Cowles Foundation Research Articles

Revisiting elastic string models of forward interest rates

Twenty five years ago, several authors proposed to describe the forward interest rate curve (FRC) as an elastic string along which idiosyncratic shocks propagate, accounting for the peculiar structure of the return correlation across different maturities. In this paper, we revisit the specific ‘stiff’ elastic string field theory of Baaquie and Bouchaud [Stiff field theory of interest rates and psychological future time. Wilmott Mag., 2004, 2–6] in a way that makes its micro-foundation more transparent. Our model can be interpreted as capturing the effect of market forces that set the rates of nearby tenors in a self-referential fashion. The model is parsimonious and accurately reproduces the whole correlation structure of the FRC over the time period 1994–2023, with an error around 1% and with only one adjustable parameter, the value of which being very stable across the last three decades. The dependence of correlation on time resolution (also called the Epps effect) is also faithfully reproduced within the model and leads to a cross-tenor information propagation time on the order of 30 minutes. Finally, we confirm that the perceived time in interest rate markets is a strongly sub-linear function of real time, as surmised by Baaquie and Bouchaud [Stiff field theory of interest rates and psychological future time. Wilmott Mag., 2004, 2–6]. In fact, our results are fully compatible with hyperbolic discounting, in line with the recent behavioral Finance literature Farmer and Geanakoplos [Hyperbolic Discounting is Rational: Valuing the Far Future with Uncertain Discount Rates, Cowles Foundation Discussion Papers, 2009 (Cowles Foundation for Research in Economics, Yale University)].

A POWERFUL SUBVECTOR ANDERSON–RUBIN TEST IN LINEAR INSTRUMENTAL VARIABLES REGRESSION WITH CONDITIONAL HETEROSKEDASTICITY

We introduce a new test for a two-sided hypothesis involving a subset of the structural parameter vector in the linear instrumental variables (IVs) model. Guggenberger, Kleibergen, and Mavroeidis (2019, Quantitative Economics, 10, 487–526; hereafter GKM19) introduce a subvector Anderson–Rubin (AR) test with data-dependent critical values that has asymptotic size equal to nominal size for a parameter space that allows for arbitrary strength or weakness of the IVs and has uniformly nonsmaller power than the projected AR test studied in Guggenberger et al. (2012, Econometrica, 80(6), 2649–2666). However, GKM19 imposes the restrictive assumption of conditional homoskedasticity (CHOM). The main contribution here is to robustify the procedure in GKM19 to arbitrary forms of conditional heteroskedasticity. We first adapt the method in GKM19 to a setup where a certain covariance matrix has an approximate Kronecker product (AKP) structure which nests CHOM. The new test equals this adaptation when the data are consistent with AKP structure as decided by a model selection procedure. Otherwise, the test equals the AR/AR test in Andrews (2017, Identification-Robust Subvector Inference, Cowles Foundation Discussion Papers 3005, Yale University) that is fully robust to conditional heteroskedasticity but less powerful than the adapted method. We show theoretically that the new test has asymptotic size bounded by the nominal size and document improved power relative to the AR/AR test in a wide array of Monte Carlo simulations when the covariance matrix is not too far from AKP.

Léon Walras, Irving Fisher and the Cowles Approach to General Equilibrium Analysis

This paper explores the relationship of Walras’s work to a particularly influential tradition of general equilibrium, that associated with the Cowles Commission for Research in Economics in Colorado in the 1930s and at the University of Chicago from 1939 to 1955, and its successor, the Cowles Foundation, at Yale University from 1955. Irving Fisher introduced general equilibrium analysis into North America with his 1891 Yale dissertation Mathematical Investigations in the Theory of Value and Prices (published 1892) and was responsible in 1892 for the first English translation of a monograph by Walras. Fisher was only able to obtain copies of books by Walras and Edgeworth when his thesis was almost ready for submission, discovering that he had independently reinvented a general equilibrium approach already developed by others, but went beyond Walras in constructing a hydraulic mechanism to simulate computation of general equilibrium and, before Pareto, in using indifference curves. Fisher was closely involved with Alfred Cowles in the Cowles Commission, the Econometric Society and Econometrica in the 1930s, promoting formal mathematical and statistical methods in economics, including drawing attention to the contributions of Walras, Edgeworth and Pareto. The first substantial, systematic work on general equilibrium at the Cowles Commission was in international trade, by Theodore Yntema, research director of the Cowles Commission from 1939 to 1942 and author of A Mathematical Reformulation of the General Theory of International Trade (1932) and by Yntema’s student, Jacob Mosak, author of General Equilibrium Theory in International Trade (1944). A subsequent, much better-known body of work on existence of general equilibrium at Cowles was by Kenneth Arrow and Gerard Debreu (initially independently but leading to a major joint publication) and by Lionel McKenzie, all three associated with the Cowles Commission in Chicago in the early 1950s. After Cowles moved to Yale, the focus of general equilibrium research at the Cowles Foundation was Herbert Scarf’s pioneering work on computable general equilibrium (which he linked to Fisher’s earlier attempt, first presenting his approach in his contribution to Ten Economic Studies in the Tradition of Irving Fisher, 1967). Fisher and then the Cowles Commission were the channel through which Walrasian general equilibrium analysis entered North American economics. This paper is part of a larger history of the Cowles Commission and Foundation, commissioned by the Cowles Foundation.

Jacob Marschak and the Cowles approaches to the theory of money and assets

Jacob Marschak shaped the emergence of monetary theory and portfolio choice at the Cowles Commission (which he directed from 1943 to 1948, but with which he was involved already from 1937) at the University of Chicago, where he was the doctoral teacher of Leonid Hurwicz, Harry Markowitz and Don Patinkin, and then from 1955 at the Cowles Foundation at Yale University, where he was a senior colleague of James Tobin until moving to UCLA in 1960. Marschak’s later attempts to clarify the concept of liquidity and to emphasise the role of new information for economic behaviour date back as far as to his early experiences with hyperinflationary processes in the Northern Caucasus during the Russian Revolution. Marschak came to monetary theory with his 1922 Heidelberg doctoral dissertation on the quantity theory equation of exchange (published in 1924 as “Die Verkehrsgleichung”), and embedded monetary theory in a wider theory of asset market equilibrium in studies of “Money and the Theory of Assets” (1938), “Assets, Prices, and Monetary Theory” (with Helen Makower, 1938), “Role of Liquidity under Complete and Incomplete Information” (1949), “The Rationale of the Demand for Money and of ‘Money Illusion’” (1950), and “Monnaie et liquidité dans les modèles macroéconomiques et microéconomiques” (1955), as well as in Income, Employment and the Price Level (lectures Marschak gave at Chicago, edited by Fand and Markowitz, 1951a). We examine Marschak’s analysis of money within a broader theory of asset market equilibrium and explore the relation of his work to the monetary and portfolio theories of his doctoral students Markowitz and Patinkin and his colleague Tobin and to the revival of the quantity theory of money by Milton Friedman, a University of Chicago colleague unsympathetic to the methodology of the Cowles Commission.

Léon Walras, Irving Fisher and the Cowles Approach to General Equilibrium Analysis

This paper explores the relationship of Walras’s work to a particularly influential tradition of general equilibrium, that associated with the Cowles Commission for Research in Economics in Colorado in the 1930s and at the University of Chicago from 1939 to 1955, and its successor, the Cowles Foundation, at Yale University from 1955. Irving Fisher introduced general equilibrium analysis into North America with his 1891 Yale dissertation Mathematical Investigations in the Theory of Value and Prices (published 1892) and was responsible in 1892 for the first English translation of a monograph by Walras. Fisher was only able to obtain copies of books by Walras and Edgeworth when his thesis was almost ready for submission, discovering that he had independently reinvented a general equilibrium approach already developed by others, but went beyond Walras in constructing a hydraulic mechanism to simulate computation of general equilibrium and, before Pareto, in using indifference curves. Fisher was closely involved with Alfred Cowles in the Cowles Commission, the Econometric Society and Econometrica in the 1930s, promoting formal mathematical and statistical methods in economics, including drawing attention to the contributions of Walras, Edgeworth and Pareto. The first substantial, systematic work on general equilibrium at the Cowles Commission was in international trade, by Theodore Yntema, research director of the Cowles Commission from 1939 to 1942 and author of A Mathematical Reformulation of the General Theory of International Trade (1932) and by Yntema’s student, Jacob Mosak, author of General Equilibrium Theory in International Trade (1944). A subsequent, much better-known body of work on existence of general equilibrium at Cowles was by Kenneth Arrow and Gerard Debreu (initially independently but leading to a major joint publication) and by Lionel McKenzie, all three associated with the Cowles Commission in Chicago in the early 1950s. After Cowles moved to Yale, the focus of general equilibrium research at the Cowles Foundation was Herbert Scarf’s pioneering work on computable general equilibrium (which he linked to Fisher’s earlier attempt, first presenting his approach in his contribution to Ten Economic Studies in the Tradition of Irving Fisher, 1967). Fisher and then the Cowles Commission were the channel through which Walrasian general equilibrium analysis entered North American economics. This paper is part of a larger history of the Cowles Commission and Foundation, commissioned by the Cowles Foundation.

Jacob Marschak and the Cowles Approaches to the Theory of Money and Assets

Jacob Marschak shaped the emergence of monetary theory and portfolio choice at the Cowles Commission (which he directed from 1943 to 1948, but with which he was involved already from 1937) at the University of Chicago, where he was the doctoral teacher of Leonid Hurwicz, Harry Markowitz and Don Patinkin, and then from 1955 at the Cowles Foundation at Yale University, where he was a senior colleague of James Tobin until moving to UCLA in 1960. Marschak’s later attempts to clarify the concept of liquidity and to emphasize the role of new information for economic behavior date back as far as to his early experiences with hyperinflationary processes in the Northern Caucasus during the Russian Revolution. Marschak came to monetary theory with his 1922 Heidelberg doctoral dissertation on the quantity theory equation of exchange (published in 1924 as “Die Verkehrsgleichung”), and embedded monetary theory in a wider theory of asset market equilibrium in studies of “Money and the Theory of Assets” (1938), “Assets, Prices, and Monetary Theory” (with Helen Makower, 1938), “Role of Liquidity under Complete and Incomplete Information” (1949), “The Rationale of the Demand for Money and of ‘Money Illusion’” (1950), and “Monnaie et liquidite dans les modeles macroeconomiques et microeconomiques” (1955), as well as in Income, Employment and the Price Level (lectures Marschak gave at Chicago, edited by Fand and Markowitz, 1951). We examine Marschak’s analysis of money within a broader theory of asset market equilibrium and explore the relation of his work to the monetary and portfolio theories of his doctoral students Markowitz and Patinkin and his colleague Tobin and to the revival of the quantity theory of money by Milton Friedman, a University of Chicago colleague unsympathetic to the methodology of the Cowles Commission.

Macroeconomic Dynamics at the Cowles Commission from the 1930s to the 1950s

This paper explores the development of dynamic modelling of macroeconomic fluctuations at the Cowles Commission from Roos, Dynamic Economics (Cowles Monograph No. 1, 1934) and Davis, Analysis of Economic Time Series (Cowles Monograph No. 6, 1941) to Koopmans, ed., Statistical Inference in Dynamic Economic Models (Cowles Monograph No. 10, 1950) and Klein’s Economic Fluctuations in the United States, 1921-1941 (Cowles Monograph No. 11, 1950), emphasizing the emergence of a distinctive Cowles Commission approach to structural modelling of macroeconomic fluctuations influenced by Cowles Commission work on structural estimation of simulation equations models, as advanced by Haavelmo (“A Probability Approach to Econometrics,” Cowles Commission Paper No. 4, 1944) and in Cowles Monographs Nos. 10 and 14. This paper is part of a larger project, a history of the Cowles Commission and Foundation commissioned by the Cowles Foundation for Research in Economics at Yale University. Presented at the Association Charles Gide workshop “Macroeconomics: Dynamic Histories. When Statics is no longer Enough,” Colmar, May 16-19, 2019.

The Cowles Commission and Foundation for Research in Economics

Founded in 1932 by a newspaper heir disillusioned by the failure of forecasters to predict the Great Crash, the Cowles Commission promoted the use of formal mathematical and statistical methods in economics, initially through summer research conferences in Colorado and through support of the Econometric Society (of which Alfred Cowles was secretary-treasurer for decades). After moving to the University of Chicago in 1939, the Cowles Commission sponsored works, many later honored with Nobel Prizes but at the time out of the mainstream of economics, by Haavelmo, Hurwicz and Koopmans on econometrics, Arrow and Debreu on general equilibrium, Yntema and Mosak on general equilibrium in international trade theory, Arrow on social choice, Koopmans on activity analysis, Klein on macroeconometric modelling, Lange, Marschak and Patinkin on macroeconomic theory, and Markowitz on portfolio choice, but came into intense methodological, ideological and personal conflict with the emerging “Chicago school.” This conflict led the Cowles Commission to move to Yale in 1955 as the Cowles Foundation, directed by James Tobin (who had declined to move to Chicago to direct it). The Cowles Foundation remained a leader in the more technical areas of economics, notably with Tobin’s “Yale school” of monetary theory, Scarf’s computable general equilibrium, Shubik in game theory, and later Phillips and Andrews in econometric theory but as formal methods in economic theory and econometrics pervaded the discipline of economics, Cowles (like the Econometric Society) became less distinct from the rest of economics. This entry is part of an archivally-based history of the Cowles Commission and Foundation commissioned by the Cowles Foundation.

General Equilibrium Model for an Asymmetric Information Economy Without Delivery Upper Bounds

AbstractIn this paper, we introduce production into the standard general equilibrium model with asymmetric information, which was proposed by Dubey et al. (Cowles Foundation Discussion Paper 2000; Econometrica 2005). In such an economy, there is no rational explanation for producers’ delivery upper bounds while the endowments naturally limit consumers’ deliveries. However, we show that the typical equilibrium allocation of the asymmetric information economy necessarily and substantially depends on such exogenous upper bounds (Example 1 and Theorem 1). In other words, an equilibrium existence theorem without such upper bounds, even if such exists, will typically fail to treat the asymmetric information problem, e.g., the adverse selection problem. Hence, to treat the equilibrium existence problem under the informational asymmetry appropriately, we have to extend the standard model so that the delivery upper bounds need not to be specified explicitly. For this purpose, we propose a quite natural and realistic assumption with respect to the technological condition related to the market delivery, i.e., the existence of some small standardization, commoditization, and/or transaction costs of market deliveries is shown to be sufficient (Theorem 3).

Repeated Bidding Games with Incomplete Information and Bounded Values: On the Exponential Speed of Convergence

We consider the repeated zero-sum bidding game with incomplete information on one side with non-normalized total payoff. De Meyer and Marino [(2005) Continuous versus discrete market game, Cowles Foundation Discussion Paper 1535] and Domansky and Kreps [(2005) Repeated games with asymmetric information and random price fluctuations at finance markets, Proc. Appl. Ind. Math. 12(4), 950–952 (in Russian)] investigated a game [Formula: see text] modeling multistage bidding with asymmetrically informed agents and proved that for this game [Formula: see text] converges to a finite limit [Formula: see text], i.e., the error term is [Formula: see text]. In this paper, we show that for this example [Formula: see text] converges to the limit exponentially fast. For this purpose we apply the optimal strategy [Formula: see text] of insider in the infinite-stage game obtained by Domansky [(2007) Repeated games with asymmetric information and random price fluctuations at finance markets, Int. J. Game Theor. 36(2), 241–257] to the [Formula: see text]-stage game and deduce that it is [Formula: see text]-optimal with [Formula: see text] exponentially small.

How modern economics learned French: Jacques Drèze and the foundation of CORE

The Center of Operations Research and Econometrics (CORE), founded in 1966, was one of the channels through which economic modelling practices were imported from the USA to Europe. Officially modelled after the Cowles Foundation for Economics Research, it reflected Jacques Drèze's broad experiences in the USA during the 1950s when modelling techniques were not yet anchored in disciplines. CORE gained an international reputation, however, through the rather exclusive community of Neo-Walrasian economists represented by Werner Hildenbrand, Jean Gabszewicz, and Gérard Debreu. After this community modified the disciplinary divisions at CORE, the influence of CORE on continental economics occurred mainly through disequilibrium economics, which still represents a “French accent” in modern macroeconomics. At the same time, operations research and econometrics prospered at CORE while receiving scant attention from economists. This essay tells the story of how CORE changed continental economics through the unique career path of its founder, Jacques Drèze.

KOOPMANS IN THE SOVIET UNION: A TRAVEL REPORT OF THE SUMMER OF 1965

Tjalling C. Koopmans, research director of the Cowles Foundation of Research in Economics, was the first US economist after World War II who, in the summer of 1965, travelled to the Soviet Union for an official visit to the Central Economics and Mathematics Institute of the Academy of Sciences of the USSR. Koopmans left hoping to learn from the Soviet economists’ experience with applying linear programming to economic planning. Would his own theories, as discovered independently by Leonid V. Kantorovich, help increase allocative efficiency in a socialist economy? Inspired by a vague notion of universal reason spanning the iron curtain, Koopmans may have even envisioned a research community that transcends the political divide. Yet, he came home having discovered that learning about Soviet mathematical economists might be more interesting than learning from them. On top of that, he found the Soviet scene caught in the same deplorable situation he knew all too well from home: that mathematicians are the better economists. Reconstructing Koopmans’s voyage from a first-person perspective puts the spirit of universal economic knowledge at Cowles to test: Is it capable of establishing a dialogue across the political divide of the Cold War or is it limited to the Western academic cocoon?

Testing explosive behavior in the gold market

This paper examines the explosive behavior in the gold market. Using the generalized sup ADF (GSADF) test introduced by Phillips et al. (Testing for multiple bubbles. Cowles Foundation Discussion Paper No. 1843, 2012), we quantitatively examine the existence of explosive periods in the gold market during the period between 1968 and 2013. The date-stamping strategy associated with the test provides a real-time estimation for the origination and termination dates of each explosive period in the gold market, and several explosive periods, including both the famous 1980 explosion and the most recent 2011 explosion, are identified. Our results also demonstrate that, when multiple explosive periods exist within a specific time interval, the GSADF test is more accurate and effective in detecting them than the approach introduced by Phillips et al. (Int Econ Rev 52(1):201–226, 2011), which is relatively conservative. This paper provides further evidence that gold is the safe haven for assets under huge risk and the gold price reacts to political and economic uncertainties relatively faster than other selected commodities do.

Introduction to: Jet Symposium Issue on 'Dynamic Contracts and Mechanism Design'

The Introduction to the Symposium Issue on “Dynamic Contract and Mechanism Design” of the Journal of Economic Theory provides an overview of the dynamic mechanism design literature. We then introduce the papers that are contained in the Symposium issue and finally conclude by discussing avenues for future research. Several of the papers contained in the Symposium issue were presented at the Economic Theory Workshop of the Cowles Foundation for Research in Economics at Yale University in June 2013.

Introduction to Symposium on Dynamic Contracts and Mechanism Design

The Introduction to the Symposium Issue on “Dynamic Contracts and Mechanism Design” of the Journal of Economic Theory provides an overview of the dynamic mechanism design literature. We then introduce the papers that are contained in the Symposium issue and finally conclude by discussing avenues for future research. Several of the papers contained in the Symposium issue were presented at the Economic Theory Workshop of the Cowles Foundation for Research in Economics at Yale University in June 2013.

The Limits of Inference with Theory: A Review of Wolpin (2013)

This essay reviews Kenneth I. Wolpin's (2013) monograph The Limits of Inference without Theory, which arose from lectures he presented at the Cowles Foundation in 2010 in honor of Tjalling Koopmans. While I readily agree with Wolpin's basic premise that empirical work that eschews the role of economic theory faces unnecessary self-imposed limits relative to empirical work that embraces and tries to test and improve economic theory, it is important to be aware that the use of economic theory is not a panacea. I point out that there are also serious limits to inference with theory: 1) there may be no truly “structural” (policy invariant) parameters, a key assumption underpinning the structural econometric approach that Wolpin and the Cowles Foundation have championed; 2) there is a curse of dimensionality that makes it very difficult for us to elucidate the detailed implications of economic theories, which is necessary to empirically implement and test these theories; 3) there is an identification problem that makes it impossible to decide between competing theories without imposing ad hoc auxiliary assumptions (such as parametric functional form assumptions); and 4) there is a problem of multiplicity and indeterminacy of equilibria that limits the predictive empirical content of many economic theories. I conclude that though these are very challenging problems, I agree with Wolpin and the Cowles Foundation that economists have far more to gain by trying to incorporate economic theory into empirical work and test and improve our theories than by rejecting theory and presuming that all interesting economic issues can be answered by well-designed controlled, randomized experiments and assuming that difficult questions of causality and evaluation of alternative hypothetical policies can be resolved by simply allowing the “data to speak for itself.” (JEL B41, C18)

On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14

This paper starts with a brief description of the introduction of the likelihood approach in econometrics as presented in Cowles Foundation Monographs 10 and 14. A sketch is given of the criticisms on this approach mainly from the first group of Bayesian econometricians. Publication and citation patterns of Bayesian econometric papers are analyzed in ten major econometric journals from the late 1970s until the first few months of 2014. Results indicate a cluster of journals with theoretical and applied papers, mainly consisting of Journal of Econometrics, Journal of Business and Economic Statistics and Journal of Applied Econometrics which contains the large majority of high quality Bayesian econometric papers. A second cluster of theoretical journals, mainly consisting of Econometrica and Review of Economic Studies contains few Bayesian econometric papers. The scientific impact, however, of these few papers on Bayesian econometric research is substantial. Special issues from the journals Econometric Reviews, Journal of Econometrics and Econometric Theory received wide attention. Marketing Science shows an ever increasing number of Bayesian papers since the middle nineties. The International Economic Review and the Review of Economics and Statistics show a moderate time varying increase. An upward movement in publication patterns in most journals occurs in the early 1990s due to the effect of the ‘Computational Revolution’. The paper continues using a visualization technique to connect papers and authors around important empirical subjects such as forecasting in macro models and finance, choice and equilibrium in micro models and marketing, and around more methodological subjects as model uncertainty and sampling algorithms. The information distilled from this analysis shows names of authors who contribute substantially to particular subjects. Next, subjects are discussed where Bayesian econometrics has shown substantial advances, namely, implementing stochastic simulation methods due to the computational revolution; flexible and unobserved component model structures in macroeconomics and finance; hierarchical structures and choice models in microeconomics and marketing. Three issues are summarized where Bayesian and frequentist econometricians differ: Identification, the value of prior information and model evaluation; dynamic inference and nonstationarity; vector autoregressive versus structural modeling. A topic of debate amongst Bayesian econometricians is listed as objective versus subjective econometrics. Communication problems and bridges between statistics and econometrics are summarized. A few non-Bayesian econometric papers are listed that have had substantial influence on Bayesian econometrics. Recent advances in applying simulation based Bayesian econometric methods to policy issues using models from macro- and microeconomics, finance and marketing are sketched. The paper ends with a list of subjects that are important challenges for twenty-first century Bayesian econometrics: Sampling methods suitable for use with big data and fast, parallelized and GPU calculations, complex economic models which account for nonlinearities, analysis of implied model features such as risk and instability, incorporating model incompleteness, and a natural combination of economic modeling, forecasting and policy interventions.

On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14

On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14

Book Reviews

Erin Todd Bronchetti of Swarthmore College reviews, “Finance and the Good Society” by Robert J. Shiller. The Econlit abstract of this book begins: “Examines how finance, as a science, a practice, and a source of economic innovation, can be used to advance the goals of freedom, prosperity, equality, and economic security. Discusses chief executive officers; investment managers; bankers; investment bankers; mortgage lenders and securitizers; traders and marketmakers; insurers; market designers and financial engineers; derivatives providers; lawyers and financial advisers; lobbyists; regulators; accountants and auditors; educators; public goods financiers; policymakers in charge of stabilizing the economy; trustees and nonprofit managers; philanthropists; finance, mathematics, and beauty; categorizing people—financiers versus artists and other idealists; an impulse for risk taking; an impulse for conventionality and familiarity; debt and leverage; some unfortunate incentives to sleaziness inherent in finance; the significance of financial speculation; speculative bubbles and their costs to society; inequality and injustice; problems with philanthropy; the dispersal of ownership of capital; and the great illusion, then and now. Shiller is Arthur M. Okun Professor of Economics at the Cowles Foundation for Research in Economics and Professor of Finance with the International Center for Finance at Yale University.”

Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14

After a brief description of the first Bayesian steps into econometrics in the 1960s and early 70s, publication and citation patterns are analyzed in ten major econometric journals until 2012. The results indicate that journals which contain both theoretical and applied papers, such as Journal of Econometrics, Journal of Business and Economic Statistics and Journal of Applied Econometrics, publish the large majority of high quality Bayesian econometric papers in contrast to theoretical journals like Econometrica and the Review of Economic Studies. These latter journals published, however, a few papers that had a substantial impact on Bayesian research. The journals Econometric Reviews and Econometric Theory published key invited papers and special issues that received wide attention, while Marketing Science shows an ever increasing number of papers since the middle n ineties. The International Economic Review and the Review of Economics and Statistics show a moderate time varying increase. The early nineties indicate an upward movement in publication patterns in most journals probably due to the effect of the ‘Computational Revolution'. Next, a visualization technique is used to connect papers and authors around important theoretical and empirical themes such as forecasting, macro models, marketing models, model uncertainty and sampling algorithms. The information distilled from this analysis shows the names of authors who contribute substantially to particular themes. This is followed by a discussion of those topics that pose interesting challenges for discussion amongst Bayesian econometricians, namely the computational revolution, unobserved component and flexible model structures, choice models, IV models, dynamic models and forecasting. Three issues are summarized where Bayesian and frequentist econometricians differ: Identification, the value of prior information and model evaluation; dynamic inference and nonstationarity; and vector autoregressive versus structural modeling. A major topic of debate amongst Bayesian econometricians is listed as objective versus subjective econometrics and communication problems and bridges between statistics and econometrics are summarized. The paper ends with a list of four important themes that will be a challenge for twenty-first century Bayesian econometrics: Sampling methods which are suitable for parallelization and GPU calculations, complex economic models which can account for nonlinearities, analysis of implied model features such as risk and instability and incorporating model incompleteness in econometric analysis.