Modeling Deposit Rate Pass-Through with Asymmetric Fed Funds Changes

Summary

The document presents a first-difference regression for studying how deposit rates respond to lagged changes in the Federal Funds Rate. Its interaction term switches on when the rate change is positive, allowing the estimated pass-through to differ between rising-rate and falling-rate periods. The author reports a lower coefficient for falling-rate periods and a larger combined response in rising-rate periods, contrary to the original hypothesis.

The author says the estimates are statistically significant but questions their credibility, notes that adding three lags caused collinearity, and asks whether an error-correction model would be more suitable. The document does not provide a resolution, regression diagnostics, sample details, or evidence that distinguishes a true asymmetric response from model or data problems. It is therefore a useful example of specifying an interaction and interpreting its conditional slope, but not a validated finding about deposit pricing.

Key ideas

• The interaction model allows deposit-rate pass-through to differ when the market rate rises.
• The slope in rising-rate periods is the sum of the base coefficient and the interaction coefficient.
• The reported estimates imply greater pass-through during rate increases than decreases, contrary to the stated hypothesis.
• Adding multiple rate-change lags led to collinearity in the author's model.
• The document raises error-correction modeling as an alternative but does not assess or resolve it.

Tags

# Estimating Product Rate Sensitivity to Market Rate Changes: First Difference With Interactive Variable


# Estimating Product Rate Sensitivity to Market Rate Changes: First Difference With Interactive Variable












I am currently trying to understand and estimate the sensitivity of deposit rate sensitivity to market rate changes. My current model:

$\Delta$$R_t$ $=$ $\alpha$ $+$ $\beta_1$$*$$\Delta$$FFR_{t-1}$$+$$\beta_2$($\Delta$$FFR_{t-1}$$*$$I^+$)

Where

- $\Delta$$R_t$ is the first difference deposit rate

- $\Delta$$FFR_{t-1}$ is the lagged first difference of the Fed Funds Rate

- $I^+$ is the censor variable where if $\Delta$$FFR$$<$ $0$ then $I^+$$=$$0$ otherwise $I^+$$=$$1$

I originally wanted to include 3 lags of FFR, but I run into collinearity problems. Additional, my hypothesis was that in increasing rate environments ( $\Delta$$FFR$ is positive), deposit sensitivity would be less than that in down rate environments ($\Delta$$FFR$ is negative). My results from the model estimate that in an increasing environments my deposit rate sensitivity is much larger than that in down rate environments, results below:

- $\beta_1$ $=$ $.35$

- $\beta_2$ $=$ $.40$

So in downrate environment the deposit rate sensitivity is equal to .35 while in an uprate environment the deposit rate sensitivity is equal to .75. The results are statistically significant, but I'm not convinced by the results. I am wondering if an error correction model is more appropriate in these circumstances? Further, since there is an interactive variable, $\beta_2$($\Delta$$FFR_{t-1}$$*$$I^+$), what is the best way that I fit the regression to my data?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.