How Large is the Demand for Money at the ZLB? Evidence from Japan
This paper estimates a money demand function using Japanese data from 1985 to 2017, which includes the period of near-zero interest rates over the last two decades. We compare a log-log specification and a semi-log specification by employing the methodology proposed by Kejriwal and Perron (2010) on cointegrating relationships with structural breaks. Our main finding is that there exists a cointegrating relationship with a single break between the money-income ratio and the interest rate in the case of the log-log form but not in the case of the semi-log form. More specifically, we show that the substantial increase in the money-income ratio during the period of near-zero interest rates is well captured by the log-log form but not by the semi-log form. We also show that the demand for money did not decline in 2006 when the Bank of Japan terminated quantitative easing and started to raise the policy rate, suggesting that there was an upward shift in the money demand schedule. Finally, we find that the welfare gain from moving from 2 percent inflation to price stability is 0.10 percent of nominal GDP, which is more than six times as large as the corresponding estimate for the United States.
There is no consensus about whether the interest rate variable should be used in log or not when estimating the money demand function. For example, Meltzer (1963), Hoffman and Rasche (1991), and Lucas (2000) employ a log-log specification (i.e., the log of real money balances is regressed on the log of the nominal interest rate), while Cagan (1956), Lucas (1988), Stock and Watson (1993), and Ball (2001) employ a semi-log form (i.e., the log of real money demand is regressed on the level of the nominal interest rate). The purpose of this paper is to specify the functional form of money demand using Japanese data covering the recent period with nominal interest rates very close to zero.