Conroy Lau and Alexander Torgovitsky

Table of Contents

• Introduction
• Installation
• Syntax
• Stored results
• Examples
• Help, Feature Requests and Bug Reports
• References

mivcausal is a command that tests the hypothesis about the signs of the two stage least squares (2SLS) weights. As described in proposition 5 of Mogstad, Torgovitsky and Walters (2020), the 2SLS estimand can be written as a positively-weighted average of LATEs under certain conditions. This module tests whether the weights are positive when there are two binary instruments and one binary treatment using the following tests:

1. Bonferroni test
2. Cox and Shi (2019) test (henceforth, CS test)
3. Mintest
4. Romano, Shaikh and Wolf (2014) test (henceforth, RSW test)
5. Intersection-union test (henceforth, IUT)

Please see appendix C of Mogstad, Torgovitsky and Walters (2020) for more details.

The mivcausal module can be installed in Stata by typing one of the following commands in Stata:

1. Install mivcausal from GitHub:

net install mivcausal, from("https://raw.githubusercontent.com/conroylau/mivcausal/master")

2. Install mivcausal from SSC:

ssc install mivcausal

The syntax of the mivcausal command is as follows:

mivcausal [(instd = instr1 instr2) indepvars] [if] [in] [, seed(#) precision(#) mtdraws(#) rsw(reps = #) vce(vcetype)]

The [(instd = instr1 instr2) indepvars] part is optional if it is used as a post-estimation command after ivregress 2sls. If not, this part has to be specified, where

• instd is the binary treatment.
• instr1 and instr2 are the two binary instruments.
• indepvars are the independent variables.

If the binary treatment or instruments do not equal to either 0 or 1, the module will run the test by creating a temporary variable that assigns the larger value as 1 and the smaller value as 0.

In addition, the mivcausal command has the following options:

• seed specifies the seed used to simulate the data in the Mintest and the starting seed used in the bootstrap procedure of the RSW test. The default is seed(1).

• precision specifies the number of decimal places in the p-value. This has to be a positive integer. The default is precision(3).

• mtdraws specifies the number of draws in the simulations for the Mintest. This has to be a positive integer. The default is mtdraws(10000).

• rsw specifies whether the RSW test is applied and the number of bootstrap replications in the RSW test. By default, the RSW test is not applied because of longer computational time. To apply the RSW test, specify the option rsw(reps = x) where x is the number of bootstrap replications. This has to be a nonnegative integer. Specifying the option as rsw() (i.e. without specifying the number of replications) will run the RSW test with 1,000 bootstrap replications.

• vce(vcetype) specifies the type of standard error reported. Currently, the mivcausal command supports robust (robust) or clustered standard errors (cluster(varlist)).

After applying the mivcausal command, the following are stored in r():

Scalars

Macros

Consider the sample data with one covariate (X), one binary treatment (D), two binary instruments (Z1 and Z2) and one outcome variable (Y).

First, open the data set:

use mivcausal.dta

Then, the tests can be run as follows:

mivcausal (D = Z1 Z2) X, rsw(reps = 1000)

This gives:

Results from mivcausal:
------------------------------------------------------------------------------
  Null hypothesis         |  Test                             |  p-value
--------------------------+-----------------------------------+---------------
  All weights positive    |  Bonferroni                       |  .038
                          |  Cox and Shi (2019)               |  .038
                          |  Mintest                          |  .037
                          |  Romano, Shaikh and Wolf (2014)   |  .025
--------------------------+-----------------------------------+---------------
  Some weights negative   |  Intersection-union test          |  .981
------------------------------------------------------------------------------
Parameters:
* Precision (decimal places) = 3
* Number of draws in Mintest = 10000
* Number of bootstraps in the Romano, Shaikh and Wolf (2014) test = 1000

As described above, the RSW test will be skipped if the following command is run instead.

mivcausal (D = Z1 Z2) X

This gives:

Results from mivcausal:
------------------------------------------------------------------------------
  Null hypothesis         |  Test                             |  p-value
--------------------------+-----------------------------------+---------------
  All weights positive    |  Bonferroni                       |  .038
                          |  Cox and Shi (2019)               |  .038
                          |  Mintest                          |  .037
--------------------------+-----------------------------------+---------------
  Some weights negative   |  Intersection-union test          |  .981
------------------------------------------------------------------------------
Parameters:
* Precision (decimal places) = 3
* Number of draws in Mintest = 10000

Alternatively, the mivcausal command can be applied as a post-estimation command after ivregress 2sls:

ivregress 2sls Y (D = Z1 Z2) X

Then, the tests can be applied without typing the treatment, instruments and covariates again:

mivcausal, rsw(reps = 1000)

This gives the same output as before, i.e.

Results from mivcausal:
------------------------------------------------------------------------------
  Null hypothesis         |  Test                             |  p-value
--------------------------+-----------------------------------+---------------
  All weights positive    |  Bonferroni                       |  .038
                          |  Cox and Shi (2019)               |  .038
                          |  Mintest                          |  .037
                          |  Romano, Shaikh and Wolf (2014)   |  .025
--------------------------+-----------------------------------+---------------
  Some weights negative   |  Intersection-union test          |  .981
------------------------------------------------------------------------------
Parameters:
* Precision (decimal places) = 3
* Number of draws in Mintest = 10000
* Number of bootstraps in the Romano, Shaikh and Wolf (2014) test = 1000

Please post an issue on the GitHub repository. We are happy to help.

Cox, G. and X. Shi. (2019): "A Simple Uniformly Valid Test for Inequalities," Working paper.

Mogstad, M., A. Torgovitsky, and C. R. Walters: (2020): "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," Working Paper.

Romano, J. P., A. M. Shaikh, and M. Wolf (2014): "A Practical Two-step Method for Testing Moment Inequalities," Econometrica, 82(5), 1979-2002.