IIUC
df.groupby(level=1)['military_exp'].diff()
Out[195]:
year Country
2010 USA NaN
China NaN
Korea NaN
Russia NaN
2011 USA -9477440.0
China 10993984.0
Korea 426390.0
Russia 2901560.0
Name: military_exp, dtype: float64
Обновление
df.loc[2011,'military_exp']-df.loc[2010,'military_exp']
Out[197]:
Country
USA -9477440.0
China 10993984.0
Korea 426390.0
Russia 2901560.0
Name: military_exp, dtype: float64