*! Version 1.1.0 by Francisco Perales 04-February-2013
help mundlak

Title

mundlak - Estimates random-effects regressions adding group-means of independent variables to the model

Syntax

mundlak depvar indepvars [if] [in] [, options]

options description

Main
use(varlist) adds group-means of selected independent variables only
percentage(#) sets the minimum percentage of total variance due to within-group variation required of an independent variable to be used
nocomparison supresses the display of a comparison random-effects model with no added variables
hybrid transforms the independent variables into group-mean deviations
full prints the full output for the estimated models
stats(list) allows users to select the model statistics to be reported
se asks for standard errors for the parameters on model variables to be reported
t asks for p-values for the parameters on model variables to be reported
p asks for t-values for the parameters on model variables to be reported
keep asks for any variables created by the command to be kept in the dataset

Description

mundlak estimates random-effects regression models (xtreg, re) adding group-means
of variables in indepvars which vary within groups. This technique was proposed by Mundlak (1978)
as a way to relax the assumption in the random-effects estimator that the observed variables are uncorrelated
with the unobserved variables. Additionally, the degree of statistical significance of the estimated coefficients
on the group means can be used to test whether such assumption holds for individual regressors. See also Chapter 10
in Wooldridge (2010) and Chapter 11 in Greene (2011). The command mundlak requires the data to be xtset. If no
variables vary within-groups, mundlak estimates the standard random-effects model with no additional
variables and displays a warning message. The names of the added group-mean variables will begin with the prefix mean__
followed by the original variable name. Note that the estimates from both the standard random-effects
model and the Mundlak model are kept in Stata's background memory and can be accessed via estimates dir
for further usage.

Original random-effects model: Yij = A + B1*Xij + B2*Zi + vij

Mundlak model: Yij = A + B1*Xij + B2*Zi + B3*X_bari + vij

Options

use(varlist) specifies the variables for which group-means will be added in the model. The
default is to use all the variables within the provided list of independent variables which vary within groups,
unless such variation is insufficient. The variables specified in this option do not need to be among those in
varlist, although that would be most common. If the variables specified in this option do not vary within groups,
mundlak will display an error message.

percentage(#) suppresses the inclusion in the model of group-means of variables for which within-group
variance accounts for a percentage of the total variance lower than #. When percentage(#)
is not specified mundlak operates as if # was 0. However, note that when 0% of the total variance of a given
variable is within-groups, the group-mean of such variable cannot be included in the regression due to collinearity.
If use (varlist) is also specified, mundlak will evaluate the percentage of the total variance which is
within-groups for the variables set in this option, and will only include their group-means in the Mundlak
model if they satisfy the criteria in percent(#).

nocomparison prevents the display of results from the original random-effects model. By default,
mundlak displays the results from both the original random-effects model and the Mundlak model which
includes the additional independent variables.

hybrid transforms the original independent variables into group-mean deviations, in
addition to adding their group-means as additional independent variables. In practice, when this option
is used mundlak estimates a 'hybrid model' equivalent to that described in Chapter 2 of Allison (2009). This
can be expressed as:

Yij = A + B1*(Xij-X_bari) + B2*Zi + vij

The names for the added group-mean differenced variables will begin with the prefix diff__ followed by the original variable name.

full asks for the full regression output for both the original random-effects model and the
Mundlak model to be displayed. When full is specified together with nocomp only the full output
for the Mundlak model is displayed.

stats allows users to specify the model summary statistics to be reported. These can be any scalars from Stata's xtreg, re routine.

se asks for the standard errors for the parameters on model variables to be reported. Note that specifying the option full overcomes this.

t asks for the t-values for the parameters on model variables to be reported. Note that specifying the option full overcomes this.

p asks for the p-values for the parameters on model variables to be reported. Note that specifying the option full overcomes this.

keep asks for the new variables (i.e. group-means and group-mean deviations) to be kept in the dataset.

Examples

. webuse nlswork, clear

. xtset idcode year

. mundlak ln_wage age south race

. mundlak ln_wage age south race, use(age)

. mundlak ln_wage age south race, percentage(45)

. mundlak ln_wage age south race, nocomparison

. mundlak ln_wage age south race, hybrid

. mundlak ln_wage age south race, full

. mundlak ln_wage age south race, stats(N N_g rho r2_o r2_w r2_b)

. mundlak ln_wage age south race, se t p

. mundlak ln_wage age south race, keep

. describe mean__*

Also see

Online: [R] xtreg

References

Allison, P. D. (2009) "Fixed-Effects Regression Models" Thousand Oaks

Greene, W. (2011) "Econometric Analysis (7th edition)" Prentice Hall

Mundlak, Y. (1978) "On the Pooling of Time Series and Cross-section Data" Econometrica, 46: 69–85

Wooldridge, J. M. (2010) "Econometric Analysis of Cross Section and Panel Data (2nd edition)" MIT Press

Author

Francisco Perales
School of Social Science
The University of Queensland
Brisbane
QLD 4072
Australia
f.perales@uq.edu.au