help mundlak -------------------------------------------------------------------------------

Title

mundlak - Estimates random-effects regressions adding group-means of indep > endent 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 w > ith no added variables hybrid transforms the independent variables into group-mean deviati > ons 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 variabl > es to be reported t asks for p-values for the parameters on model variables to b > e reported p asks for t-values for the parameters on model variables to b > e reported keep asks for any variables created by the command to be kept in > the dataset

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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, replace

. 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" Econ > ometrica, 46: 6985 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