I have a 20 x 4000 dataframe in Python using pandas. Two of these columns are named Year and quarter. I\'d like to create a variable called p         
        
if both columns are strings, you can concatenate them directly:
df["period"] = df["Year"] + df["quarter"]
If one (or both) of the columns are not string typed, you should convert it (them) first,
df["period"] = df["Year"].astype(str) + df["quarter"]
If you need to join multiple string columns, you can use agg:
df['period'] = df[['Year', 'quarter', ...]].agg('-'.join, axis=1)
Where "-" is the separator.
Although the @silvado answer is good if you change df.map(str) to df.astype(str) it will be faster:
import pandas as pd
df = pd.DataFrame({'Year': ['2014', '2015'], 'quarter': ['q1', 'q2']})
In [131]: %timeit df["Year"].map(str)
10000 loops, best of 3: 132 us per loop
In [132]: %timeit df["Year"].astype(str)
10000 loops, best of 3: 82.2 us per loop
more efficient is
def concat_df_str1(df):
    """ run time: 1.3416s """
    return pd.Series([''.join(row.astype(str)) for row in df.values], index=df.index)
and here is a time test:
import numpy as np
import pandas as pd
from time import time
def concat_df_str1(df):
    """ run time: 1.3416s """
    return pd.Series([''.join(row.astype(str)) for row in df.values], index=df.index)
def concat_df_str2(df):
    """ run time: 5.2758s """
    return df.astype(str).sum(axis=1)
def concat_df_str3(df):
    """ run time: 5.0076s """
    df = df.astype(str)
    return df[0] + df[1] + df[2] + df[3] + df[4] + \
           df[5] + df[6] + df[7] + df[8] + df[9]
def concat_df_str4(df):
    """ run time: 7.8624s """
    return df.astype(str).apply(lambda x: ''.join(x), axis=1)
def main():
    df = pd.DataFrame(np.zeros(1000000).reshape(100000, 10))
    df = df.astype(int)
    time1 = time()
    df_en = concat_df_str4(df)
    print('run time: %.4fs' % (time() - time1))
    print(df_en.head(10))
if __name__ == '__main__':
    main()
final, when sum(concat_df_str2) is used, the result is not simply concat, it will trans to integer.
[''.join(i) for i in zip(df["Year"].map(str),df["quarter"])]
or slightly slower but more compact:
df.Year.str.cat(df.quarter)
df['Year'].astype(str) + df['quarter']
UPDATE: Timing graph Pandas 0.23.4
Let's test it on 200K rows DF:
In [250]: df
Out[250]:
   Year quarter
0  2014      q1
1  2015      q2
In [251]: df = pd.concat([df] * 10**5)
In [252]: df.shape
Out[252]: (200000, 2)
UPDATE: new timings using Pandas 0.19.0
Timing without CPU/GPU optimization (sorted from fastest to slowest):
In [107]: %timeit df['Year'].astype(str) + df['quarter']
10 loops, best of 3: 131 ms per loop
In [106]: %timeit df['Year'].map(str) + df['quarter']
10 loops, best of 3: 161 ms per loop
In [108]: %timeit df.Year.str.cat(df.quarter)
10 loops, best of 3: 189 ms per loop
In [109]: %timeit df.loc[:, ['Year','quarter']].astype(str).sum(axis=1)
1 loop, best of 3: 567 ms per loop
In [110]: %timeit df[['Year','quarter']].astype(str).sum(axis=1)
1 loop, best of 3: 584 ms per loop
In [111]: %timeit df[['Year','quarter']].apply(lambda x : '{}{}'.format(x[0],x[1]), axis=1)
1 loop, best of 3: 24.7 s per loop
Timing using CPU/GPU optimization:
In [113]: %timeit df['Year'].astype(str) + df['quarter']
10 loops, best of 3: 53.3 ms per loop
In [114]: %timeit df['Year'].map(str) + df['quarter']
10 loops, best of 3: 65.5 ms per loop
In [115]: %timeit df.Year.str.cat(df.quarter)
10 loops, best of 3: 79.9 ms per loop
In [116]: %timeit df.loc[:, ['Year','quarter']].astype(str).sum(axis=1)
1 loop, best of 3: 230 ms per loop
In [117]: %timeit df[['Year','quarter']].astype(str).sum(axis=1)
1 loop, best of 3: 230 ms per loop
In [118]: %timeit df[['Year','quarter']].apply(lambda x : '{}{}'.format(x[0],x[1]), axis=1)
1 loop, best of 3: 9.38 s per loop
Answer contribution by @anton-vbr
def madd(x):
    """Performs element-wise string concatenation with multiple input arrays.
    Args:
        x: iterable of np.array.
    Returns: np.array.
    """
    for i, arr in enumerate(x):
        if type(arr.item(0)) is not str:
            x[i] = x[i].astype(str)
    return reduce(np.core.defchararray.add, x)
For example:
data = list(zip([2000]*4, ['q1', 'q2', 'q3', 'q4']))
df = pd.DataFrame(data=data, columns=['Year', 'quarter'])
df['period'] = madd([df[col].values for col in ['Year', 'quarter']])
df
    Year    quarter period
0   2000    q1  2000q1
1   2000    q2  2000q2
2   2000    q3  2000q3
3   2000    q4  2000q4
Use .combine_first.
df['Period'] = df['Year'].combine_first(df['Quarter'])