Examining Inferences from Neural Network Estimators of Binary Choice Processes: Marginal Effects, and Willingness-to-Pay

Abstract

To satisfy the utility maximization hypothesis in binary choice modeling, logit and probit models must make a priori assumptions regarding the underlying functional form of a representative utility function. Such theoretical restrictions may leave the postulated estimable model statistically misspecified. This may lead to significant bias in substantive inferences, such as willingness-to-pay (or accept) measures, in environmental, natural resource and applied economic studies. Feed-forward back-propagation artificial neural networks (FFBANN) provide a potentially powerful semi-nonparametric method to avoid potential misspecifications and provide more valid inference. This paper shows that a single-hidden layer FFBANN can be interpreted as a logistic regression with a flexible index function and can be subsequently used for statistical inference purposes, such as estimation of marginal effects and willingness-to-pay measures. To the authors’ knowledge, the derivation and estimation of marginal effects and other substantive measures using neural networks are not available in the economics literature and is thus a novel contribution. An empirical application is conducted using FFBANNs to demonstrate estimation of marginal effects and willingness-to-pay in a contingent valuation and stated choice experimental framework. We find that FFBANNs can replicate results from binary choice models commonly used in the applied economics literature and can improve on substantive inferences derived from these models.