*! version 1.1.1

Title

testex -- Executes a statistical test of the exclusion restriction of an instrumental variable (IV).

Syntax

testex
y
x
z
[if] [in]
[, numboot(real)]

Description

testex executes a statistical test of the exclusion restriction of an instrumental variable (IV) based on
D'Haultfoeuille, Hoderlein, & Sasaki (2021).
The command takes as input a scalar outcome variable y, a scalar endogenous variable x that is continuous, and a scalar instrumental variable z.
If the instrument is not binary, then the program transforms the original instrument into a binary one.
The output of the command includes the p-value of the test and the indicators of whether the test rejects the null hypothesis at various levels of statistical significance.
The program gives a caution when there is no crossing of conditional CDFs required by Assumption 5 in
D'Haultfoeuille, Hoderlein, & Sasaki (2021).

Option

numboot(real) sets the number of multiplier bootstrap iterations to compute the critical value of the test statistic. The default value is numboot(1000).

Examples

y outcome variable, x endogenous variable, z instrumental variable

Test of the exclusion restriction:

. testex y x z

Setting the number of multiplier bootstrap iterations to 2000:

. testex y x z, numboot(2000)

Including additive controls:

. reg y controls

. predict residy, resid

. reg x controls

. predict residx, resid

. reg z controls

. predict residz, resid

. testex residy residx residz

Stored results

testex stores the following in r():

Scalars

r(N) observations

r(nb) Number of multiplier bootstrap iterations

r(bw) Bandwidth

r(KS) KS statistic

r(p) P-value

Macros

r(cmd) testex

Reference

D'Haultfoeuille, X., S. Hoderlein, & Y. Sasaki. 2021. Testing and Relaxing the Exclusion Restriction in the Control Function Approach.
Journal of Econometrics, forthcoming.
Link to Paper.

Authors

Xavier D'Haultfoeuille, CREST-ENSAE, Palaiseau, France.

Stefan Hoderlein, Emory University, Atlanta, GA.

Yuya Sasaki, Vanderbilt University, Nashville, TN.