How to use a synthetic control group as the control group in difference-in-differences analysis in Stata

I want to analyze the impact that the introduction of Google Fiber in Kansas City had on hours worked among Kansas Citians. My initial approach was to use a DiD analysis with St. Louis as the control group since it had the closest common trend in hours worked to Kansas City in the pre-treatment (pre-2012) period. However, my professor recommended using a synthetic control group instead of choosing a control group based on the closest common trend among existing cities.

I read into the 'synth' command and have successfully used it to obtain the weighted average of other US metropolitan areas that best represents what the control group should be, but now I can't figure out how to actually see the impact of the treatment on hours worked (other than graphically). Could I somehow use this synthetic control group as a control group in my DiD analysis? Is there a way to run the 'synth' command and generate coefficient estimates? Can anyone help me out here?

Here is an example of my dataset:

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int(year metarea) float(ahrsworkt age cinethp male white black foreign_born faminc_0025 faminc_2550 faminc_5075 faminc_75100 faminc_100m hs_grad bachelors advanced_degree white_collar nyear)
2001  80 36.539803 37.974884 .55279505        .5 .8401827  .14383562  .02739726   .1820513  .3153846  .2205128  .2820513          0 .8881279  .3333333 .07990868  .3538813 18
2002  80 36.732758  38.44531         . .49609375   .84375   .1484375    .015625  .33984375    .21875 .19140625       .25          0  .921875  .3515625 .09765625  .3984375 18
2003  80 37.672672  41.40223       .56  .5223464 .8296089   .1592179  .04189944    .248538 .28070176 .19590643 .21637426  .05847953 .9553072  .3687151 .12849163  .3882681 18
2004  80  38.63687  40.90425         .  .5053192 .8510638  .13829787 .031914894   .3191489  .2074468  .1968085 .27659574          0 .9361702  .4042553 .17021276  .4734043 18
2005  80  37.46524  40.08531         .  .4881517 .8720379   .1184834  .03791469  .15135135  .3243243 .23783784 .15135135  .13513513 .9099526 .29383886 .08056872  .3601896 18
2006  80  38.84568  40.05495         .   .489011 .8681319  .12087912 .032967035  .17880794 .25827813 .26490065 .17218544  .12582782 .9120879  .2802198 .06593407  .2802198 18
2007  80  40.15892  40.64185         .  .4929078  .858156  .09574468  .07092199   .1277533  .3215859 .21585903  .1629956  .17180617 .9680851  .3333333 .14539006  .4113475 18
2008  80  38.90345  42.46584         .  .5031056 .9068323  .06832298   .0310559  .11029412  .2720588 .29411766 .13235295  .19117647 .9378882  .3229814 .11801242  .3850932 18
2009  80  38.90171  41.66788         .  .5291971  .959854  .03649635  .02189781  .11737089 .17840375   .399061 .13615024   .1690141  .919708 .22627737  .0729927  .3211679 18
2010  80  38.94382  42.02649         .  .5529801 .9503312  .04304636 .006622517  .11589404  .2152318 .29801324 .17880794  .19205298 .9337748 .20198676 .05298013 .29801324 18
2011  80  38.31602  41.72587         1 .57528955 .9111969  .06563707   .0888031   .1003861  .3166023  .2123552  .2200772  .15057915 .9227799 .24710424  .0965251  .3166023 18
2012  80  38.79832  40.34921  .7857143 .56349206 .9365079  .05555556   .0952381  .16666667  .3174603 .22222222 .11904762   .1746032 .9206349  .3015873 .07936508  .3730159 18
2013  80 37.473682  42.68077  .8701299  .5307692 .8769231  .09615385  .05384615  .15384616  .2076923 .18846154 .20384616  .24615385 .9538462  .3269231        .1        .3 18
2014  80  37.27612  41.04082         . .53061223 .8231292  .11564626  .06122449   .1292517  .3197279 .13605443 .17687075  .23809524 .9659864 .37414965 .08163265  .4081633 18
2015  80 38.115704  41.63878  .6637931 .54372627 .8212928  .10646388  .09505703  .09505703 .26615968  .2053232  .2015209  .23193917 .9391635  .4068441   .121673  .4448669 18
2016  80 36.542637  41.21168         . .50364965 .8832117  .08759124  .06569343  .11678832  .2408759  .1970803  .1970803   .2481752 .9635037  .3284672 .13868614  .4160584 18
2017  80     37.88  42.88406         . .51449275 .8768116  .07971015 .072463766  .08695652 .13043478 .29710144 .19565217  .28985506 .9275362  .3695652 .17391305  .4202898 18
2018  80  37.03521  40.85526         .  .5197368 .8881579  .07894737  .04605263  .13157895      .125 .17763157 .19736843  .36842105 .9276316  .4736842  .1644737  .4473684 18
2001 160 37.545456  40.27882  .6234568  .5093834  .919571  .06702413  .02680965       .184      .304      .236      .276          0 .8847185  .2680965 .08579089 .34316355 18
2002 160  38.62705  40.84848         .  .5113636 .9090909  .06060606  .05681818   .3636364 .14393939 .24242425       .25          0 .8977273  .3219697 .15530303  .3977273 18
2003 160  37.98953  39.81081  .6049383  .5012285 .8845209  .06879607  .07616708  .25633803  .2056338 .24507043 .25070423  .04225352 .9017199  .3660934 .14987715  .4127764 18
2004 160  39.07692  40.18269         .  .5144231 .9230769  .04326923  .03846154   .4278846 .21153846 .13461539 .22596154          0 .9134616  .3894231 .14903846  .4038461 18
2005 160   38.0991  39.92308         . .52136755 .9188034  .05128205  .06410257   .1027027  .2918919 .23243243  .1891892   .1837838 .8846154 .33760685 .11965812  .4017094 18
2006 160 37.983955      38.5         . .50510204 .8979592  .04591837 .071428575  .10650887 .28994083  .2781065   .147929   .1775148 .8826531  .3265306 .09693877  .4030612 18
2007 160  36.17699  42.44134         . .50558656 .9078212  .04748603   .0726257   .0862069        .2 .27931035 .18965517   .2448276 .9301676  .3743017  .1452514  .4329609 18
2008 160  38.87923  41.92445         . .50666666 .8355556  .09777778  .07555556  .08108108        .2  .1837838  .1945946   .3405405 .9422222  .4266667 .16444445       .48 18
2009 160  36.13408  42.83582         .  .5124378 .9079602  .03482587  .05472637  .08645533 .21902017 .19884726   .221902  .27377522 .9452736 .37810946  .1517413  .4527363 18
2010 160 36.460815  43.24079         . .53824365 .9065156  .05949008   .0509915  .08215298  .1983003 .21529745 .16997167   .3342776 .9490085  .3966006 .15014164  .4164306 18
2011 160 36.576923  43.78659         1  .5152439 .9054878  .07012195  .04268293  .09756097 .22256097  .2164634 .17987806  .28353658 .9512195  .4329268  .1585366  .4695122 18
2012 160  35.71687  43.87709  .9329609  .5139665 .9106146  .05027933  .08379889  .08938547  .2011173 .26815644 .12849163   .3128492 .9497207  .3743017 .16201118   .424581 18
2013 160 38.023254   42.9848   .962963  .5106383 .8753799  .07902735  .07598785    .112462 .18541034  .1945289  .1975684   .3100304 .9513678  .3829787  .1550152 .43465045 18
2014 160   36.7006  43.88235         .  .5187166 .8609626   .0909091  .09625668   .1764706 .19251336 .12299465 .19786096   .3101604 .9465241  .3636364  .1550802  .4064171 18
2015 160  38.31597  44.02237  .7434211  .5079872 .8690096   .0798722  .07667731  .12779553 .20447284 .15015975 .14057508   .3769968 .9488818 .39297125 .18210863  .4408946 18
2016 160  37.66418  42.41611         .  .5033557 .8724832   .0805369  .06040268  .13422818  .1543624 .08724833 .24832214   .3758389 .8993289  .3825503 .24161074  .4832215 18
2017 160 34.742332  42.59659         .  .5056818 .8181818  .13068181  .10227273   .0909091 .11363637 .13068181 .17045455   .4943182 .8977273  .4886364 .21022727  .4943182 18
2018 160  38.34108  42.11765         .  .4705882 .8014706  .13235295  .10294118  .08088236  .2352941 .13970588 .11764706   .4264706 .9338235  .5147059  .2132353 .49264705 18
2001 200  38.88652  38.73595  .4969879  .5022472 .8797753 .019101124  .11011236    .229765  .3498695   .232376 .18798956          0 .8741573 .26292136 .08539326 .28876406 18
2002 200   38.5057  39.03238         .  .5215827 .9064748  .03057554  .11690647   .3165468  .3039568 .20143884 .17805755          0  .868705  .2733813  .0971223  .3021583 18
2003 200  37.94147  39.66055 .52681386  .5034404 .8761468   .0206422  .12155963  .27078384   .283848 .21733966  .1935867 .034441806 .8704128 .25802752 .10665137  .3635321 18
2004 200  38.39479  41.01585         .  .5105634 .8521127   .0193662  .10387324   .2975352  .2447183 .21302816  .2447183          0 .8714789  .3045775 .11267605 .38732395 18
2005 200  38.49247   40.7008         . .52409637 .8855422  .04016064  .12851405  .18574513  .3045356 .25053996 .12958963  .12958963 .8514056 .32730925 .09036145  .3955823 18
2006 200  38.37054  39.62341         . .51276594 .8978723 .029787235  .13404255  .17567568  .3198198 .18693693  .1554054  .16216215 .8723404  .3085106 .11914894 .33404255 18
2007 200  38.16509  40.91026         .  .5153846 .8846154  .03076923  .11666667  .15893108 .29113925 .18706048 .15049227  .21237694 .8807693 .33846155 .13461539  .3961538 18
2008 200 38.133488  41.78448         .  .5280172     .875 .030172413  .12068965  .13705584 .23350254  .2436548  .1218274  .26395938 .8965517  .3189655 .13577586  .3663793 18
2009 200  37.45926  41.54594         .  .5312916 .8761651 .034620505  .16245006  .18793103 .27068967  .1724138  .1224138   .2465517 .8801598  .3448735  .1584554  .3981358 18
2010 200 37.256134  41.42742         . .52150536 .8440861 .034946237  .14247312  .21774194 .25134408  .2016129 .12365592  .20564516  .891129  .3346774 .14112903  .4126344 18
2011 200 37.688602  42.19857  .9942857  .5214286 .8385714 .024285715  .14428571  .17714286 .25714287 .19285715 .12714286   .2457143 .8628572  .3457143  .1642857 .41285715 18
2012 200 37.902042  41.63433  .8656716 .51492536 .8507463 .007462686  .12313433   .1641791 .23880596 .22761194 .14925373  .22014925 .9179105  .3768657  .1567164  .4664179 18
2013 200   36.2568  42.53371  .7552083 .52080345  .866571 .028694404   .1276901  .18651363  .2180775 .21520804  .1492109  .23098996 .8981349  .3601148  .1635581 .41606885 18
2014 200 37.057693  41.10638         . .52978724 .8425532 .031914894  .14042553  .22978723 .21276596 .20212767 .10638298  .24893618 .8829787   .293617 .12765957  .3574468 18
2015 200 37.992714  41.75232  .7393939 .51474303  .882898  .02021904   .1533277   .1979781  .2485257  .2064027 .12973884  .21735467  .884583  .3007582 .12805392 .35299075 18
2016 200 37.729218  41.77396         .   .504142 .8721893 .033136096   .1147929   .1514793 .24970414  .2153846 .13727811  .24615385 .9065089   .312426 .13136095  .3857988 18
2017 200 37.570652  41.82244         .  .5080148 .8816276  .03329223  .15289766  .16399507  .2318126 .22071517 .13070284  .25277436 .9087546  .3563502 .15536375  .4093711 18
2018 200 37.821007  41.78984         .  .5077574 .8801128  .03102962  .15232722  .14668547 .26375178  .2002821 .11565585  .27362484 .9040903  .3385049  .1438646  .4005642 18
2001 240  38.89368  39.80263  .5864662        .5 .9631579  .02631579  .09473684  .15479876  .3065015  .2260062  .3126935          0 .9210526 .24736843 .09736842  .3131579 18
2002 240  39.55072  39.94248         . .53097343  .960177  .02654867   .1061947  .25663716 .23451327  .1504425  .3584071          0 .8938053 .29646018 .13274336  .3893805 18
2003 240  39.00834  39.72959  .6549708 .54846936 .9438776 .017857144  .15561225  .12466124 .26287264  .2276423 .30623305  .07859079 .8903061  .3112245 .11479592  .3673469 18
2004 240  39.98421  39.56872         .  .5450237 .9241706  .04739337  .17535545  .26540285  .2464455 .26540285  .2227488          0 .8720379 .29383886 .06635071  .2748815 18
2005 240   39.6134  41.40271         . .53846157  .959276  .02714932  .11312217   .1690141  .3004695 .20657277 .07042254   .2535211 .8914027  .3484163 .13122173  .3529412 18
2006 240 38.068626  41.05804         . .51339287   .96875 .017857144  .08035714  .10243902 .22439024 .25365853 .13658537  .28292683 .9017857 .27232143 .12053572  .3169643 18
2007 240 37.789604  40.72562         .  .5260771 .9319728  .04081633  .08390023  .11508951 .23273657 .25575447 .20204604   .1943734 .8843538 .27210885 .09750567 .28798187 18
2008 240  38.82326  39.78775         .  .5102041 .9102041  .06122449  .11836734   .1146789 .19266056 .26605505  .1743119   .2522936 .9061224  .3265306 .11020408  .3714286 18
2009 240  36.49868  41.03704         .  .4976852 .8981481  .08333334  .11574074  .14402173 .24184783 .27173913 .11684783   .2255435 .9027778 .23148148 .08333334  .3472222 18
2010 240  36.96931  41.36136         .  .5022727 .9159091  .06136364  .09318182  .14318182  .2090909 .22045454  .1931818   .2340909 .9068182 .29090908 .11363637        .4 18
2011 240 37.846577  41.60235   .968504  .5435294      .88  .07294118  .14352942  .14117648  .1882353  .1952941 .20235294  .27294117 .9035294  .3058824 .09647059  .3764706 18
2012 240  38.73714  43.09948  .8848168 .57591623 .9162304  .06282722  .08900524  .06282722  .2041885 .18324608  .2041885   .3455497 .9162304  .2722513 .08376963  .3141361 18
2013 240 37.412106  42.46604  .8724832 .51990634 .9180328  .04918033  .12412178  .11241218 .23653395  .2880562 .10070258  .26229507 .9227166  .3067916 .10070258  .3185012 18
2014 240 37.640778  44.54667         . .50222224 .8977778  .05333333   .1511111  .10666667  .2088889  .2311111 .14666666   .3066667 .9066667  .3111111 .10222222       .32 18
2015 240  38.97408  43.33775      .704 .53642386 .9470199  .02317881  .12251656  .08609272  .1986755 .21192053 .22516556   .2781457 .9403973  .3145695  .0794702  .3112583 18
2016 240  38.68421  43.60563         . .52816904 .9295775  .04929578   .0915493  .09859155  .1690141 .21830986 .26760563  .24647887 .9507042  .3380282  .0915493  .3802817 18
2017 240 35.626087  43.15873         .  .4920635 .9365079 .015873017  .11904762 .071428575 .15079366 .25396827 .23015873   .2936508  .952381  .3730159 .12698413  .3968254 18
2018 240  39.83065  41.75182         .  .5328467 .9270073  .02919708   .1240876  .09489051 .15328467  .3576642 .20437956  .18978103 .9270073  .3138686 .09489051  .3722628 18
2001 440 37.286102  39.54684  .7239264  .5518987  .878481  .05316456    .078481   .1091954   .204023  .2729885  .4137931          0 .9164557 .42531645  .1949367  .3974684 18
2002 440  36.37267  40.31285         .  .5027933  .877095  .05027933   .0726257   .2849162 .12290503  .2290503  .3631285          0  .877095  .4413408  .2122905  .4301676 18
2003 440  36.86478   39.5867  .7173913  .5202312  .867052  .05202312  .06936416  .23100305  .1793313  .2036474 .27051672  .11550152 .9132948  .3959537 .16473988  .4566474 18
2004 440  37.47938  38.92694         .  .4840183 .8538813  .06392694  .11415525  .28767124 .12328767 .24657534  .3424658          0 .9041096  .4063927 .16894977  .4520548 18
2005 440 36.937107  38.00565         .  .4915254 .8531073  .04519774  .13559322  .13071896 .26797387 .19607843 .11111111  .29411766 .8983051  .4180791 .18079096 .43502825 18
2006 440  38.33846  39.93151         .  .5479452  .739726  .12328767  .16438356  .07575758 .13636364  .2121212 .07575758         .5 .9452055 .56164384  .3287671   .479452 18
2007 440 36.194443  41.25834         .        .5 .7083333  .14166667  .15833333  .11428571        .2  .2095238  .1904762   .2857143      .95  .5416667       .25  .4916667 18
2008 440 36.383335   40.6875         .   .515625  .703125    .203125    .140625  .11111111  .1851852 .12962963  .2777778   .2962963  .921875      .625   .234375    .53125 18
2009 440 34.391754  40.49557         .  .5840708 .7522124   .1061947  .14159292   .1559633 .14678898 .14678898 .21100917  .33944955 .9734513  .6017699  .2920354  .6460177 18
2010 440 35.180954  41.84071         .  .4955752 .8230088   .0619469   .1504425  .19469027  .1504425 .17699115 .17699115    .300885 .9646018  .6460177 .28318584  .6460177 18
2011 440  40.82178  42.71682         1  .4424779 .8141593  .07964602  .08849557  .09734514  .1858407  .2123894  .1061947   .3982301 .9734513   .619469  .3362832  .5840708 18
2012 440 33.648647  40.47368  .9736842 .55263156 .9210526  .02631579  .10526316   .2368421  .2368421  .2631579 .02631579   .2368421 .9736842 .28947368  .2368421  .4473684 18
2013 440 37.764706  40.56364         1  .4909091 .9181818  .02727273  .07272727  .07272727 .12727273 .15454546 .25454545   .3909091 .9909091 .56363636 .26363635 .54545456 18
2014 440      40.4  41.93103         . .51724136 .9310345  .05172414   .0862069  .03448276  .1724138  .2413793  .1724138   .3793103 .9310345  .6034483 .25862068        .5 18
2015 440  39.27184  40.61607  .8085107 .54464287 .8482143  .08035714  .13392857  .05357143 .23214285 .20535715 .10714286   .4017857 .9196429  .6071429     .3125  .6428571 18
2016 440 38.057972  41.79221         .  .5064935 .7402598  .15584415  .22077923  .14285715 .15584415  .0909091 .23376623   .3766234 .9610389  .6363636  .3116883  .6363636 18
2017 440  38.63014  44.60811         .   .527027 .7702703   .0945946  .24324325  .08108108  .0945946  .2162162 .08108108    .527027 .9864865  .7567568  .4054054  .7432432 18
2018 440  41.11111  43.51948         .  .4935065 .7532467  .12987013  .25974026  .03896104 .11688311  .1948052 .14285715   .5064935 .9480519  .6233766  .3636364  .7402598 18
2001 480  40.08823  42.36752  .5576923  .4871795 .8632479  .11111111  .05982906   .2477876 .22123894 .23893805  .2920354          0 .8803419  .2820513 .08547009  .3931624 18
2002 480      37.4  40.01923         .  .4615385 .8846154  .11538462  .03846154   .3269231 .17307693 .17307693  .3269231          0 .9230769 .23076923 .05769231  .3269231 18
2003 480  39.44555  37.19643  .6097561 .51785713 .9464286 .026785715  .04464286  .23214285       .25  .2142857 .29464287 .008928572 .8303571  .3392857 .08035714 .29464287 18
2004 480  39.98182  42.15254         .  .5084746 .9322034  .06779661 .033898305  .40677965 .23728813 .18644068 .16949153          0 .8305085 .27118644 .11864407  .3389831 18
2005 480 35.792683  39.48864         . .53409094 .9090909   .0909091  .06818182   .1904762  .3809524  .1547619 .13095239  .14285715     .875 .27272728 .10227273 .29545453 18
2006 480 37.614582        41         .  .5233645 .9813084  .01869159  .06542056  .24752475  .2970297 .21782178 .10891089  .12871288 .8878505  .3084112 .12149533  .3271028 18
2007 480  38.35571  42.28205         . .53846157 .9935898          0  .08333334  .14285715  .3265306  .2244898 .13605443  .17006803 .9166667  .4423077  .1025641  .4423077 18
2008 480  39.39024  38.14943         . .54022986 .9885057          0  .03448276  .26506025  .1566265 .27710843 .10843374  .19277108 .9195402  .3333333 .12643678  .3908046 18
2009 480  33.85294  41.89542         .  .4901961 .9607843 .006535948  .08496732  .21276596 .25531915 .29078013 .14893617  .09219858 .9084967  .3006536 .13071896  .3921569 18
2010 480      37.5  43.19728         .  .4829932 .9183673  .06122449  .08843537  .18367347   .292517   .292517  .1292517  .10204082 .9251701  .3605442 .13605443  .4353741 18
end

Here is how I get the synthetic control weights:

Code:

bysort metarea: gen nyear=[_N]
keep if nyear == 18

tsset metarea year

synth ahrsworkt age cinethp male white black foreign_born faminc_0025 faminc_2550 faminc_5075 faminc_75100 faminc_100m hs_grad bachelors advanced_degree white_collar, trunit(3760) trperiod(2012) fig keep(synthetic)

Here is my original Kansas City vs. St. Louis DiD (i.e. the regression I want to run but don't know how to with a synthetic control group):

Code:

reg ahrsworkt kc post2012  interact_kc trend_kc if (metarea == 3760 | metarea == 7040) , r

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