Social background and school track choice: An analysis informed by the rational choice framework

We investigate social inequalities based on social background in the choice of the academic track among equally performing students, and how indicators derived from the rational choice framework contribute to account for such inequalities. We discuss the main theoretical concepts underpinning rational choice theory as applied to educational decisions: perceived costs, benefits, and risks of failure; relative risk aversion; and time-discounting preferences. In the empirical section, we use a unique dataset concerning the transition to different tracks in upper secondary school in a large Southern Italian region. By using various regression methods and the Karlson/Holm/Breen decomposition technique, we show that social inequalities in access to the academic track are considerable, even in recent cohorts, and that they are largely not explained by previous academic performance. Indicators linked to key concepts proposed by the rational choice theory—as measured in this study—account, as a whole, for 31% of the gap based on parental education, and for 40% of the gap based on parental occupation. The most important sources of inequalities among those this study examines are the expected benefits associated with the educational alternatives and the time-discounting preferences, while relative risk aversion and the perceived chances of success play negligible roles.

A First-Price Sealed-Bid Asymmetric Auction When Two Bidders Have Respective CRRA and General Utility Functions

We study a first-price auction with two bidders where one bidder is characterized by a constant relative risk aversion utility function (i.e., a concave power function) while the other has a general concave utility function. We establish the existence and uniqueness of the optimal strategic markups and analyze the effects of one bidder’s risk aversion level on the optimal strategic markups of him and his opponent’s, the allocative efficiency of the auction, and the seller’s expected revenue, respectively.

Prospect theory, constant relative risk aversion, and the investment horizon

Prospect Theory (PT) and Constant-Relative-Risk-Aversion (CRRA) preferences have clear-cut and very different implications for the optimal asset allocation between a riskless asset and a risky stock as a function of the investment horizon. While CRRA implies that the optimal allocation is independent of the horizon, we show that PT implies a dramatic and discontinuous “jump” in the optimal allocation as the horizon increases. We experimentally test these predictions at the individual level. We find rather strong support for CRRA, but very little support for PT.

Time-Varying Risk Aversion and Dynamic Portfolio Allocation

Despite the overwhelming evidence of time-varying risk aversion documented in recent literature, standard dynamic portfolio theories often adopt an assumption of constant (relative) risk aversion due to analytical tractability. In “Time Varying Risk Aversion and Dynamic Portfolio Allocation,” Li et al. explicitly consider the implications of time-varying risk aversion for dynamic portfolio allocation under the framework of regime-switching models. An investor with regime-dependent utility exhibits a decreasing relative risk aversion (DRRA) and has higher risk aversion when a bear market regime is more likely in the future. They develop an efficient dynamic programming algorithm that overcomes the challenges imposed by regime-dependent preference in obtaining time-consistent portfolio policies. The empirical results show that VIX is an important predictor of regime shifts and that investors with regime-dependent risk aversion achieve better investment performance than those with constant risk aversion.

Non-parametric upper bounds on risk aversion with mean-variance utility

Based on a simple prior, this note derives upper bounds for the coefficient of absolute & relative risk aversion if utility can be written as depending linearly on the mean and variance of income.

Relative risk aversion models: How plausible are their assumptions?

This work examines the validity of the two main assumptions of relative risk-aversion models of educational inequality. We compare the Breen-Goldthorpe (BG) and the Breen-Yaish (BY) models in terms of their assumptions about status maintenance motives and beliefs about the occupational risks associated with educational decisions. Concerning the first assumption, our contribution is threefold. First, we criticise the assumption of the BG model that families aim only at avoiding downward mobility and are insensitive to the prospects of upward mobility. We argue that the loss-aversion assumption proposed by BY is a more realistic formulation of status-maintenance motives. Second, we propose and implement a novel empirical approach to assess the validity of the loss-aversion assumption. Third, we present empirical results based on a sample of families of lower secondary school leavers indicating that families are sensitive to the prospects of both upward and downward mobility, and that the loss-aversion hypothesis of BY is empirically supported. As regards the risky choice assumption, we argue that families may not believe that more ambitious educational options entail occupational risks relative to less ambitious ones. We present empirical evidence indicating that, in France, the academic path is not perceived as a risky option. We conclude that, if the restrictive assumptions of the BG model are removed, relative-risk aversion needs not drive educational inequalities.

Solution to the Equity Premium Puzzle

This study provides a solution of the equity premium puzzle. Questioning the validity of the Arrow-Pratt measure of relative risk aversion for detecting the risk behavior of investors, a new tool in the form of the sufficiency factor of the model was developed to analyze the risk behavior of investors. The calculations of this newly tested model show that the value of the coefficient of relative risk aversion is 1.033526 by assuming the value of the subjective time discount factor as 0.99. Since these values are compatible with the existing empirical studies, they confirm the validity of the newly derived model that provides a solution to the equity premium puzzle.