**3. Methodology**

The research and analysis of efficiency in city councils in Chile, evidenced in the literature, is usually carried out from microeconomic theory, which evaluates two aspects of municipal efficiency: inputs and output.

In fact, municipal efficiency is considered optimal when it reaches its maximum level of production, compared to certain inputs and the minimum level of inputs in a given product [24, 32].

In the case of Chile, the studies and methodology applied to the efficiency of the city councils are few and focused on resources, not addressing other aspects of importance and complexity for the economic reality.

In relation to the methodology, the analysis was applied to 93 communes in Chile, incorporating a diverse sample of the country, both in its politicaladministrative and geographical configuration. In other ways, the study integrates communes from the northern, central and southern macro-zones of the national territory. A cross-sectional econometric regression model was developed to explain and predict the effect over the municipal efficiency measured by Quality of Life Index (QLI) [33–36]. This is validated by the assumptions of the residual before proceeding with the second objective, which is the estimation and interpretation of results [36, 37].

In order to build the database to be used to forecast the efficiency of city councils in Chile [38], the National Municipal Information System was consulted, together

with the Library of the National Congress of Chile (BCN), as well as an approximation based on the Urban Quality of Life Index (QLI) for the year 2018, while bearing in mind the different areas of the country. The model estimate specified in Eq. (1) is presented in the following **Table 2**.

$$\begin{array}{l} \text{QLI}\_{i} = \alpha + \beta\_{i} \,\*\,\text{AveragePSU}\_{i} + \beta\_{\text{\*}} \,\*\,\text{PopulationDensity}\_{i} \\ \quad + \beta\_{\text{\*}} \,\*\,\text{Overcreouding}\_{i} + \beta\_{\text{\*}} \,\*\,\text{RateDocumentValue}\_{i} \\ \quad + \beta\_{\text{\*}} \,\*\,\text{FCM}\_{i} + \beta\_{\text{\*}} \,\*\,\text{OumIncomeIPP}\_{i} + \beta\_{\text{\*}} \,\*\,\text{Health}\,\text{Budget}\_{i} \\ \quad + \beta\_{\text{\*}} \,\*\,\text{Schularship}\_{i} + \beta\_{\text{\*}} \,\*\,\text{OtherIncome}\_{i} + \beta\_{\text{\*}} \,\*\,\text{GreenArea}\_{i} \\ \quad + \beta\_{\text{\*\*}} \,\*\,\text{Powerty}\_{i} + \mu\_{i} \end{array} \tag{1}$$

After estimating the tentative model using Stepwise Econometric Regression Models, and considering all of the variables studied to determine the quality of life of the inhabitants of a commune, the variables relevant to the determination of the study's approach, such as municipal efficiency, were selected (see **Table 1**). The variables that were greater than the minimum level of confidence (p-value ≤0.05)


#### **Table 2.**

*Estimation of general model parameters.*

**279**

*Efficiency of the City Councils Using Cross-Sectional Model: Challenges in Times of Change…*

F-statistic 0.391564 Prob. F(2.82) 0.6773 Obs\*R-squared 0.860859 Prob. Chi-Square(2) 0.6502

F-statistic 0.462869 Prob. F(27.63) 0.9852 Obs\*R-squared 15.06367 Prob. Chi-Square(27) 0.9685 Scaled explained SS 15.65709 Prob. Chi-Square(27) 0.9592

adopted for this study were eliminated from the model. In addition to this method, what was stated in the literature and determination of the endogenous variable was

Given the estimates of the variables described earlier in this chapter, a final econometric model was proposed that better and more up-to-date (**Table 1**) repre-

According to the Quality of Life Index (QLI), the variability in the efficiency of Chilean municipalities is explained by 71% (R-squared) of the following variables: Municipal Common Fund (FCM), Permanent Income from own source (IPP), Overcrowding, PSU average, population density and rate of domestic violence. As for the hypotheses associated with the residues of the model, which can compare its behavior with **Figure 1**, they do not present problems of self-correlation of the

As illustrated by **Figure 1**, we can see the distribution of the residuals, considering the data obtained through QLI, as the estimation of efficiency through the final model proposed, with the difference shown on the graph explained by the R2 adjusted for the 71.29% model. By the way, the final model for the Urban Quality of

7

This study provides us with contrasts between different municipalities that allow us to reach conclusions on the current situation in northern, central, and southern Chile. It also allows us to find and tear down certain prejudices, such as the centralization of the country, showing the variables that are influential to a greater

−

∗ − ∗

1.12 10

*RateDpmesticViolence*

∗ +∗ ∗

*QLI AveragePSU*

= +∗ −

59.44 16.37 0.00043

∗ −∗ −

*PopulationDensity Overcrowding*

nor problems of heteroscedasticity (**Table 4**) of the aforementioned.3

7

−

2.15 10

*FCM OwnIncomesIPP* (2)

79.51 0.013

(**Table 3**), nor problems of normality of

sents the factors that involve the efficiency of city councils in Chile.

residues, using the Breusch-Godfrey test1

Life Index (QLI) is [Eq. (2)].

<sup>1</sup> Breusch-Godfrey F Test: 2.82; P-value = < 0.1. <sup>2</sup> Jarque-Bera Test: 4.4654; P-value = < 0.1. <sup>3</sup> White Test F-statistic: 27.63; P-value = < 0.1.

*DOI: http://dx.doi.org/10.5772/intechopen.93655*

*Source: Own creation by means of EViews statistical program.*

*Source: Own creation by means of EViews statistical program.*

*Breusch-Godfrey serial correlation LM test.*

also considered.

*Heteroscedasticity white test.*

**Table 3.**

**Table 4.**

the residues,<sup>2</sup>

**4. Conclusions**

**Figure 1.** *Residual from the final model. Source: Own creation by means of EViews statistical program.*

*Efficiency of the City Councils Using Cross-Sectional Model: Challenges in Times of Change… DOI: http://dx.doi.org/10.5772/intechopen.93655*


**Table 3.**

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

1 2 3 4

=+ ∗ + ∗ + ∗ + ∗

*i i*

 µ

*Poverty*

ββ

ββ

5 6 7 8 9 10

+∗ +∗ + ∗ +∗ +∗ + ∗

*ii i*

 β

β

After estimating the tentative model using Stepwise Econometric Regression Models, and considering all of the variables studied to determine the quality of life of the inhabitants of a commune, the variables relevant to the determination of the study's approach, such as municipal efficiency, were selected (see **Table 1**). The variables that were greater than the minimum level of confidence (p-value ≤0.05)

**Variable Coefficient Std. error t-Statistic p-Value** RateDomesticViolence −0.012964 0.004200 −3.086408 0.0028 Health Budget 0.076376 0.053567 1.425805 0.1579 Scholarship −0.000210 8.57E-05 −2.445162 0.0167 OwnIncomesIPP 2.89E-07 1.05E-07 2.752694 0.0073 Other Incomes −3.70E-07 2.59E-07 −1.431423 0.1563 FCM 1.64E-07 2.15E-07 0.762711 0.4479 PopulationDensity −0.000564 0.000130 −4.355540 0.0000 Green Areas 1.84E-06 1.15E-06 1.598367 0.1140 Average PSU 12.81732 4.457474 2.875466 0.0052 Overcrowding −57.43565 18.52834 −3.099881 0.0027 Poverty −22.91616 13.88977 −1.649859 0.1030 C 59.64198 4.667443 12.77830 0.0000

*QLI AveragePSU PopulationDensity*

presented in the following **Table 2**.

α β

β

11

β

with the Library of the National Congress of Chile (BCN), as well as an approximation based on the Urban Quality of Life Index (QLI) for the year 2018, while bearing in mind the different areas of the country. The model estimate specified in Eq. (1) is

> *Overcrowding RateDomesticViolence FCM OwnIncomesIPP HealthBudget Scholarship OtherIncomes GreenAreas*

*i i i ii*

+∗ + (1)

*i ii*

 β

 β

**278**

**Figure 1.**

**Table 2.**

*Estimation of general model parameters.*

*Residual from the final model. Source: Own creation by means of EViews statistical program.*

*Breusch-Godfrey serial correlation LM test.*


### **Table 4.**

*Heteroscedasticity white test.*

adopted for this study were eliminated from the model. In addition to this method, what was stated in the literature and determination of the endogenous variable was also considered.

Given the estimates of the variables described earlier in this chapter, a final econometric model was proposed that better and more up-to-date (**Table 1**) represents the factors that involve the efficiency of city councils in Chile.

According to the Quality of Life Index (QLI), the variability in the efficiency of Chilean municipalities is explained by 71% (R-squared) of the following variables: Municipal Common Fund (FCM), Permanent Income from own source (IPP), Overcrowding, PSU average, population density and rate of domestic violence. As for the hypotheses associated with the residues of the model, which can compare its behavior with **Figure 1**, they do not present problems of self-correlation of the residues, using the Breusch-Godfrey test1 (**Table 3**), nor problems of normality of the residues,<sup>2</sup> nor problems of heteroscedasticity (**Table 4**) of the aforementioned.3

As illustrated by **Figure 1**, we can see the distribution of the residuals, considering the data obtained through QLI, as the estimation of efficiency through the final model proposed, with the difference shown on the graph explained by the R2 adjusted for the 71.29% model. By the way, the final model for the Urban Quality of Life Index (QLI) is [Eq. (2)].

$$\begin{array}{l} \text{QLI} = \mathfrak{g}\mathfrak{g}.\mathfrak{4}\mathfrak{4} + \mathfrak{sl}\mathfrak{sl}\mathfrak{z}\mathfrak{\*}\mathfrak{z}\mathfrak{\*}\mathfrak{a}\operatorname{ver}\mathrm{PSU} - \mathfrak{o}.\mathsf{co}\mathsf{o}\mathsf{o}\mathsf{4}\mathfrak{z}\mathfrak{z}\mathfrak{z} \\ \quad \ast \operatorname{Population}\mathrm{Density} - \mathfrak{z}\mathfrak{g}.\mathsf{z}\mathfrak{z}\mathfrak{z}\mathfrak{\*}\operatorname{Overcrowding} - \mathfrak{o}.\mathsf{o}\mathsf{z}\mathfrak{z}\mathfrak{z} \\ \quad \ast \operatorname{Rate}\mathrm{Dprestie}\mathrm{Voicence} - \mathfrak{z}\mathfrak{z}\mathfrak{z}\mathfrak{z}\mathfrak{z}\mathfrak{z}\mathfrak{z}\mathfrak{z}\mathfrak{z} \\ \quad \ast \operatorname{FCM} + \mathfrak{z}.\mathsf{12}\mathfrak{\*}\mathfrak{z}\mathfrak{z}\mathfrak{o}^{\top} \ast \operatorname{Own}\mathrm{Income}\mathrm{I}\mathrm{IP} \end{array} \tag{2}$$
