*! version 1.1.1

Title

testout -- Executes diagnostic testing of outliers by statistical tests of the bound first- and second-moment conditions for credible point estimates and credible standard errors, respectively.

Syntax

testout
y
x1 x2 ...
[if] [in]
[, iv(varlist) cluster(varname) aweight(varname) pweight(varname) k(real) alpha(real) maxw(real) prec(real)]

Description

testout executes diagnostic testing of outliers by statistical tests of the bounded first- and second-moment conditions for consistency and root-n asymptotic normality based on
Sasaki & Wang (2021).
The command takes as input a scalar dependent variable y and a list of independent variables x1, x2, ...
An iv is an option, and x1 is treated as an endogenous variable if the option iv is invoked.
The output of the command includes the p-values of the tests and the indicators of whether the tests reject the null hypotheses at the significance level alpha.
If the test rejects the null hypothesis of the bounded first-moment condition for consistency, then the point estimates of reg (or ivreg when the option iv is invoked) are unreliable.
If the test rejects the null hypothesis of the bounded second-moment condition for root-n asymptotic normality, then the standard errors of reg (or ivreg when the option iv is invoked) are unreliable.

Options

iv(varlist) sets instrumental variable(s).
If this option is not invoked, then the command executes the outlier tests for the OLS (reg).
If this option is invoked, then the command executes the outlier tests for the 2SLS (ivreg) where the first independent variable x1 is treated as an endogenous variable instrumented by the list of variables included in iv.

cluster(varname) sets a clustering variable.
If this option is not invoked, then the command does not cluster observations.

aweight(varname) sets analytic weights.
If this option is not invoked, then the command does not impose analytic weights.

pweight(varname) sets probability weights.
If this option is not invoked, then the command does not impose probability weights.

k(real) sets the number of extreme order statistics to be used for the tests.
This number has to be an integer no smaller than 3.
Not invoking this option will automatically set k to the five percent of the sample size.

alpha(real) sets the significace level of the statistical tests.
The default value is alpha(0.05).

maxw(real) sets the maximum value of the set of the tail index in the composite alternative over which the likelihood function in the numerator of the likelihood ratio test statistic is integrated with respect to the Lebesgue measure.
The default value is maxw(2).

prec(real) sets the precision of approximating the null distribution of the test statistic by simulations.
Setting this number to a smaller value results in more accurate tests and p-values at the expense of a longer execution time of the command.
The default value is prec(0.00025).

Examples

Consider the following regression:

. use "tip_chicago.dta"

. regress wh_pop_change indicat min* income vacant rent single public

The outlier tests for this regression can be implemented by:

. testout wh_pop_change indicat min* income vacant rent single public

We can repeat these lines for another city:

. use "tip_washington.dta"

. regress wh_pop_change indicat min* income vacant rent single public

. testout wh_pop_change indicat min* income vacant rent single public

Stored results

testout stores the following in r():

Scalars

r(N) observations

r(G) cluster size

r(k) number of extreme order statistics

r(alpha) level of statistical significance

r(pval1) p-value for the test of consistency

r(pval2) p-value for the test of root-n normality

Macros

r(cmd) testout

r(mtd) reg or ivreg

r(test1) result of the test of consistency

r(test2) result of the test of root-n normality

Reference

Y. Sasaki & Y. Wang. 2021. Diagnostic Testing of Finite Moment Conditions for the Consistency and Root-N Asymptotic Normality of the GMM and M Estimators,
Journal of Business & Economic Statistics, forthcoming.
Link to Paper.

Authors

Yuya Sasaki, Vanderbilt University, Nashville, TN.

Yulong Wang, Syracuse University, Syracuse, NY.