Hello,

I am trying to obtain signficance levels for a synthetic control method (SCM) result that I had gotten before. To do so, I am hoping to use difference-in-difference by using the observed unit as the treated and the synthetic unit from SCM as the control. I have no covariates involved in my regression.

Below is my dataset where _Y_treated is treated (observed) and _Y_synthetic the control from SCM. The treated dummy variable is to show that _Y_treated is treated and similarly, time is a dummy to signify treatment period. DiD is the interaction term. The code is below the data. Although I have used the diff package below, I have previously tried some different approaches with regression method and the hashtag method too.

The cause of the collinearity is glaringly obvious however, I do not know how to overcome it to get the desired results. I have a feeling my query is not particularly difficult but for some really silly reason I cannot seem to solve my issue.

Any help is massively appreciated!

Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input int year double(_Y_treated _Y_synthetic) float(treated time DiD)
1990 13075.236033310537 13064.229969791773 1 0 0
1991  11865.82340535107 12809.582282848382 1 0 0
1992 11948.485091255892 12200.496798981847 1 0 0
1993  12666.07765362244 12294.224792439196 1 0 0
1994 13328.105203227276 12723.206068804231 1 0 0
1995 13468.770647527726 13291.301199237227 1 0 0
1996 13723.506351783068 13417.546589916237 1 0 0
1997  13868.65473862296 14008.040285347932 1 0 0
1998  14207.79715012313 14494.286904203862 1 0 0
1999 14546.888269048695 14930.615285279106 1 0 0
2000 15599.383609345408 15959.718825180997 1 0 0
2001 16598.865359506875 16418.796944581212 1 0 0
2002 17603.698180723404  17152.63916879498 1 0 0
2003 18257.585818030788 17757.063504177408 1 0 0
2004 18209.756581653233 18481.478522490313 1 0 0
2005  19494.49515696955  19472.45801531873 1 0 0
2006  20235.30166315405 20230.225567799378 1 0 0
2007 20563.460050324473  21239.95197525975 1 0 0
2008 21609.551610825085  21900.13207177752 1 0 0
2009 21736.021288448075 21787.424136898848 1 0 0
2010 22831.748867021175 22602.803870210126 1 0 0
2011  23099.73739803632 22567.855970629993 1 0 0
2012 22811.263414202935 23099.542375920508 1 1 1
2013 23116.146653782016 23098.763351945272 1 1 1
2014 23701.170722645234 23598.176443746775 1 1 1
2015 25009.652164882053 25743.755791811032 1 1 1
2016 25443.407972951845 27046.947356093417 1 1 1
2017 26908.965224752807 28837.484831334223 1 1 1
2018 27928.041764413265 29354.435507782386 1 1 1
2019 29385.537713743535 30739.800278648032 1 1 1
end
Code:
 gen time = (year>=2012) & !missing(year)

. gen treated = (_Y_treated) & !missing(_Y_treated)

. gen DiD = treated*time

. diff _Y_treated, t(treated) p(time)

DIFFERENCE-IN-DIFFERENCES ESTIMATION RESULTS
Number of observations in the DIFF-IN-DIFF: 30
            Before         After    
   Control: 0              0           0
   Treated: 22             8           30
            22             8
--------------------------------------------------------
 Outcome var.   | _Y_tr~d | S. Err. |   |t|   |  P>|t|
----------------+---------+---------+---------+---------
Before          |         |         |         |
   Control      |  1.7e+04|         |         |
   Treated      |  1.7e+04|         |         |
   Diff (T-C)   | 0.000   |    .    |    .    |    .
After           |         |         |         |
   Control      |  2.6e+04|         |         |
   Treated      |  2.6e+04|         |         |
   Diff (T-C)   | 0.000   |    .    |    .    |    .
                |         |         |         |
Diff-in-Diff    | 0.000   |    .    |    .    |    .
--------------------------------------------------------
R-square:    0.58
* Means and Standard Errors are estimated by linear regression
**Inference: *** p<0.01; ** p<0.05; * p<0.1