*! version 1.1.1

Title

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 Y(t) = U(t) + V(t) where U(t) is an unobserved permanent component that follows the unit-root process U(t) = U(t-1) + W(t) and V(t) is an unobserved transitory component that follows the semiparametric ARMA(p,q) process V(t) = r(1)V(t-1) + ... + r(p)V(t-p) + G(e(t),...,e(t-q)).
The command takes p + 2q + 2 periods of y(t) as input and estimates the mean, standard deviation, skewness, and kurtosis of the permanent component U(t) and transitory component V(t). In order to estimate these statistics for time period t,
a user should use y(t-p-q)...y(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.