Hi Jesus,
Thanks for your answer. I did what you’ve suggested. It works for rbc_mod.mod but not for rbc_indivisible_mod.mod. I still get the same identical second moment for both c and y_l. When I check the latter code, there is only one small difference. In the model set up, LHS of second equation is not divided by (1-l) as in the rbc_mod.mod code. When I fix this, everything is fine. So the basic RBC model is the same as the RBC model with indivisible labor (using the same parameters). Am I right?

the indivisible labor model is different from the canonical RBC model and the difference is in the second equation. Check the original Hansen paper to understand why it so.
When you look at the second equation, you will also undrestand that consumption and labor productivity are perfectly correlated because one is propotional to the other.