correction framework. The results, however, seem to be contradictory. Price

and Insukindro (1994) use quarterly data from 1969:I to 1987:IV. The results

were based on three di¬erent methods of testing for cointegration. Eagle Grager

method show that there was weak evidence of cointegrating relationship. Fur-

thermore Johansen™s cointegration technique found up to two cointegrating

vectors, but the error correction model (ECM) didn™t ¬nd a signi¬cant rela-

tionship. In contrast, Deckle and Pradhan (1997), who use annual data, do not

¬nd any cointegrating relationship that can be interpreted as money demand

function.

6.2.2 Econometric Speci¬cation of Money Demand

Functions

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, see for

example Goldfeld and Sichel (1990), Ericsson (1999) and Holtem¨ller (2003):

o

(M — /P ) = f (Y, R1 , R2 , ...), (6.1)

where M — is nominal money demanded, P is the price level, Y is real income

(the transaction variable), and Ri are the elements of the vector of opportunity

costs which possibly also includes the in¬‚ation 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, see

106 6 Money Demand Modelling

for example Walsh (1998). An empirical standard speci¬cation of the money

demand function is the partial adjustment model (PAM). (Goldfeld and Sichel,

1990) show that a desired level of real money holdings M Rt = Mt— /Pt :

—

—

ln M Rt = φ0 + φ1 ln Yt + φ2 Rt + φ3 πt , (6.2)

where Rt represents one or more interest rates and πt = ln(Pt /Pt’1 ) is the

in¬‚ation rate, and an adjustment cost function

2 2

C = ±1 [ln Mt— ’ ln Mt ] + ±2 [(ln Mt ’ ln Mt’1 ) + δ (ln Pt ’ ln Pt’1 )] (6.3)

yield the following reduced form

ln M Rt = µφ0 + µφ1 ln Yt + µφ2 Rt + (1 ’ µ) ln M Rt’1 + γπt , (6.4)

where

γ = µφ3 + (1 ’ µ)(δ ’ 1).

µ = ±1 /(±1 + ±2 ) and (6.5)

The parameter δ controls whether nominal money (δ = 0) or real money (δ =

’1) adjusts. Intermediate cases are also possible. Notice that the coe¬cient

to the in¬‚ation rate depends on the value of φ3 and on the parameters of the

adjustment cost function. The imposition of price-homogeneity is rationalized

by economic theory and Goldfeld and Sichel (1990) proposed that empirical

rejection of the unity of the price level coe¬cient should be interpreted as an

indicator for misspeci¬cation. 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 (6.4) yields:

∆ ln M Rt = µφ0 + µφ1 ∆ ln Yt + µφ1 ln Yt’1 + µφ2 ∆Rt

+µφ2 Rt’1 ’ µ ln M Rt’1 + γ∆πt + γπt’1

γ

= µφ0 ’ µ ln M Rt’1 ’ φ1 ln Yt’1 ’ φ2 Rt’1 ’ πt’1

µ

+µφ1 ∆ ln Yt + µφ2 ∆Rt + γ∆πt . (6.6)

6.2 Money Demand 107

Accordingly, the PAM can also represented by an error-correction model like

(6.6).

Since the seminal works of Nelson and Plosser (1982), who have shown that

relevant macroeconomic variables exhibit stochastic trends and are only sta-

tionary after di¬erencing, and Engle and Granger (1987), who introduced the

concept of cointegration, the (vector) error correction model, (V)ECM, is the

dominant econometric framework for money demand analysis. If a certain set

of conditions about the number of cointegration relations and exogeneity prop-

erties is met, the following single equation error correction model (SE-ECM)

can be used to estimate money demand functions:

= ct + ± (ln M Rt’1 ’ β2 ln Yt’1 ’ β3 Rt’1 ’ β4 πt’1 )

∆ ln M Rt

error correction term

k k k k

+ γ1i ∆ ln M Rt’i + γ2i ∆ ln Yt’i + γ3i ∆Rt’i + γ4i ∆πt’i ,

i=1 i=0 i=0 i=0

(6.7)

It can be shown that (6.4) is a special case of the error correction model (6.7).

In other words, the PAM corresponds to a SE-ECM with certain parameter re-

strictions. The SE-ECM can be interpreted as a partial adjustment model with

β2 as long-run income elasticity of money demand, β3 as long-run semi-interest

rate elasticity of money demand, and less restrictive short-run dynamics. The

coe¬cient β4 , however, cannot be interpreted directly.

In practice, the number of cointegration relations and the exogeneity of cer-

tain variables cannot be considered as known. Therefore, the VECM is the

standard framework for empirical money demand analysis. In this framework,

all variables are assumed to be endogenous a priori, and the imposition of a

certain cointegration rank can be justi¬ed by statistical tests. The standard

VECM is obtained from a vectorautoregressive (VAR) model

k

xt = µt + Ai xt’i + ut , (6.8)

i=1

where xt is a (n — 1)-dimensional vector of endogenous variables, µt contains

deterministic terms like constant and time trend, Ai are (n — n)-dimensional

108 6 Money Demand Modelling

coe¬cient matrices and ut ∼ N (0, Σu ) is a serially uncorrelated error term.

Subtracting xt’1 and rearranging terms yields the VECM

k’1

∆xt’1 = µt + Πxt’1 + “i ∆xt’i + ut . (6.9)

i=1

Π and “i are functions of the Ai . The matrix Π can be decomposed into two

(n — r)-dimensional matrices ± and β: Π = ±β where ± is called adjustment

matrix, β comprises the cointegration vectors, and r is the number of linearly

independent cointegration vectors (cointegration rank). Following Engle and

Granger (1987), a variable is integrated of order d, or I(d), if it has to be

di¬erenced d-times to become stationary. A vector xt is integrated of order

d if the maximum order of integration of the variables in xt is d. A vector

xt is cointegrated, or CI(d, b), if there exists a linear combination β xt that is

integrated of a lower order (d ’ b) than xt .

6.2.3 Estimation of Indonesian Money Demand

We use quarterly data from 1990:1 until 2002:3 for our empirical analysis.

The data is not seasonally adjusted and taken from Datastream (gross na-

tional product at 1993 prices Y and long-term interest rate R) and from Bank

Indonesia (money stock M2 M and consumer price index P ). In the follow-

ing, logarithms of the respective variables are indicated by small letters, and

mr = ln M ’ ln P denotes logarithmic real balances. The data is depicted in

¬gure 6.1.

Before the appropriate econometric methodology can be chosen, the stochastic

properties of the variables have to be analyzed. Table 6.1 presents the results

of unit root tests for logarithmic real balances mr, logarithmic real GNP y,