[Carlo Lazzaro]

Zol:
p-value for -employment- up to 1940: 0.759;
p-value for -employment- from 1941 up to 1950: 0.671;
p-value for -employment- from 1951 up to 1960: 0.406.

Hence, there's no evidence that the contribution of -employment- to variations in the regressand (-ecogrowth-) varies with time.

[Zol Jargal]

Thank you very much, Carlo. I really appreciate it. Does your last sentence (Hence, there's no evidence that the contribution of -employment- to variations in the regressand (-ecogrowth-) varies with time) mean that since p-values for each period are more than 0.05, employment has no contribution to economic growth in each period?

[Carlo Lazzaro]

Zol:
yes, as there was no evidence of a substantive role of -employment- in that respect in your first regression (ie, without interaction), too.

[Zol Jargal]

Thanks for your kind reply Carlo. When you say "in that respect in your first regression (ie, without interaction), too.", are you talking about the very first regression, which included all years from 1930-1960? I attached the very first regression result. Is it right? Here, it states that "0.982". And from the above result, what do period_dummy1 and period_dummy2 mean? Thank you very much

[Carlo Lazzaro]

Zol:
yes I meant the regression you reported in your last post.
period_dummy_1 stretches over 1941-1950;
period_dummy_2 stretches over 1951-1960.

[Zol Jargal]

Thank you. As you have mentioned, period_dummy_1 stretches over 1941-1950. It indicates that the p-value of 0.002 and period dummy_2 indicates a p-value of 0.009. But which variables are included in this context? All variables which in 1941-1950 have same p-value of 0.002?

[Carlo Lazzaro]

Zol:
not quite.
The p-values indicate that, when adjusted for the remaining preedictors, the second and the third decades support the evidence of variations in the regressand.
You could also change your appoach and look for turning-points in the relationship between time (considerd as a continuos predictor) and the rgeressand via the following code:

reg ecogrowth population employment trade capital stock c.year##c.year

[Zol Jargal]

I used the code and got the result. But I don't know how to interpret the result. Especially the line with c.year#c.year. The line 'c.year#c.year' shows the p-value of 0.003 . What does it mean? Also, I still don't get the meaning of the p-value of period_dummy_1 (0.002) and period dummy_2 (0.009). What do you mean by saying when adjusted for the remaining preedictors, the second and the third decades support the evidence of variations in the regressand? I attached the result. Thank you~

[Carlo Lazzaro]

Zol:
my guess is that it's unfruitful to go on like that, as you seem to ignore the building blocks of linear regression.
I would urge you to consult any decent textbook on econometrics/statistics.
That said, you're interaction is statistically significant, meaning that the relationship between time (as a continuous predictor) and the regressand is not linear, but parabolic (ie, squared), with a maximum in:

. di -16.00301/(2*-.0040882) ///*elaborating on the first derivative*
1957.2196

that is included in the range of -year- (that actually span from 1930-1960).
Basically, when adjusted for the remaining predictors, the relationship between -time- and -ecogrowth- increases up to 1957.22 and then decreases.
As an aside, please do not post screenshots, but use CODE delimiters for sharing what you typed and what Stata gave you back (as recommended by the FAQ). Thanks:

. reg ecogrowth population employment trade capital stock c.year##c.year

      Source |       SS           df       MS      Number of obs   =        31
-------------+----------------------------------   F(7, 23)        =     52.17
       Model |  58.1339442         7  8.30484917   Prob > F        =    0.0000
    Residual |  3.66153845        23  .159197324   R-squared       =    0.9407
-------------+----------------------------------   Adj R-squared   =    0.9227
       Total |  61.7954826        30  2.05984942   Root MSE        =      .399

-------------------------------------------------------------------------------
    ecogrowth |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
   population |  -.2310529   .1992659    -1.16   0.258    -.6432659    .1811602
   employment |   .1526328   .7693422     0.20   0.844    -1.438873    1.744138
        trade |   .4895139   .2002553     2.44   0.023     .0752542    .9037736
      capital |  -.0915186   .2416362    -0.38   0.708     -.591381    .4083439
        stock |  -.0837417    .771063    -0.11   0.914    -1.678807    1.511324
         year |   16.00301    4.82715     3.32   0.003     6.017294    25.98874
              |
c.year#c.year |  -.0040882   .0012368    -3.31   0.003    -.0066468   -.0015296
              |
        _cons |     -15655   4709.208    -3.32   0.003    -25396.74   -5913.262
-------------------------------------------------------------------------------


. di -16.00301/(2*-.0040882)
1957.2196

.

[Zol Jargal]

Thanks for your reply, Carlo~

[Zol Jargal]

Hello Carlo. I have one more question. In the case of post 15(#15), p-values are(as you have mentioned):

p-value for -employment- up to 1940: 0.759;
p-value for -employment- from 1941 up to 1950: 0.671;
p-value for -employment- from 1951 up to 1960: 0.406.

My question is that coefficients of period 1(-.2133548) and period 2(-.3266391) are negative. I have tried many ways with all variables, but coefficients of period 1 and period 2 still give the negative value. If I use dummy variables, then every coefficient is negative.

Am I interpreting it the right way? If I am not interpreting right, can you give me more explanation with this result? Thank you very much~

[Carlo Lazzaro]

Zol:
you can say that, when adjusted for the remaining predictors, there's no evidence that both time-related coefficients play any role in variations of the regressand.
However, -year- as a continuous predictor can behave differently, as reported in #24.

[Zol Jargal]

Carlo, Can I ask why dummu variables(period 1 and 2) give the negative coefficients? Any way to make it positive?

[Carlo Lazzaro]

Zol:
in the regression reported in #15, -employment-, -i-period- and their interactions all gove back non-significant coefficients. Put differently, you can not rule out that those coefficients differ from zero, as you can see in the following toy-example:

use "C:\Program Files\Stata16\ado\base\a\auto.dta"
. reg price weight trunk

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.80
       Model |   186872936         2  93436468.2   Prob > F        =    0.0000
    Residual |   448192460        71  6312569.86   R-squared       =    0.2943
-------------+----------------------------------   Adj R-squared   =    0.2744
       Total |   635065396        73  8699525.97   Root MSE        =    2512.5

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |   2.266182   .5110542     4.43   0.000     1.247169    3.285195
       trunk |  -60.03885   92.85726    -0.65   0.520     -245.191    125.1133
       _cons |   148.5533   1203.406     0.12   0.902     -2250.97    2548.077
------------------------------------------------------------------------------

. test trunk

 ( 1)  trunk = 0

       F(  1,    71) =    0.42
            Prob > F =    0.5200

.

With your current sample size and remaining predictors, there's no way to make them positive and, even if they were but retained their lack of statistical significance, the previous comment about the lack of evidence of their effect on regressand variation (given the other predictors) would still hold.