No abstract

We thank Barclays Bank PLC for partial financial support of this project. There exists a collaboration with Barclays Bank PLC on ways through which the Cyclically Adjusted Price Earnings (CAPE) ratio, a valuation measure that also plays a prominent role in this paper, may be implemented in an investment. The views herein are those of the authors', and do not necessarily reflect the views of Barclays Bank PLC nor those of the National Bureau of Economic Research. At least one co-author has disclosed a financial relationship of potential relevance for this research. Further information is available online at http://www.nber.org/papers/w20370.ack NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

We construct a price, dividend, and earnings series for the Industrials sector, the Utilities sector, and the Railroads sector from the beginning of the 1870s until the beginning of the year 2013 from primary sources. To infer about mispricings in the sector markets over more than a century, we investigate the forecasting power of the Cyclically Adjusted Price-Earnings (CAPE) ratio 1 for these sectors. With regard to the CAPE ratio, which has originally been devised and employed by Campbell and Shiller (1988, 1998, 2001) as well as Shiller (2005), we define a methodological improvement to this ratio to not only be robust to inflationary changes, but also to changes in corporate payout policy. We then update the original evidence from Campbell and Shiller (1998, 2001) of the return predictability of the CAPE ratio for the overall stock market and furthermore extend this evidence to the three aforementioned sectors individually. Whereas this part of our analysis focuses on each sector of the US economy in isolation, we subsequently construct an indicator from the CAPE ratio that enables us to perform valuation comparisons across sectors. In addition to establishing the prediction of subsequent return differences based on differences in the CAPE-based valuation indicator, we also suggest a hypothetical, historical, and simple value investment strategy that rotates between the three sectors based on the valuation signals derived from the CAPE-based indicator, generating slightly more than 1.09% annualized, inflation-adjusted excess total return over the market benchmark during a period of nearly 110 years.

We conduct two experiments where subjects make a sequence of binary choices between risky and ambiguous binary lotteries. Risky lotteries are defined as lotteries where the relative frequencies of outcomes are known. Ambiguous lotteries are lotteries where the relative frequencies of outcomes are not known or may not exist. The trials in each experiment are divided into three phases: pre-treatment, treatment and post-treatment.The trials in the pre-treatment and post-treatment phases are the same. As such, the trials before and after the treatment phase are dependent, clustered matched-pairs, that we analyze with the alternating logistic regression (ALR) package in SAS. In both experiments, we reveal to each subject the outcomes of her actual and counterfactual choices in the treatment phase. The treatments differ in the complexity of the random process used to generate the relative frequencies of the payoffs of the ambiguous lotteries. In the first experiment, the probabilities can be inferred from the converging sample averages of the observed actual and counterfactual outcomes of the ambiguous lotteries. In the second experiment the sample averages do not converge.If we define fictive learning in an experiment as statistically significant changes in the responses of subjects before and after the treatment phase of an experiment, then we expect fictive learning in the first experiment, but no fictive learning in the second experiment. The surprising finding in this paper is the presence of fictive learning in the second experiment. We attribute this counterintuitive result to apophenia: "seeing meaningful patterns in meaningless or random data." A refinement of this result is the inference from a subsequent Chi-squared test, that the effects of fictive learning in the first experiment are significantly different from the effects of fictive learning in the second experiment.JEL Classification: C23, C35, C91, D03

This paper is an exposition of an experiment on revealed preferences, where we posite a novel discrete binary choice model. To estimate this model, we use general estimating equations or . This is a methodology originating in biostatistics for estimating regression models with correlated data. In this paper, we focus on the motivation for our approach, the logic and intuition underlying our analysis and a summary of our findings. The missing technical details, including proofs, are in the working paper by Bunn, et al (2013).