Time Aggregation and the Contradictions with Causal Relationships: Can Economic Theory Come to the Rescue?

Abstract

The literature on causality takes contradictory stands on the direction of causal relationships based on whether one uses temporally aggregated or systematically sampled data. As an example, using the relationship between a nominal target and the instrument used to achieve it, we show that one can fall back upon the data in itself, and analyse it from the perspective of economic theory, not only as a source of second opinion to econometric theories and Monte Carlo simulations, but also to draw proper conclusions regarding the form of the causal relationship that might be actually existing in the data.

Notes

1. See Section 2 for further details.

2. One must realize that if θ₁, θ₂,....θ_n are the roots of the non-aggregated autoregressive process, then are the roots of the aggregated process, where m is the order of aggregation (Abeysinghe and Gulasekaran, 2004a).

3. CPIX is CPI excluding mortgage rates .

4. See Ludi and Ground (2006) for an excellent summary of the history of monetary policy in South Africa.

5. The discussion in this section depends heavily on Gupta (2004).

6. Note an alternative way of looking at the analysis is formulating a restricted model of the following nature: and then designing the F-statistic_q,,n-k =[SSE_R-SSE_U)*{n- k}]/[(SSE_U)*q] by recovering the error sum of squares from the unrestricted, SSEU and the restricted, SSER versions of the model concern. Note q is the number of restrictions imposed with n = sample size and k = number of parameters estimated in the unrestricted model.

7. Such a linkage is particularly important in economics, since it characterizes the long-run equilibrium alignment that persists beyond the short-run dynamic adjustment.

8. The need to run the cointegration equations in both the directions arises from the study by Hendry (1986), who points out that both directions are equally valid apriori.

9. Stability of the VARs was ensured since no roots were found to lie outside the unit circle.

10. The optimal lag lengths for the estimated VARs were determined by the Akaike Information Criteria (AIC). Interestingly, the fact that different lag lengths were obtained in the estimated VARs of INFL- CPIX and the repo rate derived under alternative forms of aggregation, is not surprising, and has been noted before in the literature by Marcellino (1999).

11. As with the cointegration tests, the optimal lag lengths for Granger Causality tests between INFL- CPIX and REPO-AGG and INFL-CPIX and REPO-SYS were determined by the AIC, obtained by estimating the corresponding bivariate VARs. The test suggested the use of 8 lags for the model with the aggregated data, and 4 for the systematically sampled data.