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Impact of Payment Technology on Seasonality of Currency in Circulation: Evidence from the USA and India

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Abstract

This paper examines the impact of payment technology on seasonality in currency in circulation. We specify that total transaction in a period follows a Gompertz distribution over time and extend the standard Baumol–Tobin model to obtain a nonlinear expression of currency growth. In contrast to linear dummy variable models that reflect fixed seasonality, our theoretical results reflect gradually decaying seasonal coefficients over time and suggest that in the long-run, growth-in currency holdings would not be seasonal but would be affected by interest rate shocks only. Empirical applications of the model for the USA and India reveal its superior performance compared to linear dummy variable models with fixed seasonality.

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Notes

  1. In India, the total stock of currency increased by Rs. 1229.2 billion between the financial years 2011–2012 and 2012–2013. Expenditure incurred on security printing (note forms) during 2012–2013 (July–June) was Rs. 28.72 billion (RBI Annual Report, 2012–2013, p. 126). Thus, RBI spent about 2.34 % of every Rupee for its production. The same expenditure was 0.05 % of Indian GDP in 2012–2013.

  2. For example, in the obtained functional form of Baumol (1952), currency is positively related to the square roots of transaction need and the cost for such a transaction and is negatively related to the square root of interest rate that proxies the opportunity cost of holding currency.

  3. In the marketing literature, applications of sigmoid curves have a long history, e.g., BASS (1969). Mahajan et al. (1990) provides a review of this literature.

  4. See Tilley (1992) for detailed discussion on lognormal interest rate as a stochastic process.

  5. In a stinging criticism, Kirman (1992) calls the assumption of a representative agent ‘fatally flawed’ (p. 132).

  6. For example, the often cited study of Hall (1978) in the context of consumption function assumed a representative agent framework.

  7. For instance Cabrero and de España (2002) modelled and forecasted the daily currency in circulation forecasting results for Euro area by using two major approaches, i.e. the ARIMA based approach and structural time series (STS) approach. They conclude that the best forecasting model is a combination of the ARIMA and STS models. The reason for this is argued by the fact that certain seasonal patterns may not be completely captured by a linear structure.

  8. Note that zero currency growth does not imply zero currency holdings. It only implies a stable level of currency holding as long as interest rates are unchanging.

  9. Though \(D_t\) and \(M_t\) are discrete variables. We define \(D_t^*\) and \(M_t^*\), where \(D_t^*\) is a continuous variables in Akaike (1974) and Reddy (1998) and \(M_t^*\) is continuous in Akaike (1974) and Cassino et al. (1997). We also define \(h^*(D_t^*,M_t^*,F_t) \). One may approximate \(h^*(D_t^*,M_t^*,F_t)\) with respect to \(D^{*}\) and \(M^{*}\). It may be noted that the values of the \(h^*(D_t^*,M_t^*,F_t)\) for integer values of \(D^{*}\) and \(M^{*}\) would closely correspond to similar h() values.

  10. The financial year in the USA and India starts with \(1\mathrm{st}\) October and \(1\mathrm{st}\) April respectively.

  11. We also tried to capture the impact of Easter along with its lags and leads but the coefficient were found to be insignificant.

  12. The values of \(e^{-b*t}\) for the USA and India are calculated as 0.9992 and 0.9994 when \(t=1\) and 0.1950 and 0.2950 when \(t=1981\) respectively.

  13. For brevity, we are not reporting the ACF and PACF of residuals. It can be made available on request.

  14. Currency substitution occurs when the residents of a currency use a foreign currency in parallel to or instead of the domestic currency (Feige 2011). The USA dollar is one of the currency used as a substitute worldwide officially and unofficially equally (Baliño et al. 1999; Bogetic 2000). For detailed discussion on the use of USA dollar as a currency substitution abroad see Hellerstein and Ryan (2011).

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  1. Business Environment Area, Indian Institute of Management, Lucknow, India

    Kaushik Bhattacharya & Sunny Kumar Singh

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  1. Kaushik Bhattacharya
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Correspondence to Sunny Kumar Singh.

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Bhattacharya, K., Singh, S.K. Impact of Payment Technology on Seasonality of Currency in Circulation: Evidence from the USA and India. J. Quant. Econ. 14, 117–136 (2016). https://doi.org/10.1007/s40953-015-0024-1

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