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

[Sun, John]

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