Dear all,

I am currently working with a country-sector-year panel data-set, which contains values for labour productivity (lp). The data looks as follows (I only include decade data so it becomes clear that my dataset consists of multiple countries and sectors):

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input str8 country int year str4 sector float lp
"ARG" 1960 "AGR"   4127.994
"ARG" 1970 "AGR"   5716.049
"ARG" 1980 "AGR"   7340.645
"ARG" 1990 "AGR"   7826.752
"ARG" 2000 "AGR"  11798.175
"ARG" 2010 "AGR"  16190.268
"ARG" 1960 "CON"   6326.399
"ARG" 1970 "CON"    7773.84
"ARG" 1980 "CON"   7460.041
"ARG" 1990 "CON"    4453.29
"ARG" 2000 "CON"   9094.761
"ARG" 2010 "CON"   8459.559
"ARG" 1960 "FIRE" 10378.604
"ARG" 1970 "FIRE" 10840.906
"ARG" 1980 "FIRE"  11463.33
"ARG" 1990 "FIRE"  6980.222
"ARG" 2000 "FIRE"  8623.354
"ARG" 2010 "FIRE"  7328.641
"ARG" 1960 "GOV"   9412.982
"ARG" 1970 "GOV"   9608.455
"ARG" 1980 "GOV"   8566.728
"ARG" 1990 "GOV"   6305.592
"ARG" 2000 "GOV"    6279.64
"ARG" 2010 "GOV"    6142.36
"ARG" 1960 "MAN"   7614.975
"ARG" 1970 "MAN"  12927.145
"ARG" 1980 "MAN"  15444.467
"ARG" 1990 "MAN"  12530.603
"ARG" 2000 "MAN"   21147.12
"ARG" 2010 "MAN"  25071.666
"ARG" 1960 "MIN"   31663.04
"ARG" 1970 "MIN"   68859.62
"ARG" 1980 "MIN"  110079.85
"ARG" 1990 "MIN"  119446.76
"ARG" 2000 "MIN"  230808.84
"ARG" 2010 "MIN"   90408.21
"ARG" 1960 "OTH"   5753.756
"ARG" 1970 "OTH"   5606.121
"ARG" 1980 "OTH"   4998.317
"ARG" 1990 "OTH"   3679.042
"ARG" 2000 "OTH"   4011.429
"ARG" 2010 "OTH"   4534.363
"ARG" 1960 "PU"   2297.5989
"ARG" 1970 "PU"   4385.5186
"ARG" 1980 "PU"    8996.652
"ARG" 1990 "PU"   12170.942
"ARG" 2000 "PU"    20137.03
"ARG" 2010 "PU"   28556.434
"ARG" 1960 "SUM"   7292.438
"ARG" 1970 "SUM"   9459.183
"ARG" 1980 "SUM"  10741.543
"ARG" 1990 "SUM"   7988.315
"ARG" 2000 "SUM"  10429.977
"ARG" 2010 "SUM"   11703.62
"ARG" 1960 "TRA"   5709.911
"ARG" 1970 "TRA"   8175.761
"ARG" 1980 "TRA"  12398.574
"ARG" 1990 "TRA"   10746.12
"ARG" 2000 "TRA"  13155.982
"ARG" 2010 "TRA"  24833.934
"ARG" 1960 "WRT"  10518.568
"ARG" 1970 "WRT"    9730.58
"ARG" 1980 "WRT"  11062.238
"ARG" 1990 "WRT"   6516.053
"ARG" 2000 "WRT"   8259.874
"ARG" 2010 "WRT"   9496.094
"BFA" 1970 "AGR"  110.32106
"BFA" 1980 "AGR"   230.1052
"BFA" 1990 "AGR"  224.48415
"BFA" 2000 "AGR"   376.9785
"BFA" 2010 "AGR"  603.76544
"BFA" 1970 "CON"  14784.226
"BFA" 1980 "CON"   18590.33
"BFA" 1990 "CON"   8609.532
"BFA" 2000 "CON"   8166.037
"BFA" 2010 "CON"   3140.118
"BFA" 1970 "FIRE"  98228.82
"BFA" 1980 "FIRE" 121360.67
"BFA" 1990 "FIRE" 146959.22
"BFA" 2000 "FIRE"  62266.25
"BFA" 2010 "FIRE"     22497
"BFA" 1970 "GOV"   1235.855
"BFA" 1980 "GOV"   4920.595
"BFA" 1990 "GOV"   6849.526
"BFA" 2000 "GOV"   6538.629
"BFA" 2010 "GOV"   6756.323
"BFA" 1970 "MAN"  1026.6361
"BFA" 1980 "MAN"  2069.4717
"BFA" 1990 "MAN"   2499.018
"BFA" 2000 "MAN"   3014.091
"BFA" 2010 "MAN"  1275.7748
"BFA" 1970 "MIN"   4535.848
"BFA" 1980 "MIN"  14251.697
"BFA" 1990 "MIN"   5578.705
"BFA" 2000 "MIN"  1658.1753
"BFA" 2010 "MIN"  2099.5117
"BFA" 1970 "OTH"   860.5823
"BFA" 1980 "OTH"  1124.9858
"BFA" 1990 "OTH"   2475.863
"BFA" 2000 "OTH"   1739.577
end
I use the following code to estimate labour productivity growth, initial productivity, fixed effects, which I need for the regression:

Code:
** Estimate CAGR and base productivity **
gen cagr = (lp/L10.lp)^(1/10)-1
label var cagr "10-year CAGR of labour productivity"
gen base_lp = L10.lp
replace base_lp=ln(base_lp)
label var base_lp "Log initial value added per worker"
drop if missing(cagr)



gen decade=10*floor(year/10)

gen dd=(year/10-floor(year/10)==0)
Finally, for the regression, I use the following code:

Code:
** baseline specification with interaction base productivity and decade dummies-without country fixed effects
eststo: reg cagr i.decade##c.base_lp if sector=="SUM" & dd==1, vce(cluster country)
margins decade, dydx(base_lp)
marginsplot, yline(0) saving(marginsplotU_expanded10S_tot, replace) title(Average marginal effect of aggregate initial labour productivity)
testparm i.decade#c.base_lp
As the code shows, I also estimate margins and plot a marginsplot, as I have read a few times on this forum that you must be careful with the interpretation of the coefficients of a regression which features interaction terms. I present the output below:


Code:
Linear regression Number of obs = 219
F(11, 46) = 5.66
Prob > F = 0.0000
R-squared = 0.1331
Root MSE = .02455

(Std. Err. adjusted for 47 clusters in country)
----------------------------------------------------------------------------------
| Robust
cagr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------+----------------------------------------------------------------
decade |
1970 | -.0369443 .0508452 -0.73 0.471 -.1392904 .0654018
1980 | -.0325573 .0537875 -0.61 0.548 -.1408259 .0757113
1990 | -.0669999 .0462792 -1.45 0.154 -.160155 .0261553
2000 | -.0176603 .048822 -0.36 0.719 -.1159338 .0806133
2010 | .0279238 .0462706 0.60 0.549 -.065214 .1210617
|
base_lp | -.0029204 .0047142 -0.62 0.539 -.0124096 .0065689
|
decade#c.base_lp |
1970 | .0045283 .0054172 0.84 0.408 -.006376 .0154326
1980 | .0026011 .0056971 0.46 0.650 -.0088666 .0140688
1990 | .0050658 .0049548 1.02 0.312 -.0049076 .0150393
2000 | .0009163 .0051466 0.18 0.859 -.0094434 .0112759
2010 | -.0041625 .0048945 -0.85 0.399 -.0140146 .0056895
|
_cons | .0561863 .0449996 1.25 0.218 -.0343932 .1467657
----------------------------------------------------------------------------------
(est1 stored)

. margins decade, dydx(base_lp)

Average marginal effects Number of obs = 219
Model VCE : Robust

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

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
base_lp |
decade |
1960 | -.0029204 .0047142 -0.62 0.539 -.0124096 .0065689
1970 | .0016079 .0023384 0.69 0.495 -.0030991 .006315
1980 | -.0003193 .0030564 -0.10 0.917 -.0064715 .0058329
1990 | .0021455 .0020347 1.05 0.297 -.0019502 .0062412
2000 | -.0020041 .0022425 -0.89 0.376 -.006518 .0025099
2010 | -.0070829 .0018853 -3.76 0.000 -.0108778 -.003288
------------------------------------------------------------------------------


My first question is: what is the reason why one should be careful in Stata with interpreting the coefficients of a regression which contains interaction terms between the explanatory variable and (decade) dummies? I tried to find an explanation for this but I have not been succesful in this so far.

My second question is: how could it be that my marginsplot shows a significant effect for labour productivity in decade=2010, but the coefficient for this interaction term (decade#c.base_lp) in the regression is insignificant?

If anyone could help me with this, it would be much appreciated. I understand my questions relate more to theory and the understanding of Stata, hopefully these questions are allowed.

I thank you for your time.

Best,

Satya