*! version 1.1.1

Title

npss -- Executes nonparametric estimation of heteroskedastic state space models.

Syntax

npss
y1
y2
[if] [in]
[, skedastic(varname) tp1(real) tp2(real)]

Description

npss executes nonparametric estimation of conditionally heteroskedastic state space models based on
Botosaru and Sasaki (2018).
Consider a state space model y(it) = u(it) + v(it), where y(it) is observed (e.g., earnings), u(it) is unobserved (e.g., permanent component of earnings), and v(it) is unobserved (e.g., transitory component of earnings), with the process u(it) = u(it-1) + w(it). Taking y(i1) and y(i2) as input, the command nonparametrically estimates and draws the density functions of u(i1) and v(i1). Taking y(i1), y(i2) and y(i3) as input, the command also nonparametrically estimates and draws the conditional skedastic function of u(i2) given u(i1), e.g., as a measure of heterogeneous risks in permanent component of earnings.

Options

skedastic(varname) tells the command to estimate the skedastic function of u(i2) given u(i1). The input in this option is y3, the observed variable in the third time period after the first two, y1 and y2. Not calling this option tells the command to estimate only the density functions of u(i1) and v(i1).

tp1(real) sets the scale-normalized tuning parameter for estimation of the density functions. The default value is tp1(4).

tp2(real) sets the scale-normalized tuning parameter for estimation of the skedastic function. The default value is tp2(2).

Examples

(y2006, y2008, & y2010: earnings in 2006, 2008, & 2010, respectively.)

Estimation of the density functions of u(2006) and v(2006), using y2006 and y2008 as input:

. use "example_2006_2008_2010.dta"

. npss y2006 y2008

Estimation the conditional skedastic function of u(2008) given u(2006), in addition to the density functions of u(2006) and v(2006), using y2006, y2008 and y2010 as input:

. use "example_2006_2008_2010.dta"

. npss y2006 y2008, skedastic(y2010)

Stored results

npss stores the following in r():

Scalars

r(N) observations

Macros

r(cmd) npss

Matrices

r(U) density f(U) of U

r(V) density f(V) of V

r(S) conditional skedastic function sigma(U)

Reference

Botosaru, I. and Y. Sasaki. 2018. Nonparametric Heteroskedasticity in Persistent Panel Processes: An Application to Earnings Dynamics. Journal of Econometrics, 203 (2), pp. 283-296.
Link to Paper.

Authors

Irene Botosaru, University of Bristol, Bristol, UK.

Yuya Sasaki, Vanderbilt University, Nashville, TN.