*! version 3.0 3 May 2021

help for ky_estatStephen P. Jenkins and Fernando Rios-Avila (May 2021)

Post-estimation tools for ky_fit

Post-estimation tools for Kapteyn-Ypma-type (KY) models of earnings and measurement error fitted using ky_fit

Syntax

estat [option]

estat options

pr_t Provides unconditional probabilities of errors (pi_r, pi_s,
pi_w, pi_v). If any error probability is modeled as a function of
covariates, average predicted probabilities are reported.

pr_j Provides unconditional probabilities of belonging to
latent class (mixture group) j = 1, 2,..., 9. If any error
probability is modeled as a function of covariates, average predicted
probabilities are reported.

pr_sr Provides unconditional probabilities of data type
(pi_s1, pi_s2, pi_s3, pi_r1, pi_r2, pi_r3). If any error probability is modeled
as a function of covariates, average predicted probabilities are reported.

pr_all Reports all unconditional probabilities. If any error
probability is modeled as a function of covariates, average predicted
probabilities are reported.

reliability, [sim reps(#) seed(#)] Provides a full report of
the unconditional error probabilities (pi_r, pi_s, pi_w, pi_v), probabilities by
data type (pi_s1, pi_s2, pi_s3, pi_r1, pi_r2, pi_r3), probabilities of
latent class membership (pi_1, ..., pi_9), as well as means and standard
deviations of latent 'true' income (e_i) and all the errors in the model
(n_i, w_i, v_i, t_i). The option also provides two reliability statistics.

Rel1 = cov(e,x)/var(x), and Rel2 = cov(e,x)^2/(var(x)var(e)), where
"e" denotes the latent measure of 'true' log earnings and 'x' denotes the data
source (adminstrative 'r' or survey 's')

If any error probability is modeled as a function of covariates,
reliablity produces simulation-based reliability statistics. Use option
reps() to choose the number of replications used for the simulations
(default is 50), and option seed(#) to define a seed for replication
purposes.

Simulation-based reliability statistics can also be requested directly
using the option sim

xirel, [reps(#) seed(#)] Provides a report for the Reliability
statistics, MSE, E(bias) and Var(bias) for all potential estimations for
e_i(hat), via simulation. (See option predict newvar, star.)
reps() can be used to define the number of replications (default is 50),
and seed() for replication purposes.

When used after ky_fit, ky_estat automatically
identifies the previously-fitted model, and reports the appropiate statistics.

predict and margins

In addition to the standard predict and margins options
that can be used after ml estimators, you may use predict and margins
with the following options (depending on the model previously fitted).

Structural model parameters

mean_e, sig_e Mean and standard deviation of latent true earnings
e_i

mean_n, sig_n Mean and standard deviation of RTM additive error
n_i in the survey data

mean_w, sig_w Mean and standard deviation of contamination
error in the survey data

mean_v, sig_v Mean and standard deviation of RTM additive error
in the administrative data

mean_t, sig_t Mean and standard deviation of the distribution
of mismatched earnings in the adminstrative data

pi_s, pi_r, pi_w, pi_v Probabilities of: correct reporting in the
survey data (pi_s), i.e. no survey measurement error; correctly linked survey
and administrative data (pr_r), i.e. no 'mismatch'; survey data having additional
contamination (pr_w); and administrative data having measurement error (pr_v).

rho_s, rho_r Regression-to-the-mean error parameters for survey
data (rho_s), and administrative data (rho_r)

rho_w Conditional correlation between true latent earnings 'e'
and survey contamination error 'w'.

Constructed model moments

mean_r1, sig_r1 Mean and standard error of R1

mean_r2, sig_r2 Mean and standard error of R2

mean_r3, sig_r3 Mean and standard error of R3

mean_s1, sig_s1 Mean and standard error of S1

mean_s2, sig_s2 Mean and standard error of S2

mean_s3, sig_s3 Mean and standard error of S3

pi_r1, pi_r2, pi_r3 Probability observation is of type R1, R2 or R3

pi_s1, pi_s2, pi_s3 Probability observation is of type S1, S2 or S3

pi_1, pi_2 ,..., pi_9 Probability observation belongs to latent class
j = 1, 2, ..., 9

margins can be used with all options described above.

In addition, it is possible to use predict to obtain posterior
probability predictions, a Bayesian two-step classification, and predictors of
latent true earnings. They cannot be used in combination with margins.

pip_r1, pip_r2, pip_r3 Posterior probability observation is of type
R1, R2 or R3

pip_s1, pip_s2, pip_s3 Posterior probability observation is of type
S1, S2 or S3

pip_1, pip_2, ..., pip_9 Posterior probability observation belongs
to latent class i = 1, 2, ..., 9

bclass_r Bayesian classification of observation i into R1,
R2 or R3

bclass_s Bayesian classification of observation i into S1,
S2 or S3

bclass Bayesian classification of observation i into latent class
j = 1, 2, ..., 9

star, [replace surv_only] Obtains estimates for latent true
earnings e_i, combining information from the adminstrative and survey data.
Following the methods of Rohwedder and Wansbeek (2012) that they illustrated
using estimates from Kapteyn and Ypma (2007), this command obtains 7 predictors
of e_i, as default, using the declared variable name as prefix. All new
variables are created as type double.

Option replace replaces the contents of the variables if they
already exist in memory.

Option surv_only requests prediction of the latent variable
assuming you only have access to survey data.

Description

ky_fit has three types of post-estimation command.

First, you can use estat to produce reports about the
error probabilities, analytical variance and covariance matrices, and
reliability statistics.

Analytical variances and reliability statistics are unavailable if an
error probability is a function of covariates. In this case, the command
reports reliability statistics using simulated data. Using a sufficiently large
number of replications should produce statistics identical to those derived
using the analytical formulas.

Second, you can use margins to obtain marginal effects with
respect to the latent and analytical moments associated with the
previously-fitted model.

Third, you can use predict to make predictions for a larger set of
statistics of interest, including posterior probabilities, and Bayesian
classifications.

See Jenkins and Rios-Avila (2021a, 2021b, 2021c) for details.

Examples

For examples, please see do-file "ky_example.do".

Stored results

estat pr_t [pr_j pr_sr pr_all] stores the following in r():

matrix

r(bpi) contains point estimates for the associated probability.
It may include the unconditional/average error-type probability, class
probability (j = 1, ..., 9), observation type probability
(R1, R2, R3, S1, S2, S3).

r(Vpi) contains point estimates of the variance covariance matrix
of the associated probabilities. It may include unconditional/average
error-type probabilities, latent class probabilities, or observation type
probabilities.

If error probabilities are not expressed as functions of covariates,
estat rel stores the following in r():

scalar

r(pi_?) contains estimates of the probabilities associated
with error types (? = s, r, w, v).

r(pi_s#), r(pi_r#) contains estimates of the probabilities
of observation types (R1, R2, R3, S1, S2, S3)

r(pi_#) contains estimates of latent class probabilities.

r(rel#_?) contains two (# = 1, 2) relibility statistics for survey
and administrative data (? = s, r).

matrix

r(bpi) contains point estimates for the associated probabilities.

r(Vpi) contains point estimates for the variance-covariance matrix
of the associated probabilities.

r(mmsum) contains the unconditional mean, and conditional and
unconditional of the latent variables e_i, n_i, w_i and t_i.

r(rel) contains the analytical variance of r and s,
the covariance with the latent true earnings e_i, and two reliability
statistics

If estat reliability is used with covariates in the error
probabilities or the sim option, the command stores the following in
r():

scalar

r(N_reps) number of replications.

macro

r(rngstate) random-number state used.

r(seed) contains the seed used for simulations.

matrix

r(rel) contains the analytical variance of r and s,
the covariance with the latent true earnings e_i, and two reliability
statistcs.

If estat xirel is used, the following are stored in r():

scalar

r(N_reps) number of replications.

macro

r(rngstate) random-number state used.

r(seed) seed used for simulations.

matrix

r(mbv) simulated statistics for all 'e_i' predictions.

References

Jenkins, S. P. and Rios-Avila, F. (2021a).
Measurement error in earnings data: replication of
Meijer, Rohwedder, and Wansbeek’s mixture model
approach to combining survey and register data,
Journal of Applied Econometrics, online first.
https://doi.org/10.1002/jae.2811

Jenkins, S. P. and Rios-Avila, F. (2021b).
Finite mixture models for linked survey and administrative data: estimation and
post-estimation. IZA Discussion Paper, forthcoming.
https://www.iza.org/publications/dp
For submission to The Stata Journal.

Jenkins, S. P. and Rios-Avila, F. (2021c).
Reconciling reports: modelling employment earnings and measurement errors
using linked survey and administrative data.
IZA Discussion Paper, forthcoming. https://www.iza.org/publications/dp

Kapteyn, A. and Ypma, Y. A. (2007). Measurement error and misclassification: a
comparison of survey and administrative data.
Journal of Labor Economics 25 (3): 513-551.
https://www.journals.uchicago.edu/doi/abs/10.1086/513298

Meijer, E., Rohwedder, S. and Wansbeek T. (2012). Measurement error in
earnings data: using a mixture model approach to combine survey and register data.
Journal of Business & Economic Statistics 30 (2): 191-201.
https://www.tandfonline.com/doi/abs/10.1198/jbes.2011.08166

Authors

Stephen P. Jenkins

Department of Social Policy

London School of Economics and Political Science

Houghton Street, London WC2A 2AE, UK

Email: s.jenkins@lse.ac.uk

Fernando Rios-Avila

Levy Economics Institute of Bard College

Annandale-on-Hudson, NY 12504-5000, USA

Email: friosavi@levy.org