Reset a column's MultiIndex levels

Another solution is to use MultiIndex.droplevel with rename_axis (new in pandas 0.18.0):

import pandas as pd

cols = pd.MultiIndex.from_arrays([['basic_amt']*4,
                                     ['NSW','QLD','VIC','All']], 
                                     names = [None, 'Faculty'])
idx = pd.Index(['All', 'Full Time', 'Part Time'])

df = pd.DataFrame([(1,1,2,4),
                   (0,1,0,1),
                   (1,0,2,3)], index = idx, columns=cols)
                   
print (df)
          basic_amt            
Faculty         NSW QLD VIC All
All               1   1   2   4
Full Time         0   1   0   1
Part Time         1   0   2   3

df.columns = df.columns.droplevel(0)
#pandas 0.18.0 and higher
df = df.rename_axis(None, axis=1)
#pandas bellow 0.18.0
#df.columns.name = None

print (df)
           NSW  QLD  VIC  All
All          1    1    2    4
Full Time    0    1    0    1
Part Time    1    0    2    3

print (df.columns)
Index(['NSW', 'QLD', 'VIC', 'All'], dtype='object')

If you need both column names, use list comprehension:

df.columns = ['_'.join(col) for col in df.columns]
print (df)
           basic_amt_NSW  basic_amt_QLD  basic_amt_VIC  basic_amt_All
All                    1              1              2              4
Full Time              0              1              0              1
Part Time              1              0              2              3

print (df.columns)
Index(['basic_amt_NSW', 'basic_amt_QLD', 'basic_amt_VIC', 'basic_amt_All'], dtype='object')

How about simply reassigning df.columns:

levels = df.columns.levels
labels = df.columns.labels
df.columns = levels[1][labels[1]]

For example:

import pandas as pd

columns = pd.MultiIndex.from_arrays([['basic_amt']*4,
                                     ['NSW','QLD','VIC','All']])
index = pd.Index(['All', 'Full Time', 'Part Time'], name = 'Faculty')
df = pd.DataFrame([(1,1,2,4),
                   (0,01,0,1),
                   (1,0,2,3)])
df.columns = columns
df.index = index

Before:

print(df)

           basic_amt               
                 NSW  QLD  VIC  All
Faculty                            
All                1    1    2    4
Full Time          0    1    0    1
Part Time          1    0    2    3

After:

levels = df.columns.levels
labels = df.columns.labels
df.columns = levels[1][labels[1]]
print(df)

           NSW  QLD  VIC  All
Faculty                      
All          1    1    2    4
Full Time    0    1    0    1
Part Time    1    0    2    3

Zip levels together

Here is an alternative solution which zips the levels together and joins them with underscore.

Derived from the above answer, and this was what I wanted to do when I found this answer. Thought I would share even if it does not answer the exact above question.

["_".join(pair) for pair in df.columns]

gives

['basic_amt_NSW', 'basic_amt_QLD', 'basic_amt_VIC', 'basic_amt_All']

Just set this as a the columns

df.columns = ["_".join(pair) for pair in df.columns]

           basic_amt_NSW  basic_amt_QLD  basic_amt_VIC  basic_amt_All
Faculty                                                              
All                    1              1              2              4
Full Time              0              1              0              1
Part Time              1              0              2              3