The open-loop solution of the Uzawa-Lucas Model of Endogenous Growth with N agents

We solve an N 2 N player general-sum differential game. The optimization problem considered here is based on the Uzawa Lucas model of endogenous growth. Agents have logarithmic preferences and own two capital stocks. Since the number of players is an arbitrary fixed number N 2 N, the model?s solution is more general than the idealized concepts of the social planer?s solution with one player or the competitive equilibrium with infinitely many players. We show that the symmetric Nash equilibrium is completely described by the solution to a single ordinary differential equation. The numerical results imply that the influence of the externality along the balanced growth path decreases rapidly as the number of players increases. Off the steady state, the externality is of great importance, even for a large number of players. --Value Function Approach,Nash-Equilibrium,Open-loop Strategies,Ordinary Differential Equation

Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth

In this paper we solve an N N N players differential game with logarithmic objective functions. The optimization problem considered here is based on the Uzawa Lucas model of endogenous growth. Agents have logarithmic preferences and own two capital stocks. Since the number of players is an arbitrary fixed number N N N the model's solution is more realistic than the idealized concepts of the social planer or the competitive equilibrium. We show that the symmetric Nash equilibrium is completely described by the solution to one single ordinary differential equation. The numerical results imply that the influence of the externality along the balanced growth path vanishes rapidly as the number of players increases. Off the steady state the externality is of great importance even for a large number of players.Value Function Approach, Nash-Equilibrium, Open-loop Strategies, Ordinary Differential Equation.

Notes on an Endogenous Growth Model with two Capital Stocks II: The Stochastic Case

This paper extends the class of stochastic AK growth models with a closed-form solution to the case where there are two capital goods in the model. To be precise, we consider the Uzawa-Lucas model of endogenous growth with human and physical capital. The extension holds, even if an external effect in the use of human capital in goods production occurs. Using the “guess and verify” method, we determine the value function of the social planner in the centralized economy and the value function of the representative agent in the decentralized case. We show that the introduction of income taxes on wages and of a subsidy on physical capital earnings is able to help the decentralized economy in reaching the social optimum, while keeping the policy maker’s budget balanced. Then the time series implications of the model’s solution are derived. In Appendix to the paper the uniqueness of the value functions is proved by using an alternative method.closed-form solution, value function, saddle path stability, endogenous growth

Why Are More Boys Born During War? - Evidence from Germany at Mid Century

In belligerent countries, male-to-female sex ratios at birth increased during and shortly after the two world wars. These rises still defy explanation. Several causes have been suggested (but not tested) in the literature. Many of these causes are proximate in nature, reflecting behavioral responses to the dramatically changed marriage market conditions for women and men that were induced by war-related declines in adult sex ratios. Based on county-level census data for the German state of Bavaria in the vicinity and aftermath of World War II, we explore the reduced-form relationship between changes in adult and off spring sex ratios. Our results suggest that war-induced shortfalls of men significantly increased the percentage of boys among newborns.World War II, adult sex ratio, sex ratio at birth

Occupational change and status mobility

The impact of changes of the occupational field on the socio-economic status after unemployment has not received much attention in the literature so far. Due to a possible loss of occupation specific human capital the effects are assumed to be detrimental. This seems especially probable if the individual has attained specific human capital in the form of vocational training. A sample from the panel study 'Labour Market and Social Security' (PASS) was used to analyse the occupational changes of unemployed individuals upon re-entry into the labour market. Compared to occupational changes from employment, changes in the unemployment group have stronger negative effects on the difference in socio-economic status between the last and the current job. The International Socio-Economic Index (ISEI) was used as the status measure. For unemployed individuals without vocational training no significant effect could be found, whereas those with training did incur substantial status losses. In conclusion the loss of occupation specific human capital due to changes of occupation does seem to be detrimental to the socio-economic situation of unemployed individuals after re-employment. This should be considered when applying strict labour market policies possibly pressuring individuals to change their occupation in order to take up employment more quickly

Paternal Uncertainty and the Economics of Mating, Marriage, and Parental Investment in Children

We develop a theoretical model of mating behavior and parental investment in children under asymmetry in kin recognition between men and women that provides a microfoundation for the institution of marriage. In the model, men and women derive utility from consumption and reproductive success, which is a function of the number and quality of own offspring. Because of paternal uncertainty, men unlike women may err in investing resources in offspring that is not biologically theirs. As a socially sanctioned commitment device among partners, the institution of marriage reduces this risk by restraining promiscuity in society. Both women and men are shown to benefit from lower levels of paternal uncertainty, as does average child quality because of increased parental investments. As an analytical framework, the model is suitable to study a number of societal, economic, and technological changes in their effects on marriage patterns. A combination of factors is argued to underlie the demise of marriage.Mating, Paternal Uncertainty, Parental Investment, Marriage

Uncertain Paternity, Mating Market Failure, and the Institution of Marriage

This paper provides a first microeconomic foundation for the institution of marriage. Based on a model of reproduction, mating, and parental investment in children, we argue that marriage serves the purpose of attenuating the risk of mating market failure that arises from incomplete information on individual paternity. Raising the costs of mating to individuals, marriage circumscribes female infidelity and mate poaching among men, which reduces average levels of paternal uncertainty in society. A direct gain in male utility, the latter induces men to invest more in their putative offspring, a fact that benefits women because of the public good nature of children. Able to realize Pareto improvements, marriage as an institution is hence explained as the result of a societal consensus on the need to organize and structure mating behavior and reproduction in society for the benefit of paternal certainty and biparental investment in offspring.Marriage, Mating, Paternal Uncertainty, Parental Investment.

World War II, Missing Men, and Out-of-wedlock Childbearing

Based on county-level census data for the German state of Bavaria in 1939 and 1946, we use World War II as a natural experiment to study the effects of sex ratio changes on out-of-wedlock fertility. Our findings show that war-induced shortfalls of men to women significantly increased the nonmarital fertility ratio at mid century, a result that proves robust to the use of alternative sex ratio definitions, post-war measures of fertility, and estimation samples. The magnitude of this increase furthermore appears to depend on the future marriage market prospects that women at the time could expect to face in the not-too-distant future. We find the positive effect on the nonmarital fertility ratio of a decline in the sex ratio to be strongly attenuated by the magnitude of county- level shares of prisoners of war. Unlike military casualties and soldiers missing in action, prisoners of war had a sizeable positive probability of returning home from the war. Both current marriage market conditions, therefore, and foreseeable improvements in the future marriage market prospects of women appear to have influenced fertility behavior in the immediate aftermath of World War II.World War II, Sex Ratios, Out-Of-Wedlock Births.

Why Are More Boys Born During War? - Evidence from Germany at Mid Century

In belligerent countries, male-to-female sex ratios at birth increased during and shortly after the two world wars. These rises still defy explanation. Several causes have been suggested (but not tested) in the literature. Many of these causes are proximate in nature, reflecting behavioral responses to the dramatically changed marriage market conditions for women and men that were induced by war-related declines in adult sex ratios. Based on county-level census data for the German state of Bavaria in the vicinity and aftermath of World War II, we explore the reduced-form relationship between changes in adult and off spring sex ratios. Our results suggest that war-induced shortfalls of men significantly increased the percentage of boys among newborns