RDP 8903: The Relationship Between Financial Indicators and Economic Activity: Some Further Evidence 2. Background

Early work for the U.S. by Friedman and Schwartz (1963) suggested that turning points in the money stock preceded turning points in nominal income. This work was extremely influential, though a similar study for the U.K. (Friedman and Schwartz (1982)) came in for trenchant criticism from Hendry and Ericsson (1983), an example of how far econometric methodology had advanced in two decades. The monetary theory of nominal income popularised by Friedman was also embodied in econometric models of the “St Louis” tradition, such as Andersen and Jordan (1968) and Andersen and Carlson (1970), where economic activity was explained (in part) by lags of a monetary aggregate.

There was also some interest in Australia in monetary aggregates and activity. Sheppard (1972), Sharpe (1975) and Davis and Lewis (1977) all found evidence for money leading real activity. Boehm (1983), in a study of the business cycle since 1948, found that M1, M3 and bank lending all led his “reference cycle”.

Some studies used simple regression analysis to test the hypothesis that money leads income, but did not actually test the alternative hypothesis, that income leads money. This approach is potentially misleading, especially when dealing with this type of macroeconomic data. Most economic time series are autocorrelated. Where there is a relationship between two variables, this means that lags of one variable will frequently be correlated with the current value of the other. Further, the order can be reversed, often with equal statistical (and theoretical) validity.

For example, suppose m is money and y income, and e_t and u_t are uncorrelated with each other and with their own lagged values, and that will, in all likelihood, show a significant estimate for β, since β will be picking up the effect of γ and α. But to conclude from this that m_t−1 causes y_t, or even leads it in a strict sense, is unwarranted.

Then a regression such as

Sims (1972) introduced a more general testing procedure in an attempt to distinguish more clearly between the alternative hypotheses. If m_t and y_t were treated as a vector, X_t = [m_t y_t]

then the vector autoregression

where A is a matrix of coefficients, (L) denotes the lag operator and u_t is now a 2x1 vector of residuals, becomes the basic building block of the methodology. In simple language, both m_t and y_t are regressed on lags of themselves and lags of the other variable. Two hypotheses are tested: (i) that the coefficients on lags of m are jointly zero in the equation explaining y, and (ii) that the coefficients on lags of y are jointly zero in the equation explaining m. If (i) can be rejected, but (ii) cannot, then this is taken to be evidence of “Granger-causality”^[2] from m to y.

The test for “causality” is harder to pass in this case, since lags of money have to add information for predicting current income not already present in lags of income itself in order for it to be concluded that money leads income.

Sims (1972) was able to conclude (for U.S. data) that money did indeed lead income on this basis. Sims' finding, however, has not been universal.

Using similar methodology, Williams, Goodhart and Gowland (1976) found evidence of “Granger-causality” from income to money for the U.K. For Canada, Sharpe and Miller (1975) found that money led activity, but Barth and Bennett (1974) and Auerbach and Rutner (1978) found that undirectional “causation” could not be established. Sarlo (1979) found that, for Canada, the question of whether money led income depended on the exchange-rate regime: money only led for periods of floating exchange rates. Suzuki, Kuroda and Shirakawa (1988) reported that money led activity in Japan for the 1967–1987 period. For Australia, this sort of approach was used in Bullock, Stevens and Thorp (1988), where the tentative conclusion was that monetary aggregates do not, on the whole, lead measures of economic activity.

More doubt was cast over Sims' results when later studies found that the test outcomes were sensitive to model specification. Sims (1980) added interest rates to the models of money and income, and found that there was no longer strong support for money leading income. Other authors have overturned or restored the original result, with conclusions usually depending on model specification.

In many cases, these conclusions turn on how the data are detrended. Questions of econometric practice dominate this issue; these questions are taken up briefly below.

The aim of present paper is to review the tentative conclusions drawn in BMS, by applying more rigorous statistical techniques to a similar dataset. A series of vector autoregressions are estimated and tests conducted to determine whether “Granger-causal” relationships exist between the variables.

Footnote

So-named after C.W.J. Granger, who suggested the techniques (see Granger (1969)). Note that the term “causality” is used in a technical sense here. It is a short-hand way of denoting statistical significance in these tests, which help establish certain stylised facts about the data, but does not necessarily imply causality in the strict sense. [2]