Thursday, May 29, 2008

The Importance of Being Right

Day to day, being right is not so important. Goodness knows the average bloviator in academics, talk shows, or the blogosphere is judged more on their delivery, metaphors, who they know, and the popularity of what they are arguing, rather than whether they are right. But posterity has a huge bias towards those who were right, regardless of their methods.

I read Einstein's Luck, and it goes over several prominent scientists, and how they often skewed their empirical work. We see that Pasteur, for example, had good reason to be skeptical of his theory against abiogenesis given the data he had available: he didn't publish his own experimental results contradicting his theory because he believed they were 'errors'. Gregor Mendel fudged his genetics data.

And take the famous confirmation of Einstein following WW1, which was, in some sense, a grand conspiracy. Einstein’s General Theory of Relativity was only a few years old, yet academics were eager to put the nightmare of perhaps the most pointless large war in history behind them, and show the common bond of the old adversaries. Proving a German’s theory correct was perfect for the cause. The null hypothesis, set up by standard Newtonian Physics, was that there should by a 0.85 arc-second deflection in light from stars behind the sun, while Einstein predicted a 1.7 arc-second deflection.

In 1919, an eclipse offered a chance to measure the degree to which the sun bended the rays of light from far off stars, a prediction of General Relativity. Famous English physicist Arthur Eddington was a World War I pacifist, and so had a predisposition to mend the rift between German and English academics. He made a trek to the island of Principe, off the coast of West Africa, one of the best locations for observing the eclipse.

Eddington did not get a clear view of the stars in 1919 because it was cloudy during most of the eclipse. But he used a series of complex calculations to extract the deflection estimate from the data, and came up with an estimate of 1.6 arc-seconds from his African voyage. Data from two spots in Brazil were for 1.98 and 0.93. Eddington threw out the lower measurement because he was concerned that heat had affected the mirror used in the photograph, and so the standard error too large. Thus, his efforts proved Einstein's theory was correct.

Subsequently, scientists have concluded that Eddington’s equipment was not sufficiently accurate to discriminate between the predicted effects of the rival gravitational theories. In other words, Eddington’s reported standard errors were too low, and the point estimate was too high, given the data he had. Yet for decades this experiment was cited as the proof of the General Theory, but even in the 1960’s when they tried to redo the experiment given a similar eclipse and methodology, they found they could not.

In the late 1960’s, using radio frequencies as opposed to pictures from an eclipse, Eddington’s results were, ultimately, confirmed. That is, he was right, but he still tendentiously presented his data based on his prejudices, and a true scientist without any biases would have been more skeptical of the theory that light is deflected by mass until then.

In contrast, the early works supporting the CAPM by Fama and MacBeth (1973) and Black, Jensen and Scholes (1973), were used as proof of the success of the CAPM for decades: beta was positively related to stock returns. But, with better data, more data, better empirical methods, this relationship appears now to go the other way. A true theory should become more obvious with more data. I think this suggests that, unlike Einstein, Pasteur, and Mendel, the theory here is wrong, and all the Stochastic Discount Factor and Arbitrage Pricing Theory extensions are merely prolonging the life of what will be seen as a theory built on a flawed assumption. History is forgiving of tendentious tweaks to the data when you are right, but it quickly forgets you when wrong (see exposition on the theory of why it's wrong in Why Risk is Not Related to Return, and practical implications including beta arbitrage, and minimum variance portfolios).

It is important to have correct prejudices.

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