In many research areas like economics, sociology, and public health, we often deal with survey answers or ratings that are ordered but not numerical like people choosing from “Strongly Disagree” to “Strongly Agree.” To study how these kinds of answers relate to other factors, researchers usually use models like the ordered probit or ordered logit.

However, a common and serious problem in these studies is endogeneity. This happens when one of the key factors we’re studying is related to something unobserved (like a hidden variable or error), which can lead to wrong or biased results. This issue can come from missing variables, measurement mistakes, or when two things affect each other at the same time.

To solve this, researchers often use a method called Instrumental Variables (IV). This method works only if the instruments (extra variables used to fix the problem) are truly unrelated to the hidden errors. When we have more than one instrument, we can test whether they are valid using special statistical tests. But for models with ordinal outcomes and ordinal endogenous variables, these tests don’t work well or are not available.

This paper tries to fix that gap. My goal is to create a reliable test to check if the instruments are valid in models where both the outcome and the key variable are discrete and ordered. I do this by combining three advanced techniques.

First, I use the Control Function (CF) or Two-Stage Residual Inclusion (2SRI) method. This means I model the endogenous variable in the first stage and include the residuals in the second stage to correct for endogeneity.

Second, I use the Generalized Method of Moments (GMM) to test whether the instruments are truly exogenous. If they are, they should not be related to the errors in the corrected model.

Third, I apply Bootstrap Inference to improve the accuracy of the test results, especially when the sample size is small or the data is discrete.

My main contribution is this new testing method that combines CF, GMM, and bootstrap. It gives researchers a practical tool to check if their instruments are valid in complex but common situations. I show through simulations that my test works well, and I also provide software (like in Stata or R) and a real-world example to help others use it.

For the full-length manuscript, please go through this link: https://www.pubtexto.com/pdf/?a-robust-test-for-instrument-exogeneity-in-ordinal-response-models-with-endogenous-regressors-a-cfgmmbootstrap-approach