Effect of heterogenous consuming preference on wealth inequality 84

In this section, the risk averse coefficient in consumption utility will be switched from the homogenous to be heterogenous among households. The differing risk averse coefficient is set as γ_k satisfies the normal distribution that

γ_k∼ N (γ, σ_γk² ), (3.37)

the risk averse coefficient mean is located as γ = 0.2 in this simulation. σ_γk is the standard deviation, it stands for the discreteness of the different risk averse coefficient in consumption. This simulation is to investigate whether or not the discreteness of the differing risk averse coefficient γ_k in consumption is one of determinants of the wealth concentration of households.

Household income is still exogenously given and identically matched to the result generated in the simulation section (2.7, Figure 2.1) by the process, Eq. (2.6). All the other parameters are the same as the previous two simulations, only the heterogenous risk averse coefficient set. The standard deviation of risk averse coefficient ranges from 0.0105 to 0.04 with the incremental 0.0005.

Table 3.2: Summary of key parameters in case 3

Parameter Symbol Value

Household number K 100

Terminal stage T 80

Number of income risk resources d 6

Initial income level _k(0) 1

Income growth rate µ 1

Income volatility averaging σ¯_kj 0.12

std. of income volatility σ_ρ 0.02

Expected growth rate on wealth Gk 0 Risk averse coefficient averaging γ 0.2

Std. of risk averse coefficient σ_γk [0.0105 : 0.0005 : 0.04]

Figure 3.9: Consumption scatter along the varying std. of risk averse coefficient and stage

(a) gamma std. = 0.01

(b) gamma std. = 0.04

Figure 3.10: consumption spectrum with differing std. of averaging gamma 0.20

Figure 3.9 and Figure 3.10 reflect that the consumption level of households’ are changing from “parallelized” consumptions with their income level, to the switching-styled among consumptions, accompanying the widening (diverging) discreteness of risk aversion in consumption (the standard deviation of gamma moving from 0.01 to 0.04).

Figure 3.11: simulated wealth scatter along the varying std. of constant gamma 0.2 and time stage

Figure 3.11 and Figure 3.12 shown it could not prevent household’s wealth from converging to zero at the end, with adjusting the differentiation magnitude of het-erogenous consumption preference (the discreteness of differing risk aversion coeffi-cient, γ_k). However, if risk aversions are more discrete among households, then the smoother their wealth converging to the same level along time passing. In addition, the results show that the averaging level (common level) of wealth distribution at each time stage is not roughly zero anymore as similar in previous simulations. It could be argued that the discreteness of risk aversion in consumptions may have effects on the averaging level of households’ wealth.

(a) gamma std. = 0.01

(b) gamma std. = 0.04

Figure 3.12: wealth trajectory through time with differing std. of fixed gamma 0.20

(a) highest wealth surface

(b) lowest wealth surface

Figure 3.13: highest & lowest wealth surface corresponding differing std. of constant gamma 0.20

Figure 3.13 illustrates that the higher discreteness of risk aversion of household’s consumption leads the higher highest-wealth (lowest-wealth) level. The highest and lowest wealth are symmetrically converging to the zero value of capital accumulated

at the end of the dynasty.

Figure 3.14: Gini coefficient averaging vs. std. of gamma

Figure 3.15: Gini coefficient std. vs. std. of gamma

The wealth inequality roughly is positive to discreteness of risk aversion in con-sumption, however it cannot significantly influence the inequality. Similarly, there is no obvious impact of discreteness of the differing risk aversion in consumption on the volatility of wealth inequality.

3.5 Conclusion and future research

This chapter we improved it is more consistent to reality that the state price density satisfies the equilibrium level endogenously driven by risk aversion, deposit rate and household’s revenue levels jointly. This also simplify the whole modelling in describing

the wealth concentration progress. In addition, each household?s optimal consump-tion is set as maximising the utility for their accumulative consumpconsump-tions and their utility in terminal wealth at dynasty end. We are adopting quadratic utility function benefits us to extend the problem from homogenous consumption preference to the heterogeneous. This chapter illustrates the homogenous (heterogeneous) risk aver-sion can affect the progressing of wealth concentration, however cannot affect wealth inequality obviously. On the other hand, this result is equivalent to previous chap-ter conclusion, as one of robustness comparing. Moreover, the deviation magnitude among differing risk aversion has no significant impact on wealth inequality, however can influence the evolution of wealth concentrations.

For the robustness check planned in the future, subject to the Table 3.1, the expected growth rate on wealth could be set as varying in different, it could be comparing calibrations among multilateral nations, they have differentiated GDP growth rate, treating them as equivalent as the wealth growth rate. On the other hand, the in-come growth rate should be set as differentiated and consistent to its real trend.

Thereby, subject to the Figure 3.5, we may check whether the economic growth (in-come progress level) is one important determinant causing the regime-switch of wealth concentration trend through the dynasty is still existing or not.

Chapter 4

Determinants of wealth inequality with endogenous income

4.1 Introduction

This chapter is still consistent to general equilibrium framework with maximizing social welfare, achieve the Pareto optimality of household’s consumption, produc-tive factors and structures at each stage, simultaneously maximizing terminal wealth.

Hesitating from previous chapter, the market clearing condition just keep the aggre-gated incomes equal to the aggreaggre-gated consumption.

In the previous chapters, household’s income is given exogenously and only stems from labor incomes. However, the real household’s income should constitute labor wage and financial capital gain, because households contributing their labor forces and savings to different kinds of business sectors in an exchanging economy with fi-nancial market. Thus, it could be essential to see whether dynamics of factors and structures during business sector’s development have influences or not, on the evolu-tions of wealth inequality, initiated from an economic complex system.

Moreover, comparing with the previous two chapters and Karatzas (1997), we en-dogenote the wage and capital gain under a complex economic system which is not only compatible with neoclassical economic growth framework. Also, the complex economic system built in this chapter, it let us glance on if the latecomer’s advantage advocated have powerful effect on inequality on the multilateral country sides. The latecomer’s advantage is advocated by Lin (2011) to the global technological frontier,

can be adoptable for the developing counties in the globalised open trade environ-ment.

The real household’s income should constitute labor wage and financial capital gain, because households contributing their labor forces and savings to different kinds of business sectors in an exchanging economy with financial market. Contingent claim analysis is crucial for our system, it enables the allocation of output (industrial value-added) to capital suppliers and labor suppliers are dynamically varying, adaptive to the technological gap shrinking (catching up) between developing and developed countries.