Question in Testing Joint Inequality

[Peiyu Yuan]

Dear all,

I've been trying to use the supermodularity approach to check the pairwise complementarities between innovations.
My question is about testing joint inequality in STATA.

In the supermodularity approach, there is complementaritiy if C (1, 1) – C (0, 1) ≥ C (1, 0) – C (0, 0), where the binary variables indicate whether a firm conducts a type of innovation.
To test joint inequality,recent studies follow Kodde and Palm’s approach (1986) and use Wald test. They use inequality in their null hypothesis: C (11XX) – C (01XX) - C (10XX) + C (00XX) ≥ 0

The problem is that the test command, which is for Wald test, in STATA doesn't allow joint inequality, so I can only test joint equality in my null hypothesis: C (11XX) – C (01XX) - C (10XX) + C (00XX) = 0
My Stata code looks like:

 test (C1111 – C0111  - C1011 - C0011 = 0) (C1110 – C0110  - C1010 - C0010 = 0)  (C1101 – C0101  - C1001 - C0001 = 0)  (C1100 – C0100  - C1000 - C0000 = 0)  
  
  chi2     (   4) = 1.57
  Prob > chi2 = 0.8137

Currently, I run test command for Wald test after the xtprobit command.

I'm looking for a way to do this:

test (C1111 – C0111  - C1011 - C0011 >= 0) (C1110 – C0110  - C1010 - C0010 >= 0)  (C1101 – C0101  - C1001 - C0001 >= 0)  (C1100 – C0100  - C1000 - C0000 >= 0)

I wonder if you could let me know how to perform Wald test for multiple inequality constraints (joint hypotheses).

Also, I've check the FAQ: "How can I perform a one-sided test?"
https://www.stata.com/support/faqs/s...-coefficients/
But this only applies to single hypothesis, not joint hypothesis.

[Javad Feizabadi]

Hi all,
I have also the same inquiry. How to test joint inequality hypotheses? Anyone can help?!

[Md Shahiduzzaman]

Hello friends, I am having the same issue, e.g., testing joint inequality in Stata in post-estimation, can anyone please help?

[Joro Kolev]

Standard hypothesis testing is ill equipped for testing null hypotheses involving inequalities. To my knowledge there is no joint inequalities test in Stata.

As OP says, we can find a workaround for the case where we are testing a single hypothesis, by testing the null of equality but adjusting the rejection region to disregarding outcomes having the "wrong sign."

If I were in your place and I have joint inequalities to test, I would test them one by one, and then would apply a Bonferroni or Sidak multiple comparisons adjustment to the p-value, to control for the overall size of the test.

[Sneha Thayyil]

I'm late to this discussion, but was looking up the supermodularity approach to check the pairwise complementarities between variables myself.
About testing joint inequalities - maybe Stata's testnl (https://www.stata.com/manuals/rtestnl.pdf) can help? The AI answer also suggests trying lincom.

I am facing a different issue, of wanting to use the supermodularity approach for continuous variables. I guess I would need to define 'High' vs. 'Low' values, though any alternative perspective on this would be much appreciated.

[Sneha Thayyil]

As an addition to my post above, as I can no longer edit it - the solution to the issue of testing inequality constraints to use the supermodularity approach, seems to be beyond Stata. testnl does not help, I didn't try lincom in the end as it didn't seem to be a straightforward way to achieve the desired outcome. An R package does help - https://cran.r-project.org/web/packa...r/ic.infer.pdf.
If there is a direct Stata parallel to this that I have not found, any information would be most appreciated.

Best,
Sneha