Not just a random forest: Using Bayesian additive regression trees to estimate willingness to pay to protect critical habitat

Abstract We introduce a fully nonparametric estimator to estimate willingness to pay (WTP) using contingent valuation (CV) data. Traditional methods such as the probit model are used because of their roots in utility theory as well as their ease to implement. However, they are limited by their reliance on strict parametric assumptions, such as linearity and the requirement that the researcher pre‐select important covariates. While these methods are widely used, they may fail to capture complex relationships, particularly in situations involving nonlinearity or interactions among variables. This paper introduces Bayesian Additive Regression Trees (BART) as a flexible, nonparametric way to estimate WTP from CV studies. Using a simulation study, we demonstrate that BART is competitive with traditional models under strict data‐generating assumptions. When the underlying data‐generating process is more complex, BART outperforms traditional models and even other machine‐learning models. Moreover, BART automatically incorporates individual heterogeneity into estimation, making it more informative than traditional nonparametric estimators. We illustrate the breadth of the model's benefits with an empirical application estimating WTP to develop an Invasive Species Rapid Response Fund in the Hawaiian Islands. We find WTP distributional differences along the margins of gender, age, and income. We also construct willingness to pay curves out of Monte Carlo Markov Chain (MCMC) draws and calculate posterior means and credible intervals using empirical cumulative distribution functions (CDFs). We find these WTP to be lower than those from the probit. Future natural extensions of BART make this method a compelling alternative for estimating WTP in CV experiments.