Spatial Regression Models on Factors Influencing Regional Minimum Wages

Abstract


INTRODUCTION
National development is an embodiment of government policies to improve people's welfare.Such an indicator of national development's success is economic growth, both on national and regional scales.An economy is balanced if it develops and grows consistently and evenly in all districts/cities.Several indicators can represent the economic progress of a region.One of them is the regional minimum wage [1], [2].
The determination of the regional wage is based on the standard of living costs and inflation, which are also considered economic growth.The fact is often becoming a problem in determining the wage because inflation and economic development in each region are different.In contrast, the percentage increase in pay is often unable to cover the working family [2].In Indonesia, one of the provinces that often gets the public spotlight in determining the wage is East Java.It is due to East Java's role as a center for industry, manufacture, etc. [3].Therefore, this study will model the factors that affect the wage in East Java in a spatial context such that it can be input in determining the wage.
Statistics modeling is generally carried out using linear regression.However, this method's weakness is the inability to capture the relationship among space, common in economic cases [4], [5].The technique developed to deal with the spatial issue in spatial regression.This model can The year used is 2017 data for 38 districts/cities in East Java.The methods in this study include Spatial Autoregressive (SAR) and Spatial Error Model (SEM).The modeling stages are as follows.

a. Analyzing the descriptive of variables b. Identifying the relationships between variables
The relationships between variables were identified by Pearson correlation.This is to determine the strength of the relationship between the wage and all independent variables.

c. Carrying out classical regression
Classical regression is a linear regression whose parameter estimator is obtained through the Ordinary Least Squares (OLS) by minimizing the squares of error or by maximizing the likelihood function that is normally distributed [13].The following is a general equation for classical regression,   Several assumptions are ideally not violated [8], that is: 1.There was no multicollinearity or dependency, which was statistically significant between the predictors.If this assumption is broken, it can be overcome by stepwise regression.2. Homoscedastic, the residual variance of each observation ε i constant/homogenous. 3.There is no residual autocorrelation (dependency) between observations.4. Residual is usually distributed.Estimator β of the classical regression model is obtained by, d. Checking the spatial correlation on the wage variable based on Moran's I Moran's with weight w in normalized form can be calculated by, where is Moran's I index, is the number of observation, x i is the observation on -th observation, x j the observation on j-th observation, is the mean of , and w ij is the array of weight matrices.The value of ranges from −1 to 1.If = ≈ 0, then there is no spatial autocorrelation.While ≠ , presumably, there is a positive autocorrelation when is positive, and vice versa [6], [7].

e. Carrying out the spatial modeling
Spatial modeling begins with determining weighting matrices.Various weights could be used, including rook contiguity and queen contiguity.Next is testing the spatial effects with the following steps.
The decision to reject H0 is when the LM ρ value greater than χ 2 (q) , with q, is the total number of spatial parameters.Thus, if H0 is rejected, the spatial regression model is the SAR model [6], [7] The decision to reject H0 is when the LM λ value is more significant than χ2(q), with q being the total spatial parameters.If H 0 is rejected, thus the spatial regression model that exists is the SEM model.The residual ε is obtained from classical regression [6], [7].Breusch-Pagan test can be used as an indicator of spatial heterogeneity in the dependent variable (y), namely the regional minimum wage.The hypothesis is as follows.
At least there is one σ 2 k ≠ 0 (non-identical variance/indicated heterogeneity) Statistical test: with k is the total regression parameter.The decision to reject H 0 is when BP statistical test value greater than χ 2 (k-1) [6], [7].

Carrying out spatial regression and diagnostic checking
The general equation for spatial regression is   The assumptions of SAR and SEM models must be fulfilled similar to those of classical regression, where the residuals meet the identical, independent, and normally distributed [6], [7].

f. Analyzing the goodness-of-fit
The measure of the goodness-of-fit model being used is R 2 and AIC.The coefficient of determination (R 2 ) is a measure in explaining regional wage in East Java modeled by independent variables.The higher R 2 , the more accurate the regression model describes the relationship between the wage and independent variables .AIC is a measure that represents the simplicity of the regression model.The lower the AIC, the simpler the regression model is, so it is easy to interpret [4], [13].To strengthen the decision, the spatial model significance test with the Robust LM is also used.

g. Mapping the regional wage
The forecast for wage yielded from the best regression model is then mapped to see the wage gradations between districts/cities.Mapping is carried out using ArcGIS.

RESULTS
The spatial regression model is based on secondary data involving one dependent variable (regional minimum wage) and four independent variables in Table 1.The data analyzed were for 2017, with a total of 38 observation units.The first step taken is descriptive analysis.Figure 1 presents the comparison of the UMR of East Java Province with several other provinces in Java Island in 2017.Refer to Figure 1, the average wage of East Java is among the lowest ones in Java.It indicates that the welfare of workers and employees in East Java is relatively low, especially in less rapidly developing economies.Thus, study on the factors that are thought to influence the minimum wage is essential to see a more precise formula in formulating the minimum wage.Figure 2 indicates that inter-dependencies cause the wage in several geographically adjacent districts to have the same magnitude.Central regions in East Java (from north to south), such as Gresik Regency, Surabaya to Malang Regency, tend to have similar wages.Meanwhile, the wage between horseshoe regions (provinces in Madura Island, Jember, Banyuwangi, and surrounding areas) tends to be related, although not as strong as the central region of East Java.This suggests that the wage cannot be explained by classical regression alone, inline with [4] and [11].Figure 3 shows the relationship between the wage as the response variable and the four independent variables that will be regressed.Figure 3. Scatter Plot of Wages and Independent Variables Figure 3 still cannot clearly show how strong the relationship between the UMR and the independent variables, the same with the direction of the connection (whether positive or negative).This is since the linear pattern is not visible, except in the scatter plot of wage and x 1 (Total Working Population) resembles a positive practice.Therefore, a correlation coefficient, as shown in Table 2, is needed to see this formally.Based on Table 2, it can be concluded that all independent variables have a positive relationship with UMR and are statistically significant at α = 5%.That is, the classical regression model used is relatively good in explaining the effect of the independent variables on the wage.However, there are indications that such a regression model will violate the assumption of multicollinearity since x 1 (Total Working Population) and x 3 (Total Population) had significant correlation at α = 5%, so did with x 1 and x 2 (Gross Domestic, Regional Product) and variable x 2 with x 3 .
To get the factors influencing the wage, a regression model is summarized in Table 3. Refer to Table 3, there is indicated a multicollinearity where x 1 (Total Working Population) and x 3 (Total Population) are related, shown by a very high VIF, which exceeds the maximum VIF tolerance limit of 10.Thus, OLS regression is not appropriate to model the wage in East Java.To solve this problem, one solution is to apply stepwise regression.Such stepwise model estimation are shown in Table 4. Table 4 shows that almost all parameters have a significant effect on the wage at α = 5%.Thus, total working Population (x 1 ) and percentage of Population with minimum education of senior high school (x 4 ) are significant to the wage in East Java.In addition, multicollinearity is no longer found since the VIF value is less than 10.However, the R-sq is low which is 51.47%.The model is as follows.Total Working Population (x 1 ) has a positive influence on the UMR.If total working population increases by 1,000 people, it will increase the wage around IDR 1,198.Besides x 1 , percentage of population with minimum education of senior high school (x 4 ) also has a positive effect on the UMR.If it increases 1%, it will also increase the wage around IDR 28,080.Apart from R-sq, the goodness-of-fit can also be seen based on the Akaike Information Criterion (AIC).The AIC value for this model is 572.
In each regression modeling, there are several assumptions about the model residuals that should not be violated, namely homoscedasticity, no autocorrelation, and normally distributed [14].A summary of classical assumptions test is presented in Table 5.It is concluded that the residuals of the classical model have fulfilled the IIDN.However, the autocorrelation indicates that the wage should be analyzed using other modeling approaches, that is spatial regression.The spatial dependence on the wage can be identified through Moran's I. Morans' I is an index to identify the spatial correlation of the wage between 38 districts/cities in East Java.The plot of the distribution of the wage along with Morans'I coefficient is shown in Figure 4.In Figure 4, Moran's I of 0.747 indicates that the wage has positive spatial correlation.After testing based on normal distribution approach, the statistic was 6.61.with α = 5%, so the statistical test = 6.61 > z 0,95 = 1.645, therefore H 0 is rejected.At 95% confidence level, the spatial correlation of the wage is statistically significant, meaning that districts/cities that are geographically close to each other tend to have the similar wage affecting each other.This is confirmed by the distribution of the observation points in Figure 4 which resembles a positive linear trend.As an illustration, the wage in the satellite districts of Surabaya, such as Gresik and Sidoarjo, tends to have a relatively similar value to that of Surabaya, where the effect of increasing the wage in Surabaya will also encourage that of Gresik and Sidoarjo.The next step is to build a spatial regression model.In this case, the weight is used to construct the spatial regression using queen contiguity.This decision was motivated by the results of the spatial correlation which proved to be statistically significant [6], [7].This indicates that sharing boundaries are linked.After forming a spatial weightmatrix, a row-standardized matrix is normalized.To strengthen the assumption that classical regression can be better constructed using spatial information, it is necessary to measure the Morans'I Error obtained from the residuals of classical model results.Then the value of Morans'I Error is 2.4.With α = 5%, then the value = 2.4 > z 0,95 = 1.645 so the decision is reject H 0 .At confidence level 95%, the residual spatial correlation of the wage regression model is statistically significant.In addition, the BP test for heterogeneity indicated no spatial heterogeneity for the wage in East Java.Thus, there are evidence supporting the spatial regression.
After ensuring there is no spatial heterogeneity, the next step is testing the spatial dependency.The LM test is carried out to test whether there is a spatial dependence on the wage of districts/cities in East Java.Table 6 presents the LM test results for two alternative spatial regression models.Refer to Table 6, the LM of each model coefficient, SAR and SEM, is greater than χ 2 (1) at α = 5%.According to [8] and [15], this indicates the significance of spatial dependence of minimum wage in East Java.Therefore, the next step is to build SAR and SEM regression model.
The SAR model is characterized by ρ ≠ 0 and λ = 0 [6], [7].This model is based on the dependency of spatial lag.If the resulting model has spatial dependencies, then the SAR model can be used.Table 7 is the result of SAR parameters estimation for two predictor variables of stepwise regression results.Table 7 shows Total Working Population (x 1 ) and percentage of population with minimum education of senior high school (x 4 ) are significant affecting the wage in East Java at α = 5%.It is based on p-value of both parameters that are less than α = 5%.Significant ρ indicates that H 0 of SAR model is rejected such that spatial lag dependency is statistically evident on wage, particularly in West Java.The following is SAR model of regional minimum wage of East Java.This SAR model shows that Total Working Population (x 1 ) has a positive relationship with the wage in districts/cities in East Java.Such increase x 1 of 1,000 people will increase the wage about IDR 880.In addition, percentage of minimum education of senior high school (x 4 ) also has a positive relationship with the wage in East Java where the 1% increase of x 1 will increase the wage about IDR.12,570.Coefficient ρ of 0.47 indicates that the closest area to a spatial unit (regency/city) each gives almost half the effect of the wage fluctuation in that spatial unit.

Tabel 7. Parameter Estimation of SAR
High influence yielded by closest regions indicates that the welfare of workers is necessary on the spatial dependency.It is not surprising that the rally of workers in Surabaya will also be followed by similar rally in Gresik and Sidoarjo demanding increasing wage.Since this study compares spatial regression models.then next is applying SEM regression on the wage model in East Java.Such SEM is characterized by ρ = 0 and λ ≠ 0 [6], [7].This model is based on residual dependencies in a spatial context.If the residuals has spatial dependencies, then the SEM model can be considered.Table 8 shows the estimation results and testing of SEM parameters for two predictors selected by stepwise approach.Tabel 8 shows that Total Working Population (x 1 ) and percentage of high school graduates (x 4 ) are statistically significant to the regional wage in East Java at α = 5%.Significant λ indicates that H0 of SEM is rejected, so that the spatial dependency residual is significant to the wage in East Java.It means there are factors that are thought to affect the wage but are not included in the model, such as inflation.Below is estimated SEM model for minimum wage in East Java.Such equation indicates that the increase of Total Working Population (x 1 ) by 1000 people will increase the wage around IDR 850.In addition.The percentage of senior high-school graduates (x 4 ) also has a positive relationship with the minimum wage in East Java.Such increase in x 4 by 1% will increase the wage about IDR 13,430.
The best model can be identified based on R 2 value, AIC, and parameter significance.It also includes the sign of the parameter coefficient in accordance with the expected sign/prevailing theory and the fulfillment of IIDN assumptions for model residuals [14].Table 9 shows the comparison of the classical and spatial models.From the comparison in Table 9, the best model is shown by SAR model since it has higher R 2 than that of SEM model.In addition, the efficiency of SAR model is also better than that of SEM model because of lower AIC of SAR model.However, the residuals of SEM model and SAR model are not normally distributed.However, this does not necessarily affect the model since it is not intended for prediction purposes.Besides, total observations that more than 30 have met the minimum sample allocation to fulfill the residual assumptions of regression model [16].
The goodness of SAR and SEM shows the improvement over the model specification error in classical regression (multiple linear regression) where R 2 of SAR and SEM models, respectively, increased to 69.04% and 64.06% from the previous 51.47% of classical regression.Almost 65% of regional minimum wage of East Java can be explained by spatial models, while the remainder is explained by other factors not included in the model.
It is decided to choose the SAR model in modeling the minimum wage of East Java based on two influential variables, namely total working Population (x 1 ) and percentage of Population with minimum education of senior high school (x 4 ).Further testing using Robust LM statistic suggests that SAR model is better at identifying more representative spatial model.Figure 5 shows the results of the minimum wage mapping in 38 districts/cities in East Java Province using SAR model.It was shown that region in the horseshoe zone, such as Madura Island and other districts such as Banyuwangi, Bondowoso, and Jember are classified into various categories of wage with Jember falling into the higher wage category (intervals of IDR 1,836,150-IDR 2,390,600).Most of the central zone falls into category 3, medium wage.This is due to the relatively low number of working people.Based on Figure 5, it can be concluded that the welfare of workers and employees is still not guaranteed because some of the wage estimation are in the low classification (red zone), among others, Sampang and Pamekasan Districts on Madura Island and Pacitan and Trenggalek.
Through this study study, it is shown that the wage is influenced by two aspects, namely labor (represented by the total working Population) and education (represented by the percentage of the Population with a minimum education of high school).The wage between districts/cities is also proven to be connected, especially for districts/cities that are located close to each other.This confirmed the initial notion that spatial dependence was prevalent in the economic case.

CONCLUSION
There are two factors affecting the minimum wage in East Java, namely Total Working Population and percentage of Population with minimum high school education.It is found that the minimum wage between districts/cities in East Java is spatially related.Based on the selection of the best model, spatial regression is better than classical regression because it has higher R 2 and does not violate whole residual assumption.The SAR model is chosen to model the minimum wage rather than SEM because it has smaller AIC and is able to better explain the minimum wage variance and it fulfills the Robust LM test.
It is recommended that local governments do not only consider the cost of living aspect, inflation, and economic growth in determining the minimum wage.Through this study, it is shown that there are other aspects which have significant role on wage, such as manpower and education.It is expected that there is no huge gap in the minimum wage of the regions and is relevant to the economic conditions of each region and does not hurt many parties, such as the factories/employers, the workers and their families.For further research, the improvement of the model from initially spatial to spatio-temporal is also interesting to study following that the wage dynamics in the labor sector are always moving.
If ρ (spatial coefficient) and λ (spatial error coefficient) are statistically significant at α, then the model of spatial regression becomes SARMA (Spatial Autoregressive Moving Average).If only one of the spatial coefficient, ρ, is significant, then the model of spatial regression becomes SAR (Spatial Autoregressive) model with the equation as follows, Copyright © 2020, Numerical: Jurnal Matematika dan Pendidikan Matematika Print ISSN: 2580-3573, Online ISSN: 2580-2437 101If only the coefficient λ is statistically significant, then the model of spatial regression becomes SEM (Spatial Error Model) with the equation as follows,

Figure 1 .
Figure 1.Wage Comparison of Java's Provinces in 2017

Figure 2 .
Figure 2. Minimum Wage of East Java Districts /Cities in 2017 Moran's I = 0.747

Figure 5 .
Figure 5. SAR Model Estimation Mapping of East Java's Minimum Wage Figure 5 shows five categories of wage estimation generated by SAR model where Surabaya and Sidoarjo are the districts/cities with the highest wage (green gradation), if the wage is only influenced by the large total working Population and the percentage of the Population with a minimum education of SMA.This is relevant and appropriate to the real condition because those regions are the centers of medium-large scale industry which are modern and thus need a lot of labor and capital.

Table 1 .
Variable Description

Table 2 .
Variable Description

Table 3 .
Parameter Estimation and VIF

Table 4 .
Stepwise Regression Parameter Estimation and VIF

Table 5 .
The Summary of Residual Checking

Table 6 .
LM Test of Spatial Model Significance

Table 8 .
Parameter Estimation of SEM

Table 9 .
Regional Minimum Wage Model Comparison