adding the country -specific time trends as control

[Khati Zolfaghari]

hello and good day to all,
I am using the local projection method for my thesis, (panel data ) , I do not know how can I add the country-specific time trends as control, in terms of the robustness check of my estimation. my adviser told me to do some robustness check like this . I hope I receive your advice,

my baseline estimation is as follow:

local hmax = 5
forv h = 0/`hmax' {

asdoc reghdfe lnfertility`h' l(0/2)dummy_hini l(1/2)lnfertility , absorb( i.ifscode i.year) vce(cluster ifscode)

many thanks for your valuable time and advice.

best regards ,

[Daniel Feenberg]

At

https://www.stata.com/features/overview/factor-variables/

there is statement

If you want to interact a continuous variable with a factor variable, just prefix the continuous variable with c..

but if that doesn't work with -reghdfe- , why not simply create a dummy for each country and multiply by the trend? Then add all the interactions as independent variables. Stata is quite fast and -reghdfe- is necessary only for humongous projects. Stata -reg- won't mind having 200 independent variables, and the additional computation time is unlikely to be significant. 1,000 variables would slow thing down but not so much as to be impractical. 10,000 is pushing the limits..

[Khati Zolfaghari]

@[email protected] thank you so much for your reply. I apologize if I ask again, maybe because I am a bit beginner. in my estimation " dummy_hini" is a dummy variable for years of HINI, and fertility is a continuous variable. now by adding the "country-specific time trends as control" it means I do some robustness check?
it is panel data.
-- does it make sense "country-specific time trends as control" work as a robustness check?

--- if yes I become confused about to code that I have to write.

many thanks in advance for your valuable time and advice.

best regards,

[Carlo Lazzaro]

Khati:
usually time trends imply to consider -timevar- (-year-, in your case) as a continuous variable rather than a categorical one.
It is also advisable to explore whether turning points are detectable (that is, whether a non-linear relationship exists between -year- and the regressand).
That said, I share Daniel's recommendation about creating an interaction, something like:

i.country##c.year##c.year

Two further asides:
- it would be wise to consider centering -year- before creatring the interaction (ie, subtracting its panel-specific mean);
- you might have to reconsider your model as some perfect correlation with the fixed effects betwen brackets are expected.

[Khati Zolfaghari]

Carlo Lazzaro thank you so much for your reply.

If it is possiable I am so thankful to receive further advice about the way I want to do.

in my model I am interesting to use the Placebo test , to see the evaluation of the fertility before the pandemic( in my case is named "dummy_hini")
I read about it , as my estimation is fixed effect and the regression is what I mentioned . I don't know how do I do it and what should I do . I underestood theoretically but unfortunately when I want to run I become confused.

I am so thankful to receive your advice .

Many thanks for your valuable time and advice.

Best regards,

[Carlo Lazzaro]

Khati:
I would imagine something along the following lines:

reghdfe lnfertility`h' l(0/2)dummy_hini l(1/2)lnfertility i.country##c.year##c.year, absorb( i.ifscode) vce(cluster ifscode)

The two previous asides still apply:
- it would be wise to consider centering -year- before creatring the interaction (ie, subtracting its panel-specific mean);
- you might have to reconsider your model as some perfect correlation with the fixed effects betwen brackets are expected.

Basically, I think you've to challenge yourself with the abovementioned code and see whether there's something else to change in your original code to accomodate the interaction.

[Khati Zolfaghari]

Carlo Lazzaro many thanks for your reply.

But in terms of the Placebo testing , that I mean in terms of the evaluating the fertility before pandemic, in the fixed effect I have problem .
I am chalenging to do 2 or even more robustness check, one by previous valuable advice and using the interaction, and now I try to see what's happen .
but in another test Placebo test I don't know how can I do! I understand it ,I hope . But I don't know why when I want to run I cannot.
I am so thankful to receive your advice.
However I check in terms of the spesification of my model and it was correct and now I am dealing with these to check.

many thanks for valuable time and advice.

[Carlo Lazzaro]

Khati:
what if in another -reghdfe- model you replace in the interaction -i.country- with -1(0/2) dummy_hini-?

[Khati Zolfaghari]

@Carlo Lazzaro thank you so much for your reply. these are my results:

reghdfe f(0).lnfertility l(0/2)dum_recession l(1/2)lnfertility , absorb( i.ifscode i.year) vce(cluster ifscode)

HDFE Linear regression                            Number of obs   =      3,116
Absorbing 2 HDFE groups                           F(   5,    141) =    6592.37
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.9998
                                                  Adj R-squared   =     0.9998
                                                  Within R-sq.    =     0.9493
Number of clusters (ifscode) =        142         Root MSE        =     0.0190

                               (Std. Err. adjusted for 142 clusters in ifscode)
-------------------------------------------------------------------------------
              |               Robust
  lnfertility |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
dum_recession |
          --. |  -.0013254   .0015998    -0.83   0.409    -.0044881    .0018372
          L1. |  -.0015468   .0011184    -1.38   0.169    -.0037579    .0006642
          L2. |    .000273   .0010136     0.27   0.788    -.0017309    .0022769
              |
  lnfertility |
          L1. |   1.316072   .0545001    24.15   0.000     1.208329    1.423815
          L2. |    -.36521   .0512967    -7.12   0.000    -.4666201      -.2638
              |
        _cons |   .8267416   .1036365     7.98   0.000     .6218594    1.031624
-------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
     ifscode |       142         142           0    *|
        year |        22           0          22     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

the second "i delete some part here to reduce the space "

reghdfe f(0).lnfertility l(0/2)dum_recession l(1/2)lnfertility i.ifscode##c.year##c.year, absorb( i.ifscode ) vce(cluster ifscode)

HDFE Linear regression                            Number of obs   =      3,116
Absorbing 1 HDFE group                            F( 289,    141) =          .
Statistics robust to heteroskedasticity           Prob > F        =          .
                                                  R-squared       =     0.9999
                                                  Adj R-squared   =     0.9999
                                                  Within R-sq.    =     0.9730
Number of clusters (ifscode) =        142         Root MSE        =     0.0170

                                       (Std. Err. adjusted for 142 clusters in ifscode)
---------------------------------------------------------------------------------------
                      |               Robust
          lnfertility |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
        dum_recession |
                  --. |  -.0011683   .0012788    -0.91   0.362    -.0036963    .0013598
                  L1. |  -.0017493   .0009837    -1.78   0.078     -.003694    .0001954
                  L2. |  -.0014392   .0009009    -1.60   0.112    -.0032202    .0003417
                      |
          lnfertility |
                  L1. |   .9268426   .0606532    15.28   0.000     .8069354     1.04675
                  L2. |  -.1757083   .0581169    -3.02   0.003    -.2906014   -.0608152
                      |
              ifscode |
                 112  |          0  (omitted)
                 122  |          0  (omitted)
                 124  |          0  (omitted)
                 128  |          0  (omitted)
                 132  |          0  (omitted)
                 134  |          0  (omitted)
                 136  |          0  (omitted)
                 138  |          0  (omitted)
                 142  |          0  (omitted)
                 144  |          0  (omitted)
                 146  |          0  (omitted)
                 156  |          0  (omitted)
                 158  |          0  (omitted)
                 172  |          0  (omitted)
                   |
                 year |   .7701481   .1158359     6.65   0.000     .5411485    .9991477
                      |
       ifscode#c.year |
                 112  |   1.202214   .0983473    12.22   0.000     1.007789     1.39664
                 122  |  -.4316194   .1567109    -2.75   0.007     -.741426   -.1218127
                 124  |   .9874051   .0513702    19.22   0.000     .8858498     1.08896
                 128  |  -.1841739    .064904    -2.84   0.005    -.3124847   -.0558632
                 132  |   .3507392   .0238882    14.68   0.000     .3035138    .3979645
                 134  |   -1.29308   .1940718    -6.66   0.000    -1.676747   -.9094134

                   |
        c.year#c.year |   -.000192   .0000288    -6.66   0.000     -.000249    -.000135
                      |
ifscode#c.year#c.year |
                 112  |  -.0002986   .0000245   -12.19   0.000     -.000347   -.0002502
                 122  |   .0001083    .000039     2.77   0.006     .0000311    .0001855
                 124  |  -.0002454   .0000128   -19.20   0.000    -.0002707   -.0002202
                 128  |   .0000462   .0000162     2.86   0.005     .0000143    .0000782
                 132  |  -.0000868   5.96e-06   -14.58   0.000    -.0000986    -.000075
                 134  |   .0003227   .0000483     6.68   0.000     .0002271    .0004183
                 136  |  -.0003202   .0000148   -21.67   0.000    -.0003494    -.000291

and thee last :

reghdfe f(0).lnfertility i.ifscode## l(0/2)dum_recession l(1/2)lnfertility , absorb( i.ifscode i.year) vce(cluster ifscode)

HDFE Linear regression                            Number of obs   =      3,116
Absorbing 2 HDFE groups                           F( 418,    141) =          .
Statistics robust to heteroskedasticity           Prob > F        =          .
                                                  R-squared       =     0.9999
                                                  Adj R-squared   =     0.9998
                                                  Within R-sq.    =     0.9592
Number of clusters (ifscode) =        142         Root MSE        =     0.0183

                                          (Std. Err. adjusted for 142 clusters in ifscode)
------------------------------------------------------------------------------------------
                         |               Robust
             lnfertility |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
                 ifscode |
                    112  |          0  (omitted)
                    122  |          0  (omitted)
                    124  |          0  (omitted)
                    128  |          0  (omitted)
                    132  |          0  (omitted)
                    134  |          0  (omitted)
     1.dum_recession |  -.0094881   .0014007    -6.77   0.000    -.0122572   -.0067191
                         |
         L.dum_recession |
                      1  |  -.0184645   .0011252   -16.41   0.000    -.0206889   -.0162401
                         |
        L2.dum_recession |
                      1  |  -.0092814   .0017303    -5.36   0.000    -.0127021   -.0058608
                         |
   ifscode#dum_recession |
                  112 1  |   .0219358   .0005806    37.78   0.000     .0207881    .0230835
                  122 1  |  -.0070678   .0013495    -5.24   0.000    -.0097356      -.0044
                  124 1  |   .0066007   .0025396     2.60   0.010     .0015802    .0116213
                  128 1  |  -.0051546   .0020429    -2.52   0.013    -.0091933   -.0011159
                  132 1  |   .0094328   .0009712     9.71   0.000     .0075128    .0113528

                      1  |  -.0092814   .0017303    -5.36   0.000    -.0127021   -.0058608
                         |
   ifscode#dum_recession |
                  112 1  |   .0219358   .0005806    37.78   0.000     .0207881    .0230835
                  122 1  |  -.0070678   .0013495    -5.24   0.000    -.0097356      -.0044
                  124 1  |   .0066007   .0025396     2.60   0.010     .0015802    .0116213
                  128 1  |  -.0051546   .0020429    -2.52   0.013    -.0091933   -.0011159
                  132 1  |   .0094328   .0009712     9.71   0.000     .0075128    .0113528
                  134 1  |   .0027178   .0010994     2.47   0.015     .0005443    .0048912
                  136 1  |   .0077008   .0010595     7.27   0.000     .0056062    .0097955
                  138 1  |  -.0055421   .0013525    -4.10   0.000    -.0082158   -.0028684
                  142 1  |   .0216603   .0036928     5.87   0.000       .01436    .0289607
                  144 1  |   .0175783   .0011186    15.71   0.000     .0153669    .0197897
                  146 1  |   .0248947    .001485    16.76   0.000     .0219589    .0278305
                  156 1  |   .0104841   .0011642     9.01   0.000     .0081826    .0127856
                  158 1  |   .0077476   .0022326     3.47   0.001     .0033338    .0121614
                  172 1  |   .0089601   .0011608     7.72   0.000     .0066653    .0112549
                  174 1  |   .0220988   .0013673    16.16   0.000     .0193958    .0248018
                  178 1  |   .0093952   .0037131     2.53   0.012     .0020548    .0167357
                  182 1  |  -.0402799   .0022054   -18.26   0.000    -.0446399     -.03592
                  184 1  |  -.0038044   .0012204    -3.12   0.002    -.0062172   -.0013917
                  186 1  |   .0122282   .0016754     7.30   0.000      .008916    .0155403
                  193 1  |   .0058021   .0020443     2.84   0.005     .0017607    .0098436
                  196 1  |   .0017512   .0025138     0.70   0.487    -.0032184    .0067207
                  199 1  |   .0139528   .0016655     8.38   0.000     .0106603    .0172452
                  213 1  |   .0109575   .0014223     7.70   0.000     .0081457    .0137693
                  218 1  |   .0062407   .0012205     5.11   0.000      .003828    .0086535
                  223 1  |   .0124039   .0014561     8.52   0.000     .0095252    .0152826
                  228 1  |   .0108287   .0014679     7.38   0.000     .0079268    .0137306
                  233 1  |   .0151788   .0016093     9.43   0.000     .0119973    .0183603
                  238 1  |   .0134144   .0015196     8.83   0.000     .0104103    .0164184
                  243 1  |   .0097257   .0012233     7.95   0.000     .0073073     .012144
                  248 1  |   .0138735   .0016452     8.43   0.000     .0106211    .0171258
                  253 1  |   .0096791   .0015856     6.10   0.000     .0065445    .0128136
                  258 1  |   .0051429   .0012489     4.12   0.000     .0026738    .0076119
                  263 1  |   .0099982   .0015511     6.45   0.000     .0069317    .0130647
                  268 1  |   .0144905    .001699     8.53   0.000     .0111316    .0178493
                  273 1  |   .0161362   .0020973     7.69   0.000     .0119901    .0202823
                  278 1  |   .0117638   .0015481     7.60   0.000     .0087034    .0148242
                  283 1  |   .0119612    .001348     8.87   0.000     .0092964    .0146261
                  288 1  |   .0120495   .0016052     7.51   0.000     .0088763    .0152228
                  293 1  |   .0100959    .001623     6.22   0.000     .0068872    .0133045
                  298 1  |   .0144597   .0018065     8.00   0.000     .0108883     .018031
                  299 1  |    .010999    .001429     7.70   0.000     .0081739    .0138241
                  343 1  |   .0034659   .0007296     4.75   0.000     .0020235    .0049083
                  429 1  |     .02881   .0031954     9.02   0.000     .0224928    .0351272
                  433 1  |   .0113177   .0016326     6.93   0.000     .0080902    .0145452
                  436 1  |   .0089193   .0022051     4.04   0.000     .0045599    .0132787
                  439 1  |   .0247828   .0022934    10.81   0.000     .0202489    .0293167
                  443 1  |   .0112768   .0018196     6.20   0.000     .0076796    .0148741
                  446 1  |   .0192683    .001646    11.71   0.000     .0160143    .0225223
                  449 1  |   .0091778   .0010537     8.71   0.000     .0070946    .0112609
                  453 1  |   .0354367   .0032464    10.92   0.000     .0290188    .0418545
                  456 1  |   .0145474   .0018392     7.91   0.000     .0109115    .0181833
                  466 1  |   .0259293   .0031786     8.16   0.000     .0196455    .0322131
                  469 1  |   .0306169    .002438    12.56   0.000     .0257971    .0354366
                  474 1  |   .0064403   .0008458     7.61   0.000     .0047681    .0081124
                  512 1  |   .0064266   .0019538     3.29   0.001     .0025641    .0102891
                  513 1  |   .0067945   .0018315     3.71   0.000     .0031736    .0104153
                  518 1  |   .0027406   .0019232     1.43   0.156    -.0010614    .0065427
                  522 1  |   .0081886   .0018254     4.49   0.000     .0045799    .0117974
                  524 1  |   .0174479   .0022089     7.90   0.000      .013081    .0218147
                  532 1  |  -.0209738   .0015706   -13.35   0.000    -.0240788   -.0178689
                  534 1  |   .0092797   .0015957     5.82   0.000      .006125    .0124343
                  536 1  |   .0131025   .0018854     6.95   0.000     .0093753    .0168297
                  542 1  |   .0530192   .0012898    41.11   0.000     .0504694    .0555689
                  544 1  |   .0094016   .0018453     5.09   0.000     .0057536    .0130496
                  548 1  |   .0090883   .0015141     6.00   0.000      .006095    .0120816
                  558 1  |   .0067583   .0018253     3.70   0.000     .0031498    .0103669
                  564 1  |    .009951   .0018232     5.46   0.000     .0063467    .0135553
                  566 1  |   .0171517     .00195     8.80   0.000     .0132966    .0210068
                  576 1  |  -.0799986   .0032928   -24.30   0.000    -.0865082    -.073489
                  578 1  |   .0100481   .0013808     7.28   0.000     .0073184    .0127778
                  582 1  |    .011339   .0016031     7.07   0.000     .0081698    .0145081
                  612 1  |   .0263761   .0027201     9.70   0.000     .0209987    .0317535
                  614 1  |   .0152669   .0017777     8.59   0.000     .0117525    .0187812
                  616 1  |   .0153784   .0016022     9.60   0.000     .0122109    .0185459
                  618 1  |   .0082761   .0014743     5.61   0.000     .0053615    .0111907
                  622 1  |   .0133503   .0019245     6.94   0.000     .0095456    .0171549
                  626 1  |   .0144331   .0024354     5.93   0.000     .0096184    .0192477
                  628 1  |   .0130822   .0017484     7.48   0.000     .0096258    .0165386
                  634 1  |   .0108157   .0016408     6.59   0.000      .007572    .0140594
                  636 1  |   .0102415   .0017616     5.81   0.000     .0067589    .0137241
                  638 1  |          0  (empty)
                  643 1  |    .012889   .0018799     6.86   0.000     .0091725    .0166054
                  644 1  |   .0153372   .0021126     7.26   0.000     .0111607    .0195136
                  646 1  |  -.0009445    .001316    -0.72   0.474    -.0035461     .001657
                  648 1  |   .0055059   .0013415     4.10   0.000     .0028537     .008158
                  652 1  |    .015359   .0019189     8.00   0.000     .0115655    .0191526
                  654 1  |   .0073588   .0017985     4.09   0.000     .0038033    .0109142
                  656 1  |   .0049106   .0009563     5.14   0.000     .0030201    .0068011
                  662 1  |   .0080125   .0014245     5.62   0.000     .0051963    .0108287
                  664 1  |   .0107652   .0019301     5.58   0.000     .0069496    .0145808
                  666 1  |   .0133842   .0020495     6.53   0.000     .0093325    .0174359
                  668 1  |   .0002118    .000935     0.23   0.821    -.0016367    .0020603
                  672 1  |   .0110766   .0016899     6.55   0.000     .0077358    .0144174
                  674 1  |   .0086334   .0015043     5.74   0.000     .0056595    .0116074
                  676 1  |   .0191826   .0024923     7.70   0.000     .0142554    .0241097
                  678 1  |   .0057264    .000825     6.94   0.000     .0040955    .0073573
                  682 1  |   .0042501   .0018309     2.32   0.022     .0006305    .0078697
                  686 1  |   .0214315     .00209    10.25   0.000     .0172997    .0255634
                  688 1  |   .0108245   .0018795     5.76   0.000     .0071088    .0145402
                  692 1  |  -.0016925   .0031572    -0.54   0.593     -.007934    .0045489
                  694 1  |   .0085333   .0008934     9.55   0.000     .0067672    .0102994
                  698 1  |   .0060564   .0015836     3.82   0.000     .0029258    .0091871
                  714 1  |   .0018898   .0019635     0.96   0.337    -.0019919    .0057715
                  722 1  |    .004867    .001433     3.40   0.001     .0020341    .0076999
                  724 1  |   .0080212   .0013293     6.03   0.000     .0053933    .0106491
                  728 1  |   .0182595   .0020919     8.73   0.000      .014124    .0223949
                  732 1  |   .0126681   .0015243     8.31   0.000     .0096548    .0156815
                  738 1  |   .0111565   .0019134     5.83   0.000     .0073739     .014939
                  742 1  |    .009815   .0018893     5.20   0.000       .00608    .0135501
                  744 1  |   .0207907    .001981    10.50   0.000     .0168744     .024707
                  746 1  |   .0125311    .001941     6.46   0.000     .0086938    .0163683
                  748 1  |          0  (empty)
                  754 1  |   .0139835   .0020707     6.75   0.000     .0098899    .0180772
                  853 1  |   .0112024   .0018227     6.15   0.000     .0075991    .0148057
                  911 1  |   .0111548   .0019024     5.86   0.000      .007394    .0149157
                  912 1  |  -.0010319   .0017195    -0.60   0.549    -.0044313    .0023676
                  913 1  |   .0220925   .0020727    10.66   0.000     .0179949    .0261901
                  914 1  |   .0219062   .0019185    11.42   0.000     .0181134    .0256989
                  915 1  |    .020563   .0027954     7.36   0.000     .0150367    .0260893
                  916 1  |  -.0983044   .0018389   -53.46   0.000    -.1019399    -.094669
                  917 1  |    .004686    .001872     2.50   0.013     .0009853    .0083868
                  918 1  |   .0862602   .0029589    29.15   0.000     .0804107    .0921097
                  921 1  |   .0066885    .001819     3.68   0.000     .0030924    .0102846
                  922 1  |   .0116018   .0024709     4.70   0.000      .006717    .0164865
                  923 1  |    .016432   .0019715     8.33   0.000     .0125345    .0203295
                  924 1  |   .0070047    .001006     6.96   0.000     .0050159    .0089936
                  925 1  |          0  (empty)
                  926 1  |  -.0058966   .0033402    -1.77   0.080    -.0124999    .0007067
                  927 1  |          0  (empty)
                  935 1  |  -.0014177   .0012926    -1.10   0.275     -.003973    .0011377
                  936 1  |   .0266758   .0021015    12.69   0.000     .0225212    .0308304
                  941 1  |  -.0162989   .0022486    -7.25   0.000    -.0207443   -.0118536
                  944 1  |   .0314296   .0011475    27.39   0.000     .0291609    .0336982
                  946 1  |    .017938   .0033484     5.36   0.000     .0113185    .0245575
                  948 1  |   .0177718   .0019178     9.27   0.000     .0139804    .0215632
                  960 1  |   .0238572   .0015067    15.83   0.000     .0208786    .0268358
                  961 1  |   -.013943   .0035327    -3.95   0.000    -.0209269    -.006959
                  962 1  |   .0169512   .0017464     9.71   0.000     .0134985    .0204038
                  963 1  |   .0109994    .001588     6.93   0.000       .00786    .0141389
                  964 1  |  -.0004089     .00467    -0.09   0.930    -.0096413    .0088234
                  968 1  |    .006755   .0026267     2.57   0.011     .0015621    .0119479
                         |
 ifscode#L.dum_recession |
                  112 1  |   .0144857   .0016985     8.53   0.000     .0111279    .0178434
                  122 1  |   .0357219   .0011919    29.97   0.000     .0333656    .0380781
                  124 1  |   .0339151   .0021178    16.01   0.000     .0297284    .0381019
                  128 1  |   .0373216    .001534    24.33   0.000      .034289    .0403541
                  132 1  |   .0258757   .0010285    25.16   0.000     .0238423    .0279091
                  134 1  |   .0282798   .0010517    26.89   0.000     .0262007     .030359
                  136 1  |   .0226647    .000966    23.46   0.000     .0207549    .0245744
                  138 1  |   .0258774   .0010961    23.61   0.000     .0237106    .0280443
                        |
ifscode#L2.dum_recession |
                  112 1  |   .0134589   .0013683     9.84   0.000     .0107538     .016164
                  122 1  |   .0013534   .0024328     0.56   0.579     -.003456    .0061628
                  124 1  |  -.0095588   .0033774    -2.83   0.005    -.0162357   -.0028819
                  128 1  |  -.0250644   .0019972   -12.55   0.000    -.0290128   -.0211161
                |
             lnfertility |
                     L1. |   1.287877   .0605922    21.25   0.000     1.168091    1.407664
                     L2. |  -.3357204   .0573512    -5.85   0.000    -.4490998    -.222341
                         |
                   _cons |   .8049052   .1109069     7.26   0.000     .5856498     1.02416
------------------------------------------------------------------------------------------

I am so thankful to recieve the interpreter . i think the first estimation is more robust)
moreover you mention to this point that "- it would be wise to consider centering -year- before creatring the interaction (ie, subtracting its panel-specific mean)" , unfortunately I do not know how should I do it in Stata.

many thanks for your valuable time and advice .

best regards ,

[Carlo Lazzaro]

Khati:
the main issue here, shared by all the models, is that you probably have some quasi-extreme multicollinearity issues.
I suspect it from the sky-rocketing R_sq within coupled with a half of coefficients that do not reach statistical significance (1st model).
The issuse is the same with the two last models, that, in addition, include too many parameters (and this makes your model really difficult to explain to your audience).
Hence, I would go for a more parsimonious model in testing for robustness:

reghdfe f(0).lnfertility l(0/2)dum_recession l(1/2)lnfertility  c.year##c.year, absorb( i.ifscode ) vce(cluster ifscode)

as -i.ifscode- when included in the interaction is actually omitted,

And you can replicate the same approach for the Placebo Group.
As an aside, I do not think there's need for centering -year- before interaction.

[Khati Zolfaghari]

@Carlo Lazzaro thank you so much for your reply. based on your valuable advice , I did as follow:

reghdfe f(0).lnfertility l(0/2)dum_recession l(1/2)lnfertility c.year##c.year, absorb( i.ifscode ) vce(cluster ifscode)

and this is my result:

HDFE Linear regression                            Number of obs   =      3,116
Absorbing 1 HDFE group                            F(   7,    141) =    6362.70
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.9998
                                                  Adj R-squared   =     0.9998
                                                  Within R-sq.    =     0.9613
Number of clusters (ifscode) =        142         Root MSE        =     0.0194

                               (Std. Err. adjusted for 142 clusters in ifscode)
-------------------------------------------------------------------------------
              |               Robust
  lnfertility |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
dum_recession |
          --. |   -.002172   .0014253    -1.52   0.130    -.0049898    .0006458
          L1. |   -.002055   .0010383    -1.98   0.050    -.0041076   -2.33e-06
          L2. |  -.0015105   .0009418    -1.60   0.111    -.0033723    .0003514
              |
  lnfertility |
          L1. |   1.299065   .0564496    23.01   0.000     1.187468    1.410662
          L2. |  -.3490047   .0530449    -6.58   0.000    -.4538709   -.2441386
              |
         year |     .34806   .0599631     5.80   0.000     .2295171    .4666029
              |
c.year#c.year |  -.0000865   .0000149    -5.80   0.000     -.000116    -.000057
              |
        _cons |  -349.1136   60.21582    -5.80   0.000    -468.1561    -230.071
-------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
     ifscode |       142         142           0    *|
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

--- some point:
here it is based on the adding the time as control? (I am so thankful to recieve your advice if I am wrong)

-- for Placebo, unfortunately again I do not know what should I do in STATA , or maybe now I become a bit confused between Placebo and adding the year as an interaction term and interpretation. because in previous by adding the time interaction it means I add the time as control? now , for Placebo I do not know how to do ! and the exact differences. I apologize a lot.



---you mention to this point that " there's need for centering -year- before interaction." , I apologize for this question. during which condition I have to do? and what is the best way to do ?

many thanks for your valuable time and advice,

best regards,

[Carlo Lazzaro]

Khati:
1)

c.year##c.year

support your search from turning points concerning the relationship between -time- as a continuous variable (ie, -c.year-) and your regressand (and yes, you can considere it as a control).
gives back both coefficients (I mean the linear and the squared one) reaching statistical significant. Hence, your model has a turning point (a maximum) that you can identify by studying the first derivative:

di -( .34806/(2*-.0000865))
2011.9075

What above means that the non-linear (ie, squared) relationship between -time- and the regressand reaches a maximum in 2012 and then declines from 2012 on.
I think that this is a good point to comment on in your research report.
Again, forget my previous advice about centering and keep things as they are.
As far as what you call Placebo is concerned, you may want to try:

reghdfe lnfertility`h' l(0/2)dummy_hini##c.year l(1/2)lnfertility , absorb( i.ifscode) vce(cluster ifscode)

and see what Stata gives you back.

[Khati Zolfaghari]

@Carlo Lazzaro I am really thankful to receive your valuable advice and guidance to understand how can I mention to the point in my research. i did also the Placebo based on your valuable advice ,

reghdfe f(0).lnfertility l(0/2)dum_recession##c.year l(1/2)lnfertility , absorb( i.ifscode ) vce(cluster ifscode)

and this is my result:

HDFE Linear regression                            Number of obs   =      3,116
Absorbing 1 HDFE group                            F(   9,    141) =    5544.34
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.9998
                                                  Adj R-squared   =     0.9998
                                                  Within R-sq.    =     0.9604
Number of clusters (ifscode) =        142         Root MSE        =     0.0196

                                         (Std. Err. adjusted for 142 clusters in ifscode)
-----------------------------------------------------------------------------------------
                        |               Robust
            lnfertility |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
        1.dum_recession |  -.7334894   .4514924    -1.62   0.106    -1.626059    .1590802
                        |
        L.dum_recession |
                     1  |   .4409399   .3392378     1.30   0.196      -.22971     1.11159
                        |
       L2.dum_recession |
                     1  |   .0126148   .3334525     0.04   0.970     -.646598    .6718277
                        |
                   year |   .0004041   .0001013     3.99   0.000     .0002039    .0006044
                        |
   dum_recession#c.year |
                     1  |   .0003644   .0002244     1.62   0.107    -.0000792     .000808
                        |
 L.dum_recession#c.year |
                     1  |  -.0002202   .0001689    -1.30   0.194    -.0005541    .0001136
                        |
L2.dum_recession#c.year |
                     1  |  -6.74e-06   .0001659    -0.04   0.968    -.0003348    .0003213
                        |
            lnfertility |
                    L1. |   1.329687   .0547504    24.29   0.000     1.221449    1.437924
                    L2. |  -.3820503   .0511628    -7.47   0.000    -.4831956    -.280905
                        |
                  _cons |   .0691466   .1713065     0.40   0.687    -.2695146    .4078079
-----------------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
     ifscode |       142         142           0    *|
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

- I do it for 5-time horizons to get the impulse response function. before using the Placebo the coefficient that was interesting to the IRF was the " dum_recession", but now when I consider here the result is inverse, I mean my graph before was decreasing but now it is increasing. ( again here for IRF I consider the coefficient of "dum_recession" h=0= -.7334894 and so on till h=5) . I apologize for asking, here because it considers randomly the result it would be inverse?

cap drop b u d Years Zero
gen Years =_n-1 if _n<=`hmax'
gen Zero = 0   if _n <=`hmax'
gen b=0
gen u=0
gen d=0
local hmax = 5

forv h = 0/`hmax' {

asdoc reghdfe lnfertility`h' l(0/2)dum_recession##c.year l(1/2)lnfertility , absorb( i.ifscode ) vce(cluster ifscode) nest reset dec(4)
replace b = _b[dum_recession]                    if _n == `h'+1
replace u = _b[dum_recession] + 1.645* _se[dum_recession]  if _n == `h'+1
replace d = _b[dum_recession] - 1.645* _se[dum_recession]  if _n == `h'+1
}

many thanks for your valuable time and advice.

Best regards,

[Carlo Lazzaro]

Khati:
the results of -dum_recession_ changed due to the interaction.
It would seem that -year- reaches statistical significance when -1.dum_recession-.
Again, what hits reader's eyes is that the -dum_recession- predictor does not seem to have any role in explaining the variation of the regressand.

[Khati Zolfaghari]

@Carlo Lazzaro many thanks for your valuable time and advice.

best regards.