Recent research has shown the importance of time horizons in models of learning in finance. The dynamics of how agents adjust to believe that the world around them is stationary may be just as crucial in the convergence to a rational expectations equilibrium as getting parameters and model specifications correct in the learning process. This paper explores the process of this evolution in learning and time horizons in a simple agent-based financial market. The results indicate that, although the simple model structure used here replicates usual rational expectations results with long-horizon agents, the route to evolving a population of both long- and short-horizon agents to long horizons alone may be difficult. Furthermore, populations with both short- and long-horizon agents increase return variability, and leave patterns in volatility and trading volume similar to actual financial markets.

Previous studies investigating threshold behavior in real-exchange-rate and price difference data have used rather ad hoc statistical methods and have focused on univariate threshold models for relative prices. We utilize a general multivariate threshold cointegration model and develop a systematic testing and estimation strategy for this model, building on the work of others. Using Monte Carlo experiments, we systematically compare the use of univariate and multivariate techniques for testing threshold cointegration, estimating various threshold models, and testing specifications. We apply our methodology to a large set of U.S. disaggregated CPI data. We find evidence of threshold cointegration mainly for tradable goods. However, the type of threshold nonlinearity that we find generally does not support the transaction-cost view of commodity arbitrage.

Paul A. Volcker has spent most of his life in public service, at the Treasury under President Kennedy (1962–1965) and then as Undersecretary for Monetary Affairs under President Nixon (1969–1974), as President of the Federal Reserve Bank of New York (1975–1979), and finally as Chairman of the Board of Governors of the Federal Reserve System under both President Carter and President Reagan (1979–1987). Born in 1927, his world view was formed by childhood experience of the Great Depression and World War II, times of great national trial that led ultimately to recommitment and reconstruction. He went into public service in order to be a part of the rebuilding effort, but it was his fate instead to be involved mainly in managing pressures that would ultimately lead to the breakdown of the Bretton Woods system internationally and the Glass–Steagall banking system domestically. Consequently, there is some sadness today when he looks back on his career, but there is also a sense of accomplishment. In spite of everything, there was no depression and there was no world war. The possibility and hope for progress in years to come remains alive.

The interview took place in Volcker's office at Rockefeller Center in New York City. His fourth-floor windows look out over the sunken plaza to the gold-leafed statue of Prometheus stealing fire from the gods, and then on farther to the elegant GE building, which is familiar to anyone who has visited New York. Over the front entrance it is just possible to see the inscription adapted from Isaiah 33:6, “Wisdom and Knowledge shall be the stability of thy times.” It strikes me as an appropriate inscription for the building, reminding one that this most beautiful complex was built in the years of the Great Depression. Today, with the forthcoming interview in mind, it reminds me also of the stakes involved in the conduct of monetary policy.

We investigate the size and power properties of the AH test of evolutionary change. This involves examining whether the size results are sensitive to both the number of individual frequencies estimated and the spectral shape adopted under the null hypothesis. The power tests examine whether the test has good power to detect shifts in both spectral position (variance) and spectral shape (autocovariance structure).

“His views have had as much, if not more, impact on the way we think about monetary policy and many other important economic issues as those of any person in the last half of the twentieth century.” These words in praise of Milton Friedman are from economist and Federal Reserve Chair Alan Greenspan. They are spoken from a vantage point of experience and knowledge of what really matters for policy decisions in the real world. And they are no exaggeration. Many would say they do not go far enough.

It is a rare monetary policy conference today in which Milton Friedman's ideas do not come up. It is a rare paper in macroeconomics in which some economic, mathematical, or statistical idea cannot be traced to Milton Friedman's early work. It is a rare student of macroeconomics who has not been impressed by reading Milton Friedman's crystal-clear expositions. It is a rare democrat from a formerly communist country who was not inspired by Milton Friedman's defense of a market economy written in the heydays of central planning. And it is a rare day that some popular newspaper or magazine around the world does not mention Milton Friedman as the originator of a seminal idea or point of view.

Any one of his many contributions to macroeconomics (or rather to monetary theory, for he detests the term macroeconomics) would be an extraordinary achievement. Taken together they are daunting:

[bull ] permanent income theory;

[bull ] natural rate theory;

[bull ] the case for floating exchange rates;

[bull ] money growth rules;

[bull ] the optimal quantity of money;

[bull ] the monetary history of the United States, especially the Fed in the Great Depression, not to mention contributions to mathematical statistics on rank-order tests, sequential sampling, and risk aversion, and a host of novel government reform proposals from the negative income tax, to school vouchers, to the flat-rate tax, to the legalization of drugs.

Milton Friedman is an economist's economist who laid out a specific methodology of positive economic research. Economic experts know that many current ideas and policies—from monetary policy rules to the earned-income tax credit—can be traced to his original proposals. He won the Nobel Prize in economics in 1976 for “his achievements in the field of consumption analysis, monetary history and theory and for his demonstration of the complexity of stabilization policy.” Preferring to stay away from formal policy-making jobs, he has been asked for his advice by presidents, prime ministers, and top economic officials for many years. It is in the nature of Milton Friedman's unequivocally stated views that many disagree with at least some of them, and he has engaged in heated debates since graduate school days at the University of Chicago. He is an awesome debater. He is also gracious and friendly.

Born in 1912, he grew up in Rahway, New Jersey, where he attended local public schools. He graduated from Rutgers University in the midst of the Great Depression in 1932. He then went to study economics at the University of Chicago, where he met fellow graduate student Rose Director whom he later married. For nearly 10 years after he left Chicago, he worked at government agencies and research institutes (with one year visiting at the University of Wisconsin and one year at the University of Minnesota) before taking a faculty position at the University of Chicago in 1946. He remained at Chicago until he retired in 1977 at the age of 65, and he then moved to the Hoover Institution at Stanford University.

I have always found Milton and Rose to be gregarious, energetic people, who genuinely enjoy interacting with others, and who enjoy life in all its dimensions, from walks near the Pacific Ocean to surfs on the World Wide Web. The day of this interview was no exception. It took place on May 2, 2000, in Milton's office in their San Francisco apartment. The interview lasted for two-and-a-half hours. A tape recorder and some economic charts were on the desk between us. Behind Milton was a floor-to-ceiling picture window with beautiful panoramic views of the San Francisco hills and skyline. Behind me were his bookcases stuffed with his books, papers, and mementos.

The interview began in a rather unplanned way. When we walked into his office Milton started talking enthusiastically about the charts that were on his desk. The charts—which he had recently prepared from data he had downloaded from the Internet—raised questions about some remarks that I had given at a conference several weeks before—which he had read about on the Internet.

As we began talking about the charts, I asked if I could turn on the tape recorder, since one of the topics for the interview was to be about how he formulated his ideas—and a conversation about the ideas he was formulating right then and there seemed like an excellent way to begin the interview. So I turned on the tape recorder, and the interview began. Soon we segued into the series of questions that I had planned in advance (but had not shown Milton in advance). We took one break for a very pleasant lunch and (unrecorded) conversation with his wife Rose before going back to “work.” After the interview, the tapes were transcribed and the transcript was edited by me and Milton. The questions and answers were rearranged slightly to fit into the following broad topic areas:

[bull ] money growth, thermostats, and Alan Greenspan;

[bull ] causes of the great inflation and its end;

[bull ] early interest in economics;

[bull ] graduate school and early “on-the-job” training;

[bull ] permanent income theory;

[bull ] return of monetary economics;

[bull ] fiscal and monetary policy rules;

[bull ] use of models in monetary economics;

[bull ] use of time-series methods;

[bull ] real business-cycle models, calibration, and detrending;

[bull ] natural rate hypothesis;

[bull ] role of debates in monetary economics;

[bull ] capitalism and freedom today;

[bull ] monetary unions and flexible exchange rates.

We extend the conventional cointegrated VAR model to allow for general nonlinear deterministic trends. These nonlinear trends can be used to model gradual structural changes in the intercept term of the cointegrating relations. A general asymptotic theory of estimation and statistical inference is reviewed and a diagnostic test for the correct specification of an employed nonlinear trend is developed. The methods are applied to Finnish interest-rate data. A smooth level shift of the logistic form between the own-yield of broad money and the short-term money market rate is found appropriate for these data. The level shift is motivated by the deregulation of issuing certificates of deposit and its inclusion in the model solves the puzzle of the “missing cointegration vector” found in a previous study.

The standard approach to modeling consumption/saving problems is to assume that the decisionmaker is solving a dynamic stochastic optimization problem. However, under realistic descriptions of utility and uncertainty, the optimal consumption/saving decision is so difficult that only recently have economists managed to find solutions, using numerical methods that require previously infeasible amounts of computation. Yet, empirical evidence suggests that household behavior conforms fairly well with the prescriptions of the optimal solution, raising the question of how average households can solve problems that economists, until recently, could not. This paper examines whether consumers might be able to find a reasonably good rule-of-thumb approximation to optimal behavior by trial-and-error methods, as Milton Friedman proposed long ago. We find that such individual learning methods can reliably identify reasonably good rules of thumb only if the consumer is able to spend absurdly large amounts of time searching for a good rule.

We study comparative statics results for the steady-state monetary equilibria of a simple random matching model of money with endogenous prices and no extrinsic uncertainty. Some of the results appear counterintuitive (both when take-it-or-leave-it offer or when Nash–Rubinstein bargaining is used in the model). Consistency of the equilibrium expectations causes the partial equilibrium intuitions to be reversed. We then proceed to apply the new insights to the analysis of sunspot equilibria in these type of models of bilateral trade with money.

We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for theselearning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time-series data for U.S. stock returns and per-capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.

Clive W.J. Granger has summarized his personal viewpoint on testing for causality in numerous articles over the past 30 years and has outlined what he considers to be a useful operational version of his original definition of Granger causality, which he notes is partially alluded to in the Ph.D. dissertation of Norbert Wiener. This operational version of Granger causality is based on a comparison of the one-step-ahead predictive ability of competing models. However, Granger concludes his discussion by noting that it is common practice to test for Granger causality using in-sample F-tests. The practice of using in-sample type Granger causality tests continues to be prevalent. In this paper we develop simple (nonlinear) out-of-sample predictive ability tests of the Granger non-causality null hypothesis. In addition, Monte Carlo experiments are used to investigate the finite sample properites of the test. An empirical illustration shows that the choice of in-sample versus out-of-sample Granger causality tests can crucially affect the conclusions about the predictive content of money for output.

This paper analyzes the joint time-series properties of the level and volatility of expected excess stock returns. An unobservable dynamic factor is constructed as a nonlinear proxy for the market risk premia with its first moment and conditional volatility driven by a latent Markov variable. The model allows for the possibility that the risk–return relationship may not be constant across the Markov states or over time. We find an overall negative contemporaneous relationship between the conditional expectation and variance of the monthly value-weighted excess return. However, the sign of the correlation is not stable, but instead varies according to the stage of the business cycle. In particular, around the beginning of recessions, volatility rises substantially, reflecting great uncertainty associated with these periods, while expected return falls, anticipating a decline in earnings. Thus, around economic peaks there is a negative relationship between conditional expectation and variance. However, toward the end of a recession expected return is at its highest value as an anticipation of the economic recovery, and volatility is still very high in anticipation of the end of the contraction. That is, the risk–return relation is positive around business-cycle troughs. This time-varying behavior also holds for noncontemporaneous correlations of these two conditional moments.

A genetic algorithm (GA) is used to model learning in a financial model similar to the Grossman–Stiglitz model. Individuals need to learn how to use a signal, how to make an inference about a signal from a market-clearing price, and whether or not a signal is worth acquiring. We provide examples in which the GA does and does not converge to the rational expectations equilibrium. Similar to earlier results, the behavior depends heavily on the rate of experimentation or mutation in the GA and the size of the risky-asset supply noise in the economy.