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  • LM Test Result in Random Effect Model

    Dear members,
    I'm quite newbie here. I'm so confused in determining the perfect model for my regression. I have conducted the LM test to determine whether should I use the Random Effect model or common OLS. Please help me

    Here's my result on RE Regression:

    Random-effects GLS regression Number of obs = 160
    Group variable: bank Number of groups = 32

    R-sq: Obs per group:
    within = 0.0000 min = 5
    between = 0.3439 avg = 5.0
    overall = 0.2313 max = 5

    Wald chi2(9) = 11.53
    corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.2412

    ------------------------------------------------------------------------------
    LDR | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    x1 | 7.71892 7.445196 1.04 0.300 -6.873397 22.31124
    x2 | -7.521882 12.34695 -0.61 0.542 -31.72147 16.6777
    x3 | -13.53032 9.615677 -1.41 0.159 -32.3767 5.31606
    x4 | -4.638333 8.831311 -0.53 0.599 -21.94738 12.67072
    x5 | -1.266607 10.72728 -0.12 0.906 -22.29168 19.75847
    x6 | -14.92695 9.851367 -1.52 0.130 -34.23528 4.381369
    x7 | 1.04999 .9551709 1.10 0.272 -.8221106 2.92209
    x8 | -1.253508 .7169643 -1.75 0.080 -2.658732 .1517162
    x9 | 14.31133 6.478638 2.21 0.027 1.613433 27.00923
    _cons | 109.6411 24.82635 4.42 0.000 60.98236 158.2999
    -------------+----------------------------------------------------------------
    sigma_u | 7.8450711
    sigma_e | 6.7056952
    rho | .57782631 (fraction of variance due to u_i)
    ------------------------------------------------------------------------------

    Here's my LM test after the regression:

    Breusch and Pagan Lagrangian multiplier test for random effects

    LDR[bank,t] = Xb + u[bank] + e[bank,t]

    Estimated results:
    | Var sd = sqrt(Var)
    ---------+-----------------------------
    LDR | 110.5734 10.51539
    e | 44.96635 6.705695
    u | 61.54514 7.845071

    Test: Var(u) = 0
    chibar2(01) = 69.98
    Prob > chibar2 = 0.0000

    Should I use RE regression model over Common OLS model?
    Thanks in advance!

  • #2
    Gabriel:
    welcome to this forum.
    The -xttest0- outcome seemts to reject the null of random panel-wise effect.
    It may well be that you should go -fe- (if the F-test appearing as a footnote of the -xtreg,fe- outcome table [please note that that the statistic works with default standard errors only] reaches ststistical significance):
    Code:
    . use "http://www.stata-press.com/data/r15/nlswork.dta"
    (National Longitudinal Survey.  Young Women 14-26 years of age in 1968)
    
    . quietly xtreg ln_wage i.race tenure, fe
    
    . estimates store fe
    
    . quietly xtreg ln_wage i.race tenure, re
    
    . xttest0
    
    Breusch and Pagan Lagrangian multiplier test for random effects
    
            ln_wage[idcode,t] = Xb + u[idcode] + e[idcode,t]
    
            Estimated results:
                             |       Var     sd = sqrt(Var)
                    ---------+-----------------------------
                     ln_wage |   .2282906       .4777976
                           e |   .0921585       .3035762
                           u |   .1130513        .336231
    
            Test:   Var(u) = 0
                                 chibar2(01) = 21783.90
                              Prob > chibar2 =   0.0000
    
    . estimates store re
    
    . hausman fe re
    
                     ---- Coefficients ----
                 |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
                 |       fe           re         Difference          S.E.
    -------------+----------------------------------------------------------------
          tenure |    .0341807     .0376405       -.0034598        .0002187
    ------------------------------------------------------------------------------
                               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(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                              =      250.35
                    Prob>chi2 =      0.0000
    
    .
    Kind regards,
    Carlo
    (Stata 18.0 SE)

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