STATA-ME-test

Authors : Young Jun Lee and Daniel Wilhelm

This project provides the STATA command dgmtest which implements the test for significance by Delgado and Manteiga (2001) and can be used to test for the presence of measurement error as described in Wilhelm (2018) and Lee and Wilhelm (2018).

Files contained in this package:

• The file dgmtest.ado contains the dgmtest command.
• The file dgmtest.sthlp contains the Stata helpfile for the dgmtest command.
• The files example_DGM2001.ado and simul_DGM2001.do contain the code to replicate the simulations in Delgado and Manteiga (2001).
• The files example_Wilhelm2018.ado and simul_Wilhelm2018.do contain the code to replicate the simulations in Wilhelm (2018).
• The file example.do contains the simple simulation example shown below.

Installation

1. Download the package.
2. Change into the directory containing this package.
3. Use the command dgmtest as described below.

Syntax

The command dgmtest tests the null hypothesis

H0:   E[Y | X, W, Z] = E[Y | X, W]

against the alternative that the null does not hold, where

• Y is a scalar dependent variable
• X and W are vectors of explanatory variables
• Z is a vector of explanatory variables

The vector of explanatory variables, W, may contain elements that enter the conditional expectation in a linear, additively separable fashion. For example, decompose W=(W1,W2) where W1 enters nonseparably and W2 enters in a linear, additively separable fashion,

E[Y | X, W, Z] = f(X,W1,Z) + pi*W2

where f is some function and pi a row-vector of the same dimension as W2. In the presence of variables W2, we apply the test in Delgado and Manteiga (2001) after replacing Y with (Y - pihat*W2), where pihat is Robinson (1988)'s estimator of pi.

Syntax:

dgmtest depvar expvar [if] [in] [, qz(integer) qw2(integer) teststat(string) kernel(string) bootdist(string) bw(real) bootnum(integer) ngrid(integer) qgrid(real)]

where

• depvar is the outcome variable Y
• expvar is a list of variables containing all elements of X, W, and Z. The order of variables in the list should be: X, W, Z)

The options are as follows:

• qz is the dimension of Z (default = 1).
• qw2 is the dimension of W2 (default = 0).
• teststat is the type of test statistic to be used: Cramer-van Mises (CvM, default) or Kolmogorov-Smirnov (KS).
• kernel is the kernel function: biweight, epanechnikov (default), epan2, epan4, normal, rectangle, triangular.
• bw is the bandwidth (default = n^(-1/3q), rule of thumb, where n is the sample size and q the dimension of X1).
• bootnum is the number of bootstrap samples for the computation of the test's critical value (default = 500).
• bootdist is the distribution of the bootstrap multiplier variable: mammen (default), rademacher, uniform.
• ngrid is the number of equally spaced grid points used to compute the supremum of the KS statistic, if that statistic is chosen via the option teststat. The default is 0 which means that the sample serves as the grid.
• qgrid is a number between 0 and 1 to define the min and max values of the grid in the previous option. The min value is the qgrid-quantile and the max value is the (1-qgrid)-quantile. The default is 0 so that in that case the grid ranges from the min to the max value in the sample.

If options are left unspecified, the command runs on the default settings.

Testing for the presence of measurement error

Wilhelm (2018) shows that, under some conditions, the null hypothesis H0 is equivalent to the hypothesis of no measurement error in X. In this context, the variable Z must be excluded from the outcome equation. For example, it could be a second measurement or an instrumental variable. See Wilhelm (2018), Lee and Wilhelm (2018), and the examples below for more details.

Examples

Generate explanatory variables

set obs 200

// true regressor
generate Xstar = runiform()

// measurement error in X
generate etaX = runiform()

// mismeasured regressor
generate X1 = Xstar + 0.5*etaX

// additively linear control variable
generate X2 = runiform()

// measurement error in Z
generate etaZ = runiform()

// second measurement of true regressor
generate Z = Xstar + 0.5*etaZ

// regression error
generate epsilon = runiform()

Generate outcome variable

We generate an outcome in two different ways, in a regression with and without additively separable, linear controls:

// outcome equation without controls
generate Y1 = Xstar^2 + 0.2*Xstar + 0.5*epsilon

// outcome equation with controls
generate Y2 = Xstar^2 + 0.2*Xstar + 0.5*X2 + 0.5*epsilon

Perform the test of no measurement error

Perform the test using default options:

// perform the test of the hypothesis of no measurement error in X1
dgmtest Y1 X1 Z
dgmtest Y2 X1 X2 Z, qw2(1)

Perform the test, choosing the triangular kernel function:

// perform the test of the hypothesis of no measurement error in X1
dgmtest Y1 X1 Z, kernel(triangular)
dgmtest Y2 X1 X2 Z, qw2(1) kernel(triangular)

References

Delgado, M. and Manteiga, W. (2001), "Significance Testing in Nonparametric Regression Based on the Bootstrap", Annals of Statistics, 29(5), p. 1469-1507

Robinson, P. M. (1988), "Root-N-Consistent Semiparametric Regression", Econometrica, 56(4), p. 931-954

Wilhelm, D. (2018), "Testing for the Presence of Measurement Error", CeMMAP Working Paper CWP45/18

Lee, Y. and Wilhelm, D. (2018), "Testing for the Presence of Measurement Error in Stata", working paper available soon