Dirk Bethmann

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.

Solving macroeconomic models with homogeneous technology and logarithmic preferences

In a stylised Robinson Crusoe economy, we illustrate basic dynamic programing techniques. In a first step, we define state‐like and control‐like variables. In a second step, we introduce the value‐function‐like function. While the former step reduces the number of variables that have to be considered when solving the model, the latter step reduces the dimensionality of the Bellman equation associated with the optimisation problem. The models solution is shown to be saddle‐path stable, such that the phase diagram associated with the Bellman equation has two solution branches. The simplicity of our model allows us to state both the stable and the unstable branch explicitly. We also explain the usefulness of logarithmic preferences when studying the continuous‐time Hamilton‐Jacobi‐Bellman equation. In this case, the utility maximisation problem can be transformed into an initial value problem for an ordinary differential equation.

War, Marriage Markets, and the Sex Ratio at Birth

In belligerent countries, male-to-female sex ratios at birth increased during and shortly after the two world wars. These rises occurred amidst dramatically changed marriage-market conditions caused by war-related declines in adult sex ratios, and still defy explanation. Based on county-level census data for the German state of Bavaria in the years just before and immediately after World War II, we explore the reduced-form relationship between changes in marriage-market tightness (the adult sex ratio) and changes in the offspring sex ratio, and we discuss potential mechanisms that might link the two. Our results suggest that war-induced shortfalls of men significantly increased the percentage of boys among newborns.

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.

A Theory of Child Adoption

Women can bear own children or adopt them. Extending economic theories of fertility, we provide a first theoretical treatment of the demand for adoption. We show that the propensity to adopt a child increases in the degree of own altruism, infertility, relatedness to the child, costs of own child birth, and any adoption-specific monetary return that is received net of the costs of adopting the child. Our model makes several testable predictions which receive empirical support. These include a higher propensity to adopt among infertile adults, relatives, women with high earnings potential, and celebrities.

An Improvement to Jensen's Inequality and its Application to Mating Market Clearing when Paternity is Uncertain

Jensens inequality can be tightened in the context of binomially distributed random variables. The suggested new inequality coincides with Jensens inequality only when the expected value of the random variable is an integer, in all other cases the inequality is tighter than Jensens. This improvement is used to derive a welfare result in the context of a mating market where male agents are exposed to paternal uncertainty. It is shown that social welfare is highest when paternity is certain, a result that can not be obtained when relying on Jensens inequality.

MACROECONOMIC THEORY – A DYNAMIC GENERAL EQUILIBRIUM APPROACH, M.R. Wickens, Princeton University Press, Princeton, 2008, 496 pages (hardback), ISBN 0691116407

Dynamic general equilibrium modelling is considered as the standard approach in modern macroeconomics. Kydland and Prescott (1982) became famous for their pioneering role in the (neoclassical) real business cycle theory and as such in establishing dynamic general equilibrium modelling in macroeconomic theory. At its core, the approach applies Walrasian general equilibrium theory to aggregate economic phenomena. Being completely microfounded, models that are based on this approach are shielded from the Lucas critique. Soon, New Keynesian macroeconomists Rotemberg and Woodford (1997) took the opportunity and added Keynesian features to the model, thereby putting Keynesian theory on a more solid ground and protecting it against accusations of being ‘ad hoc’. As a result, both the neoclassical and the New Keynesian school of thought are nowadays using the dynamic general equilibrium framework as their workhorses.

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.

An Analytical Introduction to Dynamic Optimization: The Robinson Crusoe Economy

Dynamic optimization is an essential tool of modern macroeconomics. We suggest to teach this technique based on a simplified version of the Uzawa-Lucas model of endogenous growth. Using this model it is possible to present the key concepts of dynamic optimization without applying linearization techniques. Even though the model assumes a concave utility function and a neoclassical production technology, we will state the stable and the unstable solution branches in the phase diagram in closed-form. Saddle path behaviour and the role of transversality conditions can therefore be studied extensively without using complicated mathematical tools. We also show how homogeneity in the initial conditions, a property that applies to almost all macroeconomic models, can be used to introduce a simple numerical solution method.

Notes on an Endogenous Growth Model with two Capital Stocks I

This paper extends the class of AK models with an explicit solution to the case where there are two capital goods in the model. this extension holds, even if an external effect in the use of human capital in goods production ia assumed.