Explaining correlations
26 November 2003
It is common knowledge in statistics that the existence of a correlation does not necessarily imply the existence of a cause-and-effect relationship. Even when it does, the direction of the relationship is not always apparent. In their eagerness to announce conclusions, some researchers forget this.
In an article in Morgan Stanley's Global Economic Forum on 24 November, Karin Kimbrough stated that, contrary to conventional wisdom, a strong equity market is likely to lead to currency depreciation. This conclusion was based on the existence of a negative correlation between monthly excess stock returns and currency returns in the G10 markets.
While the negative correlation may be a statistical fact, the conclusion actually proposed is not warranted. One could easily argue instead that currency depreciation leads to a more competitive economy, which sets the stage for improved corporate performance and results in strong equity performance in anticipation. Or that both currency depreciation and strong equity performance are the result of lower interest rates.
In some circumstances, a strong stock market performance may induce capital inflow, which in turn leads to currency appreciation, resulting in a positive correlation. A good example of this was in the late 1990s, when both the US dollar and stock market appreciated strongly. So the dynamics involved between the stock market and the currency exchange rate are not so straightforward.
Determining the cause-and-effect relationship between two variables is easier when the cause leads the effect by a relatively clear interval. For example, interest rate cuts are followed months later by economic recovery (although recent experience shows that even this relationship should not be taken for granted). The problem comes when the interval is indistinct, or inconsistent, or when other variables occasionally intrude into the relationship and upsets the correlation -- for example, in the late 1990s, when rising risk aversion caused capital to be diverted from emerging economies into the US, driving up both the stock market and the US dollar simultaneously, and turning the normally-negative correlation into a positive one.
Compared to the hard sciences, economists tend to rely more on statistics because experiments are difficult to conduct in their realm of study. In this regard, correlation analysis is an important tool in their trade. But the art of using statistics is to understand its limitation. Statistics is reputed to be deceiving, but that is only because users allow themselves to be deceived.
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