The dynamics of economic growth and income inequality in Romania: a statistical analysis of economic transformation in post-eu accession (2006-2021)

Research Hypothesis

The central hypothesis of this study is that economic growth, as represented by Romania's Gross Domestic Product (GDP), significantly impacts income inequality, measured using the GINI index. Specifically:

Null Hypothesis (H₀): There is no statistically significant relationship between GDP and the GINI index in Romania from 2006 to 2021. This implies that changes in GDP do not influence income inequality.
Alternative Hypothesis (H₁): There is a statistically significant negative relationship between GDP and the GINI index in Romania from 2006 to 2021. This suggests that as GDP increases, income inequality decreases.

Data Description and Collection

The study relies on secondary data sourced from the World Bank Open Database. Two primary variables were used:

Gross Domestic Product (GDP):
Representing Romania's economic output, GDP was measured in constant USD to account for inflation. It reflects the total value of goods and services produced within the country each year.
This variable serves as the independent variable, influencing income inequality.

GINI Index:
The GINI index quantifies income inequality on a scale of 0 to 100, where 0 represents perfect equality and 100 represents maximum inequality.
This variable acts as the dependent variable, influenced by changes in GDP.

The dataset spans 2006 to 2021, providing a comprehensive view of Romania’s economic and social landscape during its post-European Union (EU) accession period.
Methodology
Linear Regression Analysis

To test the relationship between GDP and the GINI index, a simple linear regression model was constructed.

Diagnostic Checks

Several diagnostic tests were conducted to validate the regression model:

Residual Analysis: Checked for normality using the Shapiro-Wilk test.
Homoscedasticity: Assessed using the Breusch-Pagan test to verify constant variance in residuals.
Autocorrelation: Evaluated using the Durbin-Watson test to detect correlations in residuals over time.

Findings
Model Results

Correlation Coefficient (R): 0.739

F-Statistic: 16.850 (p = 0.001)
Indicates that the overall model is statistically significant at a 1% level, reinforcing the relationship between GDP and the GINI index.

GDP Coefficient (Unstandardized): -2.472E-11

P-Value for GDP Coefficient: 0.001
Demonstrates that the relationship between GDP and the GINI index is statistically significant.

Diagnostic Test Results

Homoscedasticity: The Breusch-Pagan test identified evidence of heteroscedasticity (p = 0.033), indicating non-constant variance in residuals.
Autocorrelation: The Durbin-Watson statistic (1.126) revealed some positive autocorrelation in residuals, suggesting temporal patterns in unexplained factors.

研究假设

本研究的核心假设是，以罗马尼亚国内生产总值（GDP）为代表的经济发展，对收入不平等（使用基尼系数衡量）产生显著影响。具体而言：

零假设（H₀）：从2006年至2021年，罗马尼亚的GDP与基尼系数之间不存在统计意义上的显著关系。这意味着GDP的变化不会影响收入不平等。

备择假设（H₁）：从2006年至2021年，罗马尼亚的GDP与基尼系数之间存在统计意义上的负相关关系。这表明，随着GDP的增加，收入不平等程度降低。

数据描述与收集

本研究依赖于从世界银行开放数据库获取的二手数据。使用了两个主要变量：

国内生产总值（GDP）：

代表罗马尼亚的经济产出，GDP以固定美元计价，以考虑通货膨胀。它反映了该国每年生产的商品和服务的总价值。

该变量作为自变量，影响收入不平等。

基尼系数：

基尼系数量化了收入不平等，其范围为0到100，其中0表示完全平等，100表示最大不平等。

该变量作为因变量，受GDP变化的影响。

数据集涵盖了2006年至2021年，全面展现了罗马尼亚在欧洲联盟（EU）加入后的经济和社会发展态势。

方法论
线性回归分析

为了检验GDP与基尼系数之间的关系，构建了一个简单的线性回归模型。

诊断检验

进行了多项诊断检验以验证回归模型的有效性：

残差分析：使用Shapiro-Wilk检验检查正态性。

同方差性：使用Breusch-Pagan检验评估，以验证残差的恒定方差。

自相关：使用Durbin-Watson检验评估，以检测残差随时间的变化相关性。

发现
模型结果

相关系数（R）：0.739

F统计量：16.850（p = 0.001）

表明该模型在1%的显著性水平上整体具有统计学意义，强化了GDP与基尼系数之间的关系。

GDP系数（非标准化）：-2.472E-11

GDP系数的P值：0.001

表明GDP与基尼系数之间的关系在统计意义上是显著的。

诊断检验结果

同方差性：Breusch-Pagan检验发现异方差性的证据（p = 0.033），表明残差存在非恒定方差。

自相关：Durbin-Watson统计量（1.126）揭示了残差中存在一定的正自相关，表明未解释因素存在时间模式。