Calculating 3-firm HHI in Pandas

Question

So I have a Pandas DataFrame with panel data containing interaction between buyers and sellers on a monthly basis:

       Buyer       Seller       Month            Amount      Amounttotal 
0      Buyer1      Seller1 2009-07-31 00:00:00   10             255
1      Buyer1      Seller2 2009-07-31 00:00:00   15             255
2      Buyer1      Seller3 2009-07-31 00:00:00   120            255
3      Buyer1      Seller4 2009-07-31 00:00:00   110            255 
4      Buyer1      Seller1 2009-08-31 00:00:00   5              427
5      Buyer1      Seller2 2009-08-31 00:00:00   12             427
6      Buyer1      Seller3 2009-08-31 00:00:00   20             427
7      Buyer1      Seller4 2009-08-31 00:00:00   180            427
8      Buyer1      Seller5 2009-08-31 00:00:00   210            427

I have data for multiple sellers , e.g. Buyer1, Buyer2, Buyer3 etc. Amounttotal is the amount the buyer1 has bought for in total during the month. I am looking to calculate, for each buyer in each month, it's 3-firm HHI, meaning the sum of the squared value of the percentage of total monthly volume from the buyers’ three largest interactions. In the example above the 3-firm HHI would be 0,41 for 2009-07 and 0,42 for 2009-08. It seems to me that the calculation will have to involve groupby, however I am trouble figuring out how to find the largest, second largest and third largest value in each groupby element. Help is much appreciated!

Answer 1

Just take the Amount column, sort it, and take the first 3 elements. And you don't even need the amount total column since you can sum the Amount column.

def compute_hhi(buyer_month):
    total = float(buyer_month['Amount'].sum())
    top_3_amts = buyer_month['Amount'].order(ascending = False)[0:3]
    hhi_elements = [(value/total)**2 for value in top_3_amts]
    hhi = sum(hhi_elements)
    return hhi

grouped = df.groupby(['Buyer','Month'])
hhis = grouped.apply(compute_hhi)