# Interpretation of Translog regression

I'm a beginner in R and Im wondering how to interprete my results..... My question is about the results that I got after I did a regression on the Translog production function for panel data: $log(y)=log(A) + \alpha_{K} log(K) + \alpha_{L} log(L) + \beta_{KL} log(K)log(L) + \beta_{L^2} log^2(L) + \beta_{K^2} log^2(K)$

L stands for labour and K for Kapital.

The results I got for the Within, Random and first difference a the following: Within:

  #Within
Coefficients :
Estimate  Std. Error  t-value Pr(>|t|)
K   1.0902e-05  1.0654e-06  10.2326   <2e-16 ***
L  -2.4009e-06  1.5086e-07 -15.9150   <2e-16 ***
LK  1.9788e-03  3.6069e-03   0.5486   0.5833
LL  3.0511e-02  1.3141e-03  23.2173   <2e-16 ***
KK  5.0333e-02  2.6650e-03  18.8868   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Total Sum of Squares:    6886.3
Residual Sum of Squares: 1983.9
R-Squared      :  0.71191
F-statistic: 10729.1 on 5 and 21709 DF, p-value: < 2.22e-16

> #regression random translog
> tl.random<-plm(Y ~ K + L + LK + LL + KK, data=panel, model="random")
> summary(tl.random)
Oneway (individual) effect Random Effect Model
(Swamy-Aroras transformation)

Call:
plm(formula = Y ~ K + L + LK + LL + KK, data = panel, model = "random")

Balanced Panel: n=462, T=48, N=22176

Effects:
var std.dev share
idiosyncratic 0.09139 0.30230 0.397
individual    0.13856 0.37224 0.603
theta:  0.8836

Residuals :
Min.  1st Qu.   Median  3rd Qu.     Max.
-3.16000 -0.14200  0.00724  0.15400  4.89000

Coefficients :
Estimate  Std. Error  t-value Pr(>|t|)
(Intercept)  1.6266e+00  3.9030e-02  41.6763   <2e-16 ***
K            9.0932e-06  1.0552e-06   8.6178   <2e-16 ***
L           -2.5192e-06  1.5023e-07 -16.7684   <2e-16 ***
LK           2.7566e-03  3.6102e-03   0.7636   0.4451
LL           2.9491e-02  1.3138e-03  22.4474   <2e-16 ***
KK           4.8817e-02  2.6659e-03  18.3117   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Total Sum of Squares:    7183.6
Residual Sum of Squares: 2070.2
R-Squared      :  0.71181
F-statistic: 10951.9 on 5 and 22170 DF, p-value: < 2.22e-16

> #regression first difference translog
> tl.fd<-plm(Y ~ K + L + LK + LL + KK-1, data=panel, model="fd")
> summary(tl.fd)
Oneway (individual) effect First-Difference Model

#First difference regression
Call:
plm(formula = Y ~ K + L + LK + LL + KK - 1, data = panel, model = "fd")

Balanced Panel: n=462, T=48, N=22176

Residuals :
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-1.4900 -0.0321  0.0199  0.0202  0.0715  0.9860

Coefficients :
Estimate  Std. Error t-value  Pr(>|t|)
K   2.3847e-07  2.8965e-06  0.0823 0.9343856
L  -8.0238e-07  2.3128e-07 -3.4693 0.0005229 ***
LK -2.6986e-02  6.7755e-03 -3.9829 6.831e-05 ***
LL  5.6920e-02  2.3933e-03 23.7830 < 2.2e-16 ***
KK  3.7811e-02  5.1254e-03  7.3773 1.674e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Total Sum of Squares:    426.54
Residual Sum of Squares: 269.92
R-Squared      :  0.38799