# 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
Adj. R-Squared :  0.69692
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
Adj. R-Squared :  0.71162
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
Adj. R-Squared :  0.3879


My question are:

1) Is there a reason why the estimation for coefficient for LK is not significant in both within and random? but in first diff?

2) Why give within and random so similar results, and why first difference is different from them?

3)Can I interpret Standard error and R squared? Is there anything else I can interpret? Which is the best model of the three?

Thank you so much for your help!

• up please help me – Charlotte Apr 21 '13 at 20:14