11.1 Specification of Money Demand Functions

Major central banks stress the importance of money growth analysis and of a stable money demand function for monetary policy purposes. The Deutsche Bundesbank, for example, has followed an explicit monetary targeting strategy from $ 1975$ to $ 1998$, and the analysis of monetary aggregates is one of the two pillars of the European Central Bank's (ECB) monetary policy strategy. Details about these central banks' monetary policy strategies, a comparison and further references can be found in Holtemöller (2002). The research on the existence and stability of a money demand function is motivated inter alia by the following two observations: (i) Money growth is highly correlated with inflation, see McCandless and Weber (1995) for international empirical evidence. Therefore, monetary policy makers use money growth as one indicator for future risks to price stability. The information content of monetary aggregates for future inflation assessment is based on a stable relationship between money, prices and other observable macroeconomic variables. This relationship is usually analyzed in a money demand framework. (ii) The monetary policy transmission process is still a ``black box'', see Mishkin (1995) and Bernanke and Gertler (1995). If we are able to specify a stable money demand function, an important element of the monetary transmission mechanism is revealed, which may help to learn more about monetary policy transmission.

There is a huge amount of literature about money demand. The majority of the studies is concerned with industrial countries. Examples are Hafer and Jansen (1991), Miller (1991), McNown and Wallace (1992) and Mehra (1993) for the USA; Lütkepohl and Wolters (1999), Coenen and Vega (1999), Brand and Cassola (2000) and Holtemöller (2004b) for the Euro area; Arize and Shwiff (1993), Miyao (1996) and Bahmani-Oskooee (2001) for Japan; Drake and Chrystal (1994) for the UK; Haug and Lucas (1996) for Canada; Lim (1993) for Australia and Orden and Fisher (1993) for New Zealand.

There is also a growing number of studies analyzing money demand in developing and emerging countries, primarily triggered by the concern among central bankers and researchers around the world about the impact of moving toward flexible exchange rate regimes, globalization of capital markets, ongoing financial liberalization, innovation in domestic markets, and the country-specific events on the demand for money (Sriram; 1999). Examples are Hafer and Kutan (1994) and Tseng (1994) for China; Moosa (1992) for India; Arize (1994) for Singapore and Deckle and Pradhan (1997) for ASEAN countries.

For Indonesia, a couple of studies have applied the cointegration and error-correction framework to money demand. Price and Insukindro (1994) use quarterly data from the period 1969:1 to 1987:4. Their results are based on different methods of testing for cointegration. The two-step Engle and Granger (1987) procedure delivers weak evidence for one cointegration relationship, while the Johansen likelihood ratio statistic supports up to two cointegrating vectors. In contrast, Deckle and Pradhan (1997), who use annual data, do not find any cointegrating relationship that can be interpreted as a money demand function.

The starting point of empirical money demand analysis is the choice of variables to be included in the money demand function. It is common practice to assume that the desired level of nominal money demand depends on the price level, a transaction (or scaling) variable, and a vector of opportunity costs (e.g., Goldfeld and Sichel; 1990; Ericsson; 1999):

$\displaystyle (M^*/P) = f(Y,R_1,R_2,...),$ (11.1)

where $ M^*$ is nominal money demand, $ P$ is the price level, $ Y$ is real income (the transaction variable), and $ R_i$ are the elements of the vector of opportunity costs which possibly also includes the inflation rate. A money demand function of this type is not only the result of traditional money demand theories but also of modern micro-founded dynamic stochastic general equilibrium models (Walsh; 1998). An empirical standard specification of the money demand function is the partial adjustment model (PAM). Goldfeld and Sichel (1990) show that a desired level of real money holdings $ MR_t^*=M_t^*/P_t$:

$\displaystyle \ln MR_t^* = \phi_0 + \phi_1 \ln Y_t + \phi_2 R_t + \phi_3 \pi_t,$ (11.2)

where $ R_t$ represents one or more interest rates and $ \pi_t=\ln(P_t/P_{t-1})$ is the inflation rate, and an adjustment cost function:

$\displaystyle \textrm{C} = \alpha_1\left( \ln M_t^*-\ln M_{t}\right)^2 + \alpha...
...M_t - \ln M_{t-1} \right) + \delta\left( \ln P_t - \ln P_{t-1}\right)\right\}^2$ (11.3)

yield the following reduced form:

$\displaystyle \ln MR_t = \mu\phi_0 + \mu\phi_1\ln Y_t + \mu\phi_2 R_t + (1-\mu)\ln MR_{t-1} + \gamma\pi_t,$ (11.4)

where:

$\displaystyle \mu=\alpha_1/(\alpha_1+\alpha_2)\qquad\textrm{and}\qquad\gamma = \mu\phi_3+(1-\mu)(\delta-1).$ (11.5)

The parameter $ \delta$ controls whether nominal money ($ \delta=0$) or real money ( $ \delta=- 1$) adjusts. Intermediate cases are also possible. Notice that the coefficient to the inflation rate depends on the value of $ \phi_3$ and on the parameters of the adjustment cost function. The imposition of price-homogeneity, that is the price level coefficient in a nominal money demand function is restricted to one, is rationalized by economic theory and Goldfeld and Sichel (1990) propose that empirical rejection of the unity of the price level coefficient should be interpreted as an indicator for misspecification. The reduced form can also be augmented by lagged independent and further lagged dependent variables in order to allow for a more general adjustment process.

Rearranging (11.4) yields:

$\displaystyle \Delta\ln MR_t$ $\displaystyle =$ $\displaystyle \mu\phi_0+\mu\phi_1\Delta\ln Y_t + \mu\phi_1\ln Y_{t-1} + \mu\phi_2\Delta R_t$  
    $\displaystyle + \mu\phi_2 R_{t-1} - \mu\ln MR_{t-1} + \gamma\Delta\pi_t + \gamma\pi_{t-1}$  
  $\displaystyle =$ $\displaystyle \mu\phi_0-\mu\left(\ln MR_{t-1}-\phi_1\ln Y_{t-1}-\phi_2 R_{t-1} - \frac{\gamma}{\mu}\pi_{t-1}\right)$  
    $\displaystyle + \mu\phi_1\Delta\ln Y_t + \mu\phi_2\Delta R_t + \gamma\Delta\pi_t.$ (11.6)

Accordingly, the PAM can also be represented by an error-correction model like (11.6).