POLICY RESEARCH WORKING PAPER 1396
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Janine Aron
Ibrabim Elbadawiv
The World Bank f-4
Policy Rmarch Deparlmet
MacroecononEics and Growth Division
Deemiber 1994
POLICY RESEARCH WORKING PAPER 1396
Summary findings
In this analytical sequel to A Typology of Foreign rule. When bidders learn such a rule, speculative bidding
Exchange Auction Markets in Sub-Saharan Africa, Aron diminishes.
and Elbadawi compare the micromanagement of * The management of a credible, sustainable reserve
different foreign exclhange auctions in Sub-Saharan price policy requires an efficient secondnry market.
Africa. A simple underlying model, synthesized from the
Multi-unit auctions for foreign exchange were theoretical literature on auctions, specifies the auction
introduced in a number of countries in tde 1980s and rate as a function of fundamental variables and struccural
199Os, in a transitional step toward a credible, shift dummies. The repeated, sequential narure of these
sustainable, unified regime, such as an efficient interbank multi-unit auctions and the nonstationary nature of most
ma'cet. But there is little understanding of how auction of the auction variables are captured empirically by a
markets function in Sub-Saharan Africa, and there has cointegrated (error correction) framework.
been virtually no research on the causes of frequent In addition to consistendy estimating long-run and
policy reversals or of auction failure. short-run parameters of auction fundamentals, the error
One possible cause of failure - apart from thin correction model allows asymptotically efficient testing
markets, macroeconomic laxity, and vulnerability to of three policy hypothcses deriving from auction theory:
terms-of-trade shocks and fluctuations in the the competitiveness hypothesis, the effect of uncermtinty
disbursement of foreign aid - is the inappropriate on the auction-determined rate, and the revenue-
design and management of auctions. equivalence hypothesis.
Aron and Elbadawi estimate models for the In other words, they used these models to test the
microdetermiinants of the auction rate, using weekly data impact on the level of the auction rate of increased
on foreign exchange auctions for Ghana, Nigeria, competiton among bidders, of the effect of uncertainty
Uganda, and Zambia. Among the poliqc lessons: (proxied by a volatile supply of foreign exchange), and of
N Nigeria and Zambia failed to unify and stabilize the different pricing mechanisms (Dutch and marginal
exchange rate pardy because there was no reserve price pricing).
This paper-a product of the Macroeconomics and Growih Division, Policy Research Department-is part of the departmental
project "Forcign Exchange Auction Markets and Exchange Rare Unification in Sub-Saharan Africa. Copies of this paper are
available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Raquel Luz, room Ni 1-053,
extension 39059(38 pages). December 1994.
*)e Paltry Rcscarch WEork Paper beys dthemts Poie Resa of Wori sina tioD aCente c r cr of s abost
deldopmctr i#An objectm ofth sbes is toge She f A rm oa qty, emif tkc prcimonsare Icss dsm fsdly,poise lec
popes carry the crmof rtceautsors ad douU be u axd citedaccordngly.Th cfdsg$ barpns,t and cogdul˘are the
atahor'own and should not be crncd to tlk Worfid Baslk its Excautivc Board of Dirtors. or any of isrk mber comtres.
Produced byr the Policy Rescarch D)issemination Ccnter
FOREIGN EXCHANGE AUCTION MAARETS IN SUB-SAHARAN AFRICA
DYNAMIC MODELS FOR TEIE AUCTION EXCIIANGE RATES
Janine Aron and IbTrahim Flbadawi
The authors are very gratefiul for comments from Miguel Kiguel, John Muellbauer, Stephen O'Connell,
Rafael Tenorio, Kathryn Dominguez, Chad Leechor and Lant Pritchett.
TABLE OF CONTENTS
1. INTRODUCTON ............................................
2. THEORETICAL ISSUES . . 4
2.1 Towards an Empirical Model of the earing Auction Rate . . 5
2.2 Policy hypotheses motivated by auction theory .. 9
3. DATA AND EMPIRICAL METHODOLOGY. . . .. 12
........................................................ 12
3.1. Cointegration Modelling in Repeated, Sequential Auctions . .12
4- ESTIATION AND HYPOTHESIS TESTING ................... 15
4.2 Testing policy hypotheses .................................... 19
5.CONCLUSIONS.. 22
5.1 Summary of results . ...................................... 23
5.2 Policy lessons .................. 24
REFERENCES ............................. . 27
APPENDIX I:Econometric methodology. ............................ .. 38
LIST OF TABLES
TABLE 1: Tests for unit roots with structural breaks .......................... 30
TABLE 2: Estimation of the equilibrium auction rate for Zambia, Uganda, Ghana and
Nigeria .........- 32
LIT OF FIGURES
FIGURE 1 a:b,c,d: Regime shifts and the equilibrium auction price in the SSA
auctions .36
1. INTRODUCTION
One of the most dramatic manifestations of the economic crisis that swept Sub-Saharan Africa
since the second half of the 1970s, has been the emergence and the subsequent expansion of parallel
markets for foreign exchange. Relative to other developing regions, the parallel premia and the size of
these markets have tended to be much larger in SSA (Kiguel and O'Connell, 1992). In fact the parallel
premium in most of the Sub-Saharan African countries constitutes a major economic signal reflecting
policy incredibility, therefore influencing short-run as well as long-nm economic decisions (e.g. Aron
and Elbadawi, 1992). It is by now widely accepted that unifying the exchange rates (official and parallel)
and integrating the parallel market into the regular economy should be a major policy objective for
reforming African countries (e-g. Kiguel and O'Connell, 1992). Recent evidence, however, shows that
achieving exchange rate unification, and more importandy sustaining it, has been a rather elusive goal.'
The received wisdom suggests that the "best" approach to unification might be to start with nominal
devaluations and gradually liberalize foreign trade transactions - the pace of reform being set by the speed
and credibility of fiscal adjustment (Pinto, 1990). It is also important to emph2size that unification is a
complex process that may require institutional changes as well as behavioral adjustments on the part of
market participants (Agenor and Flood, 1992).
During the 1980s and 1990s, two types of flexible exchange rate regimes have been introduced
in SSA, with one important goal being the sustainable unification of multiple markets for foreign
exchange These are decentralised interbank markets in foreign exchange,' and the innovative use of
centralised foreign exchange auction markets? Auctions may have advantages over moving directly to
interbank markets where there is insufficient institutional depth to allow effective functioning of a
decentralized foreign exchange market, where a few commercial banks have historically been dominant
and there is a danger of collusion, or where there are limited sources of foreign exchange (Quirck et al,
1987, Krumm, 1985). The extent of macroeconomic imbalances (especially fiscal) that have prevailed in
SSA, and the rudimentary nature of economic instittions (such as the banking system), provide a strong
case for a more gradualistic approach to exchange rate unification in SSA. Where auctions have proved
'The term unification in the SSA contxt rcfers to eradication of the paralld market However, since these countries are
likely to maintain capital controls in die medium term, there would remain a small role for the parallel makt in meeting
ponfolio demand. Our conceptof unification in SSA is thus a substntial- reduction of the parallel market so that i. is no longer
a major signal in the economy.
2 Counties which have used interbanic markets include Zaire, The Gambia, Sierra Leone, Ghana Uganda and Nigeria (in
tandem with an auction).
3Countries which have esablished various types of exchange rate auctions include Bolivia (1985 onwards). Jamaica (1984-
89) and African countries, Ghana (1986.92), Nigeria (198694), Guinea (1986.), Zambia (1985-87), Sier Leone (198283),
Uganda (1982-85, 1992-93) and Ethiopia (1993-).
-2
successful in SSA, their primary role has been as a transitional medium towards a unified interbank
market.
Two types of multi-unit foreign exchange auctions have been employed in SSA: first, retail
auctions, where the bidders are private and public sector importing firms, channelling integrated price-
quantity bids for foreign exchange through the non-competing banks; and secondly, wholesale auctions,
where the bidders are registered banks or foreign exchange dealers. In the latter case, there may either
be a free secondary (importers') market for foreign exchange, so that banks compete freely in -the auction;
or the banks may be restricted to submitting composite bids for foreign exchange which exactly cover
importers' (and possibly their own) requirements in a strictly monitored secondary market. Two types
of pricing mechanisms have been used in these auctions. These are the discriminatory or Dutch auctions,
where bidders pay their own price for each urit; and competitive auctions, where bidders pay the lowest
accepted bid price for each unit
The experience with auctions in SSA has included some notable successes (e.g. auctions in Ghana
and Uganda); but equally, other countries have experienced damaging speculative episodes and policy
reversals (Nigeria and Zambia). The rather mixed outcome in these countries for unification and
stabilisation of the exchange rate was discussed in Aron and Elbadawi (1994). The weekly evolution of
the auction rates is illusted in Figure 1. Although auctions continue to be introduced (e.g. Ethiopia in
1993), and despite the obvious policy importance. the functioning of these markets and the causes of
policy reversals in SSA remains poorly understoodl. Apart from supply problems due to initial conditions
of market thinness and vulnerability to terms of trade shocks and fluctuations in the disbursement of
foreign aid, potential causes of failure include macroeconomic laxity, inappropriate auction design and
poor micro-management of auctions. It is generally accepted that a successfil exchange rate reform
depends crucially on a stable macroeconomic environment. In the context of Sub-Saharan Africa, the
decision to unify exchange rates essentially amounts to a commitment by the authorities to shift the
nominal anchor from the exchange rate to the money supply. However, the micro-design features of a
foreign exchange auction are more than merely a transmission mechanism for a sufficiendy sustainable
macro-economic environment This is because macro-credibility does not only require consistent policy
in terms of fundamentals (fiscal and monetary policy), but also depends crucially on agents' responses
to their perceptions of government commitment to reform. Auction design through rules, procedures and
announcements can modify and direct the bidding behaviour of participating agents.
4 In princ4ile, auctions with limited entry restrictions could provide a viable, long-term, market-based exchange rate
arrangement. However in practice, the move to a decentralised interbank market has been favoured over retaining an auction
for a number of rmasons: the increased administrative requirements of a centalized auction system are cosdly; there is greater
potendal for govenmment mulation of dte exchange rate or for rent-seeking; there is a closer association of the government
to the politics of the exchange rate; and furthermore, even with few entry restrictions, the transactions coAts for auclion
participants particularly where donor money is being auctioned) creat a wedge between the parallel and official market rates.
-3-
Unfortunately there has been virtually no empirical research in this area: part of the reason being
that the analysis of sequentially repeated, multi-unit auctions presents substantial theoretical and empirical
difficulties. The aim of this paper is to build on an earlier institutional and statistical paper on the SSA
auctions (Aron and Elbadawi, 1994), and estimate models for the micro-deterninants of the auction rate,
based on a simple underlying model synthesized from auction theoretical literature, using weekly foreign
exchange auction data from four Sub-Saharan African countries, Zambia, Uganda, Ghana and Nigeria.
The empirical section of this paper constitutes a novel approach to empirical modelling in auction
research: in the context of a dynamic model for these repered, sequential auctions, we employ more
recent econometric techniques of cointegration for efficiert hypothesis testing in the presence of the
regime shifts (structural breaks) which characterize these liberalizadion episodes in SSA.5 We use this
empirical model to evaluate some micro-economic design and management features of the foreign
exchange auctions through testing policy propositions motivated by auction theory. We hope to shed some
light on the causes of success and failure of the auction regimes in SSA, and provide a few policy lessons
for improved design and conduct of auctions at the micro-level.
This study is partly historical, but also has substantial current relevance. Two of the countries
we examined at the time of analysis had ongoing auctions (Nigeria and Uganda), auctions were introduced
in Ethiopia in 1993, while more recently the question of introducing an auction to disburse foreign aid
has been mooted in Zambia.' Secondly, there is an increasing tendency to use auctions for the market-
pricing of credit and import quotas in Latin American and Eastern European countries. This trend appears
to be moving to SSA, so that many of the lessons from the foreign exchange auctions, which take explicit
account of the structural characteristics of these countries, will be transferable.
The structure of the paper is as follows. Section 2 discusses some analytical issues and gives an
outline of a benchmark model of the auction equilibrium selling rate. Data features and the empirical
methodology are presented in section 3. The model is estimated in section 4 and various hypotheses are
tested to clarify policy questions, using weekly auction data from Ghana, Nigeria, Zambia and Uganda.
Finally, section 5 concludes with policy lessons from SSA.
5Regime shifts and unit-root are common features of these high firquency SSA data (Aron and Elbadawi, 1994).
6Further, a numnber of Eastern European countnies employ foreign exchange auctions (eg. Romania and Khazakstan) where
stuctral characteristics may not be too different in some cases to SSA countries.
4-
2. -THERETICAL ISSUES
There is currently no single theoretical auction model which adequately describes the equilibrium
properties of the SSA foreign exchange auctions. A composite of a number o? the existing models is
probably required, and most of the restrictions that are imposed in standard models have to be relaxed.
First, the foreign exchange auctions are multi-unit auctions, which differ from conventional
auctions in that bidders select both the price and the quantity of units they wish to buy at that price. In
contrast to single-unit auctions, the submission of integrated price-quantity bids can involve strategic
behavior on the part of firms, whose payoffs may be raised by downward quantity adjustment under
competitive, though not discriminative pricing (Tenorio, 1991).
Second, the auctions are not one-shot isolated events, but repeated, sequential auctions. Thus,
they may embody interesting strategic dynamics and learning behavior, and many predictions from single
auction models will not carry over to repeated auctions (Bikhchandani, 1988). For example, a deception
effect may develop in sequential sales, where if the bidder knows his current bid will reveal information
about later sales, he will have an incentive to underbid (Hausch, 1986). Sequential auctions may also
facilitate cooperative collusive behavior amongst bidders (applying the now familiar analysis of repeated
oligopoly games). The issue of commitment by the seller is important in repeated auction games (McAfee
and McMillan, 1987), so that we might expect the credibility of the exchange rate liberalization to play
a major role.
Third, and related to the above point, the foreign exchange auctions are not isolated events, but
rather determine an integral price for the whole economy, the exchange rate. The auctions will thus also
be influenced by a combination of macro-economic policies, exogenous shocks (such as TOT shocks),
and political-economic features (such as treatment of the large stte-owned sector).
Fourth, bidders may be risk-averse. This is because foreign exchange is a crucial input in often
highly imnport-intensive production in SSA. Bidders face an uncertain supply of auctionable foreign
exchange, due to thin markets, TOT shocks, and possibly political-economic factors; and also may be
uncertain about the commitment of the seller to a market-allocation, as opposed to the prior manual
allocation, of foreign exchange.
Fifth, bidders may not be symmetric in these auctions. That is, they may fall into identifiable sub-
classes, so that instead of there being a single distribution from which bidders draw their valuations as
is usually assumed, there may be more than one distribution. SSA importers constitute an oligopolistic
set, and unquestionably some bidders are regarded as more credit-worthy. There may also be systematic
production differences between multinational firms, the domestic private sector and public enterprises.
Sixth, the number of bidders may not be exogenous. The foreign exchange auctions typizally
involve an alteration in the rules over time (for instance, as regards transactions costs, reserve pricing
rules, or information revelation), and it has been shown that different rules and formats can attract
different sets of bidders (e.g. Samuelson, 1990).
-5 -
Seventh, the relevant value assumptions (the determinants of bidders' payoffs) and distributional
assumptions (the deterninants of bidders' beliefs about their competitors) probably imply a mix of the
two rather different frameworks commonly employed in auction models: the independent private values
(IPV)7 and the common values (CV)9 models. In the retail auctions, and in those wholesale auctions
where purchase of forex is tied to restricted imports and may not be sold in a secondary market, the
auctioned object is in effect a proxy for an imported, intermediate input for firms. The IPV component
is due to the different endowments and characteristics (see above) of the competing firms. Since these are
multiple unit auctions, the diminishing marginal utility of the intermediate good suggests that additional
units of forex will also have diminishing marginal utility for the firm. Further, where the exchange
reform is expected to be short-lived, speculative behaviour will also depend on the privately observed
opportunity cost and endowments of bidders. A CV component may be injected, for instance, when public
information is used in making forecasts, resulting in value-correlations; as well as in genuine wholesale
auctions (where the banks are not merely a channel for importers' bids), since the bidders' values are then
linked to those in a secondary market (bureaux or interbank). Further, the repeated nature of these
auctions means strategic behaviour among bidders is likely, creating an interdependence of values; while
colhl;ion, tacit or deliberate, may be facilitated.
A more general model has been developed which allows a bidder's value to depend on his tastes,
those of other bidders and of non-participants, and on unobserved characteristics of the auctioned object
(Milgrom and Weber, 1982). The model embodies private values and common values components, as
well as a degree of interdependence (affiliation) amongst bidders' valuations. Unfortmately, most auction
predictions stem from pure IPV or CV models, and are not worked out for the general model.
2.1 Towards an Empirical Model of the Clearing Auction Rate
The predictions of auction theory depend centrally on the nature of the underlying distribution
of bidders' values of the auctioned object. It is clear, therefore, that a theoretically-consistent empirical
7The lPV Model cobinesassumptions of private values wit an independentdistbution of bidders' values. Thus, bidders
values of the auctioned object are treated as subjective (diffrences amongst bidders are due to differences in tas), and while
each bidder knows his own value with certaint, he wil not know the values of other bidders. The IPV model will not be
applicable in auctions where there is a resale muarket depencling on the tastes of others; nor where- the object embodies certain
discoverable but as yet unknown properties. The model would apply for the case of a finn bidding for inputs, where all the
characteristics of the input are known. Value differences will then be due only to such factors as differences in transport costs,
product mix, capacity and inventory consideradons, opporunity cost and resource differences amongst the bidding firms.
'The CV model adopts te polar opposite of the private-values hypothesis: the auctioned object has some true value which
is conmon but unknown to all bidders. Each bidder independenly estimates the true value of the auctioned object If the bidders
are treated as having symmetric information, and their estimates are unbiased, these estmates will represe independent
drawings from a probability distribution with a mean equal to the true value- This model is typically applied in minral rights
auctions, where there is considerable uncertainty about the true valuc of the mineral, and common value elements prbably
dominate any private value components.
-6 -
methodology that attempts to estimate structural models of auctions must involve as a first step the
estimation of the values distribution. However, even for the simpler auction models, where it may prove
possible to ascertain the nature of the values distribution, there are considerable difficulties in estimating
structural econometric models derived from auction theory, given the extreme non-linearities and
numerical complexity. Recent work employs advanced econometric methods to surmount some of the
empirical problems in order to estimate structural models of auctions (e.g. Lafbont et al, 1991; Laffont
and Vuong, 1992; Paarsh, 1992; Gallant and Taucheri, 1992): Laffont et at (1991) use a simulation
approach to derive the econometric model directly from the underlying theoretical model, first estimating
the distribution of private values held by bidders. These methods are computationally feasible where the
equilibrium bid has an explicit form; but it is not clear that the method can be easily generalized to more
complex auction systems. Where even a few restrictions of the simple model are relaxed, the differential
equations do not have a closed-form solution, and the numerical solutions prove computationally
excessive. Unsumrrisingly, few empirical studies have attempted to validate theoretical auction models,
and most test some implications of the theory using reduced-form models. For instance, they might try
to explain bids in terms of a reserve price, the number of potential b:dders, characteristics of the
auctioned object and characteristics of bidders which affect the common distribution of private values
(e.g. Hansen, 1985; Hendricks and Porter, 1988).
Given the complex naure of the foreign exchange auctions that we examine in this paper, our
research approach will be to follow the past tradition in empirical work and estimate an unrestricted
reduced-form model. We then aim to test the predictions of a number of simpler auction models, to see
if they apply in more general cases. In this section we posit a simple empirical model for the auction
clearing rate. We account for the auction fundamentals that have effects that can be signed a priori (e.g.
foreign exchange supply, the number of bidders and opportunity cost). Further, the model also allows
the testing of some propositions motivated by auction theory, such as the equivalence of revenue-
generation under different auction formats, the effect of uncertainty on bid levels, and the effect of
increasing the pool of bidders (see section 2.2). Being a reduced-form, our model does not offer a
structural interpretation of the latter effects. In section 4, where we estimate and test the model, we draw
on the receiv-d wisdom from auction theory, as well as the institutional features of the auctions in
question, to provide interpretation.
We begin by setting out the Harris and Raviv (1981) theory of Nash bidding behaviour, for the
case where multiple units are sold in a single auction, and bidders can purchase at most one of these
units. Following Vuong and Laffont (1992), we consider the type of empirical model that emerges from
the solved-out equilibrium bidding strategies for both competitive and discrim-inatory pricing. We then
consider the suitability of this empirical model for the more general case of endogenous quantity decisions
by bidders (bidders can purchase more than one unit of the good) and sequentially repeated auctions.
There are Q units of a homogeneous good to be sold. The market consists of N) Q bidding
agents, who each compete for one unit of the good. Assume that bidding agent i, i=1,...,N places a
-7-
monetary value v1 on a unit of the good, and that each v, is drawn with replacement from a distribution
with density function h and probability function H, where the support of h is [ 0, i] . If bidder i submits
a sealed bid b which is accepted, then the monetary gain is v, - bi , with udlity u (v, - b). It is assumed
that u (0) = 0, that u (.) is increasing, concave and differentiable, and that the utility of an unsuccessful
bid is zero. Bids b, = b(v,) are assumed to be symumetric Nash equilibrium strategies.'
These bids are arranged by the auctioneer in decreasing order of price. In the Harris and Raviv
model, the Q highest bidders in a competitiv auction receive one unit each at the price of the Q+ ith
highest bid. Harris and Raviv (1981) show thatunder competitive bidding, the Nash equilibrium bidding
strategy for each bidder (whether risk neutral or risk averse) is to bid her true monetary value:
bc(vi)= V; (1)
The competitive price (clearing rate) is then bc (vN.q) = VN..
In the discriminatory auction, the Q highest bidders pay the rate that they bid. Assume that
bidder i believes his competitors will bid according to the differentiable bidding function bq = b(vj), for
ji, where b; is increasing on [0, v] . Let r denote the inverse of b; Ci.e. r (b(vj )) = vj ). The
probability that a bid b, will be accepted, is the same as the probability that at least N-Q of the values
drawn by bidding agent i's competitors are below ?r (bJ = v, . This probability, F(-r (b..)), is given by
the distribution function of the (N-Q)th order statistic for a sample of size N-I from the distribution H:
FQ(Mb)) = (N- Q -A)(Q 1)1 [H H(v)M-Q-' [i-H(v)]'Q- h(v) dv (2)
The ith bidding agent ten has to choose b, to maximise u (vi - b) F(ir (b1)), i.e. maximise the bidder's
utility should the bid be accepted, multiplied by the probability that it will be accepted. Harris and Raviv
(1981) show that the Nash strategy emerging from the solution of the first order condition for this
maximisation problem:
bD.(v,) = Fv) x dF(x) a
9The function b(v) will be a Nash equibnum bid functon if for every i, b(vj ranmises bidder i's expected utliy, given
dia every other bidder j uses die same saegy b(vj.
-8-
where Dn indicates risk neutrality under discriminatory pricing. Harris and Raviv also prove that where
all bidders are risk averse and have the same strictly concave utility function, they will bid higher than
risk neutral bidders.
We now tum to implications of these theoretical results for the specification of a reduced-form
empirical model. ThDe bid which is of special interest to us in the context of the foreign exchange auctions
is the lowest accepted winning bid, which was defined to be the clearing rate in all the Dutch and
competitive auctions in the four countries we consider, and the rate on which the countries' exchange
rates were closely bised (Aron and Elbadawi, 1994). In the foreign exchange auctions this is generally
the only bid observed by the researcher, while actual private values and their distribution remain
unknown. The preceding discussion showed that the solution for the bid of the N-Qth bidder under
competitive or discriminatory pricing, depends on the private value of the bidder, the number of bidders,
the size of supply and the distribution of private values. The same theoretical determinants will apply
where the clearing rate is defined on the lowest accepted rather than the highest rejected bid. Following
Laffont and Vuong (1990), we observe that since equilibrium bids are functions of private values, which
are random by assumption, then observed bids for a single auction will also be random, and be uniquely
determined by the above theoretical determinants. When considering several auctions in an econometric
investigation, account also has to be taken of the fact that the distribution of private values may depend
on the heterogeneity of the auctioned object (e.g. different characteristics of the object in different
auctions that are observed by all bidders).
Based on these points, and in the auction empirical tradition, we propose a simple log-linearised,
reduced-form empirical model for the clearing rate, for a series of mutually independent (no strategic
behaviour), multi-unit auctions where bidders bid for at most one unit of a homogeneous good:
ml m,
oer, Xl |XSi, iDUMI; = f(F,) > , (4)
'i-l i-I
where oer, is the log of the auction clearing rate. The Xi = [N, Rp, Q,, ZI is a vector of variables in
logs including the number of bidders (N); a reservation price (Re), if one is used; the size of pre-
announced supply (Q); as well as the Z variables, which are variables reflecting the observable'°
characteristics of the auctioned object, and of the buyer side of the market, which may affect the
distribution of private values (Laffont et al, 1991). One important Z variable in the context of foreign
exchange auctions is the secondary market (black or bureaux) exchange rate, or ber. While the resale of
auctioned foreign exchange in the secondary market was largely prohibited in these auctions, in the event
of the bid being unsuccessful, the bidder could resort to the more expensive secondary market. The ber
"'The Z variables may be direy observable, or be variables over which bidders can form expectations.
-9-
reflects the opportunity cost to bidders; but is also a relevant indicator of macro-economic policy and
credibility of reform (Aron and Elbadawi, 1992). The size of total demand (Od) is another Z variable
which reflects the buyer side of the market. The dummy terms (DUM) reflect other qualitative auction
fundamentals or regime shifts, such as the auction type (competitive or Dutch) or policy intervention.
Note that the two auction types are not modelled separately as distinct processes, but the entire period
of auctions is considered with inclusion of a dummy term to reflect the timing of the auction regime
change; interactive terms between auction rate determinants and the auction dummy could also be
included. Finally, et is a stationary disturbance term.
If we allow quantity choice to be endogenous (bidders specify both the desired number of units
out of Q units and the price per unit in sealed bids), the maximisation of expected utility will yield two
marginal conditions, for both the price and the quantity demanded. Quantity demanded can then be solved
for and substituted into the marginal price condition. While the functional form of the solution will be
different to the single unit case, the detrminants remain identical. Thus, the above empirical specification
for oer (equation (4)), since it uses a log linear form, will also be applicable to the case of a multi-unit
auction with endogenous quantity choice. The above reduced-form model also assumes a series of
mutually independent auctions. The equilibriumi solutions for a repeated multi-unit auction are very
difficult to characterise, given the possibilities for learning by agents or strategic behaviour (e.g. Weber,
1983). We aim at least to model such dynamic behaviour empirically, by employing unrestricted
dynamics in the reduced-form equation. This is discussed further in section 3.1. In the context of repeated
auctions, uncertainty may be induced in bidders by a volatile supply, where supply is preannounced but
only after the sealed bids have been collected. Thus a measure of the volatlity of supply could be
included as a Z variable (see section 2.2). The expected signs of the fundamental variables are:
oer = F( N, Q, Qd, ber, volatility(Q))
(+) (-) (+) (+) (+)
Z.2 Policy hypotheses motivated by aucion theory.
The first policy hypothesis concerns the choice of the auction pricing mechanism. One reason
given by policy-makers for their choice of a Dutch or discriminatory auction (where each bidder pays his
own bid) over the competitive auction (where all bidders pay the marginal price) is the belief that Dutch
pricing constitutes a disincentive to devaluation, relative to the competitive auction- That is, equilibrium
price ("revenue" to the auctioneer) struck at a Dutch auction would be lower than, not equivalent to, the
equilibrium price in a competitive auction.'1 There is no theoretical basis for this claim, and to date no
"There may be some confiision of nomenclature conermning the concept of wrevenue equivalence" adopted in this paper.
The term stems from auction theory and rfers to the clearine vnice stuck at a multi-unit auction far different types of auction.
The policy relevance of this concept is dired at the rate of deprdation of the exchange rate, and therefore relates to Ihe
principal objective of exchange rate unification. This notion of gross revenue should be distinguished rom the macro-econouc
- 10 -
robust evidence to support it for die case of foreign exchange auctions. Since the introduction of a Dutch
auction may introduce other undesirable features'2, it is important to test the veracity of the policy claim.
We will use an important result of auction theory, the revenue-equivalence theorem (Vickrey,
1961, 1962), which states that for a one-shot, single-unit auction, where bidders are risk-neutral and
symmetric, and bidders' (private) valuations are uncorrelated, revenue generation is equivalent in
competitive and discriminatory auctiors. This prediction has proved sensitive to changes in the underlying
assumptions. In the single-unit case for an IPV model, replacing the assumption of risk-neutrality wit
risk-aversion leads to revenue-superiority of the discriminatory auction (Harris and Raviv, 1981).
Relaxing the IPV assumption by allowing risk-neutral bidders to have affiliated values, Weber (1983)
shows that the competitive auction earns more revenue. However, if risk-neutral bidders in an EPV
framework are not symmetric Ci.e. there are observable differences amongst their valuations), the ranking
is indeterminate (iviaskin and Riley, 1985). If entry decisions are not exogenous, then different auction
rules and formats can affect the set of bidder participants, and yield different expected revenues (e.g.
Hlarstad et al, 1990); however, which types of auctions will revenue-dominate in the presence of multiple
rule changes is not clear-cut. Finally, Robinson (1985) shows that revenue equivalence breaks down in
an WPV auction under bidder collusion. In this case the Dutch auction is revenue-dominant.
The theory has focused on single-unit and one-shot WPV auctions. Engelbrecht-Wiggans (1988)
extends the theory for endogenous quantity decisions, and finds revenue-equivalence for a one-shot, IPV
auction where risk-neutral bidders submit full demand schedules, and each uit goes to the bidder who
values it most. Taking into account that lumpy bids (several units at the same price) are in practice more
usual than full demand schedules, Tenorio (1991) models endogenous quantity choice for a one-shot
auction with risk neutral bidders. Revenue-superiority is mi nt in this model.
Each of these models separately relaxes one or two assumptions of the Vickrey model, so that
it is not clear which result would obtain under the relevant assumptions for foreign exchange auctions.
Further, it is important to note that there is no theoretical result conceming revenue-equivalence in the
repeated multi-unit case. Interpretation of our empirical results on revenueequivalence in Dutch and
competitive auctions will therefore draw on the simnpler models, and consider the relative importance of
the various assumptions for the countries in question.
concept of net revenue accruing to the governmet as a net buyerlseler of foreign exchange (which we wil examine in fhre
work).
I2 Potl disadvantages to Dutch pricing are first, if there is a large spread between bids, this may be constued as
constitutig a multiple exchange rawe systm with the avedant disadvantages (Quirki, 1987); and secondly, a smaller pool of
bidders may ensue becausethe Dutch auction introduces a barrier to entry for risk-aversebidders who are poorly informed about
marketdevelopments (Goldstein, 1962). Theorypredicts that Dutch pricing lessens collusion (Robinson, 1985); but some authors
are of dte view that drough a narrower range of bidders, Dutch pricing may also encourage collusion (Quirck et al, 1987).
- 11 -
Tae second policy hypothesis concerns the volatility of the number of multiple units offered for
sale in sequential auctions. Policy-makers have implicated the volatility of supply in auction failure
through increasing exchange rate instability. Supply to the SSA foreign exchange auctions was largely
due to foreign aid and conmmodity export receipts. Both these components are vulnerable to shocks: aid
may be suddenly withdrawn; while export concentration in primary commodities is very high in SSA,
and is subject to terms of trade swings, drougLhts and other shocks.?3 Arguably, short-term volatility
should be less important for investors than uncertainty about sustained supply in the medium-term. The
perception that supply is unsustainable would damage the credibility of the exchange reform, and induce
speculative activity, manifested in both price and allocation. The price is likely to overshoot a realistic
rate, and the premium rise to reflect incredibility; the use of funds would be skewed towards durable
goods or inventories (Calvo, 1987).'4 There may thus be important implications concerning the role of
donor aid to ensure a sustainable supply in the interim."
If bidders in repeated multi-unit auctions are risk averse, and are confronted with uncetainty in
the form of a supply of units that may be highly volatile from week to week (where supply is pre-
announced, but only after submission of all the sealed bids), theory suggests that this risk aversion will
operate to the seller's advantage (Harris and Raviv, 1981). Maginally increasing the bid increases the
probability of that bid being successful, even if profits are lowered for the bidder. Thus, controlling for
auction type, we will test if increased supply volatility (proxying for increased uncertainty) induces a risk-
premium on the bids, resulting in upward pressure on the equilibrium exchange rate
The third and final policy hypothesis relates to competition in the foreign exchange auctions. On
two of the four countries we examine the auctions were broadened over time, relaxing entry restrictions
to allow more types bidders to participate, and making more items eligible for import with winning bids.
In the other countries, the opposite occurred, inducing perceptions of the incredibility of the exchange
rate reform, and speculative bidding. The reimposition of tighter restrictions in these countries was
apparently in order to stem the more rapid increase in the auction rate (exchange rate depreciation).
We hope to test an auction-theoretic result to show that increasing the number of bidders increases
the revenue on average of the seller (Harris and Raviv, 1981). Obviously the pattern of the increase will
13 Furthermore, supply could be well .elow export eanings siuce actionable funds were frequenly decided after satisfyg
the requirements of die government and public enterprss outside the auction. For insance, auctionable fends as a proportion
of total inflows for Zambia and Uganda in the 1980s were estimatd to be as low as 25 per ceat (Quirck ct al, 1987).
14 There is evidence linking such speculative consequencerwith Iow credility in Ihe Zambanauction (Aron and Ebadawi,
1992; Bates and Collier, 1992).
'5 It is possible that these auctions experienced official intervention through supply manipulaion to prevent exchange rate
depreciation, or atain odter objectives. This does not prove a problem for our estimations in section 4, becauseempirical models
with constant parameterizations despite structnal change (Table 2) exhibit super exogeaeity, which implies weak exogeneity,
diereby sustaining valid staistical infrrence (see Gilbert, 1936). However, our future research will examine more closely the
potmtial presence of supply policy and other implicit rules.
- 12 -
depend on the type of auction, the characteristics of the auctioned object, and firm and industry
characteristics (Branmman et al, 1987). Some auction models have clear predictions for the relationship
between winning bids and the number of bidders. It may be less predictable for other types of auctions,
particularly under risk-aversion, correlated values and uncertainty concerning the value of the auctioned
object
3. DATA AND EMPICAL MEHODOLOGY.
There has been very little empirical work on foreign exchange auctions in Sub-Saharan Africa.
Apart from policy-based surveys (e.g. Krumm, 1985; Quirck et al, 1987; Roberts, 1989), only the
Zambian auctions appear to have been studied in any detail (e.g. Tenorio, 1993; Bates and Collier, 1993;
Aron and Elbadawi, 1992). To the best of our knowledge, the only micro-economic research on the SSA
auctions motivated by auction theory is due to Tenorio (1993), who tested for the revenue-equivalence
of the two types of auctiont which appeared consecutively in the eighteen month Zambian experiment. In
general, there have been no controlled experiments on foreign exchange auctions using generated data,
nor have the dynamic feaures of repeated auctions been studied.
Yet, there is enormous scope for research on foreign exchange auctions in SSA, both in
comparative time-series and cross-sectional panel data studies. The SSA case-studies present a wide
spectrum of auction designs and outcomes for cross-country comparisons. In a number of countries,
different auction types follow consecutively, allowing within-country comparisons of auction design. For
a few countries the data set includes detailed individual bidder data for each auction; this allows an
analysis of allocation, of dynamic features such as learning and strategic behavior across auctions, and
the determination of the distribution of actual bidder values. Finally, weekly parallel data is available for
most of the countries, so that the progress of unification can be followed throughout the transitional
auction phase.
A description of our data set is contained in Aron and Elbadawi (1994). The paper discusses
design characteristics for the Zambian, Ugandan, Ghanaian and Nigerian auctions, which are summarized
in its Table 1. In Table 2 of that paper, basic statistics are given for the auction data, according to auction
regimes, and ihese statistics, as well as a number of measures of nor-normality of the data (skewness and
kurtosis), are discussed in detail.
3.1t Cointegation Modelling in Repeated, Sequential Auctions
The analysis of the individual time series properties of the auction markets' pivotal variables, such
as the level and variance of the selling price (exchange rate), the black market premium, and the
demand/supply of foreign exchange, shows that the time series structures of these high frequency
- 13 -
variables are non-stationary (i.e. with infinite variances at the limit)1' and are dominated by structural
breaks and regime shifts (see Aron and Elbadawi, 1994). This finding has important implications in its
own right; for example, shocks to the auction variables tend to have high persistence. However, non-
stationarity has profound effects on the econometric modelling and estimation of the behavioral theoretical
specification suggested by auction theory (see section 2.1 above). When all or some of the variables
involved in an econometrically estimable relationship, such as the one suggested for the auction rate, are
non-stationary, it is important to guard against spurious regressions (Granger and Newbold, 1974).
However, the equilibrium relationship between a number of non-stationary variables can be expressed in
a stationary model if a linear combination of these variables can be found to be stationary (termed a
cointegrating vector)."' The Granger-Engle Representation theorem (Engle and Granger, 1987) staes
that if series are cointegrated they can be consistently represented by an error correction mechanism
(ECM), which captures the short-run dynamics of adjustment towards a long-run equilibrium relationship.
The attractiveness of this approach for our work is that we can model the weekly dynamics in repeated
auctions with non-stationary auction variables, and follow the adjustnent to unified markets in the long-
run.
Therefore, to be able to ascribe any behavioural interpretations to the estimated economic
relationship, it is important to test for cointegration in the regression specification, in addition to the
preliminary stationarity tests on individual variables. However, a challenge is presented here in a
common phenomenon in SSA countries of frequent, and often drastic, structural breaks in the series.
Recent work has shown that tests that do not account for structural breaks may erroneously find non-
stationarity (e.g. Perron, 1989; Hendry and Ericsson, 1993). Perron (1989) assumes the timing of the
regime shifts to be known, while the others cited above offer tests of a unit root that also determine the
t Formadly, let Yt TD, + Z, be an economic series composed of a deterministic trend TD, and a stochastic component
For simplicity assme that Z, can be described by an autoregressive-nmong avenge process:
A(L)ZA = B(L) e, where A(L) and B(L) are polynomials in the lag operator L and ; is a sequence of i.id. imnovations. The
noise function Z is assumed to have mean zero, the moving average polynomial is also assumed to have roots strictly outside
the unit circle. Then 7Z has a unit root if A(L) has one unit rot and all other roots stricdly outside the unit circle. In this case
(1-L)Z, = AZ: is a stationary process and (1-L)y, = Ayt is stadionary around a fixed mean. If on the otter hand A(L) has all
its roots outside the unit circle, then Z1 is a stationary process and y, is stationry around a trend.
17 The idea of cointegration basically states t even tough individual series may have a urdt root, there may exist various
linear combinations of variables which are stadonary. Stated more formally in die context of the definition of the above
footnote, let the n-vector y, be copsed of (y,, ... y,j, where yi is defined as in e footnoe above. Then y, is said to be
cointegrated if there exists at least one n-element vector 6 such that ,B'y, is trend satdonary. This is a milder definion of
cointegration (Campbell and Perron. 1991), which is more suited to analysis of economic data since it permits the inclusion of
deterninistic components (such as trends and structural break dummies) in the cointegrtion npodel along with other non-
stationary stochastic variables.
- 14-
timing of the structural breaks. In our case, since we have precise information about the structural breaks,
we opted for using Perron methodology, given its simplicity.t"
Figure 1 shows fitted trends with one-shot intercept and/or slope changes for at least two clearly
identified regimes in the auction exchange rate series for the cases of Zambia, Uganda, and Nigeria.
Three distinct regimes can be identified for Ghana. The results of the tests, and the models of structural
breaks corresponding to the fitted trends, are shown in Table 1, together with the critical values
employed. The table reveals the presence of considerable non-stationarity and regime- shifts for most of
the auction data from the four countries even when structural breaks were taken into account. This is
unsurprising in view of the stylised facts which emphasise rule changes, the non-normality of auction data
and the importance of anticipations of policy changes.
Besides generating consistent estimates of the economic parameters implied by a model
specification such as in section 2.1, the other main objective of our econometric methodology is to test
some policy propositions suggested by auction theory (see section 2.2). This requires that the equilibrium
model should be esimated asmptotically efficiently. Cointegration readily guarantees consistent (in fact
super-consistent) estimation for the eqailibrium parameters using a simple OLS regression (see Engle and
Granger, 1987)." Unfortunately, the simple cointegration regression usually produces substantially
inefficient asymptotic estimators (Phillips and Loretan, 1991). Given our interest in generating
asymptotically efficient pointwise estmators with smaller margins of errors around the true equilibrium
parameters, the direct cointegration estimation will not be adequate for the problem at hand. Phillips and
Loretan propose a modified ECM that can be used to obtain asymptotically efficient estimation of long-
run equaiibria in models with stochastic trends. Subscribing to the above empirical paradigm, we will
model the dynamic behavior of the auction variables with a single-equation error correction model
(ECM), with leads and lags in the differences of the regressors, and which includes structural break
dummy variables. This type of model will be estimated by non-linear OLS, and is recommended by
Phillips and Loretan (1991) for hypothesis testing. The form of the modified one-step ECM regression
equation is as follows:
IPedron (1989) computed critical values for a Dickey-Fuler and Augmented Dickey-Fuller tests that include two types of
stwuctual breaks: one causing a shift in the intercept, and dt other a change in the slope. A key assumption of the Perron est
is dtat these shocks are exogenous and are not a ralization of the underlying data generating mecham. Furtbermore, his test
requires hat the fiming of the shocks be known. In our ae both of these two conditions apply (Aron and Elbadawi, 1994, Table
1).
19 The justification for cointgrtion give. the short span of high frequency (weekly) data may be somewhat problematic:
ideally the requirment for non-stationarity tests to be valid is both long time saies data and high frequecy darN. However,
the span of our data is comparable with that commonly analysed in stock market and foreign exchange settings (e.g. Froot and
Obstfeld, 1991 and references cited therein).
20 Phillips and Lretan (1991) evaluatevarious empirical methods for esimating co-integting relationships, and show that
single equation ECM models are efficient asymptotic estimators of long-run equilibrium relationships when formulated non-
inearly dtough the explicit inclusion of lagged equilibria, and incorpoatig leads and lags of differenced regressors.
- 15 -
K
Aoert = Sy(f(F) - oer)ti +r Xi AF ..
(5)
fiF 4 gti +%v
i-D
where, iq is a stationary disturbance term, A is the difference operator, and f(F) is the log-linearized
specification of equation (4) above, giving the determinants of the auction clearing rate.
4. ESTIMATION AND HYPOTESIS TESTING.
This section estimates model (5) above for the micro-deteminants of the auction rate. After a
discussion of model diagnostics, and ascertaling that the model is broadly corroborated by data from the
four countries, three hypotheses motivated by auction theory which -have policy implications, will be
tested. The testing will involve the revenue equivalence and competitiveness hypotheses, and also
whether increased uncertainty (proxied by supply volatility) induces a risk premium on bids.
4.1 Evaluating the static and dynamic features of the estimations.
Given the characteristics of auction data (non-stationarity and regime shifts) and the repeated,
sequential nature of foreign exchange auctions in SSA, we argued in section 3 on the empirical
methodology for an ECM estimating framework. The ECM framework accounts for the dynamics in
weekly repeated auctions, while permitting estimation of the adjustment path towards a unified
equilibrium rate in the long-run. Furthermore, the expanded non-linear version of the ECM suggested
by Phillips and Loretan (op. cit), which we will employ here, provides asymptotically efficient estimators
for the parameters of equation (5), suitable for hypothesis testing. The empirical model is stated below.
21' '
19ogoe), = ,Y[ a + + aO log0(QSl + a2 1og9Q4d), + a3 1og(bidty +a4 MAV (Alog(qsA)_
+ a5log(ber),_, + i0 DUMDutch + 61 Di + &2 D2 + 6, D3 - log oer1,]
1 For ethositonal ournose only, the ECM is presented in a restricted form (two rror terms, one lead and two lags), but
in the estimation more general lag/lead struchtres were considered. For a fill exposition of the form and properties of the non-
linear single equation ECM enployed here, see Phillips and Loritan (op. cit.).
-16 -
+ 72 ( a0 + at Iog(Qs),2 + a2log(Qd)X.2 + a,logbidt),2 + a. MAV (Alog(qs)),.2
+ ac4ogber),., + be DUMDutch + 6O Dl + & DZ + 6, D3 - log oen.J
+ J1alog(Qu)1 + 82aIog(Qs), + P3aog(Qs).2 + P410g(QS),+l
+ P1Alog(Qd), + js&log(Qd),fr + 37Alog(Qd)..2 + 9,alog(Qd),
+ falog(ber), + ,1Oalog(ber), + fi,Alog(ber)l2 + Pf12eIog(ber),"+
+ fl13Alog(bidt), + fj44&og(bidt),1. + fi,51Log(bidt),.2 + Pj6alog(bidt),+1 (6)
The variables are as defined in equation (5) above, where oer is the auction rate; Q, and q
are, respectively, actual foreign exchange supplied and total foreign exchange demanded&% bidt is
number of total bids?"; ber is the bureaux or the parallel market exchange rate (the opportunity cost of
holding foreign exhange); MAV(6log qs) is the moving average of the monthly variance (t3, t2, t4, t)
of the rate of change in foreign exchange supply, reflecting supply variability?' DUMDutch is a
dummy for the Dutch auction, and DI, D2 and D3 stand for regime shift dummies (defined in section
4.1). The first two bracketed terms give the first and second lagged equilibrium error (the long-run
coefficients are the same). The remaining differenced lagged and lead terms represent the transitory
dynamic effects on the auction rate. The equilibrium error represent the dynamic effects on the current
auction rate of previous periods' departures from equilibrium. For example for a lagged positive
equilibrium error (i.e a more depreciated equilibrium rate than the acmal in the previous period), the
fundamentals will call for an auction rate increase (depreciation) in the current period.
We employed general-to-specific modelling (e.g. see Gilbert, 1986) when estimating the non-
linear empirical equation, and the results for the four countries are shown in Table 2. The results broadly
corroborate the predictions of the theory, in that long-run (static) determinants of the auction rate have
theoretically consistent and statistically significant effects. The data lend strong support to the ECM,
2 It is possible dtht the quantiy demanded is collinear with the number of bids, and where 2here is leaning thrugh the use
of a reserve price or pre-anonced supply, also the quantity supplied. Under non-stationarity and co-integration, however, these
foms of endogeneity should not constitute a problem for consistent OLS estimation of the paraneters of inerest, given the
super-consistency of the OLS estimator (section 3.1).
= A positive relationship is indicated by auction theory between the number of bidders and die auction rate (Branaman a
a1, 1987). Given that these are integrated price and quantity bids, total demand mnay be a better demand indicator than the.
number of bids (renorio. 1993).
2 Variance is not defined for non-statonary variables. Given the departure from normality (skewness and excess kurwsis)
found to characteriz auction data (Aron and Elbadawi (1994), skewness and excess kurtosis measures were included in our
general equations, as finther proxies for foreign exchange supply uncertinty (these were not found to be significant).
- 17 -
where the equilibrium error term in all equations is highly significant, positive and less than one.
Further, the estimates also show substantial influence on the short-run evolution of the auction rate of
transitory changes in auction fundamentals. Also other diagnostic indicators show that the estimated
models are statistically correct (e.g. in the sense of Hendry - see Gilbert (1986)),5 hence they can be
used to test economic propositions. Before considering some theoretical hypotheses we turn to the brief
description of the estimates on the effect due to the basic determinants (Qs, Qd, ber).
Table 2 contains two equations for each country. In addition to the variables estimated in
equation 1, the second equation also considers foreign exchange supply variability. The coefficient of
the error-correction term in the Nigeria equation is the highest at about 0.6 and is highly significant. The
error-correction effects for the other three countries are also statistically significant, but their numerical
values are much smaller: 0.08 for Zambia, 0.07 for Uganda and 0.02 for Ghana. This implies that
adjustment towards equilibrium was relatively fast in Nigeria and rather slow for the others, especially
Ghana. To eliminate 90% of an exogenous shock to the auction rate through automatic adjustment
alone,2' it takes only 4 weeks in Nigeria, compared to 26 for Zambia, 30 for Uganda and 120 for
Ghana. This result agrees very closelyw ith a Cochrane (1988) type analysis of persistence on the auction
rate series (see Aron and Elbadawi, 1994). This analysis showed that the share of the random walk
component in the total variance of the rate of change in the auction rate, while large for all four
countries, is noticeably smaller for Nigeria, and to some extent, Zambia. The rate of convergence also
started rather more rapidly in these two countries. This finding is consistent with the use of a stochastic
reserve pricer in Ghana and Uganda, as opposed to the frequent and direct policy interventions that
characterized the Zambian, and especially the Nigerian auctions (Figure 1).
We now consider the parameter estimates of the long-run economic equilibrium or cointegrated
relationship. Foreign exchange supply and demand are two conventional determinants of the auction rate,
that are robustly estimnated to have theoretically consistent signs: a sustainable increase in supply
(demand) should reduce (increase) the equilibrium auction rate. The estimated coefficients are highly
25 Stabiity tests (Chow tests) found parameter stability for Zambia, Nigeria and Uganda (rabic 2). The Ghana equation
marginaily failed the F test (at the I per cent level), suggesting that the relatonship modelled altered over the sample period.
This resultwas unsurprsing given the length of the data seiies (270 auctions over six years), and reinforces the authors' opinion
that the retail and wholesale auctions should be umdefled separately in ftiure research. The stability results are further reinforced
by the comparative namre of the analysis, in that similar parameter estinates were obtained for the four countries. Note hat
parameter stability implies super exogcncity, itself implying weak exogencity, necessary for valid statistical infermnce More
formally, out-of-smple forecast properties should be exanined well. However, the prevalence of structural regime shifts in these
high frequency data makes forecasting very problematic.
M6 The number of weeks to clear 100% of an exogenous shock through automatic adjustnent alone can be computed from
die formula: (1 - a) = (1 - -y)T, where -y is the coefficient of the equilibrium error term and T is the number of weeks. This
formula can be obtained by manipulating the error-correction specification in (3).
2 The reserve prices closely fallow the evolution of the bureaux or parallel rates in Ghana and Uganda which are shown
to be 1(1) series (Table 1).
- 18 -
significant for the case Ghana and Uganda. but only moderately so in the other two cases (at about 10
percent significance level).23 Another conventional effect is the opportunity cost of foreign exchange,
proxied here by the bureaux (or parallel market) rate. Aside from its role as an opportunity cost, in the
context of fbreign exchange auctions in SSA, the black /bureaux rate is a relevant indication of macro-
economic policy and credibility, and is closely linked to macro indicators such as money supply growth
and inflation (Aron & Elbadawi, 1993). In all of the four countries this variable has a highly significant
and positive estimated coefficient. The estimated elasticity is quite high in Ghana (0.7) and Zambia
(0.76), compared to the rather moderate effects estimated for Nigeria (0.21) and Uganda (0.28). One
possible explanation for this dichotomy is the degree of competitiveness in these two sets of auctions.
In Ghana (for 174/270 auctions) and Zambia, the bidders are a large number of importers; while in the
other two countries there are a limited number of banks bidding (even though the Ugandan auction is
indirectly a retail auction). Arguably in the first case the bureaux/parallel rate is an important signal, and
collusion plays no major role; hence the appreciable coefficient estimated for the black/bureaux effect.2'
Three further potential determinants of the long-run aucLion rate are: auction type (Dutch pricing
vs. competitive), the number of bids and foreign exchange supply variability. The effects due to these
three variables provide the pretext for testing three hypotheses motivated by auction theory, with
important policy implications. The Dutch auction (coefficient of DUMDutch) is found to have had
significant effects in both of Nigeria and Zambia, albeit with different signs. As predicted by theory the
number of bids has a positive elasticity (Nigerian equation)-confirming that increased competition leads
to an auction rate depreciation. Finally supply variability was not found to be relevant to the
determination of the auction rate. The interpretation of these results and discussions of the hypotheses
are provided in the following sub-section.
A number of dummies relating to rules affecting bidder participation were found to be significant.
For Nigeria two auction policy interventions are estimated to have effected a structural shift in the long-
run auction rate- In auctions 22 and 23, after an announcement concerning tightened entry restrictions,
major disqualifications of bids occurred (D2); and in auctions 60-65 various banks were barred from
participating in the auctions for the same reason; also tighter ceilings on allowable foreign exchange
purchases were introduced (D3). As expected the direct effects of these interventions should be to reduce
competition, but perhaps more importantly the credibility of the auction regime itself may have been
adversely affected as a result. Further, it is likely that adjustment had taken place already in the auction
rate prior to the time the pre-announced measure was effected. Hence it is not surprising to find highly
significant and positive effects for both of D2 and D3. In Zambia. auction 41 saw the institution of
31 Given the extent of policy intervention and disqualifications in Nigeria and Ziambia, it is likely that the auctions exhibit
rather significant departures from the competitive model.
39 Thus the hypothesis of homogeneity can be accepted for Ghana and Zambia (i.e. a change in the units of measurement
of the exchange rate will not affect the long-run solution).
_ 19 _
stringent documentation requirements, and heavy disqualifications occurred in that week, captured by
dummy D2: the reduced demand saw a sharp fall in the auction rate. Another policy intervention causing
a structural shift in the long-run rate was estimated for Uganda. Starting from auction 21, the
disbursement of foreign exchange was changed to cash basis rather than a guarantee basis. This change
improved the efficiency of the auction by reducing transaction costs and hence encouraged participation
(by drawing agents who would otherwise may prefer to purchase foreign exchange at the more expensive
but efficient bureaux de change).30
Finally, we briefly review the evidence on the short-mn influences on the auction rate.3" In all
of the four regressions, the bureaux (parallel) rate has a significant and positive impact elasticity, in
agreement with their estimated long-run effects.? In Nigeria, Zambia and Ghana, foreign exchange
supply (and demand) have (net) negative (positive) short-run impact elasticities, again consistent withi their
long-run effects. In Uganda the short-run effects of these two variables are estimated significantly, but
with opposite signs to their corresponding long-mn elasticities. Also, surprisingly, in the Nigerian
regression, an expected increase in the number of bidders (Alog(bidtQj1) was estimated to have a negative
effect on the current auction rate.
However, a possible explanation for the expected foreign exchange supply increase in Uganda,
Ghana and Nigeria, and the rise in the expeced number of biddes in Nigeria, and the expected foreign
exchange demand in Ghana, may be due to a reverse causality between these variables and the rate of
depreciation in the auction rate Ceft-hand side variable). Tnus, current depreciation by increasing the cost
of bids may have reduced the expected number of bids in Nigeria; with regard to foreign exchange
supply, the authorities may be responding to current auction rate depreciation by increasing future foreign
exchange supply to accommodate the liberalisation of entry restrictions; finally, decreased future demand
by bidders may follow for the same reason as for the case of the number of bids.
4.2 Testing policy hypotheses.
Three policy hypotheses motivated by auction theory were introduced in section 2-2 The first
policy hypothesis is the revenue equivalence hypothesis, which could be tested for Nigeria and Zambia,
since competitive and Dutch auction regimes follow consecutively in each case (Figure 1). The equations
are shown in Table 2, where the short-run dynamics of the repeated auctions are modelled, and
perceptions of changes in reform credibility are captured by including the black market rate as regressor.
3 Effors to capqe the effects of progressive phases of import liberalsauon and decreased mry requirements in Ghana
using dummies did not prove successfil, due to singularity of the datt
"It is important to note that the Phillips and Loritan (1991) methodology is concerned with efficient estimation and
hypodLesis testing in lone-run econoniic equilibria short-run dynamics may not be readily intepretable.
"Expected depreciation in the bureax (parallel) raze (logberl.1) was estimated to have a negative inpact effect of the
current auction rate. The overall net short-un effect of dte bureaux rate is still positive, however.
-20 -
We include in f (F) in the ECM model (5) of Section 4. 1, a dummy variable which captures the change
in auction regime CDUMdutch is equal to 0 for the competitive auctions and to I for the discriminatory
auctions). Referring to the empirical specification, the null hypothesis for revenue equivalence is then
Hn 6: = 0 in the long-run equilibrium term of the empirical specification (equation (6)).f The test
compares the average level of the clearing price of a series of competitive auctions with the average
clearing price of a set of discriminatory auctions. If revenue equivalence holds, the dummy variable
indicating the change of regime is not expected to be significant. If the dummy is significant and positive
this indicates that the Dutch auction is revenue-superior. If the dummy is significant and negative this
indicates that the competitive auction is revenue-superior. We consider that this method of testing for
revenue equivalence improves on an earlier analysis of this question for the foreign exchange auction in
Za:mbia.'
As discussed in section 4.1, the DUMdutch dummies are significant for both Zambiae and
Nigeria, indicating that revenue-equivalence does not obtain in these repeated, multi-unit auctions. For
Nigeria, the Dutch auction is revenue-superior, while in Zambia, the competitive auction dominates.
There are no theoretical results for revenue equivalence in repeated, multi-unit auctions. The important
result here is that a dynamic empirical framework for repeated multi-unit auctions in two different
countries found departures from revenue equivalence depending on the relevance of underlying
assumptions on bidder valuations, risk-aversion and competitiveness. The theory (section 2.2) suggests
that affiliation of bidders' values may explain the results in Zambia: bids were published for most of the
auction, and this public information would have figured in bidders' exchange rate forecasts. For Nigeria's
wholesale auction, controlling for the number of bids and rules affecting bidder participation, it appears
that collusive behaviour by the small number of banks, largely state-owned, could explain the result of
Dutch-dominance. High risk-aversion is not a convincing explanation for the Nigerian result, since banks
were guaranteed a minimum allocation. On the strength of these two results, there appears to be no clear-
33 It is important to note that we are not testing for equivalence of the average change in die exchange rate across
regimes: the left-hand variable in the long-run equation is the level of the equilibrium auction rate.
Te first-ever test of the (weak) revenue equivalencehypodtis employing acual auction dat from a repeated mulli-mt
auction is found in Tenorio (1993). He regresses the level of the auction-determined rate in Zambia on autoregssive terms in
the dependent variable, a trend term to capture any non-statonarity, controls for the supply and demand variables, and includes
an auction dumMny term, which equals O during the conmettive auction and I for the Dutch auction. However, the dynanics
in this analysis are very restrictive, including lags of the dependent variable, but without good reason excluding a nori all
lagged fundamentals. The non-stationarity of the regressors was not tested for, and a general time tend was employed to capture
non-stationarities. This is unnecessarily restrictive since the bubbles and expectational responses implied by normality and
stationarity tests are extremely unlikely to follow an infiniite linear trend. The persistence in the rate is shcOwn by huge
coefficients for the lagged rate. with all other variables insignificant save the trend and dummies.
5 Note that the same result (with a different magnitude of the coefficient) was achieved by Tenoio (1993) for Zambia.
though in the context of poorly deternmned equations (see earlier footnote).
-21 -
cut policy advantage in use of a Dutch auction to stem the pace of devaluation across repeated foreign
exchange auctions.
Note that this test for revenue equivalence can be expressed in a stronger form, by including an
interactive dummy between the number of bidders and the dummy variable for the auction method
(Hansen, 1986). In this case, the null hypothesis to accept revenue equivalence implies that the
coefficients on the interactive term and the separate auction format dummy term must be jointly zero.
This test takes into account the fact that bidder participation may be higher under different auction
formats (for instance, entry may be limited under a Dutch auction where bidding strategies are more
complex - see Goldstein (1962) in the U.S.A. Treasury Bill debates). Unfortunately this test was not
possible in the Zambian case due to the definition of bids.6 For the case of Nigeria, an F test for the
joint significance of the two dummy terms was F (2,47) = 2.983, thus still rejecting revenue equivalence
(at a 10 per cent level) in favour of Dutch revenue dominance.37
The second policy hypothesis is concerned with the effect of increased volatility of the number
of multiple units offered for sale in sequential auctions on the level of the auction rate. The hypothesis
that we test, controlling for auction type, is that periods of increased supply volatility induce a risk-
premium on the bids for risk averse bidders, resulting in upward pressure on the equilibrium exchange
rate. This hypothesis could be tested for all four countries. The Zambian, Ghanaian and Ugandan auctions
all showed a considerable degree of supply volatility (with supply not known to bidders until after the
bids were submitted) for all or part of the auction regime (Aron and Elbadawi, 1994). In Nigeria,
volatility was less pronounced since actual supply coincided with a fairly constant offered supply (Aron
and Elbadawi, 1994: Table 1). The results are shown in Table 2. In a second equation for each country,
we include in f(F) in the ECM model (5) of Section 4.1, an additional explanatory variable, the moving
average of the monthly variance of the differenced supply (which is stationary). Referring to the empirical
specification, the null hypohesis is -then H.: a 0 in the long-mn equilibrium term of the empirical
specification (equation (6)).
For all four countries supply volatility did not prove significant. Assuming risk averse bidders,
this result might be explained for the cases of Ghana and Uganda, by the use of an (unannounced) reserve
pricing rule which appeared to have been learned by bidders3. In this case, the uncertainty induced by
361 In Zambia, the number of bidders does not equal the published number of bids. This is because for reasons of trade and
exchange control. the publishod bids:were dissagregatedby usae of tbreign exchange: thus each bidder's single bid was reported
as components constained to be at die same price. It is not possible to aggregate the bids and detemnine the number of bidders
for the whole of the auction because they were only published individually for auctions 37-68. 'This unfortunatly invalidates
the attempt in Tenorio (1993) to establish "strong revenue equivalence", using an interaction dummy composed of the number
of "bidden" and the regine change.
37 Tle Dutch dummy becomes more positive, with somewhat reduced significance; the inteactive term is insignificant
3' In principle, tde presence of learning can be tested for (e.g. Doninguez. 1991). and this is a fruitful a for further
research.
22 -
supply volatility would not induce a risk premium on the bids. Alternatively, bidders may have been risk
neutral. This latter explanation probably applies for Zambia, and supports the conclusion reached on the
basis of the revenue equivalence result. For Nigeria, supply was pre-announced for all or part of the
auctions, in which case it was fairly stable relative to the variability of the auction rate. Preliminary
regressions (not reported here) suggest that supply volatility is an important determinant of exchange rate
voJatility, This would be a fruitful area for further research, with the implication that foreign aid may
have an important ameliorating effect on supply volatility induced by temporary terms of trade shocks.
The final testable hypothesis with policy implications concerns competitiveness in auctions. We
consider the following hypothesis: the level of the exchange rate rises with expansion of the auction
through expanding the number of eligible bidders/items. We test this hypothesis by including the number
of bids in f (F) in the I9CM model (5) of Section 4.1. The null hypothesis is H: as = 0 in the empirical
specification of the long-run equilibrium term (equation (6))." Unfortunately we were only able to test
this hypothesis for Nigeria. The reason is that in Ghana, total bid data is only available for the retail
auction; in Uganda, bid data refers to aggregated bids submitted by banks; in Zambia, total bids include
multiple bids at the same price by individual importers, differentiated by the use of foreign exchange. The
results for Nigeria show a significant and positive effect for the number of bids, showing that in the long-
run there is evidence for the theoretically-predicted competitiveness effect in a multi-unit repeated auction.
It is important to note that this result obtains with the model controlling for policy interventions and the
consequent structural shifts which characterised the Nigerian auction.
5. CONCLUSIONS.
This paper has estimated models for the micro-determinants of the auction rate using weekly
foreign exchange auction data from four Sub-Saharan African countries, Zambia, Uganda, Ghana and
Nigeria. A simple underlying model synthesized from auction theoretical literature specifies the auction
rate as a linear logarithmic function of fundamental variables and structural shift dummies. It was not
possible to produce a structural model, as currently there is no available theoretical model in the literature
for repeated sequential multi-unit auctions of this type. However, the repeated, sequential nature of these
auctions and the non-stationarity of most of the individual auction variables was captured empirically by
a cointegrated (error correction) framework. Even though this model does not allow a structural
interpretation of the auction rate determinants, it permits estimation of the long-run path of the auction
"9 Cointegration has one distinct advantage when measuring the effect of competition on bid levels. Hansen (1985) points
out that with a positive reserve price, the theoretically relevant variable for the number of bidders is not the actual number of
bidders, but the umneasurable Potential number of bidders. Giley and Karcls (1981) have c-rrected for dtis tuncated error
problem by the Heckman procedure, including a dichotomous bidding decision: bid/do noi bid. However, in the context of
cointegration. the variables involved are 1(1), and the estimators wil be consistent whether or not the bidding decision dummy
variable is included.
-23 -
rate in addition to accounting for short-run dynamic behaviour. In addition to consistently estimating long-
run and parameters of auction fundamentals, a modified version of the error correction model (a la
Phillips and Loritan, 1991) allows asymptotically efficient testing of three policy hypotheses motivated
by auction theory. These are the revenue equivalence hypothesis, the competitiveness hypothesis and the
effect of uncertainty on the auction-determined rate.
5.1 Summary of results.
The variables for which theoretically predicted effects could be assigned a priori are foreign
exchange supply, demand, and the opportnity cost (parallel or bureaux exchange rate). The empirical
results strongly corroborate the theoretical predictions in that sustained increased foreign exchange supply
(demand) leads to an equilibrium auction rate appreciation (depreciation). Also, the parallel/bureaux rate
was positive and strongly significant, representing an opportunity cost to bidders, but also signalling
incredibility of macro-economic policy (see also Aron and Elbadawi, 1994). The model also lends strong
support to the error correction framework, where the curient a&kction rate is shown to adjust to previous
departures from equilibrium, while transitory movements in the fundamentals influenced the auction rate
in the short-run. Finally, dummy variables representing policy interventions in Nigeria, Uganda and
zambia were found to effect struucural shifts in the long-run auction rate.
The revenue equivalence hypothesis was tested for Nigeria and Zambia, where episodes of
competitive and Dutch auctions followed consecutively. In both cases evidence was found against the
revenue-equivalence hypothesis, with the Dutch auction (strongly) revenue-superior in Nigeria, and the
competitive auction (weakly) dominating in Zambia. The interpretation of this result, however, is not
straightforward, given that there is no theoretical result for repeated, multi-unit auctions. Theoretical
models for more restricted auctions suggest several reasons for the result of non-equivalence (section 2.2).
A possible explanation for revenue-superiority of the competitive auction is that bidders' private values
are correlated, with risk-neutral and symmetric bidders (Weber, 1983). This result seems plausible for
Zambia, given that the bids were published weekly for most of the auctions. A feasible explanation for
Dutch-dominance in the wholesale auction in Nigeria is collusive behaviour by a small number of
predominandy state-owned and risk-neutral banks (Robinson, 1985). To the extent that these results are
robust, this implies that no revenue advantage can be assigned a priori to a repeated, multi-unit auction,
irrespective of the underlying valuation characteristics of bidders. Apart from the static analysis of
Tenorio (1993), this hypothesis has not been tested for repeated multi-unit auctions using actual auction
data.
The impact of supply volatility (a proxy for uncertainty) on the level of the auction rate in
repeated auctions was tested for all four countries, controlling for auction type, but was not found to
produce a risk-preniium on the auction-determined rate in any country. In Ghana and Uganda, the use
of a reserve price served to stem downward volatility in thin markets, or where disqualification for failing
to abide by documentation requirements reduced demand. Moreover, although the rule was not pre-
- 24-
announced, it was fairly transparent to bidders, so that despite the higher supply volatility in Ghana and
Uganda relative to the other two countries, the exchange rate prescribed a fairly stable path. An
alternative explanation is that bidders were risk neutral in these auctions. This result may apply for
Zambia (where no binding reserve price was used), and accords with the conclusions above on revenue
equivalence. On the contrary, for Nigeria, supply volatility was too litnited to have the expected effect
because foreign exchange supply was used as target variable to stabilise the exchange rate (without
success). However, these results should not be taken to imply that supply volatility did not matter in these
auctions: in preliminary regressions (not reported here) we found supply volatility to be an important
determinant of exchange rate volatility. This would be a useful area for further research, with the
implication that foreign aid may ameliorate supply volatility induced by temporary terms of trade shocks.
The role of competitiveness effects in auctions could only be tested for Nigeria. Our results show
that controlling for policy intervention and consequent structural shifts which characterised the Nigerian
auction, an increased number of bidders lead to equilibrium auction rate depreciation in repeated, multi-
unit auctions. This prediction from auction theory for more restricted auctions, has been found to hold
in other types of one-shot, multi-unit auctions (McAffee and McMillan, 1987). However, this is the first
corroboration of the theory for a repeated, multi-unit auction.
5.2 Poicy lessons.
In broad. summary, these empirical results corroborate the distinction between two sets of
countries in terms of design features, auction policies and outcomes.4 Ghana and Uganda represent a
set where auctions have been largely on target in terms of the ree policy objectives of exchange rate
unification, stabilisation of the exchange rate and an efficient allocation of foreign exchange. On the other
hand, the auctions in Zambia and Nigeria were subject to frequent policy interventions, with the
consequence of unsustainable auctions, inefficient allocation through ad hoc disqualifications (at least in
Zambia), limited unification, and a rather volatile exchange rate. A number of policy lessons for
exchange rate reform in SSA can be distilled from these results.
First, in large measure, the failure to achieve exchange rate unification and a stable exchange rate
in Zambia and Nigeria can be attributed to the absence of a reserve price rule. Our results suggest that
use of a fairly predictable reserve price stabilises foreign exchange auctions, given the limited depth of
SSA financial markets. The rule is learned by bidders, and diminishes speculative bidding."
a Furhermore, othe disftibutional analysis in acompanionpaper (Aron and Elbadawi, 1994) also ueda clear distinction
between the two sets of countries. For example, the distribution of the auction rate exhibits left skewness (tendency towards
appreciadon) in Nigeria and Zambia- while the opposite was observed for Ghana and Uganda.
"In principle, a pre-announced and stable supply policy rule could achieve a similar stbilising effecL However, we have
shown that in practice the endemic potential variability of foreign exchange earnings (excluding aid) in SSA, makes it difficult
for an auctioneer to guarantee credibly a stable supply in the medium-run. Furiernore. a supply rule does not achieve the close
- 25 -
Second, the management of a sustainable and credible reserve price policy requires an efficient
secondary market. The use of legalised bureaux markets in Uganda and Ghana had two advantages in this
respect: they are likely to be deeper markets, and moreover eliminate the risk-premium associated with
illegality. Macro-economic policy remains crucial to the success of the reserve pricing policy (Aron and
Elbadawi, 1994). A stable and consistent macro-economic environment, permitted the development of
a stable and steadily depreciating bureaux rate in Ghana and Uganda, while the highly volatile illegal
parallel rate was not suitable as a guide for policy in Zambia and Nigeria.
Thire, auction rate depreciation as a consequence of increased liberalisation and hencecompetition
in the auctions, is consistent with fundamental market behaviour, and as such stabilises the auction and
fosters long-term unification. This has been the experience of Ghana and Uganda. In contrast Nigeria and
Zambia attempted to stem depreciation through increased entry restrictions (and ad hoc disqualifications)
over time: these policies back-fired and merely increased damaging speculative behaviour. Given the
initial conditions of thin and rather rudimentary financial markets in SSA, there may be advantages from
a more gradual liberalization for allowing institution-building and lea-ning by agents in the market -
bidders, bureaux, commercial banks, and the auction managers (Aron and Elbadawi, 1994). Gradualism
may also be justified from a macro-perspective, given the substantial macro-imbalances and the low
credibility that often characterise initial conditions in reforming SSA countries.
Fourth, choosing Dutch over competitive pricing does not provide an automatic revenue
advantage, though it may where there are a small number of bidders engaging in strategic behaviour, or
where risk-aversion is paramount. However, the Dutch auctiDon may introduce other undesirable features
such as a reduced pool of bidders and inefficiences associated with a multiple rate system.
Fifth, while supply volatflity - with supply announced only just before opening the sealed bids -
does not produce a risk-premium on the level of the auction rate, there is preliminary evidence that it
is important-for auction rate volatility. This finding bears further investigation, with the potential
implication that stability of foreign aid could play an important role in compensating for fluctuations in
export earnings induced by trade shocks and/or natural disasters.
Sixth, although we did not specifically address the issue of allocation in the auctions, anecdotal
evidence suggests that efficiencyr of allocation improved relative to the previous system of manual
allocation under a fixed rate. However, it is to be expected that ad hoc disqualifications as occurred in
Zambia diminished these advantages.
Finally, the evidence from Ghana and Uganda as against Nigeria and Zambia, suggests the
paramount importance of transparent policy rules and conduct of the auctions. Lack of-transparency is
tantamount to unnecessary increased discretion by the auction managers, thus exacerbating one of the
major potential weaknesses of the auction regime.
linkage with macropolicy evolution and extrnal aocks tha is imuediatel reflected in a rerve price based on a seconday
free market.
-26 -
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29 -
TABLE 1: Test for unit roote wkih stuotural breaks.
ZAMBIA model: y, - a + t + y1., + T ay,4 + DU + DT
l4g(var) + dumriri alogiverl + dumm,ies sioulver) - duwrnies Order
of I
OF ADFlk-41 DF ADFIk-41 ADFlk-41
logloerl .3.81 -3.29 -9.49 -3.84 -3.79 lii
logimxl -5.21 -3.66 -6.61 -407 -4.10 1)
lgirmini -5.28 .3.64 13.73 -4.31 -4.21 lii0
loo(msx-rninl .-4.40 -4.12 -12.83 -5.29 -5.26 1101
loglOo) *6.55 -3.40 -10.21 -5.82 -5.28 111
Iog(Gdl -4.27 -3.78 -9.83 -3.65 -3.69
logo(s/Odl -5.31 -2.65 -1 0.51 -4.93 4.85 1111
loglbidtl -3.52 -3.02 -9.02 -3.84 -3.46 1111
log(bidshJidtl -4.46 -2.78 -8.57 -4.75 -4.6 111
loglprem) -3.31 -2.92 -9.11 .3.94 -3.86 111
1. Citicl values with dumnuies (Perron. 19899: brelkpoint in sample: as0.6S lergearnple: aignificance level: t.4.2415% t.-3.95 (10%1.
2. Critia values withoutddummies 1(eneriee at a. 19921: 100 observation.: enificance levd: t..-4.04 (1%1. t-3A.5 15%l.
3. Trend dummies for breakpoint TO: t-trend: 0U,-1 if t>T*. end 0 otherwise: DT,-t if t>Tu. and 0 otherwise.
UGANDA Model: y, - cat+y1 + S..k Vv. + DU + DT
logivarl + dummies alog(varl + dummies aloalvar) - dummies Order
of 1
OF ADF(k-41 DF ADF(k-4) ADFik-41
lag(oerl -7.79 -2.97 -4.67 -5.33 -4.72 111)
lol(maxl -7.99 4.68 -12.39 -6.33 -6.34 110)
log(minl -6.70 -7.55 -27.93 -7.70 -7.90 lEO)
log(max-minl -8.89 4.32 -12.34 -6.36 -6.47 ItO)
Iog(Qsl -8.55 -3.58 -15.64 -5.29 -5.34 1(1)
lag(Od) -7.72 -4.64 -12.74 -6.13 -6.31 1(0)
lcg(OsIOdl -7.24 *4.68 -13.86 -5.20 -S.49 1(O)
log(bidt) -7.34 -2.78 -15.33 -5.20 -5.26 Iii)
log(bidslbidtl -7.63 4.68 -13.86 -5.20 -5.47 1(0)
lorWber) -0.92 -2.88 -4.80 *4.81 -3.26 111
loglprem) -2.29 -2.65 -5.24 4.02 -2.78 1f1)
1. Critcal values with dumrnie lPerron, 1989): breakpoint in sample: Of-0.3; lmeeaemPle: significance level: t- 4.17(5%1. t.o 3.B7 110%).
2. Critical values without durridmes (Banerjee at at 1992): 100 observations: significance level: t -4.04 11%). t.-3.45 (5%1.
3. Trend dumnies for breakpoint T,: t-trend: DU,-1 if t>T5. and 0 otherwise: DT,-t if t>T*. aid 0 otherwise.
- 30 -
TABLE 1: (Contd.I
GHANA medel: y, - a + t + V,., + S *y,4. + DU, I Dro
legivar) + dumres aloglvel *F- dumnrieo alolvari - dunmtEes Order
afll
OF ADFlk-41 OF ADF(k-41 ADFIk-41
loaloerl *3.74 -3.74 -14.14 -6.38 -6.41 - 11
logimaxl *3.48 -4.77 -15.00 -7.14 -7.15 1(01
logimin) -9.70 *3.57 -14.70 -5.48 -6.49 1(O0
loglmax-min) -S.44 -2.44 -22.09 -6.61 .6.52 1101
loglCal -11.79 4.89 -22.86 -11.72 -11.89 1(0)
loalOd) -8.92 -6.01 -19.67 -9.08 -9.11 1(01
loglOsIQdl 9.41 -7.07 -20.02 9.97 -9.96 1(01
loglbidtl .6.1a -4.01 -16.82 -7.68 -7.68 101)
Iog(bida/bidtd -7.08 -5.86 -16.10 -7.89 -7.89 lO0
loalbarl 0.31 -0.24 -10.13 -6.55 -5.98 111i
logiprem) 0-AS -0.48 -10.51 -6.93 -*.42 1(01
1. Critical vales with dummies IPerron. 1989): breankpoint 1 in searple: a -O.4: breakpoint 2 in so-ple: a-0.7. Using C-.0.7: large
sample. significance level: t-3.80 (5%, t.-3.51 (10%).
2. Critical values without dummiee (Bmnerjea et al. 19921: > 10D observations: significance level: to- 3.96. 11%1. t, 3.41 15%1.
3. Trend dummies for breskpoints Te: t-trend: DU,-I if t>T. mid 0 otherwisee or, -t-T, if t>T, and 0 otherwise.
4. Sanple sizes for number of bids and bureaux date wre lees than 270 lAron end Elbadawi. 1994: Table 21. hI the forner case no dummies
are used in the test.
NIGERIA rnodel: y, -c + t + Y1 + L-1v. + DU + OT
logivarl + dummies slogvarl + dufnrnies Aloglvar) - dummie Order
ofl
DF ADFlk43 DF ADFIk-4) ADFIk-4)
logioerl -5.01 -2.90 -13.86 -4.88 -4.11 1011
logimaxl -1.82 -2.88 -7.28 -4.16 -3.74 1(11
loglmin) -5.19 -3.49 -10.11 5.44 -5.60 111)
loglmax-rnin) -4.52 -3.63 -9.87 -4.70 -4.72 1M11
loglsl -5.73 -4.17 -9.49 -6.16 -4.81 1(0)
loglCd) -5.60 -3.94 -9.97 -5.39 -4.42 1(0)
log(lQQodl -5.31 -4.39 -10.51 -4.29 -4.35 1(0)
loglbidt) -5.60 -3.96 -8.70 -5.93 -5.67 1(0)
loglbidsfbidtl -5.71 -4.73 -13.41 -4.58 -4.89 110l
loglber) -3.53 -2.62 -9.59 -4.36 -4.30 111
log(preml -5.30 -3.71 -12.52 -4.00 -3.58 Iti)
1. Critical values with dummnies (Perron. 19891: breakpoint in sample: a-0.4: large sample significanee level: t-4.22 (5%). t, 3.9511 10%).
2. Critical values without dummies (Banerjee et al. 19921: 100 observations: significance level: t-=4.04 l%)L t.- 3.45 15%1.
3. Trend dumnmies for breakpoint TB: t-trend: DU,-1 Hif vT. and 0 otherwise: DT, - t if t>T, and 0 otherwise.
4. Notethat the fitted trendrshown in Figure Id could not be used in these tests due to singulrity of the date: the regime change from auction
2-3 is thus not included here.
-31-
TABLE 2: Etnmation of the equilbrkmn auction rate for Zambia. Ugundei Ghan. and Nigeria.
ZAMBIA
Equation 1 Equation 2
utrAlo:
equlibrlum error 0.83976E01 0.95212EiO1
12.17241 12.23031
constant 0.28815 022150
10.340281 10.294711
0ogIaS),., -0.79092 -0.68865
1-1.77073 (-1.78751
logiOd),., 0.65355 0.62815
11.85351 12.068U1
logIBERI,., 0.76105 0.74578
12.75331 (3.01481
MAY (lIog(qvs1, ... 0.18522
(0.702491
DUMDutch -0.55716 -0.48879
1-1.92421 (-1.92543
D2 -2.5048 -2.2399
1-1.88421 (-0.196791
dynamic:
A\bg(0s, -0.47414E-01 -0.46943E-01
1-3.70271 (-3.64003
AlooCld), 0.31940E-01 0.34691 E-01
(2.0072. (2.09543
AlogiberI, 0.60805 0.81353
(10.4512 (10.3791
Aloogbarl-, -0.10353 -0.96324E-01
(-2.30711 (-2.07233
diignoata:
(t-statistics in parentheses)
log of likelihood function = 142.331 142.587
no. of observations - 64 64
SE regression = 0.28766E-01 0.289250E-01
K-squared - 0.754487 0.921638
edjusted R-squared - 0.906852 0.905819
DW statistic 3 1.2347 1.2299
sum of squared residuais 3 0.438597E-01 0.435067E-O1
ADFI4i residual - 4.94 -4.99
CHOW F(9.442 1.273191
- 32 -
TABLE 2: (Contd.l
NIGERIA
Equation 1 Equation 2
satad:
equilbrium error 0.55960 0.65928
(6.436S1 16.3630)
constmnt 0.26381 0.25274
10.803201 10.71291)
-0.17620 *0.17566
1-11.60601 1-1.581 51
lolO{d!,,, 0.19982 0.20074
(1.7649) (1.74672
log(BEFR,., 0.20691 0.15219
(2.29671 (1.59291
log(bidtl,.. 0.1 5225 0.20950
11.61101 (2.19251
MAV 1Alog(qu2., ... 0.30276E-01
(0.89207E-01)
DUMDutdc 0.73946E-01 0.73533E-01
(1.9860) (1.93901
D2 0.11321 0.11277
(2.7757) 12.71 5SI
D3 0.24356 0.24218
14.2873) 14.07461
dynamic:
AIog(Os), -0.31 201 -0.31 179
(-4.751! (-4.02791
AICOM4,, -0.78437E-01 -0.78090E-01
(-1.8689) (-1.8510)
AloglOs)..- 0.21655 0.21 643
15.0387) (4.98131
oog(Cld), 0.24647 0.24695
14.2691) (4.21511
Alog(ber),., 0.36113 0.35918
12.2747) (2.21 862
blog(bidtI., -0.11894 -0.11698
(-2.3799) (-2.1 2292
dgnostic: (t-ststistics in parentheses)
log of likelihood function 124.551 124.556
no. of observations = 63 63
SE regresion - 03S389E-01 0.387926E-01
R-squared 0.754487 0.754529
adiusted R-squared = 0.6S2879 0.676187
DW statistic - 2.0934 2.1039
sum of squared residuals = 0.707408E-01 0.707289E-01
ADF141 residual = -4.47 -4.45
CHOW Fl13.351 - 1.513739
- 33 -
TAME 2: (Contd.)
- ~~~~GHANA
Equation 1 Equation 2
equlilbrium error 0.1 873BE-01 0.18B67E-01
14.37441 (4.33291
conatent 0.1B04B 0.11443
(0.244031 10.155801
log.s)., - -0.31869 -0.30229
(-2.4983) (-2.40011
klogadil, 0.86500 0.86011
14.2207) 14.17711
log(BEl`Q,, 0.77307 0.77751
M4.S9453 14.9073)
MAV (Alog(qel,., ... 0.91587E-01
10.77940)
dynamic:
AIog(CLsl, -0.895111E-02 -0.87323E-02
I-4.50941 (-4.3784)
AMog(axL., -0.41 345E-02 *0.41 627E-02
(-2.42531 (-2.44573
AlaglOs),., 0.5411 5E-02 0.55080E 02
(3.20451 (3.26471
Alog(Od), 0.17074E-01 0.17049E-01
18.98471 (8.94861
dlog(Od3,.1 .0.3S971 E0 02 -0.40007E-02
1-2.6323) (-2.6871)
AloglQdl . 0.35241 E-02 0.351 06E-02
(2.1075) 12.09841
AloglOQdi,, -OA51 30E-02 -0.43208E-02
(-2.6181) (-2.4807)
Alog(berl, ... 04090SBE-01
,. .(1.5777)
AlogIber),.2 0.63480E01 0.65041E1-01
12.49153 (2.5533)
d':
ft-statirstcs in perenthesesl
log of likelihood function 970.719 972.235
no. of obsarvdions - 266 266
SE regression - 0.645304E-02 0.64418SE02
RPquared = 0.459540 0.465665
adjusted R-squared - 0.433905 0.435862
OW statisc - 1.9582 1.9525
sum of squared residudsl 0.105354E-01 0.104160E-01
ADF(41 residual - -6.25 -6.30
CHOW F1l3.2013 a 2.586580
- 34 -
TABLE 2: (Connd.l
UGANDA
Equaton 1 Equation 2
stati:
equilibrium error 0.74353E-01 0.7501 0E01
14.4143) (4.41421
constant 4.9556 4.9849
(5.82873 15.8731)
bolas)1., -0.29391E-01 -0.282556E01
(-2499631 (-2.87081
loglOdl,., 0.44105EE01 0.42668E-01
13.62131 (3.5095)
bogIBERI., 0.27697 0.27292
12.3066) 12.2770)
MAV (Alog(q.ll,., ... *0.38358E-05
.-0.512841
DUMguarantee 0.11474E-01 0.1 1360E-01
11.985969) (1.9633)
dclnarnio:
Aiogial. 0.93263E-03 0.901164E-03
(2.2358) 12.1315)
Alog(quI,, -0.59881 E-03 0.56979E-03
(3.2272) 12.95661
AlolodI. - 0.95845E-03 0.95213E-03
(2.97899 12.9376)
AIoo(01,1 4-0.11450E-02 -0.11068E-02
(-2.399B) 1-2.28181
AlogIberl. 0.85835E-01 0.12322
(2.1438) (3.08961
Aloglbarl,., 0.1204.3 0.92119E-01
13.0604) (2.21471
diagnostice:
(t-statistics in parenthesial
log of likelihood function - 337.319 337.56D
no. of observations 58 58
SE regressimn - 0.809678E-03 0.81 5224E-03
R-squared - 0.635630 0.B38651
adjustd R-squared = 0.54849 0.542291
DW Bstaistic 1.8440 1.8867
sum of squared residuals . 0.301566E-04 0.299066E-04
ADOF41 residual - -3.54 -3.59
CHOW F1l11.351 1.098098
- 35 -
EIGURE 1 a,b,c,d: Regime shifts and the equilibrium auction price in
the SSA auctions.
ZAMBIA 19B5-87.
2.6-
2.4 DOMETIIlVE DrGI
2.2.
2.0-
1.4
1 5 9 13 17 21 25 29 33 37 . l A5 49 53 S 61 6S
3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 63 67
aotion mnnber
la cation rate tHted rend |
UGANDA 1992-93.
6.95 UARANTE CAM
6.94
6.93-
=6.92
6.91
1 5 9 13 17 21 25 29 33 37 4a 45 49 53 57 61 65
3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 53 67
auction nbter
| Euceton rate - ited fr
- 36 -
GHANA 1986-92.
6
5.48
5.2
5 RETAIL WHOLESALE
1 23 45 67 59 tI1 133 155 177 199 221 243 255
12 34 56 75 100 122 144 106 158 210 232 254
auwiTon ntnber
- auctIo rte - fited trend
NIGERIA 1986-88.
1.7-
1.6 8
1.5
1.4.
1.3
1.2-
1.1
I 5 9 13 17 21 25 29 33 37 41 45 49 5357 61 65
3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 63 67
wxiion mnter
- auction relet- hedrend |
- 37 -
APPENDIX I: Econometric methodology.
The main objective of this research is generating an asymptoticallv efficient
estimates for the equilibrium model of section 2. The existence of cointegration readily
guaranteed consistent (in fact super-c)insistent) estimation for the equilibrium parameters
from a simple OLS regression of equation (1) above (Engle and Granger (1987)). This
important property has been the main reason behind the enormous popularity of
cointegration regression in the past few years. As pointed by Phillips and Loreton
(1991), however, the cointegration regression usually produces substantially inefficient
arjmptotic estimations. Given our interest in generating asymptotic point estimators with
smaller margin of errors for the true equilibrium, the direct cointegration estimation will
not be adequate for the problem at hand.
Fortunately, Phillips and Loretan (1991) propose a useful empirical paradigm
based on statistical distribution theory that can be used to generate asymptotically efficient
estimation in the context of single equation cointegration (or error-correction)
econometrics. Phillips and Loretan show that asymptotic efficiency obtains in the case
of cointegration regression only for the fully modified OLS (Phillips and Hansen (1990)-
with semiparametric serial correlation and endogeneity corrections). And in the case of
a modified non-linear single equation error-correction specification (with lagged
equilibrium relations and both lags and leads of AF, as regressors). In what follows we
will discuss the modified ECM, since it will turn out to be a direct generalization of the
ECM consistent long-run cointegration equilibrium.
Consider the following typical cointegrated systems: let Y. = [e] be an n-
vector with an I(1) process and (& = ['] be an n-vector stationary time series, with
n = m+ 1. Now the cointegration equilibrium can be represented by the following
systems (Phillips and Loretan (1991), Phillips (1991)):
e,= #IF (1')I
AF, = L (2')
a.a
As.suming that,y1 = S Aj etj, d0=[ E j1r I Al || < o, where e-iid N (O, ); Philips
j.O J-O
and Loretan (1991) show that system (1') and (2') is equivalent to the following
expression:
et = 'Ft +4E djj (e -3'Ft) + d BAF j + (3)2
i-I j-o
Z Phillips and Lorctan (199 1) emphasize the point that asymptotic theory requires dhis particular nonlinear formulation of
the ECM, as opposed to die other frequendy used formulation in die literature based on using Ae; instead of (;i - lB, this
is because lags of Ae, are not in genral an adequate proxy for dte past history of pi,, because of die persistence in the effects
of the innovaiions that arises from die presence of unit roots in the system.
- 38 -
where tj, = p,, - Ep,,X1 .,) is a Martingale difference sequence with respect to the
filtration X,, a =(Ae1,,Ae,_2...,AFAFt-1....). A suitably truncated version of (3)
above has been employed in single equation error correction (SEECM) empirical work
(e.g. Hendry and von Ungern-Sternberg (1981)).
Phillips and Loretan (1991), however, show that a truncated version of (3) will
fail to produce asymptotically efficient estimators, because the truncation error is non-
negligible due to shock persistence. Also Phillips (1988a) show that there is a general
failure of valid conditioning-a desirable feature in the Hendry-Richard metholoy;f -due
to the presence of feedback from A, to ga. To rectify the failure of equation (3) to
produce asymptotically efficient estimators of 6l, Phillips and Loretan (1991) show that
this needs the elimination of this feedback, and they suggested including leads of AF, in
the regression of (3) so that in the limit p, is orthogonal to the entire history (AF1)Z..
Their revised version of (3), therefore,.has the following fbrm.
C a
et = pPT E d,1(e,j - 6'F,j) r djAF_j
j-l j-0
'E d/AF1.., v
where v, =, - r d3gZ1,-jI and is a martingale difference sequence with respect to the
.-.
filtration p'--, = r , t *..t (,uQA.
A truncation of (4) that will be estimated in this paper allows for two lags and
one lead (Phillips and Loretan (1991))t
=et =IF + d,1(e., - Ft_,) + d,n(et,, - PT,-_)
: dAF + d21'AF,-2 + dAFt-2 (5)
+ dX,AFt.[ + v,
a The Hendry-Richard approach (see Gilbert, 1986) suggests that a successfil single-equaton ECM should meet tde
following critemia: (1) data coherency; (2) valid conditonian, (3) encompassing; (4) theory compatibility; (5) parsimonious
orthogonal decision variables; (6) prameter constncy.
The relative successful order (2, 1) truncated model simulated by Philips and Loretan (1991), however. contains only
two long-run parameters.
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