Different regression methods to proof

[Dominik Miksch]

Hello,

I have a question regarding different regression methods to proof my assumption. I want to know how ICT adoption influences the innovativeness of a firm. I have paneldata and two waves of observations. My simple OLS model is

 reg Inno dum_ICT firmage l10 c3 b2b i.a4a i.a1

where Inno is the innovation index (values from 1 to 4), dum_ICT is the ICT adoption dummy, l10 is a dummy if the firm offered formal training programmes last year, c3 is a dummy if the firm applied for a electrical connection last year, b2b is the percentage of the firm owned by foreigners, a4a is a dummy for the industry sector and a1 is a dummy for the country. In the model above, ICT is highly significant and it turns out that if a firm generally adopted ICT their innovativeness increases. Here you can see the outcome without all the dummies for the industry sector and the countries.

. regress Inno dum_ICT firmage l10 c3 b2b i.a4a i.a1

      Source |       SS           df       MS      Number of obs   =     5,167
-------------+----------------------------------   F(53, 5113)     =     56.83
       Model |  3378.29391        53  63.7413945   Prob > F        =    0.0000
    Residual |  5735.11813     5,113   1.1216738   R-squared       =    0.3707
-------------+----------------------------------   Adj R-squared   =    0.3642
       Total |  9113.41204     5,166  1.76411383   Root MSE        =    1.0591

------------------------------------------------------------------------------
        Inno |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     dum_ICT |   .2775897    .046647     5.95   0.000     .1861417    .3690376
     firmage |   -.000695   .0010344    -0.67   0.502    -.0027229    .0013329
         l10 |    .447571    .033803    13.24   0.000     .3813027    .5138393
          c3 |   .1906314   .0429038     4.44   0.000     .1065216    .2747412
         b2b |   .0007365   .0005533     1.33   0.183    -.0003482    .0018211
             |

But now I want to include different types of regressions with the same model in order to convince the reader that my hypothesis, that firms with higher ICT adoption perform better, is true. So I want further proof.
Therefore I adapted the model obove in order to see if firms which had zero ICT in year 1 but adapted ICT between year one and year 2 perform better:

.  xtset panelid year
       panel variable:  panelid (strongly balanced)
        time variable:  year, 1 to 2
                delta:  1 unit

.  regress Inno dum_ICT firmage l10 c3 b2b i.a4a i.a1 if year==2 & L.dum_ICT==0

      Source |       SS           df       MS      Number of obs   =     3,103
-------------+----------------------------------   F(52, 3050)     =     42.74
       Model |  2659.28191        52  51.1400367   Prob > F        =    0.0000
    Residual |  3649.46382     3,050  1.19654552   R-squared       =    0.4215
-------------+----------------------------------   Adj R-squared   =    0.4117
       Total |  6308.74573     3,102  2.03376716   Root MSE        =    1.0939

------------------------------------------------------------------------------
        Inno |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     dum_ICT |   .2845822   .0697638     4.08   0.000     .1477933     .421371
     firmage |  -.0010243   .0015315    -0.67   0.504    -.0040271    .0019784
         l10 |   .5705493   .0458074    12.46   0.000     .4807328    .6603659
          c3 |   .1032498   .0581832     1.77   0.076    -.0108325    .2173322
         b2b |    .000677   .0007668     0.88   0.377    -.0008264    .0021804
             |
         a4a |
          2  |  -.2885407   .2943741    -0.98   0.327    -.8657323    .2886509
          3  |  -.2833497   .3388527    -0.84   0.403    -.9477525    .3810531
          4  |   .0474887    .355741     0.13   0.894    -.6500278    .7450051
          5  |  -.4421766   .2829037    -1.56   0.118    -.9968779    .1125246
          6  |  -.4162328   .2702835    -1.54   0.124    -.9461891    .1137235
          7  |  -.0908338   .3143731    -0.29   0.773    -.7072384    .5255707
          8  |  -.3757523   .2803625    -1.34   0.180    -.9254708    .1739663
          9  |  -.5647735   .2802044    -2.02   0.044    -1.114182    -.015365
         10  |  -.5570642   .4010146    -1.39   0.165     -1.34335     .229222
         11  |   .0529539   .4912183     0.11   0.914    -.9101984    1.016106
         12  |  -.1009795   .3189997    -0.32   0.752    -.7264557    .5244966
         13  |   -.197411   .2702716    -0.73   0.465    -.7273438    .3325219
         14  |  -.6717909   .4492206    -1.50   0.135    -1.552597    .2090148
         15  |  -.1987418   .3154601    -0.63   0.529    -.8172777    .4197941
         16  |    .290117   .3185079     0.91   0.362    -.3343948    .9146287
         17  |   -1.44027   .8197693    -1.76   0.079    -3.047626    .1670859
         18  |   .5777043   .8202959     0.70   0.481    -1.030684    2.186093
         19  |  -.3818752   .2680905    -1.42   0.154    -.9075315    .1437811
         20  |  -.2772761   .2735206    -1.01   0.311    -.8135795    .2590272
         21  |  -.6216942   .3072893    -2.02   0.043    -1.224209   -.0191792
         23  |  -.4837853   .3432089    -1.41   0.159    -1.156729     .189159
         24  |  -.4641845   .2853611    -1.63   0.104    -1.023704     .095335
         25  |   -.971511   .3362687    -2.89   0.004    -1.630847   -.3121749
             |
          a1 |
         11  |   .1634681   .1675756     0.98   0.329    -.1651045    .4920408
         12  |  -.3999711   .1618933    -2.47   0.014     -.717402   -.0825401
         13  |  -.1681401   .2141821    -0.79   0.432     -.588096    .2518158
         14  |  -.2134868   .2321303    -0.92   0.358    -.6686344    .2416608
         15  |   .3120863   .1438212     2.17   0.030       .03009    .5940826
         16  |  -.2574673   .1790772    -1.44   0.151    -.6085916     .093657
         17  |  -.1769258   .1475234    -1.20   0.231    -.4661812    .1123295
         18  |   .4848021   .1341442     3.61   0.000       .22178    .7478242
         19  |   1.083772   .1396287     7.76   0.000     .8099967    1.357548
         20  |   1.801743   .2438499     7.39   0.000     1.323616     2.27987
         21  |   1.915563     .14788    12.95   0.000     1.625609    2.205518
         22  |  -.0225719   .1868979    -0.12   0.904    -.3890305    .3438867
         23  |   1.349221   .1709095     7.89   0.000     1.014112    1.684331
         25  |  -.0714195   .1505803    -0.47   0.635    -.3666687    .2238297
         27  |   1.790655   .1183697    15.13   0.000     1.558562    2.022747
         28  |   1.999689   .1823233    10.97   0.000       1.6422    2.357178
         29  |   .9985773   .1282099     7.79   0.000     .7471907    1.249964
         30  |   .6118559   .1740438     3.52   0.000     .2706009     .953111
         31  |  -.4342055   .1394508    -3.11   0.002    -.7076325   -.1607785
         32  |   2.301774   .1525156    15.09   0.000      2.00273    2.600817
         33  |   .7592134   .2025517     3.75   0.000     .3620618    1.156365
         34  |   1.854734   .1338328    13.86   0.000     1.592322    2.117146
         35  |   1.692545   .1409749    12.01   0.000      1.41613    1.968961
         36  |   .7192039   .1578082     4.56   0.000     .4097826    1.028625
             |
       _cons |   .2699117    .281987     0.96   0.339     -.282992    .8228155
------------------------------------------------------------------------------

So it turns out yes, they do.

But I want further proof so I include Treatment effects and here a propensity score model (logistic).
Outcome variable: Inno
Treatment variable: dum_ICT
Treatment independent: firmage l10 c3 b2b

. teffects psmatch (Inno) (dum_ICT firmage l10 c3 b2b)

Treatment-effects estimation                   Number of obs      =      6,460
Estimator      : propensity-score matching     Matches: requested =          1
Outcome model  : matching                                     min =          1
Treatment model: logit                                        max =        206
------------------------------------------------------------------------------
             |              AI Robust
        Inno |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ATE          |
     dum_ICT |
   (1 vs 0)  |   .3910807   .0534788     7.31   0.000     .2862642    .4958973
------------------------------------------------------------------------------

Also that model shows that ICT adoption is significant and if a firm adopts ICT their innovativeness increases. My question now is, what else would you suggest to do in order to proof my assumption? Would you suggest to use another estimation technique? I also think about interaction terms in order to see why ICT adoption positively affects Innovation. Therefore I am curious about interesting interactions with ICT.
By the way, I will do all the regressions I showed above for the dependent variables:

Capacity Utilization
Export Rate
Gross Profit Margin
Labor Productivity and
Cost of Material Ratio

in order to show how ICT adoption affects overall firm performance.

Thank you very much.


Kind regards
Dominik

[Dominik Miksch]

I would really appreciate if someone can help me.

Kind regards
Dominik

[Carlo Lazzaro]

Dominik:
first off, why considering -regress- as your first choice if you actually have panel data?
At the top of that, you run an OLS with no clustered standard errors; it tells Stat that all your observations are independent, whereas, due to the panel structure of your data, it's not the case.
Morerover, you do not tell us whether any postestimation analysis has been carried out on your OLS in order to check if its specification fits your data.
It is also redundant to -xtset- your data and then go OLS.
Eventually, presenting many regression models to prove the same assumption is less rewarding that performing a methodologically correct model that gives a fair and true view of the data generating process underlying your data: see the literature in your research field on that.

[William Lisowski]

I will agree with almost everything Carlo wrote, and certainly with all the statistical advice.

The xtset was done at my advice in a previous topic to make it easy to use the value of dum_ICT in wave 1 to construct the if clause in the OLS regression. I did not review the advisability of the modeling, which did not mention the first model including both waves, beyond pointing out in a second post that dum_ICT should at a minimum have been included in the model as i.dum_ICT, and perhaps that dum_ICT need not have been created at all, but just included (in the model and in the if clause) using factor variable notation applied to some other categorical variable.

The previous topic is at

https://www.statalist.org/forums/for...if-and-command

[Dominik Miksch]

Carlo Lazzaro Thank you very much for your answer. Whould you rather argue with the propensity score model first and afterwards the xtset command and the regress command? Or can you recommend other, more suitable regressions to me?

Regarding the standard errors, can I use the

, robust

command in order to avoid telling Stata that all my observations are independent?
Regarding the postestimation analysis: I indeed havn't done it so far but also William Lisowski gave me that hint, thank you for that. I used the margin command and Stata gave me the following:

. margins

Predictive margins                              Number of obs     =      3,103
Model VCE    : OLS

Expression   : Linear prediction, predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   1.109571   .0196369    56.50   0.000     1.071068    1.148074
------------------------------------------------------------------------------

That means my average predicted value is approximately 1.11?
If I hold the variable c3 constant at 1 (as it is a dummy) Stata tells me that if a firm applied for a electrical connection last year, the degree of innovation is higher whereas if they don't it is lower?

. margins, at (c3=(0 1))

Predictive margins                              Number of obs     =      3,103
Model VCE    : OLS

Expression   : Linear prediction, predict()

1._at        : c3              =           0

2._at        : c3              =           1

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   1.094165   .0214704    50.96   0.000     1.052067    1.136263
          2  |   1.197415   .0532544    22.48   0.000     1.092997    1.301833
------------------------------------------------------------------------------

If I compute the margins for the percentage of foreign ownership from 0 to 100% in 10% intervalls I get the following:

margins, at(b2b=(0(10)100))

Predictive margins                              Number of obs     =      3,103
Model VCE    : OLS

Expression   : Linear prediction, predict()

1._at        : b2b             =           0

2._at        : b2b             =          10

3._at        : b2b             =          20

4._at        : b2b             =          30

5._at        : b2b             =          40

6._at        : b2b             =          50

7._at        : b2b             =          60

8._at        : b2b             =          70

9._at        : b2b             =          80

10._at       : b2b             =          90

11._at       : b2b             =         100

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |     1.1028   .0210815    52.31   0.000     1.061464    1.144135
          2  |    1.10957   .0196369    56.50   0.000     1.071067    1.148073
          3  |    1.11634   .0210801    52.96   0.000     1.075007    1.157672
          4  |    1.12311   .0249142    45.08   0.000     1.074259     1.17196
          5  |    1.12988   .0302431    37.36   0.000     1.070581    1.189179
          6  |    1.13665   .0364165    31.21   0.000     1.065247    1.208053
          7  |    1.14342   .0430727    26.55   0.000     1.058965    1.227874
          8  |    1.15019   .0500194    22.99   0.000     1.052115    1.248265
          9  |    1.15696   .0571507    20.24   0.000     1.044902    1.269018
         10  |    1.16373   .0644054    18.07   0.000     1.037448    1.290012
         11  |     1.1705    .071746    16.31   0.000     1.029825    1.311176
------------------------------------------------------------------------------

So also here I can see that if the percentage of foreign ownership increases, the innovativeness increases.

But whould you suggest to add any further proof or tests?

Kind regards
Dominik

[Dominik Miksch]

Hello Statalist community,

can you help me please with the interpretation of the following postestimation command(margins)?

. regress Inno c.ICT_percentage##c.ICT_percentage firmage l1 c3 c6 i.a4a i.a1 if year==2 & L.ICT_percentage <=20

      Source |       SS           df       MS      Number of obs   =     1,370
-------------+----------------------------------   F(53, 1316)     =     29.31
       Model |  1602.20862        53  30.2303513   Prob > F        =    0.0000
    Residual |  1357.48481     1,316  1.03152341   R-squared       =    0.5413
-------------+----------------------------------   Adj R-squared   =    0.5229
       Total |  2959.69343     1,369  2.16193823   Root MSE        =    1.0156

---------------------------------------------------------------------------------------------------
                             Inno |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------------------+----------------------------------------------------------------
                   ICT_percentage |   .0454914   .0081069     5.61   0.000     .0295875    .0613952
                                  |
c.ICT_percentage#c.ICT_percentage |  -.0005593   .0001138    -4.92   0.000    -.0007825   -.0003361
                                  |
                          firmage |  -.0018753   .0018048    -1.04   0.299    -.0054159    .0016654
                               l1 |   .0000724   .0000664     1.09   0.276    -.0000578    .0002026
                               c3 |   .1530584   .0860939     1.78   0.076    -.0158379    .3219548
                               c6 |    .212252   .0782352     2.71   0.007     .0587727    .3657313
                                  |
                              a4a |
                               2  |  -.2159865   .3155645    -0.68   0.494    -.8350509    .4030778
                               3  |  -.1121895   .3594475    -0.31   0.755    -.8173421    .5929631
                               4  |   .1377966    .366335     0.38   0.707    -.5808678     .856461
                               5  |   -.369737    .312782    -1.18   0.237    -.9833428    .2438689
                               6  |  -.1021984   .2997502    -0.34   0.733    -.6902388     .485842
                               7  |   .3783254   .3764894     1.00   0.315    -.3602595     1.11691
                               8  |  -.2286283   .3232605    -0.71   0.480    -.8627905     .405534
                               9  |  -.5167653   .3201113    -1.61   0.107     -1.14475    .1112189
                              10  |  -.5089456   .4209658    -1.21   0.227    -1.334783    .3168918
                              11  |  -.0188958   .4809339    -0.04   0.969    -.9623767    .9245851
                              12  |  -.0364887   .3448283    -0.11   0.916    -.7129618    .6399844
                              13  |  -.2166198   .3018173    -0.72   0.473    -.8087154    .3754758
                              14  |  -.7490697   .4605976    -1.63   0.104    -1.652656    .1545161
                              15  |   .0098462   .3360175     0.03   0.977    -.6493422    .6690346
                              16  |   .0345462   .3457821     0.10   0.920    -.6437982    .7128906
                              17  |  -1.535198   .7771162    -1.98   0.048     -3.05972   -.0106756
                              18  |   .7230056   .7772562     0.93   0.352    -.8017909    2.247802
                              19  |    .003666   .3002322     0.01   0.990      -.58532     .592652
                              20  |  -.2453396   .3100887    -0.79   0.429    -.8536617    .3629825
                              21  |  -.6512664   .3425804    -1.90   0.058     -1.32333     .020797
                              23  |  -.2782228   .4207066    -0.66   0.509    -1.103552    .5471062
                              24  |  -.3946428    .312745    -1.26   0.207    -1.008176    .2188905
                              25  |  -.8228146   .4210755    -1.95   0.051    -1.648867    .0032378
                                  |
                               a1 |
                              11  |   .1831849   .2303103     0.80   0.427    -.2686305    .6350004
                              12  |  -.2348465   .2086304    -1.13   0.261    -.6441311     .174438
                              13  |  -.0641707   .2316078    -0.28   0.782    -.5185315      .39019
                              14  |  -.0637736   .3177197    -0.20   0.841    -.6870661    .5595188
                              15  |    .446383   .2105295     2.12   0.034      .033373    .8593931
                              16  |  -.0317801     .26037    -0.12   0.903    -.5425657    .4790056
                              17  |  -.0240553    .235726    -0.10   0.919    -.4864951    .4383844
                              18  |   .9233698   .1894059     4.88   0.000     .5517993     1.29494
                              19  |   1.171866   .1880565     6.23   0.000     .8029431     1.54079
                              20  |   2.916206   .3526687     8.27   0.000     2.224351     3.60806
                              21  |   1.952961   .1924001    10.15   0.000     1.575517    2.330405
                              22  |   .1510064   .2610799     0.58   0.563    -.3611718    .6631847
                              23  |   1.865506   .2886291     6.46   0.000     1.299282    2.431729
                              25  |  -.0319352   .2357815    -0.14   0.892    -.4944839    .4306134
                              27  |   2.475708   .2012857    12.30   0.000     2.080833    2.870584
                              28  |   2.547968   .2713736     9.39   0.000     2.015596     3.08034
                              29  |   1.363376   .2194429     6.21   0.000     .9328798    1.793872
                              30  |   .8566836   .2694809     3.18   0.002     .3280245    1.385343
                              31  |  -.1555558   .1806095    -0.86   0.389    -.5098698    .1987582
                              32  |   2.498109   .2081875    12.00   0.000     2.089694    2.906525
                              33  |   .8483156   .2646769     3.21   0.001     .3290809     1.36755
                              34  |   2.556525   .1998441    12.79   0.000     2.164477    2.948573
                              35  |   1.970318   .1993008     9.89   0.000     1.579336      2.3613
                              36  |   .8531095   .2026048     4.21   0.000     .4556458    1.250573
                                  |
                            _cons |  -.4396663   .3421566    -1.28   0.199    -1.110898    .2315656
---------------------------------------------------------------------------------------------------

.
end of do-file

. do "C:\Users\domin\AppData\Local\Temp\STD18f4_000000.tmp"

. margins, at(ICT=(0(10)100))

Predictive margins                              Number of obs     =      1,370
Model VCE    : OLS

Expression   : Linear prediction, predict()

1._at        : ICT_percen~e    =           0

2._at        : ICT_percen~e    =          10

3._at        : ICT_percen~e    =          20

4._at        : ICT_percen~e    =          30

5._at        : ICT_percen~e    =          40

6._at        : ICT_percen~e    =          50

7._at        : ICT_percen~e    =          60

8._at        : ICT_percen~e    =          70

9._at        : ICT_percen~e    =          80

10._at       : ICT_percen~e    =          90

11._at       : ICT_percen~e    =         100

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .4894287     .11085     4.42   0.000     .2719667    .7068907
          2  |   .8884117   .0479881    18.51   0.000     .7942701    .9825532
          3  |   1.175533   .0317861    36.98   0.000     1.113176     1.23789
          4  |   1.350793   .0516731    26.14   0.000     1.249423    1.452164
          5  |   1.414192   .0681875    20.74   0.000     1.280424     1.54796
          6  |   1.365729   .0861601    15.85   0.000     1.196703    1.534755
          7  |   1.205405   .1207255     9.98   0.000     .9685695     1.44224
          8  |   .9332193   .1810877     5.15   0.000     .5779673    1.288471
          9  |   .5491723   .2680958     2.05   0.041     .0232304    1.075114
         10  |   .0532637   .3804306     0.14   0.889     -.693053    .7995805
         11  |  -.5545062   .5170702    -1.07   0.284    -1.568878    .4598657
------------------------------------------------------------------------------

.
end of do-file

. do "C:\Users\domin\AppData\Local\Temp\STD18f4_000000.tmp"

. marginsplot, recast(line) recastci(rarea) name(MarginsForeignOwnership, replace)

  Variables that uniquely identify margins: ICT_percentage

I did it like Alan Neustadtl at minute 09:35 (https://www.youtube.com/watch?v=tJFzwFOKEcc) but I don't understand why he makes an interaction term between education and education?
He also mentions that in his case it seems like there is an interaction effect.
Well, also my "interaction term" is significant but does it make sense? I attached a picture how it looks like. As I said, I would really appreciate if you help me with the interpretation in my case.


Kind regards
Dominik

[Dominik Miksch]

Please, if one of you can help me I would appreciate it

[Carlo Lazzaro]

Dominik:
1) interacting a given predictor with itself aims at investigating whether a squared relationship exists with the dependent variable;
2) as far as -ITC_percentage-, you can calculate the absolute maximum of your parabola via the following formula:
-b (b=coefficient of the linear term, that is the first derivative of the parabola) divided by
2a (a=coefficient of the squared term).
In your case, you should obtain:

. di .0454914/(2*.0005593)
40.668157

If this percentage values (about 40.67%) falls within the range of your -ITC_percentage- variable, you can state that, other things being equal, the regessand reaches its maximum value when -ITC-percentage-=40.67% and then it decreases.

[Dominik Miksch]

Dear Carlo Lazzaro thank you very much for your support! That helped me a lot.

[Dominik Miksch]

Carlo Lazzaro One last question regarding this topic. Because propensity score matching compairs (in my case) the Innovativeness of a group of individuals who adopted ICT with those who didn't, can I conclude the following: Firms who adopted ICT up to 40.67% are more innovative compared to the group who did not adopt ICT. And if firms have an ICT adoption index higher than 40.67% their innovativeness is lower compared to the group of individuals who did not adopt ICT?

That would be really helpful if you can answer that last question. Thank you so much for your help, Carlo!

Kind regards
Dominik

[Carlo Lazzaro]

Dominik:
I would say that, other things being equal (ie, when adjusted for the other predictors), the dependent variable (say, innovation_attitude) increases until ICT adoption reaches 40.67% (where innovation_attitude reaches a maximum) and then decreases. Provided that this stuff if miles away from my research field, I think it would be interesting to explain in your paper why your analysis seems to support that, other things being equal, increasing the ICT_adoption beyond 46.67% does not produce an increase in innovation_attitude.

[Dominik Miksch]

Dear Carlo Lazzaro thank you very much! That is indeed interesting, but how would you approach to investigate about that? By using interactions between the other indenpendent variables in my model and ICT adoption at the levels >46.67%?

[Carlo Lazzaro]

Dominik:
no, I did not mean statistically, but comparing your results with the findings of other similar studies in your research field (something to be included in the Discussion section of your paper).