American economist Franco Modigliani (1918–2003) won the Nobel Prize for Economics in 1985 for a career that began in his native Italy when he won a prize for an economics essay during his second year at the University of Rome. With prospects for a bright future dimming under the rise of Fascism in Mussolini's Italy as it began to collaborate with Hitler's Germany, he left Italy and joined his future wife and her parents in Paris. With World War II about to engulf Europe, Modigliani, himself a Jew, decided it best to leave for America. In August 1939, a few days before the war in Europe broke out, they arrived in New York.
Privilege Was No Escape
Modigliani was born on June 18, 1918, in Rome, Italy. His father, Enrico Modigliani, was a prominent pediatrician and his mother, Olga Flaschel Modigliani, was a volunteer social worker. He described himself in his autobiography for the Nobel Prize committee as being a "good" student "though not outstanding." When he was 13 his father died unexpectedly due to an operation. Modigliani was traumatized, and for the next three years his performance at school reflected his grief. It was inconsistent at best. He then transferred to Liceo Visconti, considered the best high school in Rome, and there he began to flourish. Because of his excellent progress, he took the university exam and was able to skip his last year in high school and begin his college career at age 17. Family hopes that he would follow his father's path into medicine did not last for Modigliani, who admitted a low tolerance for suffering and blood. Instead he initially decided on pursuing a law degree which he saw as opening the door to many possibilities in Italy. That plan, too, was about to change.
In his second year at the University of Rome Modigliani entered an economics essay in a contest by a student organization. He won. It was at that moment that he realized his interest was in economics. Prospects for getting a proper education there were not good due to fascism. Economics education was grim. Instead he decided he would continue to study on his own with the assistance of a few economists he knew personally and whom he valued, especially Riccardo Bachi. He began to read the English and Italian versions of the classics in the field. The same organization that had sponsored the prize, I Littoriali della Coltura, had also helped put him into contact with other anti-fascists. His political philosophy changed in that direction, as did his involvement with his future wife, Serena Calabi, and her father, Giulio, both anti-fascists.
Modigliani recalled that, "In 1938 the Italian racial laws were promulgated and at the invitation of my future in-laws, I joined them in Paris, where, in May 1939, Serena and I were married." What was a joyful time in his personal life was shadowed by the state of affairs in Europe. He was not impressed with his classes at the Sorbonne in Paris, and spent his time studying on his own at the St. Genevieve Library (Bibliotheque St. Genevieve). In June he had returned briefly to Italy to discuss his thesis and to receive his Doctor of Juris degree from the University of Rome. But with the certainty of war, Modigliani, his wife, and her parents applied for immigration to the United States. They arrived in August 1939, and the war in Europe began a few days later.
New School for a New Life
When it was apparent that Modigliani would not be returning to Europe for quite a long time, he enrolled at the New School for Social Research in New York City and was awarded with a free tuition scholarship by the Graduate Faculty of Political and Social Science. The New School had been newly created and provided an academic haven for many Europeans, especially Jews, who had escaped the persecutions that had come with Hitler and the other fascist dictatorships. He began studies in the fall of 1939 and continued his studies for three years at night, while he sold European books during the day to support his growing family that would eventually include his two sons, Andre and Sergio. In 1941 he began his first teaching job at the New Jersey College for Woman. The following year he became an instructor in economics at Bard College, which was at the time a residential college of Columbia University. In 1944, he received his doctorate in economics from the New School. His first publication, in January 1944, was in Econometrica, which, he noted, was essentially his dissertation, entitled, "Liquidity Preference and the Theory of Interest and Money." It was Modigliani's model present in his dissertation that would provide the core of the Neo-Keynesian Synthesis of post-war macroeconomics, according to the New School website page on Modigliani. An explanation of the economics system he proposed noted that, "In sum, Modigliani proposed that with sticky wages money is non-neutral: an increase in the nominal money supply M raises the price level less-then-proportionally, decreases the interest rate and raises employment and output. If money wages are fully flexible, as in the earlier case, then money is neutral it affects neither interest nor employment nor output and increases the price level proportionally. Thus, Modigliani concludes, Keynes' (Economist John Maynard Keynes) theory only works if there is sticky or rigid money wages."
He returned to the New School to become a lecturer and research associate at the Institute of World Affairs. His project was published in National Income and International Trade. He also created his first proposal for saving, known as the Duesenberry-Modigliani hypothesis.
Modigliani left New York in 1948 to study at the University of Chicago after receiving the nod for the Political Economy fellowship. At the same time he joined the Cowles Commission for Research in Economics as a research consultant. He soon accepted a position as director of a research project at the University of Illinois on "Expectations and Business Fluctuations." In 1952 Modigliani left Chicago to join the faculty at the Carnegie Institute of Technology, now Carnegie-Mellon University, and stayed there until 1960. While there he completed two important papers that would set the foundation of his "Life Cycle Hypothesis," as well as a collaboration on a book and two essays with another economist, Merton H. Miller. He then spent a year at Massachusetts Institute of Technology (MIT) as a visiting professor. After another year teaching at Northwestern, he returned to MIT and stayed the duration of his career.
With Nobel, Criticism for President
Modigliani was announced as the recipient of the 1985 Nobel Prize for Economics in October 1985, the 13th American to win the prize since its establishment in 1969. David Warsh of the Boston Globe broke the story on the local honoree that was more than simply one expressing Modigliani's pleasure in receiving the nod. "After receiving news of the award," Warsh wrote, "he immediately rebuked President Reagan for coining political positions that contradicted virtually all of the findings of Modigliani's 40 years of investigations." Modigliani seemed to be leveling only criticism at the president that first year of his second term for insisting that the growing deficit did nothing to hurt savings. He also criticized the president for doing everything to undermine the economy except to raise taxes. On a lighter note at his press conference that day in Cambridge, Modigliani said that, "I sometimes think that my work on this subject was colored by the savings bank where I was banking at the time when I was working on this. Their motto was, 'Save it when you need it least, have it when you need it most.'" He also mentioned his appreciation of an early collaborator at Illinois. Richard Brumberg was a "brilliant" graduate student, according to Modigliani, who had been working with him as the "Life Cycle Hypothesis" began to unfold. The plan that was outlined in 1953 and 1954 had laid the foundation for the future evolution of the project. Each of them then went to pursue other work: Brumberg to Johns Hopkins to complete his Ph.D. studies, and Modigliani to Carnegie. Brumberg died suddenly in 1955 of a brain tumor. Modigliani's shock and grief over the untimely death prevented him from publishing the second paper until 1980. Paul Samuelson, the first Nobel Economics winner in 1970 and an MIT colleague of Modigliani, reacted to the announcement of his prize as saying, "With many people with respect to the Nobel Prize, it's a question of 'if;' with Franco, it was only a question of 'when.'"
Modigliani's fame in the United States among his peers, students, and the circle of economists was not nearly as great as it was in Italy, where he was actually a celebrity. He wrote for a leading news magazine there, advised politicians and bankers, and sponsored many Italian students to attend MIT. John Bossons, an economist at the University of Toronto, noted at the time of his Nobel that Modigliani was "a very enthusiastic advocate," and had "inspired a lot of people."
Modigliani published prolifically, particularly in economic journals. In 2003 he published an autobiography titled, Adventures of an Economist.
Modigliani, a naturalized United States citizen, was a member of the National Academy of Sciences and theAmerican Academy of Arts and Sciences, and at the time he was honored with the Nobel, the only man to serve as president of both the American Economic Association and the American Finance Association. He also served as president of the American Econometric Society. In addition to advising Italian banks and politicians, Modigliani acted as a consultant to the United States Treasury, the Federal Reserve System, and numerous European banks.
Modigliani died in his sleep on September 25, 2003, at his home in Cambridge, Massachusetts, at the age of 85. When he died, an obituary in the Economist related an interesting, and amusing, story. "Serena Modigliani warned her husband not to turn around if someone shouted his name on the streets of Rome. 'Otherwise they'll shoot you,' she said. It was the winter of 1978, and Italy was gripped by political violence and economic chaos. Franco Modigliani, an economist at the Massachusetts Institute of Technology, had returned to the country of his birth to take part in a televised debate, urging unpopular reforms. When Mr. Modigliani left his hotel the next morning, he heard a man behind him call his name. He tried to walk faster, but his pursuer drew nearer, and finally caught him, grabbing his jacket. An assassin? No: a cobbler, in fact, desperate to tell him that, of all the bigwigs on the television the previous night, Mr. Modigliani had been the only one to say, 'anything comprehensible.'"
Boston Globe, October 16, 1985; December 5, 1985.
CFO, The Magazine for Senior Financial Executives, November 2003.
Economist, October 4, 2003.
The Guardian, October 1, 2003.
MIT News, September 25, 2003.
Science, November 7, 1986.
" Adventures of an Economist, by Franco Modigliani," Texere Publishing website,http://www.etexere.com (January 16, 2004).
"Dining With Nobel Laureate Franco Modigliani," Massachusetts Institute of Technology (MIT) News website,http://www-tech.mit.edu (January 16, 2004).
"Franco Modigliani Autobiography," Nobel Museum website,http://www.nobel.se (December 31, 2003).
"In memory of Franco Modiglian, (Pierleone Ottolenghi)," Open Democracy website,http://www.opendemocracy.net (January 16, 2004).
"Neoclassical Keynesian Synthesis," New School for Social Research website,http://cepa.newschool.edu (January 16, 2004).
"A Solution to the Social Security Reform," Massachusetts Institute of Technology web,http://web.mit.edu/francom/ (January 16, 2004).
Modigliani, Franco 1918-2003
Franco Modigliani was an Italian-born Jewish-American economist. He fled the fascist and anti-Semitic regime of Benito Mussolini (1883–1945) in 1939 and migrated to the United States with a doctor of law degree (1939) from the University of Rome. He earned a doctorate in economics from the New School University in New York in 1944, writing his dissertation on the Keynesian liquidity preference. In his dissertation, he reworked the Hicksian IS and LM curves to present a new version of Keynesian economics. His Keynesian paradigm laid the foundation for the Federal Reserve Bank econometric model. In 1962 Modigliani joined the economics department of the Massachusetts Institute of Technology, where he stayed for the rest of his career.
Liquidity preference explains unemployment without wage rigidity. It posits a relationship of money to prices. The price of money is anything that can be exchanged for it. Money in the future is also a price with a discount rate Rt = (1 + rt )-1. Being flexible, the rate of interest will rise in tight money situations. People will raise cash by liquidating money instruments or through borrowing. Investment and savings will fall and be subsequently followed by a fall of income and employment. The demand for money will then fall to equal its supply. Essentially, Modigliani argued for a “rate of interest” to “output” adjustment consequent to a tight monetary policy, in contrast to classical economists, who argued for a “rate of interest” to “price of all goods” adjustment. By keeping policymakers on guard to supply an adequate quantity of money or to fix an appropriate interest rate, Modigliani made unemployment an equilibrating mechanism.
Modigliani rid the investment concept in corporate finance of its traditional utility and production analyses. The Modigliani-Miller hypothesis first argued that a firm trying to increase its value by moving from only equity to a mixture of debt and equity positions will encourage arbitrage among individual investors that would undo its actions, making value invariant to the debt/equity ratio. Second, the rate of return on equity is linearly dependent on the debt/equity ratio. If a firm's stock is $1,000, debt is $400, interest on debt is 0.05, and the expected rate of return is 0.1, then its return on equity will be . Third, new invest-600 ment opportunities are also independent of the debt/equity ratio. This three-part hypothesis abstracted from the effects of taxes and bankruptcy. The discussion was extended to a dividend invariance value model.
In Modigliani's second best-known hypothesis, the life-cycle hypothesis of saving (LCH), consumers receive income, Y, up to the end of their working life, N. They accumulate savings during their working year, and consume, C, uniformly during their lifetime, L > N. Since lifetime consumption must equal lifetime income, assuming no bequest, we can express CL = NY, or C = (N ǀ L ) Y, in which case the terms in parentheses represent the marginal propensity to consume. Fitting the LCH to labor income and net assets, A, the equation C = .766 Y + .073 A reconciled some anomalies of the post-World War II (1939–1945) period.
For his contributions to investment and consumption theories, Modigliani received the Nobel Prize in economics in 1985. He also contributed to economic policy debates, evolving the NIRU (noninflationary rate of unemployment) concept through the Phillips curve, and Okun's unemployment versus the gross domestic product gap relationship, public deficits, and reinstated personal savings into the post-Keynesian debate on the equilibrium profit rate, creating the dual or anti-Pasinetti theorem.
SEE ALSO Life-Cycle Hypothesis; Modigliani-Miller Theorems
Modigliani, Franco. 1944. Liquidity Preference and the Theory of Interest and Money. Econometrica 12: 45–88.
Modigliani, Franco. 1949. Studies in Income and Wealth. Vol. 11: Fluctuations in the Saving-Income Ratio: A Problem in Economic Forecasting. New York: National Bureau of Economic Research.
Modigliani, Franco. 1963. The Monetary Mechanism and Its Interaction with Real Phenomena. Review of Economics and Statistics 45: 79–107.
Modigliani, Franco. 1986. Life Cycle, Individual Thrift, and the Wealth of Nations. American Economic Review 76 (3): 297–313.
Modigliani, Franco. 1988. MM-Past, Present, Future. Journal of Economic Perspectives 2 (4): 149–158. Modigliani, Franco. 2003. The Keynesian Gospel According to Modigliani. American Economist 47 (1): 2–24. Modigliani, Franco, and Richard Brumberg. 1954. Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data. In Post-Keynesian Economics, ed. Kenneth K. Kurihara, 388–436. New Brunswick, NJ: Rutgers University Press.
Ramrattan, Lall, and Michael Szenberg. 2004. Franco Modigliani, 1918–2003: In Memoriam. American Economist 43 (1): 3–8.
Ramrattan, Lall, and Michael Szenberg. 2007. Franco Modigliani, A Mind That Never Rests: An Intellectual Biography. Houndmills, U.K.: Palgrave Macmillan.
(b. 18 June 1918 in Rome, Italy; d. 25 September 2003 in Cambridge, Massachusetts), Italian-American economist of Jewish descent and MIT professor emeritus whose innovative work on savings and financial markets earned him the Nobel Prize in Economic Sciences in 1985.
Modigliani was the second of two sons of Enrico Modigliani, a pediatrician, and Olga (Flaschel) Modigliani, a volunteer social worker. Modigliani’s childhood was marked by the trauma of his father’s unexpected death in 1932. “I suddenly realized how deeply I loved and admired him and at 13 my whole world seemed to collapse,” Modigliani recalled. Modigliani was able to react when he enrolled at one of the most prestigious high schools in Rome, the Liceo Visconti. Because of his excellent marks, his teachers advised Modigliani to skip the last year of secondary school and take the tests to enter university two years ahead of his fellow students. Modigliani passed all the required tests and became a student of the University of Rome at seventeen years old. In spite of family pressure for him to study medicine as his father had done, Modigliani chose law. From his second year he started to be increasingly interested in economics, and this interest resulted in his entry to the national competition “I Littoriali della Cultura” in that category. His essay won the first prize. Yet Modigliani soon realized that under the Fascist regime research in economics was extremely limited. Therefore he established personal contacts with the few Italian economists he respected and asked them for suggestions on how to improve his knowledge of economics. Riccardo Bachi was particularly influential and advised Modigliani to read the Italian and British classics.
Modigliani’s interest in economics was paralleled by his growing opposition to the Fascist regime. He soon came into contact with anti-Fascist groups and individuals. His future wife, Serena Calabi, had a clearly anti-Fascist family background, which contributed to the formation of Modigliani’s political beliefs. The promulgation of the racial laws in 1938 legally sanctioned discrimination against Jews in Italy. Jews could not serve in the armed forces or in government positions, marriages between Jews and Christians were banned, and Jewish students found it increasingly difficult to continue their studies. The Calabis had already immigrated to France, and at their invitation Modigliani joined them in Paris, where he married Serena on 22 May 1939. The couple had two children. Modigliani briefly attended the Sorbonne but found the teaching disappointing and thus carried on his studies on his own. He finished his undergraduate thesis, which he was able to discuss in Rome in June 1939, earning a JD and the title of Doctor Juris. Yet there was no time for celebrations. Fearing that Europe was on the brink of war, Modigliani and his wife applied for and received a visa for the United States, arriving in August.
When World War II broke out a few days after his arrival in New York, Modigliani realized that his stay in the United States could be a long one and resolved to carry on there his interest in economics. He successfully applied for a free-tuition fellowship from the Graduate Faculty of Political and Social Science of the New School for Social Research, an institution created for European researchers and scholars who had been forced to emigrate because of Fascist persecution. Modigliani worked during the day selling European books and studied at night. While his early years in America were difficult and Modigliani had to work hard to support his family, he remembers the time with excitement: “I was discovering my passion for economics, thanks also to excellent teachers, including... Jacob Marschak.... He helped me develop solid foundations in economics and econometrics, some mathematical foundations, introduced me to the great issues of the day and gave me... constant encouragement.” From Marschak, Modigliani learned to combine theory and empirical analysis, a feature that would characterize much of his future research. Marschak also introduced Modigliani to a circle of important economists with whom he was able to discuss ideas at informal seminars in New York City during 1940–1941. Those who attended included the future Nobel Prize–winner Tjalling Koopmans as well as Abraham Wald and Oscar Lange.
In 1941 Modigliani obtained his first teaching position, at the New Jersey College for Women. The following year Modigliani was hired as an instructor of economics and statistics at Bard College, where he recalled having the opportunity “to appreciate the unique qualities of life in an American college campus, especially the intimate association with first rate students.” In 1944 Modigliani earned his PhD from the New School for Social Research and published his first article in English, based on the research for his doctoral dissertation, which is considered one of his major works: “Liquidity Preference and the Theory of Interest and Money.” The article and the dissertation are part of Modigliani’s project to reconcile the theories of the British economist John Maynard Keynes with mainstream economic theory. The same year Modigliani went back to the New School for Social Research as a lecturer and research associate at the Institute of World Affairs. In this period Modigliani started to work on an analysis of savings, which would later become known as the Duesenberry-Modigliani hypothesis (coauthored with James Duesenberry). The name of the hypothesis suggests one of the major features of Modigliani’s work: his partnership with other economists. In an interview the Nobel laureate declared, “I am a believer in cooperation. Basically, I have so many things [in mind] I can’t do them all, so I give some of them to others.” In 1946 Modigliani became an American citizen.
Important institutions were eager to have Modigliani on staff. In 1948 the University of Chicago awarded Modigliani a prestigious Political Economy Fellowship, and the Cowles Commission for Research in Economics invited him to join them as research consultant. In the early 1950s Modigliani was the director of a University of Illinois research project, Expectations and Business Fluctuations. Although his stay at Illinois was brief, Modigliani teamed up with his student Richard Brumberg to elaborate the core of the life-cycle hypothesis of saving. The hypothesis concluded that people put aside savings during their earlier working lives to spend in old age, not to pass on to their children. From the mid-1950s to 1960 Modigliani worked at the Carnegie Institute of Technology (now Carnegie-Mellon University), where he perfected the life-cycle hypothesis and contributed other important publications to economic science. Also in the 1950s Modigliani devised with his fellow Nobel winner Merton H. Miller the Modigliani-Miller theorems, which determined that the market value of a stock depends primarily on expectations of what the company will earn in the future rather than on the financial structure of the company.
Modigliani first went to the Massachusetts Institute of Technology (MIT) in 1960 as a visiting professor, and apart from one year at Northwestern University he stayed at MIT for the rest of his career. At MIT, Modigliani continued his studies in macroeconomics and his test of the life-cycle hypothesis. He also developed new interests such as international finance and the international payment system, the effects of inflation, credit rationing, interest rates, and the valuation of speculative assets. In the late 1960s Modigliani was asked by the Federal Reserve Bank to design a large-scale model of the U.S. economy, the MPS. (The model’s name comes from MIT, the University of Pennsylvania, and the S ocial Science Research Council, where its developers worked.) In 1970 MIT named Modigliani an Institute Professor, an appointment reserved for scholars of distinction. In 1985 Modigliani won the Nobel Prize in Economic Sciences and MIT’s James R. Killian Faculty Achievement Award. Three years later he became professor emeritus. During the 1980s his Collected Papers (6 vols., 1980–2005) were first published. Modigliani served as a consultant for the Federal Reserve System, the U.S. Department of the Treasury, the Bank of Spain, and the Bank of Italy. He was a senior adviser for the Brookings Panel on Economic Activity from 1971 to 2003.
Modigliani was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He also served as president of the Econometric Society, the American Economic Association, and the American Finance Association. The Modigliani Professorship of Financial Economics, an endowed chair at MIT, was established in 1995. Modigliani maintained close links with his native Italy throughout his life, and in his later years he became a fierce critic of the economic policies of the center-right governments led by the media millionaire Silvio Berlusconi. Modigliani also criticized Berlusconi for his statement that Mussolini had not murdered anyone, thus ignoring the persecution of Jews and political opponents in Fascist Italy.
Modigliani was often praised for his variety of interests—so much so that the fellow Nobel laureate and MIT professor emeritus Paul A. Samuelson went as far as claiming that Modigliani “could have gotten a Nobel Prize for several different subjects.” Modigliani’s enthusiasm made him an inspirational figure for generations of students and fellow scholars. Respected among his American colleagues, Modigliani was a celebrity in Italy. He died in his sleep at home in Cambridge.
Information on Modigliani’s life and work is in Franco Modigliani, Adventures of an Economist (2001), and Lall Ramrattan and Michael Szenberg, “Franco Modigliani, 1918–2003: In Memoriam,” American Economist 48, no. 1 (Mar. 2004): 3–8. The Massachusetts Institute of Technology hosts a memorial website (http://mitsloan.mit.edu/fm-memorial). Obituaries are in the Boston Globe and New York Times (both 26 Sept. 2003).
MODIGLIANI, Franco. American (born Italy), b. 1918. Genres: Economics, Money/Finance. Career: Professor of Economics and Finance, since 1962, and Institute Professor, since 1970, Massachusetts Institute of Technology, Cambridge (Visiting Professor of Economics, 1960-61). Instructor in Economics and Statistics, New Jersey College for Women, New Brunswick, 1942; Instructor to Associate in Economics and Statistics, Bard College, Columbia University, NYC, 1942-44; Lecturer to Assistant Professor of Mathematics, Economics, and Econometrics, New School for Social Research, NYC, 1943-44, 1946-48; Research Associate and Chief Statistician, Institute of World Affairs, NYC, 1945-48; Research Consultant, Cowles Commission on Research in Economics, University of Chicago, 1949-54; Professor of Economics and Industrial Administration, Carnegie Institute of Technology, Pittsburgh, Pa., 1952-60; Visiting Professor of Economics, Harvard University, Cambridge, Massachusetts, 1957-58; Professor of Economics, Northwestern University, Evanston, Illinois, 1960-62. Recipient: Nobel Prize for Economics, 1985. Publications: National Incomes and International Trade, 1953; Planning Production, Inventories and Work Forces, 1960; The Role of Anticipations and Plans in Economic Behavior and Their Use in Economic Analysis and Forecasting, 1961; New Mortgage Designs for Stable Housing in an Inflationary Environment, 1975; The Determinants of National Savings and Wealth, 1983; The Debate over Stabilization Policies and Other Macroeconomic Issues, 1986; The Collected Papers of Franco Modigliani, 5 vols., 1980-89; (co-author) The Management of an Open Economy with 100%Plus Wage Indexation, 1990. Died 2003.
MODIGLIANI, FRANCO (1918–2003), economist and Nobel Prize laureate. Modigliani was born in Rome. After earning a law degree at the University of Rome, he escaped the Fascist regime in Italy and moved to the United States in 1939. In New York he studied at the New School for Social Research, obtaining his Ph.D. in social sciences in 1944. Modigliani taught at the New School from 1944 to 1949 and was a research consultant to the Cowles Commission at the University of Chicago from 1949 to 1952. He was a professor at Carnegie Institute of Technology from 1952 to 1960 and at Northwestern University from 1960 to 1962. He was on the faculty of the Massachusetts Institute of Technology from 1962, becoming professor emeritus in 1988. He served as president of the American Economic Association in 1976.
Modigliani's research work focused on the analysis of household savings, wherein he determined that people save towards retirement rather than amass money to be left as inheritance for the next generation, and on the different types of national pension programs and their effects. He also was highly influential in the area of corporate finance by directing attention to the fact that future earnings of a company serve to determine stock market values. The Nobel Prize in economic science for 1985 was awarded to him for "his pioneering analyses of saving and financial markets," for work that he published in the second half of the 1950s.
Modigliani's autobiography is entitled Adventures of an Economist (2001). His other publications include The Debate over Stabilization Policy (1986); Capital Markets (with F. Fabozzi, 1992); Foundations of Financial Markets and Institutions (with F. Fabozzi and M. Ferri, 1994); and Rethinking Pension Reform (with A. Muralidhar, 2004).
[Ruth Beloff (2nd ed.)]