Economic impact due to Cimanuk river flood disaster in Garut district using Cobb-Douglas analysis with least square method

Cimanuk River, Garut District, West Java which have upper course in Papandayan Mountain have an important purpose in dialy living of Garut people as a water source. But in 2016 flash flood in this river was hitted and there was 26 peple dead and 23 peole gone. Flash flood which hitted last year make the settlement almost align with the ground, soaking school and hospital. BPLHD Jawa Barat saw this condition as a disaster which coused by distroyed upper course of Cimanuk River. Flash Flood which happened on the 2016 had ever made economic sector paralized. Least square method selected to analyze economic condition in residents affected post disaster, after the mathematical equations was determined by Cobb Douglas Method. By searching proportion value of the damage, and the result expected became a view to the stakeholder to know which sector that become a worse and be able to make a priority in development


Introduction
Since long time ago, people have settled near the river and today this condition still continued. River becomes one choice for transportation, provides a water for industry and agriculture also be able to increase the quality of life because living in the in the middle of a beautiful nature. But, living near a river have a risk of flood, one of the most dangerous disaster on earth [1]. Cimanuk River location in Garut Resident, West Java, Indonesia which the upstream in Papandayan Mountain have an important role in daily life of Garut citizen such as a source of water. In 2016, was happened a big flash flood in this river and as a consequence there was 26 deaths dan 23 gone also the the economic activity was paralyzed. BPLH (Environmental Management Agency) Jawa Barat saw this condition caused by the damaged land in upstream of Cimanuk River. The flash flood in Cimanuk River in 2016 was the most damage flood ever in Garut. Data from BPLHD (Disaster Management Agency) Garut Resident showed that economic lost in that disaster touch 671 billion rupiahs [2]. In this case, the civilization activity still 2 1234567890''"" near river like hospital, school and housing that means just only upstream and river revitalization can make this disaster stopped. In the other side, upstream revitalization need a time so this this paper aimed to model the economic lost if the condition still the same.
Some research related to this paper are Develop a dynamic optimization model, where inter-temporal decision of an economic agent are interacts with the hydrological system [3]. Input-Output Tables used to study the analysis of the economic impact of a Natural Disaster Tokai Flood in 2000 in Japan [4]. They proposed analysis methodology to estimate returns to scale in case of Cobb-Douglas production function [5]. Partial least square used to identify the information about the correlation of multivariate cognitive abilities and local brain structure in children and adolescents [6] This paper showed the mathematical model which formed by Cobb-Douglas Method and the index and constant gotten by Partial Least Square Method. The main data was generated by normal distribution. This paper aims to derive a mathematical model of Cimanuk river flash flood, that can be used to predict the total of economic lost

Preliminaries
This section describe the main theoretical tools that used to formed mathematical model for flash flood in Cimanuk River.

Cobb-Douglas Method.
Cobb-Douglas production function is a function or a model that involves a dependent variable and two or more independent variables. The model can be written as follow: b c 1 2 Y=aX X (1) Where: Y is an output a is an efficiency index 1 2 X ,X is a kind of input b,c is a production elasticity from the used input In order for data to be obtained can be analysed by Cobb-Douglas Method, so the data must be transformed into a linier form by using natural Logarithm (Ln). The model showed: lnY = ln a+ b ln 1 X + c ln 2 X .
(2) and transform back to (1) [7] 2.2. Partial Least Square Method Partial Least Square (PLS) Method designed to be an alternative from Structural Equation Modelling (SEM) which used to solved the condition between variable really complex but the sample size is small [8]. This method was introduced by Herman O.A Wold to forming a prediction model. (Talbot) PLS used to predict the effect of X variable to Y variable and explained the theoretical correlation between the variable. PLS is a regression method that can be used to identify the factor which combination X variable as an explanation and Y variable as a response.
PLS regression is a method to find a component from X variable which have correlation with Y variable. The concept of PLS regression is describing Y variable as a response and X variable as a predictor by equation: H accepted so the lost of housing, lost of infrastructure, lost of social criteria, lost of economic source and lost of cross sector simultaneous have a correlation into the economic impact.

Wald Test (t test)
Test t aims to determine the differences of each other data by means. The t test also showing how significant the difference are. The t test is done by comparing the value of t-test and t- If 05 H accepted so cross sector have correlation to economic impact.

Normality assumption test
Normality test aims to measure the data having the normal distribution so be able to use on parametric statistic. In this case, Kolmogorov-Smirnov test used to determine the normal distribution from data. If the probability > 0.05 so the data is normal distribution and if probability ≤ 0.05 the data is not normal distribution instead.

Results and Discussion
To know the economic impact, the data using the total economic loss ( Y ) which consist in 5 variable there are 1. The loss of housing 39.318% ( 1 X ), 2. Loss of infrastructure 15,477% ( 2 X ), 3. Social 4,779% ( 3 X ), 4. Economic source 7,021% ( 4 X ), 5. Cross sector such as banking and living environment 33,405% ( 5 X ). Those data will generated into 50 data using Normal Distribution with 1% standard deviation from original data.

Significance Test (F statistics test)
After the data convert to logarithm natural and processed with the F test, the result is

Wald Test (t test)
After the data convert to logarithm natural and processed with the t test, the result is

Normality assumption test
After the data convert to logarithm natural and processed with the normality assumption test, the result is