STABLE MONEY DEMAND AND NOMINAL MONEY CAUSALITY … · STABLE MONEY DEMAND AND NOMINAL MONEY CAUSALITY OF OUTPUT GROWTH: A MULTIVARIATE COINTEGRATION ANALYSIS OF CROATIA Dario Cziráky

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STABLE MONEY DEMAND AND NOMINAL MONEY CAUSALITY OF OUTPUT GROWTH: A MULTIVARIATE

COINTEGRATION ANALYSIS OF CROATIA

Dario Cziráky Department of Statistics, London School of Economics (LSE), London, UK

Max Gillman

Department of Economics and Center for Policy Studies, Central European University, Budapest, Hungary

Abstract The paper identifies monetary economic features of the post-transition Croatian economy, with a view towards using inflation rate targeting to reach European Union (EU) inflation targets as required by EU accession. If focuses on the demand for real money balances, the Fisher equation of interest rates, and the effect of nominal money on output, for Croatia over the 1994-2002 period. The real money demand is found to be stable using cointegration techniques after the inclusion of inflation rate in addition to the nominal interest rate. Including the inflation rate ameliorates the failure of the nominal interest rate to move one-for-one with inflation as predicted by the Fisher equation of interest rates, which is found not to hold. In addition a vector error-correction model finds that money grow rates Granger-cause output growth rates, in line with the literature on the negative effect of inflation on growth. With a stable money demand and indications of the negative growth effect of inflation, the targeting of a low inflation rate emerges as a plausible policy for establishing EU monetary accession criteria and for increasing economic growth.

Keywords: Money demand, output-growth, monetary policy, cointegration, inflation, Fisher effect, Granger causality

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1 Introduction The issue of economic growth continues to be prominent, including its study among transition countries (Christoffersen and Doyle, 2000; Coricelli, 1998; Denizer and Wolf, 2000; Kalra and Slok, 1999; Havryltshyn, 2001). One dimension of the growth literature includes the negative effect of money growth and inflation on the output growth rate (Gillman, Harris, and Matyas, 2003; Gillman and Kejak, 2003a,b; Harris and Gillman, 2003). For some advanced transition countries that are soon to accede to the European Union (EU), empirical evidence relatedly supports causality from money and inflation to economic growth (Nakov and Gillman, 2003). Such findings indicate that achieving low inflation, as required by EU accession, plausibly will come with the benefit of higher growth even besides the other possible growth benefits of joining the larger market of the EU. This paper examines what can be expected in Croatia in terms possibly higher growth because of lower inflation, as Croatia converges to the EU inflation criterion. We establish that despite its transition status and relatively short time series availability, Croatia exhibits a stable money demand function, and also the expected causality from money growth rates to output growth rates. The Fisher interest rate relation, however, does not hold, as has been the case with many studies. Hence, on the basis of allowing for the Fisher relation breakdown, we specify the money demand function that proves to be stable. Together these empirical findings support central tenets of a general equilibrium monetary economy with endogenous growth. This leads us to predict that the use of inflation targeting in Croatia will achieve the EU target of low inflation while also contributing to increased growth. The focus of the paper is empirical; a section on the theoretical background below briefly discusses how the empirical results can be viewed relative to certain general equilibrium economies. 1.1 Monetary background and policy debate in Croatia The output growth rate in Croatia rose dramatically after the ending of the 100% inflation of 1993. Since then the inflation rate has trended downwards with an uptick in 1997 and 1999, while the growth rate has averaged 3% with a significant downtick in 1998. In addition, a notable downward trend in money velocity is characteristic for this period, which might be explained by the downward trend in inflation (see e.g. Kontolemis, 2002). Croatian monetary policy since 1994 was based on floating exchange rates and strict monetary discipline in respect to nominal money growth. The monetary policy that the Croatian National Bank (CNB) used to successfully combat inflation was based on “strict exchange rate targeting” (see Billmeier and Bonato, 2002). Current policy of the CNB is directed toward maintaining price stability hence exchange rate targeting is having somewhat smaller importance. However, because of the pronounced “dollarization” of the Croatian economy the “fear of floating” (Calvo and Reinhart, 2000) continues to drive Croatian monetary policy into keeping low tolerance toward the exchange rate movements and systematically intervening to smooth the volatility in the exchange rate. Hence, a close link between the exchange rate and inflation can be expected in Croatia, as well as for the exchange rate policy. There are various debates surrounding the CNB’s use of exchange rate targeting versus the use of traditional monetary policy tools. Kraft (2003), for example, argues that monetary policy is ineffective at stabilising output because increases in the money supply lead to an exchange rate depreciation, which in turn raises interest rates and creates a negative demand effect. Or put differently, such an exchange rate depreciation can create a negative

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monetary shock. This leads to a difficulty in output stabilization through monetary policy while also following a policy of exchange rate targeting. Instead of business cycle or exchange rate management, we turn the focus towards the role of monetary policy in the long run growth potential of Croatia, through the widely adopted policy of inflation rate targeting. The stable low inflation rates that result from such targeting are generally incompatible with traditional business cycle or exchange rate management (see Svensson, 2003, for a review, as well as Woodford, 2001, and Taylor, 2001) 1 . We support this focus with new empirical evidence based on multivariate cointegration analysis, structural modelling and causality testing. The key empirical issues relate to the stability of the long-run money demand relation and to the effect of money on output growth. Similarly important is the relationship among inflation, exchange rates and interest rates.

First, we focus on estimation of the long-run money demand relation using the Johansen (1995) approach and investigate whether the inclusion of inflation in the money demand equation can remedy instability of the system that is do to interest rates volatility. Following this we argue that inclusion of the inflation rate in addition to the nominal interest rate, as is in Cuthbertson (19--)[or any other UK reference], can be justified by the fact that the Fisher equation does not hold in Croatia. In addition, on the grounds of a high ‘pass-through’, we estimate an alternative money-demand specification with the Euro (HRK/€) exchange rate instead of the inflation rate and show that, in each specification, real money is cointegrated with nominal interest rates and output. After such inclusion of either the inflation rate or the exchange rate, this results in a well performing system with consistent coefficients that passes an extensive battery of diagnostic and evaluation tests. Having empirically established a stable long-run money demand relation we investigate both short- and long-run relationships between the nominal money supply and the real output growth. We find a stable long-run cointegrating relationship among nominal money, output, interest rates and inflation. We test for Granger non-causality of money to output and to interest rates and find significant evidence of causality of money to output and to interest rates. This suggests that inflation targeting rules that are related to money supply growth rate management, as McCallum (1999, 2001) and Alvarez, Lucas, and Weber (2001) discuss, can be effective. The paper is organised as follows. The second section describes the data; the third section explains the econometric methodology while the fourth section presents the empirical results. The fifth section concludes. 2 Theoretical background Linking together the long-run, balanced-growth path, monetary features of an economy in general equilibrium is possible using monetary economies, such as the cash-in-advance models (Lucas, 1980; Lucas and Stokey, 1987), the shopping time economies (Goodfriend, 1997; Lucas, 2000), or money-in-the-utility function economies (Eckstein and Leiderman, 1992; Lucas, 2000). In these economies the nominal money stock is exogenously supplied by the government, and the rate of growth of the money supply causes a certain inflation rate. There is some interplay between the money supply, the inflation rate, and the real output growth rate, when an endogenous growth setting is used (Gomme, 1993; Gillman and Kejak, 2002, 2003). Here the higher money supply growth, which can be used to finance government

1 Svensson (2003) discusses interest rate and exchange rate smoothing; he states that “I find the case for explicit instrument-rate stabilization and/or smoothing objectives quite weak.”

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purchases, causes higher inflation and lower real output growth. This is because the inflation acts as a tax on human capital, whereby it lowers the return on human capital and drags down the growth rate of the whole economy. The endogenous growth effect of inflation can cause the real interest rate to decline if the return on human capital gets driven down, and for example Ahmed and Rogers (2000) find long run evidence of the inflation rate causing the real interest rate to decrease. In this case the nominal interest rate does not rise one for one with the inflation rate, as in the standard Fisher equation of interest rates. Inflation pushes up the nominal interest rate significantly, but because the real interest rate also declines, the nominal rate does not rise by as the increase in the inflation rate. Money demand functions are implicit in all such general equilibrium approaches. In some economies the form of the function is similar to Cagan’s (1956) constant semi-interest elasticity money demand function in which the magnitude of the interest elasticity rises with the level of the inflation rate (Eckstein and Leiderman, 1992, Gillman and Kejak, 2002). And this type of money demand function has been found supported empirically (Mark and Sul, 2002, Gillman and Otto, 2002) and to be useful in explaining the nature of the negative effect that inflation has been found to have in international panel evidence (Gillman, Harris, and Matyas, 2003). Taken together some of these models and evidence exhibit “stable” money demand functions, a negative effect of inflation on growth, caused by an exogenous money supply growth rate increase, and a Fisher type relation of interest rates in which the long run real rate is not constant and indeed can fall as inflation increases. In empirical testing, a stable long run money demand, Granger-causality from nominal money supply growth to real output growth, and a “failure” of the Fisher equation can be evidence in support of such endogenous growth monetary economies. 3 Data and descriptive analysis We use the monthly time series data from the IMF’s International Financial Statistics data base on industrial production, money, consumer prices, exchange rate, and the money market interest rate (Table 1). The variables are in natural logarithms of the indices with the base year 1995. The data span is from April 1994 till August 2002 for all series. All variables are seasonally adjusted using the X12 ARIMA procedure.

Table 1. Definition of variables Symbol Definition

it Industrial production mt Money

(m − p)t Real money pt CPI prices ∆pt Inflation ext HRK/€ exchange rate rt Money market interest rate vt Money velocity (pt + yt − mt)

Visual inspection of the level plots (Figure 1) indicates the presence of a notable upward trend in all series except the interest rate which trends downwards. This is highly indicative of non-stationarity or presence of stochastic trend in the series.

5

1995 2000

5

6Money Real money

1995 2000

4.6

4.7

4.8

4.9Output

1995 2000

2

3

4

5

Interest rates

1995 2000

4.6

4.7

4.8

4.9 Prices Exchange rate

1995 2000

-.01

0

.01

.02

Inflation

1995 2000

4

4.5

5 Velocity

Figure 1. Time series plots of mt, (m − p)t, yt, rt, pt, ext, Dpt, and vt

Augmented Dickey-Fuller (ADF) unit root tests for the order of integration (Table 2) do not reject the hypothesis that the tested series have a unit-root and are thus I(1). The ADF tests were performed by considering all options regarding deterministic components (i.e. trend and constant) and in all cases the unit-root hypothesis could not be rejected. We additionally performed ADF tests on first-differences of all series and found strong rejection of the unit-root null in all series.

Table 2. Augmented Dickey-Fuller unit root tests

Variable t-ADF β(yt-1) σ j* t-∆yt-j t-probamt −1.815 0.937 0.026 9 3.333 0.001bmt

0.166 1.002 0.026 9 3.029 0.003apt –1.542 0.883 0.005 5 –1.847 0.068bpt −1.018 0.995 0.005 4 –1.847 0.068ait –2.326 0.589 0.032 9 2.097 0.039bit –0.644 0.966 0.033 2 –4.708 0.000

a(m − p)t −1.794 0.939 0.026 9 3.623 0.001b(m − p)t

0.113 1.002 0.026 9 3.299 0.002bDpt

–6.999 0.038 0.005 1 –0.125 0.901aext

−1.033 0.966 0.007 2 −2.183 0.032bext −1.725 0.971 0.007 2 −2.333 0.022art –1.485 0.893 0.195 5 1.975 0.052brt 0.713 1.023 0.199 5 1.707 0.092

* Highest significant lag in the ADF regression. a Trend and constant included in the regression: 5% critical value = −3.461, 1% = −4.066 b Constant included in the regression (no trend): 5% critical value = −2.895, 1% = −3.507. The inflation series, on the other hand, deserves special consideration. The importance of the integration order of inflation, which is given by the logarithm of the ratio of current and

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previous period price index, is rather high in the context of cointegration and long-run modelling where the analysed variables should be of the same integration order (generally I(1), or first-difference stationary). Given the unit root in the price series, we note that since the tested variables were in logarithms, the inflation is in fact the first-difference of the log price index, and therefore if pt ~ I(1) it follows that ∆pt ~ I(0). The issue of the integration order of inflation series is generally an unresolved issue in the literature (Culver and Papell, 1997; Benati and Kapetanious, 2002) and there is much evidence that inflation rate is stationary in most western countries. Croatian case is likely to be similar to the low-inflation regimes because of the CNB’s stabilisation policy. In fact, Croatian inflation rate (∆pt) does not appear to be trending (Figure 1). The visual impression is further confirmed by the unit-root tests (Table 2), which strongly rejects the null up to the fifth lag in the ADF regression (however, as no lagged differences are significant, simple DF test suffices; the t-DF value is −9.653 with the β(yt-1) = 0.026). 4 Econometric methodology The main methodological framework is based on multivariate cointegration analysis, which commences from estimation of an un-restricted vector autoregressive (VAR) system in levels. Such an approach enables joint modelling of all relevant variables without a priory making assumptions about their exogeneity or endogeneity status, which is necessary in single equation approaches.2 Specifically, consider the VAR(p) system containing n endogenous variables (i.e. yt ∈ Rn) of the form

yt = B0 + B1yt-1 + B2yt-2 + … + Bpyt-p + et, et ~ i.i.d. (1) where B0 is n-vector of intercepts, Bi’s are the coefficient matrices. Define Y′t ∫ (yp, yp+1, …, yT), Ÿt-i ∫ (yp-i, yp-i+1, …, yT-i), where i = 0, 1, …, p, and E′t ∫ (ep, ep+1, …, eT) so that (1) can be written in ‘full-sample’ notation as

Y′t = B0 + B1Ÿt-1 + B2Ÿt-2 + … + BpŸt-p + Et. (2) Now let Π ∫ (B0, B1, …, Bp,) and Yt-i ∫ (1′, Ÿ′t-1, Ÿ′t-2, …, Ÿ′t-p), where 1 is a unit vector, hence Eq. (2) can be compactly written in the form

t t i t−′ ′ ′= +Y ΠY E . (3) Note that Y′t, E′t ∈ R[n × (T − p)], Y′t-i ∈ R[(np + 1) × (T − p)], and Π ∈ R[n × (np + 1)]. It follows that Π can be estimated by OLS applied to each equation separately or by multivariate least squares estimator Y′tYt-i(Y′t-iYt-i)−1. However, empirical selection of the parameter p, following the general-to-specific approach, requires testing for the validity of omitting one or more lags of yt from the system, which is originally specified with a large p.3 To construct an appropriate test statistic, first note that Π can be partitioned into (Π1 : Π2) where Π2 contains the imposed

2 See e.g. Cziráky (2002) for a single equation analysis of Croatia; Banerjee et al. (1993) covers in detail both single equation and systems approaches 3 The maximum feasible initially set p depends on practical data limitations. With monthly data, it is common to initially set p ≥ 12.

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zero restrictions, Π1 is (n × k1) and Π2 is (n × k2), such that k1 + k2 = (np + 1). Similarly, partition Y′t-i into (Y′1t-i : Y′2t-i) where Y1t is [k1 × (T − p)] and Y2t is [k2 × (T − p)]. To test the hypothesis that Π2 = 0 vs. Π2 ≠ 0, a likelihood ratio statistic is given by (|S||S0|−1)T/2, which is asymptotically distributed c2 with d.f. = nk2, where S = T−1 Y′t[I − Yt-

i(Y′t-iYt-i)-1Y′t-i]Yt and S0 = T−1Y′t[I − Y1t-i (Y′1t-iY1t-i)-1Y′1t-i]Yt. An F-test approximation (Anderson, 1984; Rao, 1973; Doornik and Hendry, 1997) can be calculated as4

( )( )

( )

1/10

2 21/10

1 1 1~ F( , )

1 1

s

s appNs nk nk Ns

−

−

− − −

− −

Σ Σ

Σ Σ, (4)

where N = T − k1 − k2 − ½(n − k2 + 1), and ( ) ( )2 2 2 22 24 5s n k n k= − + − .

Once an appropriate VAR is determined and given the modelled variables are of appropriate integration order, the estimation proceeds by re-parametrising the VAR in levels in a vector error-correction form (VECM), where cointegrating vectors are estimated with the Johansen maximum likelihood technique (Johansen, 1995). Consider the VAR(p) system from (1) and additionally assume that yt ~ I(1) and et ~ IN[0, Ω]. Rewriting the system in the VECM form5 we obtain

Dyt = G0 + G1Dyt-1 + G2Dyt-2 + … + Gp-1Dyt-p-1 + Ξyt-1 + et, et ~ IN[0, Ω], (5) where Ξ = αb′ for α, b ∈ R(n × r) such that rank(α) = rank(b) = r. Define DY′t ∫ (1′, Dy′t-1, Dy′t-1, …, Dy′t-p-1) and G ∫ (G0, G1, …, Gp-1,) so that (5) can be equivalently written as Dyt = GDY′t + Ξyt-1 + et. The VECM system (2) can be estimated using the Johansen’s (1995) maximum likelihood procedure. The Johansen procedure requires two auxiliary multivariate regressions, Dyt = Λ(1)DYt + rot and yt-1 = Λ(2)DY′t + r1t. Defining the residual matrices R′0 = (rop, rop+1, …, roT) and R′1 = (r1p, r1p+1, …, r1T), and residual covariance matrices Sij = T−1R′iRj.6 The Johansen estimate of the cointegrating vectors b is obtained by maximising the following likelihood (ignoring a constant term)

L(b) = − 2T ln|S00 − S01b(b′S11b)−1bS10|. (6)

The hypothesis on the number of cointegrating relations (r) can be tested in this framework using the l-trace or l-max statistics, which are defined as

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ˆ ˆ-trace ln(1 ), -max ln(1 )n

i ri r

T Tλ λ λ λ += +

= − − = − −∑ , (7)

where for i = 0, 1, …, n the iλ ’s are the Eigenvalues from the characteristic equation |lS11 − S10S00

−1S01| = 0. Linear restrictions on α and b can be tested by the likelihood ratio test 2

0 1 ( )1[ln(1 ) ln(1 )] ~

r

i i ri

T λ λ χ=

− − −∑ , (8)

where loi and l1i are the Eigenvalues from the constrained and unconstrained models, respectively. Finally, we note that testing for Granger non-causality in cointegrated systems cannot be performed with classical Granger non-causality tests. Mosconi and Giannini, (1992)

4 Note that this formulation of the test is valid only for VAR systems. 5 For more details see e.g. Banerjee, et al. (1993). 6 For i, j = 0, 1 these matrices are S00 = T−1R′0R0, S11 = T−1R′1R1, S10 = T−1R′1R0, and S01 = T−1R′0R1.

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developed a Granger non-causality test suitable for cointegrated systems, i.e., for testing Granger non-causality among cointegrated variables. Rault (2000) proposed an improvement to the Mosconi-Giannini test, which is, however, suitable for longer time series with T > 200, which for monthly data requires at least 17 years of data. Toda and Yamamoto (1995) developed a Granger non-causality test (MWALD test) with better small-sample performance, thus more appropriate for shorter time series. The Toda-Yamamoto MWALD test can be constructed as follows. Let yt ∈ Rn be a vector of n cointegrated variables, with cointegrating rank r ≤ n. Then, consider a VAR(q + dmax) of the form t t i t−′ ′ ′= +Y AY E , where dmax is the maximum order of integration in the system.7 We use the same notation as above assuming that p = q + dmax. Now, let  = Y′tYt-i(Y′t-iYt-i)−1 be the multivariate least squares estimate of A. Define Âv ∫ vec(Â) and note that Âv = [(Y′t Yt)−1 ⊗ In]vec(Y′t). It follows that the covariance matrix of Âv is given by S = (T − p)(Y′t-iYt-i) −1 ⊗ Y′t-i[I − Yt-i(Y′t-iYt-i)−1Y′t-i]Yt-i. The Toda and Yamamoto (1995) test for Granger causality (MWALD) is given by T(SÂv)′(SSÂS′)−1(SÂv ~ c2

(J) where J is equal to the number of joint Granger-causality tests and S is a [J × (n + pn2)] selection matrix that selects the restricted elements in Âv.8 5 Estimation results 5.1 Money velocity Because of the close link between the standard money demand equation, in which real money is modelled as a function of output and interest rates i.e. (m − p)t = αyt − brt, and money velocity (n), defined as (pt + yt − mt), it follows that the velocity can be written as n = (1 − α)yt + brt.9 Thus, for α > 1 and constant interest rates, velocity will decrease as output increases (Brand and Cassola, 2000; Brand, et al. 2002). Aside of this explanation there are few other possible reasons for declining money velocity including the wealth effects, negative inflation trend and asset prices (for further details see Kontolemis, 2002). We firstly test whether the observed downward trend in money velocity is deterministic or stochastic, because in the former case this implies a constant annual percent decline in velocity. In the later case, however, it would be necessary to analyse whether the non-stationary velocity is cointegrated with other macroeconomic variables or whether its long-run movements could not be successfully modelled. Commencing from an unrestricted VAR10 in levels, we test for the number of cointegrating vectors using Croatian monthly seasonally adjusted money and output series (mt, yt). Estimation of the VECM system specified as

( ) ( )1111 11 12 11 1211 12

( ) ( )1 22 21 22 21 2221 22

i it t i t t

i iit t i t t

m m my y y

εµ α α β βγ γεµ α α β βγ γ

−

= −

′∆ ∆ = + + + ∆ ∆

∑ (9)

7 We consider only I(1) systems, hence we let dmax = 1. 8 For example, for testing the null hypothesis that y1t does not simultaneously Granger-cause both y2t and y3t the MWALD c2 test has two degrees of freedom. In this example, the R matrix selects the coefficients of q lags of y1t in the equations for y2t and y3t. 9 We assume all variables are in logarithms. 10 The lag-length of the VAR was determined by sequential testing for the validity of the system’s reduction, starting with 12 lags (i.e. one year of data) and reducing one lag at the time. The reduction from 12 to 11 lags was not rejected while all further reductions were strongly rejected by the system reduction F-tests (Eq. (4)).

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gives the results in Table 3. The Johansen cointegration tests suggest there is one cointegrating vector between money and output. Both l-max and l-trace statistics are above their 95% critical values with l-max being significant at above 0.01 level.

Table 3. Johansen cointegration tests: VAR(11) with y′ = (mt, yt) (Eigenvalues: l1 = 0.280, l2 = 0.050)

H0: r = p l-max 95% CV l-trace 95% CV p = 0 29.53 19.0 25.79 25.3 p £ 1 4.60 12.3 4.60 12.3

The (first) cointegrating vector including coefficients of mt, yt, and t (time trend) is estimated as b′ = (1, −6.6, 0.01) with the accompanying adjustment coefficient vector α = (0.05, −0.02). This implies a long-run relationship pt + 6.6yt − mt. Rather large income elasticity is estimated, which agrees with the conjecture that growth in output could have caused continuous decline in velocity, though such conclusion depends on the behaviour of the interest rates. Imposing the restriction 11 b′ = (1, −1, *) results in the estimated trend coefficient of −0.05 and α = (−0.03, 0.1), which is, however, strongly rejected by the LR c2

(1) = 22.3. It is clear then that the restriction b′ = (1, −1, 0), being even more restricted, cannot hold either (which is confirmed by the highly significant LR c2

(2) test of 24.64). These findings imply that n ~ I(1) regardless of the presence of deterministic trend in the cointegration space, i.e., an apparently systematic decline in the money velocity is in fact stochastic and no fixed per annum percent decline or deterministic downward trend can be claimed. Therefore, it follows that long-run stability of the money demand equation requires taking into consideration additional variables such as interest rates, inflation, and exchange rate. 5.2 The long-run money demand and the Fisher equation A useful empirical money demand model should, at minimum, establish a long-run relationship among real money, output, and interest rates and also capture the observed declining money velocity. It is informative to firstly investigate the bivariate correlations among variables in levels and differences (Table 4). It is noticeable that the real money strongly correlates to output, prices, exchange rate, and (negatively) to interest rates. The correlations with differenced variables are much smaller in magnitude which is expected for I(1) series. While real money strongly correlates with output (in levels), a negative correlation can be observed between the growth in (nominal) money and the level of output. The correlation between the money growth and output growth is positive but small. Because we model (m − p)t, yt, and rt in a multivariate cointegration framework, the order of the estimated VECM is rather important and the system should be properly specified in terms of the lag-length selection before commencing with the cointegration analysis. Formal tests of system’s reduction validity (Eq. (4)), staring from VAR(12) and progressively reducing the number of lags in the system (Table 5) reject all reductions beyond VAR(11), thus we use 11 lags in the cointegration analysis. 11 The asterisk implies an unrestricted coefficient.

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Table 4. Correlations mt (m – p)t yt pt rt ext ∆mt ∆(m – p)t ∆yt ∆pt ∆rt ∆ext

mt 1.00 (m – p)t 0.99 1.00

yt 0.89 0.87 1.00 pt 0.94 0.90 0.89 1.00 rt −0.88 −0.87 −0.83 −0.86 1.00

ext 0.62 0.54 0.66 0.81 −0.58 1.00 ∆mt −0.14 −0.14 −0.12 −0.14 0.02 −0.07 1.00

∆(m – p)t −0.12 −0.11 −0.10 −0.12 −0.00 −0.07 0.99 1.00 ∆yt 0.00 0.01 0.28 −0.00 −0.02 0.00 0.05 0.06 1.00 ∆pt −0.13 −0.14 −0.10 −0.08 0.13 −0.02 0.04 −0.11 −0.05 1.00 ∆rt −0.17 −0.18 −0.13 −0.14 0.29 −0.10 −0.06 −0.10 −0.02 0.13 1.00 ∆ext 0.05 0.05 −0.01 0.03 0.07 0.10 −0.29 −0.28 −0.07 −0.10 0.20 1.00

Table 5. System reduction tests System reduction F-test d.f. F-value p-value VAR(10) VAR(9) F( 9, 134) 2.154 0.029 VAR(11) VAR(9) F(18, 147) 2.618 0.001 VAR(12) VAR(9) F(27, 143) 2.346 0.001 VAR(11) VAR(10) F( 9, 126) 2.894 0.004 VAR(12) VAR(10) F(18, 139) 2.301 0.004 VAR(12) VAR(11) F( 9, 119) 1.632 0.114

The system is specified as three-variable VECM of the form

( ) ( ) ( )1 11 12 1311

( ) ( ) ( )2 21 22 23

1 ( ) ( ) ( )3 31 32 33

11 12 13 11 12 13 1

21 22 23

31 32 33

( ) ( )

i i it t i

i i it t i

i i i it t i

m p m py yr r

µ γ γ γµ γ γ γµ γ γ γ

α α α β β β βα α αα α α

−

−=

−

∆ − ∆ − ∆ = + ∆

∆ ∆

+

∑

14 1

121 22 23 24 2

131 32 33 34 3

( )tt

tt

tt

m pyrt

εβ β β β εβ β β β ε

−

−

−

− ′ +

(10)

Estimation of the system (10) using the Johansen maximum likelihood technique indicated two stationary combinations among (real) money, output, and interest rates variables (see Table 6). Two of the three Eigenvalues are significant on basis of both l-max and l-trace statistics, thus the third vector is apparently non-stationary. These results support the conclusion that only two of the tree linear combinations are cointegrating vectors, while the third one is I(1).

Table 6. Johansen cointegration tests: VAR(11) with y′ = [(mt,− pt), yt, rt] (Eigenvalues: l1 = 0.419, l2 = 0.253, l3 = 0.050)

H0: r = p l-max 95% CV l-trace 95% CV p = 0 48.900 25.5 79.800 42.4 p £ 1 26.250 19.0 30.900 25.3 p £ 2 4.653 12.3 4.653 12.3

11

The estimated standardised b coefficients and their accompanying adjustment coefficients α are estimated by the Johansen’s maximum likelihood procedure as

1.00 2.25 0.44 0.01 0.01 1.00 0.10 0.00

12.75 7.78 1.00 0.13

− ′ = −

β , 0.03 0.50 0.00 0.14 0.68 0.001.22 2.41 0.01

− = − − − − −

α

We can conveniently identify the first cointegrating vector (or long-run equation) as money demand relation in the form (mt − pt) = 2.25yt − 0.44rt − 0.01t. The second cointegrating vector could be interpreted as an “excess-demand” equation (see e.g. Hendry and Ericsson, 1991). We additionally test for the reduced rank r = 2 and (jointly) for the exclusion of deterministic trend from the cointegrating space. The exclusion of trend is strongly rejected by the LR c2

(2) = 25.36, which is highly significant. However, an immediate problem with the estimated model is a notable lack of parameters’ stability (or constancy). Figure 2 shows 1-step and breakpoint Chow tests for the individual equations and for the entire system. It is seems that the problem creates interest rates series that might be causing instability of the entire system which fails both 1-step and breakpoint Chow tests. To improve the money demand model, Baba, Hendry, and Starr (1992) consider the inclusion of inflation in the money-demand relation, on the grounds that the Fisher equation might not hold exactly (i.e. without lags) in the USA, which we test empirically for Croatia. Assuming fully anticipated inflation the classical Fisher equation implies that the nominal rate of interest on assets with returns fixed in money terms is the sum of the real rate of return on assets with returns fixed in real terms and the anticipated rate of inflation. Denoting the nominal interest rate in period t by rt, the real interest rate by ρt, and inflation by πt, the Fisher equation (Fisher, 1930; see also Dimand, 1999) can be written as rt = ρt + πt. With the additional assumption that ρt = α + εt (i.e. real interest rate is constant), where εt ~ i.i.d., the Fisher equation becomes rt = α + πt + εt, which implies independence of the real interest rate and inflation. The equation is usually estimated in log-levels as ln(rt) = β0 + β1 ln(πt) + ut and a test of the restriction β1 = 1 is taken to be the test of the (long-run) validity of the Fisher equation. The constant β0 can be interpreted as the long-run equilibrium real rate of interest. Note that when the variables are in logarithms inflation measured as ln(πt) = ln(pt/pt-1) is equivalent to a simple difference in the log of the price index, i.e., ∆ln(pt), hence the classical Fisher equation can be stated as12

0 1 1ln( ) ln( ) , ~ i.i.d., 1t t t tr p u uβ β β= + ∆ + = (11) This relationship was often critiqued as overly simplistic and dynamically misspecified. Most of the empirical evidence, hence, fails to support the classical Fisher equation, generally reporting β1 < 1.13 In fact, Fisher himself conjectured that the inflation expectation formation

12 An alternative version of the Fisher equation, given constant money velocity, is ∆mt = ∆pt, (see e.g. Monnet and Weber, 2001). This, however, is not suitable for the cases where velocity is clearly not constant 13 There were several major attempts in the literature to reconcile empirical evidence with the theory, focusing either on theoretical adjustments or on estimation methods. In an early paper, Sargent (1972) derived a version of the Fisher equation that relates interest rate to distributed lags of money and inflation, i.e.,

1 1n mi it i t i i t ir mα ϕ θ π= =− −= + +∑ ∑ , thus suggesting a direct modification of the original equation, which otherwise

might be misspecified. The Fisher equation (11) also fails when Cov(rt, pt) ≠ 0, a situation known as the “Gibson paradox”. The earliest explanation of the paradox was provided by Fisher himself who pointed out to the

12

process is a distributed lag of the form ( )11t i

t i

m ppit ivπ −− −

∆== ∑ , where pt is the price level at time t

and vi and m are parameters. When variables are in logarithms, this becomes simply 1ln( ) ln( )m

it i t i tr v pα ε= −= + ∆ +∑ .14 A possible theoretical explanation for the empirical evidence against the Fisher equitation is the existence of the ‘Mundell-Tobin’ effect. Namely, the real interest rates in the long-run equals the marginal product of capital, which in the long-run equals households’ marginal rate of time preference. It follows that the interest rate will be independent from the inflation rate under the assumption of constant time preferences. However, if the rate of time preference is a function of household’s wealth or utility, then it is possible that inflation will effect negatively the marginal product of capital, which is known as the Mundell-Tobin effect. The Mundell-Tobin effect in the form of a decline in the marginal product of capital due to the real balance response to inflation can hence invalidate the classical Fisher equation through the negative effect of inflation to money demand, which simultaneously negatively effects real wealth; in turn, if the time preferences are a function of wealth, then wealth can lower the rate of time preference causing additional capital accumulation. Therefore, the Mundell-Tobin effect can explain the negative effect of inflation on interest rates, though as indicated by Lucas (1980), if money growth is assumed to be superneutral, such effect should exist only in the short-run.15

2000

-.05

0

.051-step residuals (m-p)

2000

-.1

0

.11-step residuals (y)

2000

-.25

0

.25 1-step residuals (r)

2000

.51

1.5 5% 1-step Chow test (m-p)

2000

.5

1 5% 1-step Chow test (y)

2000

123

5% 1-step Chow test (r)

2000

1

2 5% system 1-step Chow test

2000

.5

1 5% break-point Chow test (m-p)

2000

.5

1 5% break-point Chow test (y)

2000

1

2

3 5% break-point Chow test (r)

2000

.5

1 5% system break-point Chow test

Figure 2. Stability tests for the VECM with (m − p)t, yt, and rt

existence of very long lags in the formation of inflation expectations which might explain the empirically observed high correlation between interest rates and price level (see e.g. Sargent, 1973). 14 Note that rt = ρt + πt which can be rewritten as ( )11

t it i

m ppit t ir vρ −− −

∆== + ∑ , and with a further assumption that ρt =

α + εt, this becomes ( )11t i

t i

m ppit i tr vα ε−− −

∆== + +∑ . This immediately follows by noting that ( )1ln t i

t ip

p−

− −∆ =

[ ]1 1ln ( ) /t i t i t ip p p− − − − −− = [ ]1ln ( / ) 1t i t ip p− − − − = 1ln( / )t i t ip p− − − = 1ln( ) ln( ) ln( )t i t i t ip p p− − − −− = ∆ . Therefore, the Fisher equation in log-linear form becomes 1ln( ) ln( )m

it i t i tr v pα ε= −= + ∆ +∑ . 15 Note, however, the Mundell-Tobin effect might not provide sufficient theoretical justification for the Fisher equation not holding as the bulk of empirical evidence suggests that inflation affects negatively interest rates much more then capital. Fried and Howitt (1983) offer and alternative explanation suggesting that “inflation reduces the equilibrium real rate of return on money, which is jus the negative of the rate of inflation” and that “it is also reasonable to suppose that it also reduced the equilibrium real rate of return on assets that are close substitutes form money because of their similar liquidity characteristics, even if it has little effect on relatively illiquid assets such as physical capital.

13

More recently, the validity of inference in the Fisher equation was questioned from the statistical point of view. Rose (1988), Mishkin (1982), and Evans and Lewis (1995) pointed out that a regression of interest rate which is often non-stationary, i.e., I(1) on inflation which is most likely stationary, i.e., I(0) yields invalid statistical inference and causes spurious results. Assuming that both rt ~ I(1) and ∆pt ~ I(1), Crowder and Hoffman (1996), estimated the long-run Fisher equation in a multivariate cointegration framework using US data and reported 1.34 < β1 < 1.37 and 0.97 < β1 < 1.01, without and with tax adjustment, respectively. Crowder (2001) reports similar findings using Canadian quarterly data, also using multivariate cointegration analysis. The cointegration approach, while substantively appealing, rests on the validity of the integration order of interest rates and inflation series, which should be the same, i.e. I(1), otherwise cointegration between interest rates and inflation is not possible and thus the Fisher equation apparently fails. The main problem here is the integration order of inflation, which is I(0) in most countries according to the bulk of empirical evidence (e.g. Culver and Papell, 1997; Benati and Kapetanios, 2002). The new (sequential-break) unit-root testing procedure applied by Benati and Kapetanious (2002) strongly supports stationarity of the inflation, including US inflation, thus refuting the cointegration arguments originally advocated by Mishkin (1982) and thus seriously questioning the validity of methods employed by Crowder and Hoffman (1996) and Crowder (2001). We test the Fisher equation in Croatia using several specifications including Fisher’s distributed lag, Sargan’s (1972) extended Fisher equation and the cointegration approach based on the Johansen’s maximum likelihood technique (Crowder and Hoffman, 1996; Crowder, 2001). We first estimate the “classical” form of the Fisher equation by initially ignoring the order of integration of the modelled series. Using the specification

0 1ln( ) ln( )t t tr p uβ β= + ∆ + we obtain the following estimates

(0.10) (15.46)ln( ) 3.65 20.03 ln( )t t tr p u= + ∆ +

R2 = 0.017, s = 0.783, DW = 0.081

It is evident that the null hypothesis H0: b1 = 0 cannot be rejected, and in addition, a low Durbin-Watson statistic implies dynamic misspecification. The ADF unit root test on ut produced a t-value of 0.519 where the highest significant lag was 4, which clearly cannot reject that ut ~ I(1). Note that this can also be inferred from the fact that ln(rt) ~ I(1) while Dln(pt) ~ I(0), therefore it must be that "g, [ln(rt) − g Dln(pt)] ~ I(1). Estimation of the Sargent’s (1972) “extended” Fisher equation, with n = m = 3 produced

1 2 3

1 2 3

(0.45) (1.15) (1.62) (1.61) (1.05)

(6.23) (6.12) (6.13) (6.15)

ln( ) 13.74 2.17 ln( ) 2.16ln( ) 1.08ln( ) 3.46

6.44 ln( ) 0.74 ln( ) 0.70 ln( ) 2.68 ln( )

t t t t t

t t t t t

r m m m m

p p p p u

− − −

− − −

= − − − +

+ ∆ + ∆ + ∆ − ∆ +

R2 = 0.863, s = 0.305, DW = 0.570 Here, while the Durbin-Watson statistic is still indicative of some remaining residual autocorrelation, the fit is improved and the residuals close to stationary,16 however inflation is not significant at any lag, which is better seen in the long run solution

16 ADF t-value was −2.637 with 7 lags included in the regression, which is above the 1% critical value of −2.591 for the regression without trend or constant.

14

(0.45) (0.08) (12.95)ln( ) 13.74 1.95 ln( ) 5.19 ln( )t t t tr m p u= − + ∆ + ,

WALD c2(2) = 548.32 (p < 0.000)

where only money is significant. Similar results are obtained by estimating the distributed lag version of the Fisher equation (Sargent, 1973, Fisher, 1930), which is specified as a special case of the “extended” equation, i.e., 1ln( ) ln( )m

it i t i tr v pα ε= −= + ∆ +∑ . Estimation of this equation produced insignificant coefficients of inflation at all lags (including up to 12 lags) and similarly insignificant long-run coefficient (results omitted). In addition, the residuals were found to be non-stationary confirming the previous conclusion about the integration orders. Following Crowder and Hoffman (1996) and Crowder (2001) we also estimate a bivariate VECM system using the Johansen technique where the specification is

( ) ( )111 11 11 12 11 1211 12

2 2( ) ( )1 1 22 21 22 21 2221 22

i it t i t t

i iit t i t t

r r rp p p

εµ α α β βγ γεµ α α β βγ γ

− −

= − −

′∆ ∆ = + + + ∆ ∆ ∆

∑ .

Estimation of the above system produced Eigenvalues l1 = 0.109 and l2 = 0.055, l-max and l-trace statistics of 10.31 and 15.38, respectively, which is well bellow their 95% critical values of 19 and 25.3.17 These results clearly imply that interest rates and inflation are not cointegrated, thus according to these results, the long-run Fisher equation does not hold. The above results followed the main approaches to testing the Fisher equation in the literature, however, as we have pointed out, the problem of the integration order of interest rates and inflation variables, and the empirical result that the Croatian inflation is I(0) make these approaches generally invalid.18 To avoid the integration order problems and consistently estimate the b1 coefficient from the classical Fisher equation, 0 1ln( ) ln( )t t tr p uβ β= + ∆ + , we use the OLS estimator19

21

1 221

ln( ) ln( )

ln( )

Tt tt

Ttt

p r

pβ =

=

∆ ∆=

∆

∑∑

. (12)

It is easy to show that 1β is asymptotically normally distributed since ln(rt) ~ I(1) fi Dln(rt) ~ I(0), while Dln(pt) ~ I(0) fi D2ln(pt) ~ I(0), thus this estimator uses only I(0) variables and the standard distribution theory applies. To see that 1β is a consistent estimator of b1, observe that

1 0 1 0 1 1 1

21

ln( ) ln( ) ln( ) ( ln( ) )

ln( ) ln( )t t t t t t

t t t

r r p u p u

r p v

β β β β

β− − −− = + ∆ + − + ∆ +

⇒ ∆ = ∆ +,

where D2ln(pt) ∫ Dln(pt) − Dln(pt-1) = ln(pt) − 2ln(pt-1) + ln(pt-2), and vt ∫ (ut − ut-1). However, the b0 coefficient from 0 1ln( ) ln( )t t tr p uβ β= + ∆ + , i.e., the long-run equilibrium real rate of interest, cannot be estimated. Estimation of the equation 2

1ln( ) ln( )t t tr p vβ∆ = ∆ + by OLS produced the following results

2

(2.69)ln( ) 3.56 ln( )t t tr p v∆ = ∆ + .

R2 = 0.018, s = 0.190, DW = 2.04 17 A linear trend was included in the cointegrating space in the estimation. 18 Sargent’s (1972) extension that includes levels of money will, however, yield valid inference given money is I(1) and cointegrated with interest rates, hence the I(0) inflation would enter merely as an additional stationary regressor. 19 We assume the variables are measure in deviations from the means.

15

These results allow drawing correct statistical inference on the estimated coefficients, and also the Durbin-Watson statistic is indicative of no remaining autocorrelation in the residuals. However, the standard error of b1 coefficient is 2.69, which gives a t-ratio of 1.33, hence we cannot reject the null hypothesis H0: b1 = 0. This finding, coupled with the above results obtained from the alternative estimation approaches implies that the Fisher equation does not hold in Croatia, therefore, the interest rates and inflation do not equal in the long-run, and thus inflation can enter the long-run money-demand relation as a separate variable along with the interest rates. We re-estimate the money-demand system from Eq. (10) now including inflation (Dpt) hence we estimate a VECM with Dyt = [D(m − p)t, Dyt, D2pt, Drt]. The tests for the number of cointegrating relations (Table 7) cannot reject that r = 2, thus there appear to be two cointegrating vectors.

Table 7. Johansen cointegration tests (l1 = 0.528, l2 = 0.336, l3 = 0.161, l4 = 0.075)

H0: r = p l-max 95% CV l-trace 95% CV p = 0 66.110 31.5 124.500 63.0 p £ 1 36.030 25.5 58.400 42.4 p £ 2 15.480 19.0 22.370 25.3 p £ 3 6.888 12.3 6.888 12.3

The estimates of the cointegrating vectors and their adjustment coefficients are similar to those from the model estimated above without inflation. The adjustment coefficients for the first two equations are also similar to the previously obtained. The b and α are now estimated as

1.00 2.66 17.00 0.36 0.00790.02 1.00 3.40 0.09 0.0002

0.00 0.01 1.00 0.00 0.000018.45 15.30 147.46 1.00 0.1223

− − − − ′ = − − − − − −

β ,

0.09 0.58 4.93 0.0023 0.20 0.99 0.23 0.00250.02 0.02 1.18 0.00052.42 3.34 15.53 0.0027

− − − − = − − − −

α

Restricted estimation where the rank condition (r = 2) and weak exogeneity of inflation were jointly imposed produced an LR c2

(2) test of 3.733 (p = 0.155), thus we cannot reject the joint hypothesis that r = 2 and that inflation is weakly exogenous in respect to the long-run parameters. The restricted estimates of b and α are

0.23 0.59 3.04 0.08 0.00180.02 0.67 2.06 0.06 0.0002− − − − ′ = − − −

β ,

0.37 0.860.99 1.51

10.71 4.97

− − − − = − − −

α ,

Normalising the first cointegrating relation to (m − p)t and the second one to yt, and writing the long-run relationships in equation format, we get the following long-run money demand and “excess demand” equations

(m − p)t = 2.57yt − 13.22 Dpt − 0.35rt − 0.01t

yt = 0.03(m − p)t + 3.07Dpt − 0.09rt + 0.003t

16

The parameter constancy and the stability of the system (Figure 3) now appears more satisfactory, though interest rate remains problematic. The system stability is more satisfactory with the recursive break-point Chow tests generally bellow the 95% critical value, while the 1-step Chow test detects an outlier in March 2000.

2000

-.05

0

.051-step residuals (m -p)

2000

-.1

0

.11-step residuals (y)

2000

-.02

0

.021-step residuals (Dp)

2000

-.25

0

.251-step residuals (r)

2000

1

2

5% 1-step Chow test (m -p)

2000

.5

1 5% 1-step Chow test (y)

2000

.5

1 5% 1-step Chow test (Dp)

2000

.51

1.5 5% 1-step Chow test (r)

2000

.51

1.5system 1-step Chow test

2000

.5

1break-point Chow test (m -p)

2000

.5

1break-point Chow test (y)

2000

.5

1break-point Chow test (Dp)

2000

.5

1

1.5break-point Chow test (r)

2000

.5

1system break-point Chow test

Figure 3. Stability tests for the VECM with (m − p)t, yt, Dpt, and rt

We consider one further modification to the estimated money-demand model. Croatia is considered to be heavily “dollarized” economy (see e.g. Ize and Yeyati, 1998; Ize, 2001) and a pronounced “fear of floating” (Calvo and Reinhart, 2000), even after achieving low inflation, continues to drive Croatian monetary policy into keeping low tolerance toward the exchange rate movements and systematically intervening to smooth the volatility in the exchange rate. Hence, a close link between the exchange rate and inflation can be expected in Croatia, i.e., it is likely that the exchange rate movements pass through to domestic prices. Billmeier and Bonato (2002) report a significant pass-through in Croatia, thus implying the “pass-through” link between domestic inflation and the HRK/€ exchange rate. Therefore, it can be argued that exchange rate might be included in the money demand relation in place of inflation.20

Table 8. Johansen cointegration tests (l1 = 0.498, l2 = 0.430, l3 = 0.256, l4 = 0.127)

H0: r = p l-max 95% CV l-trace 95% CV p = 0 60.62 31.5 149.00 63.0 p £ 1 49.96 25.5 88.37 42.4 p £ 2 26.32 19.0 38.41 25.3 p £ 3 12.09 12.3 12.09 12.3

An additional statistical argument is that exchange rate is I(1), while inflation is I(0), hence its inclusion in the VECM together with I(1) variables was only possible on the grounds that other variables were cointegrated among themselves. We now replace inflation with exchange

20 For some examples of using exchange rate in macroeconomic models of transitional countries see Petrovic and Mladenovic, (2000); Petrovic and Vujosevic, (1996a); Petrovic and Vujosevic, (1996b); Petrovic, et al. (1999).

17

rate (ext), and estimate a VECM system with Dyt = [D(m − p)t, Dyt, Dext, Drt]. The results of the cointegration tests shown in Table 8 now indicate that there might be as much as three cointegrating vectors. The unrestricted estimates of the b and l matrices are similar to the ones obtained with inflation instead of exchange rate, with an apparent difference in the adjustment coefficient in the “excess demand” equation which is now considerably smaller in magnitude

1.00 2.91 0.12 0.31 0.00680.08 1.00 0.15 0.12 0.0021

0.56 0.55 1.00 0.07 0.00871.60 14.09 13.71 1.00 0.0525

− − − ′ = − − −

β ,

0.02 0.03 0.31 0.0096 0.18 1.16 0.09 0.00120.06 0.08 0.29 0.00841.72 4.27 0.87 0.0093

− − − − − = − − − − − −

α

Restricting the cointegrating rank to r = 2 given the third cointegrating vector would have no meaningful substantive interpretation, and constraining the third raw of α to zero thus imposing weak exogeneity of the exchange rate, gave the following estimates

0.48 1.69 0.10 0.17 0.0050.16 1.62 0.30 0.20 0.004− − − ′ = − − −

β ,

0.03 0.020.30 0.72

3.10 2.65

− − − − = − − −

α

The LR test for the imposed restrictions has a c2(2) of 2.226 (p = 0.329), which does not reject

the joint restriction that r = 2 and that exchange rate is weakly exogenous for the long-run parameters. A notable difference, however, is in the smaller speed of adjustment parameters in the money-demand equation. The adjustment in the “excess demand” equation is still very fast. The normalised long-run relationships in equation form are similar to those obtained with inflation variable, yet with larger output elasticity in the money demand equation, i.e.,

(m − p)t = 3.52yt + 0.21ext − 0.35rt − 0.01t yt = 0.10(m − p)t − 0.19ext − 0.12rt − 0.00t

Finally, the coefficient constancy tests (Figure 4) now indicate reasonable stability of the system, without any significant breaks. The interest rates, however, still show relatively inconstant behaviour, though this does not affect the system as a whole. Comparing the last two estimated models—with inflation and exchange rate, respectively—we conclude both versions indicate stable long-run money demand relation. The difference due to replacement of inflation with the exchange rate can most notably be seen in a much smaller adjustment coefficients in the later model, hence the long-run money demand relation, while stable and statistically satisfactory, does not adjust to the short-run with the exchange rate replacing inflation. The slow adjustment to the short-run, while it might not be immediately apparent, is an argument against the exchange rate targeting policy, and thus supports an inflation targeting policy. In addition, this result also tells us about the pass-through effect, namely, it suggest the pass-through is rather imperfect. This leads us to argue that exchange rate targeting is not the same policy as inflation rate targeting, which has important connotations for the monetary policy in transitional countries.

18

1999 2000 2001 2002 2003

.5

1 5% break-point Chow test (m-p)

1999 2000 2001 2002 2003

.5

1 5% break-point Chow test (y)

1999 2000 2001 2002 2003

.5

1 5% break-point Chow test (ex)

1999 2000 2001 2002 2003

.5

1

5% break-point Chow test (r)

1999 2000 2001 2002 2003

.5

1 5% system break-point Chow test

Figure 4. Stability tests for the VECM with (m − p)t, yt, ext, and rt

5.3 The relationship between money and growth Having empirically established a stable long-run money demand relation, we investigate both short- and long-run relationship between money and output, focusing on nominal money growth that can be used as monetary policy instrument. We start the analysis again in the multivariate framework and estimate the following VECM system using the Johansen technique with the purpose of obtaining the long-run cointegrating relationships

( ) ( ) ( ) ( )1 11 12 13 14

( ) ( ) ( ) ( )12 21 22 23 24

( ) ( ) ( ) ( )13 31 32 33 34

( ) ( ) ( ) ( )4 41 42 43 44

i i i it t i

i i i it t i

i i i iit t i

i i i it t i

m my yex exr r

µ γ γ γ γµ γ γ γ γµ γ γ γ γµ γ γ γ γ

−

−

= −

−

∆ ∆ ∆ ∆ = + ∆ ∆ ∆ ∆

1

111 12 13 14 11 12 13 14 15 1

121 22 23 24 21 22 23 24 25 2

31 32 33 34 31 32 33 34 35 31

41 42 43 44 41 42 43 44 45 4

tt

tt

tt

tt

myexrt

α α α α β β β β β εα α α α β β β β β εα α α α β β β β β εα α α α β β β β β ε

−

−

−

′ + +

∑

. (13)

Note that we include a time trend in the cointegrating space to take account of long-run exogenous growth (see e.g. Hendry and Mizon, 1993). The results of the cointegration rank tests are shown in Table 9. It is most likely that there are only two cointegrating vectors, though the third one appears marginally significant. The estimated unrestricted coefficient matrices indicate relatively high money elasticity in the output equation (−0.34) with a notably fast adjustment coefficient (−0.67), i.e.,

19

1.00 0.34 0.02 0.10 0.007.49 1.00 2.11 0.98 0.03

0.56 0.57 1.00 0.07 0.0121.52 2.39 19.97 1.00 0.07

− − − − − − − ′ = − − −

β ,

0.67 0.13 0.05 0.000.02 0.01 0.25 0.01

0.22 0.01 0.26 0.00 5.31 0.55 0.88 0.00

− − − − − = − −

α

Estimation of a restricted model with imposed r = 2 and weak exogeneity of both money and exchange rate resulted in the estimates

1.74 0.52 0.11 0.17 0.0021.57 0.25 0.52 0.21 0.007

− − − ′ = − − β ,

0.36 0.63

3.18 2.65

− − − − = − − −

α ,

and a likelihood ratio test with c2(4) = 3.109 (p = 0.540), which does not reject the imposed

restrictions. The two long-run relationships can be interpreted normalised to output and to interest rates, i.e., yt = 0.30mt − 0.06ext + 0.10rt + 0.001t, and rt = −7.48yt + 1.19mt + 2.48ext − 0.033t. From the exchange rate targeting policy perspective it might be interesting to re-normalised the second long-run relationship as ext = 3.02yt − 0.48mt + 0.40rt + 0.014t, however because the exchange rate was found to be weakly exogenous to the long-run parameters, the interest rates interpretation of the second cointegrating vector appears statistically more reasonable. Finally we note that the estimated system displays acceptable stability with constant parameters and no significant break points (Figure 5).

Table 9. Johansen cointegration tests (l1 = 0.515, l2 = 0.408, l3 = 0.218, l4 = 0.128)

H0: r = p l-max 95% CV l-trace 95% CV p = 0 64.36 31.5 145.10 63.0 p £ 1 49.64 25.5 80.69 42.4 p £ 2 21.92 19.0 34.06 25.3 p £ 3 12.14 12.3 12.14 12.3

Having obtained the long-run (cointegrating) relationships, we move on to modelling the short-run structure of the VECM system which is relevant in respect to the short-run adjustment behaviour of the modelled variables (see Hendry and Doornik, 1994). We proceed by following the general-to-specific approach and estimate a short-run VAR in the error-correction form (VECM) using two error-correction terms (lagged one period) defined by

ECM1t-1 ∫ 1.74yt-1 − 0.52mt-1 + 0.11ext-1 − 0.17rt-1 − 0.002(t − 1)

ECM2t-1 ∫ 1.57yt-1 − 0.25mt-1 − 0.52ext-1 + 0.21rt-1 + 0.007(t − 1) We include the two additional error-correction terms as regressors in the VECM and condition on the exchange rate and money, which were found to be weakly exogenous in the long-run above.21 Proceeding with modelling the VECM system with only two equations (for Dyt and Drt), given weak exogeneity of money and exchange rate, we progressively reduce the

21 We also tested the short-run weak exogeneity with a Wald test for zero restrictions on lags of first differences of money and exchange rate in the output and interest rate equation, which confirmed the long-run weak exogeneity results.

20

system to a parsimonious VECM (PVECM) by eliminating lagged variables that were jointly insignificant across all equations, followed by elimination of variables that were insignificant in individual equations. This last reduction moves us from the PVECM to a structural equation model (SEM) of the system.22 The validity of the system reduction is formally tested and the results are reported in Table 10. The system S1 is the full VECM estimated for the purpose of cointegration modelling, while S4 is the most restricted system. Moving from S4 to a model of the system in which all insignificant variables were removed (hence the two equations no longer include the same lagged variables) resulted in an LR test with c2

(9) = 3.817 (p = 0.923), which does not reject the final reduction. The final short-run model consists of an equation for output growth which relates output growth to its lags and the lags of money growth, in the short run, as well as to the two error-correction terms (ECM1t-1 and ECM2t-1) corresponding to the above estimated long-run relations, i.e.,

3 7 8 9

2 3 7 12

1 1

(0.301) (0.073) (0.095) (0.107) (0.091)

(0.115) (0.125) (0.121) (0.104)

(0.079)

2.999 0.227 0.213 0.278 0.234

0.361 0.419 0.253 0.243

0.585 0

t t t t t

t t t t

t

y y y y y

m m m m

ECM

− − − −

− − − −

−

∆ = + ∆ + ∆ + ∆ + ∆

− ∆ − ∆ − ∆ + ∆

− ∆ + 2 1(0.009).064 t tECM ε−∆ +

The second equation relates the change in interest rates to output growth (lagged ten months), its own lags, lags of nominal money, and to two error-correction terms

10 6 7

2 3 10 12

1 1

(1.725) (0.392) (0.096) (0.094)

(0.666) (0.740) (0.676) (0.620)

(0.058) (0.058)

3.487 1.165 0.210 0.220

1.574 3.177 2.129 2.350

+ 2.498 0.216

t t t t

t t t t

t

r y r r

m m m m

ECM ECM

− − −

− − − −

−

∆ = − − ∆ + ∆ + ∆

− ∆ − ∆ − ∆ + ∆

∆ + ∆ 2 1t tυ− +

The above short-run model establishes significant short-run link between output growth and money growth, where the short-run effect of money is significantly negative at all lags but the 12th (one year), with significant and fast adjustment to the long-run equilibrium value (ECM1t-

1) that (as shown by the cointegration analysis results) establishes a positive long-run relationship between output and money in levels. It is also interesting that exchange rate, while relevant in long-run (which also holds for inflation) was found to be insignificant at all lags in both equations in the short-run. The effect of the exchange rate, therefore, goes only through the adjustment coefficients, i.e., error-correction terms, and it affects output and interest rates only in the long-run. Such finding suggests that the current policy of “silent” exchange rate targeting might be unnecessary. However, it is also noticeable that interest rates do not appear to affect output in the short-run, and the effect of money growth on the change in interest rates, while positive in the long-run, is in fact negative at all except 12th (one year) lag.

22 We note that Hendry and Doornik (1994) allow for a possibility of post-hock inclusion of contemporaneous variables into the model arrived at through a series of encompassing general-to-specific reductions. This, however, might invalidate the statistical inference in the model as such simultaneous equation model is not a special case of the initially estimated VECM, namely, the included error-correction terms containing cointegrating relationships were estimated from a different model, i.e., one without contemporaneous variables in the short-run. Nevertheless, we tested inclusion of the contemporaneous values of output growth and growth of interest rates finding both variables statistically insignificant.

21

1999 2000 2001 2002 2003-.1

0.1

recursive residuals (y)

1999 2000 2001 2002 2003

-.050

.05.1 recursive residuals (m)

1999 2000 2001 2002 2003-.05

0.05

recursive residuals (ex)

1999 2000 2001 2002 2003-.25

0.25 recursive residuals (r)

1999 2000 2001 2002 2003

.5

1 5% break-point Chow test (y)

1999 2000 2001 2002 2003

.5

1 5% break-point Chow test (m)

1999 2000 2001 2002 2003

.5

1 5% break-point Chow test

1999 2000 2001 2002 2003

.51

1.5 5% break-point Chow test (r)

1999 2000 2001 2002 2003

.5

1

5% system break-point Chow test

Figure 5. Stability tests for the VECM with yt, mt, ext, and rt

The estimated model passes an extensive battery of diagnostic tests (Table 11) thus indicating good statistical properties. In addition, Figure 6 shows plots and cross plots of actual and fitted values as well as empirical residual densities, which indicate close fit of the model.

Table 10. System reduction statistics System Removed variables F-test d.f. F-value p-valueS3 S4 Drt-2, Dext-2, Dmt-1 F(6, 138) 0.990 0.434S2 S4 Dyt-1, Dyt-11, Drt-2, D rt-5, Dext-1, Dext-2, Dext-9,

Dext-10, Dmt-1, Dmt-8, Dmt-11

F(22, 122) 1.029 0.434

S1 S4 Dyt-1, Dyt-2, Dyt-4, Dyt-5, Dyt-6, Dyt-11, Dyt-12, Drt-1, Drt-2, Drt-3, Drt-4, Drt-5, Drt-8, Drt-9, Drt-10, Drt-11, Drt-12, Dext-1, Dext-2, Dext-3, Dext-4, Dext-5, Dext-6, Dext-7, Dext-8, Dext-9, Dext-10, Dext-11, Dext-12, Dmt-1, Dmt-4, Dmt-5, Dmt-6, Dmt-8, Dmt-9, Dmt-11

F(72, 72) 1.089 0.358

S2 S3 Dyt-1, Dyt-11, Drt-5, Dext-1, Dext-9, Dext-10, Dmt-8, Dmt-11

F(16, 122) 1.042 0.417

S1 S3 Dyt-1, Dyt-2, Dyt-4, Dyt-5, Dyt-6, Dyt-11, Drt-5, Dext-1, Dext-9, Dext-10, Dmt-8, Dmt-11, Dyt-12, Drt-1, Drt-3, Drt-4, Drt-8, Drt-9, Drt-10, Drt-11, Drt-12, Dext-3, Dext-4, Dext-5, Dext-6, Dext-7, Dext-8, Dext-11, Dext-12, Dmt-4, Dmt-5, Dmt-6, Dmt-9

F(66, 72) 1.094 0.353

S1 S2 Dyt-2, Dyt-4, Dyt-5, Dyt-6, Dyt-12, Drt-1, Drt-3, Drt-4, Drt-8, Drt-9, Drt-10, Drt-11, Drt-12, Dext-3, Dext-4, Dext-5, Dext-6, Dext-7, Dext-8, Dext-11, Dext-12, Dmt-4, Dmt-5, Dmt-6, Dmt-9

F(50, 72) 1.097 0.354

Finally, we test for Granger non-causality of money to output and money to interest rates, using the Toda-Yamamoto MWALD test. Formally, we test the hypotheses

22

(1) (2)0 0H : , H :t t t tm y m r→ → .

The calculated MWALD test for (1)0H : t tm y→ has a value of 29.129, which is significant at

0.0038 level, hence the hypothesis that money does not Granger-cause output is strongly rejected. Similar result is obtained in testing (2)

0H : t tm r→ , where the MWALD test has the value of 28.976, which is significant at 0.004 level, therefore, we can also reject that money does not Granger-cause interest rates. 6 Conclusion By focusing on the demand for real money balances, the Fisher equation of interest rates, and the effect of nominal money on output in Croatia over the 1994-2002 period, we find a stable long-run money demand with the inclusion of inflation rate in addition to the nominal interest rate. Inclusion of inflation in the long-run money demand relationship is justified by the failure of the nominal interest rate to move one-for-one with inflation, as predicted by the Fisher equation, which we find not to hold in Croatia. We also find that the negative trend in money velocity cannot be explained by a deterministic trend. Hence an apparently systematic decline in the money velocity is stochastic and this implies that no fixed annual percent decline can be expected.

In addition, following the “pass-through” argument, we estimate an alternative money-demand model with the HRK/€ exchange rate instead of the inflation rate and show that money demand remains stable in the long-run. However, we also find a difference from the model with inflation, namely, inclusion of the exchange rate in place of inflation causes a loss in the speed of adjustment to the short-run thus arguing against an exchange rate targeting policy, and instead additionally supporting an inflation targeting policy. This also suggests that the pass-through effect is imperfect in Croatia and as a corollary that exchange rate targeting is not an equivalent policy to inflation rate targeting.

Table 11. Diagnostic tests for the structural equation model Test Equation Test value p-value

Dyt 5.077 − Portmanteau (10 lags) Drt 7.893 − Dyt 1.385 0.233 AR 1−6 F(6, 67) Drt 1.110 0.365 Dyt 2.731 0.255 Normality c2

(2) Drt 3.523 0.171 Dyt 1.035 0.411 ARCH 6 F(6,61) Drt 1.246 0.295 Dyt 0.429 0.989 xi

2 F(28,44)* Drt 1.341 0.187

Vector portmanteau (10 lags) PVECM 28.210 − Vector AR 1−6 F(24, 130) PVECM 1.107 0.344 Vector normality c2

(4) PVECM 6.265 0.180 Vector xi

2 F(84, 141)* SEM 0.949 0.598 * Inclusion of squared variables

23

1995 2000

0

.1Dy Fitted

-.05 0 .05 .1

0

.1Dy x Fitted

1995 2000

-1012 residual (Dy)

-4 -3 -2 -1 0 1 2 3 4

.2

.4

Densityresidual (Dy) N(0 ,1 )

1995 2000

-.5

0

.5 Dr Fitted

-.6 -.4 -.2 0 .2 .4

-.5

0

.5 Dr x Fitted

1995 2000

-101 residual (Dr)

-4 -3 -2 -1 0 1 2 3

.2

.4 Densityresidual (Dr) N(0 ,1 )

Figure 6. Evaluation graphics for the structural equation model

Focusing on the nominal money supply, which can be used as a monetary policy instrument, we estimate the long-run relationship among money, output, exchange rate, and interest rates, as well as the short-run model for their growth rates. This includes an error-correction adjustment mechanism to the long-run equilibrium. The short-run model (SEM) with nominal money establishes a significant short-run link between output growth and money growth, with a significant and fast adjustment towards the long-run equilibrium value. We find that money growth initially (in the very short run) negatively affects output, while turning positive in later periods. The movements in nominal money are positively related to the movements in output.

In addition, we find no evidence of a significant short-run effect of the exchange rate either on the interest rates or on the nominal money supply, noting that both the nominal money supply and the exchange rate are weakly exogenous to the long-run parameters. Therefore, the effect of the exchange rate on output exists only in the long run (i.e. in levels), and its effect on the short-run output growth goes only through the adjustment coefficients. A similar conclusion holds for the effect of exchange rate on the short-run growth in interest rates; we find no significant effect of exchange rate on interest rates in the short-run.

The results suggest that the current policy of “silent” exchange rate targeting might be unnecessary. Coupled with the finding of a loss in the adjustment speed in the money demand relation due to the replacement of inflation with the exchange rate, these results further support an inflation targeting policy and reinforce the conclusion that exchange rate targeting differs from inflation targeting. Tests for the causality of (nominal) money to output and to interest rates strongly support causality effects in both cases. Applying Granger non-causality tests for cointegrated variables and modelling the short-run dynamics we find significant evidence that nominal money causes output in the long run, and similarly that nominal money growth causes output growth in the short-run. However, the initial effect of the money growth on output growth, as indicated by the short-run model, is negative, while money growth starts to positively affect output growth with a one-year lag, and similarly the relationship remains positive in the long-run. Therefore, we generally conclude that, once proper attention is paid to the statistical properties of the series and the appropriate econometric methods are used, the empirical

24

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