Pandas : how do I create a column based on data from the same dataframe?

You can try merge:

(df.merge(df.assign(year=df['year']-1)[['id','year','value']],
          on=['id','year'],
          how='left',
          suffixes=['','_y'])
   .fillna(0)
)

Output:

   id  year type  value  value_y
0   1  2010    A     20      0.0
1   2  2010    B      2      8.0
2   2  2011    B      8      0.0
3   3  2010    A      3      0.0

You can use the method shift:

# first, you need to sort by id, type and year (already sorted in example)
df = df.sort_values(['id', 'type', 'year'])
cols = ['id', 'type']

mask = (df[cols].shift(-1, fill_value=False) == df[cols]).all(axis=1)
df['value'].shift(-1, fill_value=0).where(mask, 0)

Output:

0    0
1    8
2    0
3    0
Name: value, dtype: int64

Here is another solution involving dictionary.

# Creating a key column
df['key'] = df[['id','year','type']].astype(str).sum(axis=1)
print(df)
       id  year type  value     key
    0   1  2010    A     20  12010A
    1   2  2010    B      2  22010B
    2   2  2011    B      8  22011B
    3   3  2010    A      3  32010A

Now, creating a dictionary.

# Creating a dictionary
dict_of_columns = dict(zip(df.key, df.value))
print(dict_of_columns)
    {'12010A': 20, '22010B': 2, '22011B': 8, '32010A': 3}

Now, we are creating new year column obtained by adding 1 to every year and creating the corresponding key 'new_value' and creating new keys.

df['next_year']=df['year'] + 1
df['new_value'] = df[['id','next_year','type']].astype(str).sum(axis=1)
print(df)
       id  year type  value     key  next_year new_value
    0   1  2010    A     20  12010A       2011    12011A
    1   2  2010    B      2  22010B       2011    22011B
    2   2  2011    B      8  22011B       2012    22012B
    3   3  2010    A      3  32010A       2011    32011A

Finally, mapping the new key - new_value to the dictionary we have created and dropping the created columns.

df['new_value'] = df['new_value'].map(dict_of_columns).fillna(0)
df = df.drop(['key','next_year'],axis=1)
print(df)
       id  year type  value  new_value
    0   1  2010    A     20        0.0
    1   2  2010    B      2        8.0
    2   2  2011    B      8        0.0
    3   3  2010    A      3        0.0