On a gap between rational annuitization price for producer and price for customer

The paper studies pricing of insurance products focusing on the pricing of annuities under uncertainty. This pricing problem is crucial for financial decision making and was studied intensively, however, many open questions still remain. In particular, there is a so-called "annuity puzzle" related to certain inconsistency of existing financial theory with the empirical observations for the annuities market. The paper suggests a pricing method based on the risk minimization such that both producer and customer seek to minimize the mean square hedging error accepted as a measure of risk. This leads to two different versions of the pricing problem: the selection of the annuity price given the rate of regular payments, and the selection of the rate of payments given the annuity price. It appears that solutions of these two problems are different. This can contribute to explanation for the "annuity puzzle"

Understanding the Evolution of the U.S. Wage Distribution: A Theoretical Analysis

In this paper we present an analytically tractable overlapping generations model of human capital accumulation, and study its implications for the evolution of the U.S. wage distribution from 1970 to 2000. The key feature of the model, and the only source of heterogeneity, is that individuals differ in their ability to accumulate human capital. Therefore, wage inequality results only from differences in human capital accumulation. We examine the response of this model to skill-biased technical change (SBTC) theoretically. We show that in response to SBTC, the model generates behavior consistent with several features of the U.S. data including (i) a rise in overall wage inequality both in the short run and long run, (ii) an initial fall in the education premium followed by a strong recovery, leading to a higher premium in the long run, (iii) the fact that most of this fall and rise takes place among younger workers, (iv) a rise in within-group inequality, (v) stagnation in median wage growth (and a slowdown in aggregate labor productivity), and (vi) a rise in consumption inequality that is much smaller than the rise in wage inequality. These results suggest that the heterogeneity in the ability to accumulate human capital is an important feature for understanding the effects of SBTC, and interpreting the transformation that the U.S. economy has gone through since the 1970's.

An analysis of spending behaviour under liquidity constraints with an application to financial hedging

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A Quantitative Analysis of the Evolution of the U.S. Wage Distribution: 1970-2000

In this paper, we construct a parsimonious overlapping-generations model of human capital accumulation and study its quantitative implications for the evolution of the U.S. wage distribution from 1970 to 2000. A key feature of the model is that individuals differ in their ability to accumulate human capital, which is the main source of wage inequality in this model. We examine the response of this model to skill-biased technical change (SBTC), which is modeled as an increase in the trend growth rate of the price of human capital starting in the early 1970s. The model displays behavior that is consistent with several important trends observed in the US data, including the rise in overall wage inequality; the fall and subsequent rise in the college premium, as well as the fact that this behavior was most pronounced for younger workers; the rise in within-group inequality; the stagnation in median wage growth; and the small rise in consumption inequality despite the large rise in wage inequality. We consider different scenarios regarding how individuals' expectations evolve during SBTC. Specifically, we study the case where individuals immediately realize the advent of SBTC (perfect foresight), and the case where they initially underestimate the future growth of the price of human capital (pessimistic priors), but learn the truth in a Bayesian fashion over time. Lack of perfect foresight appears to have little effect on the main results of the paper. Overall, the model shows promise for explaining a diverse set of wage distribution trends observed since the 1970s in a unifying human capital framework.

Risk Aversion and the Value of Risk to Life.

The standard literature on the value of life relies on Yaari’s (1965) model, which includes an implicit assumption of risk neutrality with respect to life duration. To overpass this limitation, we extend the theory to a simple variety of nonadditively separable preferences. The enlargement we propose is relevant for the evaluation of life-saving programs: current practice, we estimate, puts too little weight on mortality risk reduction of the young. Our correction exceeds in magnitude that introduced by the switch from the notion of number of lives saved to the notion of years of life saved.Lifecycle Behavior; Life Insurance; Value of Statistical Life; Cost-Benefit Analysis;

Risk Aversion and the Value of Risk to Life

The standard literature on the value of life relies on Yaari’s (1965) model, which includes an implicit assumption of risk neutrality with respect to life duration. To overpass this limitation, we extend the theory to a simple variety of nonadditively separable preferences. The enlargement we propose is relevant for the evaluation of life-saving programs: current practice, we estimate, puts too little weight on mortality risk reduction of the young. Our correction exceeds in magnitude that introduced by the switch from the notion of number of lives saved to the notion of years of life saved.Value of Statistical Life; Lifecycle Behavior; Cost-benefit Analysis

Global Climate Policy Architecture and Political Feasibility: Specific Formulas and Emission Targets to Attain 460 ppm CO2 Concentrations

Three gaps in the Kyoto Protocol most badly need to be filled: the absence of emission targets extending far into the future, the absence of participation by the United States, China, and other developing countries, and the absence of reason to think that members will abide by commitments. To be politically acceptable, any new treaty that fills these gaps must, we believe, obey certain constraints regarding country-by-country economic costs. We offer a framework of formulas that assign quantitative allocations of emissions, across countries, one budget period at a time. The two-part plan: (i) China and other developing countries accept targets at BAU in the coming budget period, the same period in which the US first agrees to cuts below BAU; and (ii) all countries are asked in the future to make further cuts in accordance with a formula which sums up a Progressive Reductions Factor, a Latecomer Catch-up Factor, and a Gradual Equalization Factor. An earlier proposal for specific parameter values in the formulas – Frankel (2009), as analyzed by Bosetti, et al (2009) – achieved the environmental goal that concentrations of CO2 plateau at 500 ppm by 2100. It succeeded in obeying our political constraints, such as keeping the economic cost for every country below the thresholds of Y=1% of income in Present Discounted Value, and X=5% of income in the worst period. In pursuit of more aggressive environmental goals, we now advance the dates at which some countries are asked to begin cutting below BAU, within our framework. We also tinker with the values for the parameters in the formulas. The resulting target paths for emissions are run through the WITCH model to find their economic and environmental effects. We find that it is not possible to attain a 380 ppm CO2 goal (roughly in line with the 2°C target) without violating our political constraints. We were however, able to attain a concentration goal of 460 ppm CO2 with looser political constraints. The most important result is that we had to raise the threshold of costs above which a country drops out, to as high as Y =3.4% of income in PDV terms, or X =12 % in the worst budget period. Some may conclude from these results that the more aggressive environmental goals are not attainable in practice, and that our earlier proposal for how to attain 500 ppm CO2 is the better plan. We take no position on which environmental goal is best overall. Rather, we submit that, whatever the goal, our approach will give targets that are more practical economically and politically than approaches that have been proposed by others.International Climate Agreements

Intertemporal Asset Pricing Without Consumption Data

This paper proposes a new way to generalize the insights of static asset pricing theory to a multi-period setting. The paper uses a loglinear approximation to the budget constraint to substitute out consumption from a standard intertemporal asset pricing model. In a homoskedastic lognormal selling, the consumption-wealth ratio is shown to depend on the elasticity of intertemporal substitution in consumption, while asset risk premia are determined by the coefficient of relative risk aversion. Risk premia are related to the covariances of asset returns with the market return and with news about the discounted value of all future market returns.