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  • Plotting graph for curvilinear relationships

    Dear readers

    I am currently trying to plot a curvilinear relationship between two behaviors (certain domestic and international behaviors).
    I use a heckman method for my empirical analysis, given those firms that choose to select to go international may qualitatively differ from those that do not.

    The codes I use are the following:
    Code:
    heckman intratio2_w c.L1.usratio2_w##c.L1.usratio2_w L1.intratio2_w L1.annualreturn5_w L1.regul2 $key_control i.fyear, select(intl = L1.intratio2_w L1.siznumfxhedge_w $key_control i.fyear) twostep
    Furthermore, I test interaction effects with some domestic country level variables, such as:
    Code:
    heckman intratio2_w c.L1.usratio2_w##c.L1.usratio2_w##c.L1.annualreturn5_w L1.regul2 L1.intratio2_w $key_control i.fyear, select(intl = L1.intratio2_w L1.siznumfxhedge_w $key_control i.fyear) twostep
    The results show that there exists a curvilinear relationship between the the variables usratio2_w and intratio2_w as shown below

    Code:
    heckman intratio2_w c.L1.usratio2_w##c.L1.usratio2_w L1.intratio2_w L1.annualreturn5_w L1.regul2 $key_
    > control i.fyear, select(intl = L1.intratio2_w L1.siznumfxhedge_w $key_control i.fyear) twostep 
    note: 2015.fyear omitted because of collinearity
    
    Heckman selection model -- two-step estimates   Number of obs     =      1,398
    (regression model with sample selection)              Selected    =        366
                                                          Nonselected =      1,032
    
                                                    Wald chi2(29)     =     280.91
                                                    Prob > chi2       =     0.0000
    
    ---------------------------------------------------------------------------------------------
                                |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
    ----------------------------+----------------------------------------------------------------
    intratio2_w                 |
                     usratio2_w |
                            L1. |   .2720963   .1278018     2.13   0.033     .0216094    .5225832
                                |
    cL.usratio2_w#cL.usratio2_w |   -.288744   .1455788    -1.98   0.047    -.5740733   -.0034147
                                |
                    intratio2_w |
                            L1. |   .5211206   .0653576     7.97   0.000      .393022    .6492192
                                |
                annualreturn5_w |
                            L1. |   973.2645   1098.729     0.89   0.376    -1180.205    3126.734
                                |
                         regul2 |
                            L1. |   -.017766   .3312482    -0.05   0.957    -.6670005    .6314685
                                |
                   ln_firmage_w |
                            L1. |  -.0135679   .0209061    -0.65   0.516    -.0545431    .0274074
                                |
                        ln_at_w |
                            L1. |  -.0141518   .0068556    -2.06   0.039    -.0275885   -.0007151
                                |
                       tobinq_w |
                            L1. |   .0318719   .0118094     2.70   0.007      .008726    .0550179
                                |
                        slack_w |
                            L1. |   .1102677   .0534081     2.06   0.039     .0055896    .2149457
                                |
                   constraint_w |
                            L1. |   .0030768   .0016573     1.86   0.063    -.0001714    .0063251
                                |
                      entropy_w |
                            L1. |  -.0045865   .0376501    -0.12   0.903    -.0783793    .0692064
                                |
                  ln_tenure_y_w |
                            L1. |  -.0059873   .0137784    -0.43   0.664    -.0329926    .0210179
                                |
                    isfounder_w |
                            L1. |   .0100584   .0269353     0.37   0.709    -.0427339    .0628507
                                |
                          fyear |
                          1999  |  -.4294316   .3530869    -1.22   0.224    -1.121469     .262606
                          2000  |  -.6200813   .6436681    -0.96   0.335    -1.881648     .641485
                          2001  |  -.2670098   .2043539    -1.31   0.191     -.667536    .1335164
                          2002  |  -.1345528   .1770313    -0.76   0.447    -.4815277    .2124222
                          2003  |  -.0704241   .0874952    -0.80   0.421    -.2419116    .1010634
                          2004  |  -.1022615    .055527    -1.84   0.066    -.2110925    .0065696
                          2005  |  -.1420184   .1794518    -0.79   0.429    -.4937375    .2097007
                          2006  |  -.1305091   .1355871    -0.96   0.336    -.3962549    .1352367
                          2007  |  -.0117517   .0917541    -0.13   0.898    -.1915866    .1680831
                          2008  |   .0544525   .0590393     0.92   0.356    -.0612624    .1701674
                          2009  |  -.2999764   .3494616    -0.86   0.391    -.9849084    .3849557
                          2010  |  -.1411477   .1266843    -1.11   0.265    -.3894443    .1071488
                          2011  |   .0914906   .0591742     1.55   0.122    -.0244887    .2074698
                          2012  |    .003273   .0605795     0.05   0.957    -.1154607    .1220067
                          2013  |  -.1230197   .1748139    -0.70   0.482    -.4656486    .2196093
                          2014  |   .0185745    .067795     0.27   0.784    -.1143012    .1514502
                          2015  |          0  (omitted)
                                |
                          _cons |  -.1252836   .4639153    -0.27   0.787    -1.034541    .7839736
    ----------------------------+----------------------------------------------------------------
    intl                        |
                    intratio2_w |
                            L1. |   4.834204   .3503738    13.80   0.000     4.147484    5.520924
                                |
                siznumfxhedge_w |
                            L1. |   .2002537   .0511131     3.92   0.000     .1000739    .3004336
                                |
                   ln_firmage_w |
                            L1. |   .4141059   .0889329     4.66   0.000     .2398006    .5884112
                                |
                        ln_at_w |
                            L1. |    .102695   .0317659     3.23   0.001     .0404351     .164955
                                |
                       tobinq_w |
                            L1. |   .0066423   .0559791     0.12   0.906    -.1030748    .1163593
                                |
                        slack_w |
                            L1. |   .1194309   .2371617     0.50   0.615    -.3453975    .5842593
                                |
                   constraint_w |
                            L1. |  -.0130778   .0087029    -1.50   0.133    -.0301351    .0039795
                                |
                      entropy_w |
                            L1. |   2.104377   .3152062     6.68   0.000     1.486584     2.72217
                                |
                  ln_tenure_y_w |
                            L1. |  -.2524318   .0708367    -3.56   0.000    -.3912692   -.1135944
                                |
                    isfounder_w |
                            L1. |    .151132    .135638     1.11   0.265    -.1147136    .4169775
                                |
                          fyear |
                          1999  |    .023452    .385552     0.06   0.951    -.7322161    .7791201
                          2000  |   .0603861   .3656494     0.17   0.869    -.6562735    .7770457
                          2001  |   .4129523   .3549258     1.16   0.245    -.2826895    1.108594
                          2002  |   .5593425    .344546     1.62   0.104    -.1159553     1.23464
                          2003  |  -.2778826   .3745286    -0.74   0.458    -1.011945    .4561799
                          2004  |   .0300237   .3712949     0.08   0.936    -.6977008    .7577483
                          2005  |   .1178042   .3588525     0.33   0.743    -.5855339    .8211422
                          2006  |  -.0076683    .364267    -0.02   0.983    -.7216186    .7062819
                          2007  |  -.3606981   .3688887    -0.98   0.328    -1.083707    .3623105
                          2008  |  -.0865687   .3575869    -0.24   0.809    -.7874262    .6142887
                          2009  |  -.1584412   .3629916    -0.44   0.662    -.8698916    .5530093
                          2010  |  -.0909428   .3651831    -0.25   0.803    -.8066886    .6248029
                          2011  |  -.4961573   .3778998    -1.31   0.189    -1.236827    .2445126
                          2012  |  -.0677228   .3594602    -0.19   0.851    -.7722519    .6368063
                          2013  |  -.5144314   .3728328    -1.38   0.168     -1.24517    .2163074
                          2014  |  -.5559093   .3892982    -1.43   0.153     -1.31892    .2071012
                          2015  |  -.6956374   .4077328    -1.71   0.088    -1.494779    .1035043
                          2016  |  -5.076546          .        .       .            .           .
                                |
                          _cons |  -2.824338   .4026681    -7.01   0.000    -3.613553   -2.035123
    ----------------------------+----------------------------------------------------------------
    /mills                      |
                         lambda |   .0133232   .0364566     0.37   0.715    -.0581304    .0847768
    ----------------------------+----------------------------------------------------------------
                            rho |    0.06670
                          sigma |  .19974236
    ---------------------------------------------------------------------------------------------
    
    . 
    end of do-file
    I did not include the results for the interaction, because it would make the post too lengthy.

    My ultimate goal is to plot a graph of the inverted-U shaped findings, and it would be ideal if I could do this in one graph with separate lines showing the original relationship and the interacted relationships.
    I have tried many ways including the margins command but I keep hitting the wall due to my inexperience in Stata (I'm currently using Stata 16, if it helps).
    In addition, I'm not sure if the usage of the Heckman method should somehow influence how I should plot the graphs.

    Thank you very much in advance.
    Your help is greatly appreciated.
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