Is the “Beckerian” quantity-quality tradeoff regarding the offspring always true? Analysis of NTA data

The "Beckerian" theory of the quantity-quality tradeoff between the number of children and their quality is deeply permeates all the literature dealing with fertility rate analysis. It has great influence to the new direction of growth models, which derives the growth opportunities from the number and "quality" of the population growth (or decrease). In these models human capital investments play crucial role (see Lee and Mason (2010) 1 ). In our paper we argue that Lee and Mason (2010) could not lead to a precise interpretation because they deal only with average data. We show that by calculating the correlation between the human investment and fertility rate using a continuous relationship between the two variables, a modified result is obtained. In the first part of our paper we build an overlapping generation (OLG) model, similar to that in Lee and Mason (2010), but with altered human capital elasticity. Additionally we include two other modifications: i) four overlapping generations instead of three are introduced, and ii) transfer to oldest generation is provided by the second and the third generations. We seek answers to the following question: How much consumption is provided for the youngest andthe oldest generations as a function of the fertility and survival rates? The different paths of our model show that there are difficulties if the fertility rate is extremely high or extremely low. In both cases elderly could improve their own situation if they work and receive labourincome. Children can consume at a proper level only if the fertility rate is not remarkably high. One way to decide the relevance of quantity – quality choice is to find out the relationship between the families’ human investments into their children and the fertility rate of the same families. Data usually do not allow this kind of analysis, because the determination of the level of human investment is a very difficult task. However the National Transfer Account Project (www.ntaccounts.org) provides unique opportunity to evaluate how strong the correlation between the human investment and the fertility was, because the countries in the project collected detailed income and consumption data for all ages of their population. The pioneering work of Lee and Mason (2010), using NTA data, found a negative and significant correlation between the number of children and the human investment into children. In our paper we argue that their analysis could lead to a false interpretation because they deal only with average data. Grouping NTA countries upon their latest fertility ratio could modify the results. We show that if we calculate the correlation between the human investment and fertility rate splitting the countries into two groups (low and close or above the replacement level fertility rate) we receive a slightly modified result. In the first part of our paper we present these calculations. In the second part we show two overlapping generation (OLG) models, similar to that in Lee and Mason (2010), but we quantify these models separately for our two groups of countries. In the third part of our paper we use a more sophisticated OLG model, and explain the new consequences. Finally we conclude.