Title
mmsel -- Simulate (counterfactual) distributions from quantile regressions (w/optional sample selection correction)
Syntax
mmsel depvar [indepvars] {if} [, options]
options Description -------------------------------------------------------------------------
Main group(var) Group identification binary variable pooled/incgrp/group1 Reference wage structure (see below) percentile Print results for each percentile reps(#) Number of repetitions filename(foo) Filename given to log files and graphs
Sample Selection (see below) grponlysel Single group for sample selection correction single(indepvars) Single index generation for sample selection correction (32bit only) method(#) Method of estimation adjust(var) Single index generated power series variable constraint(con) Reduced sample constraint reduced(indepvars) Reduced model
Description
mmsel Simulates (counterfactual) distributions from quantile regressions. Based on Machado and Mata (2005). An option to correct for sample selection has been added, using an adaptation of the procedure described in Albrecht et. al (2009). Multiple options available for different reference groups, following Oaxaca (1973), Blinder (1973) Oaxaca Ransom (1994) and Jann (2008). After simulation of conditional distributions, the differences between these distributions are decomposed and graphed into explained and unexplained components.
To keep working directory clean, the program creates four directories (tmp, results, logs, data) which contain all the files needed for troubleshooting and/or analysis.
WARNING - Depending on options selected, may take days to run - test using sample 10 or other low number (uses 10% of sample).
NOTE - This program requires a pid variable: a personal identification variable for each individual in the sample
Options
+------+ ----+ Main +-------------------------------------------------------------
pooled/incgrp/group1 Reference wage structure:
pooled Uses the pooled wage structure estimated from a model using the pooled sample (including both groups) (See Oaxaca & Ransom 1994)
incgrp Uses the pooled wage structure (including the group binary variable) estimated from a model using the pooled sample (including both groups) (See Jann(2008))
group1 Uses the wage structure of group for which that group binary variable equals 1 estimated from a model using only that group's sample. (If the group binary variable is coded as male=1 male and male=0 female, then selecting the group1 option will use as reference wage structure the male wage structure) (See Oaxaca (1973) & Blinder (1973))
percentile Using this option forces the module to provide a table with decomposition results for each percentile, rather than the default of every 5 percentiles
reps(#) Number of repetitions used in the Machado & Mata counterfactual distribution simulations (default value: 200)
+-----------------------------+ ----+ Sample Selection Correction +--------------------------------------
grponlysel Single group for sample selection correction - Sample selection correction only takes place for individuals where the group dummy is equal to zero (default is both groups are corrected for sample selection)
single(indepvars) Single index generation for sample selection correction - This option launches the single index generation process proposed by Ichimura (1993), as documented in Albrecht et. al (2009), prior to sample selection corrected decompositions. It must ONLY be run on a full dataset that includes censored observations. The independent variables are variables that are thought to affect whether an observation is censored or not. Following the single index generation process, censored observations are dropped from the sample. Censored observations automatically identified by the option as those observations where depvar (in the mmsel) is missing or equal to 0.
method(#) (Only for testing purposes) Method of estimation - Whether method(1) or method(2) selected the same results should be generated (Default setting is method(2)).
adjust(var) Single index generated power series variable - The variable predicted from a single index model applied to the whole working and non-working sample, needed for sample selection correction. The Inverse Mills Ratio can also be used although many assumptions must be relaxed for this to be a valid move. NOTE: If the single() option is used, "var" MUST be replaced with "Ps1". If not, "var" should be a single index generated over the full censored and non-censored sample.
constraint(con) Reduced sample constraint - a constraint in Stata format with the aim of constraining the sample temporarily to a sample for which the probability of being in work is close to unity. This is a second-best solution to estimating the true constant of an earnings equation while correcting for sample selection across the earnings distribution
reduced(indepvars) Reduced model - List of independent variables without the variable(s) used for the sample constraint above.
Example without sample selection correction
. mmsel y x1 x2 x3 x4, group(female) filename(foo) reps(100) pooled
Example with sample selection correction
. mmsel y x1 x2 x3 x4, group(female) grponlysel single(z1 z2 z3) filename(foo) reps(100) pooled adjust(Ps1) reduced(x1 x3) cons(x2=1&x4<56|x2=0&x4<24)
References
Albrecht, J van Vuuren, A and Vroman, S (2009). “Counterfactual distributions with sample selection adjustments: Econometric theory and an application to the Netherlands Labour Economics.” Labour Economics 16(4); 383-396.
Blinder, A S (1973). “Wage Discrimination: Reduced Form and Structural Estimates.” The Journal of Human Resources 8; 436–455.
Ichimura, H (1993). “Semiparametric least squares (SLS) and weighted SLS estimation of single index models.” Journal of Econometrics 58; 71–120.
Jann, B (2008). “The Blinder–Oaxaca decomposition for linear regression models.” Stata Journal 8(4); 453-479.
Mata, J & Machado J A F, (2005). “Counterfactual decomposition of changes in wage distributions using quantile regression.” Journal of Applied Econometrics 20(4); 445-465.
Oaxaca R L & Ransom M R (1994). “On discrimination and the decomposition of wage differentials.” Journal of Econometrics, 61(1); 5-21.
Oaxaca, R L (1973). “Male-Female Wage Differentials in Urban Labor Markets.” International Economic Review, 14(3); 693-709.
Author
Sami Souabni, Swansea University, sami@souabni.com, who bears no responsibility for any errors.
Acknowledgements
Single index generation based on publicly available original code by Aico van Vuuren (http://members.chello.nl/a.vuren1/Ado.exe), who bears no responsibility for any errors.
Machado & Mata decomposition based on original code by Mark Bryan, ISER,