Difference between the mean of X during the last and first weeks of a month

[Anthony Macedo]

Greetings,

I have a specific index for 365 pairs of countries between 1 January 2020 and 30 September 2022 (daily data). Follows an example of my data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int date float day byte month int year str3(iso3_o iso3_d) float country_pair double index
21915  1 1 2020 "AUS" "ARE" 1 12.979732513427734
21916  2 1 2020 "AUS" "ARE" 1 13.065977096557617
21917  3 1 2020 "AUS" "ARE" 1 11.556705474853516
21918  4 1 2020 "AUS" "ARE" 1 11.211729049682617
21919  5 1 2020 "AUS" "ARE" 1 12.462267875671387
21920  6 1 2020 "AUS" "ARE" 1 12.850366592407227
21921  7 1 2020 "AUS" "ARE" 1 14.833980560302734
21922  8 1 2020 "AUS" "ARE" 1 15.825786590576172
21923  9 1 2020 "AUS" "ARE" 1 15.955153465270996
21924 10 1 2020 "AUS" "ARE" 1   13.4109525680542
21925 11 1 2020 "AUS" "ARE" 1 16.041397094726563
21926 12 1 2020 "AUS" "ARE" 1 16.429494857788086
21927 13 1 2020 "AUS" "ARE" 1 15.135834693908691
21928 14 1 2020 "AUS" "ARE" 1 15.437688827514648
21929 15 1 2020 "AUS" "ARE" 1 14.489004135131836
21930 16 1 2020 "AUS" "ARE" 1 13.324708938598633
21931 17 1 2020 "AUS" "ARE" 1 12.332901954650879
21932 18 1 2020 "AUS" "ARE" 1 12.462267875671387
21933 19 1 2020 "AUS" "ARE" 1 13.540319442749023
21934 20 1 2020 "AUS" "ARE" 1 12.807244300842285
21935 21 1 2020 "AUS" "ARE" 1 11.427339553833008
21936 22 1 2020 "AUS" "ARE" 1 10.737386703491211
21937 23 1 2020 "AUS" "ARE" 1 10.651143074035645
21938 24 1 2020 "AUS" "ARE" 1 10.176800727844238
21939 25 1 2020 "AUS" "ARE" 1  9.702458381652832
21940 26 1 2020 "AUS" "ARE" 1  10.69426441192627
21941 27 1 2020 "AUS" "ARE" 1  10.69426441192627
21942 28 1 2020 "AUS" "ARE" 1 10.478654861450195
21943 29 1 2020 "AUS" "ARE" 1  9.745579719543457
21944 30 1 2020 "AUS" "ARE" 1 10.004312515258789
21945 31 1 2020 "AUS" "ARE" 1 10.090556144714355
21946  1 2 2020 "AUS" "ARE" 1 10.263044357299805
21947  2 2 2020 "AUS" "ARE" 1  9.874945640563965
21948  3 2 2020 "AUS" "ARE" 1  11.12548542022705
end
format %tdnn/dd/CCYY date

What I would like to do is to compute the difference between a) the average index during the last week of a month and b) the average index during the first week of a month.
The following code gives me almost what I want:

bysort country_pair month year (date) : gen YYY = (index[1]+index[2]+index[3]+index[4]+index[5]+index[6]+index[7])/7
bysort country_pair month year (date) : gen ZZZ = (index[_N]+index[_N-1]+index[_N-2]+index[_N-3]+index[_N-4]+index[_N-5]+index[_N-6])/7
gen XXX= ZZZ-YYY

The problem is that the word “almost” makes all the difference here, and with this code YYY and ZZZ are missing when there are observations missing in index. I would like to compute the average index, even if there are days with missing data in the first and last weeks. Therefore, for a certain month, there would be only a missing value in my final variable if data for the entire first/last week is missing.
Could someone help me with this?
Best regards.

[Clyde Schechter]

gen mdate = mofd(date)
format mdate %tm
by iso3_o iso3_d mdate, sort: egen first_week_mean = ///
    mean(cond(inrange(date-firstdayofmonth(date), 0, 6), index, .))
by iso3_o iso3_d mdate: egen last_week_mean = ///
    mean(cond(inrange(lastdayofmonth(date)-date, 0, 6), index, .))
gen difference = last_week_mean - first_week_mean

Added: Actually, your code in #1 may even be farther from correct than you have described. It is, as you note, giving missing values if the value of the index is missing in some of the relevant days. But if, on top of that, there are dates that are completely absent from the data set (i.e. there is no observation corresponding to that date for that country pair), then the references to index[...] will incorrectly include other dates that do not even belong to the first or last week.

The code presented here is robust to both problems.

[Anthony Macedo]

Great, thank you very much.
I did not know these two time functions. However, I get the error unknown function with both of them (I used exactly the code you suggested). Any suggestion?

Regarding the other limitation of my previous code, I was aware of that. I did not highlight that because it is not the case with my data.
Best regards.

[Nick Cox]

Which version of Stata are you using? It is possible that you need to upgrade or use other code. See the FAQ Advice to declare the version of Stata you are using if it is not the latest.

[Nick Cox]

These function were introduced in Stata 17. For some versions before that, here are two of various ways to get the first and last days of the current month.

The first day is easy once you've pulled out the current month and the current year.

The last day is trickier as we don't want to write code for whether there are 28 29 30 31 days in the current month. But the last day is one before the first day of the next month.

clear 
set obs 14
gen date = mdy(1, 24, 2020) + _n

gen firstdayofmonth = mdy(month(date), 1, year(date))
gen lastdayofmonth = dofm(mofd(date) + 1) - 1 

format date first last %td 

list, sep(7)


     +-----------------------------------+
     |      date   firstda~h   lastday~h |
     |-----------------------------------|
  1. | 25jan2020   01jan2020   31jan2020 |
  2. | 26jan2020   01jan2020   31jan2020 |
  3. | 27jan2020   01jan2020   31jan2020 |
  4. | 28jan2020   01jan2020   31jan2020 |
  5. | 29jan2020   01jan2020   31jan2020 |
  6. | 30jan2020   01jan2020   31jan2020 |
  7. | 31jan2020   01jan2020   31jan2020 |
     |-----------------------------------|
  8. | 01feb2020   01feb2020   29feb2020 |
  9. | 02feb2020   01feb2020   29feb2020 |
 10. | 03feb2020   01feb2020   29feb2020 |
 11. | 04feb2020   01feb2020   29feb2020 |
 12. | 05feb2020   01feb2020   29feb2020 |
 13. | 06feb2020   01feb2020   29feb2020 |
 14. | 07feb2020   01feb2020   29feb2020 |
     +-----------------------------------+

More at

SJ-19-3 dm0100 . . . . . . . . . . Speaking Stata: The last day of the month
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. J. Cox
Q3/19 SJ 19(3):719--728 (no commands)
discusses three related problems about getting the last day
of the month in a new variable

https://journals.sagepub.com/doi/pdf...36867X19874247

[Anthony Macedo]

Ok, so that was the problem, I have Stata 16.
Thanks for the alternative solution. It worked perfectly.