经济学大咖索洛（Solow）逝世，享年99岁

来源：社科学术汇、中国经济学教育科研网

Robert Merton Solow

据《纽约时报》（The New York Times）消息，1987年诺贝尔经济学奖获得者罗伯特·默顿·索洛（Robert Merton Solow）于2023年12月21日去世，享年99岁。

罗伯特·默顿·索洛（Robert Merton Solow），美国经济学家，以其新古典经济增长理论而闻名。他于1961年获得约翰·贝茨·克拉克奖章，1987年获得诺贝尔经济学奖，2014年获得总统自由勋章。他的四位博士生George Akerlof，Joseph Stiglitz，Peter Diamond和William Nordhaus都曾获得诺贝尔经济学奖。

索洛出生于纽约的布鲁克林，1942年到1945年服兵役，1951年获得哈佛大学博士学位。他的导师是以研究投入产出模型而著称的1973年诺贝尔奖得主华西里·列昂惕夫。从1949年起，索洛在麻省理工学院任教。

新古典经济增长模型由于索洛的开创性工作而称之为“索洛经济增长模型”（Solow Growth Model），该模型是经济增长理论中不可或缺的内容。在索洛模型中，对经济总体的增长贡献被设定为由劳动、资本和技术进步三者组成，并假设边际生产递减的一次齐次的总生产函数、满足稻田条件、储蓄率一定，技术进步为外生等的条件。在此基础上得出了政府政策对于经济增长的作用是无效的结论。虽然其众多苛刻的假设条件和得出的政府政策无效论使人感觉消极，但在罗伊·哈罗德和埃弗塞·多马的极其不稳定的刀锋增长模型（哈罗德-多马模型）一直让人们担心资本主义社会中的经济增长，特别是长期增长是不稳定的当时，索洛模型提出的增本主义模式的资本积累过程从长期来讲将收敛于经济增长稳定状态（Steady state）的这一结论无疑是给关心经济增长问题的经济学界注入了一剂强心针。

索洛的开创性工作之后，许多在此基础上的扩充模型被不断提出。例如实际经济周期理论（Real Business Cycle Theory）就是在索洛模型基础上考虑最优消费问题的一个崭新的新古典派经济学基础理论。但是，这些模型基本上把技术进步视为某种外生的冲击，与80年代中后期产生的注重技术进步内生化的新经济增长模型（或内生经济增长模型）形成鲜明对照。

Robert Merton Solow, GCIH (/ˈsoʊloʊ/; August 23, 1924 – December 21, 2023) was an American economist and Nobel laureate whose work on the theory of economic growth culminated in the exogenous growth model named after him. He was Institute Professor Emeritus of Economics at the Massachusetts Institute of Technology, where he had been a professor since 1949. He was awarded the John Bates Clark Medal in 1961, the Nobel Memorial Prize in Economic Sciences in 1987, and the Presidential Medal of Freedom in 2014. Four of his PhD students, George Akerlof, Joseph Stiglitz, Peter Diamond and William Nordhaus, later received Nobel Memorial Prizes in Economic Sciences in their own right.

罗伯特-默顿-索洛（Robert Merton Solow, GCIH，/ˈsoʊloʊ/；1924 年 8 月 23 日-2023 年 12 月 21 日）是美国经济学家、诺贝尔经济学奖获得者，他在经济增长理论方面的研究成果最终形成了以他名字命名的外生增长模型。1961 年，他获得约翰-贝茨-克拉克奖章， 1987 年获得诺贝尔经济学奖， 2014 年获得总统自由奖章。 他的四位博士生乔治-阿克洛夫、约瑟夫-斯蒂格利茨、彼得-戴蒙德和威廉-诺德豪斯后来都获得了诺贝尔经济学奖。

Robert Solow was born in Brooklyn, New York, into a Jewish family on August 23, 1924, the oldest of three children. He regarded his parents as being very intelligent despite their not being able to attend college due to the necessity to work. He was well educated in the neighborhood public schools and excelled academically early in life.In September 1940, Solow went to Harvard College with a scholarship at the age of 16. At Harvard, his first studies were in sociology and anthropology as well as elementary economics.

1924 年 8 月 23 日，罗伯特-索洛出生在纽约布鲁克林的一个犹太家庭，是三个孩子中的老大。他认为自己的父母都非常聪明，尽管他们因为工作的需要而没能上大学。在哈佛，他首先学习的是社会学和人类学以及初级经济学。

In 1941, Solow left the university and joined the U.S. Army. Because he was fluent in German, the Army put him on a task force whose primary purpose was to intercept, interpret, and send back German messages to base. He served briefly in North Africa and Sicily, and later in Italy until he was discharged in August 1945. Shortly after returning, he proceeded to marry his girlfriend, Barbara Lewis, whom he had been dating for six months.

1941 年，索洛离开大学，加入美国陆军。由于他能说一口流利的德语，陆军将他安排在一支特遣部队中，该部队的主要任务是拦截、解释并向基地发回德国信息。 他曾在北非和西西里短暂服役，后来又在意大利服役，直到 1945 年 8 月退伍。回国后不久，他便与交往了六个月的女友芭芭拉-刘易斯（Barbara Lewis）结婚。

He returned to Harvard in 1945, and studied under Wassily Leontief. As Leontief's research assistant he produced the first set of capital-coefficients for the input–output model. Then he became interested in statistics and probability models. From 1949 to 1950, he spent a fellowship year at Columbia University to study statistics more intensively. During that year he also worked on his Ph.D. thesis, an exploratory attempt to model changes in the size distribution of wage income using interacting Markov processes for employment-unemployment and wage rates.[38]

1945 年，他回到哈佛大学，师从瓦西里-列昂惕夫。作为列昂惕夫的研究助理，他为投入产出模型编制了第一套资本系数。之后，他对统计学和概率模型产生了兴趣。1949 年至 1950 年，他在哥伦比亚大学获得了一年的奖学金，更加深入地学习了统计学。在这一年里，他还撰写了博士论文，该论文是利用就业-失业和工资率的交互马尔可夫过程来模拟工资收入规模分布变化的探索性尝试[38]。

In 1949, just before going off to Columbia, he was offered and accepted an assistant professorship in the Economics Department at Massachusetts Institute of Technology. At M.I.T. he taught courses in statistics and econometrics. Solow's interest gradually changed to macroeconomics. For almost 40 years, Solow and Paul Samuelson worked together on many landmark theories: von Neumann growth theory (1953), theory of capital (1956), linear programming (1958) and the Phillips curve (1960).

1949 年，在前往哥伦比亚大学之前，他获得并接受了麻省理工学院经济系助理教授的职位。在麻省理工学院，他教授统计学和计量经济学课程。索洛的兴趣逐渐转向宏观经济学。在近 40 年的时间里，索洛和保罗-萨缪尔森共同研究了许多具有里程碑意义的理论：冯-诺依曼增长理论（1953 年）、资本理论（1956 年）、线性规划（1958 年）和菲利普斯曲线（1960 年）。

Solow also held several government positions, including senior economist for the Council of Economic Advisers (1961–62) and member of the President's Commission on Income Maintenance (1968–70). His studies focused mainly in the fields of employment and growth policies, and the theory of capital.

索洛还担任过多个政府职务，包括经济顾问委员会高级经济学家（1961-62 年）和总统收入维持委员会成员（1968-70 年）。他的研究主要集中在就业和增长政策以及资本理论领域。

In 1961 he won the American Economic Association's John Bates Clark Award, given to the best economist under age forty. In 1979 he served as president of that association. In 1987, he won the Nobel Prize for his analysis of economic growth and in 1999, he received the National Medal of Science. In 2011, he received an honorary degree in Doctor of Science from Tufts University.

1961 年，他获得了美国经济协会颁发给 40 岁以下最佳经济学家的约翰-贝茨-克拉克奖。1979 年，他担任该协会主席。1987 年，他因对经济增长的分析获得诺贝尔奖；1999 年，他获得美国国家科学奖章。2011 年，他获得塔夫茨大学荣誉科学博士学位。

Solow is the founder of the Cournot Foundation and the Cournot Centre. After the death of his colleague Franco Modigliani, Solow accepted an appointment as new Chairman of the I.S.E.O Institute, an Italian nonprofit cultural association which organizes international conferences and summer schools. He is a founding trustee of the Economists for Peace and Security.

索洛是库诺基金会和库诺中心的创始人。他的同事弗朗哥-莫迪利亚尼去世后，索洛接受任命，担任意大利非营利文化协会 I.S.E.O Institute 的新任主席，该协会负责组织国际会议和暑期学校。他还是经济学家促进和平与安全组织的创始理事。

Solow's past students include 2010 Nobel Prize winner Peter Diamond, as well as Michael Rothschild, Halbert White, Charlie Bean, Michael Woodford, and Harvey Wagner. He is ranked 23rd among economists on RePEc in terms of the strength of economists who have studied under him.

索洛过去的学生包括 2010 年诺贝尔奖得主彼得-戴蒙德，以及迈克尔-罗斯柴尔德、哈尔伯特-怀特、查理-宾、迈克尔-伍德福德和哈维-瓦格纳。在 RePEc 上，就师从索洛的经济学家的人数而言，他在经济学家中排名第 23 位。

Solow was one of the signees of a 2018 amicus curiae brief that expressed support for Harvard University in the Students for Fair Admissions v. President and Fellows of Harvard College lawsuit. Signers of the brief include Alan B. Krueger, George A. Akerlof, Janet Yellen, and Cecilia Rouse.

索洛是 2018 年法庭之友书状的签署人之一，该书状在 "学生争取公平入学诉哈佛大学校长和研究员 "诉讼案中表达了对哈佛大学的支持。该辩护状的签名者包括艾伦-克鲁格（Alan B. Krueger）、乔治-阿克洛夫（George A. Akerlof）、珍妮特-耶伦（Janet Yellen）和塞西莉亚-劳斯（Cecilia Rouse）。

Solow is a Democrat, supporting Joe Biden's Inflation Reduction Act of 2022.

Solow died on December 21, 2023, at his home in Lexington, Massachusetts, at the age of 99.

索洛是民主党人，支持乔-拜登的《2022 年通货膨胀削减法案》。

索洛于 2023 年 12 月 21 日在马萨诸塞州列克星敦的家中去世，享年 99 岁。

Solow's model of economic growth, often known as the Solow–Swan neoclassical growth model as the model was independently discovered by Trevor W. Swan and published in "The Economic Record" in 1956, allows the determinants of economic growth to be separated into increases in inputs (labour and capital) and technical progress. The reason these models are called "exogenous" growth models is the saving rate is taken to be exogenously given. Subsequent work derives savings behavior from an inter-temporal utility-maximizing framework. Using his model, Solow (1957) calculated that about four-fifths of the growth in US output per worker was attributable to technical progress.

索洛的经济增长模型通常被称为索洛-斯旺新古典增长模型，因为该模型是由特雷弗-W-斯旺（Trevor W. Swan）独立发现的，并于 1956 年发表在《经济实录》上。这些模型之所以被称为 "外生 "增长模型，是因为储蓄率是外生给定的。随后的研究从效用最大化的跨期框架中推导出储蓄行为。索洛（1957 年）利用他的模型计算出，美国工人人均产出的增长约有五分之四归因于技术进步。

Solow also was the first to develop a growth model with different vintages of capital.[47] The idea behind Solow's vintage capital growth model is that new capital is more valuable than old (vintage) capital because new capital is produced through known technology. He first states that capital must be a finite entity because all of the resources on the earth are indeed limited. Within the confines of Solow's model, this known technology is assumed to be constantly improving. Consequently, the products of this technology (the new capital) are expected to be more productive as well as more valuable.[47] The idea lay dormant for some time perhaps because Dale W. Jorgenson (1966) argued that it was observationally equivalent with disembodied technological progress, as advanced earlier in Solow (1957). It was successfully advanced in subsequent research by Jeremy Greenwood, Zvi Hercowitz and Per Krusell (1997), who argued that the secular decline in capital goods prices could be used to measure embodied technological progress. They labeled the notion investment-specific technological progress. Solow (2001) approved. Both Paul Romer and Robert Lucas, Jr. subsequently developed alternatives to Solow's neo-classical growth model.

索洛也是第一个提出不同年份资本增长模型的人。 索洛的年份资本增长模型背后的理念是，新资本比旧（年份）资本更有价值，因为新资本是通过已知技术生产出来的。他首先指出，资本必须是一个有限的实体，因为地球上的所有资源确实都是有限的。也许是因为戴尔-约根森（Dale W. Jorgenson，1966 年）认为，从观察角度看，这种观点等同于索洛（1957 年）早先提出的非实体技术进步，所以这种观点沉寂了一段时间。杰里米-格林伍德、兹维-赫尔科维茨和佩尔-克鲁塞尔（1997 年）在随后的研究中成功地提出了这一观点，他们认为资本货物价格的长期下降可以用来衡量实体技术进步。他们将这一概念称为 "特定于投资的技术进步"。索洛（2001 年）对此表示赞同。保罗-罗默（Paul Romer）和小罗伯特-卢卡斯（Robert Lucas）随后提出了索洛新古典增长模型的替代方案。

To better communicate the meaning behind his work, Solow used a graphical design to illustrate his concepts. On the x-axis he puts capital per worker and for the y-axis he uses output per worker. The reason for graphing capital and output per worker is due to his assumption that the nation is at full employment. The first (top) curve represents the output produced at each given level of capital. The second (middle) curve shows the depreciating nature of capital which remains constantly positive. The third curve (bottom) conveys savings/investment per worker. As the old machinery wears down and breaks, new capital goods must be bought to replace the old. The point where the two lines meet is known as the steady state level, which means that the nation is producing just enough to be able to replace the old capital. Countries that are closer to the steady state level, on the left side, grow more slowly when compared to countries closer to the vertex of the graph. However, when countries are to the right of the steady state level, they are not growing because all the returns they create needs to go to replacing and repairing their old capital.

为了更好地传达他的工作背后的意义，索洛使用了一种图形设计来说明他的概念。他在 x 轴上标注了工人人均资本，在 y 轴上标注了工人人均产出。之所以用工人人均资本和人均产出作图，是因为他假设国家处于充分就业状态。第一条（上）曲线表示在每个给定的资本水平下产生的产出。第二条曲线（中间）显示了资本的贬值特性，即资本始终为正值。第三条曲线（下）表示每个工人的储蓄/投资。随着旧机器的磨损和损坏，必须购买新的资本货物来替代旧机器。两条曲线的交汇点被称为稳态水平，这意味着国家的生产量刚好能够替换旧的资本。与更靠近图表顶点的国家相比，更接近稳态水平的国家（在左侧）增长更慢。然而，当国家处于稳态水平的右侧时，它们就不会增长，因为它们创造的所有回报都需要用于替换和修复旧资本。

Since Solow's initial work in the 1950s, many more sophisticated models of economic growth have been proposed, leading to varying conclusions about the causes of economic growth. For example, rather than assuming, as Solow did, that people save at a given constant rate, subsequent work applied a consumer-optimization framework to derive savings behavior endogenously, allowing saving rates to vary at different points in time, depending on income flows, for example. In the 1980s efforts have focused on the role of technological progress in the economy, leading to the development of endogenous growth theory (or new growth theory). Today, economists use Solow's sources-of-growth accounting to estimate the separate effects on economic growth of technological change, capital, and labor.

As of 2022, Solow is still an emeritus Institute Professor in the MIT economics department, and previously taught at Columbia University.

自索洛在 20 世纪 50 年代的最初研究工作以来，人们提出了许多更为复杂的经济增长模型，并对经济增长的原因得出了不同的结论。例如，后来的研究不再像索洛那样假定人们的储蓄率是恒定的，而是采用消费者优化框架来内生地推导储蓄行为，允许储蓄率在不同的时间点根据收入流量等因素而变化。20 世纪 80 年代，人们开始关注技术进步在经济中的作用，从而提出了内生增长理论（或新增长理论）。如今，经济学家使用索洛的增长源核算来估算技术变革、资本和劳动力对经济增长的不同影响。

截至 2022 年，索洛仍是麻省理工学院经济系的名誉研究所教授，此前曾在哥伦比亚大学任教。

In the early 1960s the Massachusetts Institute of Technology (MIT) was the home of the "growthmen". Its leading light, Paul Samuelson, had published a pathbreaking undergraduate textbook, Economics: An Introductory Analysis. In the sixth edition of Economics, Samuelson (1964) added a "new chapter on the theory of growth". Samuelson drew on the work on growth theory of his younger colleague Robert Solow (1956)—an indication that growthmanship was taking an analytical turn. The MIT economists were thus growthmen in two senses: in seeing growth as an absolutely central policy imperative and in seeing the theory of growth as a focus for economic research. What the MIT growthmen added was a distinctive style of analysis that made it easier to address the dominant policy concerns in tractable formal models. Solow's (1956) model was the perfect exemplar of the MIT style. It provided the central framework for the subsequent developments in growth theory and secured MIT as the center of the universe in the golden age of growth theory in the 1960s (Boianovsky and Hoover 199–200).

20 世纪 60 年代初，麻省理工学院（MIT）是 "增长派 "的发源地。其领军人物保罗-萨缪尔森（Paul Samuelson）出版了一本开创性的本科教科书--《经济学入门分析》：入门分析》。在《经济学》第六版中，萨缪尔森（1964 年）增加了 "关于增长理论的新章节"。萨缪尔森借鉴了他的年轻同事罗伯特-索洛（Robert Solow，1956 年）在增长理论方面的研究成果，这表明增长主义正在转向分析主义。因此，麻省理工学院的经济学家在两种意义上都是增长主义者：将增长视为绝对核心的政策要求，将增长理论视为经济研究的重点。麻省理工学院的增长学家们所补充的是一种独特的分析风格，这种风格使得在可操作的正式模型中解决主要的政策问题变得更加容易。索洛（1956 年）的模型是麻省理工学院风格的完美典范。它为后来增长理论的发展提供了核心框架，并使麻省理工学院成为 20 世纪 60 年代增长理论黄金时代的宇宙中心（Boianovsky 和 Hoover 199-200）。

Grand-Cross of the Order of Prince Henry, Portugal (September 27, 2006)

葡萄牙亨利王子大十字勋章（2006年9月27日）

Member, American Academy of Arts and Sciences (1956)

美国艺术与科学院院士（1956 年）

Member, United States National Academy of Sciences (1972)

美国国家科学院院士（1972年）

Member, American Philosophical Society (1980)

美国哲学学会会员（1980 年）

Dorfman, Robert; Samuelson, Paul; Solow, Robert M. (1958). Linear programming and economic analysis. New York: McGraw-Hill.

Solow, Robert M. (October 15, 1970). Growth Theory: An Exposition (1970, second edition 2006). Oxford University Press. ISBN 978-0195012958.

Solow, Robert M. (1990). The Labor Market as a Social Institution. Blackwell. ISBN 978-1557860866.

Book chapters

Solow, Robert M. (1960), "Investment and technical progress", in Arrow, Kenneth J.; Karlin, Samuel; Suppes, Patrick (eds.), Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium, Stanford mathematical studies in the social sciences, IV, Stanford, California: Stanford University Press, pp. 89–104, ISBN 9780804700214.

Solow, Robert M. (2001), "After technical progress and the aggregate production function", in Hulten, Charles R.; Dean, Edwin R.; Harper, Michael J. (eds.), New developments in productivity analysis, Chicago, Illinois: University of Chicago Press, pp. 173–78, ISBN 9780226360645.

Solow, Robert M. (2009), "Imposed environmental standards and international trade", in Kanbur, Ravi; Basu, Kaushik (eds.), Arguments for a better world: essays in honor of Amartya Sen | Volume II: Society, institutions and development, Oxford New York: Oxford University Press, pp. 411–24, ISBN 9780199239979.

Journal articles

Robert Merton Solow (January 1952). "On the Structure of Linear Models". Econometrica. 20 (1): 29–46. doi:10.2307/1907805. JSTOR 1907805.

Solow, Robert M. (1955). "The Production Function and the Theory of Capital". The Review of Economic Studies: 103–107.

Solow, Robert M. (February 1956). "A contribution to the theory of economic growth" (PDF). Quarterly Journal of Economics. 70 (1): 65–94. doi:10.2307/1884513. hdl:10338.dmlcz/143862. JSTOR 1884513.

Solow, Robert M. (1957). "Technical change and the aggregate production function". Review of Economics and Statistics. 39 (3): 312–20. doi:10.2307/1926047. JSTOR 1926047. S2CID 153438644. Pdf.

Solow, Robert M. (May 1974). "The economics of resources or the resources of economics". The American Economic Review: Papers and Proceedings. 64 (2): 1–14. JSTOR 1816009.

Solow, Robert M. (September 1997). "Georgescu-Roegen versus Solow/Stiglitz". Ecological Economics. 22 (3): 267–68. doi:10.1016/S0921-8009(97)00081-5.

See also: Nicholas Georgescu-Roegen and Joseph Stiglitz.

Solow, Robert M. (November 2003). "Lessons learned from U.S. welfare reform". Prisme. 2. Archived from the original on May 16, 2015.

Solow, Robert M. (Spring 2007). "The last 50 years in growth theory and the next 10". Oxford Review of Economic Policy. 23 (1): 3–14. doi:10.1093/oxrep/grm004。