A Two-Period Decision Model for Central Bank Digital Currencies and Households

Abstract

Central bank digital currencies (CBDCs) give rise to many possibilities including those of negative interest rates. A two-period decision model is presented between one central bank and one representative household. The central bank applies the Taylor (1993) rule to choose its interest rate. The household allocates its resources strategically to production, consumption, CBDC holding, and non-CBDC holding. The results are determined analytically and illustrated numerically by varying 19 parameter values. Interesting novelties of the article are that the central bank may choose negative CBDC interest rates when the household holds far more CBDC than non-CBDC, for low inflation rates, low real interest rates, low household’s potential production, low weight assigned to inflation in the Taylor (1993) rule, high target inflation rate, and high household’s production parameter. That usually causes the household to decrease its CBDC holding and increase its non-CBDC holding, production and consumption. The central bank may increase its CBDC interest rate to compete with an increasing non-CBDC interest rate if the household’s transaction efficiencies for CBDC and non-CBDC increase, or the household’s transaction efficiency for consumption decreases. Shocks to production, inflation and interest rates are analyzed.

Comparative Analysis of Households and Digital Currencies for the US, China and Russia

“…The model predicts that Russia should choose the CBDC interest rate 6.82%, which is slightly above its empirical interest rate 6.75%. Compared to the benchmark in G. Wang and Hausken (2022), Russia's high CBDC interest rate 6.82% induces the household to hold slightly more CBDC and earn slightly higher utility, and hold slightly less non-CBDC and produce and consume slightly less.…”

“…The article extends G. Wang and Hausken (2022) in a series of two articles by comparing a decision model with the empirics for the US, China and Russia. In period 1 the central bank chooses positive or negative interest rate.…”

“…Whereas the benchmark in G. Wang and Hausken (2022) assumed the inflation rate 3% and the target inflation rate 2%, the US's October 2021 empirical inflation rate is 6.2%, with a target 2% inflation rate. The model predicts and quantifies how the US should choose a substantially higher CBDC interest rate 7.56% than its empirical interest rate 0.125%, in order to suppress the high inflation rate.…”

“…This article is the second in a series of two articles. The first article, G. Wang and Hausken (2022), builds a decision model with a central bank applying the Taylor (1993) rule and a representative household choosing strategically, and compares with a plausible benchmark solution. This second article compares with the empirics for the US, China and Russia.…”

A Generalized Interest Rates Model with Scaling

“…money supply rules (Ascari and Ropele, 2013;Auray and Fève, 2003;Schabert, 2005;Srinivasan, 2000), McCallum rule Razzak (2003), Friedman rule (Srinivasan, 2000), etc. The literature also links monetary policy to macroeconomics (Clarida et al, 2000;Schabert, 2009;Wijngaard and Van Hee, 2021;Woodford, 2001), to the Phillips (1958) curve (Wang and Hausken, 2022a), adopts the Taylor (1993) rule to design decision models (Wang and Hausken, 2022b), and builds dynamic stochastic general equilibrium models (Ferrari Minesso et al, 2022;Oh and Zhang, 2020).…”