I have done some tests myself but all has been unsuccessful, but if I am missing something please feel free to ask for more information.
I have a spreadsheet with contract numbers on the rows and amortizations on the columns, like the following example:
Original Value
2011
2012
2013
2014
2105
1001
2000
10
10
10
10
10
1002
1500
20
20
20
20
20
1003
1200
0
0
15
15
15
1004
3000
0
0
0
0
10
Using DAX is there a good way to make a calculated value for the present value for each of the time frames? As the example below show:
Original Value
PV2101
PV2102
PV2103
PV2114
PV2105
1001
2000
1990
1980
1970
1960
1950
1002
1500
1480
1460
1440
1420
1400
1003
1200
0
0
1185
1170
1155
1004
3000
0
0
0
0
2990
So a calculated value that sums upp all prior amortizations dependant on the date in the x-axis and reduces that amount from the original value.
I can see two options:
You create a pivoted table:
|ID |Year|Value|
|----|----|----|
|1001|2011| 10|
|1001|2012| 10|
|1001|2013| 10|
|1001|2014| 10|
|1001|2015| 10|
|1002|2011| 20|
And then your measure will be trivial:
Calculated Value =
VAR dt_year = YEAR(SELECTED(date[date]))
RETURN SUM(table[Original Value]) +
CALCULATE(SUM(amort[Value]), amort[Year] <= dt_year)
Or you create some measure that adds up the individual columns:
Calculated Value =
VAR dt_year = YEAR(SELECTED(date[date]))
RETURN SUM(table[Original Value]) +
IF(dt_year >= 2011, SUM(table[2011]), 0) +
IF(dt_year >= 2012, SUM(table[2012]), 0) +
IF(dt_year >= 2013, SUM(table[2013]), 0) +
IF(dt_year >= 2014, SUM(table[2014]), 0) +
IF(dt_year >= 2015, SUM(table[2015]), 0)
Option 1 is a lot nicer.
Related
Let's imagine the following table ...
obs
State
Imp
i
i2
1
me
100
100
2
me
90
100
100
3
me
80
100
100
4
me
70
100
100
5
me
1000
1000
100
6
me
900
1000
1000
7
me
800
1000
1000
8
me
0
1000
1000
9
me
2000
2000
1000
10
me
1900
2000
2000
11
gu
20
2000
2000
12
ca
40
2000
2000
13
ca
50
2000
2000
14
ca
30
2000
2000
15
ca
10
2000
2000
as you can see column "i2" is lag (i). What I want to do is:
1.- column "i" finds the maximum value as it progresses, so i want to reset that column
"i" every first "state", in order to get that maximum value of each state.
2.- modify the column "i2" so that it is as follows:
that each first value of "State" (obs 1-me, 11-gu and 12-ca) column "i" has the value
of column "imp"
obs
State
Imp
i
i2
1
me
100
100
100
2
me
90
100
100
3
me
80
100
100
4
me
70
100
100
5
me
1000
1000
100
6
me
900
1000
1000
7
me
800
1000
1000
8
me
0
1000
1000
9
me
2000
2000
1000
10
me
1900
2000
2000
11
gu
20
20
20
12
ca
40
40
40
13
ca
50
50
40
14
ca
30
50
50
15
ca
10
50
50
i have tried with this code, but it doesn't work
data metodo;
set sa80;
retain i;
if first.state then i=max(imp);
else i = max(imp,i);
i2 = lag(i);
run;
data final;
set metodo;
retain i2_aux;
if first.state then i2_aux = total;
else i2_aux = i2;
run;
Hope you could help, and thank you in advance
The main thing it not use an existing variable as the new RETAINed variable because then each time the SET statement executes the value retained is replaced with the value read from the input.
It also helps if the data is sorted by the key variable, although you can use the NOTSORTED keyword on the BY statement to process grouped, but not sorted, data.
data have;
input state $ imp ;
cards;
ca 40
ca 50
ca 30
ca 10
gu 20
me 100
me 90
me 80
me 70
me 1000
me 900
me 800
me 0
me 2000
me 1900
;
data want;
set have ;
by state notsorted;
retain i;
i=max(i,imp);
if first.state then i=imp;
i2=lag(i);
if first.state then i2=imp;
run;
Results:
Obs state imp i i2
1 ca 40 40 40
2 ca 50 50 40
3 ca 30 50 50
4 ca 10 50 50
5 gu 20 20 20
6 me 100 100 100
7 me 90 100 100
8 me 80 100 100
9 me 70 100 100
10 me 1000 1000 100
11 me 900 1000 1000
12 me 800 1000 1000
13 me 0 1000 1000
14 me 2000 2000 1000
15 me 1900 2000 2000
Fixed order of resetting I and LAG(I) call.
I'm trying to figure out a concise way to keep only the two years before and after the year in which an event takes place using daily panel data in Stata. The panel is unbalanced. Ultimately, I'm trying to conduct an event study but I experienced issues because the unique groups report inconsistent years.
The data looks something like this:
ID year month day event
1 1999 1 1 0
1 1999 1 2 0
1 1999 1 3 0
1 1999 1 4 0
1 1999 1 5 0
1 1999 1 6 0
1 1999 1 7 0
1 1999 1 8 0
1 1999 1 9 0
1 1999 1 10 0
1 1999 1 11 0
1 1999 1 12 0
1 1999 1 13 0
1 1999 1 14 0
1 1999 1 15 0
1 1999 1 16 0
1 1999 1 17 0
1 1999 1 18 0
1 1999 1 19 0
1 1999 1 20 0
1 1999 1 21 0
1 1999 1 22 0
1 1999 1 23 0
1 1999 1 24 0
1 1999 1 25 0
1 1999 1 26 0
1 1999 1 27 0
1 1999 1 28 0
1 1999 1 29 0
1 1999 1 30 0
1 1999 1 31 0
1 1999 2 1 1
1 1999 2 2 1
In this case, the event takes place in February 1999. The event is monthly, but I need the daily data for a later part of the analysis. I want to somehow tag the 24 months before February 1999 and the 24 months after February 1999. However, I need to do this in a way that won't codify any months in 2002 if group 1 reported no data in 2000.
I got the following to work on a similar set of monthly data but I can't figure out a way to do it with daily data. Furthermore, if anyone has suggestions for a less clunky solution, I would be very appreciative.
bys ID year (month) : egen year_change = max(event)
bys ID (year month) : replace year_change = 2 if ///
(year_change[_n+24] == 1 & year[_n] == year[_n+24] - 2) | ///
(year_change[_n+12] == 1 & year[_n] == year[_n+12] - 1) | ///
(year_change[_n-12] == 1 & year[_n] == year[_n-12] + 1) | ///
(year_change[_n-24] == 1 & year[_n] == year[_n-24] + 2)
keep if year_change >= 1
It seems that your event date is the first date with event 1. So,
gen dailydate = mdy(month, day, year)
bysort id : egen key = min(cond(event == 1, dailydate, .))
gen wanted = inrange(dailydate, key - 730, key + 730)
Check that wanted gives the dates you want and then modify the rule or keep accordingly.
This code doesn't assume that the event date is the same for each panel, but that would not be a problem.
See this paper for a review of related technique.
For your task, I suggest you to work use actual Stata dates, instead of relying on year + month + day variables - this way, it would be easier to add/subtract 24 months without relying on data sorting (the "_n+24" part in your code) and the codification would not suffer from the issue with missing data that you outline in the question.
I see a straightforward solution, which relies on an assumption I made on your setting (that you did not specify, but is the general form of event studies): the event date is unique for all IDs, hence there is no group-specific "treatment" date.
g stata_date = mdy(month, day, year) // generate variable with Stata date
/* Unique event on Feb 1, 1999 */
bys ID: egen treat_group = max(event) // indicator for an ID to ever be "treated"
g event_window = (stata_date >= td(01Feb1997) & stata_date < td(01Feb2001)) // indicator for event window - 2 years before and after Feb 1, 1999
g event_treatment = treat_group * event_window // indicator for a treated ID during the event window
I have the following dataset:
data have;
input year firm_id location_id action action_amount operate new_entry
;
cards;
2013 28013 6085 1 10000 0 0
2015 28013 6085 1 12000 0 0
2015 28013 29189 1 10000 0 0
2016 28013 34019 1 5000 1 1
2017 28013 34019 0 0 1 2
2011 120609 9003 1 7000 0 0
2012 120609 9003 0 0 1 1
2013 120609 9003 1 5000 1 2
2012 247908 23001 1 9000 0 0
2013 247908 23001 1 8000 0 0
2014 247908 23001 1 8500 1 1
2015 247908 23001 0 0 1 2
2003 356123 1001 0 0 0 0
2004 356123 1001 0 0 0 0
2009 356123 1001 1 9800 1 1
;
run;
I want to add additional rows and two new variables called "pre_action" and "pre_action_amount" to obtain the following dataset:
data want;
input year firm_id location_id action action_amount operate new_entry pre_action pre_action_amount
;
cards;
2013 28013 6085 1 10000 0 0 . .
2014 28013 6085 0 0 0 0 1 10000
2015 28013 6085 1 12000 0 0 . .
2016 28013 6085 0 0 0 0 1 12000
2015 28013 29189 1 6500 0 0 . .
2016 28013 29189 0 0 0 0 1 6500
2016 28013 34019 1 5000 1 1 0 0
2017 28013 34019 0 0 1 2 . .
2011 120609 9003 1 7000 0 0 . .
2012 120609 9003 0 0 1 1 1 7000
2013 120609 9003 1 5000 1 2 . .
2012 247908 23001 1 9000 0 0 . .
2013 247908 23001 1 8000 0 0 1 9000
2014 247908 23001 1 8500 1 1 1 8000
2015 247908 23001 0 0 1 2 . .
2003 356123 1001 0 0 0 0 . .
2004 356123 1001 0 0 0 0 0 0
2005 356123 1001 0 0 0 0 0 0
2009 356123 1001 1 9800 1 1 0 0
;
run;
The rules are as follows:
1) First, consider only the rows with operate = 0.
For each firm_id and location_id pair, if in the following year there is no row with the same firm_id and location_id, then create a new row with the following year and same firm_id and location_id pair. The variables action, action_amount, operate, and new_entry are all set to 0, while pre_action and pre_action_amount is set to be the value of action and action_amount in the previous year. Example: In year 2013, for the firm_id/location_id pair 28013/6085, we have operate = 0. But in 2014, there are no observations for this firm_id/location_id pair. So we set action, action_amount, operate, and new_entry to be 0 and pre_action=1 and pre_action_amount=10000 which are the values for action and action_amount in 2013.
For each firm_id and location_id pair, if in the following year there is a row with the same firm_id and location_id, then simply set pre_action and pre_action_amount to be the value of action and action_amount in the previous year. Example: In year 2011 for firm_id/location_id 120609/9003, we have operate=0. But in the next year 2012, there is a row with this firm_id/location_id pair. So we set pre_action=1 and pre_action_amount=7000 which are the values for action and action_amount in 2011. Another example is in year 2003, for the firm_id/location_id 356123/1001.
2) Now consider the rows with new_entry=1 that do not yet have a value of pre_action and pre_action_amount. Set both pre_action and pre_action_amount to be 0.
3) All other values of pre_action and pre_action_amount are empty.
I am unsure of how to create these new rows given the complicated rules above, any help would be appreciated.
If your main problem is how to access information from the next record to determine if there is a gap in year (as there is no lead() function in SAS), following is an example that shows the use of the POINT= option of the SET statement to do precisely that.
The example is based on a slightly modified version of your data since:
it reduces the number of observations and variables in the dataset.
it uses just one variable to define the observation ID.
Example code:
/* Example that shows how to use the POINT= option of the SET statement
to look ahead at the next observation and decide whether there is a gap in YEAR. */
data example;
input year id action_amount;
cards;
2013 28013 10000
2015 28013 12000
2016 28013 5000
2017 28013 0
2003 356123 250
2004 356123 320
2009 356123 9800
;
run;
* Observations should be sorted by ID and YEAR for the next data step;
proc sort data=example; by id year; run;
* Process
data example_filled;
set example;
by id year;
* Create the variable that will be used in the POINT= option of the SET statement
* to retrieve information from the next observation;
_next_obs = _N_ + 1;
* Compute variables storing values from the previous observation;
retain pre_action_amount;
pre_action_amount = lag(action_amount);
if first.id then
call missing(pre_action_amount);
* Analyze possible YEAR gaps in a BY group and partly fill them;
if last.id then do;
*** No gaps to check => simply output the last observation of the BY group;
output;
end;
else do;
*** We should check for gaps in YEAR;
* 1) Send the current observation to the output dataset;
output;
* 2) Check if there is a gap > 1 based on the YEAR value from the next observation,
* and if so, fill in (just) ONE observation
* Note the use of the POINT= option of the SET statement to access info from next obs;
set example(keep=year rename=(year=next_year)) POINT=_next_obs;
if next_year > year + 1 then do;
* Compute pre action values as the action values of the obs just output above;
* All the other variables still maintain their values and will be carried over
* this newly created obs;
pre_action_amount = action_amount;
year = year + 1;
* Output the filled observation;
output;
end;
end;
drop next_year;
run;
Expected output dataset example_filled (the new filled observations are Obs = 2 and Obs = 8):
action_ pre_action_
Obs year id amount amount
1 2013 28013 10000 .
2 2014 28013 10000 10000
3 2015 28013 12000 10000
4 2016 28013 5000 12000
5 2017 28013 0 5000
6 2003 356123 250 .
7 2004 356123 320 250
8 2005 356123 320 320
9 2009 356123 9800 320
You may find handy to use this example as a basis to implement the logic you described in order to compute pre_action and pre_action_amount.
Note: here are other ways to access information from the next observation in a data step:
https://blogs.sas.com/content/sgf/2015/06/19/can-you-lag-and-lead-at-the-same-time-if-using-the-sas-data-step-yes-you-can/
I have two different files; A reference file and a data sets with different length.
A reference file ("location.dat") contains:
40505 5.0666667 102.2166667
40517 5.6833333 101.8500000
40586 5.7666667 102.2000000
40587 5.8166667 102.0500000
40663 6.0333333 102.1166667
41525 5.5500000 100.4833333
41529 5.3500000 100.4000000
...............
...............
A data sets ("input.dat") contains:
40517 2014 12 18 0 17.4
40586 2014 12 18 0 9.9
40587 2014 12 18 0 15.5
40663 2014 12 18 0 30.9
41525 2014 12 18 0 0
41529 2014 12 18 0 0
41540 2014 12 18 0 0
41543 2014 12 18 0 0
41548 2014 12 18 0 0
41549 2014 12 18 0 0
41551 2014 12 18 0 0
41610 2014 12 18 0 0
Question:
How to search and match data set so that the output file will combine certain selected values from both files like this:
output.dat
40517 5.6833333 101.8500000 17.4
40586 5.7666667 102.2000000 9.9
40587 5.8166667 102.0500000 15.5
............
...........
The current script is:
data1=np.loadtxt('location.dat')
lats1=data1[:,1]
lons1=data1[:,2]
code1=data1[:,0]
data2=np.loadtxt('input.dat')
rain=data2[:,5]
code2=data2[:,0]
ind=[]
for i in range(len(data1)):
dist=code1[i]
ind.append(np.where(dist==np.int(dist))[0][0])
rain2=rain[ind]
data3=np.array([code1,lats1,lons1,rain2])
data3=np.transpose(data3)
np.savetxt('output.dat',data3,fmt='%9.3f')
The current result
40517.000 5.683 101.850 0.000
40586.000 5.767 102.200 0.000
40587.000 5.817 102.050 0.000
40663.000 6.033 102.117 0.000
41525.000 5.550 100.483 0.000
41529.000 5.350 100.400 0.000
41540.000 5.383 100.550 0.000
The rain2 values did not properly append from the input file. How to convert the first column output to be integer?.Any ideas of what went wrong??.TQ
The line
ind.append(np.where(dist==np.int(dist))[0][0])
does not make sense in your code. This will always append 0 if distis an integer (as dist==np.int(dist) is simply the array [True])
A better way to solve your problem is to create a look-up table from the data in location.dat
data1=np.loadtxt('location.dat')
lookup = {int(round(id_)):(lat,long) for id_, lat, long in data1}
Please note that the best way to convert a float to an int in python is to use int(round(i))
You can then iterate over the data in your other file and create the proper line
data3 = []
for line in data2:
ind = int(round(line[0]))
data3.append([ind, lookup[ind][0], lookup[ind][1], line[5]])
To save the data, you may want to format and write the line one after the other or use savetxt.
I am working with a spell dataset that has the following form:
clear all
input persid start end t_start t_end spell_type year spell_number event
1 8 9 44 45 1 1999 1 0
1 12 12 60 60 1 2000 1 0
1 1 1 61 61 1 2001 1 0
1 7 11 67 71 1 2001 2 0
1 1 4 85 88 2 2003 1 0
1 5 7 89 91 1 2003 2 1
1 8 11 92 95 2 2003 3 0
1 1 1 97 97 2 2004 1 0
1 1 3 121 123 1 2006 1 1
1 4 5 124 125 2 2006 2 0
1 6 9 126 129 1 2006 3 1
1 10 11 130 131 2 2006 4 0
1 12 12 132 132 1 2006 5 1
1 1 12 157 168 1 2009 1 0
1 1 12 169 180 1 2010 1 0
1 1 12 181 192 1 2011 1 0
1 1 12 193 204 1 2012 1 0
1 1 12 205 216 1 2013 1 0
end
lab define lab_spelltype 1 "unemployment spell" 2 "employment spell"
lab val spell_type lab_spelltype
where persid is the id of the person; start and end are the months when the yearly unemployment/employment spell starts and ends, respectively; t_start and t_end are the same measures but starting to count from 1st January 1996; event is equal to 1 for the employment entries for which the previous row was an unemployment spell.
The data is such that there are no overlapping spells during a given year, and each year contiguous spells of the same type have been merged together.
My goal is, for each row such that event is 1, to compute the number of months spent as employed in the last 6 months and 24 months.
In this specific example, what I would like to get is:
clear all
input persid start end t_start t_end spell_type year spell_number event empl_6 empl_24
1 8 9 44 45 1 1999 1 0 . .
1 12 12 60 60 1 2000 1 0 . .
1 1 1 61 61 1 2001 1 0 . .
1 7 11 67 71 1 2001 2 0 . .
1 1 4 85 88 2 2003 1 0 . .
1 5 7 89 91 1 2003 2 1 0 5
1 8 11 92 95 2 2003 3 0 . .
1 1 1 97 97 2 2004 1 0 . .
1 1 3 121 123 1 2006 1 1 0 0
1 4 5 124 125 2 2006 2 0 . .
1 6 9 126 129 1 2006 3 1 3 3
1 10 11 130 131 2 2006 4 0 . .
1 12 12 132 132 1 2006 5 1 4 7
1 1 12 157 168 1 2009 1 0 . .
1 1 12 169 180 1 2010 1 0 . .
1 1 12 181 192 1 2011 1 0 . .
1 1 12 193 204 1 2012 1 0 . .
1 1 12 205 216 1 2013 1 0 . .
end
So the idea is that I have to go back to rows preceding each event==1 entry and count how many months the individual was employed.
Can you suggest a way to obtain this final result?
Some suggested to expand the dataset, but perhaps there are better ways to tackle the problem (especially because the dataset is quite large).
EDIT
The correct labeling of the employment status is:
lab define lab_spelltype 1 "employment spell" 2 "unemployment spell"
The number of past months spent in employment (empl_6 and empl_24) and the definition of event are now correct with this label.
A solution to the problem is to:
expand the data so to have it monthly,
fill in the gap months with tsfill and finally,
use sum() and lag operators to get the running sum for the last 6 and 24 months.
See also Robert solution for some ideas I borrowed.
Important: this is almost surely not an efficient way to solve the issue, especially if the data is large (as in my case).
However, the plus is that one actually "sees" what happens in background to make sure the final result is the one desired.
Also, importantly, this solution takes into account cases where 2 (or more) events happen within 6 (or 24) months from each other.
clear all
input persid start end t_start t_end spell_type year spell_number event
1 8 9 44 45 1 1999 1 0
1 12 12 60 60 1 2000 1 0
1 1 1 61 61 1 2001 1 0
1 7 11 67 71 1 2001 2 0
1 1 4 85 88 2 2003 1 0
1 5 7 89 91 1 2003 2 1
1 8 11 92 95 2 2003 3 0
1 1 1 97 97 2 2004 1 0
1 1 3 121 123 1 2006 1 1
1 4 5 124 125 2 2006 2 0
1 6 9 126 129 1 2006 3 1
1 10 11 130 131 2 2006 4 0
1 12 12 132 132 1 2006 5 1
1 1 12 157 168 1 2009 1 0
1 1 12 169 180 1 2010 1 0
1 1 12 181 192 1 2011 1 0
1 1 12 193 204 1 2012 1 0
1 1 12 205 216 1 2013 1 0
end
lab define lab_spelltype 1 "employment" 2 "unemployment"
lab val spell_type lab_spelltype
list
* generate Stata monthly dates
gen spell_start = ym(year,start)
gen spell_end = ym(year,end)
format %tm spell_start spell_end
list
* expand to monthly data
gen n = spell_end - spell_start + 1
expand n, gen(expanded)
sort persid year spell_number (expanded)
bysort persid year spell_number: gen month = spell_start + _n - 1
by persid year spell_number: replace event = 0 if _n > 1
format %tm month
* xtset, fill months gaps with "empty" rows, use lags and cumsum to count past months in employment
xtset persid month, monthly // %tm format
tsfill
bysort persid (month): gen cumsum = sum(spell_type) if spell_type==1
bysort persid (month): replace cumsum = cumsum[_n-1] if cumsum==.
bysort persid (month): gen m6 = cumsum-1 - L7.cumsum if event==1 // "-1" otherwise it sums also current empl month
bysort persid (month): gen m24 = cumsum-1 - L25.cumsum if event==1
drop if event==.
list persid start end year m* if event
The posted example is of little utility in developing and testing a solution so I made up fake data that has the same properties. It's bad practice to use 1 and 2 as values for an indicator so I replaced the employed indicator with 1 meaning employed, 0 otherwise. Using month and year separately is also useless so Stata monthly dates are used.
The first solution uses tsegen (from SSC) after expanding each spell to one observation per month. With panel data, all you need to do is to sum the employment indicator for the desired time window.
The second solution uses rangestat (also from SSC) and does the same computations without expanding the data at all. The idea is simple, just add the duration of previous employment spells if the end of the spell falls within the desired window. Of course if the end of the spell falls within the window but not the start, days outside the window must be subtracted.
* fake data for 100 persons, up to 10 spells with no overlap
clear
set seed 123423
set obs 100
gen long persid = _n
gen spell_start = ym(runiformint(1990,2013),1)
expand runiformint(1,10)
bysort persid: gen spellid = _n
by persid: gen employed = runiformint(0,1)
by persid: gen spell_avg = int((ym(2015,12) - spell_start) / _N) + 1
by persid: replace spell_start = spell_start[_n-1] + ///
runiformint(1,spell_avg) if _n > 1
by persid: gen spell_end = runiformint(spell_start, spell_start[_n+1]-1)
replace spell_end = spell_start + runiformint(1,12) if mi(spell_end)
format %tm spell_start spell_end
* an event is an employment spell that immediately follow an unemployment spell
by persid: gen event = employed & employed[_n-1] == 0
* expand to one obs per month and declare as panel data
expand spell_end - spell_start + 1
bysort persid spellid: gen ym = spell_start + _n - 1
format %tm ym
tsset persid ym
* only count employement months; limit results to first month event obs
tsegen m6 = rowtotal(L(1/6).employed)
tsegen m24 = rowtotal(L(1/24).employed)
bysort persid spellid (ym): replace m6 = . if _n > 1 | !event
bysort persid spellid (ym): replace m24 = . if _n > 1 | !event
* --------- redo using rangestat, without any monthly expansion ----------------
* return to original obs but keep first month results
bysort persid spellid: keep if _n == 1
* employment end and duration for employed observations only
gen e_end = spell_end if employed
gen e_len = spell_end - spell_start + 1 if employed
foreach target in 6 24 {
// define interval bounds but only for event observations
// an out-of-sample [0,0] interval will yield no results for non-events
gen low`target' = cond(event, spell_start-`target', 0)
gen high`target' = cond(event, spell_start-1, 0)
// sum employment lengths and save earliest employment spell info
rangestat (sum) empl`target'=e_len ///
(firstnm) firste`target'=e_end firste`target'len=e_len, ///
by(persid) interval(spell_end low`target' high`target')
// remove from the count months that occur before lower bound
gen e_start = firste`target' - firste`target'len + 1
gen outside = low`target' - e_start
gen empl`target'final = cond(outside > 0, empl`target'-outside, empl`target')
replace empl`target'final = 0 if mi(empl`target'final) & event
drop e_start outside
}
* confirm that we match the -tsegen- results
assert m24 == empl24final
assert m6 == empl6final