Proceeding ICST (2021) e-ISSN: 2722-7375 Vol. 2, June 2021 Poverty data modelling in West Nusa Tenggara Province using panel data regression analysis Shilvia Aodia, Nurul Fitriyani, Marwan Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Mataram, Jl. Majapahit 62, Mataram, Indonesia Author’s e-mail: [email protected], [email protected], [email protected] Abstract. Nowadays, Indonesia is still facing poverty issues. One of which is in its province, West Nusa Tenggara. This study aimed to build a poverty model and determine the dominant factors affecting the number of poor people in West Nusa Tenggara Province using panel data regression analysis. The fixed-effect model, with different intercept values for each individual, was selected as the panel data regression model. Based on the research conducted, we derive the best model as follows. 10 ˆ ˆ 10 10 log Y=β0i+0,234908 log X1− ,2112122 log X2 The values of each individual's intercept were as follows: Bima Regency at 7.347; Dompu Regency at 7.101; West Lombok Regency at 7.508; Central Lombok Regency at 7.559, East Lombok Regency at 7.714; North Lombok Regency at 7.376; Sumbawa Regency at 7.346; West Sumbawa Regency at 7.020; Bima City at 6.905; and Mataram City at 7.310. The two most dominant factors affecting the number of poor people in West Nusa Tenggara Province were population (X 1 ) and Human Development Index (X 2 ), with a positive and negative effect, respectively. The model obtained can explain the diversity of the number of poor people in West Nusa Tenggara Province by 64.4%. Keywords: Fixed-effect model; panel data regression model; poverty; West Nusa Tenggara 1. Introduction Many countries in the world are faced with the problem of poverty, including Indonesia [1]. In Indonesia, it is marked by the number of people living below the poverty line [2]. The government continues to reduce this problem, and several efforts have succeeded in reducing the poverty rate in Indonesia [1]. However, the increasing population of Indonesia each year and the diverse characteristics of Indonesia's regions are a challenge in overcoming this poverty problem [3]. West Nusa Tenggara Province is one of among ten provinces with high poverty rates in Indonesia according to Central Statistics Agency (BPS) data in September 2018. Therefore, the government must pay special attention and take appropriate policies according to the province's characteristics and know the ICST conference, December 14 th 2020, published online: June 1 st 2021 698 factors that affect the number of poor people in the West Nusa Tenggara area. In this research, we used regression analysis to determine the factors that affect the number of poor people in the West Nusa Tenggara area [4]. Regression analysis is a study of the dependence of one dependent variable with one or more independent variables to estimate or predict the population mean or average value of the dependent variable based on the independent variable's known value. The purpose of regression analysis is to estimate the mean and value of the dependent variable based on the value of the independent variable so that this can be used in determining the factors that affect the number of poor people in West Nusa Tenggara Province. However, ordinary regression analysis is not suitable if the data used is panel data or data combining cross-section and time series. That is because there is still the possibility of effect from individual units or units of time. This condition can be overcome by using panel data regression analysis. Panel data is useful for seeing the economic impact inseparable between each individual in several periods and is not obtained from cross-section data and time-series data separately [5]. Some of the advantages of using panel data are heterogeneous data, more informative, varied, the greater degree of freedom, more efficient, superior in studying dynamic changes, more able to detect and measure unobservable effects on pure cross-section data and time series purely, and minimizes bias [6]. 2. Research Methods Based on the data and the results to be achieved, this research is a type of applied research using R- Studio software. This study uses secondary data from the Central Statistics Agency (BPS), West Nusa Tenggara Province. This data is divided into districts/cities in West Nusa Tenggara Province with ten districts/cities. This data uses annual data taken from 2014 to 2018. The research variables used are dependent variable,namely the number of poor people in the soul ( Y ) with the independent variable, namely the number of people in the soul ( X 1 ), The human development index in the index ( X 2 ), the average age at first marriage of women aged ten years and over in years ( X 3 ), and the percentage of illiteracy of the population aged 15 years and over in percent ( X 4 ). The data analysis steps carried out in this study are as follows. 1. Preparing the dependent variable and independent variable and exploring general poverty data. 2. Checking the multicollinearity assumptions in the regression model using the following equation. 2 K VIF j = 11 − R j ; j = ,2,1 ,k 3. Performing a regression analysis using the Ordinary Least Square (OLS) method with equations βˆ = (X' X)−1 X' Y . Then choose the best independent variable into the model using the Backward Elimination method. 4. Estimating the parameters of the Common Effect Model using the Ordinary Least Square ˆ −1 method with equations βmg = (X' X) X' Y , the estimation of Fixed Effect Model parameters ˆ ~ ~ −1 ~ ~ using the Fixed Effect Within Group (WG) method with equations βk = ( X'X ) Y'X for * ~ ~ −1 ~ ~ individual effect and βˆ = (X* ) X' * (X* ) Y' * for time effect, and the estimation of the Random k ( ) Effect Model parameters using the Generalized Least Square (GLS) method with equations: ˆ −1 −1 −1 βmpa = (X' V X) (X' V Y − X' μ) . 5. Selecting a panel data regression estimation model between the Common Effect Model and the Fixed Effect Model using the Chow test with the following equation. ICST conference, December 14 th 2020, published online: June 1 st 2021 699 Chow = JKG − JKG N −1 JKG NT − N − k for individual effect, and ( mg mpt ) ( mpt ) Chow = JKG − JKG T −1 JKG NT −T − k to time effect. ( mg mpt ) ( mpt ) ~ ~ ~ ~ with JKG = Y' Y − βˆ X'' Y and JKG = Y'Y * − βˆ Y'X' . mg mpt k 6. Selecting the panel data regression estimation model between the Fixed Effect Model and the Random Effect Model using the Hausman test with the following equation. ˆ ˆ ' ˆ ˆ −1 ˆ ˆ Hausman = (βmpa − βmpt ) (var( βmpa − βmpt )) (βmpa − βmpt ) 7. Selecting the panel data regression estimation model between the Common Effect Model and the Random Effect Model using the Lagrange Multiplier (LM) test. 8. Testing the residual assumption test. a. Normality test, using the Jarque-Bera test with the following equation. S 2 (K − )3 2 JB = n + 6 24 3 2 n n 2 n n 3 2 4 2 with S = (ε i − ε ) n (ε i − ε ) n and K = (ε i − ε ) n (ε i − ε ) n . i=1 i=1 i=1 i=1 b. Homoscedasticity test, using the Lagrange Multiplier test with the following equations. 2 2 N T ε it NT i=1 t =1 LM = N T −1 . (2 T − )1 2 ε it i=1t = 1 c. Independence test, using the Durbin-Watson test with the following equations. =ni =ni 2 2 d = ()ε i − ε i−1 ε i . i=2 i=1 9. Handling assumptions if there is a violation of the residual assumption. If the residuals are not normally distributed, then use data transformation. If there is heteroscedasticity in the residuals, use GLS, and if the residuals are not independent, use Feasible Generalized Least Square (FGLS). 10. Test the feasibility of the panel data regression model by testing the model parameters that have 2 2 been selected simultaneously with the equation F hitung = (R 2) (1− R NT − N − K ) and partially with equations t = βˆ SE βˆ and checking the determinant coefficient of the model with the hitung i ( i ) equation R 2 = [βˆ X'' Y − (Y'11' Y n)] [Y' Y − (Y'11' Y n)]. Furthermore, interpreting the significant coefficient to obtain the best model. 11. Making conclusions. 3. Results and Discussion 3.1. Data Exploration The Figure 1 is the graph of the number of poor people in West Nusa Tenggara from 2014 to 2018. Based on the figure, it can be seen that East Lombok Regency has the highest number of poor people from year to year. The high number is thought to follow the population because this district has the largest population. The district/city with the least number of poor people is Bima City, and it can be ICST conference, December 14 th 2020, published online: June 1 st 2021 700 seen in the graph that Bima City has several poor people only in the range of tens of thousands of people. Figure 1. Number of Poor Population in West Nusa Tenggara 2014-2018 (Thousands of People) The graph shows that each district/city has a poverty plotline that tends to be different. East Lombok Regency has the top plot and is separate from others, which shows that this district has the largest number of poor people. The plots between districts/cities tend to be different due to different poverty rates in each district/city. 3.2. Regression Analysis Regression analysis is carried out after examining the multicollinearity assumptions used to check for the relationship between the independent variables seen from the Variance Inflation Factor (VIF) value generated from the regression model.