Running head: HIERARCHICAL LINEAR REGRESSION

Paper #5: Hierarchical Multiple Linear Regression

Maximo Rangel

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Introduction

The objective of this paper is to use the Hierachical Linear Regression technique to analyze possible causal relationships among several variables contained in the Democracy Cross-National Data (Norris), which is an aggregated dataset of macroeconomic and demographic variables, compiling information about 191 countries, comprising 69 variables.

More specifically, the objective is to use Hierarchical Linear Regression to assess the effect of being a democracy and gender empowerment on GDP per capita, after controlling for the effect of Government Effectiveness, decentralization level and Gini Coefficient.

Many authors have studied the link between diverse measures of social fairness, gender equality and government efficiency with the economic growth and prosperity of a nation, and this Democracy Cross-National dataset will serve the objective of addressing such link, due to the nature the variables it contains, and are related to economic prosperity and social fairness.

Data and Measures

The main purpose of this paper is to assess the idea that economic growth is affected by the social fairness, gender equality and government effectiveness in a country. For this purpose, the variable GDP per capita from the Democracy Cross-National dataset will be used as the dependent variable (DV). This dependent variable is measured at the ratio level. Five predictors (IV) will be considered for this multiple linear regression analysis:

• Percent of women in lower house of parliament, 2009 (measured at the ratio level)
• Government effectiveness scale (measured at the interval level)
• Being a democracy (1 = Yes, 0 = No, measured at the nominal level)
• Gini Coefficient (measured at the interval level)
• Decentralization level (measured at the interval level)

The Percent of women in lower house of parliament, 2009 predictor, Government effectiveness scale , Gini Coefficient and Decentralization level are continuous predictors, whereas Being a Democracy . In the context of a hierarchical linear regression, the effect of Being a Democracy and Percent of women in lower house of parliament on GDP per capita will be assessed AFTER controlling for the effect of Government effectiveness scale , Gini Coefficient and Decentralization level . Considering the fact that the DV is highly positively skewed (See Figure 1 below), the DV that will be used is Log(GDP Per capita) instead.

Figure 1: Boxplot of GDP per capita (in $10,000’s)

Results

The first objective is to run multiple regression model to assess the relationship between GDP per capita and the predictors Government effectiveness scale , Gini Coefficient and Decentralization level . These demographic/macroeconomic variables are expected to have a strong effect on the DV, GDP per capita. The results are show in Figure 2 below.

Figure 2 : Regression Results for ln( GDP per capita ) versus Government effectiveness scale , Gini Coefficient and Decentralization level .

The model is significant overall, with F( 3 , 60) = 106.1 , p < .001 . This model explains 83.35% of the variation in ln(GDP per capita). Observe that Government Effectiveness is individually significant ( p < . 001), but Decentralization Level ( p = .421 > .05 ) and Gini Coefficient (p =.716> .05 ) are not individually significant. The model is

ln(GDP Per Capita) = -4.147343 + 0.054448*Government Effectiveness + 0.148839*Decentralization Level – 0.002939*Gini Coefficient

The slope coefficient of government effectiveness is 0.054448, which indicates that an increase in 1 point in the government effectiveness leads to an increase of 5.4448% in GDP per capita. The other two predictors are not individually significant so then the interpretation of their respective slope coefficients is meaningless.

For the second part of the analysis, the effect of Percent of women in lower house of parliament and Being a democracy on ln(GDP per capita) will be assessed after controlling for the effect of Government Effectiveness , Decentralization Level and Gini Coefficient .

Figure 3 : Regression Results for ln( GDP per capita ) versus Percent of women in lower house of parliament and Being a democracy , after controlling for Government effectiveness scale , Gini Coefficient and Decentralization level

The model is significant overall, with F( 4 , 46 ) = 61.61 , p < .001 . The model explains 82.9% of the variation in ln(GDP per capita). The following null and alternative hypotheses will be tested with the information obtained from the full and reduced model:

\(\begin{aligned}

& {{H}_{0}}:{{\beta }_{4}}={{\beta }_{5}}=0 \\

& {{H}_{A}}:\text{ At least one of the above slope coefficients is different from zero} \\

\end{aligned}\)

A partial F-squares test will be used to test the above hypotheses. The following F-ratio is obtained

The p-value is p = Pr(F _{2, 46} > 10.75826) = .000146892 < .05, it is concluded that the contribution of Percent of women in lower house of parliament and Being a democracy is significant, after controlling for Government effectiveness scale , Gini Coefficient and Decentralization level . This is the conclusion obtained with the partial sum of squares test. Though, the value of Adj. R ² for the reduced model is 83.35%, whereas the the value of Adj. R ² for the full model is 82.9%, so then, it is rather the case that the contribution of Percent of women in lower house of parliament and Being a democracy is not of practical significance.

The conclusion is that the main factor (among the ones that were analyzed) in predicting GDP per capita is Government Effectiveness. Other demographic factors, macroeconomic variables and measures of social fairness do not seem to contribute significantly to explain the variation in the dependent variable.

References

The University of Texas at Arlington, Department of Political Science. Democracy Cross-National Data . Retrieved from http://www.uta.edu/faculty/story/DataSets.htm on Dec. 16th, 2015.

Norris, P. Democracy Cross-National Data . Retrieved from http://www.uta.edu/faculty/story/DataSets.htm on Dec. 16th, 2015.

Appendix

R Code

library(foreign)

dataset = read.spss("C:\\World.sav", to.data.frame=TRUE)

gdp_perc<-dataset$gdp_10_thou

women_lowerhouse<-dataset$women09

govern_effectiveness<-dataset$ effectiveness

boxplot(gdp_perc)

ln_gdp_perc <- log(gdp_perc)

democracy<-dataset$democ_regime

democracy_rec<- ifelse(democracy=="Yes",1, 0)

gini<-dataset$gini04

decentralization<-dataset$decentralization

model1<-lm(ln_gdp_perc~govern_effectiveness+decentralization+gini)

summary(model1)

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