ABSTRACT

This paper explored the fractal nature of the annual family income distribution data which appears in the 2006 Family In-come and Expenditure Survey (FIES) by the Philippine Na-tional Statistics Office. The fractal nature was investigated by determining the degree of the power law behaviour and frac-tal dimension of Cumulative Family Annual Income vs. Cumu-lative Number of Family graph for each region in the Philippines. The said fractal dimensions were correlated with the different socio-economic parameters. The fractal dimen-sions show strong correlation (R > 0.8) with average family in-come, average family expenditure, and employment.

Fractal dimension is a good indicator of income distribution inequality among Filipino families. Since, fractal nature assumes scale invariance, it is also possible to see how re-gional family income distributions are reflected in the na-tional family income distribution.

MODEL FORMULATION

The income classes are grouped as follows: (1) Below 40,000.00, (2) 40,000.00 to 59,999.00, (3) 60,000.00 to 99,999.00, (4) 100,000.00 to 249,000.00 and (5) 250,000.00 and above. For a power law graph, the equation should be

I = k Na (Equation 1)

where I is the cumulative family annual income N is the cumulative number of family k is a constant a is the power law exponent or the fractal dimension

Equation 1 cab be rewritten as,

ln(I) = ln(k) + a ln(N) (Equation 2)

Equation 2 shows linear relation between ln(N) and ln(I) which has a slope that is equivalent to the value of fractal di-mension. The slope of Equation 2 can be computed using linear regression. Also, Equation 2 suggests that the degree of fitness of the Cumulative Family Income (I) and Cumulative Number of Family (N) to a power law equation can be com-puted by calculating the degree of linearity (Person’s Coeffi-cient, R) that exists between ln(N) and ln(I).

The nearness of the value of R to number one shows that the Cumulative Family Income—Cumulative Number of Family graph has a high degree of power law behaviour showing the fractality of the income distribution.

RESULTS AND DISCUSSION

The fractal dimension of the Philippines is 1.21 comparable to the fractal dimension of the Cordillera Administrative Re-gion (CAR) which is 1.20. The top five regions (NCR, III, IVA, I, II) with highest fractal dimension are from Luzon (Northern Philippines). The National Capital Region posses the highest fractal dimension of 2.90 which is a large led from the second placer which is Region III (a=1.81). Region IX (Zamboanga Peninsula) has the lowest fractal dimension of 0.72. Higher value of fractal dimension signifies that the income distribu-tion favour higher income earners than the lower income earners.

College of Arts and Sciences, University of the Philippines Los Baños, College, Laguna

Region R

ARMM Autonomous Region of Muslim Mindanao 0.8686

VI Western Visayas 0.9147

XIII Caraga 0.9156

VIII Eastern Visayas 0.9169

V Bicol Region 0.9181

IVB Mimaropa 0.9186

XII Soccsksargen 0.9229

II Cagayan Valley 0.9293

X Northern Mindanao 0.9310

IX Zamboanga Peninsula 0.9354

I Ilocos Region 0.9458

XI Davao Region 0.9472

CAR Cordillera Administrative Region 0.9503

Philippines 0.9536

VII Central Visayas 0.9638

III Central Luzon 0.9649

IVA Calabarzon 0.9758

NCR National Capital Region 0.9833

0

1

2

3Philippines

NCRCAR

I

II

III

IVA

IVBV

VIVII

VIII

IX

X

XI

XII

XIIIARMM

Fractal Dimension of the Philippines and its Regions

Fractal Dimension (a)

Table 1. Pearson’s Coefficient (R) of the Philippines and its Regions

It is noteworthy to state that five out of the top six regions with highest value of R belong to the regions with top urban centers, they are as follows: NCR (1st) , IVA (2nd), III (3rd), VII (4th) and XI (6th). NCR is country’s capital and the most ur-banized region having 16 cities and 1 municipality. Regions IVA and III are nearby regions of NCR which are located south and north of NCR, respectively. Both regions are few minutes-drive from NCR. Region VII houses the metropolis of Visayas (Central Philippines), in which Metro Cebu is lo-cated. Region XI is Davao Region which houses Davao City, the premier city of Mindanao (Southern Philippines).

Table 2. Correlation of Region’s Fractal Dimension and Degree of Power Law Behaviour with other parameters in the 2006 Family Income and Expenditure Survey

Table 3. Correlation of Region’s Fractal Dimension and Degree of Power Law Behaviour with other parameters re-leased by the National Statistics Office

It is also important to point out that based from the same FIES survey, that the National Capital Region has the highest total annual family income, average annual family income, total family expenditure, and average family expenditure while the Autonomous Region of Muslim Mindanao has the lowest. This study shows that the income distribution in the differ-ent regions of the Philippines as reflected in the 2006 Family Income and Expenditure Survey is fractal, i.e. it follows power law and scale invariance. Such distribution can be quantitatively described using fractal dimension and can be correlated with the different socio-economic parameters.

Parameters R

Total Annual Family Income 0.8956

Ave. Annual Family Income 0.8779

Total Family Expenditure 0.8872

Ave. Family Expenditure 0.8908

Number of Families 0.7552

Parameters Correlation Coefficient

2007 Population 0.7508

2000 Population 0.7475

1995 Population 0.7720

2003 Functional Literacy 0.6179

2003 Functional Literacy (Male)

0.7070

2003 Functional Literacy (Female)

0.4833

2006 Employment -0.8711

2006 Underemployment -0.5641

Poster Presentation, 2nd CAS Student-Faculty Conference

December 14, 2009

University of the Philippines Los Baños