ASGEN command for weighted average

[Margherita Lazzeri]

Hello everyone,


I have to compute the weighted average of democratic scores in the destination countries, weighted it with my shares of emigrants in a certain province in a year.
This is the Stata command i am using:

bysort provincia year: asgen weighted_average= democracy_polity if democracy_polity!=. & share_emigration!=., weight(share_emigration)

However, the new variable does not make much sense since the values do not sum up to 1. How can I create the right variable?

Thank you,
Best,
Margherita

[Nick Cox]

I don't know anything about the detail of asgen (from SSC, as you are asked to explain). But weighted averages are if I understand the idea just

total of weights X values / total of weights.

Why anything there should add to 1 is hard to see. Naturally we can always recast that as

total of fractional weights X values

if each weight is divided by their total.

Here is a silly example of mpg weighted prices with the auto data.

. sysuse auto, clear
(1978 automobile data)

. egen double numer = total(mpg * price) , by(rep78)

. egen double denom = total(mpg), by(rep78)

. gen double wanted = numer/denom

. tabdisp rep78, c(wanted)

----------------------
Repair    |
record    |
1978      |     wanted
----------+-----------
        1 |  4511.7143
        2 |  5559.9608
        3 |  6003.6244
        4 |  5986.6795
        5 |  5394.4319
        . |  5924.3738
----------------------

. * check one case 

. su price [aw=mpg] if rep78 == 5

    Variable |     Obs      Weight        Mean   Std. dev.       Min        Max
-------------+-----------------------------------------------------------------
       price |      11         301    5394.432   2223.194       3748      11995

If that doesn't help with your problem, I think we need to see a data example together with an explanation of what it is that does not sum to 1 and why that is wrong.