Heterogeneity and option pricing

An economy with agents having constant yet heterogeneous degrees of relative risk aversion prices assets as though there were a single decreasing relative risk aversion pricing representative agent. The pricing kernel has fat tails and option prices do not conform to the Black-Scholes formula. Implied volatility exhibits a smile. Heterogeneous beliefs about distribution parameters also implies non-lognormal pricing kernels with fatter tails and over-pricing of out-of-the-money options. Heterogeneity as the source of non-stationary pricing fits Rubinstein’s (1994) interpretation of the over-pricing as an indication of crash-o-phobia. Rubinstein’s term suggests that those who hold out-of-the-money put options have relatively high risk aversion or relatively high subjective probability assessments of low market outcomes. The essence of this explanation is heterogeneity in investor attitudes towards risks and probability beliefs.

Private and Social Incentives for Fertility: Israeli Puzzles

Whereas most of the world has experienced decreasing fertility during the past half century, Israel has experienced a puzzling mix of trends. Completed fertility has decreased sharply in some ethnic-religious groups (Mizrahi Jews and non-Bedouin Arabs) and increased moderately in other groups (non-ultra-orthodox Ashkenazi and Israeli-born Jews). In a phenomenon that can only be described as a reverse fertility transition, fertility has increased substantially (from about 3 to 6 children per women) among ultra-orthodox Ashkenazi and Israeli-born Jews. This paper explores how private and social incentives for fertility may have combined to produce the complex pattern of fertility in Israel. Theoretical analysis of the social dynamics of fertility shows that this pattern could have been generated by the joint effects of (a) private preferences for childbearing, (b) preferences for conformity to group fertility norms, and (c) the major child-allowance program introduced by the Israeli government in the 1970s. Econometric analysis of fertility decisions shows that fundamental identification problems make it difficult to infer the actual Israeli fertility process from data on completed fertility. Hence we are able to conjecture meaningfully on what may have happened, but we cannot definitively resolve the Israeli fertility puzzles.

Heterogeneity and option pricing

An economy with agents having constant yet heterogeneous degrees of relative risk aversion prices assets as though there were a single decreasing relative risk aversion pricing representative agent. The pricing kernel has fat tails and option prices do not conform to the Black-Scholes formula. Implied volatility exhibits a smile. Heterogeneous beliefs about distribution parameters also implies non-lognormal pricing kernels with fatter tails and over-pricing of out-of-the-money options. Heterogeneity as the source of non-stationary pricing fits Rubinstein’s (1994) interpretation of the over-pricing as an indication of crash-o-phobia. Rubinstein’s term suggests that those who hold out-of-the-money put options have relatively high risk aversion or relatively high subjective probability assessments of low market outcomes. The essence of this explanation is heterogeneity in investor attitudes towards risks and probability beliefs

Cereals, appropriability and hierarchy

We propose that the development of social hierarchy following the Neolithic Revolution was due to the ability of the emergent elite to appropriate crops from farmers, rather than a result of increased productivity, as usually maintained. Since cereals are easier to appropriate than roots and tubers, we argue that regional variations in the suitability of land for the cultivation of these different crop types can account for differences in the formation of hierarchies and states. Our empirical investigation supports a causal effect of the cultivation of cereals on hierarchy, and the lack of a similar effect of land productivit

The Optimal Two-Bracket Linear Income Tax

We investigate the optimal rate structure of an income tax system that is constrained to have only two brackets, plus a demogrant. We find that, in a two-class economy, Pareto efficient tax schedules feature at least one marginal tax rate equal to zero, and that the marginal tax rate may be increasing or declining. We next use numerical optimization techniques to study the optimal structure of such a tax system in a multi-person model that is a stylized version of an actual economy. We discover that in all cases the tax rate in the second (higher) bracket is less than the tax rate that applies to the first bracket but that progressivity, in the sense of a uniformly rising average tax rate, generally obtains. Compared to the optimal one-bracket (linear) tax system, both the highest and lowest income individuals are better off, while a middle range of taxpayers is worse off.