Accounting for Expectational and Structural Error in Binary Choice Problems: A Moment Inequality Approach∗

Many economic decisions involve a binary choice for example, workers choosing between education and labor force participation, consumers determining whether to buy a good, firms selecting whether to enter a market or whether to adopt a new technology. In such settings, agents’ choices often depend on imperfect expectations of the future payoffs from their decision (expectational error) as well as on factors that are unobserved to the econometrician (structural error). In this paper, we show that expectational error made by rational expectations agents is statistically equivalent to classical measurement error, and propose a novel moment inequality estimator that accounts for both expectational and structural error. Both with simulated data and Chilean firm level customs data, we illustrate the identifying power of our inequalities and the biases arising from ignoring either source of error. We use this export data to estimate the different costs exporters face when entering a new market.