What Are the Benefits of High-Frequency Data for Fixed Effects Panel Models?

Abstract

High-frequency panel data sets, where outcomes and regressors are observed at a daily or hourly frequency, are increasingly available in environmental and resource economics. To understand the potential gains from these richer data sets, this paper compares fixed effects estimators using high-frequency data with those using temporally aggregated data. We provide a set of conditions under which both estimators are consistent for the same parameter. Three departures from these conditions are (1) response heterogeneity at the high-frequency dimension, (2) differential response to high- and low-frequency variation in the regressor, and (3) nonlinearities in the relationship between the high-frequency outcome and regressor. Under these alternative conditions, the two estimators converge to different probability limits. In general, we recommend that empirical researchers think carefully about the features of the “true” high-frequency outcome equation to understand the effects of high-frequency data and temporal aggregation. We illustrate our results using an application to the energy-temperature relationship.