Discussion Paper

No. 2015-38 | May 29, 2015
Knightian Uncertainty and Stock-Price Movements: Why the REH Present-Value Model Failed Empirically


Macroeconomic models that are based on either the rational expectations hypothesis (REH) or behavioral considerations share a core premise: all future market outcomes can be characterized ex ante with a single overarching probability distribution. This paper assesses the empirical relevance of this premise using a novel data set. We find that Knightian uncertainty, which cannot be reduced to a probability distribution, underpins outcomes in the stock market. This finding reveals the full implications of Robert Shiller’s ground-breaking rejection of the class of REH present-value models that rely on the consumption-based specification of the risk premium. The relevance of Knightian uncertainty is inconsistent with all REH models, regardless of how they specify the market’s risk premium. Our evidence is also inconsistent with bubble accounts of REH models’ empirical difficulties. We consider a present-value model based on a New Rational Expectations Hypothesis, which recognizes the relevance of Knightian uncertainty in driving outcomes in real-world markets. Our novel data is supportive of the model’s implications that rational forecasting relies on both fundamental and psychological factors.

JEL Classification:

E44, G12


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Cite As

Roman Frydman, Michael D. Goldberg, and Nicholas Mangee (2015). Knightian Uncertainty and Stock-Price Movements: Why the REH Present-Value Model Failed Empirically. Economics Discussion Papers, No 2015-38, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2015-38

Comments and Questions

Romar Correa - paper by Frydman, Godlberg, Mangee
June 05, 2015 - 08:31

Congratulations, Frydman, Goldberg and Mangee (FGM) on a fine paper. What follows is an attempt to clear the air for me, at least. I begin with the conflation of the efficient markets hypothesis with the REH in the third paragraph. It is the former that is the joint hypothesis ...[more]

... although there is the well known connection with a form of the REH. In the beginning, before the REH, was the neoclassical model of capital asset pricing and FGM have no quarrel with it. With both REH and NREH, the fundamentals are captured in the probability distribution Ft. Let me call this the objective distribution. Agents will have their own subjective distributions, but, recalling the EMH again, the ratex practitioner would assume that agents use relevant information instantaneously and costlessly. The information set, FGM’s νt, includes surprises the market may throw up. In an expectations sense, the two distributions converge. FGM would have it otherwise and proceed to formalize their ideas on page 8. It may be just me but I was confused by the movement from equations (1) to (2). What does the additional subscript to the u term in (2) mean? Is (2) no more than a forecasting error that stubbornly resists extinction by the expectations operator?
A probability distribution is an encapsulation of the past and the present. Future date-state configurations are captured in the Arrow-Debreu model. Positioned in the present, the model-builder will construct a tree with branches extending outwards. In each period, and in the real world, we are bombarded with novelty. Our PDFs will accordingly be updated. A PDF like Ft will be changed with a change of production function.
I was also puzzled by equations (5) and (6). The left-hand side of (5) is a characterization of uncertainty. In the absence of uncertainty, upt would be zero. The right-hand side is the difference in the premia of the bulls and bears which would be equal, in magnitude, in that case. I am not sure of the uncertainty tag attached to them as well later but, in (6), are not bulls and bears defined by their responses to the magnitude and sign of the time-varying gap? What need of the gammas?

Roman Frydman, Michael D. Goldberg, and Nicholas Mangee - FGM-Response to Romar Correa
July 28, 2015 - 19:11

Thank you Romar Correa for your useful comments. In the attachment, we respond to them. We also attach a revised paper that incorporates your comments to our response to referee 1.

Anonymous - Referee Report 1
June 29, 2015 - 12:15

The paper focuses on a well defined and of course extremely relevant issue, it is well written, clear, readable. I think the paper can be shortened and some repetitions avoided. For instance there are repeated references to work on REH models in which the probability distribution characterising outcomes changes over ...[more]

... time. Having said that, I am not entirely convinced that fluctuations such as those in figures 1 and 2 stem from structural changes and therefore unpredictable and subject to Knightian uncertainty. I think the authors argue forcefully in favour of this idea but I am somehow still skeptical. The paper however deserves to be published.

Roman Frydman, Michael D. Goldberg, and Nicholas Mangee - FGM-Response to Referee 1
July 28, 2015 - 19:14

We are grateful for referee 1’s useful comments. Upon reflection, we share the referee’s skepticism whether the fluctuations in the frequency of news-mentions in dividends and interest rates displayed in figures 1 and 2 provide evidence of quantitative structural change. We do provide additional evidence supportive of our interpretation of ...[more]

... figures 1 and 2. However, our main objective in the paper is to provide evidence that the process underpinning dividends, interest rates and prices not only undergoes structural change, but that this change cannot be foreseen in advance with a probabilistic rule. Thus, even if figures 1 and 2 might be suggestive of structural change, the referee is right that they could not be convincingly interpreted as providing evidence that this change is unforeseeable, that is, subject to Knightian uncertainty. We therefore have taken out of the main text our interpretation of the fluctuations evidence, including figures 1 and 2. We now mention this evidence briefly in footnote 24 (the old footnote 2 on p. 18) and refer readers interested in this evidence to our working paper. With this change, the paper now focuses on the evidence that Knightian uncertainty underpins structural change in stock-price movements.
This revision also shortens the paper, which addresses the referee’s other comment. We have also edited the paper to eliminate repetitions concerning work on REH models with structural change. Footnote 1, which briefly summarizes Hamilton and how REH models of change imply an overarching distribution, has been deleted. We also moved the sketch of Hamilton’s Markov switching model from the main text of section 6.2 to a footnote in the second full paragraph in section 2 on p. 7. We have also eliminated the part of this paragraph, which largely repeated the text in the new footnote.

Please see the revised version attached as PDF

Anonymous - Referee Report 2
July 29, 2015 - 12:28

I really liked this paper. It is clearly written if a little overlong. In terms of layout I found the section on structural change a little convoluted, but the authors have found a rich vein to mine in this area. It could be a paper on its own. Of course ...[more]

... Knightian uncertainty, which occupies 2 or three pages of the introduction, then gets all of section 6.2 as well. So maybe there is scope for cutting there. I found the discussion of the ‘channels’ a little arbitrary I have to say. In a world of high uncertainty and fat tails which the authors lionize, why do they focus on dividends and discount rates when, say, one of the liquidity issues (of which there are 59 mentions in the data set) could have ‘caused’ say 90% the movement?

I loved the section on the data-gathering in the appendix. It is scholarly and gives a strong sense of the authors wanting this to be reproducible as a piece of research.

The Knightian uncertainty premium comes out well, but isn’t it just a retitled expected value of the bulls-bears premium on assets held long?

I’d like to know, anecdotally, whether this method has made the authors real money. I imagine it could.

Roman Frydman, Michael D. Goldberg, and Nicholas Mangee - FGM - Response to Referee 2
August 04, 2015 - 10:14

We thank referee 2 for useful comments. Referee 1 also suggested that we trim the introduction and section 6 concerning structural change, which we did. Referee 2 suggests that we may want to trim these sections further with regards to Knightian uncertainty. However, the discussions of Knightian uncertainty in these ...[more]

... two sections are different; the introduction is more general, while section 6.2 provides specific examples of historical events and helps the reader understand why the structural change that they engender could not be foreseen with a probabilistic rule. In our view, trimming these sections any further would weaken our argument.
We agree with the referee that the motivation for focusing on the present value model’s two main channels is cryptic. We have revised the introduction to section 7 to address this problem. We now make clear on p. 20 that rejecting the REH present value model's quantitative predictions leaves open the question whether its qualitative predictions have empirical support. The model’s qualitative predictions involve the present value model’s two main channels, namely the market forecast of dividends and it forecast of the discount rate. Section 7 examines how frequently these two channels are mentioned in Bloomberg’s wrap reports?
Thank you for questioning whether mentions of liquidity issues are consistent with the present value model’s two channels. Liquidity issues largely involve central bank injections of liquidity into the banking system, which ease borrowing constraints. Bloomberg wrap reports indicate that these injections can influence the market through the dividend or the discount rate channel.
Although we lionize Knightian uncertainty, arguing that it is the central issue facing macroeconomics and finance theory, we do not “lionize fat tails”. Unforeseeable structural change implies that no one distribution, either with fat or normal tails, will characterize the unfolding of future stock prices.
We agree with the referee that it is helpful to point out that the market’s uncertainty premium can be thought of as an expected return on holding a long position in the market. We do this in a new footnote on p. 26. But, we also point out in this footnote that this premium is a weighted average of the expectations of bulls and bears, where bears' expectations of the return are of course negative.
The predictability of the net UCI is suggestive that it may be useful for trading in the stock market. However, we have not explored this possibility.

Please see the revised version attached as PDF