Economic Analysis of Fertility Rate Fluctuation

传统的增长理论方法将增长过程建模为投资于物质资本和技术进步的决策。巴罗和贝克尔（1989）最近的一个模型将生育决策或关于生育子女数量的决定纳入了增长理论的背景下。儿童的福利（通过他们的人均消费）被纳入父母的效用。由于必须牺牲消费来教育子女，在这种情况下，投资决策变得更加复杂。允许父母投资子女的人力资本，以提高他们的生产力，可以进一步丰富这一模式。我们建议研究将技术进步和人力资本引入内生生育率模型的影响。技术进步的含义之一是，稳定状态不再处于水平状态；它们代表了产出、资本消费等人均变量的增长路径。然后，我们表明，实物资本的动态行为将是单调的或振荡的，这取决于某个“利他主义”函数的弹性，这也可以被视为儿童逆向需求曲线的弹性。这种弹性在Barro和Becker模型中等于统一性，在确定多个稳态是否存在方面也起着重要作用。从经验的角度来看，多重稳定状态可能有助于解释一些穷国和富国之间增长率的持续差异。

Traditional approaches to growth theory have modeled the process of growth as arising from decisions to invest in physical capital and from technological progress. A recent model by Barro and Becker (1989) has incorporated fertility decisions, or decisions about the number of children to have, into a growth theoretic context. The welfare of children (through their per capita consumption) is incorporated into their parents utility. Since consumption must be sacrificed to educate children, the investment decisions become more complex in such a setting. The model can further be enriched by allowing parents to invest in the human capital of their children in order to raise their productivity. We propose to study the implications of introducing technologial progress and human capital into the model of endogenous fertility.One of the implication of technical progress is that steady states are no longer in levels ; they represent growths path of per capita variables like output, consumption on capital. We then show that the dynamic behavior of physical capital will be monotonic or oscillatory, depending on the elasticity of a certain "altruism" function which may also be viewed as the elasticity of an inverse demand curve for children. This elasticity, which is equal to unity in the Barro and Becker model, also plays a major role in determining the existence of multiple steady states. From an empirical perspective multiple steady states may be useful to explain persistent differentials between growth rates of some poor and rich countries.