Economist Robert Shiller, in 2005, described the rapid rise of housing prices as a bubble and warned that prices could fall by 40 per cent.
Five years later, with home prices well on the way to fulfilling Dr Shiller's prediction, economist Eugene Fama said he still did not believe there had been a bubble.
"I don't even know what a bubble means," said Dr Fama, author of the theory that asset prices perfectly reflect all available information. "These words have become popular. I don't think they have any meaning."
The two men, leading proponents of opposing views about the rationality of financial markets - a dispute with important implications for investment strategy, financial regulation and economic policy - were joined in an unlikely union this week as winners of the Nobel prize in economic science.
Dr Fama's seminal theory of rational, efficient markets inspired the rise of index funds and contributed to the decline of financial regulation. Dr Shiller, perhaps his most influential critic, assembled evidence of irrational, inefficient behaviour and gained a measure of fame by predicting the fall of stock prices in 2000 as well as the housing crash that began in 2006.
They will share the award with US economist Lars Peter Hansen, who developed a method of statistical analysis to evaluate theories about price movements now widely used by other social scientists.
The three economists, who worked independently, were described as collectively illuminating the workings of financial markets by showing that stock and bond prices move unpredictably in the short term but with greater predictability over longer periods. The prize committee said these findings showed that markets were moved by a mix of rational calculus and irrational behaviour.
Dr Fama and Dr Hansen are professors at the University of Chicago, known as the home of free-market economics; Dr Shiller is a professor at Yale University. Their work "laid the foundation for the understanding of asset prices", said a statement from the Royal Swedish Academy of Sciences, which awards the annual prize.
Yet, in jointly honouring the work of Dr Fama and Dr Shiller, the prize highlighted how far economics remains from agreeing on the answer to a basic question: How do markets work?
"It encapsulates the state of modern economics," said Justin Wolfers, an economist at the University of Michigan. "We have big, important questions that remain largely open and we have giants bringing evidence to bear. And the answer turns out to be more complicated than [are markets efficient or not]."
The dispute is not merely academic. The deregulation of financial markets, beginning in the 1980s, was justified by the view that markets are rational and efficient. Complacence about rising home prices in the 2000s similarly reflected the view that prices are inherently rational.
After the crisis, the work of Dr Shiller and other proponents of behavioral economics - the integration of psychology into economic models - has been influential in shaping an intensification of financial regulation. And US Federal Reserve officials are now debating whether bubbles can be identified and when they should be popped.
Dr Fama, 74, was honoured for showing in the 1960s that asset prices are "extremely hard to predict over short horizons". His theory basically asserted, in the words of economist Burton Malkiel, that "a blindfolded monkey throwing darts at a newspaper's financial pages could select a portfolio that would do just as well as one carefully selected by experts".
It has been repeatedly validated. And while many on Wall Street still thrive by claiming they can offer investments that consistently beat the market averages, Dr Fama has influenced the way millions invest, contributing to the popularity of index funds that hold broad, diversified baskets of equities.
Dr Shiller, 67, introduced in the early 1980s an important limitation on the idea that markets operate efficiently. He showed that the volatility of stock prices was greater than the volatility in corporate dividends. Moreover, he found that some of those irrational deviations fell into predictable patterns.
Dr Fama is among the economists who have since documented other patterns of predictable price movements, although he explains these patterns as a form of compensation for the greater risk associated with some assets.
Dr Shiller, by contrast, has argued that the predictability of prices reflects irrational but repeating patterns in human behaviour. He wrote in Market Volatility, published in 1989, that the assertion stock prices were rational was "one of the most remarkable errors in the history of economic thought".