Appendix B: Estimation of Demand Elasticity | RDP 2024-03: Demand in the Repo Market: Indirect Perspectives from Open Market Operations from 2006 to 2020

RDP 2024-03: Demand in the Repo Market: Indirect Perspectives from Open Market Operations from 2006 to 2020 Appendix B: Estimation of Demand Elasticity

Chris Becker, Anny Francis, Calebe de Roure and Brendan Wilson

May 2024

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To estimate the elasticity of demand, we assume the following specification:

(B1)

\ln (Q_{d t}) = β b_{d t} + Δ_{d} + Δ_{t} + ε_{i j t}

where b_dt is a bid rate (as a spread to OIS) and Q_dt is the cumulative quantity bid for at that bid for term d on day t. $Δ_{d}$ and $Δ_{t}$ are term and day fixed effects.

Day fixed effects control for all that affects the quantity bid (for each term) equally in a given day, (e.g. quarter-end effects, the level of exchange settlement balances, risk aversion).

Term fixed effects control for any time-invariant term premia that may exist.

Because of this specification, the coefficient $β$ does not vary across terms or time. Thus, we estimate the price elasticity of demand over a given period as:

η = β \times \hat{b}

where $β$ is estimated using Equation (B1) and all observations over the period and $\hat{b}$ is the mean cut-off rate calculated for the period.

Table B1: Descriptive Statistics and Estimation Output
	Mean cut-off rate as a spread to OIS (bps)	Mean quantity supplied Q_dt ($m)	Estimated elasticity $η$	Response to 1 per cent price change ($m)
2009–14	3.3	1,303	−0.5	7
2016–19	25.7	2,098	−2.9	61
Sources: Authors’ calculations; RBA