Effects of temporal aggregation and systematic sampling on model dynamics and causal inference

Abstract

Many economic time series are available only in temporally aggregated or systematically sampled forms depending on whether they are flow or stock variables. It was known in the theoretical literature that temporal aggregation might distort causal relationships between variables while systematic sampling would preserve the causal direction. These findings are, however, limited to stationary series. This thesis re-examines these issues under both stationary and non-stationary scenarios and provides a quantitative assessment of the distortions by deriving the limiting values of least squares estimates and t statistics under temporal aggregation and systematic sampling. It is observed that in general the most distorting causal inferences occur at low levels of temporal aggregation. At high levels of aggregation, causal information concentrates in contemporaneous correlations. Quite contrary to the stationary case, this study finds that systematic sampling of integrated series may induce spurious causality. Since it is unavoidable to use temporally aggregated or systematically sampled data in causal inferences, the best approach to take is to formulate causality-testing procedures within a co-integrating framework. It is well established that integration and co-integration are invariant to temporal aggregation and systematic sampling. Co-integration also implies Granger causality though the direction is unknown. This study formulates a causality-testing procedure within an error correction format and fills a very important gap that existed in the literature.