Stata Command: cdecompose
Stata Command: cdecompose.ado
The Stata output displayed below summarizes estimates of the mean, standard deviation, skewness and kurtosis of each of the permanent component Uit of earnings and the transitory component Vit of earnings for U.S. men at the age of 40 who have strong labor force attachment. The base model is the canonical permanent-transitory model (Hu, Moffitt, and Sasaki, 2019) with ARMA(2,1) transitory process. Both the permanent earnings and transitory earnings exhibit negative skew, implying that the tails are on the poorer side. The distributions of the permanent and transitory earnings are also leptokurtic, implying that they have a heavier tail than the normal distributions. These results illustrate features of permanent earnings inequality in the U.S. The results can be produced by the STATA command cdecompose as follows:
Installation:
. ssc install cdecompose
Usage:
. cdecompose y37 y38 y39 y40 y41 y42, p(2) q(1)
Help:
. help cdecompose
Reference: Hu, Y., R. Moffitt, and Y. Sasaki (2019) Semiparametric Estimation of the Canonical Permanent‐Transitory Model of Earnings Dynamics. Quantitative Economics, 10 (4), pp. 1495-1536. Paper.
cdecompose -- Executes estimation of canonical permanent-transitory state space models.
Syntax
cdecompose y1 y2 ... yT [if] [in] [, p(real) q(real) delta(real) nboot(real)]
Description
cdecompose executes estimation of canonical permanent-transitory state space models based on Hu, Moffitt, and Sasaki (2019). Consider the state space model Yi,t = Ui,t + Vi,t where Ui,t is an unobserved permanent component that follows the unit-root process Ui,t = Ui,t-1 + Wi,t and Vi,t is an unobserved transitory component that follows the semiparametric ARMA(p,q) process Vi,t = ρ1 Vi,t-1 + ... + ρp Vi,t-p + G(εi,t, ..., εi,t-q). The command takes p + 2q + 2 periods of yi,t as input and estimates the mean, standard deviation, skewness, and kurtosis of the permanent component Ui,t and transitory component Vi,t. In order to estimate these statistics for time period t, a user should use yi,t-p-q...yi,t+q+1 as input.
Options
p(real) sets the AR order p of the ARMA(p,q) model of transitory process. The default value is p(1).
q(real) sets the MA order q of the ARMA(p,q) model of transitory process. The default value is q(1).
delta(real) sets a precision parameter for computing numerical derivative in approximating derivatives of empirical characteristic functions for moment estimation. The default value is delta(5).
nboot(real) sets the number of bootstrap iterations for approximating standard errors. The default value is nboot(1000).
Examples
(y37...y42 earnings at ages 38...42, respectively)
Estimation at age 40 under the ARMA(1,1) transitory process:
. cdecompose y38 y39 y40 y41 y42
Estimation at age 40 under the ARMA(2,1) transitory process:
. cdecompose y37 y38 y39 y40 y41 y42, p(2) q(1)
(Note that it is a common practice in the earnings dynamics literature that y37...y42 are defined as the residual of earnings on observed attributes.)
Stored results
cdecompose stores the following in e():
Scalars e(N) observations e(p) AR order e(q) MA order
Macros e(cmd) cdecompose e(properties) b V
Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators e(rho) AR coefficients
Functions e(sample) marks estimation sample
Reference
Hu, Y., R. Moffitt, and Y. Sasaki. 2019. Semiparametric Estimation of the Canonical Permanent‐Transitory Model of Earnings Dynamics. Quantitative Economics, 10 (4), pp. 1495-1536. Link to Paper.
Authors
Yingyao Hu, Johns Hopkins University, Baltimore, MA. Robert Moffitt, Johns Hopkins University, Baltimore, MA. Yuya Sasaki, Vanderbilt University, Nashville, TN.