Revealed Preference Tests of Collectively Rational Consumption Behavior: Formulations and Algorithms

This paper focuses on revealed preference tests of the collective model of household consumption. We start by showing that the decision problems corresponding to testing collective rationality are NP‐complete. This makes the application of these tests problematic for (increasingly available) large(r)‐scale data sets. We then present two approaches to overcome this negative result. First, we introduce exact algorithms based on mixed‐integer programming (MIP) formulations of the collective rationality tests, which can be usefully applied to medium‐sized data sets. Next, we propose simulated annealing heuristics, which allow for efficient testing of the collective model in the case of large data sets. We illustrate our methods by a number of computational experiments based on Dutch labor supply data.