Beyond biases: Exploring endogeneity in the allocation function of latent class models for environmental valuation

Despite its implications for parameter estimation, endogeneity is often overlooked in applications of discrete choice modeling. In environmental valuation, research on endogeneity typically focuses on the case when it originates in the utilities of the underlying random utility maximization model rather than in the class allocation probabilities of a latent class model (LCM). This paper addresses that gap by assuming the allocation function of an LCM includes an endogenous latent variable and examining four scenarios: (i) omitting this latent variable, (ii) directly including an endogenous indicator, (iii) using a multiple indicator solution that accounts for endogeneity, and (iv) employing a hybrid choice model. Simulation results reveal that while the allocation function parameters suffer bias in the first two scenarios, they are consistently estimated in the latter two. Notably, willingness to pay estimates remain unbiased in all these scenarios. We support these findings through simulation studies and draw connections to the existing statistical literature. Furthermore, we apply these insights to a case study focusing on seaweed-based renewable energy in the UK.