A Utility-Maximization Model for the Joint Determination of Response Time and Accuracy in Timed Tests

We propose a utility maximization model for timed tests. In this model, respondents allocate time across items to maximize expected performance subject to a fixed time budget, so response time and accuracy are determined jointly and endogenously. The framework captures the time–accuracy trade-off within and across items and naturally yields the inverted U-shaped relation between time and accuracy observed in data. Using TIMSS data, the model reproduces item-level response times in a low-stakes setting: agreement between observed and predicted times is reasonably high overall, higher for stronger performers, and lower for respondents who finish quickly. We also find evidence of systematic time misallocation and miscalibrated beliefs about item properties during the test. Overall, the model offers a practical tool for analyzing response time data and for understanding respondents' test-taking behavior and strategies.