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Hildegart Ahumada, Banco Central de la Repriblica Argenti and Instituto Torcuato Di Tella, Buenos Aires, Argentina

This work models money in the complex, highly indationary environment of Ar- gentina ( 1977- 1988). First, cointegration techniques proposed by Engle and Granger (1987) and extended by Johansen ( 1988) are applied anJ show that real cash balances, income and inflation are cointegrated. Second, data information are used to specify the dynamics of this relationship, following the “general-to-specific” methodology developed by Hendry et al. The model selected appears to be a satisfactory represen- tation of money demand, including being empirically constant over 1985- 1988, during which there were major policy change s. However, constant, well-specified inflation or interest rate equations cannot be &a.ined by inverting the money demand equation, given the results found when testing for s1zpzr exogeneity.

1. INTRODUCTION

This work models real cash balances in the complex highly inflation- ary environment of Argentina (1977-1988). First, the paper analyzes the long-run determinants using an information set which includes inter- est rates, domestic prices. and transactions volumes. Cointegration techniques, proposed by Englz and &anger ( 1587 j and extended by Jo- hansen (1988), are applied to evaluate the long-run hypothesis that real money, real income, and the inflation rate are cointegrated. Second, data information are used to specify the dynEtics of the model follow- ing the “general-to-specific” methodology developed by Hendry et al.

The selected model incorporates a linear error correction term and an asymmetric effect of inflation. It has a suitable economic interpre- tation and satisfies a range of statistical criteria, so it is considered a tentative approximation to the underlying data-generating process of

AdUress correspondence to Hil&gart Ahumordo. Banco Central & la Repriblica Argentina,

Reconquista 264. (1003) Buenos Aires, Argentina.

The author wishes to acknowledge useful comments from an anonymous tkferee and is my indebted to Neil Ericsson for his encouragement and valuable help in improving an earlier version. Remaining errors and the views expressed in the paper are solely the responsibility of the author.

Received March 1991; final draft accepted August I99 i .

Journal of Policy Modeling 143):335-36 I ( 1992) Q Society for Policy Modeling, 1992

336

real cash balances. For policy model remains constant up to withstanding its constancy, the

ation or the interest rate

H. Ahumada

purposes it shoi%l be noted that the the outbreak of hyperinflation. Not-

1 model is not useful to derive a model by inversion.

t

The next section summarizes the money-demand theory and the Argentine institutions and data. Section 3 describes cointegration tech- niques and their relation to error correction models. The long-run hypothesis via cointegration techniques are evaluated in Section 4. Section 5 reports results of modeling short-run dynamics, and section 6 discusses the model obtained. Section 7 concentrates on exogeneity issues. Finally, conclusions are stated in Section 8.

EORY, INSTITUTIONS, AND DATA

The basic model of the demand for money inclcldes transactions (Y) and the opportunity cost of holding real cash balances as explanatory variables. Total final domestic expenditure (GDP plus imports minus exports) in real terms is used for Y, since it has proven to be more useful than other definitions. Both infIation (n) and interest rates (R) may help measure the opportunity cost. ’

Although usual theories of the demand for money include interest rates, several problems are found empirically ior Argentina. For in- stance, in periods of regulated interest rates, no records exist for the differential paid in the black market, which probably has varied with the levels of restrictions. Friedman (1956) and Cagan (1956) stress the impor?ance of the effect of inflation on real cash balances when inflation is high. However, whether inflation dominates the interest rate at high inflation rates is an empirical issue. In the long run, nevertheless, inflation and interest rates are supposed to move together, in a rela- tionship similar to that of the Fisher hypothesis. At high inflation rates, deviations between them seem to be negligible in the long run, although substantial deviations may occur in the short run.

In the last decade, the Argentine economic authorities tried different strategies to moderate inflation. These attempts included price controls, fixed interest rates, and fixed exchange rates, alternated with tough monetary policies which derived mainly from high compulsory reserve requirements, aimed at increasing the spread of domestic over foreign asset returns. As a consequence- it is sometimes believed that data

‘See appendix for data definitions and sources. Unless otherwise indicated, capital letters denote the generic names while logs of the scnlars are in lower case. The price index (P) is CPI and n = (p, – p, ,j. The interest rate is the rate on savings and the interest rate enters the lrrnllel ES r = !n( 1 + R).

THE DEMAND FOR CURRENCY IN ARGENTI

-2.30

-2.68

L – ’ – ‘. 1 _ I _ I – a – : ., . 1 ., . I.

1978 1979 1988 1981 1982 1983 1924 198s 1986 a987 1988 198;

Figure 1. Real cash balances ( m -p ),.

may not always reflect the underlying behavior of monetary variables and that it is not possible to find constant econometric relationships even over a few years. The model developed in Sections 4-7 provides evidence against these views.

Before modeling the data, we should consider its basic statisti properties. Figure 1 shows monthly real cash balances (or “money”) from 1977 to 1988. That spans the period from the monetary reform that ended the system of nationalized deposits until the appearance of hyper- infIation at the beginning of 1989. Real holdings of money, m – p, de- clined during the early 198Os, but increased sharply after the reform of June 1985, the Austral Plan. That reform included a combination of or- thodox and heterodox policies and is associated with the main recuper- ation of real cash money holdings in the sample period. It was followed by a new demonetization period with partial recoveries in I987 and f 988 until August 1988, when the “Primavera” plan, was launched.

Figure 2 charts real money with inflation, in which the former has been transformed to a pseudo-velocity measure [ – Cm – p – OSv)]. The figure suggests a close relation between them. Also, -(m L p – 0.5~) looks verv similar to the inversion of m – implying that the” transactions are not moving

in Figure 1, muc relaiive to

338

.388

r

H. Ahumada

.a569

.2W

i

t

.15e –

.lW –

,858 –

I. 1. “I.‘. ’ – ’ – 1. ’ – ’ – ‘. ‘. 4 1978 1979 1988 1981 1982 1983 ii984 1985 1986 1987 1988 1989

Figure 2. The inflation rate 7~, and the pseudo-velocity, – (m -p-‘/24’),, matched by ranges.

m – p. The transaction’s behavior can be observed in Figure 3. Both transactions and real balances also shobv seasonal behavior; that of money holdings is mainly associated with the two complementary payments received in July and December by all wage earners.

3. DYNAMIC SPECIFICATION: COINTEGRATION AND CORRECTION MECHANISMS

This section discusses the relation of the dynamic error-correction (EC) model to the “general-to-specific” modeling approach and to cointegration.

A common practice in applied econometrics has been to estimate regressions in differences of the variables to avoid the spurious cor- relation problem of trending series discussed by Granger and Newbold ( 1?77). Mowever, this kind of dynamic model is unable to display long-run behavior, e.g., to solve for the levels of the variables when these grow at constant rates. For that reason, among others, other authors have attained stationarity through error-correction models, which not only encompass models in differences, but also have a

THE DEMAND FOR CURRENCY 1

2.35

t.‘-‘.‘……-……….~ 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 6989

Figure 3. The volume of transactions y,.

suitable economic interpretation. For the first versions, see Phillips ( 1957) and Sargan ( 1964), and for more recent versions, see Davidson et al. ( 1378) and Hendry and Mizon ( 1978), among others.

For a linear single-equation model with two variables, x and y, and one lag, the EC representation is

A,v, = &, + f&Ar, – (I – f&My – Ax), , + e, 4, – N(O,d. (1)

In practice x and y often are logs of the underlying economic series, denoted X and Y. The rate of growth of Yd depends not only on that of X, (short-run impact), but also on the past disequilibrium (y – A&,- 1. If the long-run equilibrium is static (t = t – 1 and Ay = Ax = C), then (1) implies Y = K l XA, where In K = &,/( 1 – p3) (which simplifies to proportionality for A = 1).

For steady-state growth with Ay = Ax = T, Equation 1 implies Y = K’XA, where Ink? – $ f3, – 1)7)/f 1 – p3). The economic

relevance of a model like ? follows ‘because many economic theories suggest long-run ion&y, e.g., the Permanent Income Hypothesis and the Quant ot lMsney. Further 1 cm be derived from a certain kind of optimizing agents responding to their past disequilibrium. For instance, gro

340 H. Ahumada

in Y, will be greater than l3, times the growth in X, if Y,_ l was less than its long-run desired value. Thus, this representation is more gen- eral than that of differences models while still obtair ‘irg stationarity in the variables included. For a comparison with other dynamic spec- ifications, see Hendry, Pagan, and Sargan (1984).

In the “general to specific” approach to modeling, Equation 1 is equivalent to the unrestricted dynamic regression of y on x,

Y, = PO + IO, + P9, I + thy, I + 4,. (2)

where A = (PI + PM1 – fi3). If X and Y are proportional in the long run, then A = 1 or, equivalently, 131 + p2 + p3 = 1.

The study of long-run relationships between economic time series variables has been developed further through the cointegration concept proposed by Engle and Granger ( 198?).* The basic idea is that indi- vidual economic time-series variables wander considerably, but certain linear combinations of the series do not move too far apart from each other. Econoi+ ffirofi 1 b LvIbbs tend to bring those series into line, e.g., as hypothesized by economic theory. The series in such a relationship are said to be cointegrated.

More formally, if yt and x, are both I( 1 ), then it is possible that a linear combination of them,

ii, = y, – Ax,, (3)

is I(0). If so, y and x are cointegrated with a cointegration vector (1: -A)‘. The errOr u, measures the disequilibrium present between y, and x,. Since it is I(O), u,_ 1 can be used as regressor in a representation that includes AyI as dependent variable, which is also I(0) (Hendry, 1986).

Two properties of cointegration should be emphasized. First, Engle and Granger (1987) show that cointegrated series have an EC repre- sentation and that EC mechanisms imply cointegrated variables. Sec- ond, Stock (1987) shows that when variables are cointegrated, ordinary least squares (QLS) estimates of cointegration parameters converge to their true values more rapidly than with stationary variables. Thus, Engle and Granger (1987) suggest a two-step estimation approach for dynamic specification, each step requiring only GLS. In the first step, A is estimated by regressing y, on x,. In the second step, u,_ 1 (using a) is included as regressor to explain Ay, as part of the systematic dynamics. As a test of cointegration, they propose evaluating whether

*See also the special issue on cointegration of the O_rjkd Bulletin of Economics and Sturisdcs ! 1?%).

THE DEMAND FOR C ,341

u, is I(0) after testing that x and y are I( I ). Sev the most common being the (possibly augment statistic and the Cointegrating Regression Durbin-Watson statistic (CRDW) (Dickey and Fuller, 1979 and 198 1 and 1983). However, the long-run parameter A esti regression can be severely biased in finite samples, as B (1986) demonstrate. In particular, when R’ is sm regression, static and dynamic estimates can suggest full dynamic modeling as an alternative.

An improved procedure for testing cointegration, allowing for mo than one cointegration vector, is that suggested in Johansen ( 1988) generalized in Johansen and juselius ( 1990). Based on the unrestri estimation of a system, parameterized in terms of levels and differ- ences, they propose Likelihood Ratio statistics for testing the number of cointegration vectors. The coefficient matrix for levels contains information about long-run relationships between variables in the data vector. Since its rank is the number of non-z eigenvalues in a determinental equation closely related to estimating the system, the number of cointegrating vectors i termined by testing how many of those eigenvalues are nonzero. e cointegrating vectors (denoted B’) are shown to be a subset of the associated eigenvectors. Further- more, the associated weighting coefficients (denoted cy) can be useful to evaluate weak exogeneity, because it is lost if a cointegration vector appears in the conditional and marginal models (Johansen, 1990).

In Section 4, both Engle-&anger and Johansen techniques are ap plied to testing a long-run hypothesis about the demand for money in the Argentine case. Section 5 presents the results of modeling that function by using the ’ ‘general-to-simple” approach. -i

4. LONG-RUN BEHAVIOR

Given the basic economic model of the demand for money and the variables’ behavior, real money balances are hypothesized to be coin- tegrated with the volume of real transactions and the opportunity cost of holding money, defined as ?r. Cointegration has been tested with two different measures of opportunity cost: r and m. The seccnd is preferred in terms of the stability of the long-run parameters, and so is the only one presented below.

From Table 1, all variables appear to be I( 1). Inflation may be an exception, as its statistics are very sensitive to the sample

“He&y’s (1989) PC-GIVE was used for estimation.

342 II. Ahumada

Table 1: Tests of theOrder of Integration of Individual Variables

m-p Y 77 r

l(0) DW 0.23 0.22 0.40 0.18

mF(3) – 2.7 – 2.6 -3.3 -2.5

I(i) DW 1.72 2.00 2.27 1.70

ADF(3) – 7.9 -6.3 – 7.9 -6.9

DW and ADF are the Durbin-Watson and augmented Dickey-Fuller statistics (Sargan and Bhargava, 1983; Dickey and Fuller, 1979, 1981).

sen. Even so, ?t is considered to be I(i), having the same order of integration as that of r.4

The static Engle-&anger cointegration regression is

m-p= –3.1 + 0.534, – 2.3~; ‘Ir = 139[77(6) – 88(12)], CRDW = 0.68,

DF = -5.3, DFAi 13) = – 4.0, R* = 0.62. (4)

All the statistics reject the hypothesis of noncointegration at the critical values provided by Engle and Yoo (1987) for the three- variable case. The low R2 may imply bias in estimating the long- run parameters.

To analyze cointegration of these series further, the system-based procedure from Johansen ( 1988) and Johansen and Juselius ( 1990) is applied to m – p, TT, and y with six lags, a constant, and seasonal dummies. Table 2 lists the eigenvalues frcm the smallest (closest to a

Table 2: Cointegration Results: Eigenvalues and Related Test Statistics

Eigenvalues

Maximal eigenvalues

StatisticS 95% critical value

Eigenvalue trace

Statistics 95% critical value

1 0.030 4.07 8.08 4.07 8.08 2 0.05 1 6.96 14.60 11.02 17.84 3 0.150 21.51* 21.28 32.53* 31.26

The statistics are defined in Johansen (1988) and Johansen and Juselius (1990) and critical values are taken from the latter’s Table A2.

*Significant at the 95% critical value.

‘ADF statistics for this set of variables are very sensitive to the sample size, the inclusion or exclusion of a constant or trend, and the model of seasonality (deterministic or autoregressive). However, the estimation of the unrestricted model suggests that the assumed order of integration is approphate .

THE DEMAND FOR CURRENCY IN ARGE 343

Table 3: Cointegration Results: Normalized a and p’ Matrixes

Variable a (weighting matrix)

m-p -0.234 – 0.026 – 0.034 1.000 2.776 – 0.482 m -0.001 – 0.032 0.026 -0.129 1.000 1.048 Y 0.069 -0.051 – 0.007 0.112 – 3.020 1.m

unit root) to the largest (most stationary) and the LR statistics based on the maximal eigenvalue and on the eigenvalue trace. Table 3 PIE- sents the normalized weighting matrix, (Y, and the matrix of cointe- grating vectors, 9’.

Both statistics in Table 2 indicate that there is one cointegration vector. Furthermore, the cointegration vector (row 1 of Table 3) has a coefficient close to 0.5 on transactions and a coefficient on inflation of – 2.78, similar to those obtained by the static regression, Equation 4. Note that this remarkable similarity may due to the large variation of the data involved. Also note that the cointegration vectors estimated by both procedures are very close to the square-root law of the Baumol- Tobin model.

From the weighting values in Table 3, the cointegrating vector enters the money equation with a coefficient of -0.23 while the money- demand cointegrating vector does not appear to enter the equations for v or y. That is necessary for w and y to be weakly exogenous in a conditional money-demand equation (Johansen, 1990).

5. SHORT-RUN DYNAMICS AND THE HYPOTHESIS OF ASYMMETRY

Asymmetric effects of inflation on real cash balances have been hypothesized for Argentina. In empirical studies, that hypothesis has been tested using a ratchet effect based upon the maximum of past W. This ratchet reinforces the asymmetric effect of m in a Cagan equation, as in Piterman ( 1988) and Melnick (1989). Ahumada ( 1989) discusses some problems of this empirical measure. In particular, the assumption of irreversibility associated with it ensures the ratchet’s role in the long-run relationship. From the above cointegration analysis, it seems empirically possible to ignore this hysteresis effect in the long-run relationship. This does not preclude asymmetric effects in the short run, and therefore, separate effects for rising and falling inflation are included as regressors in modeling short-run dynamics.

To model dynamics and the long run jointly, an unrestricted auto-

344 H. Ahumada

regressive distributed lag of m – p on y, 7t, and r is estimated with seven successive lags, seasonal lags (12 and 13), and monthly dum- mies. Furthermore, a dummy variable (denoted by WD, equal to 1 for April and May 1982) is included in the unrestricted regression to take into account the jump in the demand for currency during the war conflic; over the Malvinas. No significant loss of information is found in re- stricting the model to three lags and four seasonal dummies (SD) for July, August, November, and December. Also, long-run price hom- ogcneity is not rejected when tested by including p,-, in the lat- ter regression; its coefficient is not significant. Table 4 presents the autoregressive-distributed lag for m – p where A$, Am,, and their lag? are included along with IT,. The terms Am,+ and An*- denote max(0, ATT,) and min(O, Am,). This parameterization is a generalization of iilc!uding 7c, and its lags, with the latter imposing coefficient equality on An;‘_j and An,j.

The solved long-run solution to Table 4 is

m-p = -2.7 -I- 0.35~ – 2.71~ + 0.54r + 1.8WD f &SD,. (5) (1.1) (0.45) (1.9) (2.2) (0.8)

This confirms the results of the last section but with a wider information set. The coefficient of n is similar to that of Equation 4, whereas that of r is positive. That supports the view of a long-run relationship between real balances, transactions, and 7t alone. The long-run coef- ficient of y is similar to the Baumol-Tobin elasticity obtained in Equa- tion 4, albeit with a large standard error.

S&&ntial sequential rr;duction from: T&k 4 results in the foilowing restricted conditional model:

A(m – p), = 0.13A(m – /I),_, + 0.32Ati,_, – 0.78A,r, – 1.2OAn,+ – 0.53Av; (6)

(0.04) (0.07) (0.12) (0.19) (0.15)

– O.l4[m – p – osy – (-3 – 2.3~)],_, + 0.2OWD + &SD, – 0.0050;

(0.03) (0.02) (0.0055)

T = 136[77(9) – 88(12)],

R2 = 0.87, u = 3.4%, BP$( 13) = 15.9. AR1 -7F(7,117) = 0.52, ARCHI – 7F(7,110) =

1.46, RESET F( 1,123) = 0.76. NORM x’(2) = 4.6, X,ZF( 16,107) = 1.98, ENCF( 19,104) =

0.96,

where ENCF(q, T – K – q) evaluates q-parameter restrictions relative to Table 4 (Johnston, 1963). Equation 6 has much simpler dynamics than Table 4. Equation 6 also imposes the Baumol-Tobin long-run income elasticity of l/2, and imposes the long-run inflation elasticity of – 2.3 from Equation 4. The next section discusses the properties of Equatioll 6.

THE DEMAND FOR CURRENCY IN ARGENTINA 345

Table 4= Autoregressive Distributed Lag Representation for (m -p)

Lag, (or index)

Variable 0 I 2 3 Zj=,

W-P),-,

r,-,

Yl-,

SD,-,

SD,-,-,

SD,-,-,

WD

Constant

-1.0

LO) – .305

(203)

– .805

(302)

– .310

(.234)

– .790

(.177)

.087

(. 140)

– .019 (.020)

-020 (.023)

.207 (-030)

– .310

(.192)

.918

(.083)

– .337

(294)

.I95

(.208)

– -029

(266)

-349

(. 181)

-016 (.017)

– .005

(.020)

.037 (-024)

– .095 (.123)

– -248

(-269)

– .I59

(168)

-519

(289)

– .102

(. 184)

.I00 (-017)

– .034 (021)

– .008

(019)

.063 ( .077)

.361

(244)

– .294 (132)

-.060

(-018)

.I49 (021)

– 005 (.017)

-0.114

ww – 0.305

l.203)

– 1.390

( .58O)

-0 274

(.415)

0.061 (.236)

0.040

( .058)

T = 135[77(10)-88(12)],

R2 = 0.975, 0 = 3.48%, BfX’(16) = 17.8, AR 1-7 F(7,97) = 1.31, ARCH I-7F(7,90) =

1.88, RESETF( I, 103) = 0.17, NoRMX’(2) = 4.2, XfF(36.67) = 0.71, where o is the estimated standard deviation of residuals, standard errors are in parentheses and Bpx’(q) is Box-Pierce

statistic for qti-order; AR 1-q F(q, T-K- 1) is the LM statistic for q*-order ARCH (Engle, 1982); NORM x2(2) is Jarque-Bera statistic (1980); Xf F(q, T-K-q-l) is the statistic for heteroskedasticity quadratic in regressors (White, 1980; Nicholls and Pagan, 1983); RESET F(q, T-K-q) is Ramsey’s statistic.

6. EVALUATION’

Equation 6 has a clear economic interpretation. Real holdings of currency are determined by transactions and inflation in the Img run.

‘For the different criteria and information sets for model design and evaluation see Hendry

and Richard ( 1982), Hendry ( 1983), and Hendry ( 1989).

346 H. Ahumada

In the short nrn, agents increase (decrease) their money holdings by 14 percent of the past month’s excess demand (supply).

Notwithstanding that disequi ibrium effect, inflation has an asymmet- ric effect on real money, the effect depending on whether inflation is ris- ing or falling, since both AT + and AK enter Equation 6. The coefficient on Am is 72 increases and – Q.53 when it falls. The effect of A~F+ a can be interpreted as a part of a for- ward-looking model of inflation. in which these variables are data-based predictors of n,+ 1 (Campos and Ericsson, 1988 and Hendry and Erics- son, 199 1 b). Furthermore, money holdings depend on contempora- neous changes in the interest rate and lagged changes in transactions.

From the diagnostic statistics, the residual of the estimated equation appears to be white noise (BPx',ARF), homoscedastic (ARCH r"; White’s standard errors of coefficients are also similar to those OLS estimated), and an innovation (ENC F)? The LM statistic based on the squares of regressors (XfF) indicates some misspecification, per- haps the need for a nonlinear error correctio;; A cubic relationship was tried and the derived regressor (u,_ l – 0.14)& I was’ini%tded in the model. This error correction response is similar to that found for the United Kingdom (Hendry and Ericsson, 1991a). Although this representation reduces the LM statistic to F( 16,107) = 1.32, it exhibits parameter instability for the period of increasing monetization after the economic plan known as “Primavera. ” The instability seems to be derived from the real money respo;lses to excess demand, which is increasing in that cubic function (although it may be appropriate for the cases of excess supply, above a certain level). Even so, the linear error correction model is preferred, given its much better predictive performance in the last 3 years.

Parameter constancy is ev luated over three periods, which include the main attempts at econ ic stabilization. First, for the last 40 months-l 985(9)- 1988( 12~the Chow and forecast x2 statistics are CHOW F(40,84) = = 0.95. These statistics indicate that the null hypothesis of parameter constancy cannot be rejected. Figure 4 charts the one-step prediction for this subsample.

An earlier, overlapping sample, 1985(6)-1988(9), includes the in- troduction of the Austral Plan in June 1985. The corresponding sta- tistics become CHOW F(40,Sl) = 1.11 and x2/(40)/40 = 1.39.

I986 1987 1988

Figure 4. Equation 6: One-step-ahead forecasts of A(m -p),, with 2 2 forecast standard errors.

Although the overall statistics are insignificant, the forecasted change in real cash balances for June 1985 is somewhat higher th

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