**Brief Recap**

In the last edition, I introduced the impact of the One-Child Policy on wealth inequality in China through an intuitive example, which contributes to the argument that the policy had an amplifying effect on wealth inequality in China. With wealth and assets accumulated by a pair of the first generation (simply put, the parents) during their lifetime, having only one child might lead to wealth precipitating down to the only second generation a family has, causing the wealth inequality within the second generations to be larger than the first generations. Through the lens of mathematical and graphical analysis, I illustrated the failure of the Gini coefficient in capturing the magnifying effect on wealth inequality. One may understand from the calculations I did in the last edition, theoretically, the concentration of wealth in the second generation is cancelled out by the shrinking population. As the Gini coefficient is confined to defining inequality at a given time, only illustrating inequality in terms of the distribution of the proportion of wealth held by a particular social stratum, it is insufficient to show the dynamics of changing population size and wealth inheritance.

**Some inspirations**

As there is very scarce research studying the effect of the One-Child Policy, modelling wealth distribution under the Policy could be a more viable approach. I thereby start looking into literatures that model the dynamic process of the changing wealth distribution between generations, where I could draw valuable insights into modelling the issue in question.

The early work of modelling the distribution of income and wealth inequality was very focused but simplified, illustrating the factor of bequest on economic inequality, in a one-period model neglecting the effect of any other variables (Davies, 1982). Here, the author vaguely defined the economic inequality as a measurement of “distribution of income, wealth and other lifetime resources”, though he did not focus on specifying and quantifying lifetime resources. Despite being a static one-period model, Davies’s work sheds light on one of the most important factors – voluntary inheritance – in shaping wealth distribution. It is important to distinguish voluntary and involuntary inheritance, where the latter is accidental or not in the knowledge of the second generation. Without knowing that they might receive a random amount of capital in the form of assets or cash, when descendants plan and smooth their consumption over the course of their lifetime, this particular amount of wealth in not taken into account. Understandably, involuntary inheritance is much harder to model, as it may create a new variable specifying the probability of receiving a certain amount of money at a particular time. This variable is then related to the growing probability of predecessors passing away as they become older. However, if one just assumes that death and fertility are random, cancelling out the probability factor, one might end up with a high level of aggregate flow of accidental bequests (Gokhale et al, 1998), which not only destabilises the consumption smoothing pattern of second generations, but is inapplicable when modelling the significance of flow of planned inheritable wealth under the circumstances of the One-Child Policy. This paper, nevertheless, provided clues as to how one may model accidental involuntary inheritance. One might expect relatively high levels of planned inheritance as opposed to involuntary inheritance, but it is essential to take both elements into account.

Aside from physical capital inheritance, which takes a major part in shaping wealth distribution under the One-Child Policy, one should also consider human capital inheritance as an important factor. Human capital inheritance is built into any system, but one may consider the effect of a disparity of capital wealth on the transferability of human capital, more specifically, through education. Becker, et al (1979) modelled the transferability of both physical and human capital from the first to the second generations. It is essential to note that both physical and human capital are mutually related, as families with higher propensity to invest in children’s education are more likely to have socially and academically better-performing children (Becker et al, 1979), who might earn higher incomes, adding to the wealth they inherit from their parents. On the other hand, they concluded that the marginal rate of return to investments in children’s education is diminishing, which ensures that the extremely rich are not in an overly advantaged position in terms of education investment.

One may safely argue that genetics might also be a factor here, but biologists are not certain of what traits can be viably passed onto the next generation with any given level of certainty. What could provide us with a certain level of theoretical basis to the clues of generalisation is that a big population is likely to be subject to regression to the mean. It is a statistical phenomenon that a sample from a population with two measures imperfectly correlated, when the first takes an extreme value, is likely to have a second taking a value nearer to the medium. This shows many second generations might not be able to out-perform their successful parents in terms of income or intelligence, as their ability tends to be more mediocre. It is common to see in many research papers that they assume the so-called “ability” factor is constant or a simple linear function of the fraction of parent’s income spent on education, isolating it from genetic factors. With intricate relationships between physical capital and human capital, and generalisation of regression to the mean on either side of the theoretical spectrum, it is up to the researchers to build their assumptions, upon which the general direction of research is then decided. I would hesitate to conclude further on what assumptions I would make under this perspective.

Another perspective that one could consider is introducing parent-child interaction by the “warm glow” factor (Nardi, 2004), since the first generations might derive utility from giving their wealth to their kids. One may incorporate the amount of inheritance bestowed to the second generations into the lifetime utility function of their parents. Parents then maximise their overall utility function and assign a consumption level to each annuity period. Nardi (2004) modelled the utility function of bequest by a decreasing function taking the discount rate as the factor, implying that bequest utility has a decreasing return with accelerating decreasing marginal return. This captures an important fact that parents might have growing concerns over passing a high amount of their wealth to their kids. People’s altruistic nature might have significant influence in the case of China, as it has become quite a social norm that parents bestow wealth to their kids, particularly in the forms of illiquid assets such as cars, houses or shares in their family businesses. When the “warm glow” factor is taken into consideration regarding lifetime consumption of the first generations, saving patterns might change and this could ultimately affect wealth accumulation. These factors then feed back into the decisions on investing more on education, affecting human capital inheritance for the second generations.

**Remarks**

I have discussed several areas that have inspired me in my future research on this topic. Notwithstanding, there is a lot more to discuss, but I have picked out some of the most important ideas and constructs when modelling the dynamics of wealth distribution, from voluntary inheritance to altruistic behaviour. As models take more and more factors into account, it is more likely to resemble reality. However, this is not entirely the purpose of this edition, as I am trying to lay out what could be the perspectives that I would look into when I initiate my own model. I hope I can be as informative as possible, but the time I have is very limited. Therefore, in the next edition, I will move swiftly onto constructing my dynamic model and start to illustrate the dynamic wealth distribution process.

Junzhao Shi

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