One of the most important issues in economic development is the examination of the convergence phenomenon. The convergence analysis has been enhanced with the efforts of various economists and the convergence trends in all areas of the economic system have been determined with the help of applied analysis. As well as income convergence analysis among countries, the convergence dynamics in health expenditures have become popular in recent years. Therefore, the main motivation of this study is to examine the convergence process of health expenditures in the European Union member countries using a geographically weighted regression analysis of the period 1970 to 2017. The results of the analysis indicate that a statistically strong convergence is valid in “the Six” and the Eurozone, while there is not any statistically significant convergence in non-member states of the Eurozone. Also, the findings of the panel cross-country analysis also point out the nonexistence of the convergence. Finally, the analysis is extended to examine convergence by adding some control variables.
TopIntroduction
The concept of convergence that emerges with the neoclassical school is developed under the pioneering work of Solow (1956) and convergence process is defined as follows: underdeveloped or developing countries will grow faster than developed countries and the per capita income level differences in these country groups will close. Besides, convergence hypothesis is defined as the coming back of a country to its own steady state by growing or shrinking at a certain rate. The basis of the convergence hypothesis is that there is a negative relationship between per capita income and the growth rate of per capita income. Neoclassical theory states that underdeveloped countries with lower capital/labor ratio and lower per capita income will grow faster than developed countries due to the fact that capital is subject to diminishing returns to scale. The fact that capital is subject to diminishing returns reflects that the return generated by an additional unit of capital will be higher in poorer countries than in rich countries. Therefore, the convergence hypothesis suggests that economic growth will be slower in countries with higher per capita income than that of in other countries (Mbaku and Kimenyi, 1997, p. 121; Akıncı, 2017, p. 340).
The convergence hypothesis is based on three theories. These are can be noted as “Beta 
Convergence”, “Sigma 
Convergence” and “Log-Per Capita Income Convergence.” Beta convergence is a phenomenon within the concept of unconditional convergence, which is based on the assumption that all countries have the same structural characteristics, in other words, all countries have the same steady state equilibrium. The relationship between average growth rate of per capita income and per capita income level in the beginning year can be expressed with the help of equation numbered (1) (Arbia and Piras, 2005, p. 13):
(1) where
indicates the level of output per capita in country
i,
means the per capita income level of the beginning year, the left side of the equation reflecting the dependent variable is the level of income growth,
is constant term;
is the convergence coefficient and
is the error term. It is mentioned that there is convergence process if
coefficient takes a statistically significant negative value and divergence process if
coefficient takes a statistically significant positive value.
The sigma convergence demonstrates the distribution of per capita income over a given period of time and assumes that the differences in per capita income distributions of the economies will decrease over time (Sala-i-Martin, 1996, p. 1020). Standard deviation 
is the main criterion which is taken into consideration to measure sigma convergence. If standard deviation tends to decrease in a given period of time, convergence is mentioned; otherwise it is possible to say the validity of divergence process (Valdes, 1999, p. 41). Sigma convergence can be expressed with the help of equation numbered (2) (Gündem, 2010, p. 3094):
(2) where
I refers to the country considered in the analyzes,
reflects the income level of country
i in period
t and
points out the average income level of all other countries in period
t.