This paper explores single-equation nonlinear error correction (NEC) models with linear and nonlinear cointegrated variables. Within the class of semiparametric NEC models, we use smoothing splines. Within the class of parametric models, we discuss the interesting properties of cubic polynomial NEC models and we show how they can be used to identify unknown threshold points in asymmetric models and to check the stability properties of the long-run equilibrium. A new class of rational polynomial NEC models is also introduced. We found multiple long-run money demand equilibria. The stability observed in the money-demand parameter estimates during more than a century, 1878 to 2000, is remarkable.

It is customary for the Interviewer to begin with an introduction describing the circumstances of the interview and providing an overview of the nature and importance of the work of the interviewee. However, in this case, as Editor of this journal, I feel it would be presumptuous of me to provide my own overview and evaluation of the work of this great man, Paul Samuelson. The scope of his contributions has been so vast (averaging almost one technical paper per month for over 50 years) that it could be particularly difficult to identify those areas of modern economic theory to which he has not made seminal contributions.Perhaps those rare exceptions might include game theoretic and topological models and maybe the recent literatures on complex unstable nonlinear dynamics, sunspots, and incomplete markets. But I would not be surprised, if he were to correct those speculations as misperceptions, if I were to ask. In addition to his over 550 published papers, his books are legendary. He once said: “Let those who will—write the nation's laws–if I can write its textbooks.”

Instead of attempting to provide my own overview, I am limiting this introduction to the following direct (slightly edited) quotation of a few paragraphs from the Web site, The History of Economic Thought, which is maintained online by the New School University in New YorkThe current URL of that Web site is http://cepa.newschool.edu/het/home.htm.: Perhaps more than anyone else, Paul A. Samuelson has personified mainstream economics in the second half of the twentieth century. The writer of the most successful principles textbook ever (1948), Paul Samuelson has been not unjustly considered the incarnation of the economics ‘establishment’—and as a result, has been both lauded and vilified for virtually everything right and wrong about it.Samuelson's most famous piece of work, Foundations of Economic Analysis (1947), is one of the grandest tomes that helped revive Neoclassical economics and launched the era of the mathematization of economics. Samuelson was one of the progenitors of the Paretian revival in microeconomics and the Neo-Keynesian Synthesis in macroeconomics during the post-war period.The wunderkind of the Harvard generation of 1930s, where he studied under Schumpeter and Leontief, Samuelson had a prodigious grasp of economic theory, which has since become legendary. An unconfirmed anecdote has it that at the end of Samuelson's dissertation defense, Schumpeter turned to Leontief and asked, ‘Well, Wassily, have we passed?’ Paul Samuelson moved on to M.I.T. where he built one of the century's most powerful economics departments around himself. He was soon joined by R.M. Solow, who was to become Samuelson's sometime co-writer and partner-in-crime.Samuelson's specific contributions to economics have been far too many to be listed here—being among the most prolific writers in economics. Samuelson's signature method of economic theory, illustrated in his Foundations (1947), seems to follow two rules which can also be said to characterize much of Neoclassical economics since then: With every economic problem, (1) reduce the number of variables and keep only a minimum set of simple economic relations; and (2) if possible, rewrite it as a constrained optimization problem.In microeconomics, he is responsible for the theory of revealed preference (1938, 1947). This and his related efforts on the question of utility measurement and integrability (1937, 1950) opened the way for future developments by Debreu, Georgescu-Roegen, and Uzawa. He also introduced the use of comparative statics and dynamics through his ‘correspondence principle’ (1947), which was applied fruitfully in his contributions to the dynamic stability of general equilibrium (1941, 1944). He also developed what are now called ‘Bergson-Samuelson social welfare functions’ (1947, 1950, 1956); and, no less famously, Samuelson is responsible for the harnessing of ‘public goods’ into Neoclassical theory (1954, 1955, 1958).Samuelson was also instrumental in establishing the modern theory of production. His Foundations (1947) are responsible for the envelope theorem and the full characterization of the cost function. He made important contributions to the theory of technical progress (1972). His work on the theory of capital is well known, if contentious. He demonstrated one of the first remarkable ‘Non-Substitution’ theorems (1951) and, in his famous paper with Solow (1953), initiated the analysis of dynamic Leontief systems. This work was reiterated in his famous 1958 volume on linear programming with Robert Dorfman and Robert Solow, wherein we also find a clear introduction to the ‘turnpike’ conjecture of linear von Neumann systems. Samuelson was also Joan Robinson's main adversary in the Cambridge Capital Controversy—introducing the ‘surrogate’ production function (1962), and then subsequently (and graciously) relenting (1966).In international trade theory, he is responsible for the Stolper–Samuelson Theorem and, independently of Lerner, the Factor Price Equalization theorem (1948, 1949, 1953), as well as (finally) resolving the age-old ‘transfer problem’ relating terms of trade and capital flows, as well as the Marxian transformation problem (1971), and other issues in Classical economics (1957, 1978).In macroeconomics, Samuelson's multiplier-accelerator macrodynamic model (1939) is justly famous, as is the Solow–Samuelson presentation of the Phillips Curve (1960) to the world. He is also famous for popularizing, along with Allais, the ‘overlapping generations’ model which has since found many applications in macroeconomics and monetary theory. In many ways, his work on speculative prices (1965) effectively anticipates the efficient markets hypothesis in finance theory. His work on diversification (1967) and the ‘lifetime portfolio’ (1969) is also well known.Paul Samuelson's many contributions to Neoclassical economic theory were recognized with a Nobel Memorial prize in 1970.

This paper studies the role played by differences in risk aversion in affecting the long-run distribution of wealth across agents in the context of an endowment economy. The economy is populated by two types of Epstein-Zin agents who differ only in their attitudes toward risk. By choosing riskier portfolio strategies, less-risk-averse agents enjoy returns on their investments characterized by a higher mean and a higher variance than the ones enjoyed by more-risk-averse agents. The former effect tends to make less-risk-averse agents wealthier over time, whereas the latter tends to make them poorer. The paper shows that, contrary to the results obtained using standard expected utility preferences, for some parameter values the long-run distribution of wealth is dominated by more-risk-averse agents.

In this paper, I study the effect that switching to a voucher system of educational finance has on the distribution of income. The model is calibrated to U.S. data, and simulated for two different forms of education finance: a voucher system and a completely private system of schools. All voucher policies considered result in welfare gains and reductions in income inequality. A private system entails a welfare loss and an increase in income inequality. The more important the peer group is to future income, the smaller the welfare gains and reductions in inequality associated with voucher systems, and the greater the welfare cost and increase in inequality associated with a private system.

The Encyclopedia Americana, 2002 edition, concludes its entry on Milton Friedman as follows: “His major work, A Monetary History of the United States, 1867–1960, was published in 1963.” That might be seen as an indirect compliment to Anna J. Schwartz, who coauthored the Monetary History with Friedman but is not mentioned in the encyclopedia entry. Similarly, the Nobel Committee neglected to mention Schwartz when, in awarding Friedman his Prize in 1976, it described A Monetary History as “[h]is major work [and] … one of Friedman's most profound and also most distinguished achievements.” Fortunately, the economics profession as a whole has not been so negligent, and the phrase “Friedman and Schwartz” has become second nature to economists when discussing the importance of monetary policy.

Beside her collaborations with Friedman, Anna Schwartz is perhaps best known for her longevity, which is on an epoch-shattering scale. Her career as an economic researcher began a quarter-century before the publication of A Monetary History, and has continued in the 40 years since. Schwartz's first journal article was published in May 1940, the month Winston Churchill became Prime Minister of the United Kingdom and over 18 months before the United States entered World War II. She has worked at the National Bureau of Economic Research in New York City continuously since 1941. Monetary economics has been a constant interest for her, and she is the only person to have had items published in the inaugural issues of both the Journal of Money, Credit, and Banking (February 1969) and the Journal of Monetary Economics (January 1975).The JME piece was a book review, and so does not appear in the bibliography below. Schwartz's numerous book reviews make rewarding reading and include a prediction in Kyklos in 1968 of an era when economists would use Internet connections to download macroeconomic databases. The JME moved into its fiftieth volume in 2003, and Schwartz became one of only two authors (the other being Thomas Sargent) to have published in both volumes 1 and 50 of the journal. With the NBER branching out in the 1970's into a national network of researchers, Schwartz has been for a quarter century an unmistakable fixture at the NBER monetary economics program's regular meetings at Cambridge, Massachusetts. At the time of the interview, her contributions to the NBER's various working paper series spanned from NBER Technical Paper No. 4, 1947, to NBER Working Paper No. 9321, November 2002. The latter paper covered the issue of equity price behavior, the same subject of her 1940 publication, implying that Schwartz had entered a remarkable seventh decade of research in that area. Much of Schwartz's early research was on UK economic growth and fluctuations in the nineteenth century, and was reflected in a two-volume study essentially completed in the early 1940's but not published until 1953 [Gayer et al. (1953)]. Robert Lucas, who read the volume as a graduate student in history, describes it as “an amazingly ambitious and exciting mix of history and theory.”

Schwartz's collaboration with Milton Friedman on the relationship between the quantity of money and other variables began in 1948. Their early findings on the importance of money were reported by Friedman in a 1952 American Economic Review paper, but, by and large, he had problems promoting their work in the 1950's. Friedman's solo work in the fifties on flexible exchange rates, the consumption function, and the limits of stabilization policy would cement his reputation and be cited in his eventual Nobel award, but the monetary policy studies initially made a much more limited impact. All of Friedman's remaining 1950's writings on money were in “in-house” University of Chicago publications or in congressional testimony.A short excerpt from a Journal of Political Economy paper by Friedman on money did appear in the 1959 proceedings issue of the American Economic Review. Two books by Friedman in the early 1960's previewed some findings from the monetary history project with Schwartz. The first of these, A Program for Monetary Stability, is now recognized as a classic, but its muted reception is evidenced by the fact that economists have never been able to agree on which year it was published. The second book, Capitalism and Freedom (1962), was intended for a wide audience, but was virtually driven underground when all major U.S. newspapers declined to review it. In 1969, a Federal Reserve Bank of New York official, Richard Davis, gave this perspective on reactions to early monetarist work of the 1950's and early 1960's: “[E]conomists regarded this group—when they regarded it at all—as a mildly amusing, not quite respectable collection of eccentrics…. The fact is that the view held by Friedman and others on the predominant importance of money was just not given serious attention by most economists.”

The turning point was in 1963, when Friedman and Schwartz's 15 years of research finally saw print in their Monetary History and the article “Money and Business Cycles.” The Monetary History is justly celebrated, and has remained in print for 40 years.Furthermore, of the 93 books listed by Princeton University Press in its Economics and Finance Catalogue 2003, the Monetary History is the only pre-1994 publication included. The “Cycles” paper, as Davis acknowledged, provided “[b]y far the largest mass of evidence” on the cyclical relation between money and output. In addition, the paper's “tentative sketch” of the monetary transmission mechanism became a cornerstone of the monetarist literature, and an inspiration to many monetary economists, including the late Rudiger Dornbusch, as they endeavored to escape the “single interest rate channel” view of the transmission mechanism.

Schwartz began the 1970's with another collaboration with Friedman, Monetary Statistics, and went on in 1973 to join a number of economists, including fellow monetarists Karl Brunner and Allan Meltzer, in forming the Shadow Open Market Committee (SOMC). The SOMC commented regularly on U.S. economic policy and, in particular, offered monetary policy recommendations to address the severe inflation problem of the 1970's. Schwartz remains on the SOMC 30 years later, the only founding member to serve since the SOMC's inception.

Friedman and Schwartz's final major collaboration, Monetary Trends in the United States and the United Kingdom, was published in 1982. Among monetary economists, the response to Monetary Trends was mild compared to the reception for the Monetary History. Work by Friedman and Schwartz and other monetarists had already changed macroeconomic thinking substantially, and most academic work was now concerned with rigorous modeling of short-run dynamics, rather than the empirical evidence on long-run relations that concerned Friedman and Schwartz in their Trends study.

Schwartz's own work over the past 20 years has been prolific, and has often been in collaboration with Michael Bordo, with whom she has written some 25 articles. While her areas of research have included banking regulation and the role of international financial institutions, Bordo's and her mutual interest in monetary economics and economic history has repeatedly been evident in their work. Among the issues that their studies, sometimes with further collaborators, have addressed are the role of monetary targets in Canada and the United Kingdom in the face of money demand instability, whether monetary policy rules could have avoided the Great Contraction, the historical record of alternative monetary policy regimes, and the history of economic thought, including the development of monetarism.

Axel Leijonhufvud made an enormous impact on macroeconomics in the late 1960s with the publication of his book On Keynesian Economics and the Economics of Keynes: A Study of Monetary Economics (1968). In this famous book, Leijonhufvud argued that the standard neoclassical synthesis (Hicks–Hansen IS-LM) interpretation of the General Theory totally misunderstood and misinterpreted Keynes. However, during the 1970's, interest in Keynes and Keynesian models waned as new classical equilibrium models became all the rage. Nevertheless, Leijonhufvud, from a position outside the mainstream, continued his research into problems of unemployment, business cycles, and inflation—issues that from his perspective are problems of coordination failure in complex dynamical systems. Axel Leijonhufvud is currently Professor Emeritus at the University of California, Los Angeles, and, since 1995, Professor of Monetary Economics at the University of Trento, Italy. In this interview the author discusses with Leijonhufvud a wide range of issues relating to his own work as well as his views on the development of macroeconomics after Keynes.

We use two-stage optimal control techniques to solve some adoption problems under embodied technical change. We first solve a benchmark problem without learning behavior. At the date of switching, the consumption level is shown to drop, as the relative price of capital goes down (obsolescence). In such a case, the economy sticks to the initial technology, or immediately switches to a new technology with a higher level of embodiment, depending on how the obsolescence costs compare to the induced growth advantage. In a second step, we introduce learning. The learning curve involves fixed costs and incentives to wait as well. Adoption is shown to depend on the growth advantage of switching net of obsolescence and learning fixed costs. The economy will switch if and only if this indicator is positive. If it is big enough to “compensate” the option of waiting, then the economy switches immediately. Otherwise, the economy waits.

This paper uses daily observations for the Canadian dollar–U.S. dollar exchange rate over the recent flexible exchange-rate period (from January 2, 1974, to October 28, 2002), and various tests from dynamical systems theory, such as a chaos test, a self-organized criticality test, and a threshold effects test, to support a stochastic nonlinear origin for the series.

This paper explores the possible real effects of inflation within a two-sector neoclassical growth model of the Heckscher–Ohlin type with a cash-in-advance constraint on the purchases of consumption goods. The main findings are that the relative prices of both factors and of both goods, which are linked via a Stolper–Samuelson relation, depend only on the rate of time preference, not on any monetary variable; that the steady-state level of total capital can be influenced by inflation if the capital intensities and the cash requirements in both sectors differ, leading to Tobin effects or reversed Tobin effects; and that higher inflation unambiguously reduces total labor supply and leads to a reversed Tobin effect in most cases if the labor/leisure choice is endogenized.

Christopher Sims is a well-known intellectual leader in time-series econometrics and applied macroeconomics. Among his many honors and distinctions, he has been the President of the Econometric Society and he is a member of the National Academy of Sciences. He has made fundamental contributions to both statistical theory of time series and empirical macroeconomics. Sims' work is influential precisely because it was motivated by important problems in macroeconomics. Not only did Sims study questions of statistical approximation in abstract environments, he showed how to apply the resulting apparatus to a variety of specific problems confronting applied researchers. The applications include seasonality in economic time series, aggregation over time, and approximation in formulating statistical models with economic underpinnings. Moreover, Sims' contributions to causality in time series and to the development of vector autoregressive methods were complemented by an important body of empirical research. Sims has served as an effective advocate and critic of the extensively used vector autoregressive statistical methods. Motivated by his own and related empirical research, Sims is one of the leaders in rethinking how monetary policy should be modeled and reconsidering the channels by which monetary policy influences economic aggregates. This interview with Chris Sims gives an opportunity to explore further the context of many of these contributions. Sims typically has a unique perspective on many economic problems, a perspective that is articulated in his answers to a variety of questions.

A recent article in The Economist magazine divided economists into “poets” and “plumbers,” the former articulating radical new visions of the field and the latter patiently installing the infrastructure needed to implement those visions. Bob Shiller is the rare economist who is both poet and plumber. Not only that, he is also entrepreneur and pundit. His work has fundamentally changed the theory, econometrics, practice, and popular understanding of finance.

Starting in the late 1970's, Bob boldly challenged the prevailing orthodoxy of financial economics. He showed that financial asset prices often deviate substantially from the levels predicted by simple efficient-markets models, and he developed new empirical methods to measure these price deviations. In the early 1980's, Bob went on to argue that economists need a much more detailed understanding of investor psychology if they are to understand asset price movements. He pioneered the emerging field of behavioral economics and its most successful branch, behavioral finance. At the end of the century, Bob articulated his vision of finance in a wildly successful popular book, Irrational Exuberance. He became so well known that TIAA-CREF asked him to appear in a series of full-page advertisements in the popular press.

Although Bob does not believe that investors use financial markets in a perfectly rational manner, he does believe that these markets offer great possibilities to improve the human condition. His recent work asks how existing financial markets can be used, and new financial markets can be designed, to improve the sharing of risks across groups of people in different regions, countries, and occupations. He has explored risk-sharing possibilities not only in journal articles, but also in business ventures and a 2003 book, The New Financial Order: Risk in the 21st Century.

It was a great privilege for me to interview Bob Shiller. Bob's arrival at Yale when I was a Ph.D. student there set the course of my career as an economist. Bob reinvigorated the Yale tradition of macroeconomics, with its emphasis on the central role of financial markets in the macroeconomy and its idealism about the possibility of improving macroeconomic outcomes. First as a thesis adviser, then as a coauthor, mentor, and friend, Bob showed me how to contribute to this tradition.

The interview took place at the 2003 annual meetings of the Allied Social Science Associations in Washington, D.C. We met in a hotel suite, ate a room service meal, and had the enjoyable conversation that is reproduced below.