Consistent High-Frequency Calibration

Economic models are meant to provide a framework to describe real-world economic activities. In principle, how well a model performs this task can be evaluated by how close the model's simulated activities track the observed ones. A necessary first step in simulating a model is to choose values for the model's parameters in accordance with actual economic data. A fundamental problem in economic modelling, however, is that actual economic data are sampled at time intervals that are typically longer than the decision intervals of actual economic agents. One popular resolution of this problem is to constrain the length of the decision intervals of theoretical economic agents to be equal to the length of the actual data-sampling intervals. This widely adopted approach makes it feasible to directly calibrate theoretical models to the observed data, but it can introduce substantial biases in the models' empirical performance, as demonstrated by recent research that has allowed the decision intervals to be shorter than the data-sampling intervals. This alternative, high-frequency modelling approach, however, has brought with itself a fundamental issue that direct calibration of the models' parameters is no longer feasible. In response, researchers have employed a simple, yet ad hoc, rule to transform commonly chosen lower-frequency parameter values (which can be calibrated directly from the available data) to their high-frequency counterparts. We show in this paper that this simple transformation rule has three major drawbacks. First, it produces internal inconsistencies in steady- state equilibrium conditions. Second, it is sometimes at odds with microeconomic evidence. And third, it can result in inaccurate log- linear approximations to the models' true equilibrium solutions by worsening the fit of both the transition dynamic coefficients and the point of approximation itself. We present here an alternative, coherent transformation rule for calibrating high-frequency models that directly addresses these three shortcomings. We then use our consistent transformation rule to calibrate high-frequency versions of two well- known economic models and show how it improves these models' empirical performance.