In this study, correlation between the error term and regressors associated with the introduction of lag values of the dependent variable affects its current value.
Following Zheng and Henneberry ([2010]), the parameter for the pdf δi represents the covariance between the error term in the budget share equation (4) and the error term of the multivariate probit model.
Where ( {varphi}_{ji}=frac{left {beta X}_i+{gamma}_j{epsilon}_{ji}/{sigma}_jright)}{sqrt{1-{gamma}_j^2}} ), j = 0, 1 with γ j denoting the correlation coefficient between the error term of criterion function, i.e., u i and the errors of outcome functions, i.e., ϵ ji.
Sometimes, however, there are challenges such as the values of H missing in the dataset for some of the observations, correlation between the error term in the model and Z, and non linear interaction between Z and some unobservable factors that causes the effect of Z on H to differ amongst population subjects [25]-[27] [25]-[27]
Failure to reject the null hypothesis of no correlation between the error term and any of the regressors in such a test would suggest that some of the regressors are endogenous, which, in turn, would suggest a failure to properly identify the regression equation.
We focused on two main empirical difficulties in estimating social network effects within reference groups: firstly, that friendship selection is non-random, which leads to correlation between the error term and friend's health, and, secondly, that confounding factors affect all members of the reference group.
Lastly, we vary the level of positive correlation between the error terms in the model estimating the link between external locus of control and NEET status.
With the exception of men at medium-sized firms, the correlation between the error terms in the two equations, ρ, is positive.
They then test for jointness post hoc via hypothesis testing for the correlation parameter (rho) between the error terms of the simultaneous equations.
In this way, it is possible to consider the potential for unobserved heterogeneity that could produce a correlation between the error terms in the two probit models.
Soleimani et al. (2009) showed that the existing auto-correlation between the error terms within each profile affects the performance of the control charts for simple linear profiles.
