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 

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