BJ Data Tech Solution: Margins for Interaction Term

I have run the following regression and am trying to analyse whether the initial level of Income of a country affects changes the effect of inequality on growth (i.e the relationship could be non-linear among developed and developing countries). I have included an interaction term to do this which shows that as inequality is negative and the interaction term is positive, inequality negatively affects the growth of a country with lower initial income.

However, I am trying to find if this weakens as the income per capita increases or turns positive for higher income countries and hence believe the

Code:

margins

command is appropriate. But, I am unsure of the code required for this. i have the following:

Code:

. xtdpdgmm growth_rate c.l.gini_disp##c.l.ln_Income l.EFW l.ln_pl_i l.fyr_sch_sec l.myr_sch_sec,
>  model(fod) gmm(l.(c.gini_disp##c.ln_Income EFW ln_pl_i fyr_sch_sec myr_sch_sec), lag(0 0)) gm
> m(l.(c.gini_disp##c.ln_Income EFW ln_pl_i fyr_sch_sec myr_sch_sec), lag(0 0) diff model(level)
> ) two w(ind) teffects
note: standard errors can be severely biased in finite samples

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  .00142514
Step 2         f(b) =  .88647575

Group variable: ncountry                     Number of obs         =       708
Time variable: period                        Number of groups      =       112

Moment conditions:     linear =     156      Obs per group:    min =         1
                    nonlinear =       0                        avg =  6.321429
                        total =     156                        max =        11

-------------------------------------------------------------------------------------------
              growth_rate |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
                gini_disp |
                      L1. |  -.0092847   .0008463   -10.97   0.000    -.0109434    -.007626
                          |
                ln_Income |
                      L1. |  -.0522122   .0039198   -13.32   0.000    -.0598949   -.0445296
                          |
cL.gini_disp#cL.ln_Income |   .0009942    .000096    10.36   0.000     .0008062    .0011823
                          |
                      EFW |
                      L1. |   .0078056   .0006158    12.68   0.000     .0065987    .0090124
                          |
                  ln_pl_i |
                      L1. |  -.0054779   .0009282    -5.90   0.000    -.0072971   -.0036586
                          |
              fyr_sch_sec |
                      L1. |   .0001479   .0015346     0.10   0.923    -.0028598    .0031556
                          |
              myr_sch_sec |
                      L1. |   .0119233   .0016257     7.33   0.000      .008737    .0151097
                          |
                   period |
                    1970  |   .0047695   .0008684     5.49   0.000     .0030676    .0064715
                    1975  |  -.0028515   .0012079    -2.36   0.018    -.0052189    -.000484
                    1980  |  -.0152241   .0011472   -13.27   0.000    -.0174725   -.0129757
                    1985  |  -.0064175   .0021772    -2.95   0.003    -.0106847   -.0021503
                    1990  |  -.0024537   .0019021    -1.29   0.197    -.0061817    .0012744
                    1995  |  -.0099781   .0023262    -4.29   0.000    -.0145373   -.0054189
                    2000  |   -.017659   .0021014    -8.40   0.000    -.0217777   -.0135404
                    2005  |  -.0088494   .0021685    -4.08   0.000    -.0130995   -.0045992
                    2010  |   -.013366   .0027469    -4.87   0.000    -.0187499   -.0079821
                    2015  |  -.0326874   .0030746   -10.63   0.000    -.0387135   -.0266612
                          |
                    _cons |   .4437157   .0332909    13.33   0.000     .3784667    .5089647
-------------------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(fodev):
   1965:L.gini_disp 1970:L.gini_disp 1975:L.gini_disp 1980:L.gini_disp
   1985:L.gini_disp 1990:L.gini_disp 1995:L.gini_disp 2000:L.gini_disp
   2005:L.gini_disp 2010:L.gini_disp 2020:L.gini_disp 2025:L.gini_disp
   1965:L.ln_Income 1970:L.ln_Income 1975:L.ln_Income 1980:L.ln_Income
   1985:L.ln_Income 1990:L.ln_Income 1995:L.ln_Income 2000:L.ln_Income
   2010:L.ln_Income 2015:L.ln_Income 2020:L.ln_Income 2025:L.ln_Income
   1965:cL.gini_disp#cL.ln_Income 1970:cL.gini_disp#cL.ln_Income
   1975:cL.gini_disp#cL.ln_Income 1980:cL.gini_disp#cL.ln_Income
   1985:cL.gini_disp#cL.ln_Income 1990:cL.gini_disp#cL.ln_Income
   2000:cL.gini_disp#cL.ln_Income 2005:cL.gini_disp#cL.ln_Income
   2010:cL.gini_disp#cL.ln_Income 2015:cL.gini_disp#cL.ln_Income
   2020:cL.gini_disp#cL.ln_Income 2025:cL.gini_disp#cL.ln_Income 1965:L.EFW
   1970:L.EFW 1975:L.EFW 1980:L.EFW 1990:L.EFW 1995:L.EFW 2000:L.EFW
   2005:L.EFW 2010:L.EFW 2015:L.EFW 2020:L.EFW 2025:L.EFW 1965:L.ln_pl_i
   1970:L.ln_pl_i 1980:L.ln_pl_i 1985:L.ln_pl_i 1990:L.ln_pl_i 1995:L.ln_pl_i
   2000:L.ln_pl_i 2005:L.ln_pl_i 2010:L.ln_pl_i 2015:L.ln_pl_i 2020:L.ln_pl_i
   2025:L.ln_pl_i 1970:L.fyr_sch_sec 1975:L.fyr_sch_sec 1980:L.fyr_sch_sec
   1985:L.fyr_sch_sec 1990:L.fyr_sch_sec 1995:L.fyr_sch_sec 2000:L.fyr_sch_sec
   2005:L.fyr_sch_sec 2010:L.fyr_sch_sec 2015:L.fyr_sch_sec
 2, model(level):
   1970:D.L.gini_disp 1975:D.L.gini_disp 1980:D.L.gini_disp 1985:D.L.gini_disp
   1990:D.L.gini_disp 1995:D.L.gini_disp 2000:D.L.gini_disp 2005:D.L.gini_disp
   2010:D.L.gini_disp 2015:D.L.gini_disp 2020:D.L.gini_disp 2025:D.L.gini_disp
   1965:D.L.ln_Income 1970:D.L.ln_Income 1975:D.L.ln_Income 1980:D.L.ln_Income
   1985:D.L.ln_Income 1990:D.L.ln_Income 1995:D.L.ln_Income 2000:D.L.ln_Income
   2005:D.L.ln_Income 2015:D.L.ln_Income 2020:D.L.ln_Income 2025:D.L.ln_Income
   1965:D.cL.gini_disp#cL.ln_Income 1970:D.cL.gini_disp#cL.ln_Income
   1975:D.cL.gini_disp#cL.ln_Income 1980:D.cL.gini_disp#cL.ln_Income
   1985:D.cL.gini_disp#cL.ln_Income 1990:D.cL.gini_disp#cL.ln_Income
   1995:D.cL.gini_disp#cL.ln_Income 2000:D.cL.gini_disp#cL.ln_Income
   2005:D.cL.gini_disp#cL.ln_Income 2010:D.cL.gini_disp#cL.ln_Income
   2015:D.cL.gini_disp#cL.ln_Income 2020:D.cL.gini_disp#cL.ln_Income
   2025:D.cL.gini_disp#cL.ln_Income 1965:D.L.EFW 1970:D.L.EFW 1975:D.L.EFW
   1980:D.L.EFW 1985:D.L.EFW 1990:D.L.EFW 1995:D.L.EFW 2000:D.L.EFW
   2005:D.L.EFW 2010:D.L.EFW 2015:D.L.EFW 2020:D.L.EFW 2025:D.L.EFW
   1965:D.L.ln_pl_i 1970:D.L.ln_pl_i 1975:D.L.ln_pl_i 1980:D.L.ln_pl_i
   1985:D.L.ln_pl_i 1990:D.L.ln_pl_i 1995:D.L.ln_pl_i 2000:D.L.ln_pl_i
   2005:D.L.ln_pl_i 2010:D.L.ln_pl_i 2015:D.L.ln_pl_i 2020:D.L.ln_pl_i
   2025:D.L.ln_pl_i 1965:D.L.fyr_sch_sec 1970:D.L.fyr_sch_sec
   1975:D.L.fyr_sch_sec 1980:D.L.fyr_sch_sec 1985:D.L.fyr_sch_sec
   1990:D.L.fyr_sch_sec 1995:D.L.fyr_sch_sec 2000:D.L.fyr_sch_sec
   2005:D.L.fyr_sch_sec 2010:D.L.fyr_sch_sec 2015:D.L.fyr_sch_sec
   2020:D.L.fyr_sch_sec
 3, model(level):
   1970bn.period 1975.period 1980.period 1985.period 1990.period 1995.period
   2000.period 2005.period 2010.period 2015.period
 4, model(level):
   _cons

Code:

. margins, dydx(l.gini_disp) at(l.ln_Income = (0(0.1)10))

Average marginal effects                        Number of obs     =        708
Model VCE    : Conventional

Expression   : Linear prediction, predict()
dy/dx w.r.t. : L.gini_disp

1._at        : L.ln_Income     =           0

2._at        : L.ln_Income     =          .1

3._at        : L.ln_Income     =          .2

4._at        : L.ln_Income     =          .3

5._at        : L.ln_Income     =          .4

6._at        : L.ln_Income     =          .5

7._at        : L.ln_Income     =          .6

8._at        : L.ln_Income     =          .7

9._at        : L.ln_Income     =          .8

10._at       : L.ln_Income     =          .9

11._at       : L.ln_Income     =           1

12._at       : L.ln_Income     =         1.1

13._at       : L.ln_Income     =         1.2

14._at       : L.ln_Income     =         1.3

15._at       : L.ln_Income     =         1.4

16._at       : L.ln_Income     =         1.5

17._at       : L.ln_Income     =         1.6

18._at       : L.ln_Income     =         1.7

19._at       : L.ln_Income     =         1.8

20._at       : L.ln_Income     =         1.9

21._at       : L.ln_Income     =           2

22._at       : L.ln_Income     =         2.1

23._at       : L.ln_Income     =         2.2

24._at       : L.ln_Income     =         2.3

25._at       : L.ln_Income     =         2.4

26._at       : L.ln_Income     =         2.5

27._at       : L.ln_Income     =         2.6

28._at       : L.ln_Income     =         2.7

29._at       : L.ln_Income     =         2.8

30._at       : L.ln_Income     =         2.9

31._at       : L.ln_Income     =           3

32._at       : L.ln_Income     =         3.1

33._at       : L.ln_Income     =         3.2

34._at       : L.ln_Income     =         3.3

35._at       : L.ln_Income     =         3.4

36._at       : L.ln_Income     =         3.5

37._at       : L.ln_Income     =         3.6

38._at       : L.ln_Income     =         3.7

39._at       : L.ln_Income     =         3.8

40._at       : L.ln_Income     =         3.9

41._at       : L.ln_Income     =           4

42._at       : L.ln_Income     =         4.1

43._at       : L.ln_Income     =         4.2

44._at       : L.ln_Income     =         4.3

45._at       : L.ln_Income     =         4.4

46._at       : L.ln_Income     =         4.5

47._at       : L.ln_Income     =         4.6

48._at       : L.ln_Income     =         4.7

49._at       : L.ln_Income     =         4.8

50._at       : L.ln_Income     =         4.9

51._at       : L.ln_Income     =           5

52._at       : L.ln_Income     =         5.1

53._at       : L.ln_Income     =         5.2

54._at       : L.ln_Income     =         5.3

55._at       : L.ln_Income     =         5.4

56._at       : L.ln_Income     =         5.5

57._at       : L.ln_Income     =         5.6

58._at       : L.ln_Income     =         5.7

59._at       : L.ln_Income     =         5.8

60._at       : L.ln_Income     =         5.9

61._at       : L.ln_Income     =           6

62._at       : L.ln_Income     =         6.1

63._at       : L.ln_Income     =         6.2

64._at       : L.ln_Income     =         6.3

65._at       : L.ln_Income     =         6.4

66._at       : L.ln_Income     =         6.5

67._at       : L.ln_Income     =         6.6

68._at       : L.ln_Income     =         6.7

69._at       : L.ln_Income     =         6.8

70._at       : L.ln_Income     =         6.9

71._at       : L.ln_Income     =           7

72._at       : L.ln_Income     =         7.1

73._at       : L.ln_Income     =         7.2

74._at       : L.ln_Income     =         7.3

75._at       : L.ln_Income     =         7.4

76._at       : L.ln_Income     =         7.5

77._at       : L.ln_Income     =         7.6

78._at       : L.ln_Income     =         7.7

79._at       : L.ln_Income     =         7.8

80._at       : L.ln_Income     =         7.9

81._at       : L.ln_Income     =           8

82._at       : L.ln_Income     =         8.1

83._at       : L.ln_Income     =         8.2

84._at       : L.ln_Income     =         8.3

85._at       : L.ln_Income     =         8.4

86._at       : L.ln_Income     =         8.5

87._at       : L.ln_Income     =         8.6

88._at       : L.ln_Income     =         8.7

89._at       : L.ln_Income     =         8.8

90._at       : L.ln_Income     =         8.9

91._at       : L.ln_Income     =           9

92._at       : L.ln_Income     =         9.1

93._at       : L.ln_Income     =         9.2

94._at       : L.ln_Income     =         9.3

95._at       : L.ln_Income     =         9.4

96._at       : L.ln_Income     =         9.5

97._at       : L.ln_Income     =         9.6

98._at       : L.ln_Income     =         9.7

99._at       : L.ln_Income     =         9.8

100._at      : L.ln_Income     =         9.9

101._at      : L.ln_Income     =          10

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
L.gini_disp  |
         _at |
          1  |  -.0092847   .0008463   -10.97   0.000    -.0109434    -.007626
          2  |  -.0091853   .0008367   -10.98   0.000    -.0108253   -.0075453
          3  |  -.0090859   .0008272   -10.98   0.000    -.0107072   -.0074645
          4  |  -.0089864   .0008177   -10.99   0.000    -.0105891   -.0073837
          5  |   -.008887   .0008082   -11.00   0.000     -.010471    -.007303
          6  |  -.0087876   .0007987   -11.00   0.000     -.010353   -.0072222
          7  |  -.0086882   .0007892   -11.01   0.000    -.0102349   -.0071414
          8  |  -.0085887   .0007797   -11.02   0.000    -.0101169   -.0070606
          9  |  -.0084893   .0007702   -11.02   0.000    -.0099988   -.0069798
         10  |  -.0083899   .0007607   -11.03   0.000    -.0098807    -.006899
         11  |  -.0082905   .0007511   -11.04   0.000    -.0097627   -.0068182
         12  |   -.008191   .0007416   -11.04   0.000    -.0096447   -.0067374
         13  |  -.0080916   .0007322   -11.05   0.000    -.0095266   -.0066566
         14  |  -.0079922   .0007227   -11.06   0.000    -.0094086   -.0065758
         15  |  -.0078928   .0007132   -11.07   0.000    -.0092906    -.006495
         16  |  -.0077934   .0007037   -11.08   0.000    -.0091725   -.0064142
         17  |  -.0076939   .0006942   -11.08   0.000    -.0090545   -.0063333
         18  |  -.0075945   .0006847   -11.09   0.000    -.0089365   -.0062525
         19  |  -.0074951   .0006752   -11.10   0.000    -.0088185   -.0061717
         20  |  -.0073957   .0006657   -11.11   0.000    -.0087005   -.0060908
         21  |  -.0072962   .0006563   -11.12   0.000    -.0085825     -.00601
         22  |  -.0071968   .0006468   -11.13   0.000    -.0084645   -.0059291
         23  |  -.0070974   .0006373   -11.14   0.000    -.0083465   -.0058482
         24  |   -.006998   .0006279   -11.15   0.000    -.0082286   -.0057674
         25  |  -.0068985   .0006184   -11.16   0.000    -.0081106   -.0056865
         26  |  -.0067991    .000609   -11.17   0.000    -.0079927   -.0056056
         27  |  -.0066997   .0005995   -11.18   0.000    -.0078747   -.0055247
         28  |  -.0066003   .0005901   -11.19   0.000    -.0077568   -.0054438
         29  |  -.0065009   .0005806   -11.20   0.000    -.0076389   -.0053628
         30  |  -.0064014   .0005712   -11.21   0.000    -.0075209   -.0052819
         31  |   -.006302   .0005618   -11.22   0.000     -.007403    -.005201
         32  |  -.0062026   .0005523   -11.23   0.000    -.0072851     -.00512
         33  |  -.0061032   .0005429   -11.24   0.000    -.0071673   -.0050391
         34  |  -.0060037   .0005335   -11.25   0.000    -.0070494   -.0049581
         35  |  -.0059043   .0005241   -11.27   0.000    -.0069315   -.0048771
         36  |  -.0058049   .0005147   -11.28   0.000    -.0068137   -.0047961
         37  |  -.0057055   .0005053   -11.29   0.000    -.0066959   -.0047151
         38  |   -.005606   .0004959   -11.30   0.000    -.0065781    -.004634
         39  |  -.0055066   .0004866   -11.32   0.000    -.0064603    -.004553
         40  |  -.0054072   .0004772   -11.33   0.000    -.0063425   -.0044719
         41  |  -.0053078   .0004678   -11.35   0.000    -.0062247   -.0043908
         42  |  -.0052084   .0004585   -11.36   0.000     -.006107   -.0043097
         43  |  -.0051089   .0004492   -11.37   0.000    -.0059893   -.0042286
         44  |  -.0050095   .0004398   -11.39   0.000    -.0058716   -.0041474
         45  |  -.0049101   .0004305   -11.40   0.000    -.0057539   -.0040663
         46  |  -.0048107   .0004212   -11.42   0.000    -.0056363   -.0039851
         47  |  -.0047112   .0004119   -11.44   0.000    -.0055186   -.0039038
         48  |  -.0046118   .0004027   -11.45   0.000     -.005401   -.0038226
         49  |  -.0045124   .0003934   -11.47   0.000    -.0052835   -.0037413
         50  |   -.004413   .0003842   -11.49   0.000    -.0051659     -.00366
         51  |  -.0043135    .000375   -11.50   0.000    -.0050485   -.0035786
         52  |  -.0042141   .0003658   -11.52   0.000     -.004931   -.0034972
         53  |  -.0041147   .0003566   -11.54   0.000    -.0048136   -.0034158
         54  |  -.0040153   .0003474   -11.56   0.000    -.0046962   -.0033343
         55  |  -.0039158   .0003383   -11.58   0.000    -.0045789   -.0032528
         56  |  -.0038164   .0003292   -11.59   0.000    -.0044616   -.0031712
         57  |   -.003717   .0003201   -11.61   0.000    -.0043444   -.0030896
         58  |  -.0036176   .0003111   -11.63   0.000    -.0042272   -.0030079
         59  |  -.0035182    .000302   -11.65   0.000    -.0041101   -.0029262
         60  |  -.0034187   .0002931   -11.67   0.000    -.0039931   -.0028443
         61  |  -.0033193   .0002841   -11.68   0.000    -.0038762   -.0027624
         62  |  -.0032199   .0002752   -11.70   0.000    -.0037593   -.0026804
         63  |  -.0031205   .0002664   -11.71   0.000    -.0036426   -.0025983
         64  |   -.003021   .0002576   -11.73   0.000    -.0035259   -.0025161
         65  |  -.0029216   .0002489   -11.74   0.000    -.0034094   -.0024338
         66  |  -.0028222   .0002402   -11.75   0.000     -.003293   -.0023514
         67  |  -.0027228   .0002316   -11.76   0.000    -.0031767   -.0022688
         68  |  -.0026233   .0002231   -11.76   0.000    -.0030606    -.002186
         69  |  -.0025239   .0002147   -11.76   0.000    -.0029447   -.0021031
         70  |  -.0024245   .0002064   -11.75   0.000     -.002829     -.00202
         71  |  -.0023251   .0001982   -11.73   0.000    -.0027135   -.0019366
         72  |  -.0022257   .0001901   -11.71   0.000    -.0025983    -.001853
         73  |  -.0021262   .0001822   -11.67   0.000    -.0024834   -.0017691
         74  |  -.0020268   .0001745   -11.62   0.000    -.0023687   -.0016849
         75  |  -.0019274   .0001669   -11.55   0.000    -.0022545   -.0016003
         76  |   -.001828   .0001596   -11.46   0.000    -.0021407   -.0015152
         77  |  -.0017285   .0001525   -11.34   0.000    -.0020274   -.0014297
         78  |  -.0016291   .0001457   -11.18   0.000    -.0019146   -.0013436
         79  |  -.0015297   .0001392   -10.99   0.000    -.0018025   -.0012568
         80  |  -.0014303   .0001331   -10.74   0.000    -.0016912   -.0011693
         81  |  -.0013308   .0001275   -10.44   0.000    -.0015807    -.001081
         82  |  -.0012314   .0001223   -10.07   0.000    -.0014711   -.0009917
         83  |   -.001132   .0001177    -9.62   0.000    -.0013627   -.0009013
         84  |  -.0010326   .0001137    -9.08   0.000    -.0012554   -.0008097
         85  |  -.0009332   .0001104    -8.45   0.000    -.0011496   -.0007167
         86  |  -.0008337   .0001079    -7.73   0.000    -.0010452   -.0006223
         87  |  -.0007343   .0001061    -6.92   0.000    -.0009424   -.0005263
         88  |  -.0006349   .0001053    -6.03   0.000    -.0008412   -.0004286
         89  |  -.0005355   .0001053    -5.09   0.000    -.0007418   -.0003291
         90  |   -.000436   .0001061    -4.11   0.000     -.000644    -.000228
         91  |  -.0003366   .0001078    -3.12   0.002     -.000548   -.0001252
         92  |  -.0002372   .0001104    -2.15   0.032    -.0004535   -.0000209
         93  |  -.0001378   .0001137    -1.21   0.225    -.0003605     .000085
         94  |  -.0000383   .0001176    -0.33   0.744    -.0002689    .0001922
         95  |   .0000611   .0001222     0.50   0.617    -.0001785    .0003007
         96  |   .0001605   .0001274     1.26   0.208    -.0000892    .0004102
         97  |   .0002599    .000133     1.95   0.051    -8.34e-07    .0005207
         98  |   .0003593   .0001391     2.58   0.010     .0000867     .000632
         99  |   .0004588   .0001456     3.15   0.002     .0001734    .0007441
        100  |   .0005582   .0001524     3.66   0.000     .0002595    .0008569
        101  |   .0006576   .0001595     4.12   0.000     .0003451    .0009702
------------------------------------------------------------------------------

. marginsplot

  Variables that uniquely identify margins: L.ln_Income

Array

But, I am not sure if this is the appropriate code for the information I am trying to get. Any help understanding the appropriate code would be greatly appreciated.

BJ Data Tech Solution

Saturday, February 29, 2020

Margins for Interaction Term

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