Methods of Investigating Causal Relationships Between Time Series

The paper aims to evaluate two methods which have been used for the purpose of establishing the presence of a causal relationship between a pair of variables. Since the results of exercises of this type have often been inconclusive there is a need to establish what the methods can show about the relationships between variables and under what conditions one method might be able to give more reliable information on a given relationship than the other. The literature in the area of causality and prediction is quite extensive and is surveyed in section two of the paper to put the work reported here in perspective. In the main part of the paper, a relationship between a pair of variables is established using artificially generated data so that the properties of the methods can be abstracted from the properties of the data. Two types of causal relationships appear to be important in economies. The analysis presented here takes both types into account. The first envisages no particular theoretical framework relating the pair of variables being analysed while the second regards the two variables as being related within a theoretical framework. The results obtained suggest the following: (i) neither method is successful in all circumstances; (ii) unless explicit time lags are present between the variables neither method can tell us anything; (iii) the correlation approach can do a reasonable job of picking up the order of a lagged relationship provided the underlying generating process is not too complex. The spectral technique on the other hand cannot indicate the order of the lags but it is more successful than the correlation approach in detecting the presence of a lead or lag relationship when the generating process is allowed to become more complex.