Use the new estat mundlak postestimation command after xtreg to choose between random-effects (RE) and fixed-effects (FE) or correlated random-effects (CRE) models, even with cluster–robust, bootstrap, or jackknife standard errors.

Let's see it work

We often use a Hausman specification test to decide between a more efficient RE model or an FE model. But this test cannot be performed after estimation using cluster–robust, bootstrap, or jackknife standard errors. In that case, we can use a fully robust Mundlak specification test. Unlike a Hausman test, we do not need to fit both the RE and FE models to perform a Mundlak test.

We are interested in how the number of registrations of a dog breed with the American Kennel Club (AKC), registered, is affected by dogs being the protagonists in a movie, movie. We surmise that the number of registrations increases if the dog breed appears as the protagonist in a movie. We also think that registrations increase if the dog has won the Best in Show award, best, from the Westminster Kennel Club in the 10 years before 2034 and that we need to control for year effects.

We would like to determine whether the more efficient RE model is applicable to our data instead of the FE model that allows for correlation of the regressors with the unobserved panel-level effects. We believe we should use cluster–robust standard errors during estimation to control for heteroskedasticity and within-breed correlation. As such, we cannot use our traditional Hausman specification test, but we can use the new estat mundlak command to perform a Mundlak specification test.

We first fit an RE model:

. webuse akc
(Fictional dog breed and AKC registration data)

. xtset breed year

Panel variable: breed (strongly balanced)
 Time variable: year, 2031 to 2040
         Delta: 1 unit

. xtreg registered i.movie i.year, vce(cluster breed)

Random-effects GLS regression                   Number of obs     =      1,410
Group variable: breed                           Number of groups  =        141

R-squared:                                      Obs per group:
     Within  = 0.4503                                         min =         10
     Between = 0.8271                                         avg =       10.0
     Overall = 0.5491                                         max =         10

                                                Wald chi2(10)     =    1029.05
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                (Std. err. adjusted for 141 clusters in breed)


             
 
               Robust                                           
  registered 
 
 Coefficient  std. err.      z    P>|z|     [95% conf. interval]
 
 
 
     1.movie 
 
   2044.629   84.89458    24.08   0.000     1878.238    2211.019
             
 
                                                                
        year 
 
                                                                
       2032  
 
  -21.57447   48.27095    -0.45   0.655    -116.1838    73.03485
       2033  
 
   48.84397    52.5138     0.93   0.352    -54.08118    151.7691
       2034  
 
  -93.29443   55.78234    -1.67   0.094    -202.6258    16.03694
       2035  
 
   15.84741   51.68324     0.31   0.759    -85.44988    117.1447
       2036  
 
  -22.61986   52.46455    -0.43   0.666    -125.4485    80.20877
       2037  
 
   30.05085   58.58148     0.51   0.608    -84.76674    144.8684
       2038  
 
   9.667868   52.75853     0.18   0.855    -93.73696    113.0727
       2039  
 
   103.4693   59.89955     1.73   0.084    -13.93167    220.8702
       2040  
 
    128.143    61.8632     2.07   0.038     6.893406    249.3927
             
 
                                                                
       _cons 
 
   1001.901   35.62685    28.12   0.000     932.0734    1071.728
 
 
 
     sigma_u 
 
  24.169801                                                     
     sigma_e 
 
  494.41332                                                     
         rho 
 
  .00238413   (fraction of variance due to u_i)                 

To perform a Mundlak specification test, we type

. estat mundlak

Mundlak specification test
H0: Covariates are uncorrelated with unobserved panel-level effects

    chi2(1) =   5.73
Prob > chi2 = 0.0167

Notes: Fixed effects and correlated random effects are
       consistent under H0 and Ha.
       Random effects are efficient under H0.

We reject the null hypothesis that regressors are uncorrelated with the breed-specific effects, which is assumed by an RE model. This suggests that fitting an FE model (xtreg, fe) or a CRE model (xtreg, cre) is more sensible.

In the example above, we used a cluster–robust variance–covariance matrix estimator, but we could have used bootstrap or jackknife. And we could have fit an FE or CRE model first and then used estat mundlak.