A framework for the analysis of legal and fraudulent trade transactions in “Parallel” exchange markets

A Framework for the Analysis of Legal

and Fraudulent Trade Transactions in

"Parallel" Exchange Markets

By

Jagdeep S. Bhandari and Bernard D e c a l u w e

Contents: I. Introduction. - II. The Analytical Framework. - III. The Rational Expectations Solution. - IV. Dynamic Adjustment with Incomplete Market Separation. - V. Instantaneous and Stationary-State Effects of Structural Disturbances. - VI. Stationary- State Effects. - VII. Conclusion.

I. Introduct ion

" / ~ i rticle VIII, Section 3, of the Fund's Articles of Agreement prohibits " ~ a member from engaging i n . . . any discriminatory currency arrange-

ments or multiple currency practices without approval of the Fund. . . " [IMF, 1982]. Despite its continuing unfavorable attitude toward such arrangements however (especially for current account transactions), the Fund reports that ". . . 42 members maintained multiple currency practices at the end of March 1982" of which nine members did so without approval of the Fund 1.

Of the 42 countries reported to be engaging in some form of multiple currency practices, at least 10 can be identified as maintaining widespread legal dual exchange markets as of end 1981 (the rest employ parallel markets for only limited categories of transactions). These are Belgium-Luxembourg, Costa Rica, Dominican Republic, Ecuador, Egypt, Nicaragua, Paraguay, E1 Salvador, Sudan and Syria. In addition, the French and Italian experiences with two-tier regimes in the early 1970s are well-documented.

It is clear therefore that there has been a wide variety of experience with officially sanctioned dual exchange markets. Despite the fact that the BLEU (Belgo-Luxembourg Economic Union) has continuously operated such a system since 1957, economic analyses of two-tier systems did not begin until the early 1970s. The last decade however, has witnessed several attempts to address two principal questions - the efficacy of monetary and fiscal policies under such regimes and the insulation properties of the latter. The papers by Fleming [1971], Barattieri, Ragazzi [1971], Salin [1971], Decaluwe [1974], Swoboda [1974], Argy, Porter [1972], Decaluwe, Steinherr [1976], Cumby

It is clear that if one includes those countries that have "black" markets (or "curb" markets) for foreign exchange, despite officially unified rates, then the number of countries on a de facto multiple exchange rate system is far greater than the 42 reported by the IMF.

234 l a g d e e p S. B h a n d a r i and B e r n a r d D e c a l u w e

[1984], and Aizenman [1985] fall in the first category; while those by Dornbusch [1976], Flood [1978], Fleming [1974], Marion [1981] and Flood, Marion [1982] are more concerned with the formation of expectations and the insulation properties of such systems. Discussion of actual experiences with two-tier systems (such as those in France, Italy and the BLEU) can be found in Talent [1970], Abraham, Martin [1970], Abraham [1974], Decaluwe [1975] and Lanyi [1975; see also Adam, 1982].

A curious feature of all of the above-mentioned theoretical analyses is the universal assumption that dual exchange markets can be and are effectively segmented with no inter-market "leakage". Such an assumption, while analytically convenient, is patently false on account of two complementary reasons. First, illegal cross operations between the financial and commercial exchange markets are widespread. Evidence on the existence of illegal transactions can be found by comparing export and import invoices which fail to match. This point has been noted before by Lanyi [1975] in the context of France, Italy and the BLEU 2. In fact, the existence of illegal transactions through an expanding "parallel market" may have been the principal catalyst in the demise of the dual rate systems in both France and Italy. According to the Banca d'Italia itself, by the time the system was abolished, the financial exchange market "had lost all practical significance" [Banca d'Italia, 1975]. Second, and more importantly, a certain amount of leakage is officially sanctioned in every country that engages in dual exchange rate practices (either currently or in the past, such as France and Italy). Thus, several important categories of current account transactions are (were) officially assigned to the financial exchange market.

Tables 1 and 2 provide a summary picture of the nature of dual market arrangements and of legally sanctioned "leakage" in various countries including France and Italy for the early 1970s. Additional information regarding these institutional arrangements is available in the relevant country pages of the Annual Report of the International Monetary Fund. It is immediately clear that certain types of invisible current account transactions are settled in the financial market in every country mentioned in these tables (in three countries, all invisibles are transacted in parallel markets). More importantly, Table 1 reveals that with the exception of Ecuador and Paraguay, certain merchandise trade items (both exports and imports) must also be settled at the financial exchange rate(s) in the remaining seven countries. In most instances, this is effected by requiring that specified proportions of export receipts may be surrendered at the financial exchange rate (for example, Sudan, Syria, Costa Rica) or that only certain categories of imports (deemed to be "priority" imports) may be financed via the commercial exchange market (Egypt, Dominican Republic, E1 Salvador, Sudan).

2 Italy for example, witnessed fraudulent imports of gold, allegedly for industrial purposes.

"Parallel" Exchange Markets 235

T a b l e 1 - Exchange Rate Arrangements in Multiple-Rate Countries

Average Dual market Exchange market Exchange Met- In- Private Private premium (%)

system controls chandise visibles transfers capital as of dec. 3t, 1981 Official Free trade

dec. 31, 1981

Ecuador Pegged tc Contrc llec $ U.S. via Ye,, O-F 31

interve, tiol

Dominican Pegged tc Republic $ U.S. Yes Ye~ O-F 29-30

Egypt Pegged tc $ U.S. Yes Yes O-F 18

El Salvador Pegged tc $ U.S. Yes Yes O-F 40

Paraguay Pegged tc $ U.S. Yes Yes F 27-34

Sudan Pegged to $ U.S. Yes Yes F 70-132

Syria Pegged to $ U.S. Yes Yes O-F No data

Costa Rica Pegged to $ U.S. Yes No F 80

Nicaragua Pegged to No data $ U.S. Yes Yes O-F C (spread

controlled) Note: O: Official; F: Free; O-F: Depending on nature of transaction.

Source: Constructed by the authors from IMF, Country Pages.

Tab l e 2 - Exchange Rate Arrangements in France, BLEU and Italy

Merchandise trade Invisibles Private transfers . . . . . Public sector current account transactions.

Belgium-Luxembourg Italy France

1971-1975 1955-1971 Dec. 1981 1973-1974

In Out In Out In Out

O O O-F O-F F F

O Option O-F O-F

Option F

O-F O-F

O O O - F O - F F F

O - F O - F 0 0

0 O-F F

O

Note: O: Official; F: Free; O-F: Depending on nature of transaction; Option: Transaction can be settled in either market.

Source: IMF, Country Pages.

256 Jagdeep S. Bhandar i and Bernard Deca luwe

An important and relevant question to ask therefore, relates to the operation of a dual exchange market system, given incomplete segmentation. In particular, what are the properties of a regime characterized by inter- market transactions, with respect to dynamic stability, domestic economic policy and to externally-occurring disturbances etc.? And, how does the degree of leakage - determined (at least in part) by administrative fiat, as noted above - impinge upon these properties? These questions have not been previously asked, much less answered in the previous literature 3.

The present paper is intended to fill these lacunae in the literature. Specifically, we construct a simple stochastic equilibrium model of the open economy operating under a dual exchange market regime 4. While there are at least two varieties of two-tier systems, the regime we analyze, involves a pegged commercial (official) rate and a floating financial (parallel) rate. With the exception of Italy which employed a two-tier float for a brief period in 1974, this is in fact the type of regime that is currently in operation in all nine countries listed in Table 1, in addition to the BLEU (the commercial rate in the latter is managed within narrow limits as prescribed by the "Snake" arrangement). Exchange markets in our framework are not completely segmented and a proportion of commercial trade transactions are settled in the financial market, in accordance with the stylized facts noted above ~.

While a complete statement of our results would occupy considerable space, the following observation is in order here. In the absence of intermarket transactions or leakage, a floating financial exchange rate ensures that no net accumulation/decumulation of foreign assets can occur and the intrinsic dynamics of the economy are governed solely by reserve accumulation/ decumulation. With cross-operations, however, changes in the stock of domestically-held foreign assets do occur since the floating financial rate ensures that the capital account plus leakage is now zero. Thus, the dynamics

s There has been some attempt in the earlier "black" market or smuggling literature to discuss the linkage between official and "black" markets. Essentially, there appear to be two strands to this earlier literature. One line of inquiry is non-monetary in nature and is in the context of pure trade models. I~ypical questions addressed here relate for example to the welfare effects of smuggling. Much of this work has been pioneered by Bhagwati and is collected in Bhagwati [1974]. The other strand of literature employs simple non-stochastic monetary models. Representative works in this area include Culbertson [1975] and Gupta [1980;1981]. As will become clear, the present paper represents a much more general equilibrium approach than either type of inquiry mentioned above. In addition, we conduct our analysis in the context of a stochastic rational expectations model which emphasizes capital mobility and expectations (i.e., the ingredients that have become well-established and popular in current macromodeling).

4 Except for Flood, Marion [1982] none of the previous analyses are conducted in the context of a stochastic rational expectations framework.

5 There is also some "reverse leakage" in the sense that a limited number of capital account items are required to be settled in the commercial market in some countries. However, these items primarily involve some public sector capital transactions, the actual empirical importance of which does not appear to be significant (see also Lanyi [1975] in this regard).


of such an economy are capable of exhibiting richer patterns of adjustment, being guided by changes in both reserve stocks and foreign asset stocks.

The rest of the paper is organized as follows. The next section specifies the analytical framework, while the technique for deriving the ultimate rational expectations solution to the model is briefly discussed in Section III. Section IV analyzes the nature of dynamic adjustment in the model, while in Section V, we investigate the one-period and steady-state effects of various structural disturbances. The conclusion contains a statement of our principal findings.

II. The Analytical Framework

The hypothetical world of this model consists of an open economy operating under a system of dual exchange rates with a pegged commercial exchange rate and a freely floating financial exchange rate. Domestic output is limited to a single final commodity which is perfectly substitutable (on the demand side) with foreign output. The domestic economy is small in all international markets; specifically, the foreign currency price of output as well as the foreign interest rate are regarded as exogenously given parameters. Goods are perishable so that domestic residents must allocate their wealth between the available financial assets. These are domestically issued money and a one-period, riskless internationally issued security 8. There is no "currency-substitution", no physical capital accumulation and no transactions or transport costs.

We assume that the use of the Lucas supply function is no longer contentious. Thus, domestic output supply is governed by 7

(1) Yt = ff + b (Pt - Et-1, Pt)

where Yt is the current level of output in logarithmic form, ff the level of "trend" output and Pt the logarithm of the domestic price level. The operator E is an expectations operator and the subscript indicates the period in which this expectation is formed (based upon information available at that time). More elaborate supply functions based on either the real rate of return, incomplete contemporaneous wage indexation or multi-period contracts can clearly be employed, but lead to fruitless complexities at this stage.

Given the presumed absence of transportation and transactions costs, the domestic currency price of output is determined via a purchasing-power- parity relationship

(2) Pt = st + Pt* e It is not difficult to extend the model to incorporate two goods, i.e. an exportable and an

importable. In principle, it is also possible to extend the menu of assets by including domestically issued bonds. However, in order to focus on the problem at hand (i.e. leakage) we have elected to retain the simpler structure utilized in the text.

7 All parameters are defined positively, in what follows.

238 J a gde e p S. B h a n d a r i and B e r n a r d D e c a l u w e

where Pt* is the logarithm of the foreign currency price of the (single) commodity, while st is defined as the logarithm of the effective commercial exchange rate. Because of leakage from the commercial to the financial exchange market, the aggregate exchange rate relevant for commercial trade transactions is not the official commercial rate, but rather the effective commercial rate, where, the latter is a function of the commercial and financial rates, i.e.

St = F (X, E)

A logarithmic linear approximation to the unkown function F is given by

( 3 ) st = a ~ + (1 - a ) xt

0 < a < 1

where ~ and x~ are logarithms of the commercial and financial exchange rates respectively, while a is an arbitrary linearization point. On a formal level, a is defined as the initial share of trade transactions settled in the commercial exchange market to total trade transactions a. It is this parameter that we identify as the (inverse of) the legally sanctioned degree of leakage. Admini- strative fiat, however, is not the only reason why certain merchandise trade transactions are settled in the financial exchange market. To the extent that the financial rate is relatively depreciated compared with the commercial rate (Table 1 reveals that this is invariably the case), then private exporters have an incentive to circumvent government regulations by illegally surrendering export receipts at the financial rate. We turn to a more specific description of the trade balance next.

Note first that the total real trade balance (equivalent to real saving) in terms of natural units, is given definitionally by

(4) Tt = Yt - Ct

where C t is real aggregate consumption and where other components of domestic expenditure such as physical investment have been ignored in the interest of simplicity. Aggregate real consumption is determined by the level of income and real wealth so that the trade balance is given by the function 9

(5) T t = T (Yt, Wt/Pt)

TI>O, T2<O

a Technically, a represents a value share. However, provided that the initial spread between the two exchange rates is small, a can also approximate the relevant real share.

g It is possible to incorporate other determinants of aggregate consumption, such as nominal or real interest rates. These extensions serve merely to complicate the algebra without providing any new insights.


Since the marginal propensity to spend is less than unity, the trade balance surplus is positively related to income. It is negatively related to real wealth since an increase in the latter increases consumption (see (4)). A logarithmic approximation to (5) is assumed to be given by

(6) In T t = T + 61 Yt - 62 (wt - Pt)

where T represents an autonomous component of the trade balance 1~ Total real exports (i.e. Tt) are composed of two components; one component (denoted by T ~) is settled at the commercial exchange rate, while the other (T x) is settled in the financial exchange market1 k The component T x subsumes both legally sanctioned as well as illegal transactions in the financial market. As indicated previously, leakage from the commercial to the financial market is of both varieties. We hypothesize the following functional forms for the logarithms of T e and T x

(7a) In T e = ~'e + ~ Yt -- 8[ (W t -- Pt) -- V~ (Xt -- e)

(7b) l n T x = ~ + 5 7 y t - 5 ~ ( w t - p t ) + Y T ( x t - ~ )

According to (6) and (7), an increase in aggregate income (wealth) increases (decreases) total exports, which is then allocated to each component as determined by the elasticities 54 (69 and 57 (5~). By contrast, an increase in the spread between the two exchange rates (i.e. (xt - ~)), has no scale effect upon total exports and leads only to compositional changes. Specifically, private exporters find it more favorable to illegally divert some of their trade transactions to the financial market from the commercial market. The magnitudes of the relevant elasticities V~ and u are clearly (inversely) related to the perceived implicit and explicit costs of engaging in illegal transactions and to the degree of enforcement of exchange regulations, etc. Statistically estimated trade balance .functions for Belgium reveal the presence of a strong response to the spread [see Decaluwe, 1975]. It is readily demonstrated the parameters in (6) and (7) must satisfy the following "adding-up" conditions

(8) a5~+(1-a) 57=5~; aS~+ ( 1 - a ) 5~=52

-aye+ (1-a) y~=0

~o An equation very similar to (6) has been employed by Turnovsky, Bhandari [1982] among others. At this stage it may also be noted that if the country in question is an importer (so that Tt< 0), then it is necessary to replace (6) with a function that associates the trade deficit (negatively) with income. Throughout this paper, we assume without consequence that the domestic economy is an exporter.

i1 Note that owing to the one-good nature of the model, the trade surplus (Tt> 0) is synonymous with total exports.

240 Jagdeep S. Bhandari and Bernard Decaluwe

The next stage in the development of the model involves the specification of asset market relationships. The logarithm of the expected opportunity cost of holding domestic money as opposed to (internationally issued) securities can be calculated as follows. One unit of domestic currency purchases 1/X t units of capital account foreign exchange which will yield Xt+l/X ~ next period (recall that there is no leakage from the financial to the commercial market). During the period 1/X t earns an interest return of it*/X t which may be repatriated into domestic money in the amount [it* Ea/X~ + it* Xt+l (1-a)/Xt].

In computing the latter expression, it is assumed that the proportion a of service account proceeds is settled at the commercial rate and the remainder at the financial rate (in accordance with our treatment of merchandise trade items). Thus the overall actual yield is

(9) (1 + i't) = (Xt+l/Xt) [(ait* E/Xt+l) -1- ( l - a ) It* + 11

where we define (1+it') as the actual opportunity cost. Thus, the logarithm of the expected opportunity cost can be closely approximated by '2

(10) it = (Et, xt+l - xt) + Et, Zt where

Z t --- ~it*E/Xt+ 1 + ( l - a ) it*

In what follows, we assume that the service component of the current account is small enough to be safely ignored in the short run. Such an assumption has been made by several previous authors as well. Under these circumstances, the expression involving Zt may be ignored in (10) above.

We adopt a simple portfolio-balance view with respect to the specification of asset demand functions. In terms of natural units, money demand and demand for foreign assets are given by

M d W t ( l la ) ~ - t = g [ E ( l + i ' t ) , Y t ] p~-

K~X~ W~ ( l lb) - h [E (1 + i't), Yt] - - P, p,

where g and h are positive fractions that add up to unity, Yt is real income, Mtd and K~ are nominal stock demands for money and foreign assets, respectively, while W t denotes nominal wealth, i.e.,

(12) W t _---- M t + X t K~

Only one of (11a) and (11b) is an independent relation and in what follows,

12 This derivation extends a similar procedure in Flood, Marion [1982], by incorporating leakage.


we do not utilize ( l lb ) . The logarithmic form of ( l l a ) is assumed to be given by

(13) mt d - wt = - ~,it + q0 Yt

while (12) can be approximated via the first-order logarithm Taylor expansion

(14) w t = d I m I + (l-d1) (x t + kt)

where d~ _-- (M/W) ~ > 0 is an initial l inearization point. Domest ic money supply (in natural units) is given by

(15) M~ = D t + ERt

where D t denotes domestic credit and official r e s e r v e s (Rt) are evaluated at the commercia l exchange rate, as is appropriate . A logarithmic expression for (15) is given by

(16 ) mt s = d o d t + (1 - d ~ (~ + rt)

d o - (D/M0 ~ > 0

We now turn to the specification of the dynamic processes governing the economy. The model involves two sources of dynamic adjustment, i.e. reserve accumulat ion and foreign asset accumulat ion. It is to be emphasized that changes in the stock of domestically-held foreign assets is a direct consequence of inter-market leakage. If it is assumed (as in the previous literature) that the two exchange markets are completely segmented, then the floating financial rate ensures that no net movemen t in foreign asset stocks can occur. Given incomplete segmentat ion however, it is the sum of the capital account plus the leakage that is now zero. fI'his process has been noted in the descriptive literature, for example, Lanyi [1975].) Thus, the foreign asset accumula t ion process is formally described by

(17a) X t (K t - Kt_l) = PI* Xt Tx

Note that the real amount of the leakage T x has been t ransformed to domestic currency terms by applying the conversion factor let* Xt (rather than the aggregate price level Pt) as is appropriate . The other dynamic process governing the economy involves foreign reserve accumulat ion. In the absence of the service account, this is the counterpar t of TL i.e. of that c o m p o n e n t of total exports that is t ransacted in the commerc ia l market . Hence,

(17b) E (R t - Rt_l) = Pt* E T e

Eqs. (17) and (18) may be t ransformed into the following logari thmic forms

(18a) k t - z' kt_ 1 = (1-z') (Pt* + lnTx)

(18b) r t - z ~ rt_ 1 = (1-z ~ (Pt* + lnTe)

242 Jagdeep S. B h a n d a r i and B e r n a r d D e c a l u w e

where z' and z ~ are initial linearization points that are bounded between zero and unity and are defined a s

z' - (Kt_l/Kt)~ z ~ - (Rt_l/Rt)~ 0 < z 0, z a < 1

The final step in the formulation of the model involves the specification of the relevant stochastic processes in the economy. In this paper, we consider only two types of disturbances - foreign price disturbances and domestic credit disturbances. A host of other disturbances (to domestic supply or to various components of the trade balance for example) can of course be incorporated; we leave these extensions to the interested reader. Foreign prices and domestic credit evolve according to the following stationary processes

(19a ) Pt* = P* + ~lt

(19b) d t = d + ~2t

where ~* and d are systematic components, while the [ ' s denote unanticipated disturbances each with zero mean and finite variance.

The description of the model is completed by noting that continuous equilibrium prevails in all markets and that expectations are determined rationally in the sense of Muth.

III. The Rational Expectations Solution

The rational expectations solution to the model described above requires that expectations be consistent with available knowledge of the structure of the model itself. Given the linear structure of the model, it is clear that the ultimate reduced-form solution is linear in the vector of all exogenous variables. For convenience we set the anticipated components d and ~ equal to zero. Thus, the stable components of the solutions to x t, r t and k t a r e hypothesized to be of the following form

(20a) x t ~ fllrt_l + fl2kt_l -1- rl3p* -t- n4~lt + F15~2t

(20b) r t = Jlrt_~ + J2kt_~ + J3P* + L~lt + Js~2t

(20c) k t = Nlrt_ 1 + N2kt_ 1 + N3~* + N4~lt + Ns~2t

Given the structure of the model, the potentially stable trajectory of the state vector [xt, rt, kt] is fully determined by the vector of predetermined and exogenous variables included in (20).

In order to solve for the reduced-form coefficients in (20), it is necessary to derive three sets of simultaneous relations involving each of the five triples. These relations are obtained by reducing each of (18a), (18b) and the money market equilibrium relation consecutively, to final form. The details of these

"Paral le l" E x c h a n g e Marke t s 243

relations are not included for reasons of space and may be obtained from the authors. It turns out, however, that one of these relations is intrinsically non-linear and contains product terms. There are no known analytical methods for solving such simultaneous systems. In order to make progress therefore, we have relied on a variant of the Newton-Raphson search algorithm to numerically isolate the solutions for nl and n 2 given a plausible parameter grid. This experiment was repeated for several alternative values of a, since our objective, as stated previously, is to conduct sensitivity analysis with respect to the degree of leakage. Once the solutions for nl and n 2 are determined all other solutions follow easily.

Our search procedure isolated four pairs of solutions to (nl, a2) for the chosen parameter grid. Of these solutions, only a single pair was found to be consistent with dynamic stability. Thus, in practice, no potential problems of either non-existence or non-uniqueness of the solution were found to arise. Dynamic stability is discussed in the next section. Meanwhile, we state the parameter values chosen for our experiments.

d, = .80, d o = .80, z ~ = .80, z ' = .80, ~, = 7.5, qo = 1, b = 3,

y~ = . 5 0 , ~,~ = . 5 0 a / ( 1 - a ) , 51 = 1 .2 , 5~ = 1, 5~ = ( 1 . 2 - a ) / ( 1 - a )

62 = .50, 6~ = .3o, 6~ = (.50 -.50a)/(1-a) a = .10, .30, .50, .70, .90

It is assumed that the country in question enjoys a net creditor position in foreign assets and the initial ratios of domestic money to wealth (i.e., dl) as well as of domestic credit to money (d ~ are each .80. It is known that a net debtor position in foreign assets is associated with problems of dynamic instability [see Henderson, Rogoff, 1982]. Further, the initial rates of accumulation of both foreign assets and foreign reserves are assumed to be 20 percent each; hence the chosen values of z ~ and z'. 13 The income elasticity of money demand (q0) is unity, while the interest rate semi-elasticity (~) is 7.5. This value corresponds to an interest rate elasticity of .30 and a quarterly interest yield of 4 percent. The slope of the Phillips curve (b) is assumed to be 3. This value is consistent with the fact that b can be shown to be given by (0/(1-0)) where 0 is the share of labor in total output and 0 = 3/4, as is the case in most empirical studies. There are virtually no estimates for the elasticity of commercially settled exports with respect to the exchange rate spread (u We have chosen a value consistent with Decaluwe's [1975] investigation of Belgian trade balance functions in the early 1970s. The income elasticity of total exports (61) is assumed to 1.2 while the wealth elasticity (52) is .50. This value is in conformity with estimates for most industrial countries [see Goldstein, 1980]. There are no estimates of all (that we are aware of) for 5~

~3 The initial ra te of a ccumula t i on of reserves in (Rt-Rt_l)~ ~ = 1 - (Rt_l/Rt) ~ = ( l - z ~

244 J a g d e e p S. B h a n d a r i a n d B e r n a r d D e c a l u w e

and 6~ (income and wealth elasticities of commercially settled exports); we chose 5~ = 1 and 6~ = .30. The choice of 6~ (6~) and u implies values for 5~ (6~) and u via the "adding-up" conditions stated in (8). Finally the value of a is assumed to be given successively by .10, .30, .50, .70 and .90. The numerical solution to all coefficients of interest was computed for each of these values.

IV. Dynamic Adjustment with Incomplete Market Separation

It is clear at the outset that the dynamic evolution of the economy is guided by a second-order difference equation system, as expressed by the simultaneous equations system (20b) - (20c). This is to be contrasted with the corresponding no-leakage economy wherein there is no net accumulation of foreign assets. This technical point aside, our more immediate concern is the effect of variations in the degree of leakage (a) upon the nature of dynamic adjustment in the present context.

The eigenvalues of the homogeneous part of the dynamic system are given by

(21) Sx, S2 = { (J1 + N2) + [(J1 + N 2 ) 2 - 4 (J1N2-NIJ2)] '~ } / 2

Table 3 reports the stable solutions for nl and n 2 as well as associated eigenvalues for various values of a. TM

Table 3 - Stable Values of nl, n 2 and Associated Eigenvalues

a = .10 a = .30 a = .50 a = .70 a = .90

n 1 n 2 S l S 2

.0184

.0180

.0177

.0156

.0140

- . 0 9 2 5 - . 0 9 0 9 - . 0 8 9 0 - . 0 7 8 1 - . 0 6 7 5

.7986

.7960

.7910

.7812

.7381

.7980

.7982

.7982

.7984

.7986

A general feature of the (unique) set of stable solutions is that n 1 > 0, while rh< 0.15 Such a pattern is readily reconciled with the structure of the model. A positive (negative) sign on n 1 (n2) implies that a ceteris paribus increase in the stock of reserves (foreign assets) leads in the next period to a depreciation (appreciation) of the financial exchange rate. For example, a decrease in the magnitude of reserve accumulation over the previous period implies a lower trade surplus T e, via (18b). The latter in turn, is accomplished by a current period depreciation of the financial rate as witnessed by (7a). On the other

~4 In each case, the produc t term NIJ 2 is less than 10 .5 so tha t S 1 = N 2 while S 1 ~- J1.

~s The other three pairs of solutions for n 1 and n 2 involved the following conf igura t ions of signs (+ +), (- -) and ( - +). Each of these pairs was found to be unstable.


hand, a decline in the magnitude of asset accumulation over the last period, necessitates financial appreciation, in order to lower T x in (18a).

The implications of changes in the degree of leakage as parameterized by a, may now be noted. Specifically, Table 3 reveals that increasing leakage (i.e. declining a) is characterized by increasing values of one of the roots (S~) with virtually no change in the other root ($2). Now the solutions for the paths of say, reserves and the financial exchange rate, are of the form

(r t - ~) = A1S ~ + AzS t and (x t - :~) = B1S~ + B2S~

where a "~" denotes stationary-state values while the (Ai, Bi) are fixed constants which are determined by initial conditions (i.e. z ~ and z'). An increase in $1, unaccompanied by an offsetting change in $2, consequently implies that, for the same values of t, the deviations of reserves and the financial exchange rate from their stationary-state levels, are correspondingly larger. In this specific sense therefore, an increased degree of leakage can be regarded as being costly to the economy.

This dynamic cost of increased leakage (i.e., a greater degree of "persistence") is to be contrasted with its potential impact benefits to which we turn below.

V. Instantaneous and Stationary-State Effects of Structural Disturbances

In this section we consider the first-period and stationary-state effects upon the domestic economy of three types of disturbances; these are anticipated foreign price disturbances, unanticipated foreign price shocks, and domestic credit innovations. In each case, we report the results of the sensitivity analysis with respect to the degree of leakage a given the chosen values of other parameters indicated earlier. We also performed sensitivity analysis with respect to the penalty-cost parameter y~.16 For reasons of space, a brief summary of the results relating to perturbations in y~ is provided in Footnote 16.

~8 Sensitivity analysis with respect to V~, i.e. the penalty cost of engaging in illegal trade transactions indicates that reduced values of y~ (i.e., higher penalty cost) unambiguously lead to increased values of both roots $1 and S 2 for corresponding values of a, the larger changes being generally concentrated in the root S v Thus, a higher penalty cost (low y~) implies a greater degree of persistence in the economy (via larger values of Sland $2). These properties suggest the presence of a policy dilemma in the sense that an attempt by the authorities to lower the extent of illegal transactions by increasing penalty costs attributed to the latter is not without costs of its own.

Variations in V~ also affect the impact properties of the model. For unanticipated foreign price innovations for example, lower values of y~ (higher penalty cost) imply sharper financial appreciation but reduced domestic inflation and reserve accumulation effects for corresponding degrees of leakage a. In this sense, a higher penalty cost may be viewed as providing insulation to the domestic price level from external inflation. A higher penalty cost (low y~) is also found to enhance the effectiveness of domestic credit policy. Thus, lower values of ,r imply enhanced price-output effects and sharper financial depreciation for corresponding values of a, given a domestic credit expansion. For both

Weltwirtschaftliches Archly Bd. CXXII. 3

246 Jagdeep S. B h a n d a r i and B e r n a r d D e c a l u w e

1. F i r s t - P e r i o d Ef fec t s

a. Anticipated Foreign Price Disturbances

The effects of an anticipated foreign price increase (as represented by an increase in the component ~*) upon the financial exchange rate, on reserves and on foreign asset stocks, are represented by the reduced-form coefficients n3, J3, and N 3. Given the effect on the financial exchange rate, the movement in the domestic price level can be calculated by reference to (2) and (3), i.e., f r o m

(22) Pt = ( l - a ) [Fllrt_ 1 + n2kt_ 1 + FI3p* + n4~lt + 1"15~2t ] -[- p * + ~lt

T h u s Pt responds to the extent [(l-a) n3+l ]. Furthermore, the anticipated nature of the disturbance implies that domestic output (which responds only to price "surprises") is unaffected. Table 4 reports in the first three columns the computed values of percentage changes in the financial exchange rate, reserves and the price level (following a 1 percent anticipated increase in foreign prices) for various values of a.

Table 4 - First-Period Effects of Disturbances on the Financial Exchange Rate, Reserves and Price Level

a = .10 a = .30 a = .50 a = .70 a = .90

Foreign Price Increase

anticipated unanticipated

xt rt Pt xt rt Pt

-.6291 .2630 .4331 -.3380 .6510 .6956 -.5430 .2541 .6190 -.3645 .6861 .7440 -.4570 .2452 .7715 -.3911 .7212 .8041 -.2950 .2290 .9113 -.4410 .7707 .8671 -.1326 .2131 .9862 -.4909 .8190 .9509

Domestic credit

innovation

xt rt Pt

.0144 .0061 .0150

.0156 .0048 .0109

.0165 .0032 .0081

.0171 .0012 .0052

.0182 -.0007 .0016

For all values of a, the external price increase leads to financial appreciation, domestic price inflation and reserve accumulation. Given a less than proportionate appreciation of the financial exchange rate (and consequently an even smaller appreciation of the effective commercial rate), the price level increase falls short of a unitary response. Since income is unaffected, the total trade balance is not altered; however, as is clear from (7a) and (7b), the volume of exports settled in the commercial market increases at the expense of an equivalent decline in financial market exports T x. Finally, an increase in

types of disturbances therefore (i.e., foreign price innovations and domestic credit disturbances), a higher penalty cost is seen to be generally beneficial from the point of view of impact properties of the model. These potential impact benefits are to be weighed against the increased dynamic costs noted above.


the foreign currency value of commercially-settled exports is reflected in accumulation of foreign reserves (see (18b)).

Table 4 also reveals the implications of changes in the degree of leakage, as parameterized by a. As seen above, increasing values of a (i.e., declining degrees of leakage) are accompanied by diminishing financial appreciation and increasing inflationary effects. The latter can readily be explained. Specifically, as a increases, the effective commercial rate st becomes increasingly fixed, thus providing a lower offset to the increase in ~*. Consequently, the domestic price level responds to a larger extent, as is clear from (22). Finally, a reduced extent of financial appreciation implies a smaller increase in the commercially-settled trade balance (see (7a)) and therefore, lower reserve accumulation, as is borne out by Table 4.

The above properties suggest the presence of a macroeconomic tradeo[[ between the severity of domestically-induced effects in response to changes in the degree of leakage. While increased leakage (i.e., lower a) can be viewed as "insulating" from the point of view of domestic price effects, this insulation is achieved at the expense of sharper financial exchange rate and reserve stock realignments. Such a tradeoff is not present if external unanticipated price disturbances are considered.

b. Unanticipated Foreign Price Disturbances

The domestic implications of unexpected disturbances in the foreign price level are summarized by the coefficients r h, J4, and N 4. Meanwhile, the effect on the domestic price level is obtained from (22) and is [ ( l -a) n 4 + 1]. Table 4 reports in the three middle columns the simulated percentage responses in x t, r t and Pt, following a 1 percent unexpected increase in the foreign price level, corresponding to several alternative values of a.

The table reveals that for all values of a considered, the domestic economy experiences price inflation coupled with financial appreciation and reserve accumulation, in response to unanticipated increases in the foreign price level. In this respect, these effects are similar to those previously noted in the first three columns. There are, however, several noteworthy differences between the two cases. First, the unanticipated nature of the disturbance in the present case calls forth an income expansion. The latter, in turn, contributes to a sharper increase in T ~ and thus to stronger reserve accumulation effects. This property is borne out by a comparison of reserve effects in the two cases. Second, while increasing values of a lower the extent of financial appreciation in the first three columns, in the present case diminishing leakage is associated with sharper financial appreciation, along with sharper price and reserve effects. Thus, unlike the previous case, changes in the degree of leakage are not associated with a tradeoff in the present instance; a decrease in a is unambiguously beneficial from the point of view of insulation, although substantial exchange rate, price and reserve effects are

3*

248 Jagdeep S. Bhandar i and Bernard Decaluwe

still found to remain for values of a as low as .10. A final comparison between columns 1-5 and 4-6 of Table 4 that deserves note refers to price effects in the two cases. It is seen that the issue of whether anticipated or unanticipated external disturbances are more detrimental from the point of view of domestic inflation, depends upon the existing degree of leakage. For low values of a, the price effects reported in columns 4-6 are relatively sharper than those in columns 1-5 and conversely for higher values of a.

c. Domestic Credit Innovations

The effects of domestic credit innovations upon the financial exchange rate and the stock of reserves are given by the coefficients 0 5 and ]5, respectively, while the impact upon the domestic price level is ( l - a ) n s. Table 4 reports in the last three columns the relevant responses. It is shown that domestic credit innovations are accompanied by generally weak effects upon the financial exchange rate, reserves and the price level. The domestic economy experiences financial depreciation (to an extent that falls well short of a proportionate response) as well as price inflation. Increasing values of a (i.e., decreased leakage) are accompanied by an increasing extent of financial depreciation and by diminishing price and reserve effects. For values of a that are sufficiently high, the domestic economy experiences reserve decumulation. To the extent then, that ~2 can be interpreted as the unanticipated component of deliberately conducted monetary policy, increased leakage clearly enhances its price-output stabilization role. This result can readily be explained as follows. As a increases, the effective commercial rate becomes increasingly fixed and the behavior of the system begins to approximate that of a uniform fixed exchange rate regime. As is well-known, the combination of purchasing power parity and uncovered interest parity eliminates entirely any stabilizer role of domestic credit policy. Specifically, price, output and interest rate levels are set by world conditions in such circumstances and any domestic credit expansion must be offset by an equivalent reserve loss in order to keep real money supply unchanged. Tendencies towards reserve decumulation and progressively smaller domestic price effects are evidenced in the last three columns of Table 4. Finally, increasing financial depreciation (with a) may be rationalized in the following manner. At a constant level of the financial rate xt, an increase in a reduces the resulting output expansion and consequently the increase in T x. The latter in turn implies that k t and hence w t increases tess. The result is a larger excess supply of money which necessitates a sharper expected appreciation in order to restore monetary equilibrium. Given the transitory nature of the innovation, this can only be accomplished via a sharp current-period financial depreciation.

We turn now to a brief discussion of the stationary-state effects of these disturbances.


VI. Stationary-State Effects

The stat ionary state of the economy is at tained when all accumula t ion - of both foreign assets and reserves - has ceased. From the specification of the model, it is clear such a state implies tha t bo th componen t s of the t rade balance and consequently, the total t rade balance as well as the capital account, must each be zero (see (17)) 17 . Thus, the s tat ionary state is characterized by r t = I t _ 1 = r and k t = k t _ , = k .

It is straightforward to derive the analytical expression for the solutions to ? and k as well as ~ and p, in terms of their ul t imate determinants . First solve (20b) and (20c) simultaneously as

(23a) ~ = J3P* + Y4~lt "1- ~5~2t

(23b) k = lq3~* + R4~1, + lqs~2t

[(l-N2) 13 + 12N3] [( l-N2) 14 + J2N4] where J3 ----" " J4 ---- '

- [(1-1,) (1-N2)-N,J2] ' [(1-1,) (1-N2)-N,12] '

[(l-N2) 15 + JaNs] N,i3 N3

J5 - [(1_11 ) (I_N2)_N,Iz] ; N 3 - l_N2 + l_N2 ;

N,J4 N4 N1J5 N5 lq4 - 1 -N 2 + 1 - N ~ ; l q s - 1 - N 2 + 1 -N 2

Given these solutions, ~ can be directly obtained from (20a), i.e.

(23c) .~ = fi3P* + N4 ~lt Jr N5 ~2t

where fi3 - (nl J3 + n2/~13 + n3); fi4 - (nl Y4 Jr I"12 i~ 4 "]- n4); fi5 --- (FI1 i5 Jr I"12 i~ 5 "~- ns). Finally, the stationary-state effects on the price level (~) are obta ined f rom (2) and (3). Table 5 reports the stationary-state responses of.~, ? and ~ to the three disturbances ~*, ~lt and ~2t, for various values of a.

It is reassuring to note that the qualitative nature of the effects repor ted in Table 5, as well as their sensitivity characterist ics with respect to a, is precisely the same as the corresponding one-per iod responses. Specifically, both anticipated and unanticipated increases in the foreign price level lead to financial appreciation, reserve accumulation and price inflation. And, increasing values of a exacerbate the reserve and price effects in both instances. However, the response of the financial exchange rate to changes in a depends upon the nature of the disturbance, as in the one-per iod case. The stat ionary- state implications of domestic credit innovat ions are also qualitatively identi- cal to those reported in Table 4 above.

~7 If the service account were incorporated, the description of the stationary state must be modified. See Rodriguez [1979] in this regard.

250 J a g d e e p S. B h a n d a r i and B e r n a r d D e c a l u w e

Table 5 - Stationary-State Effects of Disturbances on the Financial Exchange Rate, Reserves and Price Level

a = .10 a = .30 a = .50 a = .70 a = .90

Change in ~*

- .6931 1.3471 .3755 - .5972 1.2980 .5810 - .5016 1.2481 .7492 - .3220 1.1512 .9032 - ,1421 1.0683 .9851

Change in [~t

- .6011 3.3862 .4580 - .6430 3.5671 .5491 - .6839 3.7480 .6572 - .7561 4.0043 .7730 - .8290 4.2602 .9168

Change in ~t

.0106 .0320 .0091

.0120 .0250 .0082

.0131 .0180 .0060

.0132 .0082 .0040

.0133 - .0009 .0013

These qualitative similarities notwithstanding, there are significant quan- titative differences between first-period and corresponding stationary-state effects. First, for each value of a and for every disturbance considered (i.e., ~*, [n and ~2t), the stationary-state effects upon the reserve level are substantially larger than the analogous first-period responses (the largest reserve effects being, once again, observed for ~,-disturbances). Further, for both types of external price disturbances, the extent of stationary-state financial appreciation is larger than the corresponding first-period appreciation, for each value of a (compare columns 1 and 4 with columns 1 and 4 in Table 4). Since a sharper appreciation for given values of a implies a larger "offset" in (2) to the external price disturbance, it follows that the stationary-state domestic inflation effects are less severe than the analogous short-run (first-period) effects. This property is clearly evidenced by comparison of Table 5 with the previous table. Such a comparison also reveals that for domestic credit innovations, both ~ and ~ are smaller, at each value of a, than the effects reported in the last three columns of Table 4.18 For every disturbance considered then, it is seen that short-run price effects overstate the ultimate stationary-state responses. Finally, domestic credit innovations also imply short-run overadjustment or "overshooting" of the financial exchange rate, in comparison with the corresponding stationary-state effect.

VII. Conclusion

This paper has constructed and analyzed a model of dual exchange markets. A key feature of our model - one that distinguishes the present framework from previous analyses - is the incorporation of the fact that certain current account transactions are often settled in the financial exchange market. This scenario accords with prevailing economic reality in

IB For domestic credit innovations, Pt is a linear, positive function o f x t (see (2) and (3)). Thus, a lesser financial depreciation necessarily implies a lesser extent of domestic inflation.


the countries engaging in dual exchange rate practices. It was seen that both dynamic and static properties of an economy characterized by such inter- market leakage are quite different from those of a regime in which the two markets are effectively segmented. There is a sense in which cross-transactions impose a dynamic cost upon the economy by leading to a greater degree of "persistence" in the adjustment of various macrovariables. However, this cost is to be weighed against the potential impact benefits of leakage, where the latter are measured in terms of generally reduced vulnerability of the domestic economy to external inflationary disturbances and in terms of imparting "effectiveness" to domestic credit policy where there was none without leakage.

Several extensions of the simplified framework utilized in this paper are clearly possible. One fruitful line of future enquiry would seem to be the construction of a two-good model, incorporating both an exportable and an importable commodity. Once this is done, the (presumably) differing implications of assigning certain exports versus imports to the financial exchange market can usefully be investigated.

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252 Jagdeep S. Bhandari and Bernard Decaluwe

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"Parallel" Exchange Markets 2 5 3

Z u s a m m e n f a s s u n g : Ein Rahmen ffir die Analyse legaler und illegaler Handelstransak- tionen auf parallelen Devisenm~irkten. - In diesem Aufsatz wird ein stochastisches Gleichge- wichtsmodell fiir eine offene Volkswirtschaft mit dualem Devisenmarkt konstruiert and analysiert. In diesem Rahmen sind die Devisenm/irkte nicht vollst~indig gegeneinander abgeschottet, und ein Teil der Warenhandelstransaktionen wird auf den Finanzm~irkten abgewickelt - sowohl wegen einer rechtlich gestatteten Durchl~issigkeit als auch deshalb, weil es illegale Transaktionen gibt, die auch in der Realit~it vorkommen. Der Modellrahmen wird benutzt, um Fragen zu behandeln, die sich fiber die kurz- und langfristigen Wirkungen ver- schiedener struktureller St6rungen hinaus auf die dynamische Anpassung in einer solchen Volkswirtschaft beziehen.

R6sum6: Un cadre pour l'analyse des transactions 16gales et frauduleuses de commerce en march6s de change parall~les. - D a n s cet article les auteurs construisent un module d'6quilibre stochastique d'une 6conomie ouverte ~ un r6gime dual de march6 de change. Dans ce cadre ses march6s de change ne sont pas compl~tement segment6s et une part des transactions commerciales du commerce ext6rieur est r6gl6e en march6 financier ~ cause du ~coulage~ 16galement sanctionn6 aussi bien qu'~ cause des transactions frauduleuses en conformit6 avec la r6alit6 6conomique. Les auteurs appliquent le cadre pour r6pondre aux questions qui s 'occupent de l 'ajustement dynamique dans une telle 6conomie et des effets de court et de long terme de quelques perturbances structurelles.

Re s u m e n: Un marco para el an~ilisis de transacci6nes comerciales legales y fraudulentas en el mercado paralelo de cambios. - En este trabajo se construye y analiza un modelo estoc~stico de equilibrio para una economia abierta que funciona con un mercado de cambios dual. En el presente marco el mercado de cambios no est~i completamente segmentado. Una parte de las transacci6nes comerciales se rigen segtin el mercado finan- ciero, tanto en forma legal como fraudulenta, de acuerdo con la realidad econ6mica existente. Se utiliza este marco para estudiar cuestiones relacionadas con el ajuste din~imico en este tipo de economfa como tambi6n las consecuencias a corto y largo plazo que puedan tener distintos disturbios estructurales.

Documents

A framework for the analysis of legal and fraudulent trade transactions in “Parallel” exchange markets