Zellner: Frankly, I don’t believe that many of us are expert in the philosophy of science and thus sometimes our disagreements on concepts of probability, causality, axiom systems, and so on are not well founded and more emotional than rational. What saves the day, I think, are pragmatic considerations. For example, we take a problem and work it from the Bayesian and non-Bayesian points of view and compare solutions. If one’s better than the other, I’ll use the better solution.

Aczel: You’ve been very active in the Bayesian Society; tell us what is currently happening with the group.

Zellner: We just had the first world meeting of the International Society for Bayesian Analysis (ISBA) with over 200 attending sessions on Friday and Saturday (August 93). Stu Hunter, President of ASA, addressed the banquet and wished the group well. As I mentioned earlier, we concentrated on Bayesian analysis in the natural, biological and social sciences as well as on technical statistical aspects of Bayesian analysis. We had sessions on Bayesian analysis in astronomy, physics, psychology, econometrics, the earth sciences and many other areas. In the earth sciences, a paper on earthquakes was featured, quite appropriate for a meeting held in San Francisco. There was also a session on Bayesian analysis on Wall Street. Jose Quintana, a vice president at Chase-Manhattan Bank in New York, reported on his work using Bayesian time series analysis techniques to track stock prices and form portfolios. Also, workers at the investment company Goldman-Sachs are employing Bayesian portfolio analysis to help clients with their investment decisions. In this and the other areas that I mentioned, workers are employing Bayesian techniques to learn from data, make decisions, and predict. In many of the papers presented, the performance of Bayesian and non-Bayesian techniques was compared. Also, we had a number of sessions devoted to development of new Bayesian statistical techniques. We’re looking forward to having a good meeting in Alicante at a resort hotel. We’ll work hard and also have a good time. As you know, the old saying is that Bayesians have more fun.

Aczel: But some people would say that they’re still stuck with their priors, right?

Zellner: Oh, that’s been mentioned before. Usually, that’s what people say, "stuck," but what they don’t realize is that in many problems in business, engineering, and other areas, people use judgement. Of course, if you don’t have data and have to make decisions and forecasts, judgement is all that you have. By use of priors, we are just formalizing, and hopefully improving, what is already being done. If you’re in business and you don’t have good judgement, you’re out of business very quickly. Thus engineers, businessmen, scientists, and policy makers have background information that they want to formalize and use to solve all kinds of problems. The prior helps them to achieve this goal.

Aczel: Would the Bayesian approach give you some edge in forecasting that would give you an advantage over somebody else in the sense that your forecast of tomorrow’s price may be better than anybody else’s?

Zellner: Well, as I said before, forecasting stock prices well is very hard. But there are many who do forecast. For example, Jose Quintana, a vice president at the Chase-Manhattan Bank in New York, reported (at the International Society for Bayesian Analysis) on his use of Bayesian state-space models for forecasting returns in world markets and the use of the forecasts in forming portfolios. He has compared his forecasts with those provided by the traditional random walk models, and so on.

Aczel: How does he do in comparison with random walk forecasts?

Zellner: He thinks that he does better. You can ask him for his papers and judge for yourself. In our work on forecasting growth rates of real GNP or GDP for eighteen countries, we definitely can beat random walk model forecasts. In this work, we have used Bayesian shrinkage forecast techniques. Use of the (prior) information that the countries’ coefficient vectors are not too far different in value has improved our forecasts. Many others have also found this to be the case.

Aczel: What is this shrinkage? Do you reduce the standard error somehow?

Zellner: You are essentially pulling in outlying forecasts toward a meanlike forecast. In terms of overall performance, this gives you improvement in the overall countries’ mean square error of forecast, but not necessarily for each and every country. And in empirical forecasting year by year, you can see the effect when you do the calculations. In an article that I wrote with Franz Palm, we tried to explain why a simple average of forecasts would work better than individuals’ forecasts. It may be that individual biases are being averaged out by the simple averaging.

Aczel: How about if they are all biased?

Zellner: That’s what probably happened in 1982. The forecasters didn’t expect a change in policy that probably produced the –2.5 percent growth rate in the U.S. economy. Many forecasts were in the vicinity of (positive) 2 percent, perhaps all biased upward because of a lack of information about a policy change. However, my colleague Walter Fackler somehow came up with a December 1981 forecast for 1982 of –1.1 percent or –1.2 percent GNP growth. On checking his annual forecasts against those of the Blue Chip Company sample, his RMSE was somewhat smaller. However, as Steven McNees of the Federal Reserve Bank of Boston has shown, no single forecaster in the Blue Chip Company sample has beaten the simple averages on all the variables being forecasted. That simple averages of forecasts can perform that well in actual forecasting is remarkable.

Aczel: Going back to the philosophy of science for a moment and to statistics and economics, what is your view? Do you favor applications first and theory second?

Zellner: Sometimes the theory comes first and the applications later, or as in the Stein shrinkage problem, the applications were there in the 1920s and the theory came later. I do not know whether he knew about these applications. In current research, theorists are finding it difficult to produce good, dependable macroeconomic theory. Thus, we have developed relatively simple models that forecast reasonably well and then determine which macroeconomic theories can explain why. Here we are going from the application to the theory. In physics, many times experiments produce unusual results that challenge theorists. For example, no ether drift in the Michelson-Morley experiment that Einstein explained later after attempts by Lorenz and others. Thus sometimes you get the empirical result and then the theoretical result or new statistical method. Other times, the theory comes first and the empirical validation comes later. Another thing that is important in this area is unusual facts and what Huxley called a tragedy of science, namely the destruction of a beautiful hypothesis or theory by an ugly fact.

Aczel: Hit by the real world…

Zellner: That’s right. I think that we need to produce more unusual and ugly facts since this prompts many people to think about new theories to explain them. For example, the fact that there was no ether drift was unusual. In statistics, there isn’t much guidance with respect to methods for producing unusual and ugly facts. It’s an area that needs more attention in my opinion. Many of the Nobel prizewinners in economics, including Friedman, Kuznets, Modigliani, Tobin, and others produced new theories of consumption and saving to explain Kuznet’s unusual and ugly fact. It’s very important to produce unusual facts. In an essay in my book, Basic Issues in Econometrics, I put forward eight procedures for producing unusual facts. I don’t see this topic emphasized in textbooks.

Aczel: You think it is important?

Zellner: Yes, very important.

Aczel: Tell us about yourself, your early days and what attracted you to different areas, statistics and others.

Zellner: I received a PhD at Berkely years ago. My brother, Norman, did a PhD at Berkeley too, in agricultural economics, while I did mine in economics. I did my undergraduate work at Harvard and got a degree in physics. I took an introductory course in economic statistics and several courses in economics but found courses in physics and math more appealing. After my undergraduate work, I spent a summer working as a physicist at the Naval Ordnance Testing Station at Inyokern on the Mojave Desert in California before beginning graduate work in physics at Berkeley. My brother and his friends in agricultural economics were working on interesting problems using econometric and statistical methods that were of great interest to me. So, I decided to switch to economics with special emphasis on econometrics and statistics. Ever since, I’ve taught econometrics and economic statistics, first at the University of Washington in Seattle, then at the University of Wisconsin in Madison, and since 1966 at the University of Chicago. It turned out that working in econometrics and statistics has been quite enjoyable and rewarding, my cup of tea, you might say.