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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!

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  • $\begingroup$ up please help me $\endgroup$ – Charlotte Apr 21 '13 at 20:14

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