Using .loc on just second index in multiindex

If you prefer loc, you can use:

In [245]: df.loc[(slice(None), 'Ai'), :]
     ...: 
Out[245]: 
           value
year name       
1921 Ai       90
1922 Ai        7

I would use .xs on the first level of your multiindex (note: level=1 refers to the "second" index (name) because of python's zero indexing: level 0 is year in your case):

df.xs('Ai', level=1, drop_level=False)
# or
df.xs('Ai', level='name', drop_level=False)

           value
year name       
1921 Ai       90
1922 Ai        7

@sacul has the most idiomatic answer, but here are a few alternatives.

MultiIndex.get_level_values

df[df.index.get_level_values('name') == 'Ai']

           value
year name       
1921 Ai       90
1922 Ai        7

DataFrame.query

df.query('name == "Ai"')

           value
year name       
1921 Ai       90
1922 Ai        7

DataFrame.loc(axis=0) with pd.IndexSlice

Similar to @liliscent's answer, but does not need the trailing : if you specify axis=0.

df.loc(axis=0)[pd.IndexSlice[:, 'Ai']]

           value
year name       
1921 Ai       90
1922 Ai        7

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