Eben Lazarus

When people receive new information, sometimes they revise their beliefs too much, and sometimes too little. In this paper, we show that a key driver of whether people overinfer or underinfer is the strength of the information. Based on a model in which people know which direction to update in, but not exactly how much to update, we hypothesize that people will overinfer from weak signals and underinfer from strong signals. We then test this hypothesis across four different environments: abstract experiments, a naturalistic experiment, sports betting markets, and financial markets. In each environment, our consistent and robust finding is overinference from weak signals and underinference from strong signals. Our framework and findings can help harmonize apparently contradictory results from the experimental and empirical literatures.

We measure investors’ short- and long-term stock-return expectations using both options and survey data. These expectations at different horizons reveal what investors think their own short-term expectations will be in the future, or forward return expectations. While contemporaneous short-term expectations are not countercyclical across all data sources, we find that forward expectations are consistently countercyclical, and excessively so: in bad times, forward expectations are higher than justified by investors’ own subsequent short-term return expectations. This excess volatility in forward expectations helps account for excess volatility in prices, inelastic demand for equities, and stylized facts about the equity term structure.

We derive new bounds on the rational variation in asset prices over time. We focus specifically on risk-neutral beliefs implied by option prices. While risk preferences distort prices away from physical beliefs, one can nonetheless bound risk-neutral belief movement under a general assumption on the stochastic discount factor. The resulting test requires no knowledge of the objective distribution, and it allows significantly more flexibility in preferences and discount rates than in standard volatility tests. Implementing our test empirically using index options, we find that there is so much movement in risk-neutral beliefs that the bounds are routinely violated.

I present evidence from index options that the price of risk over the value of the S&P 500 increases as the investment horizon becomes shorter. I show first how these risk prices may be estimated from the data, by translating the risk-neutral probabilities implied by options prices into physical probabilities that must provide unbiased forecasts of the terminal outcome. The risk price can be interpreted as the marginal investor’s effective risk aversion, and estimating this value over different option-expiration horizons for the S&P, I find that risk aversion is reliably higher for near-term outcomes than for longer-term outcomes: the market’s relative risk aversion over terminal index values decreases from around 15 at a one-week horizon to around 3 at a 12-week horizon. It is difficult to reconcile these findings with leading asset-pricing models, and I discuss necessary conditions for any such rational model to produce such a pattern. Models with dynamically inconsistent risk preferences, however, are capable of straightforwardly producing the findings presented here, and I discuss possible specifications of such models and their applicability to related results from previous literature.

We propose a duration-based explanation for the premia on major equity factors, including value, profitability, investment, low-risk, and payout factors. These factors invest in firms that earn most of their cash flows in the near future and could therefore be driven by a premium on near-future cash flows. We test this hypothesis using a novel data set of single-stock dividend futures, which are claims on dividends of individual firms. Consistent with our hypothesis, the expected CAPM alpha on individual cash flows decreases in maturity within a firm, and the alpha is not related to the above characteristics when controlling for maturity.

Heteroskedasticity and autocorrelation-robust (HAR) inference in time series regression typically involves kernel estimation of the long-run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test’s null rejection rate and power, and that this tradeoff differs across kernels. We formalize this intuition: using higher-order expansions, we provide a unified size-power frontier for both kernel and weighted orthonormal series tests using nonstandard “fixed-b” critical values. We also provide a frontier for the subset of these tests for which the fixed-b distribution is t or F. These frontiers are respectively achieved by the QS kernel and equal-weighted periodogram. The frontiers have simple closed-form expressions, which upon evaluation show that the price paid for restricting attention to tests with t and F critical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.

The classic papers by Newey and West (1987) and Andrews (1991) spurred a large body of work on how to improve heteroscedasticity- and autocorrelation-robust (HAR) inference in time-series regression. This literature finds that using a larger-than-usual truncation parameter to estimate the long-run variance, combined with Kiefer-Vogelsang (2002, 2005) fixed-b critical values, can substantially reduce size distortions, at only a modest cost in (size-adjusted) power. Empirical practice, however, has not kept up. This article therefore draws on the post-Newey-West/Andrews literature to make concrete recommendations for HAR inference. We derive truncation parameter rules that choose a point on the size-power tradeoff to minimize a loss function. If Newey-West tests are used, we recommend the truncation parameter rule S = 1.3T^1/2 and (nonstandard) fixed-b critical values. For tests of a single restriction, we find advantages to using the equal-weighted cosine (EWC) test, where the long run variance is estimated by projections onto Type-II cosines, using ν = 0.4T^2/3 cosine terms; for this test, fixed-b critical values are, conveniently, t_ν or F. We assess these rules using first an ARMA/GARCH Monte Carlo design, then a dynamic factor model design estimated using 207 quarterly U.S. macroeconomic time series.

In recalling a list of previously experienced items, participants are known to organize their responses on the basis of the items’ semantic and temporal similarities. Here, we examine how spatial information influences the organization of responses in free recall. In Experiment 1, participants studied and subsequently recalled lists of landmarks. In Experiment 2, participants played a game in which they delivered objects to landmarks in a virtual environment and later recalled the delivered objects. Participants in both experiments were simply asked to recall as many items as they could remember in any order. By analyzing the conditional probabilities of recall transitions, we demonstrate strong spatial and temporal organization of studied items in both experiments.