Background: The analysis of the problems derived from globalization has become one of the most densely studied topics at the beginning of this millennium, as they can have a crucial impact on present and future sustainable development. This paper analyzes the differential patterns of globalization in four worldwide areas predefined by The World Bank (namely, High-, Upper-Middle-, Lower-Middle-, and Low-Income countries). The main objective of this work is to estimate the effect of globalization on some economic development indicators (specifically per capita income and public expenditure on health) in 217 countries over the period 2000–2016. Methods: Our empirical approach is based on the implementation of a novel econometric methodology: The so-called Toda–Yamamoto procedure, which has been used to analyze the possible causal relationships between the involved variables. We employ World Development Indicators, provided by The World Bank, and the KOF Globalization Index, elaborated by the KOF Swiss Economic Institute. Results: The results show that there is a causal relationship in the sense of Granger between globalization and public expenditure on health, except in High-Income countries. This can be interpreted both negatively and positively, confirming the double character of globalization, as indicated by Stiglitz.