**Part 4: Remedy**

**4.3 Recommendations**

**4.3.3 Development of Overall Education Level in Workforce**

It is a long-run strategy to deal with income inequality problem. As we have validated, education determines the potential increase of the salary level in a particular profession. Thus, it is urgent to distribute more incentives among low-income class in purpose of a high average education level. We encourage the government to:

Prolong the duration of compulsory education applicable to all local citizens in the long term. It will effectively reduce the number of people without any education.

Strengthen the education fund by giving out more tuition assistantship so that more people can afford to school

Construct public education facilities such as libraries, museums and etc

Provide professional/diploma programs in institutes of higher education such as University of Macau.

In conclusion, the income inequality can be reduced to an acceptable level as long as the government makes full use of the three-tier distribution system to balance economic structure, improve social welfare system and

**Remedy **

**UMBERET PRESENT | Tears behind the Diamond ** 37
popularize higher education.

**Appendix **

**UMBERET PRESENT | Tears behind the Diamond ** 38

**5.1 Calculation of Gini Index ** **5.2 Reference **

**PART FIVE ** **APPENDIX **

**Appendix **

**UMBERET PRESENT | Tears behind the Diamond ** 39

**5.1 Calculation of Gini Index **

**We will demonstrate how Monte Carlo Simulation is used to retrieve estimated Gini coefficients in 2008, and it **
applies identically to the rest of years. The software realizing the simulation is EXCEL and its macro functions, and
data pre-processing is jointly performed by MATHEMATICA. In general, the process consists of two steps:

**5.1.1 Generation of random numbers under log-logistic distribution **

EXCEL does not provide built-in function specifically for log-logistic distribution. However, EXCEL macro enables us to insert program to create a user-defined function. Characterizing the features of log-logistic model, the function is programmed to be varied with two parameters m and k by using log-logistic density function.

We‟ve already known the value of m previously, and subsequently we need to identify the most suitable value for parameter k. In order to generate random numbers, we arbitrarily give a value for k. The population size is 314,700, and we simplify it to 3,147 by dividing 100. Afterwards, we obtain the 3,147 random numbers and reclassify them into income range by counting how many random numbers fall into each corresponding range, and the results is shown in Table 5.1.

**Table 5.1 – Presentation of income reclassification into original income range**^{17}**Income Range ** **Fitting ** **Real ** **Error ** **MSE ** **MAD ** **CHISQ **

≦ 3 499 344 334 -10 100 10 0.29

**3 500 - 3 999 ** 96 64 -32 1024 32 10.67

**4 000 - 4 499 ** 98 151 53 2809 53 28.66

**4 500 - 4 999 ** 110 113 3 9 3 0.08

**5 000 - 5 999 ** 242 279 37 1369 37 5.66

**6 000 - 7 999 ** 479 483 4 16 4 0.03

**8 000 - 9 999 ** 425 350 -75 5625 75 13.24

**10 000 - 14 999 ** 694 707 13 169 13 0.24

**15 000 - 19 999 ** 305 272 -33 1089 33 3.57

**20 000 - 29 999 ** 201 229 28 784 28 3.90

**30 000 - 39 999 ** 67 89 22 484 22 7.22

**40 000 - 59 999 ** 46 48 2 4 2 0.09

**60 000 - 79 999 ** 20 13 -7 49 7 2.45

≧80 000 20 15 -5 25 5 1.25

**Total ** **3147 ** **3147 ** **- ** **968.28 ** **23.14 ** **77.35 **

*Units: in hundred people *

*Source: Employment survey 2008, DSEC *

In the Table 5.1, we can also obtain values for error measurements, MSE, MAD and CHISQ respectively. They are

17 It is just one of the many possible results as the simulation will change every time

**Appendix **

**UMBERET PRESENT | Tears behind the Diamond ** 40
**the criteria for us to find the optimal value for k. Then, we What-If analysis to simulate the values for three error **
indicators for 300 times, and subsequently obtain the average value for MSE, MAD and CHISQ, using Equation [5],
[6] and [7]. The most interesting phenomenon is that there is only one variable in the complicated deduction
process. Therefore, Solver function built in EXCEL can be applied to search for the optimal value for k on
condition that it minimizes the value of CHISQ. As a result, we can find out the best value for k and the log-logistic
distribution is then permanently positioned by two known parameters.

**5.1.2 Attainment of the Lorenz Curve and Gini coefficient **

In fact, by knowing the two given parameters, Equation [9] can directly estimate the Gini coefficients for 2008.

However, in order to depict a vivid picture of status-quo of income inequality in Macau, we need to graph the Lorenz Curve as visual aid for understanding.

Now that the two-parameter log-logistic distribution is obtained, the cut-off points to divide the population into ten equal shares can be calculated by Equation [3] in Part One. For example, if the first cut-off point is assumed to be Mop 3,647, it basically means that on average there are statistically 10% of people with monthly salary below this point. Likewise, the other 9 cut-off points can be estimated, and subsequently, 10 new income classes can be arrayed between each two cut-off points in ascending order. According to Equation [10], by integrating the log-logistic distribution function for an income class, say from 0 to 3,647, we can get the total income earned from this group. Repeating the procedures to other income classes, we are able to construct the table as follows:

**Table 5.2 – Presentation of constructing new income class with income share in the population **

**Decile ** **Cumulative % **
**of population **

**Cut-off **
**Point **

**New Income **
**Class (Mop) **

**Income in **
**million **

**Income **
**Share **

**Cumulative **
**Share **

**1 ** 0.1 3647 ≦ 3647 80284.1 2.17 2.17

**2 ** 0.2 5060 3648-5060 137886 3.73 5.90

**3 ** 0.3 6290 5061-6290 178679 4.83 10.72

**4 ** 0.4 7518 6291-7518 216970 5.86 16.59

**5 ** 0.5 8854 7519-8854 256857 6.94 23.53

**6 ** 0.6 10429 8855-10429 302494 8.17 31.70

**7 ** 0.7 12465 10430-12466 358537 9.69 41.39

**8 ** 0.8 15494 12467-15494 435668 11.77 53.17

**9 ** 0.9 21494 15495-21494 567799 15.34 68.51

**10 ** 1 NA ≧ 21495 1165230 31.49 100.00

- - Total 3700404 100 -

Apparently, the top 10%, namely the richest, accumulates 31.49% of the total wealth, much more than the 10% at the bottom, which only has 2.17%. Plot the cumulative income share with the cumulative population size, the Lorenz Curve can be graphed on the next page.

**Appendix **

**UMBERET PRESENT | Tears behind the Diamond ** 41
In terms of the accuracy of the estimations, we will compare the three actual Gini coefficients in 1998/1999,
2002/2003, and 2007/2008 with those searched by computers.

**Table 5.3 – Comparison of actual and estimated Gini coefficients **

**1998** **2002 ** **2007 **

**Actual ** 0.43 0.45 0.38

**Estimated ** 0.413 0.458 0.403

**Error ** 4.2% -1.7% -5.7%

As we can see from the Table 5.3, the error of estimation is quite small, less than 5% overall. The difference could be jointly caused by unavoidable error of using log-logistic distribution to fit the true population and the partial representations of income level by salaries. However, we deem the methodology is still valid as it provides a relatively accurate results, and we are not interested in predicting the values of Gini coefficients, where forecasting usually requires to minimize error measures among all kinds of distributions. In other words, it is sufficient for us to conduct good regression analysis to study the significance of influencing factors.

0 10 20 30 40 50 60 70 80 90 100

0 20 40 60 80 100

**Figure 5.1 - Estimated Lorenz Curve**

**Lorenz Curve** **Diagonal-perfectly Equitable Income Distribution**