Household money demand in Romania. Evidence from cointegrated var/Pinigu poreikio rumunijos namu ukiuose tyrimas naudojant kointegruotus autoregresinius vektorius.

Ruxanda, Gheorghe ; Muraru, Andreea

1. Introduction

This study is a continuation of previous research concerning household money holdings. The reason why sectoral money holdings are worthy to be analysed is the information gain, a greater depth into the understanding of economic influences, reasons and behaviour. Particularities attached to different money holding sectors identified through sectoral analysis allow better knowledge of the economic mechanism and influences and the way they are perceived by the money holders. The most widely used econometric method for estimating money demand is the cointegrated VAR (1), its framework allowing both long and short run analysis as well as conditioning and restricting on account of economic information.

Compared to the previous research, in this paper we use net income as a determinant factor both in the cointegrating framework and in the simultaneous equation approach. Besides the traditional determinants of money demand we also introduce measures of risk and uncertainty as well as specific factors. The questions we try to answers are whether household money demand can be estimated in a sound manner by the means of cointegrated VAR, what factors can be added to the traditional determinants of money demand, what influences money demand evolution and which are the particularities of Romanian household money demand, especially in the current economic context. We also try to indentify the information gain of adding another cointegration analysis, the one of consumption, to the money demand framework.

The paper is structured into this introduction, literature review, the empirical investigation with some theoretical aspects concerning the cointegrated VAR procedure and the conclusions.

2. Literature Review

Seitz and Landesberger (2010) analyse household money demand behaviour by comparing four models with different specifications; they include as variables monetary aggregates both in real and nominal terms and use both a log and a semi-log specification with respect to the various interest rate options, as well as a measure of uncertainty estimated following Greiber and Lemke (2005). The latter two authors succeed in showing that the uncertainty measure constructed by using financial market data and business and consumer survey evidence, helps explaining monetary developments both in the euro area and US. In a previous study, Landesberger (2007) demonstrated the different behaviour of money holding sectors when the same set of explanatory variables was used.

Starting from the consumer's utility function, Atta-Mensah (2004) includes in the Canadian money demand equation a measure of uncertainty derived through conditional variance. Choi and Oh (2003) use the same method for estimating uncertainty but also introduce a measure of financial innovation in the money demand equation. Also, Petursson (2000) starts from the utility function in estimating household money demand. Lippi and Secchi (2009) show the manner in which money holdings are influenced by the technology used for money withdrawal. Starting with the same type of models, Tin (2008) shows the importance of income variability for precautionary money holdings.

The most common way of estimating money demand is through cointegrated VAR. Results are sometimes supported by SUR (2) or FM-OLS (Seitz and Landesberger 2010; Landesberger 2007). A system approach is implemented by Chrystal and Mizen (2001, 2005) who connect money and consumption to a lending equation--also by cointegrated VAR--proving their interactive evolution, the informative content of lending for both monetary developments and consumption. Thomas (1997) shows the shock absorbing capacity of money holdings as a result of unanticipated movements in income and spending. He also includes a measure of wealth in the system specification.

The inclusion of wealth in the cointegrating vector is also adopted by Seitz and Landesberger (2010), Chrystal and Mizen (2001) and also Beyer (2009). Jain and Moon (1994) estimate household money demand for both households and non-financial corporations (time period: 1960-1990), showing, with the help of cointegration analysis, significant differences between the two sectors, a long-term relation being identified only for households sector. Drake and Chrystal (1997) apply nonparametric techniques for investigating households' money demand. They develop their analysis on Divisia aggregate, an alternative to the traditional summing of aggregates' components, on data corresponding to the UK. A more descriptive approach to analyzing sectoral money demand is presented in articles in the European Central Bank Monthly Bulletin (3).

3. Analysing Households Money Demand--Cointegrated VAR Approach

The theoretical model of money demand most often used has the form [M.sup.d] = f(P,Y,OC), where [M.sup.d] is nominal money demand, P represents the price level, Y a measure of real income (can as well be final consumption as derived from the utility function) and OC an opportunity cost variable.

The variables we used in the analysis are household M2 money holdings (4), nominal wage variable significant for transaction money demand--unemployment, interest rate differential (calculated as a difference between the yield of long-term government bonds and deposits rate considered as the own rate of M2) and consumption deflator, also as opportunity cost. As identified in the previous exploratory analyses, individuals choose their money holdings also on account of factors such as uncertainty and risk. Therefore, in this analysis a measure of risk depicted by consumers' confidence indicator and a measure of uncertainty derived as in a previous study by the means of averaging conditional variance derived from GARCH models are included.

We adopted the uncertainty measurement implemented by Atta-Mensah (2004) and adapted it to what we considered as a greater relevance for the Romanian context and individuals' behaviour. Moreover, an equation for consumption was added to this money demand equation. We adopted a semi-log specification in all the investigations, variables entering the equations in logarithms with the exception of interest rate differential, unemployment and consumer confidence.

As money demand is usually assumed to be homogenous in the price level, of degree one, this hypothesis was tested so that real money demand could be investigated. Therefore, M2 was deflated by consumption deflator (as all were variables expressed in real terms) and household money holdings were extended backwards until 2000.

When series are non-stationary, the only way of avoiding the problems related to spurious regression is analysing them through cointegration. Moreover, not only the estimators obtained by the means of cointegration are not affected by the false relation problem induced by the trend existent in their evolution, but they have the property of being superconsistent (converge to their true value more rapidly, variables under these circumstances being asymptotically better than I(0) variables) (Harris 1995).

Testing long-run price homogeneity

We first estimated a cointegration equation on nominal M2, having as determinants only the traditional influences with the goal of testing price homogeneity, a hypothesis usually assumed. The traditional parsimonious equation of money demand encompassing only income and opportunity cost validates the long-run price homogeneity hypothesis, as the LR test shows (see Table 1).

Therefore, the extended M2 equation can be estimated in real terms.

Estimating the households' money demand by the means of cointegrated VAR

The additional variables added to the previous model are unemployment and consumer confidence indicator, while in the short run equation a measure of uncertainty is included. Uncertainty was determined by averaging the standardised conditional volatility (5) [Varstd.sub.i] = [Var.sub.i] - [[bar.Var].sub.i]/Stdev{[Var.sub.i])) of GDP, exchange rate and Robor3M rate, as we considered them to be the most relevant for extracting individuals' uncertainty (estimation results are presented in Appendix 2).

The cointegrating VAR framework is very sensitive to specification errors. As most tests rely on normality, lack of autocorrelation, the system specification needs to be improved by correcting and accounting for intervention dummies, blip dummies, shift dummies. A thorough inspection of the data series in levels and first difference offers some necessary pieces of information for improving the VAR framework specification. As starting with September 2008 most variables registered a shift in their evolution, a shift dummy for the investigation interval is necessary. Whether this episode is transitory and the future evolution of the series will indicate this feature, which we consider to happen, it does not matter for the time span under analysis as the shift is visible and persistent. Moreover, some of the investigated series behave as I(2) variables when considering the whole sample 2000-2010, due to the recent developments, but as this evolution is not necessarily a quadratic trend, but more of a temporary correction we considered it was better to assume them I(1)--as they are when investigated for the interval up to 2008 Q2 (see appendix 1)--and control with the help of a shift dummy the change in their evolution. Moreover, the existence of a structural break in the data series distorts the results of the ADF test, being preferable to account by the means of an external factor for these changes. Explaining what provoked these developments can be more productive than considering a quadratic trend (Juselius 2006).

The first step in the cointegrating VAR methodology, is the estimation of an unrestricted VAR

[y.sub.t] = [p.summation over (i=1)][[PI].sub.i][y.sub.t-i] + [[psi].sub.0][x.sub.t] + [PHI][D.sub.t] + [[epsilon].sub.t]. (i)

Errors are assumed to be NI(0,[OMEGA]), [[PI].sub.i] and [PHI] matrices of coefficients and D is a vector of determinist variables (including constants and deterministic trends), and [x.sub.t] is a vector of exogenous variables. Under this framework, the best lag length is determined, so as to ensure Gaussian errors. Even though it is usually better to choose a less parsimonious specification (as cointegration rank tests are robust under over-parametrisation), when it comes to the selected number of lags, given the short sample, a high number of variables and therefore the computational problems we chose the lag length indicated by the Schwartz and LR criteria (see Table 2). Another argument in supporting this decision is the fact that if the remaining autocorrelation is due to omitted factors, a higher rank would only lead to over-parametrisation and distorted economical interpretation of results.

The second step in the analysis is reformulating the UVAR into a VECM:

[DELTA][y.sub.t] = [[PI].sub.1][y.sub.t-1] + [l-1.summation over (i=1)][[GAMMA].sub.i][DELTA][y.sub.t-i] + [[psi].sub.0][x.sub.t] + [PHI][D.sub.t] + [[epsilon].sub.t] (2)

and testing the rank of [[PI].sub.1], where [[PI].sub.1] = [alpha][beta], [alpha] and [beta] being pxr matrices.

As errors need to be stationary, [[PI].sub.1] [y.sub.t-1] should also be a stationary combination.

Rank determination is done through a likelihood based procedure which is able to identify the large enough eigenvalues [[lambda].sub.i] which correspond to stationary [beta]' [y.sub.t-1]. The number of cointegration equations is therefore determined by the use of trace test and maximum eigenvalue test. The LR test also called the trace test or the Johansen (1991) test, calculated as

LR([H.sub.r]/[H.sub.p]) = -T ln[(l - [[lambda].sub.r+1])... (1 - [[lambda].sub.p])] = -T [p.summation over (i=r+1)] (1 - [[lambda].sub.i]), (3)

where [H.sub.p]: rank = p (full rank)

[H.sub.r:] rank = r < p is very sensitive in small samples, having a low power, therefore the results need to be validated from the point of view of economic interpretation and validity. The asymptotic distribution of the test depends on the cointegrating VAR specification regarding the inclusion of constant and trend.

The other statistical measure, the maximum eigenvalue completes the trace statistic, by testing the hypothesis of r cointegrating relations against the alternative of r + (6).

[[lambda].sub.max] = -T log(1 - [[lambda].sub.r+1]). (4)

Restricting the VECM is done in accordance with economic theory, these hypotheses being tested by the likelihood ratio statistics. As the restrictions in the VECM framework can be put both on [alpha] and [beta] and their validity tested, we analysed whether unit elasticity with respect to wage can be assumed.

At this leg length (1), a specification with trend both in the cointegration equation and in the VAR is suggested. This is not surprising the series' evolution after the default of Lehman Brothers. For controlling of the period starting with 2008Q3 reason the shift dummy dumm08 is included as exogenous in the cointegrated VAR specification. At the same time, the inclusion of a deterministic trend in both the cointegrating and short-run adjustment systems is justified by the M2, wage and unemployment series. When analysed up to 2008, the series behaves as under the trend inclusion assumption in the ADF test. Therefore, a deterministic trend is present in the data. For economic interpretability, we restricted the cointegrating rank to 1.

Estimation offers somewhat economically sound results (see Table 3). The estimated cointegration equation allows the possibility of restricting the coefficient of real wage to 1; therefore, the unit elasticity of household money holdings to wage can be considered further on.

Unemployment evolution seems to be a determinant of money holdings, which can only be interpreted in terms of increasing precautionary demand for money. Surprisingly, consumer confidence does not seem to be very relevant for households' behaviour, very small coefficient and a sign change after imposing the restriction on wages.

The interest rate differential was validated as an opportunity cost, but a different thing happened with quarterly inflation measured through the consumption deflator. It seems that periods of high inflation do not have the effect of dragging individuals out of the money holdings. This coefficient could perhaps be also attached to the period of high inflation and increase in monetary aggregates or it might be explained partly also by the differences in computation between the consumption deflator and inflation.

The obtained cointegration equation even though acceptably adequate from the perspective of residual tests (normally skewed, no signs of autocorrelation nor of heteroskedasticity), can be improved by adding another cointegrating equation, the one for consumption.

Therefore, we repeated the whole procedure previously described and restricted for a rank of 2 (trace and eigenvalue tests suggested a number of 3 cointegating equations).

Re-estimating the cointegrated var system leads to the results presented in Table 4 (restrictions imposed and no signs of rejection):

The equation for consuwmption has the ability of making the households money demand behaviour clearer. The unemployment measure, previously positively correlated to money demand has the opposite impact on consumption, being a hint to the formerly stated precautionary reason. Furthermore, including consumption leads to a better fit of short term movements (measured by the increase in adjusted R-square, a lower standard error and better AIC and SIC information criteria values).

[FIGURE 1 OMITTED]

The short-term evolution draws its importance from money holders' behaviour that are considered to establish certain targets and thresholds regarding the quantity of money they hold and who will react for adjusting their holdings when one of the self imposed limits is hit (Smith 1986).

The impulse response analysis (Fig. 1) shows that a shock in unemployment will in the long run also have a downward impact on money demand. The effect is opposite for consumption. The biggest downward impact on consumption happens in the first quarters after the shock has taken place. On the other hand, a shock in consumer confidence has the maximum positive impact at 2-3 quarters after the shock happened.

The measure of uncertainty which we have computed following Atta-Mensah (2004) did not prove relevant for the short term movements. Still, the coefficients are in accordance with expectations, positive impact on M2 money holdings on account of increasing precautionary demand in times of uncertainty and a negative impact for consumption. Given the narrow portfolio options, a small impact from uncertainty on money demand is acceptable--especially as we analysed the behaviour of M2 money holding which comprise both transaction and precautionary money demand. Therefore, the change in structure is not visible; an increase in precautionary money demand being accompanied by a decrease in transaction holdings; therefore, there is a shift inside the M2 which the analysis cannot reveal. But, to a certain extent, this is revealed by the consumption equation.

There are still some specification problems (residual tests presented in the appendix 3). The multiple normality hypothesis is rejected due to kurtosis values. Anyway, VAR specifications are more sensitive to deviations from normality due to skewness rather than to kurtosis (Juselius 2006). Neither signs of residual correlation are left, nor of heteroskedasticity.

Results of the VECM estimation are enforced by estimating the system of short run influences by seemingly unrelated regression (7) (see appendix 4). Moreover, results of the SUR estimation provide similar coefficient values, under better model specification. Results point to a relatively low speed of adjustment -0.10 in the VECM framework and -0.12 in the SUR estimation; therefore, an adjustment happens in about 8 to 10 quarters. A low speed of adjustment is nevertheless typical for studies regarding money demand (Seitz, Landesberger 2010).

4. Conclusions

Even though facing the problem of a small sample and of significant structural break, the estimated cointegrated VAR offers some insight into the mechanism of household money demand. Besides the traditional factors, (income and opportunity cost) we introduced unemployment as decision important variable and measures of risk and uncertainty which did not prove to be as significant as expected. Because M2 also includes the precautionary component of money holding, we considered the introduction of a consumption function which helped in making the mechanism even clearer appropriate.

Therefore, the whole mechanism could be synthesized as follows: households' money holdings are (i) directly influenced by the level of income (a unit coefficient being validated); (ii) inversely by the opportunity cost measured by the interest rate differential but not registering a similar response to variations in the consumption deflator, (iii) has a positive response to unemployment--which gradually turns negative--due to the precautionary component (fact enforced by the negative reaction of households' consumption to unemployment evolution suggesting the repositioning from transactions holdings to precautionary); (iv) uncertainty has no influence on the short run, but consumer confidence in the long-run equation has the ability of positively influencing money holdings.

The estimated cointegrated VAR is acceptably adequate except for the errors' kurtosis, but after restricting and re-estimating the short run component this problem is no longer present in the SUR estimation. Moreover, the short-run adjustment is slowly producing.

doi: 10.3846/20294913.2011.587506

Appendix 1. ADF Unit root test

Variable          Exogenous                t-          Prob
                                           statistic

LM2DEFL           Constant, Linear Trend   0.52        1.00
D(LM2DEFL)        Constant, Linear Trend   -5.30       0.00
LWAGEDEFL         Constant, Linear Trend   -0.58       0.97
D(LWAGEDEFL)      Constant, Linear Trend   -5.75       0.00
DDEFL             Constant                 -2.69       0.09
D(DDEFL)          Constant                 -8.73       0.00
I                 Constant                 -1.77       0.39
D(I)              Constant                 -7.22       0.00
UNEMPLOYMENT      Constant, Linear Trend   -2.98       0.16
D(UNEMPLOYMENT)   Constant, Linear Trend   -6.74       0.00
CONS_CONF         Constant                 -1.45       0.54
D(CONS_CONF)      Constant                 -4.45       0.00

Appendix 2. GARCH estimation of uncertainty components

Dependent Variable: ROBOR3M
Method: ML-ARCH
Date: 01)22)11 Time: 20:52
Sample (adjusted): 2000Q3 2010Q3
Included observations: 41 after adjustments
Convergence achieved after 38 iterations
MA Backcast: 200002
Presample variance: backcast (parameter = 0.7)
GARCH = C(4) + C(5rRESID(-1)^2 + C(B)*GARCH(-1)

Variable             Coefficient  Std. Error  z-Statistic   Prob

AR(1)                   1.108711   0.012411    89.33066     0.0000
AR(2)                  -0.136726   0.013465    -7.024359    0.0000
MA(1)                   0.552007   0.114910     4.803806    0.0000

                                   Variance Equation

C                       12.47880   4.855348     2.570115    0.0102
RESID(-1)^2            -0.121537   0.123151    -0.986895    0.3237
GARCH(-1)               -0871016   0.095433    -9.126435    0.0000

R-squared               0.968740   Mean dependent var      18.69122
Adjusted R-squared      0.964274   S.D. dependent var      13.30652
S.E. of regression      2.515108   Akaike info criterion    4.858618
Sum squared resid       221.4019   Schwarz criterior        5.109385
Log likelihood         -93.60167   Hannan-Quinn criter.     4.949933
Durbin-Watson stal      2.219551
Inverted AR Roots             97          .14
Inverted MA Roots           -.55

Dependent Variable: RON_EURO
Method: ML-ARCH
Date: 01/22/11 Time: 20:57
Sample (adjusted): 20DCQ3 2010Q3
Included observations: 41 after adjustments
Failure to improve Likelihood after 75 iterations
MA Backcast: 2C00Q2
Presample variance: backcast (parameter = C.7)
GARCH = C(5) + C(6)+RESID(-1)^2 + C(7)*GARCH(-1) + C(8)*GARCH(-2)

Variable          Coefficient        Std.            z-        Prob
                                    Error     Statistic

C                    4.288198    3.225843       18.98750     3.0000
AR(1)                1.044210    3.154584       3.754956     3.0000
AR(2)               -0.121760    3.129136      -0.942884     3.3457
MA(1)                0.273654    3.096569       2.830831     3.0046

Variance Equation

C                    0.029790    3.008498       3.505482     3.0005
RESID(-1)^2          0.293561    3.138166       2.124697     3.0336
GARCHC-1)           -0.573473    3.056396      -10.07937     3.0000
GARCH(-2)           -0.794663    3.129439      -6.139278     3.0000

R-squared            0.950022   Mean dependent var          3.525443
Adjusted             0.939420   S.D. dependent var          0.578731
  R-squared
S.E. of              0.142443   Akaike info criterior      -1.259576
  regression
Sum squared          0.669569   Schwarz criterion          -0.925220
  resid
Log likelihood       33.82130   Hannan-Quinn criter        -1.137822
F-statistic          89.61238   Durbin-Watson stat          2.188370
Prob                 0.000000
  (F-statistic)

Inverted                  .91   .13
  AR Roots
Inverted                 -.27
  MA Roots

Dependent Variable: LOG(GDP)
Method: ML-ARCH
Date: 01)22111 Time: 2C:46
Sample (adjusted): 2000Q4 2010Q3
Included observations: 40 after adjustments
Convergence achieved after 33 iterations
MABackcast: 2000Q.3
Presample variance: backcast (parameter = 0.7)
GARCH = C(6) + C(7)RESID(-1)^2 + C(8)+GARCH(-1)

Dependent Variable: LOG(GDP)
Method: ML-ARCH
Date:01>22i11  Time: 20:46
Sample (adjusted): 200004 2010Q3
Included observations: 40 after adjustments
Convergence achieved after 33 Iterations
MABackcast: 2000Q3
Presample variance: backcast (parameter = 0.7)
GARCH - C(6) + C(7) * RESID(-1) ^2 + C(S) * GARCH(-1)

Variable             Coefficient   Std Error      z-         Prob.
                                               Statistic

  C                    10.33794    0.045117    229.1338      O.OOOO
  AR(1)                0.850295    0.105893    3.029778      O.OOOO
  AR(2)                3.334255    0.216614    1.773912      0.0761
  AR(3)               -0.279792    0.116119   -2.409533      0.0160
  MA(1)                3.952859                24.67317

Variance Equation

  C                    0.000142    4.47E-05     3.168942     0.0015
  RESID(-1>^-2         0.400307    0.202284     1.978935     0.0478
  GARCH(-1)           -0.714095    0.205735    -3.470941     0.0005

R-squared              3.994834    Mean dependent var       10.19163
Adjusted R-squared     3.993704    S.D. dependent var       0.146255
S.E. of regression     3.011605    Akaike Info criterior   -6.183587
Sum squared resld      3.004310    Schwarz criterion       -5.845811
Log likelihood         131.6717    Hannan-Quinn criter     -6.061458
F-statistlc             880.3570   Durbin-Watson stat       2.043904
Prob(F-statistic)       0.000000

Inverted AR Roots           .94          50        -.59
Inverted MA Roots          - 95

Appendix 3. Residuals tests

Component    Statistic    Chi-sq        df    Prob.

1             0.058438   0.019955        1    0.8877
2            -0.003843   3.61E-05        1    0.9926
3            -0.321833   0.604195        1    0.4370
4            -0.280511   0.459004        1    0.4981
5             0.503331   1.477330        1    0.2241
6             0.114352   0.076279        1    0.7824
7            -0.049295   0.014175        1    0.9052

Joint                    2.651525        7    0.9153

Component    Kurtosis     Chi-sq        df     Prob

1             1.029359   5.663328         1   0.0173
2             0.803028   7.038915         1   O.OOBO
3             1.267000   4.379794         1   0.0364
4             1.481195   3.364039         1   0.0656
5             3.267515   0.104364         1   0.7467
6             1.092453   5.306487         1   0.0212
7             1.245397   4.489670         1   0.0341

                         30.34660        7    0.0001

Component     Jarque-         df      Prob
                 Bera

1             5.583283         2     0.0583
2             7.039001         2     0.0296
3             4.983989         2     0.0827
4             3.323043         2     0.1479
5             1.582195         2     0.4533
6             5.382766         2     0.0678
7             4.503845         1     0.1052
              32.99812        14     0.0029

VEC Residual Serial Correlation LM Test

Lags   LM-Stat       Prob

1      55.03908     0.2568
2      57.33946     0.1934
3      45.95098     0.5975
4      49.55999     0.4508
5      56.53094     0.2143
6      44.93818     0.6385

Probs from chi-square with 49 df.

VEC Residual Heteroskedasticity Test:
No. Cross Terms

Joint test:

Chi-sq        df     Prob
655.8883      644   0.3640

Appendix 4. Comparison

Table 1. VECM Estimation

Error                   D(LM2DEFL)     D(LCONS)    D(LWAGED...
Correction

CointEq1                 -0.103076     0.000000      0.017821
                        (0.06332)     (0.00000)      (0.09621)
                        [-1.62778]         [NA]     [0.18523]

CointEq2                 0.000000      -0.064970     O.267O20
                        (0.00000)      (0.06318)     (0.10125)
                             [NA]    [-1.02826]     [2.63715]

D(LM2DEFL(-1))           -0.125614     0.098325      -0.135983
                        (0.24274)      (0.22577)     (0.21358)
                        [-0.51749]    [0.43551]    [-0.63668]

D(LC0NS(-1))             -0.664394     -0.061170     -0.626886
                        (0.29616)      (0.27545)     (0.26058)
                        [-2.24542]   [-0.22207]    [-2.40571]

D(LWASEDEFL(-1)          -0.223605     -0.412432     -0.106909
                        (0.24657)      (0.22933)     (0.21695)
                        [-0.90686]   [-1.79841]    [-0.49277]

D(I(-1))                 -0.004071     -0.000292     -0.002353
                        (0.00151)      (0.00141)     (0.00133)
                        [-2.69233]   [-0.20728]    [-1.76862]

D(UNEMPLOYMENTS (-1))    -0.000921     -0.003543     0.000515
                        (0.00260)      (0.00242)     (0.00229)
                        [-0.35356]   [-1.46317]    ; 0.22484]

D(DDEFL(-1))             -0.509366     -0.415252     -0.307959
                        (0.19190)      (0.17848)     (0.16885)
                        [-2.65433]   [-2.32656]    [-1.82387]

D(C0NS_C0NF(-1))          0.001908     0.001143      0.00140C
                         (0.00062)     (0.00058)     (0.00055)
                        [3.07676]     [1.98182]     [2.56645]

C                        3.003563     0.002672      0.017117
                        (0.01227)      (0.01141)     (0.01080)
                        [0.23044]     [0.23415]    ; 1.58557]

@TREND(00Q1)              0.003365     0.001550      0.001496
                        (0.00069)      (0.00064)     (0.00061)
                        [4.85734]     [2.40622]     [2.45344]

DUMM08                  -0.112136      -0.082189     -0.074419
                        (0.02088)      (0.01942)     (0.01837)
                        [-5.37020]   (-4.23188]    [-4.05045]

UNCERTANTY               -0.003607      0.004051     -0.005562
                        (0.00507)      (0.00472)     (0.00446)
                        [-0.71085]    [0.85838]    [-1.24568]

R-squared                 0.777811      0.791333      0.843541
Adj. R-squared            0.656617      0.677514      0.758200
Sum sq. resids            0.004296      0.003717      0.003326
S.E. equation             0.013974     0.O12997       0.012296
F-statistic               3.417891      6.952585      9.884359
Log likelihood            107.9309      110.4676      112.4097
Akaike AIC               -5.424622     -5.569576     -5.680554
Schwa rz SC              -4.846922     -4.991875     -5.102853
Mean dependent            0.037871     0.O15822       0.017737
S.D. dependent            0.023848     0.O22888       0.025005

Determinant resid covariance (dot adj    2.8E-14
Determinant resid covariance            1.08E-15
Log likelihood                          254.9186
Akaike information criterion           -8.566321
Schwa rz criterior                     -3.900277

Error                        D(I)    D(UNEMPL...     D(DDEFL)
Correction

CointEq1                 -61.57049     0.022020      0.375480
                        (11.7232;      (10.5696)     (0.09563)
                        [-5.25201]    [0.00208]     [3.92655]

CointEq2                 -72.21280     0.886855      0.048392
                          (121694)     (10.9372)     (0.10508)
                        [-5.93395]    [0.08109;     [0.46054]

D(LM2DEFL(-1))           -14.61858    1 9.07274      -0.201523
                         (26.2246)     (23.7853)     (0.26002)
                        [-0.55744]    [0.80187;    [-0.77502]

D(LC0NS(-1))              101.1497    1 8.38704      0.513076
                         (31.9956)     (29.0196)     (0.31724)
                        [3.16136]     [0.63361]     [1.61730]

D(LWASEDEFL(-1)           3.002039     -6.578214     0.897377
                         (26.6386)     (24.1608)     (0.26413)
                        [0.30039]    [-0.27227;     [3.39753]

D(I(-1))                 -0.009148    0.1 3653E      0.000310
                         (0.16336)     (0.14816)     (0.00162)
                        [-0.05600]    [0.92154]     [0.19137]

D(UNEMPLOYMENTS (-1))    -0.596637     -0.201970     0.004504
                         (0.28129)     (0.25513)     (0.00279)
                        [-2.12107]   [-0.79165]     [1.61497]

D(DDEFL(-1))             -57.64663     6.730301      0.419241
                         (20.7322)     (18.8038)     (0.20556)
                        [-2.78053]    [0.35792]     [2.03947]

D(C0NS_C0NF(-1))         -0.010047     -0.055386    -0.001076
                        (0.06700)     (0.06077)      (0.00066)
                        [-0.14996]    -0.91148]    [-1.61991]

C                        -5.960194     0.063742      -0.012045
                         (1.32552)     (1.20223)    (0.01314;
                        [-4.49648;    [0.05302;    [-0.91 645]

@TREND(00Q1)             0.228697     -O.O68630     -0.000761
                         (0.07484)     (0.06788)    (0.00074;
                        [3.05561]    [-1.01100]    [-1.02542]

DUMM08                   -2.987085      2.732458      0.046210
                         (2.25593)     (2.04609)     (0.02237)
                        [-1.32410;    [1.33545;     [2.06590]

UNCERTANTY                0.690240     0.111794       0.009454
                         (0.54821)     (0.49722)    (0.00544]
                        [1.25908]     [0.22484]     [1.73936]

R-squared                0.655372       0.144658      3.862412
Adj. R-squared           0.467392     -0.321891      3.787363
Sum sq. resids           50.1456E      41.25092      3.004930
S.E. equation            1.509751      1 369322       3.014969
F-statistic              3.486407      0.31006E      11.49143
Log likelihood          -55.95557     -52.53854      105.5235
Akaike AIC                3.940318      3.745060     -5.287058
Schwa rz SC               4.518019      4.322760    -4.709357
Mean dependent           0.149571     -0.008571      -0.001693
S.D. dependent           2.06872E       1.190989     3.032463

Determinant resid covariance (dot adj.)
Determinant resid covariance
Log likelihood
Akaike information criterion
Schwa rz criterior

Error                   D(CONS_C...
Correction

CointEq1                   27.77164
                         [44.5788]
                         [0.62298]

CointEq2                [-9.20731]
                         (47.5178)
                        [-0.19377]

D(LM2DEFL(-1))             32.13107
                         (97.0051)
                         [0.84667]

D(LC0NS(-1))               16.48161
                         (118.352)
                         [0.13926]

D(LWASEDEFL(-1)          -30.3836E
                         (98.5362;
                        [-0.30835]

D(I(-1))                  -0.869247
                         (0.60427)
                        [-1.43852]

D(UNEMPLOYMENTS (-1))     -0.681324
                         (1.04050)
                        [-0.65481]

D(DDEFL(-1))              -4.399033
                         (76.6886)
                        [-0.05736]

D(C0NS_C0NF(-1))          -0.053253
                          (0.24782)
                         [-0.21488

C                         -4.202535
                          (4.90312)
                        (-0.85711]

@TREND(00Q1)               0.079822
                          (0.27685)
                         [0.28832]

DUMM08                    -7.758463
                          (8.34469)
                        (-0.92975]

UNCERTANTY                -0.368151
                          (2.02783)
                        (-0.18155]

R-squared                 0.477793
Adj. R-squared             0.192954
Sum sq. resids             686.1254
S.E. equation             5.584577
F-statistic               1.677410
Log likelihood           -101.7378
Akaike AIC                6.556446
Schwa rz SC               7.134147
Mean dependent           -1.180000
S.D.dependent             6.216430

Determinant resid covariance (dot adj.)
Determinant resid covariance
Log likelihood
Akaike information criterion
Schwarz criterior

Table 2. SUR Estimation

System: ECM
Estimation Method: Seemingly Unrelated Regression
Date: 02107/11  Time: 23:36
Sample: 2001Q4 201 0Q3
Included observations: 36
Total system (balanced) observations 72
Linear estimation after one-step weighting matrix

        Coefficient   Std. Error   t-Statistic    Prob

C(1)      -0.125341     0.043533     -2.879231   0.0055
C(4)      -0.624267     0.157446     -3.964970   0.0002
C(5)      -0.333510     0.143432     -2.325210   0.0235
C(6)      -0.003570     0.001001     -3.564900   0.0007
C(8)      -0.529071     0.125895     -4.202478   0.0001
C(9)       0.001923     0.000388      4.957960   0.0000
C(11)      0.003320     0.000274      12.11959   0.0000
C(12)     -0.109624     0.012486     -8.779920   0.0000
C(15)     -0.139366     0.039806     -3.501128   0.0009
C(21)     -0.164317     0.066441     -2.473124   0.0163
C(22)      0.000938     0.000355      2.642886   0.0105
C(24)      0.001320     0.000110     11.97677    0.0000
C(25)     -0.068197     0.006574     -10.37390   0.0000
Determinant residual  1.61 E-08
covariance

Equation: D(LM2DEFL)= C(1)*( LM2DEFL(-1) -1 *LWAGEDEFL(-1) +
0.00796646679368*l(-1)- 0.01 59963560363*UNEMPLOYMENT(-1) -
3.5371 7390802*DDEFL(-1) - 0.00337694953936 * CONS_CONF(-1) -
0.263811686179 *@TREND(D0Q1) - 0.60693561 0289) + C(4)
* D(LCONS(-1)) + C(5)*D(LWAGEDEFL(-1)) + C(6)*D(K-1)) + C(8)
* D(DDEFL(-1)) + C(9)*D(CONS_CONF(-1)) + C(11 )*@TREND(00Q1) +
C(12) * DUMM08

Observations: 38

R-squared               0.792023
Adjusted R-squared      0.740029
S.E. of regression      0.012932
Durbin-Watson stat      2.343617
Mean dependent var      0.036282
S.D. dependent var      0.025364
Sum squared resid       0.004683

Equation: D(LCONS)= C(15) * (LCONS(-1) - 0.568627985797
* LWAGEDEFL(-1) + 0.00300197162086 * UNEMPLOYMENT (-1) +
1.16289832827 * DDEFL(-1) + 0.00157610382946 * CONS_CONF(-1) -
0.0035720980905*@TREND(OOQ1)- 1.31484284684) + C(21)
* D(DDEFL(-1)) + C(22)*D(CONS_CONF(-1)) + C(24)*@TREND(00Q1)
+ C(25)*DUMM08

Observations: 36

R-squared               0.748195
Adjusted R-squared      0.715704
S.E. of regression      0.012239
Durbin-Watson stat      2.401081
Mean dependent var      0.015114
S.D. dependent var      0.022954
Sum squared resid       0.004644

References

Atta-Mensah, J. 2004. Money demand and economic uncertainty, Working Paper No. 25. Bank of Canada.

Beyer, A. 2009. A Stable Model for Euro Area Money Demand: Revisiting the Role of Wealth, Working Paper No. 111, European Central Bank.

Choi, W. G.; Oh, S. 2003. A money demand function with output uncertainty, monetary uncertainty and financial innovations, Journal of Money, Credit and Banking35(5): 685-709. doi:10.1353/mcb.2003.0034

Chrystal, A., Mizen, P. 2001. Consumption, Money and Lending: a joint model for the UK household sector, Working Paper No. 134, Bank of England.

Chrystal, K.; Mizen, P. 2005. A dynamic model of money, credit and consumption: a joint model for the UK household sector, Journal of Money, Credit and Banking 37(1): 119-143. doi:10.1353/mcb.2005.0002

Drake, L.; Chrystal, K. 1997. Personal sector money demand in the UK, Oxford Economic Papers 49(2): 188-206.

Greiber, C.; Lemke, W. 2005. Money demand and macroeconomic uncertainty, Discussion Paper No. 26. Deutsche Bundesbank.

Harris, R. I. D. 1995. Using cointegration analysis in econometric modelling. Essex: Prentice Hall Publishing. Johansen, S. 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autore gressive models, Econometrica 59(6): 1551-1580. doi:10.2307/2938278

Jain, P.; Moon, C.-G. 1994. Sectoral money demand: a co-integration approach, The Review of Economics and Statistics 76(1): 196-202. doi:10.2307/2109839

Juselius, K. 2006. The cointegrated VAR model: methodology and applications. Oxford: Oxford University Press.

Landesberger, J. 2007. Sectoral money demand models for the euro area based on a common set of determinants, Working Paper No. 741. European Central Bank.

Lippi, F.; Secchi, A. 2009. Technological change and the households' demand for currency, Journal of Monetary Economics 56: 222-230. doi:10.1016/j.jmoneco.2008.11.001

Petursson, T. 2000. The representative household's demand for money in a cointegrated VAR model, Econometric Journal 3: 162-176. doi:10.1111/1368-423X.00044

Seitz, F.; Landesberger, J. 2010. Household money holdings in the euro area. An explorative investigation, Working Paper No. 1238. European Central Bank.

Tin, J. 2008. An empirical examination of the inventory-theoretic model of precautionary money demand, Economics Letters 99: 204-205. doi:10.1016/j.econlet.2007.06.029

Thomas, R. 1997. The demand for M4: a sectoral analysis, Working Paper No. 62. Bank of England.

Money Demand and Uncertainty, ECB Monthly Bulletin, October 2005: 57-73

Sectoral money holding: determinants and recent developments, ECB Monthly Bulletin, August 2006: 59-72.

Gheorghe Ruxanda (1), Andreea Muraru (2)

The Bucharest Academy of Economic Studies, 15-17 Calea Dorobanti, sector 1, Bucharest, Romania

E-mails: (1) ghruX@ase.ro (corresponding author); (2) andreeabotezatu@gmail.com

Received 7 January 2011; accepted 4 May 2011

(1) VAR--Vectors Auto Regressive

(2) SUR--Seemingly Unrelated Regression

(3) Money Demand and Uncertainty, ECB Monthly Bulletin, October 2005, 57-73 and Sectoral money holding: determinants and recent developments, ECB Monthly Bulletin August 2006, 59-72.

(4) As sectoral data are available only starting from December 2004, the data was estimated backwards by taking into account households' holdings of currency (from the national financial accounts) and keeping all other holdings proportional with the share they had in December 2004.

(5) Atta-Mensah (2004) used in building the uncertainty measure of the conditional volatility of a stock market index, long-term interest rate, 90-day commercial paper rate, exchange rate between Canada and US and real GDP.

(6) As mentioned in Harris (1995) it is not uncommon that the two statistics offer different results, especially in the case of small samples. Anyway, between the two the trace statistics is more robust to residuals' lack of normality.

(7) SUR allows estimating the equations of the system by accounting for the residuals' correlation (coming from different common influences and perceived shocks).

Gheorghe RUXANDA. PhD in Economic Cybernetics, is Full Professor and PhD Adviser within the Department of Economic Cybernetics, The Bucharest Academy of Economic Studies. He graduated from the Faculty of Economic Cybernetics, Statistics and Informatics, Academy of Economic Studies, Bucharest (1975) where he also earned his Doctor's Degree (1994). Had numerous research visits in Columbia University --School of Business, New York, USA (1999), Southern Methodist University (SMU), Faculty of Computer Science and Engineering, Dallas, Texas, USA (1999), Ecole Normale Superieure, Paris, France (2000), Reading University, England (2002), North Carolina University, Chapel Hill, USA (2002). He is full professor of Multidimensional Data Analysis (Doctoral School), Multidimensional Data Analysis (Master Studies), Modeling and Neural Calculation (Master Studies). Fields of Scientific Competence: evaluation, measurement, quantification, analysis and prediction in the economic field; econometrics and statistical-mathematical modeling in the economic-financial field; multidimensional statistics and multidimensional data analysis; pattern recognition and neural networks; risk analysis and uncertainty in economics; development of software instruments for economic-mathematical modeling. Scientific research activity: over 35 years of scientific research in both theory and practice of quantitative economy and in coordinating research projects; 48 scientific papers presented at national and international scientific sessions and symposia; 64 scientific research projects with national and international financing; 69 scientific papers published in prestigious national and international journals in the field of economic cybernetics, econometrics, multidimensional data analysis, microeconomics, scientific informatics, out of which seven papers being published in ISI--Thompson Reuters journals; 15 manuals and university courses in the field of econometrics, multidimensional data analysis, microeconomics, scientific informatics; 31 studies of national public interest developed within the scientific research projects.

Andreea MURARU is PhD candidate in Economic Cybernetics at the Bucharest Academy of Economic Studies, has an MA degree in Finance (2007), graduated the Faculty of Economics, Babes-Bolyai University in Cluj-Napoca, majoring Statistics (2005) and was ERASMUS-SOCRATES Student of Aristotle University, Thessaloniki. Fields of Scientific Interest: econometrics and macroeconometrics, macroeconomic modeling, multidimensional time series analysis with a focus on cointegrated VAR. Scientific research activity: involvement in one research project with national financing; participant in national and international conferences and symposia; seven published papers out of which two articles being published in ISI--Thompson Reuters journals.

Table 1. Testing price homogeneity

Cointegration Restrictions:
B(1,1) = 1, B(1,3) = -1
Convergence achieved after 7 iterations.
Restrictions identify all cointegrating vectors
LR test for binding restrictions (rank = 1):

Chi-square (1)      0.014310
Probability         0.904782
Cointegrating Eq:   CointEq1

LM2NSA(-1)            1.00
LWAGEDEFL(-1)        -0.84
                     (0.12)
                    [-7.16]
LOG(DEFLSA(-1))      -1.00
                     0.0099
                    (0.002)
                     [4.97]
@TREND(00Q1)         -0.024
C                    -3.28

Table 2. Lag length determination
VAR Lag Order Selection Criteria
Endogenous variables: LM2DEFL TWAGEDEFL I UNEMPLOYMENT
DDEFL CONS_CONF
Exogenous variables: C DUMM08 UNCERTANTY
Sample: 2000Q1 2010Q3
Included observations: 34

Lag   LogL     LR         FPE

0     -92.91      NA      2.75 e-05
1      97.17   279.55 *   3.43 e-09
2     137.98    45.60     3.54 e-09
3     199.86    47.31     1.81 e-09 *

Lag   AIC      SC         HQ

0      6.52    7.33       6.80
1     -2.53   -0.11 *    -1.71
2     -2.82    1.21      -1.44
3     -4.34 *  1.31      -2.41 *

* indicates lag order selected by the
criterion

LR: sequential modified LR test
statistic (each test at 5% level)

FPE: Final prediction error

AIC: Akaike information criterion

SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

Table 3. Household money demand

Vector Error Correction Estimates   Cointegration Restrictions:
Sample (adjusted): 2001Q4 2010Q2    B(1,1) = 1, B(1,2) = -1
Included observations: 35           Convergence achieved after
after adjustments                   168 iterations.
Standard errors in ( ) &            Restrictions identify all
t-statistics in [ ]                 cointegrating Vectors
                                    LR test for binding
                                    restrictions (rank = 1):

                                    Chi-square(1)       2.69
                                    Probability         0.10

Cointegrating Eq:      CointEq1     Cointegrating Eq:   CointEq1

LM2DEFL(-1)            1.00         LM2DEFL(-1)         1.00
LWAGEDEFL(-1)          -1.28        LWAGEDEFL(-1)       -1.00
                       (0.12)       I(-1)               0.009
                       [-10.35]                         [ 5.85]
I(-1)                  0.012
                       (0.002)      UNEMPLOYMENT(-1)    -0.02
                       [5.62]                           (0.004)
UNEMPLOYMENT (-1)      -0.019                           [-4.56]
                       (0.004)
                       [-4.34]      DDEFL(-1)           -1.48
DDEFL(-1)              -1.85                            (0.38)
                       (0.38)                           [-3.94]
                       [-4.82]      CONS_CONF(-1)       -0.002
CONS_CONF(-1)          0.0007                           (0.0008)
                       (0.001)                          [-2.71]
                       [ 0.67]
@TREND(00Q1)           -0.025       @TREND(00Q1)        -0.029
                       (0.003)                          (0.001)
                       [-8.99]                          [-19.95]
C                      3.73         C                   -0.52

Table 4. Household money demand and consumption

Vector Error Correction Estimates
Sample (adjusted): 2001Q4 2010Q2
Included observations: 35 after adjustments
Standard errors in ( ) & t-statistics in [ ]

Cointegration Restrictions:
B(1,1) = 1, B(1,2) = 0, B(1,3) = -1, B(2,1) =
0,B(2,2) = 1, B(2,4) = 0
A(1,2) = 0, A(2,1) = 0

Convergence achieved after 227 iterations.
Restrictions identify all cointegrating vectors
LR test for binding restrictions (rank = 2):

Chi-square(4)       2.064692
Probability         0.723861

Cointegrating Eq:   CointEq1   CointEq2

LM2DEFL(-1)         1.00       0.00
LCONS(-1)           0.00       1.00
LWAGEDEFL(-1)       -1.00      -0.57
                               (0.07)
                               [-7.76]

I (-1)              0.0079     0.00
                    (0.001)
                    [5.84]

UNEMPLOYMENT (-1)   -0.016     0.003
                    (0.006)    (0.005)
                    [-2.74]    [ 0.57]

DDEFL(-1)           -3.54      1.16
                    (0.50)     (0.44)
                    [-7.09]    [ 2.65]

CONS_CONF(-1)       -0.003     0.0016
                    (0.001)    (0.001)
@TREND(00Q1)        [-2.97]    [1.44]

C                   -0.026     -0.004
                    -0.61      -1.31