Center of Mathematical Sciences and Applications,

Harvard University

Log, Stock and Two Simple Lotteries
(Technical Supplement)

This paper studies the problem of decision-making under risk by agents whose information processing abilities may be limited. The constructed theoretical framework grounds on findings from economic laboratory experiments, incorporates existing neuroscience knowledge, and is implemented using information-theoretic formalism. Activation of the above information-processing constraints distorts the subjective perception of the objective stochastic environment the agent operates in, and the constrained-optimal decision-making requires appropriate adjustments. In the selected application, a general equilibrium macro-finance model, such biases of subjective perspective as overconfidence, pessimism and categorization thus emerge endogenously. The theoretical implications receive empirical support in a mutually consistent way: according to (cross-checked) calibrations, they allow us to reverse-engineer and rationalize the phenomena known as the equity premium/risk-free rate puzzles; as well as contribute to the understanding of such regularities as the portfolio underdiversification puzzle, style investing and the non-monotone pricing kernel puzzle. On the other hand, these results also help rationalize, by formulating certain optimizing foundations behind, the experimental evidence that underlies the Allais paradox and that is systematized in, e.g., the (cumulative) prospect theory.

Thinking on Their Feet

Limited information-processing capacity generally distorts the decision-making environment and decision outcomes of a rational investor, with the real effects amounting to welfare losses from the above distortions, including losses from subjective categorization in the multivariate case. This is shown in Verstyuk (2016), which considers an i.i.d. environment and focuses on unconditional moments (for instance, wealth invested in risky assets) as well as some cross-sectional variation (categorization of risky assets). The present paper focuses on dynamic aspects and deals with a non-i.i.d. environment. Firstly, when conditional moments such as mean or variance change, this puts a strain on information-processing capacity (technically, due to the fact that perturbations in the probability density require a corresponding adaptation of the optimal encoding of information, which is necessary for its processing, otherwise they result in an outright efficiency loss). Most straight-forwardly, this leads to larger decision errors and higher welfare losses temporarily after a regime change. On top of that, categorization induces agents to ignore some dimensions of the state-space; in particular, ignoring new information about housing or pension fund wealth delays the consumption response (without the need to resort to e.g. habit-formation arguments) with a consequence of its amplification/propagation later, while ignoring information about tax policy disrupts the Ricardian equivalence; temporarily lower effective information-processing capacity in the wake of regime change intensifies these results further, giving rise to for example stronger effects of fiscal policy during crises. Secondly, a shift in parameters entails a period of learning (via Bayesian updating, or its computationally feasible implementation based e.g. on the principles of reinforcement learning); for instance, a change in mean leads to underreaction/inertia (in perceptions and decisions), while outlier observations engender overreaction/momentum and ensuing ``excess'' volatility on financial markets. (All results are preliminary.)

Let the Market Speak for Itself

A simple Bayesian SVAR model of financial market interconnections estimated for major asset classes, with contemporaneous causal cross-effects identified relying on agnostic data-determined structure.

Solvency Strains and the Long-End of the Yield Curve.
With Francesco Garzarelli and Aqib Aslam. 2010. Goldman Sachs, *Fixed Income Monthly*, September: 5--7.

Finding `Fair Value' for the Ukrainian Currency.
With Malachy Meechan. 2009. Goldman Sachs, Global Viewpoint, 09/10.

Larger Supply No Threat to Bonds.
With Francesco Garzarelli. 2008. Goldman Sachs, *Global Economics Weekly*, 08/38: 2--5.

Larger Supply No Threat to Bonds.
2008. Goldman Sachs, *Fixed Income Monthly*, October: 5--7.

The Family of GS Curves.
2008. Goldman Sachs, Global Viewpoint, 08/16.

Linking the Term Structures of Interest Rates and Macroeconomic Expectations --- GS Yield Curve Valuation Model.
2007. In Jim O'Neill, Jens Nordvig, and Thomas Stolper, eds., *The Foreign Exchange Market: 2007*. Goldman Sachs: 45--55.

Sudoku Gets Bigger and Forward-Looking!
With Francesco Garzarelli and Michael Vaknin. 2007. Goldman Sachs, Global Viewpoint, 07/24.

Global Bonds: No Obvious Safe Haven.
With Francesco Garzarelli. 2007. Goldman Sachs, Global Viewpoint, 07/07.

Partisan Differences in Economic Outcomes and Corresponding Voting Behavior: Evidence from the U.S.
2004. *Public Choice*, 120(1-2): 169--189.