R help - Sep 2022 - How to simulate data where the covariate has large non-zero covariance with the residual and fourth moments of regressors may not exist?

Dear All,

I am writing to ask how to simulate data where the covariate has a
large-non-zero covariance with the model residual and/or the regressors do not
have finite fourth moments for regression analysis.

I want to do some empirical monte-carlo simulations for continuous dependent
variable, binary dependent variable, ordinal, categorical dependent variables
that demonstrate loss of consistency when the covariate has a covariance
non-zero with the residual for a future possible teaching project and for my own
sanity to believe that instrumental variable estimator from Econometrics
improves level-one fixed effects estimates. A source on stack-exchange with 15
votes says that when the finite fourth moments of regressors do no exist, the
estimate of variance is non-consistent,
https://stats.stackexchange.com/questions/16381/what-is-a-complete-list-of-the-usual-assumptions-for-linear-regression?noredirect=1&lq=1.

Best regards,
John