*! version 1.1.1

Title

npeivreg -- Executes estimation of nonparametric errors-in-variables (EIV) regression and construction of its uniform confidence band.

Syntax

npeivreg
y
x1
x2
[if] [in]
[, numx(real) domain(real) cover(real) tp(real)]

Description

npeivreg executes estimation of nonparametric errors-in-variables (EIV) regression and construction of its uniform confidence band based on
Kato and Sasaki (2019).
In addition to the dependent variable y, the command requires as input two measurements, x1 and x2, of the unobserved independent variable x with classical measurement errors,
e1 = x1 - x
and
e2 = x2 - x,
respectively. The output consists of a deconvolution estimate of the nonparametric EIV regression g(x) of y on x, and its uniform confidence band over a domain of x.

Options

numx(real) sets the number of grid points of x for estimation of the nonparametric EIV regression g(x) and its uniform confidence band. The default value is numx(20).

domain(real) sets the domain of estimation of the nonparametric EIV regression g(x) and its uniform confidence band. The default value domain(2) defines the domain as +/- 2 standard deviations of x.

cover(real) sets the nominal uniform coverage probability for the uniform confidence band of the nonparametric EIV regression g(x). The default value cover(0.95) constructs a 95% uniform confidence band.

tp(real) sets the scale-normalized tuning parameter. The default value is tp(0.2).

Examples

(y dependent variable, x1 1st measurement of unobserved independent variable x, x2 2nd measurement of unobserved independent variable x)

Construction of a 95% uniform confidence band:

. npeivreg y x1 x2

Construction of a 90% uniform confidence band:

. npeivreg y x1 x2, cover(0.90)

Constructing a uniform confidence band on a grid points of 100 points in the domain corresponding to +/- 3 standard deviations of x:

. npeivreg y x1 x2, numx(100) domain(3)

(huq050 number of doctor visits, bmi_exam clinically measured BMI, bmi_self self reported BMI)

Nonparametric EIV regression of the number of doctor visits on BMI, accounting for measurement errors in clinically measured BMI and/or self reported BMI:

. use "doctor_visit_male50.dta"

. npeivreg huq050 bmi_exam bmi_self, domain(1.5)

Stored results

npeivreg stores the following in e():

Scalars

r(N) observations

Macros

r(cmd) npeivreg

Matrices

r(x) vector of x

r(g) vector of g(x)

r(lower) confidence band (lower boundary)

r(upper) confidence band (upper boundary)

Reference

Kato, K. and Y. Sasaki. 2019. Uniform Confidence Bands for Nonparametric Errors-in-Variables Regression. Journal of Econometrics, 213 (2), pp. 516-555.
Link to Paper.

Authors

Kengo Kato, Cornell University, Ithaca, NY.

Yuya Sasaki, Vanderbilt University, Nashville, TN.