DIÁMETRO CUERPO PIN RELACIÓN
3. UNIDADES DE BOMBEO CON BALANCIN
3.1 TIPOS DE UNIDADES
The history of sovereign borrow ing suggests that defaults are usually associated w ith
identifiable b ad states of the w orld (nature). This is certainly true for low-incom e
countries, and has w idely been show n to be the case d u rin g the 1930s and 1980s debt
crises.36 A n im p o rtan t branch of the 1980s and 1990s deb t literatu re has show n
com pellingly th at if lenders are able to differentiate excusable defaults th a t are
associated w ith identifiable contingencies outside the debtor's control, from o utrigh t
d eb t rep u d iatio n and m isbehaviour by the debtor, debt contracts can be designed in
such a w ay th a t the debtor chooses in all states of the w orld to validate the lender's
expectations. Furtherm ore, to the extent th at lenders can d istinguish the effects of
exogenous shocks (nature) on repaym ent capacity from the effects of factors
controlled by the debtor country, state-contingent rep ay m en t elim inates the
disincentive effects of a deb t overhang, and effectively solves the lending-relief trad e
off relating to len ders' choice of action.
Again, K rugm an's (1988a) sem inal contribution provides an ideal starting po int to
illustrate the crucial advantages of indexed, or state-contingent, contracts. R eturning
to K rugm an's tw o-period m odel w ith reference to stan d ard deb t contracts, as
introduced in Section 2.3 above, consider now a country th at has inherited a stock of
debt D, repays xi in period one, and has the following uncertain resource transfer
potential in the second and final period:
X 2 = n + t (19)
W here n is a rand om variable ranging from Nt to Nh, and t is n ow the choice variable
capturing the outcom e of the deb tor's effort to adjust. In period tw o, the country
consum es o u tp u t X2 net of p aym ent to the creditors, P.
C2=xz-P (20)
36 E.g. see Eichengreen and Portes (1986) and Sachs (1982). - 6 8-
The country's social plan n er m axim ises utility by m axim ising consum ption in period
two n et of the adjustm ent costs incurred in period one, v(t).
U=C2-v(t)= X2-P-v(t)= (n+t)-P-v(t) (21)
The incentive problem arising from new lending, and the trade-off betw een new
loans and debt relief w as show n above. N ow , consider instead th at the creditor's
claim is set to vary w ith the deb to r's ability to repay, by m aking repaym ent a
function of second-period expected output, w here A and B are tw o constant
param eters set by the creditor:
P=A+Bxi 0<B<1 (22)
Thus,
Ch—xz-P— - A+(1-B)X2 (23)
A nd the debtor m axim ises expected utility over the w hole range of possible states of
nature:
A'„
t / “ p = j [ - A + (1 - B)(n + t ) ] f ( n ) d n - v(t) (24)
N,
Crucially, the first-order condition m axim ising expected utility,
SU/a
= ( l - B ) - v ' ( t ) = 0, (25)show s th at in the case of output-indexation the incentive problem is not fully
resolved, since the country will receive only a fraction (1-B) of the im proved
repaym ent capacity from adjustm ent. Hence, the trade-off betw een new lending and
debt forgiveness is still present if the claim is linked to the d eb to r's b ro ad ability to
pay. P u t differently, as long as effort (f) co-determ ines repaym ent by raising the
expected value of period-tw o output, a fraction of the benefits will go to creditors.
Therefore, a debtor in overhang will have less incentive to exert the optim al level of
effort and increase repaym en t capacity.
K rugm an (1988a) goes on to show th at only by devising a m echanism linking
pay m en t exclusively to the state of nature, that is on n only, can the incentives
problem be com pletely resolved. Crucially, the author has to ad o p t the assum ption of
perfect sym m etry of inform ation betw een the creditor and the debtor, both w ith
regard to the exogenous (n) and the endogenous com ponent (t) relating to paym ent
capacity in p eriod two. If such an assum ption does hold, a com plete contract could
specify p ay m en t to be in d ep en d en t from t:
P=A + n (26)
A nd the first-order condition w ou ld correspondingly be:
SE/St - 1 - v'(t) = 0 (27)
Thus indicating th a t the benefits from increased effort w o u ld accrue to the country in
full, since the p ay m en t only w ould d ep end on the realisation of n.
K rugm an (1998a: 26) notes that creditors could still have the incentive to set the
param eter A in the repaym ent equation (26) hig h enough to set it equal to the optim al
level t, "[...] so th at they w ould provide the debtor w ith a m arginal incentive to
adjust yet in the end capture all of the d ebtor's potential resource transfer." H ow ever,
this w o u ld no t be possible, since im plying th a t in the event of low n actual repaym ent
w ould exhaust the entire possible resource transfer capacity of the debtor, w ho,
know ing this, w o u ld again have a disincentive to adjust.
K rugm an further notes th at the m odel equally applies to n ew lending. Indeed, if
creditors im pose conditionality on new loans and dem an d m axim um resource
transfer (t+n) in every state of nature, the country will have no incentive to adjust. In
contrast, by linking n ew lending to the state of nature, the country will benefit from
adjustm ent, and therefore the incentive to adjust w ill be higher. As a result, state-
contingent loan instru m en ts effectively resolve the trade-off betw een the two
strategic choices open to the creditor com m unity in dealing w ith d ebt overhang.
The m ain th ru st of K rugm an's insightful m odel of contingent d ebt service is to have
dem onstrated in the sim plest possible term s that repaym ent indexed to the state of
nature is a superior w ay of ad dressing the debt overhang problem , com pared to
sim ple loan contracts. O bviously, the optim ality of indexation schemes crucially
hinges u p o n the assum ption of a creditor's ability to observe all exogenous factors
affecting repaym ent capacity. To the extent that they cannot, either because the state
and verified by anyone other than the debtor itself, som e degree of disincentive
lim iting a country's w illingness to perform will still be in place.
K rugm an's basic insights have found u nusually w ide acceptance - and no substantial
challenge - in the subsequent literature. Similar acceptance and b road resonance has
greeted tw o furth er influential contributions of the late 1980s, w hich elaborate on the
im plications of state-contingent debt contracts. One study, already m entioned above,
is th at of Froot et al. (1989), w hich confirms the central th ru st of K rugm an's analysis,
b u t further em phasises the lim its resulting from asym m etric inform ation. It argues
that u n d e r sym m etric inform ation, contracts m ade contingent on variables th a t are
not controlled by the debtor create no disincentive effects and lead to the first-best
level of investm ent. In contrast, paym ent m ade contingent on variables u n d er partial
control of the debtor country, such as o u tp u t and GDP, lead to m oral h azard and a
sub-optim al level of investm ent. H ow ever, Froot et al. (1989) also find that this m ay
n o t be so u n d e r conditions of asym m etric inform ation. In particular, they argue th at
if the creditors cannot fully observe the characteristics of the debtor, the latter will
have an incentive to m isrepresent its private inform ation so as to receive higher debt
relief an d /o r m ore new loans. The authors conclude th at this type of bargaining m ay
thus raise the am ou nt of relief, b u t m ay also easily cause the negotiation process to
break dow n, w ith creditors offering zero relief and debtors refusing to adjust - a
situation they call a 'stonew alling' equilibrium .
A second study, by G rossm an and Van H uyck (1988), elaborates a m odel of
contingent deb t service, w hich assum es that creditors are able to distinguish
excusable default from unjustifiable repudiation. In contrast to the m odels devised by
K rugm an and Froot et al., how ever, w hich im plicitly dow np lay the debtor's ex-post
incentive to rep ud iate deb t by focussing instead on the benefits from state-contingent
claims on investm ent decisions and the ensuing capacity to repay, G rossm an and
Van H uyck p u t at the centre stage of their analysis the role of contingent d ebt service
in validating the lenders' expectations so that the sovereign chooses in all states to
validate these expectations. The authors derive a reputational equilibrium w here
consum ption sm oothing is achieved by m aking debt service contingent on the
realisation of income. That is, the sovereign services the full am ou nt due only w hen
the state of natu re is such th at the realisation of income is high. O therw ise, the -71 -
sovereign defaults either in full or in part. H ow ever, continued access to loans is
assured to the sovereign even after the event of default, as long as it validates
lenders' expectations on debt service. A crucial assum ption for this to hold is to
abstract from savings by the sovereign, so th at the Eaton-G ersow itz (1981)
pu n ish m en t strategy of no future b orrow ing in the case of inexcusable default w ould
lim it the sovereign's future consum ption stream to future realisations of income.
More specifically, the m ain analytical structure of the m odel is based on the following
assum ptions: The sovereign invests in a concave risk-free p roductive technology37
and services debt in such a w ay as to shift to creditors the risk associated w ith
negative stochastic shocks on income. The authors em phasise the insurance role of
state-contingent debt service, noting that
"By borrowing an amount equal to the maximum indemnity for which it would contract, a large agent like a sovereign who wants to insure itself against the effects of bad states of the world can draw 011 the resources of many small and anonymous insurers, with whom it would be costly to write and to enforce contracts requiring the payment of an indemnity after the realisation of a bad state of the world." (Grossman and Van Huyck, 1989:1089)
The essential assum ption, as in K rugm an and Froot et al. (1989), is th a t the exogenous
stochastic com ponent of income is verifiable, so th at lenders can distinguish
excusable from unjustifiable repudiation. Lenders are assum ed to be also inform ed
about the sovereign's tim e discount rate and its utility function U(c). The analysis
further assum es that current consum ption is exclusively m ad e out of p ast borrow ing,
and not of current debt issuance or dom estic savings. Thus, current consum ption (a)
in period t is equal to the retu rn from the last perio d's borrow ing f(bti), plus the
stochastic income com ponent zt, m inus current debt service si.
ct=f(bt-i) + z t +s t b t - i > 0 , s t > 0 (28)
W here [f(bt-i) + zt] can be reg ard ed as the sovereign's real national income, w ith zt
reflecting the random ness of factors affecting national income, such as shocks
affecting export com m odity prices. The realisations of the state of nature, zt, range
from a good state Z, to a w orst state, z, and are assum ed to have a stationary
37 Which is assumed to be available only to itself and not to the creditors. Furthermore, the technology is assumed to be risk-free for the purpose of focussing exclusively on the risks accruing from the realisations of bad states of nature, and not the economic risk of investment itself.
probability distribution, p(zs), w ith m ean za, These assum ptions im ply th at the
sovereign faces a repeated static problem , in w hich the sovereign's objective in each
period t is to m axim ise utility given the expectations conditional on inform ation
available in f:
U l = u ( c t ) + E l J > rK(cr ) (0<P<1) (29)
r= t + l
The expected value of rep aym en t is the p ro d u ct of rep aym ent associated w ith each
state of n ature and the probability of such a state of n atu re occurring, across all
possible states of nature. This expected value sets the credit constraint im posed by
lenders:
Y P (z , )S l \ O r ) = 0 + P )b,-\ w
z
W here ( zt ) denotes the debt service lenders in period t-1 expect to be m ade in
period 1.
If creditors w ere able to irrevocably and credibly com m it in period t-1, to repay debt
according to the state-contingent contract, such a com m itm ent w o uld allow excusable
default, dep en ding on zi, b u t w o u ld exclude debtor's repudiation. In short, if lenders'
expectations on rep aym ent du e to the perfect com m itm ent technology are:
s.=5;_1(zr) = 5 /_1(zi ) (31)
the sovereign's choice in period t-1 concerns uniquely the am o un t of new borrow ing,
that is bt-i, and the debt servicing com m itm ent on new debt, b u t not the am ou nt of
income to be devoted to servicing existing debt, Sf. Hence, the solution to the social
plan ner's m axim isation problem (29) u n d er constraints (28), (30) an d (31) are such
that, in each an d every period:
b* = max [f'(bt-i)=l+p; (z a-z)/(l+p)] (for all t) (32)
W here b* represents the efficiency-m axim ising level of debt, w hich is high enough
both to allow for the m axim isation of returns on investm ent [m arginal retu rn on the
investm ent f(bt-i) equal to the risk-free interest rate (1+p)], and, as G rossm an and Van
H uyck (1989:1091) p u t it, "for its lenders to p repay the indem nity associated w ith the
w orst possible state of the w orld". This indem nity corresponds to the discounted risk
factor expressed as the difference betw een the stationary m ean an d the w orst state of
the w orld (za-z). Clearly, then, if f(bi-i)=l+p > (zn-z)/(l+p), full risk-shifting w ould
require bo rrow ing b eyond the level required for efficient inv estm ent alone.
M oreover, optim isation requires debt service com m itm ent to be fully contingent, so
that:
S*(zt) = z/-z" + (l+p)b* (for all t) (33)
T hat is, the 'n o rm al' deb t service requirem ent (l+p)b* is increased (or decreased) by
the difference betw een the realisation of z and the m ean value of z, z".
It is easy to see th at in the best state of w orld, such a rep ay m ent com m itm ent w ould
allow debt to be serviced in full (as Z-z" represents the m axim um payable), w hile in
the w o rst state (z-z17) total default w ould occur. In contrast, all other realisations
z<zi<Z w o u ld im ply partial default. In sum, this repaym ent schem e w ould shift all
the risk to the lenders, so that consum ption w ould be in d ep en d en t from the
realisations of z:
c* = f(b*) - (l+p)b* + za 38 (for all t) (34)
Since the m odel assum es consum ption sm oothing to be the function of international
borrow ing, utility is m axim ised w ith consum ption at c* for all t.
The first key result in the G rossm an an d Van H uyck m odel is thus to show that
shifting the risks associated w ith exogenous shocks affecting rep aym ent from the
bo rrow er to the creditor is the optim al repaym ent strategy w hen lenders are
inform ed about the d ebtor's characteristics (here fi), and if the latter is able to
irrevocably com m it to repay up to its capacity. In this m odel, the lender thus
explicitly acts as the insurer, w ho takes u pfro nt all the in dem nity p ay m ent by
factoring it, via ' ^ p ( z t) S t’_x(zt), into its expectations of repaym ent. It is im p ortan t to
em phasise, how ever, th a t indem nity relates to the sovereign's exposure to risk, and
n o t to the risks associated w ith the investm ent technology itself, w hich is purposely
assum ed to be risk-free. W hat creditors do, instead, is sim ply to acknow ledge ex ante
38 N ote that equation (34) is derived by substituting for b*=(za-z)/(l+p) and S*(zt)= zt-za + (l+p)b* into equation (28).
the risk com ponent of investm ent associated w ith verifiable realisations of zi. Clearly,
there w ould be no lending if the b orrow er w ere no t able to treat the lenders'
expectations on d ebt service as a choice variable, d epend in g on its ow n actions to
validate those expectations. In other w ords, if the b orrow er w ere to choose si in a w ay
to increase cu rrent consum ption c\, instead of choosing St so as to validate the lenders'