# The Correlation Between Money Base Growth and Inflation

I’ve been reading through undergraduate textbooks, trying to figure out where the idea that money base expansion must necessarily manifest itself in higher inflation. In Stephen Williamson‘s macro textbook, he argues that fears of inflation are motivated by the view that eventually, money base expansion will feed into money expansion (box on pp. 432), despite the fact that there is no obvious contemporaneous correlation between the two variables.

I would’ve agreed with that assertion in a world where no interest was paid on reserves (see here for a primer). However, even the M2 to inflation link is less than entirely convincing of a money-inflation link at the short horizon. [1] In any case, here are some scatterplots. First, 3 month changes (in log terms):

Figure 1: 3 month log difference in CPI (all) against 3 month log difference in money base, not seasonally adjusted, 1967M01-2010M10. Source: St. Louis Fed FREDII. Money base is BOGUMBNS.

These are overlapping observations. The observations in the lower left hand side quadrant pertain to period of quantitative easing. The next two graphs eliminate overlapping changes, and then the post-Lehman observations.

Figure 2: Nonoverlapping 3 month log difference in CPI (all) against 3 month log difference in money base, not seasonally adjusted, 1967M01-2010M09. Source: St. Louis Fed FREDII. Money base is BOGUMBNS.

Figure 3: Nonoverlapping 3 month log difference in CPI (all) against 3 month log difference in money base, not seasonally adjusted, 1967M01-2008M06. Source: St. Louis Fed FREDII. Money base is BOGUMBNS.

Note that a positive correlation only shows up in this third figure. However, almost none of the variation in inflation is explained by money base growth.

Professor Williamson appeals to lags as a reason to worry about money base expansion. In the next two graphs, I plot 12 month changes, both contemporaneous, and with money base growth lagged one year.

Figure 4: Nonoverlapping 12 month log difference in CPI (all) against 12 month log difference in money base, not seasonally adjusted, 1967M01-2007M12. Source: St. Louis Fed FREDII. Money base is BOGUMBNS.

Figure 5: Nonoverlapping 12 month log difference in CPI (all) against 12 month log difference in money base, not seasonally adjusted, 1967M01-2007M12. Source: St. Louis Fed FREDII. Money base is BOGUMBNS.

There does appear to be a positive correlation, although the slope coefficient p-value is 0.177, and the adjusted R2 is negative. Even this result is sensitive to slight modifications. If one normalized money base by some scale variable, like industrial production, then essentially none of the variation in inflation is explained by the growth rate of money base.

Figure 6: Nonoverlapping 12 month log difference in CPI (all) against 12 month difference in log ratio of money base, not seasonally adjusted, to industrial production, 1967M01-2007M12. Source: St. Louis Fed FREDII. Money base is BOGUMBNS.

Combine the above with this St. Louis Fed article on the various other national QE episodes, and I still wonder exactly how QE2 is going to lead to high inflation.

Final observation: The data is trying to tell us the relationship is, dropping linearity.

Figure 7: Nonoverlapping 12 month log difference in CPI (all) against 12 month difference in log ratio of money base, not seasonally adjusted, to industrial production, 1967M01-2007M12. Fitted line is locally weighted regression, nearest neighbor, bandwidth=0.3. Source: St. Louis Fed FREDII, and author’s calculations. Money base is BOGUMBNS.

Originally published at Econbrowser and reproduced here with permission.

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