cambridge.
Hudson, Pat, 1986.The Genesis of Industrial Capital：A Study of the West Riding Wool Textile Industry, c. 1750-1850.剑桥大学出版社，剑桥。
Jackson, R.V., 1987. The structure of pay in nineteenth-century britain. Economic History Review 40 (second series), 561-570.
Jackson, R.V., 1987.The structure of pay in nineteenth-century britain.Economic History Review 40 (second series), 561-570.
Kalecki, M., 1942. A theory of profits. Economic Journal 52, 258-267.
Kalecki, M., 1942.A theory of profits.Economic Journal 52, 258-267.
Kaldor, N., 1956. Alternative theories of distribution. Review of Economic Studies 23, 83-100
Kaldor, N., 1956.Alternative theories of distribution.经济研究评论》，23, 83-100
Layard, P.R.G., Sargan, J.D., Ager, M.E., Jones, D.J., 1971. Qualified Manpower and Economic Performance. Allen Lane, London.
Layard, P.R.G., Sargan, J.D., Ager, M.E., Jones, D.J., 1971.Qualified Manpower and Economic Performance.伦敦 Allen Lane 出版社。
Lewis, William Arthur, 1954. Economic development with unlimited supplies of labour. Manchester School of Economics and Social Studies .
Lewis, William Arthur, 1954.劳动力无限供给下的经济发展》。曼彻斯特经济与社会研究学院 。
Lindert, Peter H., Williamson, Jeffrey G., 1982. Revising England's social tables, 1688-1913. Explorations in Economic History 19, 385-408.
Lindert, Peter H., Williamson, Jeffrey G., 1982.Revising England's social tables, 1688-1913.Explorations in Economic History 19, 385-408.
Lucas, Robert E., 1969. Labor-capital substitution in US manufacturing. In: Harberger, Arnold, Bailey, Martin J. (Eds.), The Taxation of Income from Capital. The Brookings Institution, Washington, DC, pp. 223-274.
Lucas, Robert E., 1969.美国制造业的劳动力-资本替代。In：Harberger, Arnold, Bailey, Martin J. (Eds.), The Taxation of Income from Capital.布鲁金斯学会，华盛顿特区，第 223-274 页。
Matthews, R.C.O., Feinstein, C.H., Odling-Smee, J.C., 1982. British Economic Growth, 1856-1973. Stanford University Press, Stanford.
Matthews, R.C.O., Feinstein, C.H., Odling-Smee, J.C., 1982.British Economic Growth, 1856-1973.斯坦福大学出版社，斯坦福。
McAdam, Peter, Willman, Alpo (2006). "The Medium Run Redux," presented to the Royal Economic Society annual conference.
McAdam, Peter, Willman, Alpo (2006)."The Medium Run Redux》，在皇家经济学会年会上发表。
McCulloch, J.R., 1847. A Descriptive and Statistical Account of the British Empire, Longman, Brown, Green, and Longmans, London.
McCulloch，J.R.，1847 年。A Descriptive and Statistical Account of the British Empire》，Longman, Brown, Green, and Longmans, London。
Mitch, David, 2004. Education and skill of the British labour force. In: Floud, Roderick, Johnson, Paul (Eds.), The Cambridge Economic History of Modern Britain, Industrialisation, 1700-1860, vol. I. Cambridge University Press, Cambridge, pp. 332-356.
Mitch, David, 2004.英国劳动力的教育和技能。In：Floud, Roderick, Johnson, Paul (Eds.), The Cambridge Economic History of Modern Britain, Industrialisation, 1700-1860, vol. I. Cambridge University Press, Cambridge, pp.剑桥大学出版社，剑桥，第 332-356 页。
Mokyr, Joel, Savin, N. Eugene, 1976. Stagflation in historical perspective: the Napoleonic wars revisited. In: Uselding, Paul (Ed.), Research in Economic History, vol. I, pp. 198-259.
Mokyr, Joel, Savin, N. Eugene, 1976.Stagflation in historical perspective: the Napoleonic wars revisited.In：Uselding, Paul (Ed.), Research in Economic History, vol. I, pp.
Norton, Trist, Gilbert, 1889. A century of land values: England and Wales. reprinted in Carus-Wilson, E.M. (Ed.), Essays in Economic History, vol. III, St. Martin's Press, New York, pp. 128-131.
诺顿、特里斯特、吉尔伯特，1889 年。一个世纪的土地价值：重印于 Carus-Wilson，E.M.（编辑），《经济史论文集》，第三卷，圣马丁出版社，纽约，第 128-131 页。
O'Rourke, Kevin H., 1997. The European grain invasion, 1870-1913. Journal of Economic History 57, 775-801.
O'Rourke, Kevin H., 1997.The European grain invasion, 1870-1913.Journal of Economic History 57, 775-801.
O'Rourke, Kevin H., Williamson, Jeffrey G., 1999. Globalization and History: The Evolution of a Nineteenth Century Atlantic Economy. The MIT Press, Cambridge.
O'Rourke, Kevin H., Williamson, Jeffrey G., 1999.全球化与历史：The Evolution of a Nineteenth Century Atlantic Economy.麻省理工学院出版社，剑桥。
O'Rourke, Kevin H., Williamson, Jeffrey G., 2005. From Malthus to Ohlin: trade, industrialisation and distribution since 1500. Journal of Economic Growth 10, .
O'Rourke, Kevin H., Williamson, Jeffrey G., 2005.From Malthus to Ohlin: Trade, industrialisation and distribution since 1500.Journal of Economic Growth 10, .
Samuelson, Paul A., Modigliani, Franco, 1966. The Pasinetti paradox in neoclassical and more general models. Review of Economic Studies 33, 269-301.
Samuelson, Paul A., Modigliani, Franco, 1966.新古典和更一般模型中的帕西内蒂悖论》（The Pasinetti paradox in neoclassical and more general models.Review of Economic Studies 33, 269-301.
Sokoloff, Kenneth, 1984. Was the transition from the artisanal shop to the nonmechanized factory associated with gains in efficiency? evidence from the US manufacturing censuses of 1820 and 1850. Explorations in Economic History 21, 351-382.
Sokoloff, Kenneth, 1984.从手工作坊到非机械化工厂的转型与效率提高有关吗？来自 1820 年和 1850 年美国制造业普查的证据。Explorations in Economic History 21, 351-382.
Solow, Robert M., 1956. A contribution to the theory of economic growth. Quarterly Journal of Economics 70, 65-94.
Solow, Robert M., 1956.对经济增长理论的贡献》。经济学季刊》70，65-94。
Temin, Peter, 1997. Two views of the British industrial revolution. Journal of Economic History 57, 63-82.
Temin, Peter, 1997.英国工业革命的两种观点。Journal of Economic History 57, 63-82.
Temin, Peter, Voth, Hans-Joachim, 2005. Credit rationing and crowding out during the industrial revolution: evidence from Hoare's bank, 1702-1862. Explorations in Economic History 42, 325-348.
Temin, Peter, Voth, Hans-Joachim, 2005.工业革命时期的信贷配给与挤出：1702-1862 年胡尔银行的证据。Explorations in Economic History 42, 325-348.
Turner, M.E., Beckett, J.V., Afton, B., 1997. Agricultural Rent in England, 1690-1914. Cambridge University Press, Cambridge.
Turner, M.E., Beckett, J.V., Afton, B., 1997.Agricultural Rent in England, 1690-1914.剑桥大学出版社，剑桥。
Van Zanden, Jan Luiten, 2005. Cobb-Douglas in Pre-Modern Europe: Simulating Early Modern Growth, International Institute of Social History, Working Paper. Available from:<www.iisg.nl/staff/jvz.html>.
Van Zanden, Jan Luiten, 2005.Cobb-Douglas in Pre-Modern Europe: Simulating Early Modern Growth, International Institute of Social History, Working Paper.Available from:<www.iisg.nl/staff/jvz.html>.
Williamson, J.G., 1990. The impact of the Corn laws just prior to repeal. Explorations in Economic History 27, 123-156.
Williamson, J.G., 1990.The impact of the Corn laws just prior to repeal.Explorations in Economic History 27, 123-156.
Williamson, Jeffrey G., 1985. Did British Capitalism Breed Inequality? Allen & Unwin, Boston.
Williamson, Jeffrey G., 1985.英国资本主义滋生了不平等吗？Allen & Unwin，波士顿。