The Heckman model also uses the followingassumptions:

(ε,u)~ N(0,0,σ2ε, σ2u,ρεu)                                          

That is both error terms are normallydistributed with mean 0, variances as indicated and the error terms arecorrelated where ρεuindicates the correlation coefficient.

(ε,u)is independent of X and Z                                    

The error terms are independent of bothsets of explanatory variables.