Abstract
In applied econometric literature, the causal inferences are often made based on temporally aggregated or systematically sampled data. A number of theoretical studies have pointed out that temporal aggregation has distorting effects on causal inference and systematic sampling of stationary variables preserves the direction of causality. This paper examines the issue in detail by plugging in theoretical cross covariances into the limiting values of least squares estimates in a VAR framework. The asymptotic distributions of the estimates of systematically sampled process are expressed in terms of the cross covariances of the disaggregated process. An extensive Monte Carlo study is conducted to examine small sample results. Quite contrary to the stationary case, this paper shows that systematic sampling of integrated series may induce spurious causality. In particular, systematic sampling induces spurious bi-directional Granger causality among the variables if the uni-directional causality runs from a non-stationary series to either a stationary or a non-stationary series. On the other hand, systematic sampling preserves the uni-directional causality among the variables if the uni-directional causality runs from a stationary series to either a stationary or a non-stationary series. It is observed that in general the most distorting causal inferences are likely at low levels of sampling intervals where the order of sampling-span just exceeds the actual causal lag. At high levels of systematic sampling, causal information concentrates in contemporaneous correlations. An empirical exercise illustrates the relative usefulness of the results further.
Highlights
The use of highly temporally aggregated and systematically sampled data for causal inference is quite common in the applied econometric literature
Φ2,21 and φ1,12 at the 5% level of significance are reported in panel B of Table 1. It is clear from the results reported in panel B of Table 1 that the systematic sampling induces spurious bidirectional Granger causality when the underlying data generating process is VAR(2) regardless of order of integration
The results show that the only case where the direction of Granger causality is preserved is when all variables are stationary
Summary
The use of highly temporally aggregated and systematically sampled data for causal inference is quite common in the applied econometric literature. Breitung and Swanson (2002) examine how the spurious instantaneous relations are induced from Granger causal relationships due to temporal aggregation and systematic sampling in a VAR framework. Using the VAR(1) system in (12) with φ11 = 0 and φ22 = 0, Breitung and Swanson (2002) and Ericsson et al (2001) examined the effect of temporal aggregation on contemporaneous regression coefficient for m = 2 and observed that this coefficient could be positive, negative, or zero We generalize their result for the case of systematic sampling for any m. It can be shown that if the one-sided causality runs from a white noise series (in differences) to a differenced stationary series in the basic disaggregated form systematic sampling will not produce a spurious feedback relationship even if d1 = 1. The results are consistent with Breitung and Swanson (2002)
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