Investigation of Parabolic Relationship Between Financial Development and Income Inequality using U Test: Analysis of Financial Curve in Türkiye
Nimet Melis Esenyel İçenThis study investigates the relationship between income inequality and financial development within the framework of the financial Kuznets hypothesis. The aim of this study is to determine the effects of financial development, inflation, and per capita income variables on income inequality using annual data from Turkiye for the period 1987-2021. The share of domestic credits to the private sector provided by banks in gross domestic product is considered as a measure of financial development. The Gini coefficient is used as an indicator of income inequality. To examine the long-term relationships between variables, the ARDL Bounds test developed by Pesaran, Shin, and Smith (2001) is conducted. According to the ARDL Bounds test, it is concluded that there is a long-run relationship exists among the variables. In the estimated long-run model, when examining the signs and statistical significance of the coefficients of the financial development variable and its square, it is found that there is initially a U-shaped relationship. However, this assessment is inadequate and may lead to misleading results. Therefore, a three-step model evaluation method is employed. First, attention should be paid to the signs and statistical significance of the coefficients of the financial development variable and its square. In the second step, it is checked whether the turning point of the parabola is within the data range. Finally, the slope at the smallest and largest values of the parabola should be sufficiently steep. According to the U test conducted to verify this condition, we conclude that the U-shaped model is valid.
Finansal Gelişmişlik ve Gelir Eşitsizliği Arasındaki Parabolik İlişki Üzerine U Testi İncelemesi: Türkiye Örneği
Nimet Melis Esenyel İçenBu çalışmada gelir eşitsizliği ile finansal gelişmişlik arasındaki ilişki, finansal Kuznets hipotezi çerçevesinde araştırılmıştır. Türkiye’nin 1987-2021 yılları arası yıllık frekansta finansal gelişmişlik, enflasyon, kişi başı gelir değişkenleri alınarak, gelir eşitsizliği üzerindeki etkilerinin belirlenmesi amaçlanmıştır. Bankalar tarafından özel sektöre verilen yurt içi kredilerin gayrisafi yurt içi hasıladaki payı, finansal gelişmişlik göstergesi olarak ele alınmıştır. Gelir eşitsizliğinin bir göstergesi olarak ise Gini katsayısı kullanılmıştır. Çalışmada değişkenler arasındaki uzun dönemli ilişkinin araştırılmasında, Pesaran, Shin ve Smith (2001) tarafından geliştirilen ARDL Sınır testi yapılmıştır. ARDL sınır testine göre, değişkenler arasında eşbütünleşme ilişkisi olduğu sonucuna ulaşılmıştır. Tahmin edilen uzun dönem modelinde, finansal gelişmişlik değişkeni ve bu değişkenin karesinin katsayılarının işaretlerine ve istatistiksel anlamlılıkları incelendiğinde, önsel olarak U-tipi bir ilişkinin olduğu sonucuna ulaşılmıştır. Ancak bu değerlendirme yetersizdir ve yanıltıcı sonuçlar elde edilmesinde sebep olabilir. Bu sebeple üç aşamalı model değerlendirme yöntemi kullanılmıştır. Öncelikle, finansal gelişmişlik değişkeni ve bu değişkenin karesinin katsayılarının işaretlerine ve istatistiksel anlamlılıklarına bakılmalıdır. İkinci aşamada, parabolün dönüm noktasının veri aralığında olup olmadığı kontrol edilmedir ve son olarak parabolün en küçük ve en büyük değerlerindeki eğimi yeterince dik olmalıdır. Bu koşulun kontrol edilmesi için yapılan U testine göre, U-tipi modelin geçerli olduğu söylenebilir.
In the literature, the relationship between financial development and income inequality is tested through three different hypotheses. The first hypothesis is the Inequality Narrowing Hypothesis by Galor and Zeira (1993), which suggests a negative linear relationship between financial development and income inequality. The second hypothesis is the Inequality Widening Hypothesis, which posits a positive linear relationship between financial development and income inequality. As proposed by Rajan and Zingales (2003), this hypothesis suggests that an increase in financial development intensifies income inequality. The third hypothesis is based on the idea that a reverse U-shaped relationship between financial development and income inequality. Financial Kuznets Hypothesis proposed by Greenwood and Jovanovic (1990) is another version of Kuznets’ literature.
According to the Financial Kuznets Hypothesis (FKH), access to financial services is limited and costly in the early stages of financial development due to inadequate financial regulations. Consequently, the low-income segment cannot access financial services, whereas the high-income segment can. As a result, the gap between high- and low-income individuals widens (Keskin, 2022). However, in the later stages of economic development, as financial regulations improve, the cost of accessing financial services decreases, and more individuals benefit from these opportunities. Therefore, the income gap between high- and low-income segments narrows, leading to reduced income inequality (Greenwood and Jovanovic, 1990).
The mathematical model employed when testing the (FKH) should satisfy specific conditions that determine the shape of the curve (U-shaped, inverted U-shaped, N-shaped, inverted N-shaped) and its turning points. However, when these conditions are met, the empirical model used is validated. In this study, a quadratic model will be utilised for FKH; therefore, only the conditions of the quadratic model will be evaluated. In this case, the empirical model can be validated by examining the sign of the square of the financial development indicator used. To elucidate, we consider the quadratic model expressed by Equation (1):
𝑌 = 𝑏0 + 𝑏1𝐹 + 𝑏2𝐹 2 + E
Here, Y represents income inequality indicator and F denotes financial development indicator. Equation (1) represents the mathematical form of the (FKH). The first and second derivatives of Equation (1) relative to F are obtained as follows:
𝑑𝑌/𝑑𝐹 = 𝑏1 + 2𝑏2F
𝑑 2𝑌/𝑑𝐹2 = 2𝑏2
Where 𝑏2 < 0 and statistically significant, indicating the presence of a local maximum point and thus an inverted U-shaped relationship, while 𝑏2 > 0 and statistically significant indicates the validity of a U-shaped relationship. However, fulfilling this condition alone is not sufficient to determine the type of relationship. To determine the relationship between income inequality and financial development, Lind and Mehlum (2010) proposed a three-step approach.
The first step involves examining the sign and significance of the coefficient, as mentioned above. The second step, the slope between the minimum and maximum values of the data must be sufficiently steep. Lind and Mehlum (2010) developed a new test statistic called the U test based on the Sasabuchi (1980) test for investigating U-shaped and inverted U-shaped relationships. Finally, the third step involves the value of −𝑏1/2𝑏2 represents the turning point. Ensuring that the turning point lies between the minimum and maximum values of the data. When these three conditions are satisfied simultaneously, a U-shaped or inverted U-shaped relationship exists (Hans et al., 2016).
It is observed that the three-step method mentioned above for assessing the validity of the mathematical form has not been utilised, when examining the literature on Turkiye. Generally, studies have only evaluated the first step of the three-step method, leading to conclusions about the presence of a U-shaped or inverted U-shaped relationship. In this study, while investigating the relationship between income inequality and financial development, this three-step method is followed. It is believed that this study will contribute to the literature in this regard.
The relationship between income inequality and financial development is investigated within the framework of the FKH. The aim is to determine the effects of financial development, inflation, and per capita income variables on income inequality in Turkiye annually from 1987 to 2021. Domestic loans provided by banks to the private sector (%GDP) is considered as a measure of financial development. The Gini coefficient is used as an indicator of income inequality. According to the results obtained from the ARDL bounds test, we conclude that there is co-integration among the variables. In addition, it is found that there is a U-shaped relationship when looking at the long-term coefficients of the financial development variable and its square. However, upon a detailed examination of the conditions that the U-shaped quadratic model should satisfy, it can be concluded that the U-shaped model is valid.
