(This web page, in part, assumes knowledge from the page the compelling Real DJIA, 1924-now.)
In a 3/7/97 article in The Wall Street Journal re. the then recent use in a 12/5/96 speech of the term "irrational exuberance" by Alan Greenspan, chairman of the Federal Reserve Board in Washington, the authors wrote: "Fed chairmen usually don't say much about the stock market. In fact, the only notable earlier Fed warnings date to 1929 and 1965." (The Fed was founded in 1913.) Other reports agree -.
In a discussion of these three "warnings that the stock market was overpriced", Shiller  wrote "It appears that Fed chairmen reserve public statements about market pricing for periods of extreme mispricing.".
Evidently, in the more than 90 years since the Fed was founded in 1913, a Fed chairman has only 3 times publicly warned that the stock market was overpriced.
Each of these three warnings occurred early in the month and is therefore associated with the monthly average market datum of the preceding month: i.e., 1/29, 5/65, and 11/96. All these three warnings are shown on the Real Dow plot above, and they are seen to lie essentially on a straight line, the 3 Warnings Line.
Considering the source, the rarity, and the evident timeliness of these three warnings, I readily take them seriously as quantitative judgements. One would then like to know 'how much overpriced begot a warning' (overpriced as Fed-judged, of course). The Fed hasnt said.
I aim to get an idea of 'how much overpriced begot a warning' (overpriced as Fed-judged, of course). I suppose that 'they' warned when current stock prices were viewed as unsustainably higher than the 'ought to be' level by some certain margin. To get this 'some certain margin', I will ratio, over the 1/29-11/96 interval that includes all these three warnings, the (inferred) average warning level to the average 'ought to be' level taken as equal to the average actual Real Dow.
Assuming that the straight line through all these three warnings also reflects warning levels for intermediate times, the average warning level during the 1/29-11/96 interval was 43.20. The average Real Dow during the 1/29-11/96 interval was 23.64. The 43.20/23.64 ratio is 1.83.
So, the estimated 'how much overpriced begot a warning' (overpriced as Fed-judged, of course) is: overpriced by a multiplying factor of 1.83; or, current = 1.83 * 'ought to be'; or, 'ought to be' = current/1.83. The three warnings, each divided by 1.83, lie on the straight line, 3 Warnings Line/1.8, also shown on the plot. (The latest Real Dow is 107.5 for 9/14, which is 1.58 times the extrapolated 3 Warnings Line value of 67.9, and which is 2.89 times the extrapolated 3 Warnings Line/1.8 value of 37.2.)
(Proceeding as above in this section, but using the Real S&P, gives a similar factor of 1.74 instead of 1.83. Specifically: Real (inflation-corrected) S&P Composite Stock Price Index data were taken from Shiller and plotted; the three warnings were close to lying on a straight line, with R-squared = 0.987.)
 Christina Duff and David Wessel, Small Investors' Advice to Greenspan: Butt Out, The Wall Street Journal, March 7, 1997, p. C1.
 While this shrugging of shoulders was also seen the last two times a Fed chairman warned about an overheated stock market -- 1929 and 1965 -- a steep crash happened soon after. in Neal Goldsmith, Irrational exuberance and the future of the 'Net, San Francisco Business Times, Week of March 31, 1997, at http://sanfrancisco.bizjournals.com/sanfrancisco/stories/1997/03/31/editorial3.html
 In the past, Fed chairmen have rarely cast doubt on stock market values, and have never stuck to their guns after they were criticized. But they have been right. The most recent occurrence came on June 1, 1965, when William McChesney Martin compared that era to the 1920's. The market fell for a few weeks but then rallied until February 1966, when the Dow Jones industrial average first approached 1,000. It was still there 16 years later. The other time was in 1929, when the Fed complained on Feb. 2 that banks were using its money to finance stock market speculation. in Floyd Norris, All Hail The Great Greenspan Bull Market, The New York Times, July 6, 1997.
 It is extremely rare for a Federal Reserve Chairman to warn investors about the stock market. This has happened only twice before in this century (1929, 1965), and in both cases, a severe bear market followed that required more than 20 years to breakeven after inflation. in David Tice, Is the current stock market "a bubble"?, Forbes.com, August 19, 1997, at
 Robert J. Shiller, Irrational Exuberance, Copyright © 2000 by Princeton University Press, p. 225.
 Robert J. Shiller, at http://aida.econ.yale.edu/~shiller/data.htm