unofficial exchange rates in bangladesh: a cointegration analysis

Contemporary Economic Policy(ISSN 1074-3529)Vol. 20, No. 3, July 2002, 288–300 © Western Economic Association International

UNOFFICIAL EXCHANGE RATES IN BANGLADESH:A COINTEGRATION ANALYSIS

JALAL U. SIDDIKI*

This article estimates a structural model for unofficial market foreign exchange(forex) rates �EU� and examines the stability of the forex market in Bangladesh usingan autoregressive distributed lag approach to cointegration analysis on quarterly datafrom 1976Q2–1995Q2. It also compares the in-sample and out-of-sample (from1995Q3–1999Q2) forecasting performances of the structural model with other time-series models. With EU as a dependent variable and official exchange rates �EO�,money supply �M�, the difference between foreign and domestic interest rates �I�,forex reserves relative to imports �Q� and political along with some structural factors�D85� as explanatory variables, a multivariate cointegrated relationship is found inwhich EO�Q, and I cause an appreciation and M and D85 cause a depreciation inEU. These results imply that the overvaluation of the official exchange rate, increasesin money supply, the paucity of official forex reserves, and structural factors are themain causes for the creation of the unofficial market for forex in Bangladesh. Resultsalso reveal that the forex market in Bangladesh is stable during the sample period.The structural model performs well in in-sample prediction, and the random walkmodel performs best in out-of-sample forecasting. (JEL C22, F31, O54)

I. INTRODUCTION

The aim of this article is to explore thedeterminants of parallel or unofficial mar-kets (UMs) for foreign exchange (forex)rates in Bangladesh using quarterly datafrom 1976Q2 to 1995Q2 and to compare thein-sample and out-of-sample (from 1995Q3to 1999Q2) forecasting performances of thestructural models with other time-series mod-els. The distortions in the financial and forexsectors in developing countries generate UMsfor forex,1 misallocate national resources,and create inefficiency, which are deleteri-

∗This is a version of a paper presented at the 75thWEA International Conference, Vancouver, Canada,June 29–July 3, 2000. The author is grateful Peter L.Rodriguez, the participants of the seminar, and anony-mous referees. The author is also grateful to Paul Auer-bach, Subrata Ghatak, and Vince Daly for their helpfulcomments on earlier drafts of this paper. The usual dis-claimer applies.Siddiki: Lecturer, School of Economics, Kingston Uni-

versity, Penrhyn Road, Kingston Upon Thames,Surrey KT1 2EE, UK. Phone 44-0208-547-2000 x2579, Fax 44-0208-547-7388, E-mail [email protected]. The extent and intensity of distortions are

reflected in UM premiums measured by the margin ordifference between UM and official rates as a percent-age of official or UM rates.

ous to economic growth (Blejer, 1978; Dorn-busch et al., 1983; Fry, 1998; Kiguel et al.,1997; Phylaktis, 1992; see section III on thedeterminants of UM rates). Empirical studiesusing cross-section data and UM premiumsas summary measures of government-inducedeconomic distortions find that large and per-sistent UM premiums significantly slow eco-

ABBREVIATIONS

ARDL: Autoregressive Distributed LagCUSUM: Cumulative Sum of ResidualsCV: Critical ValueEC: Error CorrectionFDI: Foreign Direct InvestmentForex: Foreign ExchangeGDP: Gross Domestic ProductISI: Import Substitution IndustrializationMAE: Mean Absolute ErrorMAUM: Monetary Approach to Unofficial

MarketPAUM: Portfolio Approach to Unofficial MarketRMSE: Root Mean Squared ErrorTAUM: Real Trade Approach to UnofficialTIC: Theil Inequality Coefficient

MarketUM: Unofficial Market

288

SIDDIKI: UNOFFICIAL EXCHANGE RATES IN BANGLADESH 289

nomic growth. A 10% premium is associatedwith a reduction of about half a percent-age point in annual growth of gross domesticproduct (Barro and Lee, 1993). This findingis consistent with the low level of saving andinvestment, rate of economic growth, andhigh level of UM premiums in Bangladesh(section II and Table 1) (see Siddiki, 2000b).

The existence of UMs for forex could alsorender the use of official financial and forexpolicies impotent for controlling the tradebalance and forex reserves. The presence ofUMs and high UM premiums may acceler-ate speculative attacks on official forex mar-kets, cause capital flight and instability inthe forex markets, and make the forecast-ing of and government policies toward offi-cial rates problematic (Kamin, 1993). Theexistence of restrictive policies and UMsin developing countries creates rent seek-ing and corruption (Wong, 1997; Task ForceReport, 1991). Smuggling, together with cor-ruption and bribes, have helped create asmall wealthy class in Bangladesh; an esti-mated 40% of the money supply or aboutUS$1.4 billion was black money in 1983(Cowitt, 1996). In addition, Bangladesh gen-erally loses 25% of its forex earnings throughunauthorized trade with India.

There is no existing research accountingfor the presence of UMs in Bangladesh andno research that compares the out-of-sampleforecasting performance of UM rates using arange of methods. Thus, finding the determi-nants of UM rates and the in-sample and out-of-sample forecasting performance of variousmodels is novel and has important implica-tions for policy design aimed at reducing (oreliminating) distortions in both the financialand trade sectors in Bangladesh.

This article uses the recently devel-oped autoregressive distributed lag (ARDL)approach to cointegration analysis (Pesaranand Shin, 1998) (see Siddiki and Daly, 1999,for a description of the ARDL method). Themajor advantages of the ARDL method isthat it distinguishes between dependent andexplanatory variables. This method mitigatesthe effect of serial correlation and functionalmisspecification by including lagged regres-sors and thus makes the pretesting of theorder of integration redundant, which is asso-ciated with other cointegration analyses (e.g.,Engle and Granger, 1987).

This paper is organized as follows. Insection II, financial and trade policies inBangladesh during 1972–96 and their impacton UMs for forex are explained. In sectionIII, the literature on UM and its short-comings are critically analyzed. Section IVcontains the empirical model specification.Empirical results are analyzed in section V.Section VI concludes.

II. TRADE AND FINANCIAL POLICIES AND UMsFOR FOREX IN BANGLADESH: 1972–96

During the 1970s and early 1980s,Bangladesh followed import substitutionindustrialization (ISI) policies and imposedhigh rates of tariffs and quantitative andqualitative restrictions on imports and offi-cial forex markets (Bhuyan and Rashid,1993). The tariffs were also used as a majorsource of government revenue, 80% of whichwere collected from intermediate and capi-tal goods imports (Task Force Report, 1991).All inward and outward transfers of capi-tal required prior approval from the govern-ment (International Monetary Fund, 1980,p. 56). Foreign exchange was not providedfor tourists going abroad. Granting foreignexchange for other purposes, such as educa-tion and treatment abroad, was strictly con-trolled and the official supply was negligi-ble compared to the demand. Bangladeshalso followed restrictive financial policies toincrease investment to support ISI policies.The restrictive financial policies included fix-ing the nominal interest rates below the rateof inflation, allocating credit to governmentpreferential sectors and government overborrowing from the financial sector to financehigh budget deficits, all of which engenderedhigh monetary growth (Hossain and Rashid,1997). The budget deficits during the sampleperiods were around 7–9%; monetary growthwas 14.48% (M1) and 18.59% (M2), whichresulted in the high rate of inflation and neg-ative real interest rates (Table 1).

The high levels of distortion are appar-ent from the high rate of UM premiums inBangladesh. The average of the premiumsduring 1975–95 was about 116% and reached198% during 1985–92 (Table 1 and Figure 1).The high level of premiums during 1985–92 was caused by structural factors, whichincluded the high level of corruption and ille-gal fund transfers of the military government

290 CONTEMPORARY ECONOMIC POLICY

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FIGURE 1UM Exchange Rate Premiums (UMPRIM)

during 1985–91, floods between 1987 and1988, and the Gulf crisis in 1991 (Task ForceReport, 1991; Cowitt, 1996, pp. 401–04).

The floods in 1987 inundated the coun-try, with 75–90% of the land under water.Agricultural production was severely dam-aged. These floods also affected industrialareas and export processing zones. The repaircosts were calculated at US$4.5 billion. In1988, Bangladesh suffered even worse dam-ages from floods. The Gulf War in 1991reduced export earnings by approximately$500 million and remittances from the Mid-dle East countries by $100 million.

The consequences of the distortions in thefinancial and trade sectors were enormous.The dependency on imports had increasedrather than decreased. On the other hand,the restricted policies have caused a very lowlevel of saving and investment as well aslow investment efficiency, resulting in pooreconomic growth performance (see Table 1).Increasing economic growth requires highlevels of saving and investment, which inturn require foreign direct investment (FDI)because real per capita income in Bangladeshis very low (see Table 1). Note that FDI toBangladesh is less than 1% of gross domes-tic product (GDP), and the removal of dis-tortions in prices is a major prerequisite forattracting more FDI.

III. THE ECONOMICS OF UNOFFICIALEXCHANGE RATES

The following two types of theory on thedeterminants of UM rates are appropriate inthe case of Bangladesh. First, the real tradeapproach to UM (TAUM) states that ille-gal trade to avoid tariffs and legal restric-tions on official forex and international tradeis the main reason for the existence of theUM (Sheik, 1976; Pitt, 1984). The overval-uation of official exchange rates causes theofficial supply of forex to be lower than thedemand, creating excess demand met in theUMs at a market-determined rate. Conse-quently, both importers and exporters involvein over- and underinvoicing of imports andexports, respectively, and sell the unreportedforex in the UMs to earn UM premiums.Importers overinvoice imports to obtain moreforex from official sources than the amountrequired and sell the unused forex to the UMto earn UM premiums. Similarly, exportersunderinvoice exports (i.e., report less thanthe actual income from exports) and sell theunreported forex in the UMs. Exporters andimporters also engage in smuggling to avoidlegal restrictions and sell and buy, respec-tively, the proceeds in the UM.

Second, the monetary approach to UM(MAUM) predicts that excess money supplyin an economy with restricted forex markets


creates UMs for forex and UM rates dependon the extent of excess money supply (Blejer,1978). The MAUM postulates that excessmoney supply creates inflationary pressuresand causes a depreciation of UM rates. Thisapproach also predicts that an increase ininterest rates, that is, the opportunity costs ofholding money, creates excess money supply,which again increases inflationary pressuresand UM rates.

Note that the TAUM predicts that traderestrictions are the main cause of the exis-tence of UMs. However, the motivation ofpolicy makers in imposing those restrictionshas not been linked to the UM rates. In aless developed country such as Bangladesh,one of the main causes of imposing restric-tions on trade and forex is to use scarce offi-cial reserves more efficiently. Thus, futureexpectations regarding the excess demand forofficial forex, official devaluation, and UMrates are largely influenced by the avail-ability of official forex reserves relative toimports. A low (high) import capacity of offi-cial reserves leads the government to pursuemore controls (liberal policies) with respectto forex and trade.2 Thus, a low level offorex reserves signals future restrictive poli-cies, which increase the demand for forex inthe UM and, hence, a rise in UM rates. Thatis, official forex reserves negatively affecttrade restriction and UM rates (see Siddiki,2000a, for a similar analysis in the case ofIndia). Following these arguments, we mea-sure trade restrictions by the availability ofofficial forex relative to imports. Moreover,the existing literature does not include exter-nal shocks as determinants of UM rates.In this article, the external factors includepolitical and other structural factors (seesection II). Separating the impact of suchfactors is important because unacknowledgedregime changes might lead to misspecificationbias in model estimation and to misdiagnosisof the time-series properties of the data.

2. However, a country with low forex reserves mayalso be forced to liberalize its economy to attract for-eign investment and keep on defaulting on internationaldebt, as India was forced to do in 1991. Large forexreserves can vanish in a hurry when speculative attacksoccur on a currency for reasons unrelated to the UM,as happened in the Asian financial crisis in 1997. (Theauthor is thankful to an anonymous referee who broughtthe above points to my attention).

IV. THE EMPIRICAL SPECIFICATIONOF THE MODEL

Given the high rate of government mon-etary growth, the large budget deficits,trade restrictions, and financial repressionin Bangladesh (see section II), the theo-retical model is based on the MAUM andTAUM. The model predicts that the deter-minants of UM exchange rates �EU� are offi-cial exchange rates �EO�, money supply �M�,domestic interest rates �r�, trade restrictionsmeasured by official forex reserves relative toimports �Q�, and foreign price levels �PF �. Inthe model, a small, open economy producesa single commodity that is partly consumeddomestically and partly exported abroad. Theofficial market is restricted. There is a UMthat is not legal but well recognized, andlegal obligations are avoided by side pay-ments or by political and social influences.Commercial transactions are partly settledthrough the official current account at a rateEO . The remaining commercial transactionsare settled through the UM at a rate EU ,which is considered as market determined.The demand for money can be written asfollows:

Mdt /PD =KOY

�1 exp�−�2rt+ut��(1)

where Md is the demand for nominal money;PD is the general (domestic) price level, Yt

is the real income, and rt is the nominal(domestic) interest rate. Assuming that themoney market is in equilibrium, equation (1)can be written as

Mst /PD =Md

t /PD =M/PD(2)

=KOY�1 exp�−�2rt+ut�

�2A� �⇒ log�M�− log�PD�

= ko+�1 log�Yt�−�2rt+ut�

where MS is the nominal money supply;throughout the analysis, a letter with sub-script zero implies a constant. Define PD as aweighted average of the prices of traded andnontraded goods:

PD = PwT P

�1−w�N �⇒ log�PD�(3)

=w log�PT �+ �1−w� log�PN ��

where PT and PN are the prices of traded andnontraded goods, respectively; w is the share


of traded goods. In domestic markets, PT canbe written as the weighted average of foreignprices �PF ��EO , and EU�PN is the weightedaverage of PT and M . Hence the following:

PT =Q�1E�2OE

1−�2U PF �⇒ log�PT �(4)

= �1 log�Q�+ �2 log�EO�

+ �1− �2� log�EU�+ log�PF ��

PN =BOP TM

! exp�v��⇒ log�PN �(5)

= b0 + log�PT �+! log�M�+v�

with � !≥ 0�

where �2 is the share of foreign trade throughthe official market, Q and M are as alreadydefined; and ! are the elasticities of PNwith respect to PT and M , respectively. A risein the relative prices of traded goods gen-erates excess demand for nontraded goodsbecause consumers substitute the latter fortraded goods. Hence, a rise in the prices ofnontraded goods implies that ≥ 0 (Gupta,1980). Similarly, an increase in the moneysupply causes a rise in the demand for non-traded goods and their prices, that is, ! ≥ 0.Substituting equations (4) and (5) for PT andPN , respectively, into (3) and the resultingexpression for log�PD� into (2A) one obtains

log�EU�= $O−% log�EO�+& log�M�(6)

−' log�Q�+(r−) log�Y �

−* log�PF �++�

where$O =−,kO+ �1−w�bo-/.�

%= �2/�1− �2��

& = ,1− �1−w�!-/.�

'= * = �1/�1− �2��

)= �1/.�(= �2/.�

.= ,w+ �1−w� -�1− �2��

Equation (6) states that increases in r andM cause a depreciation in EU while risesin EO�Y �Q, and PF cause an appreciationin EU . The signs of the coefficients areexplained below.

This model predicts that the demand forforex in the UM is dependent on the supplyin the official market: Excess demand in the

official market creates the demand in theUM. An official depreciation increases offi-cial supply of forex and reduces the excessdemand and EU (Gupta, 1980). The nega-tive relationship between EU and EO is alsorequired for a stable forex market. An offi-cial depreciation generally raises legal tradeand the supply of official forex (a positiveeffect) and hence reduces the supply of unof-ficial forex (a negative effect). If the positiveeffect is higher than the negative one, an offi-cial depreciation causes a depreciation in EU

and vice versa. A stable forex market requiresthe negative effect should be lower in abso-lute value than the positive one to reduce theexcess demand for forex (De Macedo, 1987).Otherwise, repeated depreciations and spec-ulative attacks in EU would destabilize theofficial market.

The model also predicts that an increasein the money supply raises price levels andcauses an appreciation of the real officialexchange rates when nominal rates are fixed.Consequently, the official supply of forexdeclines, and there is a rise in excess demandand in EU . Similarly, an increase in the inter-est rate (the opportunity costs of holdingmoney) reduces the demand for and createsan excess supply of money, which raises EU .On the other hand, a reduction in traderestrictions will increase forex reserves; there-fore an increase in forex reserves relative toimports will signal that the country is pursu-ing free trade, which reduces the importanceof UMs, and hence an appreciation (fall)in UM rates.3 A rise in income raises thetransactions demand for money, and hencereduces the excess supply of money, prompt-ing a fall in EU . In addition, an increase inforeign prices causes a depreciation of thereal official exchange rate, which increasesthe supply of forex and reduces the demandin the UM, hence leading to an appreciationin EU .

V. ECONOMETRIC MODEL AND DATA

Following equation (6), the long-runmodel for UM exchange rates for Bangladeshcan be written as follows:

EU = c+$dD85+%EO+&M +'Q(7)

+(I +)Y +�PF +ut�

3. Thanks are due to an anonymous referee for com-ments to clarify this point.


where

$d > 0�% < 0� & > 0� ' < 0�

( < 0�) < 0�� < 0�

where c is a constant; D85 is a dummy thattakes on a value 1 from the third quarter of1985 to the fourth quarter of 1992,4 EU andEO are nominal official and UM exchangerates, respectively, takas per U.S. dollar; Mis nominal narrow (M1) money supply; Q istrade restrictions; I is the ratio of foreignto domestic interest rates; Y is real domes-tic product in 1990 prices;5 ut is a normallyand identically distributed error term; PF isforeign price levels measured from the logof consumer price indices (base 1990) of theUnited States. All data except I are in natu-ral logarithms. Data sources are given in theappendix. Sample periods are from the sec-ond quarter of 1976 to the second quarterof 1995.

The econometric analysis reveals that thedomestic interest rate variable gives conflict-ing results in the first step and is statisti-cally insignificant in the second step of theARDL cointegration analysis (details of theseresults are available on request). Thus, weuse the ratio of foreign to domestic inter-est rates instead of considering only domesticones because this ratio can be used for testingthe both MAUM and portfolio approachesto UM (PAUM) simultaneously. Note thata fall in I implies a relative rise in domes-tic interest rates. Thus, if the coefficient ofthis ratio is negative, we can conclude thata relative rise (decline) in domestic (foreign)interest rate creates excess money supply and,hence, a rise in EU as predicted by theMAUM. Conversely, a positive coefficient ofI is consistent with the prediction of PAUMthat a relative decline (rise) in the domes-tic (foreign) interest rate increases the stock

4. The underlying arguments for including thisdummy are explained in section II, which include large-scale corruption and money transfers of the files andranks of military government during 1985–91 throughunofficial markets, natural calamities in 1987 and 1988,and the Gulf crisis in 1991 (see section II, last two para-graphs).

5. Quarterly figures are not available and areobtained by minimizing the square of differencesbetween the successive quarterly values subject to theconstraint that the sum of the quarterly totals shouldequal to the sum of (available) yearly totals (Bootet al., 1967).

demand for forex (Dornbusch et al., 1983).Restrictions on forex markets are proxied bythe forex reserves relative to imports, thatis, forex reserves as a monthly capacity ofimports. The rationale behind this measure isexplained in section III.

A. Results of the Long-Run Relationship

In the first step of the two-step proce-dure of the ARDL approach to cointegrationanalyses (Pesaran and Shin, 1998) (see Sid-diki and Daly, 1999, for a description of theARDL method). Pesaran and Pesaran (1997)is used for our empirical analysis.

The author carried out stability testsfor examining the existence of a long-runrelationship among the variables EU , EO ,M , Q, I , and Y (Pesaran, Shein, andSmith, 1996). The error correction (EC) ver-sion of the ARDL model with variablesEU�EO�Q�M�I , and Y can be written as:

2EUt = aU0 +aUdD85+n∑

i=1

biU2iEU� t−i(8)

+n∑

i=1

ciU2iEO�t−i+n∑

i=1

diU2iMt−i

+n∑

i=1

eiU2iQt−i+n∑

i=1

fiU2iIt−i

+n∑

i=1

giU2iYt−i+91UEU�t−1

+92UEO�t−1 +93UMt−1

+94UQt−1 +95U It−1

+96UYt−1 ++t�

Note that D85 is included as an exoge-nous variable. In addition, PF is excludedfrom the empirical models because its inclu-sion does not provide economically sensibleresults regarding the long-run relationship.In fact, results from the second stage showthat PF is statistically insignificant in both theshort- and long-run models (results availableon request).

Taking into account the quarterly data andthe limited number of observations, n = 4,that is, the number of lags is four. The F -test,FEU �EU �EO�M�Q�I�Y �, is used to exam-ine existence of the stable and long-run rela-tionship. The null hypothesis of the nonexis-tence of the long-run relationship, that is, the


coefficients of all lagged level variables arejointly zero, is indicated by H0�; 91U = 92U =93U = 94U = 95U = 96U = 0�. The alterna-tive hypothesis of the existence of a long-runstable relationship is defined by H1�; 91U =0�92U = 0�93U = 0�94U = 0�95U = 0�96U =0�. The calculated F -statistic, FEU �� < < < �, isequal to 6.1978, which is higher than theupper bound critical value (CV) 3.80 for fiveregressors at a 5% significance level. There-fore, this article rejects the null of no long-run relationship where EU is a dependentvariable. Similarly, the analysis constructedanother five EC models where EO�M�Q�I ,and Y are in turn used as dependentvariables. The corresponding estimated F -statistics are: FEO�EO �EU�M�Q�I�Y � =3�1145, FM�M �EU�EO�Q�I�Y � = 0�88454,FQ�Q �EU�EO�M�I�Y � = 2�2814, FI�I �EU�EO�M�Q�Y � = 1�8524, and FY �Y �EU�EO�M�Q�I� = 0�43461. Thus, the results showthat FEU �EO � < < < � is higher than theupper bound of the CV, and FM�M � < < < �,FQ�Q � < < < �, FI�I � < < < �, and FY �Y � < < < � arelower than the CV. However, FEO�EO � < < < ��3�1145� is higher than the lower bound�2�649� but less than the upper bound ofthe CV �3�80�. That is, the computed valuefalls in the indecisive region, which neces-sitates a judgment as to whether the vari-able is I�0� or I�1�. The integration anal-yses show that all variables included in themodel are I�1� (results available on request).Hence, FEO�EO � < < < � is statistically insignif-icant because it is lower than the upperbound of CV. Therefore, it is apparent that aunique and stable long-run relationship pre-vails in which EU is a dependent variable andEO�M�Q�I , and Y are long-run forcing vari-ables (or exogenous variables).

Having found a unique and stable long-run relationship, in the next step the authorselected the order of lags in the ARDLmodel. The following ARDL�3�0�3�1�2�2�model was selected based on the Akaikeinformation criterion:

EU�t = −0�46�−0�22�

+0�30 D85∗∗t

�4�95�(9)

+0�74 E∗∗U��t−1�

�6�65�−0�32 E∗

U��t−2�

�−2�32�

+0�18 EU��t−3�

�1�93�−0�56 E∗

O�t

�−2�63�

+0�11 Mt

�0�67�−0�39 M∗

�t−1�

�−2�24�

+0�30 M�t−2�

�1�76�+0�35 M∗

�t−3�

�2�23�

−0�06 Qt

�−1�90�−0�05 Q�t−1�

�−1�78�

+0�18 I∗t�2�03�

−0�12 It−1�−1�14�

−0�21 I∗t−2�−2�25�

+0�03 Yt

�0�12�+0�67 Yt−1�1�91�

−0�66 Y ∗t−2

�−2�24��

R2 = �97781; SE of regression = �081796; F -stat. F �17�59�= 197�9844,�000-; residual sumof squares = 0�39475; DW statistic = 1�7541;AR4->2�4� = 8�1872,0�085-; AR4-F �4�55� =1�6359,0�178-; RESET->2�1�= 1�6944,0�193-;RESET-F �1�58� = 1�3050,0�258-; NOR->2�2� = 1�0994,0�577-, H->2�1� = 2�442×,0�118-; H-F �1�75� = 2�4564,0�121-, EU -F �3�59� = 24�649,0�000-, EO-F �1�59� =6�917,0�0109-, Q-F �2�59� = 3�9402,0�0248-,I-F �3�59� = 4�2629,0�0086-, M-F �4�59� =5�2179,0�001-, Y -F �3�59� = 2�7642,0�0498-,D85-F �1�59� = 24�501,0�000-; equation loglikelihood = 93�7643. Sample period is1976Q2–1995Q2.

Throughout the analyses, t-statistics arereported in the parentheses, ∗∗ and ∗ repre-sent 1% and 5% significance levels, respec-tively. Probability values are reported insquare brackets. The model passes all diag-nostic tests6 because all the statistics are sta-tistically insignificant implying no evidence ofmisspecification. In addition, all variables arestatistically significant at a 5% level,7 justi-fying their inclusion in the model. In addi-tion, actual and fitted values of EU generallymove together (Figure 2). Moreover, cumula-tive sum of residuals (CUSUM) (results avail-able on request) and CUSUM of square testswere carried to examine the stability of the

6. AR4->2 (2) and AR4-F are the chi square statisticand F -test, respectively, for fourth-order residual jointautocorrelation. RESET->2 (1) and RESET-F are chisquare and F -tests, respectively, for functional misspec-ification. NOR->2�2� is the chi square statistic for test-ing normality in error terms. H->2(1) and H-F are thechi square and F -statistics, respectively, for testing het-eroskedasticity.

7. EU -F , EO-F , Q-F , I-F , M-F , Y -F , and D85-Fare F -tests for the joint statistical significance of EU , EO ,Q, I , M , Y , and D85, respectively (contemporaneousand lagged), in the model.


FIGURE 2Plot of Actual and Fitted Values

model (Figure 3). Both of the tests reject anypossibility of parameter instability in the esti-mated model. Therefore, it is apparent thatthe overall fit of the model is very good, andit passes all diagnostic tests.

The corresponding static long-run modelof the ARDL(3, 0, 3, 1, 2, 2) model in equa-tion (9) can be written as follows.8

EU = −1�18�−0�22�

+0�76 D85∗∗

�10�24�−1�43 E∗

O

�−2�41�(10)

+0�95 M∗∗

�2�82�−0�27 Q∗

�−2�59�−0�39 I∗

�−2�10�

−0�10 Y�−0�16�

�

The static ARDL long-run model for thewhole sample periods 1976Q2–1999Q2 areused:

EU = 8�69�1�76�

+0�87 D85∗∗

�11�50�−1�15 E∗

O

�−1�76�(10A)

+1�05 M∗∗

�2�63�−0�19 Q∗

�−1�89�−0�30 I∗

�−1�51�

−0�92 Y�−1�57�

�

8. The static ARDL long-run model whendomestic interest rate is used in our analysis: EU =−1�99�−0�37�

+0�88 D85∗∗

�9�58�−0�50 E∗

O

�−1�18�+0�43 M∗∗�1�87�

−0�08 Q∗�−1�32�

−0�01 I ∗�−0�30�

+0�27 Y�0�48�

.

The EC representation of the selected ARDLmodel (equation [9]) can be written as fol-lows:

2EU�t = −0�46�−0�22�

+0�30 D85∗∗t

�4�95�(11)

+0�14 2EU��t−1�

�1�50�

−0�18 2EU��t−2�

�−1�93�

−0�56 2E∗O� t

�−2�63�+0�11 2Mt

�0�67�

−0�65 2M∗t−1

�−3�33�−0�35 2M∗

t−2�−2�23�

−0�06 2Qt

�−1�90�+0�18 2I∗t�2�03�

+0�21 2I∗t−1�2�25�

+0�03 2Yt

�0�12�

+0�66 2Y ∗t−1

�2�24�−0�39 ECM∗∗

t−1�−5�38�

�

where2 is the difference operator; ECM is theEC term; R2 = 0�50673; SE of regression =0�081796; F -stat. F �13�63� = 7�3134,�000-;residual sum of squares = 0�39475; DWstatistic = 1�7541.

It is observed that Y is statistically signif-icant only in the short run (equation [11])


FIGURE 3Plot of Cumulative Sum of Squares of Recursive Residuals

Note: The straight lines represent critical bounds at 5% significance level.

rather than in the long-run (equation [10]).Thus, EU , EO , Y , I , Q, and D85 have a coin-tegrated long-run relationship, with EU as adependent variable, and the remaining arelong-run-forcing (or explanatory) variables.There is no significant qualitative change inthe long-run parameter estimates even whenwhole sample periods (1976Q2–1999Q2) areused (see equations [10] and [10A] above).The results of the modeling are discussed.

Results of the long-run models (equation[10]) show that a rise in EO causes an appre-ciation in EU . As explained in sections III andIV, an official depreciation increases the offi-cial supply of forex (a positive effect). It alsoreduces UM premiums and, hence, a reduc-tion in the supply of forex in the UM (anegative effect). The result implies that thepositive effect dominates the negative one,and hence, an official depreciation increasesthe overall supply of forex and reduces EU ,implying that the forex market in Bangladeshis stable and instability in the UMs is unableto destabilize the overall forex market.

It is also observed that the long-run moneysupply (M) elasticity of EU is positive andsignificant (equation [10]). An increase in Mraises the demand for goods and servicesand causes domestic price levels to rise andreduces real official exchange rates whennominal rates are fixed. This appreciation in

real official rates necessitates a depreciationin EU to maintain the purchasing power par-ity condition in UMs (Blejer, 1978). Similarly,the impact of an relative increase in domestic(foreign) interest rates on EU is positive (neg-ative). A relative increase in domestic interestrates, the opportunity costs of holding money,creates excess money supply and hence a risein EU . Thus, the results of the long-run modelon money supply and interest rate differen-tials lend support to the monetary approachto UM.

In addition, it is observed that an increasein trade restrictions (Q), caused by a fall inofficial reserves relative to imports, inducesEU to be depreciated, because the lower theimport capacity of official reserves, the higherthe trade restrictions and the greater the UMpremium. This result is consistent with thefact that the increase in forex reserves inrecent years has been associated with a lowerlevel of EU . Finally, it is observed that somestructural factors (D85), which include severepolitical instability during 1985–91 along withrepeated natural calamities in 1987 and 1988and the Gulf crisis in 1991, have a posi-tive and statistically significant effect on EU .These factors adversely affected the economyand reduced the supply of forex and, hence,there was a rise in EU . It should be noted thatthis analysis failed to obtain any cointegrated


relationship and economically sensible resultsexcluding D85. Thus, D85 is included due toboth economical and statistical reasons. Theforeign price level does not enter the coin-tegrated relationship, which is not implausi-ble given the fact that the existence of UMsin Bangladesh results from trade restrictionsand excess money supply.

The EC model (equation [11]) shows thatthe coefficient of the mechanisms is neg-ative and statistically significant, indicatingthat there is a mechanism in the model thatforced UM rates toward its long-run equilib-rium relationship defined by equation (10).Thus, the negative and statistically significantcoefficient of the EC term supports the coin-tegrated relationship and the modeling of EU .In the short-run (equation [11]), the impactof EO and Q on EU is consistent with thelong-run results. In addition, while Y is sta-tistically significant and positive in the shortrun even though it is statistically insignifi-cant in the long run, the short-run impact ofmoney supply and interest rate differentialsare inconsistent with the long-run results.This short-run result on Y supports the pre-diction that an increase in income raises thetransactions demand for forex and, hence, arise in EU (Agénor, 1991). Note that in con-trast with the long-run impact, an increasein money supply and a decrease in domes-tic interest rates cause an appreciation inUM rates in the short run. This may resultfrom the positive short-run impact on out-put and exports of an increase in money sup-ply and a decrease in domestic interest rates.The increased exports raises the supply offorex, which in turn reduces UM rates. Thisshort-run impact, however, disappears in thelong run.

B. Comparing Out-of Sample and In-SampleForecasting Performances of Models

Meese and Rogoff (1983a, 1983b) argue,in the case of the G-7 exchange rate liter-ature, that in sample fit is a poor meansof assessing the robustness of exchange ratemodels.9 Out-of-sample historical simulationis a typical means of assessing the fragility of

9. The author is thankful to two anonymous refereesfor their suggestions to include such analyses. Thanksalso to Vince Daly for helpful suggestions in explainingthe results of this section.

these models. Sample periods 1995:3–1999:2were used here to compare the out-of sampleforecasting accuracy of our structural modeland various time-series exchange rate mod-els. Different measures of forecast accuracyare used, which include root mean squarederror (RMSE), mean absolute error (MAE),and the Theil inequality coefficient (TIC)(Pindyck and Rubenfeld, 1998). RMSE mea-sures the observed standard deviation of theforecast errors. MAE reports the average sizeof errors regardless of sign. TIC measures theRMSE in relative terms and can be decom-posed into bias proportion, variance propor-tion, and covariance proportion. The biasproportion quantifies the systematic errors.The variance proportion measures the abilityof the model to replicate the degree of vari-ability in the variable of interest and covari-ance proportion assesses unsystematic errors.

The results show that for in-sample pre-dictions, the structural approaches (VAR,ARDL) are noticeably more accurate thanthe nonstructural methods (random walkand AR) on all accuracy measures—RMSE,MAE, and TIC—with VAR performingslightly better than ARDL (see Table 2, top).When predicting out of sample, the rank-ings of structural versus non-structural meth-ods are reversed—as suggested by Meese andRogoff (1983a, 1983b) (see Table 2, bottom).The implied market predictions, based on theforward rate, underperform relative to struc-tural methods both in and out of sample.

Decomposition of TIC into its componentsallows some assessment of the sources of rel-ative performance of the structural methods.The in-sample superiority of the structuralmethods results from their relatively low biasand variance components, which we mightassociate with the data-fitting ability of mod-els that incorporate a variety of explanatoryvariables. Table 2 (bottom) shows that thisadvantage is lost when we consider forecastsmade for out-of-sample data periods. Thus,these results are consistent with the findingsof Meese and Rogoff (1983a, 1983b) and withthe argument that structural exchange ratemodels have explanatory power, but predictbadly because their explanatory variables arethemselves difficult to predict (Meese andRogoff, 1983a, p. 10).

It is good practice to assess the predictivepower of out-of-sample forecast. However,


TABLE 2Model Comparisons

Random ForwardWalk Rate AR VAR ARDL

Within sample period: 1976.2–1995.2

RMSE 0�612424 0�3838457 0�366870 0�083099 0�092234MAE 0�474895 2�803181 0�314228 0�0663199 0�075469TIC 0�081204 0�334938 0�046244 0�010337 0�011476BP 0�587181 0�001 0�047969 0 0�000125VP 0�239343 0�8221743 0�463000 0�0059468 0�017808CP 0�173476 0�126634 0�489031 1�0072 0�982067

Out-of-sample: 1995.3–1999.2

RMSE 0�06622 0�5 0�079667 0�24849 0�329191MAE 0�06252 15 0�075036 0�23103 0�311091TIC 0�0083 0�318316 0�009949 0�02032 0�039924BP 0�875429 0�04559 0�887110 0�77999 0�893057VP 0 0�272606 0�020782 0�0062 0�072995CP 0�12432 0�126634 0�092107 0�13849 0�033948

Notes: RMSE=Root mean squared error, MAE=mean absolute error, TIC=Theil inequality coefficient, BP= biasproportion, VP = variance proportion, CP = covariance proportion.

the main focus of this article is to esti-mate the structural parameters, which areimportant in designing policies to reduce thedistortions in forex market in Bangladesh.The benchmark method of forecasting, suchas the random walk for judging the fore-cast accuracy, offers no information at allwith respect to structural parameters. Thus,a weak performance of a structural model inout-of-sample forecasting does not mean thatit should be abandoned.

VI. CONCLUSIONS

This article explores the determinants ofUM exchange rates (EU ) in Bangladesh fromthe second quarter of 1976 to the secondquarter of 1995 using the ARDL approachto cointegration analyses. Results reveal thatthe structural models (ARDL and VAR) per-form well in in-sample prediction, whereasthe random walk model performs best inout-of-sample forecasting. The cointegrationanalyses reveal that there is a multivariatecointegrated relationship at a 5% significancelevel among EU (dependent variable), officialexchange rates (EO), nominal narrow moneysupply (M), trade restrictions (Q), the ratioof foreign to domestic interest rates (I), andreal income (Y ). The overall results mainlysupport the monetary and trade approachesto the UM for forex.

It is observed that a depreciation in EO

causes an appreciation in EU . A rise in EO

increases the official supply of forex (a pos-itive effect) and reduces the supply of forexin the UM (a negative effect) by reducing theunderinvoicing of exports and the overinvoic-ing of imports. The result implies that thenet effect is positive, and hence a deprecia-tion in EO reduces excess demand in the offi-cial market, which in turn causes an appreci-ation in EU . The result also indicates that theforex market in Bangladesh is stable becausethe stability condition requires the positiveeffect to be greater than the negative effect.Thus, instability in the UM, in the form ofrepeated depreciations in EU caused by spec-ulative attacks, is unable to destabilize theofficial forex markets. The implication of thisresult is that government forex policies areeffective in reducing the prevalence of UMsfor forex in Bangladesh.

It is also observed that an increase inmoney supply raises EU by fueling inflation-ary pressures. Similarly, a relative increase indomestic interest rates reduces the demandfor money and creates excess supply and,hence, a rise in EU . In addition, an increasein trade restrictions causes a depreciation inEU . Finally, it was also observed that politicalinstability (along with other structural factors,including natural calamities and the Gulf cri-sis in 1991) increases EU .


In short, these results reveal that theovervaluation of the official exchange rate,increases in money supply, the paucity ofofficial forex reserves, and political alongwith some other structural factors are themain causes for the creation of the UM forforex in Bangladesh. Thus the governmentshould reduce distortions in official exchangerates and control monetary expansion andtake export-friendly initiatives to raise offi-cial forex reserves. Initiatives should also beaimed at maintaining political stability aswell as transparency in the administrationto reduce the extent of UMs for forex inBangladesh.

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unofficial exchange rates in bangladesh: a cointegration analysis

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