The Return of the Liquidity Effect: A Study of the Short-Run Relation Between Money Growth and Interest Rates

Questions & answers

Q1. What two competing views does the paper test against each other, and how are they distinguished empirically?

“These two views are separated by a stylized fact. The liquidity effect explains a negative correlation between short-run movements in money growth and interest rates, whereas the anticipated inflation effect explains a positive correlation” (Introduction). Under the liquidity effect, a rise in money growth leads agents to bid up bond prices to shed excess money balances, temporarily depressing real (and nominal) rates until the higher money growth eventually shows up as inflation (attributed to a “classic exposition” in Friedman, 1968); under the anticipated-inflation view, money growth has no effect on real rates and simply signals higher future inflation, so nominal rates rise immediately. Cochrane states the paper’s headline finding at the outset: “I present evidence of a negative short-run correlation between money growth and interest rates, which I interpret as evidence that the liquidity effect dominates the anticipated inflation effect” (Introduction).

Q2. Why does Cochrane restrict his sample to the October 1979-November 1982 nonborrowed-reserve-targeting period?

Because prior liquidity-effect studies used data from periods when “the Federal Reserve Board smoothed interest-rate fluctuations,” which creates simultaneous-equations bias from feedback running from interest rates back to money growth (Section 1.1). By contrast, during nonborrowed-reserve targeting “it is likely that there is less feedback from interest rates to money growth in the short-run spectral windows” studied, making the reduced-form correlation between money growth and interest rates more interpretable as running from money to rates rather than the reverse.

Q3. What is the band-pass (spectral-window) filtering method, and why use it instead of estimating the full distributed lag directly?

The filter is a two-sided weighted moving average constructed to pass only cycles within a chosen frequency band – for example, a window covering periods of 12 to 26 weeks or 26 to 52 weeks – while blocking both very-high-frequency noise (announcement effects, lagged-reserve-accounting effects) and low-frequency movements (the long-run Fisher effect) (Sections 1.2, 1.3). Cochrane shows formally that an OLS regression of filtered interest rates on filtered money growth is “a consistent estimate of the real part of the frequency response of the underlying distributed lag” specifically within that frequency band (Section 2.2, eq. 2.12), so that regressions on filtered data amount to a restriction that the true distributed-lag coefficients are approximately constant across the chosen band – letting the researcher “estimate the effects in which we are interested without estimating the effects in which we are not interested” (Section 2.2). The approach generalizes the low-pass filters Lucas (1980) used to demonstrate long-run monetary neutrality and Summers (1983) used to study the long-run Fisher effect, and Cochrane notes it is formally equivalent to Engle’s (1974, 1978) bandspectrum regression.

Q4. What do the filtered regressions show, and in which windows and maturities is the liquidity effect strongest?

“The liquidity effect is most pronounced in the 26-52-week window for the three-month rate and in the 12-26-week window for the 20-year bond rate” (Section 2.3, Table 1), with negative money-growth/interest-rate correlations appearing across several of the spectral windows examined for both maturities. Cochrane specifically flags the 20-year bond result as unexpected: “it is surprising that the coefficient for the 20-year bond rate is negative. This suggests that market participants expect the negative impact on short rates to last a long time” (Section 2.3) – i.e., the liquidity effect’s influence appears to be priced into rates well beyond the short end of the term structure. (The precise numerical coefficients and standard errors in Table 1 were extracted via OCR from a scanned source and are not fully legible in this summary’s source text, so specific magnitudes from that table are not quoted here; the qualitative pattern of results described above is clearly stated in the paper’s prose.)

Q5. How does Cochrane test for reverse feedback from interest rates to money growth, and what does he find?

Following Geweke (1982), Cochrane implements a conventional regression test (per Feige and Pearce, 1979) for feedback on the filtered data, relying on the fact that “nonintersecting spectral windows are independent,” so that feedback outside a given window does not contaminate the regression estimated inside it (Section 2.3). He reports that “none of the tests rejected the absence of feedback” in the windows studied, supporting the interpretation of the estimated correlations as running from money growth to interest rates rather than the reverse, at least within the nonborrowed-reserve-targeting sample.

Q6. How sensitive is the finding to the choice of sample period, and what does that sensitivity suggest?

Applying the same graphs and regressions to the surrounding 1976-79 and 1982-86 subsamples, Cochrane reports that “the negative correlation is almost absent in these samples, reflecting the acknowledged short-run interest rate targeting by the Federal Reserve Board” (Section 2.3). This supports his identification strategy: the negative money-growth/interest-rate correlation shows up specifically during the 1979-82 episode when the Fed was not actively smoothing rates, consistent with the concern that Fed rate-smoothing in other periods masks or biases the underlying liquidity-effect relationship.

Q7. What does the paper’s simple theoretical model (Section 3) say about when the liquidity effect should dominate the anticipated-inflation effect, or vice versa?

Three factors determine which effect dominates: the persistence of money-growth changes, the lag from money growth to inflation, and the extent to which money-growth changes are anticipated. “The anticipated inflation effect should dominate if money growth is a good predictor of future money growth (if money growth is essentially a random walk), if the lag from money growth to inflation is short, and if changes in money growth are largely anticipated. The liquidity effect should dominate if short-term changes in money growth are typically not interpreted as signals that long-term policy has changed, if the lag from money to inflation is long, and if changes in money growth are largely unanticipated” (Introduction, formalized in Section 3). The model further shows that as money growth becomes more persistent, the anticipated-inflation correlation strengthens, and that this effect is “greatest for short maturities,” declining roughly as the inverse of bond maturity (Section 3.1).

Q8. What does Cochrane conclude the evidence implies, and what limits does he place on the interpretation of his reduced-form results?

He concludes that the finding “adds weight to the views that money-growth changes were largely unanticipated, that money growth was a poor predictor of future money growth, that inflation followed money growth with a long lag, and that real interest rates did vary in response to money-growth changes” (Conclusion). But he is explicit about the limits of a reduced-form approach: “the reduced-form correlation between money growth and interest rates documented in this article suggests that there is a liquidity effect, but it does not quantitatively answer the structural question [of] how much and for how long…interest rates decline if you raise money growth today”; he also flags that residual feedback from interest rates to money growth may remain within the spectral windows studied, and that the anticipated-inflation effect could be present but masked by a larger liquidity effect, since the reduced-form correlation does not separate the distinct effects of anticipated versus unanticipated money growth (Conclusion).