Expected utility for nonstochastic risk

Stochastic random phenomena considered in von Neumann – Morgenstern utility theory constitute only a part of all possible random phenomena (Kolmogorov (1986)). We show that any sequence of observed consequences generates a corresponding sequence of frequency distributions, which in general does not have a single limit point but a non-empty closed limit set in the space of finitely additive probabilities. This approach to randomness allows to generalize the expected utility theory in order to cover decision problems under nonstochastic random events. We derive the maxmin expected utility representation for preferences over closed sets of probability measures. The derivation is based on the axiom of preference for stochastic risk, i.e. the decision maker wishes to reduce a set of probability distributions to a single one. This complements Gilboa and Schmeidler’s (1989) consideration of the maxmin expected utility rule with objective treatment of multiple priors

Expected utility for nonstochastic risk

The world of random phenomena exceeds the domain of the classical probability theory. In the general case the description of randomness requires a specific set of probability distributions (which is called statistical regularity) rather than a singe distribution. Such statistical regularity arises as a limit of relative frequencies. This approach to randomness allows to generalize the expected utility theory in order to cover the decision problems under nonstochastic random events. Applying the von Neumann-Morgenstern utility theorem, we derive the maxmin expected utility representation for statistical regularities. The derivation is based on the axiom of the preference for stochastic risk, i.e. the decision maker wishes to reduce the set of probability distributions to a single one

Expected utility for nonstochastic risk

Stochastic random phenomena considered in von Neumann – Morgenstern utility theory constitute only a part of all possible random phenomena (Kolmogorov (1986)). We show that any sequence of observed consequences generates a corresponding sequence of frequency distributions, which in general does not have a single limit point but a non-empty closed limit set in the space of finitely additive probabilities. This approach to randomness allows to generalize the expected utility theory in order to cover decision problems under nonstochastic random events. We derive the maxmin expected utility representation for preferences over closed sets of probability measures. The derivation is based on the axiom of preference for stochastic risk, i.e. the decision maker wishes to reduce a set of probability distributions to a single one. This complements Gilboa and Schmeidler’s (1989) consideration of the maxmin expected utility rule with objective treatment of multiple priors

Measuring the Efficiency Cost of Taxing Risky Capital Income

In this paper, we derive a measure of the efficiency cost of taxing risky capital income in an infinite horizon stochastic model. The resulting measure differs from all those that have been proposed in the existing literature. It can be represented by the expression -sigma(s) T(s)c(deltaX(s)), where T(s) measures the present value of the taxes that would be paid on a unit of investment in a riskless project with the same expected depreciation rate and tax treatment as capital invested in period s, X(s), while c(X(s)) represents the certainty equivalent to the representative individual of the lottery where measures the ex post change in investment in period s due to the tax change. The paper then compares this measure with others that have appeared in the literature. We were unable to find support for the argument in Bulow-Suinmers(1984) that the efficiency cost of taxing risky capital income is much larger than that implied by the measure -sigma(s)T(s)E(deltaX(s)). In fact, we show in special cases that our measure implies a smaller efficiency cost than does the measure -sigma(s)T(s)E(deltaX(s)).

Efficiency analysis in the presence of uncertainty

In a stochastic decision environment, differences in information can lead rational decision makers facing the same stochastic technology and the same markets to make different production choices. Efficiency and productivity measurement in such a setting can be seriously and systematically biased by the manner in which the stochastic technology is represented. For example, conventional production frontiers implicitly impose the restriction that information differences have no effect on the way risk-neutral decision makers utilize the same input bundle. The result is that rational and efficient ex ante production choices can be mistakenly characterized as inefficient -- informational differences are mistaken for differences in technical efficiency. This paper uses simulation methods to illustrate the type and magnitude of empirical errors that can emerge in efficiency analysis as a result of overly restrictive representations of production technologies.

Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games under Uncertainty.

In a dynamically efficient economy, can a government roll its debt forever and avoid the need to raise taxes? In a series of examples of economies with zero growth, this paper shows that such Ponzi games may be infeasible even when the average rate of return on bonds is negative, and may be feasible even when the average rate of return on bonds is positive. The paper then reveals the structure which underlies these examples.

Certainty equivalence and model uncertainty

Simon’s and Theil’s certainty equivalence property justifies a convenient algorithm for solving dynamic programming problems with quadratic objectives and linear transition laws: first, optimize under perfect foresight, then substitute optimal forecasts for unknown future values. A similar decomposition into separate optimization and forecasting steps prevails when a decision maker wants a decision rule that is robust to model misspecification. Concerns about model misspecification leave the first step of the algorithm intact and affect only the second step of forecasting the future. The decision maker attains robustness by making forecasts with a distorted model that twists probabilities relative to his approximating model. The appropriate twisting emerges from a two-player zero-sum dynamic game.

Technology (and policy) shocks in models of endogenous growth

Our objective is to understand how fundamental uncertainty can affect the long-run growth rate and what factors determine the nature of the relationship. Qualitatively, we show that the relationship between volatility in fundamentals and policies and mean growth can be either positive or negative. We identify the curvature of the utility function as a key parameter that determines the sign of the relationship. Quantitatively, we find that when we move from a world of perfect certainty to one with uncertainty that resembles the average uncertainty in a large sample of countries, growth rates increase, but not enough to account for the large differences in mean growth rates observed in the data. However, we find that differences in the curvature of preferences have substantial effects on the estimated variability of stationary objects like the consumption/output ratio and hours worked.Business cycles - Econometric models ; Economic development