Problem with levpet and xtreg fixed-effect models

[Erick Gonzales]

Dear fellow Stata users,

The estimated coefficients for capital and labor of a Cobb-Douglas production function using levpet (LP) and xtreg, fe (FE) strongly differ with the estimated coefficients obtained by OLS, GEE, RE, and BE. Please, see results below.

I wonder if the discrepancy is because I have only two time periods, or because I have a reduced number of firms with observations in both periods, or because I am not properly using some command, among other reasons. I would highly appreciate your help as I am mainly interested in utilizing the results obtained by levpet (LP).

Results:

----------------------------------------------------------------------------------------
               (OLS)        (GEE)         (RE)         (BE)         (FE)         (LP)  
                 va           va           va           va           va           va  
----------------------------------------------------------------------------------------
k              0.379***     0.377***     0.363***     0.400***     0.122**     0.0538  
            (0.0276)     (0.0239)     (0.0273)     (0.0253)     (0.0596)      (0.107)  
 
lw             0.709***     0.703***     0.709***     0.678***     0.532**      0.542***
            (0.0376)     (0.0347)     (0.0385)     (0.0364)      (0.228)     (0.0459)  
 
_cons          5.915***     5.944***     6.063***     5.774***     9.280***            
             (0.243)      (0.203)      (0.239)      (0.213)      (0.996)               
----------------------------------------------------------------------------------------
N                971          971          971          971          971          971  
R-sq           0.671                                  0.666        0.163               
adj. R-sq      0.670                                  0.665        0.161               
rmse           1.100                     0.610        1.102        0.175               
----------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.10, ** p<0.05, *** p<0.01

Stata commands:

xtset idpanel year
*OLS
regress va k lw, vce(cluster idpanel)
*GEE
xtgee va k lw
*RE
xtreg va k lw, re vce(cluster idpanel)
*BE
xtreg va k lw, be
*FE
xtreg va k lw, fe vce(cluster idpanel)
*LP
levpet va, free(lw) proxy(e) capital(k) valueadded reps(250)

Some definitions:
k=ln(K): Capital
lw=ln(LW): Labor
va=ln(VA): Value added
VA=Y-M-E
M: Raw materials and intermediate goods
E: Electricity

Data characteristics:
My final goal is to determine Total Factor Productivity (TFP). After a data cleaning process, I have an unbalanced panel of 888 firms. Only 83 firms have observations in both time periods which give me a total number of observations of 971. All observations belong to the same 4-digit level International Standard Industrial Classification (ISIC) code.

xtdescribe
 idpanel:  101078, 101081, ..., 503957                       n =        888
    year:  1, 2, ..., 2                                      T =          2
           Delta(year) = 1 unit
           Span(year)  = 2 periods
           (idpanel*year uniquely identifies each observation)
Distribution of T_i:   min      5%     25%       50%       75%     95%     max
                         1       1       1         1         1       2       2
 
     Freq.  Percent    Cum. |  Pattern
 ---------------------------+---------
      479     53.94   53.94 |  1.
      326     36.71   90.65 |  .1
       83      9.35  100.00 |  11
 ---------------------------+---------
      888    100.00         |  XX

[Erick Gonzales]

Hello!

I could provide more information if needed.

Based on the results shown in the previous post, please see below the outcome of some tests. If not mistaken, the first two indicate that I could use random effects (RE). However, the Hausman test suggests the utilization or fixed effects (FE). How could I interpret these results? Considering that I would like to use the levpet coefficients (shown in previous post), should I compare the levpet results to the RE of FE results? I will try to execute a robust Hausman test as well. I also still wonder why the levpet coefficients for capital and labor greatly differ from the coefficients obtained by other methods (which is my main question). Theory predicts that the coefficient for labor should be smaller in levpet as compared to other methods, but the coefficient for capital is not expected to be reduced. I will highly appreciate any comment or suggestion.

*Testime for time fixed effects: no time fixed effects are needed (Prob>F is >0.05)
xtreg va k lw i.year, i(idpanel) fe
testparm i.year
 
 ( 1)  2010.year = 0
 
       F(  1,    80) =    2.07
            Prob > F =    0.1539
 
*Testing for random effects: Breusch-Pagan Lagrange multiplier (LM): I reject the null, and conclude that random effects is appropiate (no evidence of significant differences across countries)
xtreg va k lw, i(idpanel) re
xttest0
 
Breusch and Pagan Lagrangian multiplier test for random effects
        va [idpanel,t] = Xb + u[idpanel] + e[idpanel,t]
        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
                      va |   3.666755       1.914877
                       e |   .3669783       .6057874
                       u |   .8647367       .9299122
 
        Test:   Var(u) = 0
                             chibar2(01) =    13.17
                          Prob > chibar2 =   0.0001
 
*Hausman Test: suggest utilizing fixed-effects
xtset idpanel year2
xtreg va k lw avgedu, fe
estimates store fixed
xtreg va k lw avgedu, re
estimates store random
hausman fixed random, sigmamore
 
. hausman fixed random, sigmamore
 
                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference          S.E.
-------------+----------------------------------------------------------------
           k |    .0833611     .3564116       -.2730505        .0653611
          lw |    .4799264     .7050264          -.2251         .164403
      avgedu |    .0049624      .168841       -.1638786        .1002127
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg
 
    Test:  Ho:  difference in coefficients not systematic
 
                  chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       23.29
                Prob>chi2 =      0.0000

Also, find below scatter plots for the output variable (ln(Y)) as well as for capital and labor.

[Klodi Gjini]

did you get any answer from anyone? I am doing quite the same thing and I have a lot of difficulties

[Erick Gonzales]

Hello Klodi,
Thank you for your post! Unfortunately, I did not receive any reply.
I developed some hypothesis with the help of some colleagues. I state a couple of them below.
- Reduced number of periods. According to Cameron and Trivedi (2009) the “RE estimator approaches the within estimator as T gets large and as σ_α^2 gets large relative to σ_ϵ^2 because in those cases θ ̂_i→1.” Therefore, it is possible that because the number of periods is reduced, the coefficients obtained by RE do not approach the coefficients obtained by FE and LP.
- A probably more important reason is that the method by LP in Stata is only considering those observations with information in both periods (balanced).
Let me know if you find these explanations helpful. I will also appreciate if you could share with me other alternative explanations. Cheers!