Evaluating money supply as a linear leading-index baseline

Start with a reconstruction test

The leading composite is a published blend of monthly series chosen to sample several economic processes rather than a single market price. It is built to sample six economic processes through eleven monthly components. Of those eleven components, only the money-supply series measured as M2 is identified as directly government-controlled.

Editorial view: before reading that blend as a broad dashboard, scale the series, fit an explicit linear baseline on the single controlled input, and ask how much of the published index that input already recovers.

Put both series on a z-score scale

Monthly composite and money supply observations from 1948 through 1992 produced 540 paired points. Both series were then converted to z-scores. A z-score is a scale-free transform that subtracts a series mean and divides by its standard deviation so series on unlike units can be compared directly.

Do not drop the time order

The z-score cumulative distributions of the two series look similar, but that comparison removes the original time order. A time-ordered line plot of the same z-scores shows the two series moving in a similar pattern. That pattern is then checked with a scatter diagram from a simple linear regression of money supply on the composite.

Read the linear baseline first

A linear baseline is an explicit one-variable regression used as the first quantitative comparison before adding extra components or higher-order terms. In that sample the simple linear fit has a correlation of 0.9798, described as money supply accounting for about 98 percent of the composite's variability. A residual plot is supplied for that specification. A residual plot is a diagnostic chart of leftover error after a fitted line, used to inspect structure the chosen specification did not capture.

A higher-order fit is a check, not the starting point

A fifth-order polynomial regression raises the correlation to 0.9953, with a corresponding residual plot. The evaluation argues that the composite can be recovered to a reasonable degree from the money-supply regression alone, while stating that the association is not evidence that money-supply changes cause composite changes.

Editorial view: keep the one-variable linear baseline in place so extra components and higher-order terms have to beat a named comparison. A closer polynomial fit can show leftover structure, but it does not replace the first controlled test.