It defined for city banks. City banks base and often limit their banking activities to the cities in which they are located. In this formula, FEI for a city bank i operating at city m in year t to the panel maximum N. There is an underlying assumption here is homogeneity of foreign bank branches. In other words, foreign bank branches are treated equally and seen to impose the same level of influence on local Chinese banks across cities and over time.

This formula is used to calculate FEIs for national and regional banks. A national or regional bank i with a set of branches in cities m in year t. This prior assumption is valid because among Chinese banks, especially national banks, decisions on interest rate and banking services are made at the headquarters rather than at the branches.

This graph shows the distribution of FEI for Chinese banks in the sample. you can see clearly around half of the observations have FEIs=0, the other half at the two ends of the (0,1)., which reflects the geographic distribution of foreign bank branches in China. so it means large number of foreign bank branches in mega cities, such as Beijing , shanghai, and have only a few in other cities.
Disaggregate measures’ advantage is FEI captures year to year variations like aggregate measure, but also cross sectional variations. FEI obtains a more accurate assessment of the impact of this foreign presence on banking performance in China

Figure Comparison between aggregate measures and FEI
At the first stage, the empirical model is constructed as follows,

PIit is the dependent variable ( one of the three bank performance indicators : net interest margin, non interest income, and costs for domestic bank i at time t as mentioned before), FEI it is the foreign exposure index, which is the key explanatory variable
X(it)is a vector of bank variables that control for factors