an arrears crisis and stabilization failure in a transition economy

An Arrears Crisis and Stabilization Failurein a Transition Economy1

Maxim Nikitin

University of Alberta, Edmonton, Alberta T6G 2H4, Canada

E-mail: [email protected]

Received November 11, 1999; revised August 14, 2000

Nikitin, Maxim —An Arrears Crisis and Stabilization Failure in a Transition Economy

The paper addresses the problem of the arrears crises in transition economies using awar-of-attrition type dynamic game of incomplete information. Analysis of the sequentialequilibrium of the game reveals how a representative firm’s perception of the govern-ment’s ability to enforce adjustment to the announced stabilization program affects thefirm’s decision whether to adjust or to postpone adjustment and fall into arrears. Anextension of the basic model is used to explore the opportunity for the government tosignal its commitment to a tight monetary policy by applying for an IMF loan.J. Comp.Econ.,December 2000,28(4), pp. 665–699. University of Alberta, Edmonton, AlbertaT6G 2H4, Canada. © 2000 Academic Press

Key Words:arrears; credibility; sequential equilibrium; transition.

Journal of Economic LiteratureClassification Numbers: P20, P21, P30, P33.

1. INTRODUCTION

A spectacular arrears crisis was the main reason for the failure of inflationstabilization in a few post-Communist countries in the early 1990’s, includingRussia, Romania, and Ukraine. In these countries, state-owned enterprises(SOEs) responded to credit tightening with an explosive expansion of interfirmtrade credit and arrears, so that most of the firms became insolvent. In otherwords, firms substituted arrears for adjustment to the new economic conditions.2

1 I am thankful to Masaki Ayoagi, John Bonin, John Duffy, David Dejong, Juergen von Hagen,Philip Reny, Alvin Roth, Jan Svejnar, and two anonymous referees for their helpful comments on theearlier drafts of the paper. The work on the paper benefited greatly from my stay at the Center forEuropean Integration Studies at the University of Bonn. Its support and hospitality are gratefullyacknowledged. All remaining errors are my own.

2 Adjustment is defined as the termination of all short-run money-losing production activities, i.e.,for which variable cost exceeds the current price, as well as the termination of output shipments to

Journal of Comparative Economics28, 665–699 (2000)doi:10.1006/jcec.2000.1685, available online at http://www.idealibrary.com on

665 0147-5967/00 $35.00Copyright © 2000 by Academic PressAll rights of reproduction in any form reserved.

Due to the scale of the problem, the authorities were forced to bail out all thedebtors, i.e., clear up arrears with Central Bank loans. Thus, stabilization failed.By bailing out firms, the policymakers implicitly acknowledged their inability toenforce adjustment.

Liquidity crises very similar to the one described above followed eachattempt at stabilization in the former Yugoslavia in the 1960’s through the1980’s. A tightening of monetary policy in China in the early 1990’s alsocaused a steep rise in interenterprise chain debts (Rawski, 1996). Some of theeconomies in transition, including Poland, Estonia, Hungary, and Czechoslo-vakia, also experienced interfirm arrears at the beginning of transition.However, these did not become a systemic crisis and did not have significantmacroeconomic implications.

The existing literature on arrears falls into two categories. The firstincludes descriptive and empirical papers. Tyson (1977), Ickes and Ryterman(1992), Ickes and Ryterman (1993), Clifton and Khan (1993), Daianu (1994),Rostowski (1994), Calvo and Coricelli (1995), Coricelli (1996), and Alfan-dari and Schaffer (1996) discuss particular episodes of arrears crises in theformer Yugoslavia, Russia, and Romania and analyze factors affecting arrearsusing cross-section survey data. These authors make three main arguments.First, arrears have been a response of firms to a pronounced liquidity squeezeat the beginning of transition. On a micro level, overdue payables dependnegatively on profits, exports, and available bank credit, and positively onoverdue receivables. Second, in the cases of systemic crises, generalizedarrears arise among viable firms that have low, or even negative, net arrears,but high gross arrears.3 In countries that avoided systemic arrears crises,overdue payables were concentrated largely among relatively few loss-making firms in financial distress. Third, an arrears crisis erupts when thecredibility of the government’s stabilization policy is low. Firms fall intoarrears because they expect a bailout in the near future. Supporters of thishypothesis usually imply that reformist governments in Russia, Romania, andUkraine were politically weak so that firms expected the government to resignor reverse its policy soon; therefore, they postponed adjustment.

The second category includes theoretical models by Calvo and Coricelli(1994) and Perotti (1998). In Calvo and Coricelli (1994), firms face a liquidity-in-advance constraint on their purchases of material inputs, which can be slack-ened by accumulating arrears. However, arrears are costly and, depending on the

insolvent (nonpaying) customers. Hence, adjustment is a more primitive response to the changingeconomic conditions than restructuring. The latter involves investment in new production processes,the search for new markets, and the disposal of assets which are no longer needed, among otheractivities.

3 In other words, large overdue payables are mostly balanced by large overdue receivables.

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cost of arrears, there may be two different adjustment paths following a negativeliquidity shock. On one, there is accumulation of internal liquidity by firms thatcut their wage costs and recover over time their previous level of output. On theother, firms reach a maximum level of default on their input payments, whichresults in an arrears and low output trap. The limitation of the Calvo–Coricelliapproach is that the cost of arrears is given exogenously; i.e., it does not dependon the stock of arrears. Hence, this approach does not allow for an analysis of theendogenous government response to arrears accumulation. Perotti (1998) endo-genizes the government’s response to arrears and shows that if the restructuringcost is high and the Central Bank is expected to be failure averse, a tightermonetary policy can deter SOEs from restructuring and induce them to fall intoarrears, as it increases the share of insolvent firms. Consequently, the probabilityof an overall arrears bailout increases.

In the literature, there is a consensus that the lack of credibility of a no-bailoutpolicy and the political weakness of reformers are critically important forexplaining the systemic arrears crises in transition economies. However, there areseveral facts which are not easy to reconcile with this static credibility argument.First, as the transition proceeded, the adjustment behavior of SOEs was improv-ing irrespective of (and sometimes despite) exogenous political conditions. Firmsbegan to adjust, even though government reformers did not become politicallystronger; in some instances they were even weakened by electoral defeats andgovernment reshuffling. These changes in enterprise behavior made it possiblefor the government (the Central Bank) to tighten further its policy and reduce themoney growth rate. Second, lack of adjustment and overall insolvency on aRomanian or Russian scale, in which the stock of mutual debts rose to 50% ofGDP or more, would force even a determined reformist government to undertakeat least a partial bailout because there were too many insolvent firms.4 Third,international comparisons do not reveal a direct correspondence between exog-enous political conditions at the beginning of transition and the subsequentarrears and adjustment behavior of firms. For example, political factors in Polandin 1990 were not more favorable to reforms than they were in Russia two yearslater. In Russia, any organized political opposition to reforms was virtuallyabsent until April 1992, and the government dedicated to Big-Bang reforms heldemergency powers until November 1992. However, arrears began growingexplosively in February 1992. By contrast, in Poland, the government did notenjoy such wide powers. The main political force that supported reforms wasSolidarity, the labor union, with quite strong populist traditions. Moreover,Solidarity did not have a majority in the Sejm. Fourth, if reformers werepolitically weak and were certain to bail out the firms that failed to adjust, whydid they attempt to enforce adjustment in the first place?

The present paper focuses on the largely overlooked issues of the evolution of

4 See Mitchell (1993) and Perotti (1998) on the TMTF (too many to fail) problem in transition.

ARREARS CRISIS IN TRANSITION 667

arrears and considers the strategic interaction between SOEs and the government(monetary authority) in a multiperiod framework. The analysis accounts for theabove-mentioned facts and reconciles them with the credibility hypothesis of thearrears crisis. The model is a war-of-attrition type dynamic game of incompleteinformation between a government (policymaker) and a representative firm. Thegovernment tries to enforce adjustment and, in the early periods of the game,refuses to bail out a firm that fails to adjust. However, the firm may postponeadjustment and fall into arrears because it believes that the government may benot fully committed to stabilization and will eventually bail it out.

The concept of sequential equilibrium5 is employed to find dynamicallyconsistent strategies for the government and the representative firm. Analysis ofthe equilibrium of the game reveals how the firm’s decision whether or not toadjust to the government’s stabilization policy depends on its beliefs about thepolicymaker’s resolve to enforce adjustment despite the firm’s failure, the cost ofadjustment for the firm, the length of the planning horizon, and other factors. Themodel explains why the firm might switch from nonadjustment to adjustmentafter several periods of arrears standoff without observing any change in thegovernment’s behavior. It also explains why a weak government, i.e., a govern-ment not fully committed to stabilization, can find it optimal to engage in a warof attrition with the firm.

An extension of the basic model is used to explore the opportunity for thegovernment to signal its commitment to a tight monetary policy by applying foran IMF loan. Joining the IMF is costly, but the policymaker becomes eligible fordisbursements of the IMF loan every period so long as it sticks to the stabilizationprogram and refuses to bail out the firm. Although IMF conditional lendingincreases the likelihood of adjustment in general, under certain conditions, theprobability of immediate adjustment is related negatively to the size of theforthcoming IMF loan. IMF involvement reveals the government’s weakness anddeters the firm from adjustment.

Although the model was motivated by the experience of transition economieswith arrears, it is also applicable to other situations where low credibility ofgovernment policy induces agents to test the government’s resolve to enforceadjustment and leads to a costly, in terms of output and welfare, standoff betweenthe government and economic agents. Other examples would be failures ofstabilization programs in some developing countries, e.g., Brazil and Argentina,in the 1980’s and early 1990’s. Noncredible attempts to stabilize using thenominal exchange rate as an anchor resulted in high nominal and real interestrates, because economic agents expected a devaluation and monetary expansion.High real interest rates made an output collapse imminent, and interest paymentson government debt increased sharply, so that the government had to choose

5 The concept of sequential equilibrium was developed by Kreps and Wilson (1982).

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between inflation and default on its debt. Therefore, the stabilization policybecame unsustainable.6

The structure of the model is similar to dynamic games of incomplete infor-mation applied to monetary policy by Backus and Driffill (1985), Barro (1986),and Rogoff (1987), to fiscal policy by Cherian and Perotti (2000), and to relationsbetween an enterprise and a center in a reformed-planned economy by Schaffer(1989),7 which also assume uncertainty about the type of the government at thebeginning of the game and subsequent updating of beliefs about the type. In thesepapers, the government can be tough, i.e., committed to tight monetary policy(low taxes), or opportunistic, i.e., capable of inflating (imposing high taxes). Themain difference between these models and the present one is that the firm has tobear the adjustment cost only once in our model. Therefore, the solution structureis different. In the present model, the firm may adjust immediately, but if it doesnot, it mixes its strategies until the end of the game, unless the weak governmentbails it out, and it never switches from adjustment to nonadjustment.

The present paper relates to the existing literature on soft budget constraints(SBC). Kornai (1980) defines SBC in a narrow sense as an ex post bailout offailing firms due to paternalistic preferences of the government. Subsequentcontributions suggest that an ex post bailout due to informational asymmetries,including a bailout by a profit-maximizing bank or investor, also constitutes asoft budget constraint (see Berglof and Roland, 1997; Bai and Wang, 1998;Huang and Xu, 1998; Schaffer, 1998, for discussion). In our model, there isuncertainty about whether the SBC in the narrow sense of Kornai holds, i.e.,whether the government has paternalistic preferences or not. In one of theequilibria, a representative firm behaves as if it operates under SBC by postpon-ing adjustment even though the budget constraint may be actually hard, i.e., thefirm is never bailed out.

The paper is organized as follows. Sections 2 and 3 contain the formal presentationof the model. Section 4 studies a modification of the model in which the governmentcan signal its commitment to tight monetary policy by applying for a loan from aninternational financial institution (IMF). Section 5 discusses how the model is

6 The experience of Latin American countries with inflation stabilization is discussed in Bruno etal. (1988, 1991) and Calvo (1996).

7 In Schaffer (1989), the center (policymaker) is either weak, i.e., willing to bail out the enterprisein a one-shot game, or tough. Schaffer (1989) investigates how, by acquiring a reputation fortoughness, the center can credibly threaten a policy of no bailouts and make the enterprise work hard,an analog of adjustment. Similar to other dynamic games of incomplete information, Schaffer’s(1989) assumes that the disutility from working hard, i.e., an adjustment cost, is positive in eachperiod. Therefore, in early periods of the game, the enterprise always works hard, and just before theend of the game it takes it easy; i.e., it tests the government’s resolve to enforce the hard work.

One may doubt the applicability of Schaffer’s (1989) results to socialist economies. He suggeststhat, if the planning horizon is long enough, even a weak center is able to threaten credibly a policyof no bailouts for most of the game. This result is at variance with the experience of all the plannedeconomies.


consistent with stylized facts and explains the paradoxes of arrears crises andadjustment in transition economies. Part 6 concludes the paper. The Appendixcontains the derivation of the equilibrium in a multiperiod case and all the proofs.

2. A TWO-PERIOD GAME

2.1. Setup of the Model

Consider the following two-period game. There are two players, a governmentand a representative firm. At the beginning of the first period, the governmentannounces a tight monetary policy. Then, the firm can either adjust (A) or not(NA). In the first case, its payoff iss, 0 , s , 1. If it does not adjust, it becomesinsolvent. However, the government can bail it out (play B). In the latter case, thefirm gets payoff 1. If it is insolvent and is not bailed out, i.e., the governmentplays NB, its payoff is 0.

The government prefers adjustment and does not like enterprise failures andinflation. Inflation is the inevitable consequence of bailout. The government receivesthe payoff of 1 if the firm adjusts, 0 if it does not and is bailed out, andF if it doesnot adjust and is not bailed out. The value ofF is private knowledge of thegovernment. The firm believes thatF is uniformly distributed over the interval[F1, F2], whereF1 , 0 , F2 , 1. In the second period, the game is repeated withone exception. If an enterprise has adjusted in the first period, it does not bear anyadjustment cost in the second period and plays A with certainty.

Obviously the tough government, denoted byF $ 0, does not bail out the firmin either period irrespective of what the firm has done. The soft government,denoted byF , 0, is better off bailing out the firm. However, if the governmentdoes so in the first period, it reveals its type. In this case, the firm will not adjustin the second period. Therefore, the soft government may have an incentive tomimic the behavior of the tough government in the first period in order to induceadjustment in the second period. Both the firm and the government seek tomaximize the discounted sum of payoffs in both periods. The discount factor ofthe government isg and the discount factor of the firm isd. We assume thatF 1 1 g p 1 . 0; i.e., even the most failure-averse government is ready to bearthe cost of failure if it is sure that it will induce the firm to adjust in the secondperiod. Figure 1 shows the two-period game in extensive form.

2.2. Pooling Equilibrium

If the first period of the game is played only once, the government bails thefirm out if and only ifF , 0. The firm decides whether to adjust, comparing itsexpected payoff if it adjusts,p(A) 5 s, to its expected payoff if it does not,p(NA) 5 p(F $ 0) p 0 1 p(F , 0) p 1 5 2F 1/(F 2 2 F 1). The poolingequilibrium of the two-period game occurs when2F 1/(F 2 2 F 1) # s. In thiscase, the firm adjusts in the second period even if it did not adjust in the first

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period, and the government’s action in the first period does not convey anyadditional information on the actual value ofF. This makes it sequentiallyrational for the government to play NB in the first period with certainty. Updatingdoes not change the firm’s beliefs, so it has to adjust in the second period.However, it is better for the firm to adjust in the first period rather than wait untilthe second period given that the government plays NB in the first period withcertainty.Thus, in a pooling equilibrium, the firm adjusts in the first period and thegovernment commits credibly to playing NB, irrespective of its actual value ofF.

2.3. Partial Separation

Now consider the case when

2F1

F2 2 F1. s. (1)

The firm’s payoff if it adjusts,s, is smaller than its expected payoff if it does notadjust. The pooling equilibrium collapses. If any government plays NB in thefirst period, the firm does not adjust in the second one. Therefore, the governmentwith F , 0 would prefer to play B in the first period. However, if anygovernment withF , 0 plays B in the first period and the firm always adjustsin the second period whenever it observes NB in the first one, i.e., the govern-ment reveals completely its type in the first period, a government withF , 0 hasan incentive to conceal its true type by playing NB and inducing adjustment.

Therefore, in equilibrium, the firm should be able to update its beliefs aboutthe government’s type in period 0. This is possible if there exists a thresholdH , 0 such that a government withF , H plays B and a government withF $ H plays NB.8 If the firm observes B in the first period, it plays NA in thesecond one and is bailed out with certainty. If NB is observed, the firm revises

8 If F 5 H, the government is indifferent between B and NB and can mix them with anyprobability. The government’s decision in that case does not affect the firm’s strategy because itsapriori probability is 0.

FIG. 1. The two-period game in extensive form. Payoffs of the firms are on the upper line. Payoffsof the government are on the lower line.


its expectations ofF. In the latter case, it mixes A and NA strategies in thesecond period with probabilitiesa and 12 a, respectively.

To mix A and NA in the second period, the firm has to be indifferent betweenthem. Hence,

2H

F2 2 H5 s. (2)

Note thatF 5 H is a threshold if the government withF 5 H is indifferentbetween B and NB. Therefore,

H 1 ga 5 0. (3)

Solving (2) forH, we get

H 52F2s

1 2 s. (4)

Solving (3) fora, and taking into account (4), we obtain

a 5F2s

~1 2 s!g. (5)

Obviously, for the partially separating equilibrium to occur, it is necessary thatH . F 1. Lemma 1 establishes the equivalence ofH . F 1 and (1).

LEMMA 1. H . F 1 if and only if condition(1) is satisfied.

For the partially separating equilibrium to occur, it is essential thata # 1.However, this condition always holds provided thatF 1 1 g $ 1. Thus, we havean important result. Even if the beliefs about the government’s type are unfa-vorable, and the firm does not adjust in the first period, it may adjust in the secondperiod with probabilitya . 0. Anticipating this possibility, a weak governmentwith F , 0 refuses to bail out the firm in the first period, even though it woulddo so in the second one. The firm does not adjust in the first period if its expectedpayoff from playing NA in the first period is greater than its payoff from playingA. That is,

p1~A! 5 s 1 d ,~1 1 d!~H 2 F1!

F2 2 F11

ds~F2 2 H!

F2 2 F15 p1~NA! (6)

LEMMA 2. If (6) is satisfied, then(1) is satisifed as well.

If condition (1) is satisfied but condition (6) is violated, the firm adjusts in thefirst period with certainty. However, this is not the pooling equilibrium, despitethe fact that the outcome is the same as in the pooling equilibrium, because theoff-equilibrium strategies and beliefs-revision rule are different. Only govern-

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ments withF $ H are credibly committed to playing NB in the first period, andupon observing NB, the firm revises its beliefs using the rule of the partiallyseparating equilibrium.

The analysis of the equilibria presented in Sections 2.2 and 2.3 is summarizedin Proposition 1:

PROPOSITION1. If (1 1 d)(H 2 F1)/(F2 2 F1) 1 ds(F2 2 H)/(F2 2 F1) . s 1 d,the sequential equilibrium of the game is a partially separating one: the firm doesnot adjust in the first period; a government with F, H 5 2F 2s/(1 2 s) bailsout the firm; a government with F$ H 5 2F 2s/(1 2 s) does not. Uponobserving NB, the firm revises its beliefs about the government’s type; it believesthat the government’s type is uniformly distributed over the interval[H, F 2]. Inthe second period, the firm mixes its strategies A and NA with probabilitiesa 5F 2s/((1 2 s)g) and1 2 a, respectively. If the firm does not adjust, a governmentwith F , 0 bails out the firm, and a government with F$ 0 does not.

Upon observing B in the first period, the firm believes that F,H 5 2F 2s/(1 2 s) , 0 and does not adjust in the second period.

If 2F 1/(F 2 2 F 1) # s, the firm plays A in the first period with certainty andany government plays NB in the first period upon observing NA.

If 2F 1/(F 2 2 F 1) . s butp 1(NA) # p 1( A), the sequential equilibrium isa partially separating one. The firm adjusts in the first period with certainty, butonly a government with F$ H plays NB upon observing NA in the first period.

LEMMA 3.

~p1~A! 2 p1~NA!!

s. 0;

~p1~A! 2 p1~NA!!

F1. 0;

~p1~A! 2 p1~NA!!

F2. 0;

~p1~A! 2 p1~NA!!

d. 0

In words, an increase in the firm’s discount factor,d, a reduction in the firm’sadjustment cost, 12 s, and/or a higher initial probability that the government istough (F $ 0) increase the likelihood that (6) is violated and makes immediateadjustment more likely. The only counterintuitive effect comes from the gov-ernment’s discount factor,g, which is not present in (1) and (6). Therefore, aslong asF 1 1 g . 0, a further increase ing does not make adjustment in the firstperiod more likely. Moreover, in the second period, the probability of adjust-ment,a, is negatively related to the government’s discount factor. A highergimplies that the government is more strategic and makes the firm more suspiciousof the government’s actions. When the firm observes NB in the first period, ahigherg implies a higher probability that the government is actually soft (F , 0)but mimics the behavior of a tough government in order to induce adjustment.


3. AN EXTENSION OF THE BASIC MODEL: AT-PERIOD GAME

A detailed derivation of the equilibrium of a game with more than two periodsis presented in the Appendix. Similar to the two-period game, two qualitativelydifferent equilibria are possible, a pooling equilibrium, in which the firm adjustsimmediately, and a partially separating equilibrium, in which the firm does notadjust in the first period and the war of attrition begins. In this war of attrition,the firm mixes its strategies in each period, provided that it has not been bailedout. There exists a sequence of thresholdsH 1, H 2, . . . HT21 such thatH 1 , H 2 , . . . , HT21 , HT 5 0. In periodi , a government withF , Hi

plays B and a government withF $ Hi plays NB. Therefore, the firm updatesits beliefs about the government type.

Similar to the two-period game, the decision of the representative firm whetherto adjust in the first period depends on whether condition (7) holds or not.

p1~NA! 2 p1~A! 5 ~1 1 d!H 1 2 F1

F2 2 F11 sd

F2 2 H 1

F2 2 F1. s 1 d (7)

The equilibrium of theT-period game is summarized in Proposition 2.

PROPOSITION2. If (1 1 d)(H 1 2 F 1)/(F 2 2 F 1) 1 sd(F 2 2 H 1)/(F 2 2 F 1) .s 1 d, the sequential equilibrium of the game is a partially separating one: thefirm does not adjust in the first period. Starting from the second period, the firmupdates its beliefs about the actual government’s type: if it has not been bailedout, it believes at the end of period i that the government’s type is uniformlydistributed over the interval[Hi, F2], where Hi 5 (1 1 d 2 ds)Hi11/(1 2 s) 2(s 1 d 2 ds) F 2/(1 2 s), 1 # i # T 2 2, HT21 5 2sF2/(1 2 s). In periodi , the firm mixes A and NA with positive probabilities,a i and 1 2 a i ,respectively,9 where a i 5 2Hi21/¥ t51

t5T2i11 g t. In period i, the governmentplays NB if F$ Hi and B if F , Hi .

If the firm is bailed out in period i1 1, the firm believes that F, Hi andit does not adjust thereafter. The government bails it out with certainty.

If H 1 # F 1, the sequential equilibrium is a pooling one: the firm plays A inthe first period with certainty and any government plays NB in the first periodupon observing NA.

If H 1 . F 1 but p 1(NA) # p 1( A), the firm adjusts in the first period withcertainty but only a government with F$ H 1 is committed to playing NB uponobserving NA in the first period.

9 Throughout the paper, it is assumed that the conditiona i # 1 is not binding. A brief discussionof the binding case is relegated to the Appendix. A complete derivation is available from the authorupon request.

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LEMMA 4.

H i

s, 0;

H i

F2, 0;

H i

d, 0;

~p1~A! 2 p1~NA!!

s. 0;

~p1~A! 2 p1~NA!!

F1. 0;

~p1~A! 2 p1~NA!!

F2. 0;

~p1~A! 2 p1~NA!!

d. 0

In words, the higher is the discount factor of the firm,d, the lower is theadjustment cost, 12 s, and the higher areF 1 and F 2, the more likely isimmediate adjustment. The planning horizon also affects critically the likelihoodof immediate adjustment. A higherT lowers H 1 and thus makes the partiallyseparating equilibrium less likely. AsT approaches infinity,H 1 approachesminus infinity; therefore the partially separating equilibrium becomes impossible.

Figures 2 and 3 present numerical examples of the partially separating equi-librium for particular parameter values:T 5 7, g 5 0.9; s 5 0.1; d 5 0.4;

FIG. 2. Bailout thresholds in a partially separating equilibrium without signaling.


F 1 5 210, F 2 5 0.2, andF 2 5 0.4.Figure 2 illustrates the thresholdsH 1, . . . ,H 7. Threshold values are rising; i.e., every period a government of a certain typedrops out of the war of attrition by bailing out the firm if it has not yet adjusted.In the last period, the thresholdH 7 5 0; i.e., any government withF , 0 bailsout the firm. The thresholds forF 2 5 0.4 are lower than the thresholds forF 2 50.2 in each period except the last one; see Lemma 4.

Figure 3 shows the cumulative probabilities of adjustment. In the first periodprobability is 0, because there is no adjustment in the first period in the case ofthe war of attrition. Beginning with the second period, the representative firmadjusts with a positive probability provided that it has not been bailed out. Hence,the cumulative probability of adjustment is rising. The probability of adjustmentfor F 2 5 0.2 is always lower than forF 2 5 0.4 because it is negatively relatedto the bailout threshold; see Proposition 2. The lower thresholdH implies that thegovernment withF 5 H is more averse to the firm’s failure and a higherprobability of adjustment is needed to induce it to postpone the bailout.

FIG. 3. Cumulative probability of adjustment in a partially separating equilibrium withoutsignaling.

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4. AN IMF LOAN AS A SIGNALING DEVICE

A distinguishing feature of the model discussed above is that the representativefirm moves first; it decides whether to adjust or not. The tough government doesnot have an opportunity to signal its type before the firm moves. The followingextension of the model incorporates a signaling technology that helps the toughgovernment ensure adjustment.

4.1. One-Period Game

Consider the following one-period modification of the game outlined inSection 2.1. At the beginning of the game, the government has an option ofjoining an international financial institution, e.g., the IMF, and applying for aloan. It is eligible for the loan disbursement at the end of the game only if it sticksto the stabilization policy, i.e., only if it does not bail out the firm. Uponobserving the government’s choice, the representative firm decides whether toadjust or not. If it does not adjust, the government can bail it out. However, if thegovernment chooses to bail the firm out, it violates the IMF rules and becomesineligible for the loan.

We assume that the IMF is organized as a club. When a country joins the IMF,it has to make an initial contribution, i.e., pay an entrance fee. We assume thatthe IMF rules determine both the size of this contribution,X, and the size of theloan that the country can get at the end of the period,eX.10 We refer toX as thecountry’s stake in IMF ande as a remuneration ratio, and we assume thate . 1.The last assumption is that the firm would not adjust in the absence of IMF loanso that2F 1/(F 2 2 F 1) . s.

Figure 4 shows the one-period game in extensive form. Obviously, onlygovernments withF 1 eX $ 0 or F $ 2eX will play NB upon observing NA.Therefore, two equilibria are possible, the pooling equilibrium, in which all

10 All variables are measured in utility units; i.e., it is assumed that the initial contribution has autility 2 X for the government. The disutility of the contribution includes the necessity to complywith the IMF conditions.

FIG. 4. One-period game with signaling in extensive form.


governments apply for IMF loans, and the partially separating one, in whichsome governments apply and some do not.

The pooling equilibrium occurs when

s $2eX 2 F1

F2 2 F1. (8)

In this case, the firm adjusts with certainty upon observing the IMF loan contracteven if any government joins the IMF and no new information is conveyed aboutthe government’s actual type so that the firm’s beliefs do not change. However,because the firm is expected to adjust with certainty, any government will join theIMF; i.e., it will commit credibly to the tough policy.

If

s ,2eX 2 F1

F2 2 F1, (9)

the pooling equilibrium collapses. The firm will not adjust unless it gets newinformation about the type of the government. If the firm does not adjust, nogovernment withF , 2eX will benefit from joining the IMF. However, the fullseparation cannot be an equilibrium either. If this were the case, any governmentwith F , 2eX would find it optimal to mimic the behavior of the toughgovernment withF $ 2eX.

Therefore the equilibrium is a partially separating mixed strategy one. Anygovernment withF . 2eX will join the IMF and receive the loans, as will sometypes withF , 2eX. The firm revises its beliefs about the actual government’stype so that it becomes indifferent between playing A and NA. It plays eachstrategy with positive probabilitiesa and 12 a, respectively. These probabilitiesare determined in such a way that they make a government withF , 2eXindifferent between joining the IMF and revealing its weakness. The governmentdoes so with probabilitiesb and 12 b, respectively. Now,

s 5 b2eX 2 F1

F2 2 F1(10)

2X 1 a~1 1 eX! 5 0. (11)

Therefore,

a 5X

1 1 eX(12)

and

b 5s~F2 2 F1!

2eX 2 F1. (13)

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Obviously, this partially separating equilibrium exists only ifb , 1 ors(F 2 2 F 1)/(2eX 2 F 1) , 1. However, this condition is equivalent to (9).

4.2. A T-Period Game

Now assume that the game lasts forT periods. At the beginning of the firstperiod, the government decides whether to join the IMF and make the initialcontribution,X, or not. If it chooses to join the IMF, it is eligible to borroweXat the end of each period provided that it has not bailed out the representativefirm. If it does not join the IMF and if it bails out the firm, it reveals its weakness.Therefore, the firm plays NA thereafter and the government bails it out withcertainty. The assumption of equal payments after all periods is made fortechnical simplicity, but it also fits the usual IMF practice. We also assume that2X 1 eX ¥ t51

T21 g t . 0 so that the tough government always joins the IMF.The detailed derivation of the equilibrium strategies is presented in the

Appendix. Here, we summarize the analysis of the equilibrium in Proposition 3.Analogously to the model without signaling, the equilibrium involves a sequenceof thresholdsL 1, . . . , LT, such thatL 1 , L 2 , . . . , LT , 0. In periodi , agovernment withF , Li plays B, and a government withF $ Li plays NB.

PROPOSITION 3. The sequential equilibrium of the game is a pooling one, ifF1 $ L1, where Li 5 (1 1 d 2 ds)Li11/(1 2 s) 2 (s 1 d 2 ds)F2/(1 2 s)for i , T 2 1, LT21 5 2F 2s/(1 2 s) 2 eX/(1 2 s), and LT 5 2eX. In thiscase, any government joins the IMF and plays NB upon observing NA in the firstperiod. The firm adjusts in the first period with certainty.

If F 1 , L 1 but F1 $ (1 1 d 2 ds) L 1/(1 2 s) 2 (s 1 d 2 ds) F 2/(1 2s),any government joins the IMF and the firm adjusts with certainty. However,only a government with F$ L 1 plays NB upon observing NA in the firstperiod.

The sequential equilibrium of the game is a partially separating one,if F 1 , (1 1 d 2 ds) L 1/(1 2 s) 2 (s 1 d 2 ds) F 2/(1 2 s). Only agovernment with F$ L 1 joins the IMF with certainty. A government withF , L1 does so with probabilityb 5 (s1 d 2 ds)(F2 2 L1)/((12 s)(L1 2 F1)). Uponobserving the government joining the IMF, the firm updates its beliefs about thegovernment’s type using Bayes’ rule and mixes its strategies A and NA withprobabilitiesa1 and1 2 a1, respectively, wherea1 5 X/((1 1 eX) ¥t50

t5T21 gt). Uponobserving that the government does not join the IMF (NIMF), the firm believes thatF , L1 and does not adjust thereafter. In period i, i 5 1, . . . ,T, the government bailsout the firm if and only if F, Li. In period i, i 5 2, . . . ,T, the firm updates its beliefsabout the government’s type and mixes its strategies A and NA with probabilitiesai

and1 2 ai, respectively, whereai 5 (2Li21 2 eX)/((1 1 eX) ¥t51t5T2i11 gt), provided

that it has not been bailed out before. Otherwise the firm believes that F, Li anddoes not adjust thereafter.


LEMMA 5.

L1

s, 0;

L1

d, 0;

L1

F2, 0;

L1

e, 0;

L1

X, 0

In words, all main parameters of the model affect the likelihood of the poolingequilibrium with immediate adjustment in an intuitive way.

LEMMA 6.

a1

e, 0;

a i

g, 0

A higher reward for playing NB and being more strategic, i.e., a higherg, donot increase the probability of immediate adjustment. It is easy to show that theeffect of an increase ine on a i for i . 1 is ambiguous. The firm is aware of thehigher benefits to the government from its adjustment, so it is more suspiciousthat the government is actually weak but bluffing.

LEMMA 7.

b

X. 0;

b

F1. 0;

b

e. 0;

b

F2. 0

The probability that the weak government bluffs is positively related to thefirm’s beliefs about its type, its stake in IMF, and the remuneration ratio.

The last important observation is thata1 approaches zero whenX goes to zero.In other words, to be taken seriously, the signal should be costly. When the initialcontribution becomes small, the firm does not consider joining the IMF to be amanifestation of the government’s commitment to the tough policy.

Figure 5 contrasts bailout thresholds of the partially separating equilibriumwith signaling,Li , to the bailout thresholds of the equilibrium without signaling,Hi , for the following values of parameters:T 5 7, g 5 0.9, s 5 0.1, d 5 0.4,F2 5 0.2; F1 5 210; X 5 1; e 5 0.3. In all periods,Li , Hi ; i.e., the IMFconditional lending induces weak governments of certain types to postponebailout.

Figure 6 contrasts cumulative probabilities of adjustment for the equilibriawith and without signaling. In the equilibrium with signaling, adjustment ispossible already in the first period. In later periods, the probability of adjustmentis also higher in the equilibrium with signaling because the bailout thresholds arelower. A government that is more averse to the firm’s failure must be induced topostpone bailout.

Figure 7 shows the nonmonotonous relationship between the remunerationratio, e, and the probability of immediate adjustment. Here,e is the lowest value

MAXIM NIKITIN680

of the remuneration ratio that induces the tough government to join the IMF, i.e.,2X 1 eX ¥ t50

t5T21 g t 5 0. When e is increasing frome, the probability ofimmediate adjustment is falling as Lemma 6 suggests. However, whene crossesthe threshold levele#, there is a switch from the partially separating equilibriumto the pooling one, in which the firm adjusts in the first period with certainty.

5. DISCUSSION OF THE MODEL

5.1. Discussion of the Basic Model without Signaling

A few interesting features of this model explain the stylized facts of arrearscrises and adjustment in transition economies. The model allows for a dramaticshift in the adjustment behavior of firms following a marginal change in exog-enous parameters, in particular, when the sign of inequality (7) changes. There-fore, it explains the striking difference in adjustment behavior of firms indifferent countries in transition.

To determine whether a transition economy falls into an arrears crisis oradjusts quickly, one has to take into account the firm’s perceptions of the

FIG. 5. Bailout thresholds in a partially separating equilibrium with and without signaling.


government’s type, i.e.,F 1 andF 2, the firm’s discount factor,d, the adjustmentcost, 12 s, and the expected office term of the current government,T. Compare,for example, Poland and Russia. Earlier, we argued that the initial politicalconditions for reforms were not more favorable in Poland than in Russia. In otherwords, the actual value ofF for the Russian government may have been as highas in Poland. However, the firm’s perceptions of the government’s capability toenforce adjustment and sacrifice current output may have been different. In theformer Soviet Union, enterprise directors and Gosplan bureaucrats treated theeconomy as a Leontief input–output table. They understood macroeconomicpolicy management as a technical procedure of allocating material inputs andoutputs. Therefore, the idea of financial stabilization irrespective of input–outputconsiderations seemed strange and not credible to them.11

On the contrary, Poland had some experience with market reforms in the1970’s and 1980’s. This country also experienced a disruption of input–output

11 One should bear in mind that virtually all directors and enterprise managers were trained asengineers and did not have any knowledge of economics.

FIG. 6. Cumulative probability of adjustment in a partially separating equilibrium with andwithout signaling.

MAXIM NIKITIN682

chains and substantial output decline from 1980 to 1982. Hence, the govern-ment’s stabilization policy was more understandable and, therefore, more cred-ible to Polish managers (in terms of the model, Poland had higher values ofF 1

and F 2) than it was to Russian managers. An additional factor explaining thecontrast between the arrears and adjustment behavior of Polish and Russian firmsmay have been the difference in adjustment costs. Because of Poland’s experi-ence with market reforms and its closer historical and geographical ties with theWest, Polish enterprises could more easily reorient their production towardWestern markets.12

The adjustment cost argument also applies to Czechoslovakia and Hungary,but not to the Baltic states, where the cost of adjustment could have been evenhigher than in Russia, as they faced a very strong negative supply shock in 1992.However, the Baltic governments made it clear they were not going to bail outlarge state-owned enterprises of the military industry with a predominantlyRussian-speaking labor force. For political reasons, this pledge was perfectlycredible. The enterprise managers did not have any hope for subsidies, so theydid their best to adjust. In terms of the model,F 1 . 0 in the Baltic states.

The planning horizon, or expected office term of the current government, wascertainly shorter in Russia and Romania than in most successful transitioneconomies. In Russia, President Yeltsin had emergency powers to implementmarket reforms for one year only, and nobody expected Gaidar’s government tosurvive in office after that. In Romania, the reformist governments of Roman and

12 In fact, Polish manufacturing exports were booming already in 1990 and, unexpectedly, thecountry had a positive trade balance that year.

FIG. 7. The relationship between the remuneration ratio and the probability of immediateadjustment in the equilibrium with signaling.


Stolojan also stayed in office one year each. In Czechoslovakia and the Balticstates the governments who started comprehensive reforms remained in office forat least two years, and those in Hungary remained for even four years. Our modelpredicts that an increase in the planning horizon increases the likelihood ofimmediate adjustment.

The model accounts for other paradoxes of the arrears and adjustment behaviorof firms in transition economies. In the partially separating equilibrium, the firmmixes its strategies. This result explains why enterprises may switch fromnonadjustment to adjustment irrespective of, and often despite, exogenous po-litical conditions. This is exactly what happened in Russia from 1992 to 1994. Aclearance of interenterprise arrears with Central Bank credits in August throughOctober 1992 and a remarkable relaxation of monetary and fiscal policy signifieda defeat for Gaidar, the provisional prime minister of Russia, who initiatedcomprehensive market reforms in the country. In December 1992, he was forcedto resign from the government, along with most of his team. Paradoxically, thesepolitical changes were not accompanied by a new round of arrears accumulation.The stock of overdue payables of industrial firms fell from 23% of GDP at itspeak in Summer 1992 to 3% in October 1992, and it hovered at that level untilthe end of 1993 (Afanas’ev et al., 1995, p. 56). Many firms started demandingprepayment or cash on delivery from their customers and cut back their deliveriesto buyers who failed to pay promptly. Most enterprises changed their output mixin response to changes in the composition of demand. Fan and Schaffer (1994),using data from enterprise surveys and interviews with senior management staffin late 1992 and early 1993, noted that “it is perhaps surprising, given the eventsof the 1992 arrears crisis and its resolution, that . . . many enterprises, especiallythe small and medium-sized ones, are now managing their payables and receiv-ables in a more-or-less proper, market-oriented fashion” (Fan and Schaffer, 1994,p. 173).

In January 1994, reformers in Russia suffered another setback. Proreformparties lost parliamentary elections in December 1993 and two key reformers,deputy prime minister Gaidar (reappointed in the Fall 1993) and the financeminister Fedorov, left the government. The government showed its weakness inenforcing hard budget constraints. For example, in early 1994, it introduced theso-called “30:70 rule,” which allowed firms with arrears to defer payment of partof their taxes and use the money to pay wages instead. However, a considerabletightening of monetary policy in late 1993 and early 1994 did not lead to anexplosive growth of arrears as it did in 1992. Overdue payables of industrial firmsreached just 5% of GDP by the mid-1994 (Afanas’ev et al., 1995, p. 57). In 1994,total overdue trade credit in Russia was still below 10% of GDP, i.e., lower thanin most Western countries (Alfandari and Schaffer, 1996, p. 106). In other words,firms responded in a market way to the monetary contraction and reduced theiroutput. In the first quarter of 1994, real GDP (deflated by the producer priceindex) fell by 34%. Adjustment of firms allowed the Central Bank and the

MAXIM NIKITIN684

government to avoid arrears clearance and rendered the disinflation successful. Inthe first half of 1994, the CPI index increased by 72%, versus 196% in the secondhalf of 1993.13

The adjustment of firms in Russia made a gradual tightening of the monetarypolicy possible. The annual inflation rate fell to 22% in 1996, from 2260% in1992. In contrast, in the former Yugoslavia, the systematic inability of themonetary authorities to impose hard budget constraints on enterprises and avoidan accommodating monetary expansion led to an almost continuous increase inthe inflation rate since the first oil shock in the mid-1970’s. In 1989 it exceeded400% per year.

The experiences of Romania and Bulgaria also showed that the adjustmentbehavior of state-owned enterprises may improve even when the governmentlacks the credibility to impose hard budget constraints. In Romania after thearrears were cleared with Central Bank credits at the end of 1991, they rose again,but their stock never reached its prebailout level. In June 1992, the real stock ofarrears was still less than one-fourth of its prebailout level (Rostowski, 1994, p.10). In Bulgaria, the incidence of interenterprise arrears was also falling from1992 to 1993, even though the proreform right-wing government was ousted inOctober 1992 and the new government was critically dependent on the excom-munists for support. The stock of interenterprise arrears in industry was just 4.4%of GDP in 1992 (Dobrinsky, 1994, p. 47). The average collection period declinedfrom 86 days in 1991 to 52 days in 1992. In June 1993, the share of arrears inpayables of industrial enterprises remained at 40%, the same as a year before,while the share of arrears in receivables dropped to 24.1% from 48.4%.14

The model presented above allows for persistent nonadjustment. If for somereason economic agents strongly suspect that the government is capable ofinflating, i.e., the values ofF 1 andF 2 are low, and the representative firm doesnot adjust in the first period, the government cannot convince the firm that it istough and assure the adjustment. With some positive probability, the firm will notadjust at all. The Russian experience from 1993 to 1995 showed that some,especially large, enterprises continued to accumulate overdue payables and notpursue their debtors, at least not all of them. Many continued delivery on creditto traditional customers. One reason for this is an inability to find an alternative

13 There is an alternative explanation of the adjustment for Russian firms in 1994 that is consistentwith the model. The new game started after the parliamentary elections in December 1993. Enter-prises chose to adjust immediately because privatization raised the firms’ discount factor and thegovernment was supposed to stay in office for two years, until the new elections.

14 One can argue that the low level of interfirm arrears in Bulgaria was related to the availabilityof soft loans from the state banks. Although bank financing was indeed the major source of the softbudget constraint for many big enterprises, the credit policy was fairly restrictive. The average reallending rate was 36% per year between 1992 and 1995 (Avramov and Sgard, 1996, p. 89). The realstock of bank credit to industrial enterprises fell by 51% between 1992 and 1995. Therefore, onlyselected firms, usually big and well-connected ones, could get soft loans systematically.


customer because of narrow specialization. Another reason is the so-called“director’s ethic,” which determines the special treatment of traditional part-ners.15 Poor corporate control also contributed to the persistence of overduereceivables. Top managers could arrange the sale of output to private firmsowned by their cronies (or relatives) and pocket the proceeds (Bekker, 1995).Finally, some firms had overdue receivables in order to maintain a zero balanceon their bank account and avoid paying taxes.

Finally, the model explains why a soft government, i.e., a government not fullycommitted to stabilization, like the government of Romania in 1991, can chooserationally to embark on a stabilization program. This happens because, inequilibrium, the representative firm mixes its strategies, i.e., with a positiveprobability that it adjusts before the government is forced to bail it out.

5.2. Policy Implications of the Signaling Model

The model sheds some light on the problem of the low effectiveness ofconditional lending to transition economies. All these countries joined the Inter-national Financial Institutions (IFIs) at the beginning of transition and $15 b. ofIMF loans was disbursed to the region from 1990 to 1995. There are two oppositeperspectives on why IMF involvement was not effective. Sachs (1993, 1994)argues that the involvement of the West, including the IFIs, in the transitionreforms was simply not sufficient and should have been increased significantly,especially in Russia. Given the dramatic real devaluation of their currencies, arelatively small amount of external aid, some $10 b. a year in the case of Russia,would have made a big difference. The opposite view is that the role of foreignaid in transition reforms can be only marginal.16 Hence, the problems that Russia,Romania, and other transition laggards experienced could not have been resolvedby aid and soft loans from the West.17

Many aspects of IMF involvement in the transformation of the former socialistcountries are beyond the scope of the present paper. However, our model doessuggest that the impact of IMF conditional lending on the adjustment of indi-vidual firms to the government’s stabilization policy is not straightforward. Onthe one hand, a sufficiently large amount of a forthcoming IMF loan can inducea switch from the partially separating equilibrium to the pooling one, in which therepresentative firm adjusts in the first period with certainty and the war ofattrition does not unravel. On the other hand, if the initial beliefs of the firm aboutthe government’s type are unfavorable or if the amount of the prospective loan

15 Directors of state-owned, or formally state-owned, enterprises consider it unethical to stopdeliveries to their traditional state-owned customers because this would aggravate their troubles inpursuit of the short-term financial result (Dolgopyatova and Evseeva, 1995).

16 This was one of the Ten Commandments advocated by Vaclav Klaus, the former prime ministerof the Czech Republic.

17 See Gomulka (1995) for a discussion of the IMF’s role in the reforms in Russia and Poland.

MAXIM NIKITIN686

is not large enough and the war of attrition begins, the probability of immediateadjustment is negatively related to the remuneration ratio. In other words, themore money is promised to a reformist government, the higher the probabilitythat the firm decides to test its resolve to enforce adjustment. Moreover, theeffectiveness of signaling depends critically on its cost to the government. Themore the government has to contribute to the IMF,18 the higher the probability ofthe firm’s adjustment in the first period. In contrast, if the IMF tries to alleviatethe hardships of transition and does not demand a significant entrance fee or anyother painful measure before the firm decides whether to adjust, immediateadjustment becomes unlikely.

6. CONCLUSIONS

Based on a dynamic game theoretic model of an arrears crisis in a transitioneconomy, we argue that payments arrears have been a manifestation of the lowcredibility of the disinflation policy, i.e., strong prior beliefs that the governmentwill eventually bail out firms that have fallen into arrears. However, the decisionof the representative firm whether to adjust to the government disinflation policyor to fall into arrears depends on several other variables, including the adjustmentcost, the length of the planning horizon, and the discount factor. A war-of-attrition type game of incomplete information between a representative firm anda government explains a range of paradoxical phenomena observed in transitioneconomies. In particular, it explains why a soft government, i.e., a governmentnot fully committed to stabilization, can choose rationally to embark on astabilization program. The paper also explains the persistence of nonadjustmentin spite of a government’s commitment to stabilization and firms switching fromnonadjustment to adjustment without observing any change in the government’sbehavior. We argue that the ability of a government fully committed to stabili-zation to signal its commitment by applying for an IMF loan is limited. Undercertain conditions, the probability of immediate adjustment is negatively relatedto the size of the forthcoming IMF loan.

APPENDIX

A.1. The Sequential Equilibrium of the T-Period Model

For a game with more than two periods, the equilibrium can be found bybackward induction. Consider first the case in which the firm mixes A and NAin the last period. In order for that strategy to be an equilibrium, the firm hasto be indifferent between A and NA; therefore, it should have the same beliefsabout the government’s type as after the first period of the two-period game.

18 A painful market transition measure, e.g., a drastic cutting back on budget subsidies, cansubstitute for the monetary payment.


Hence, agovernment withF , HT21 5 2F2s/(1 2 s) should bail out the firm inperiodT 2 1, and a government withF $ HT21 should play NB. The representativefirm mixes its strategies in periodT and plays A with probabilityaT 5 F2s/((1 2s)g).

Such a strategy of the government can be an equilibrium in periodT 2 1 onlyif the firm mixes both strategies in this period; otherwise the government bails itout in the previous period. Therefore, the firm must be indifferent between thestrategies:

pT21~A! 5 s 1 d 5 ~1 1 d!H T21 2 H T22

F2 2 H T22 1 dsF2 2 H 2

F 2 2 H T22 5 pT21~NA!.

(14)

Solving Eq. (14) forHT22, we derive

H T22 5 F2

22s 2 d 1 sd 1 s2

~1 2 s! 2 , F2

2s

1 2 s5 H T21. (15)

As long as 0, s, 1,22s2 d 1 sd 1 s2 , 2s(1 2 s) and, therefore,HT22 , HT21.The partially separating equilibrium for all preceding periods can be calculated

sequentially in a similar way. There exists a sequence of thresholdsH1, H2, . . . ,HT21

such that in periodi the government bails out the firm if and only ifF , Hi. Thesethresholds can be computed sequentially. In every periodi . 1, the firm should beindifferent between playing A and NA provided that it has not adjusted before andit has never been bailed out. Hence, we have

s 1 Ot51

T2i

d t 5 ~1 1 Ot51

T2i

d t!H i11 2 H i

F2 2 H i 1 d~s 1 Ot51

T2i21

d t!F2 2 H i11

F2 2 H i . (16)

Equation (16) collapses to

s 1 d 5 ~1 1 d!H i11 2 H i

F2 2 H i 1 dsF2 2 H i11

F2 2 H i . (17)

We can solve (17) forHi as a function ofHi11 and the parameters of initialconditions:

H i 51 1 d 2 ds

1 2 sH i11 2

s 1 d 2 ds

1 2 sF2. (18)

As (1 1 d 2 ds)/(1 2 s) . 1 and (s 1 d 2 ds)/(1 2 s) . 0, Hi , Hi11

and, moreover,H 1 becomes infinitely large in absolute value asT goes to infinity.The probabilities that the firm plays A and NA in periodi 1 1, ai11 and 12 ai11,

respectively, can be computed from the condition that a government withF 5 Hi

should be indifferent between playing B and NB in periodi:

MAXIM NIKITIN688

H i 1 a i11 Ot51

T2i

g t 5 0. (19)

Or,

a i11 52H i

¥ t51T2i g t . (20)

This partially separating equilibrium can occur only if

H 1 . F1. (21)

If condition (21) is violated, any government will credibly commit to play NBupon observing NA in the first period. Hence, the pooling equilibrium will occurwith the firm adjusting with certainty in the first period.

The firm decides whether to adjust in the first period or not depending on itsexpected payoffs. If

p1~NA! 5 Ot50

T21

d tH 1 2 F1

F2 2 F11 ~sd 1 O

t52

T21

d t!F2 2 H 1

F2 2 F1. s 1 O

t51

T21

d t 5 p1~A!,

(22)

it does not adjust in the first period and the war of attrition between thegovernment and the representative firm begins. Inequality (22) reduces to

~1 1 d!H 1 2 F1

F2 2 F11 sd

F2 2 H 1

F2 2 F1. s 1 d. (7)

LEMMA 8. If condition (7) is satisfied, condition(21) is satisfied as well.

Lemma 8 implies that condition (7) is the only condition for the partiallyseparating equilibrium with nonadjustment in the first period. If condition (21) issatisfied but (7) is violated, the firm adjusts immediately but separation remainsas an off-equilibrium strategy. However, the equilibrium outcome, i.e., immedi-ate adjustment, is the same as in the pooling equilibrium.

A.2. The Sequential Equilibrium of the Two-Period Model with Signaling

The pooling equilibrium occurs if

s $2eX 2 F1

F2 2 F1. (23)

In the last period, the firm adjusts even if has not received any new informationabout the government’s type. Therefore, any government joins the IMF and


credibly commits to playing NB upon observing NA in the first period so that thefirm adjusts immediately.

If condition (23) is violated, there exists a thresholdL1, such that a governmentwith F $ L1 does not bail out the firm in the first period, but a government withF , L1 does. Hence, a partially separating equilibrium may occur. Upon observingNB in the first period, the firm revises its beliefs about the government’s type so thatit becomes indifferent between playing A and NA in the second period. It mixes themwith probabilitiesa2 and 12 a2, respectively, so that the government withF 5 L1

is indifferent between playing B and NB in the first period.

s 52eX 2 L1

F2 2 L1(24)

L1 1 eX 1 a2g~1 1 eX! 5 0 (25)

Using (24) and (25) to solve forL 1 anda2, we derive

L1 5 2sF2

1 2 s2

eX

1 2 s(26)

a2 5s~F2 1 eX!

~1 2 s!g~1 1 eX!. (27)

Now we analyze the equilibrium of the game in the first period. Two cases arepossible. First, a partially separating equilibrium in which any government withF , L 1 is indifferent between joining the IMF and revealing its weakness mayoccur. This determines the probability with which the firm plays A uponobserving the IMF strategy,

2X 1 a1~1 1 eX!~1 1 g! 5 0, (28)

or

a1 5X

~1 1 eX!~1 1 g!. (29)

The probability with which a government withF , L 1 bails out the firm isdetermined to make the firm indifferent between playing A and NA uponobserving IMF:

s 1 d 5b~L1 2 F1!

~F2 2 L1! 1 b~L1 2 F1!~1 1 d! 1 d

F2 2 L1

~F2 2 L1! 1 b~L1 2 F1!

(30)

b 5s 1 d 2 ds

1 2 s

F2 2 L1

L1 2 F1. (31)

MAXIM NIKITIN690

This equilibrium can occur only whenb , 1, i.e.,

F1 ,1 1 d 2 ds

s 1 d 2 dsL1 2

1 2 s

s 1 d 2 dsF2. (32)

In the second case, if condition (32) is violated, the equilibrium is still apooling one. Any government withF , L 1 joins the IMF and the firm adjustswith certainty upon observing IMF. However, only a government withF $ L 1 is credibly committed to playing NB upon observing NA in the firstperiod.

A.3. The Sequential Equilibrium of the T-Period Game with Signaling

A solution of theT-period game with signaling can be found using sequentialbackward induction. Consider first the case in which the firm mixes A and NAin the last period. In order to do that, the firm must be indifferent between themand, therefore, it should have the same beliefs about the government’s type asafter the first period of the two-period game. So,LT21 5 2F 2s/(1 2 s) 2eX/(1 2 s) and aT 5 s(F 2 1 eX)/((1 2 s)g(1 1 eX)). In other words, agovernment withF , LT21 should bail out the firm in periodT 2 1, and agovernment withF $ LT21 should play NB.

Such a strategy of the government can be an equilibrium in periodT 2 1 onlyif the firm mixes its strategies in this period. Therefore, it has to be indifferentbetween them, or

pT21~A! 5 s 1 d 5 ~1 1 d!LT21 2 LT22

F2 2 LT221 ds

F2 2 LT21

F2 2 LT225 pT21~NA!.

(33)

Using Eq. (33) to solve forLT22, we derive

LT22 51 1 d 2 ds

1 2 sLT21 2

s 1 d 2 ds

1 2 sF2. (34)

To support this equilibrium in the last two periods of the game, the governmentwith F 5 LT22 has to be indifferent between playing B and NB upon observingNA in period T 2 2.

LT22 1 eX 1 gaT21~1 1 g!~1 1 eX! 5 0 (35)

SubstitutingLT22 from (34) and (35), we have

aT21 52LT22 2 eX

g~1 1 g!~1 1 eX!. (36)

The partially separating equilibrium for all preceding periods can be calculatedsequentially in a similar way. There exists a sequence of thresholdsL 1, L 2, . . . ,


LT21 such that in periodi the government bails out the firm if and only ifF , Li . These thresholds can be computed sequentially. In every periodi . 1,the firm should be indifferent between playing A and NA given that it has notadjusted before and it has never been bailed out:

s 1 d 5 ~1 1 d!Li11 2 Li

F2 2 Li1 ds

F2 2 Li11

F2 2 Li. (37)

We can solve (37) forLi as a function ofLi11 and the parameters of initialconditions:

Li 51 1 d 2 ds

1 2 sLi11 2

s 1 d 2 ds

1 2 sF2. (38)

The probabilities of playing A and NA in periodi 1 1, a i11 and 12 a i11,respectively, can be computed from the condition that a government withF 5 Li

should be indifferent between playing B and NB in periodi ,

Li 1 eX 1 a i11~1 1 eX! Ot51

T2i

g t 5 0, (39)

or

a i11 52Li 2 eX

~1 1 eX! ¥ t51T2i g t . (40)

If

F1 $ L1, (41)

any government will credibly commit to playing NB upon observing NA in thefirst period, and the pooling equilibrium will occur with the firm adjusting withcertainty in the first period.

Otherwise, the partially separating equilibrium may occur. Analogously to thetwo-period game, two cases are possible. First, in the period any governmentwith F $ L 1 and, with a positive probability, a government withF , L 1 will jointhe IMF and apply for a loan. A government withF , L 1 is indifferent betweenjoining the IMF and revealing its weakness. The indifference condition deter-mines the probability with which the firm plays A upon observing IMF,

2X 1 a1~1 1 eX!~ Ot50

t5T21

g t! 5 0, (42)

MAXIM NIKITIN692

or

a1 5X

~1 1 eX!~¥ t50t5T21 g t!

. (43)

The probability with which a government withF , L 1 joins the IMF isdetermined in such a way as to make the firm indifferent between playing A andNA upon observing IMF,

s 1 d 5b~L1 2 F1!

~F2 2 L1! 1 b~L1 2 F1!~1 1 d! 1 ds

F2 2 L1

~F2 2 L1! 1 b~L1 2 F1!,

(44)

or

b 5s 1 d 2 ds

1 2 s

F2 2 L1

L1 2 F1. (45)

In the second case, ifb $ 1, or

F1 $1 1 d 2 ds

s 1 d 2 dsL1 2

1 2 s

s 1 d 2 dsF2, (46)

the equilibrium is still a pooling one. Any government withF , L 1 joins the IMFand the firm adjusts with certainty upon observing IMF. However, only agovernment withF $ L 1 is credibly committed to playing NB upon observingNA in the first period.

A.4. The Partially Separating Equilibrium When the Conditionai # 1 Is Binding

If

2H i

¥ t51T2i g t . 1,

whereHi is calculated using the recursive formula (18), the firm cannot adjustwith probability a i11 5 (2Hi /¥ t51

T2i g t) . 1 in period i 1 1. Hence,Hi 1¥ t51

T2i g t , 1 and a government withF 5 Hi will bail out the firm in the periodi . Therefore, the threshold in periodi is H# i 5 2¥ t51

T2i g t. If the firm observes NBin periodi , it adjusts with certainty in periodi 1 1. For the previous periodsj 51, . . . , i 2 1, bailout thresholdsBj are calculated recursively using formula (18)but takingB# i instead ofBi .

A.5. Proofs

Proof of Lemma 1.InequalityH . F 1 can be rewritten as2F 2s/(1 2 s) .F 1 or, taking into account thats , 1, 2F 2s 2 F 1 1 F 1s . 0. Given thatF 2 .F 1, (1) can also be rewritten as2F 2s 2 F 1 1 F 1s . 0. QED


Proof of Lemma 2.First, show that

p1~NA! 2 d ,2F1

F2 2 F1. (47)

To verify inequality (47), we rewrite it asH 2 F 1 1 dH 2 dF 1 1 dsF2 2dsH 2 dF 2 1 dF 1 , 2F 1. The denominator can be omitted becauseF 2 . F 1.The last inequality simplifies asH(1 1 d(1 2 s)) , dF2(1 2 s). The last conditionholds becauseH(1 1 d(1 2 s)) , 0, while dF2(1 2 s) . 0; p1(NA) 2 d . s andp1(NA) 2 d , 2F1/(F2 2 F1) guarantee that2F1/(F2 2 F1) . s. QED

Proof of Lemma 3.

H

s5 2F2

1 2 s 1 s

~1 2 s! 2 52F2

~1 2 s! 2

~p1~A! 2 p1~NA!!

s5 1 2

~1 1 d!~2F2!

~F2 2 F1!~1 2 s! 2

2d

F2 2 F1SF2 1

F2s

1 2 s2 s

2F2

~1 2 s! 2D5 1 1

F2

~F2 2 F1!~1 2 s! 2 . 0

~p1~A! 2 p1~NA!!

F15

~1 1 d!~F2 2 F1!

~F2 2 F1!2

2~1 1 d!~H 2 F1!

~F2 2 F1!2 2

ds~F2 2 H!

~F2 2 F1!2

5~1 1 d~1 2 s!!~F2 2 H!

~F2 2 F1!2 . 0

H

F25 2

s

1 2 s

Hence,

~p1~A! 2 p1~NA!!

F25 2

~1 1 d!~2s/1 2 s!~F2 2 F1! 2 ~H 2 F1!

~F2 2 F1!2

1 ds~1 1 ~s/1 2 s!!~F2 2 F1! 2 ~F2 2 H!

~F2 2 F1!2

52F2s~1 1 d~1 2 s!! 1 F1~1 1 d 2 s!

~1 2 s!~F2 2 F1!2 . 0

~p1~A! 2 p1~NA!!

d5 1 2

~H 2 F1! 1 s~F2 2 H!

F2 2 F1

. 1 2~H 2 F1! 1 ~F2 2 H!

F2 2 F15 0. QED

MAXIM NIKITIN694

Proof of Lemma 4.InequalitiesH1/s , 0, H1/F2 , 0, andH1/d , 0can be proven by induction. First, note thatHT21/s 5 2F2/(1 2 s)2 , 0,HT21/F2 5 2s/(1 2 s) , 0, andH1/d 5 0. For an arbitraryi , T 2 1,

H i

s5

2d~1 2 s! 1 ~1 1 d 2 ds!

~1 2 s! 2 H i11 11 1 d 2 ds

~1 2 s! 2

H i11

s

2~1 2 d!~1 2 s! 1 s 1 d 2 ds

~1 2 s! 2 F2

5H i11

~1 2 s! 2 11 1 d 2 ds

1 2 s

H i11

s2

F2

~1 2 s! 2 , 0

H i

F25

1 1 d 2 ds

1 2 s

H i11

F22

s 1 d 2 ds

1 2 s, 0

H i

d5 H i11 1

1 1 d 2 ds

1 2 s

H i11

d2 F2 , 0.

To prove the second group of inequalities, letm 5 (H 1 2 F 1)/(F 2 2 F 1).Therefore, 12 m 5 (F 2 2 H 1)/(F 2 2 F 1).

m

s5

1

F2 2 F1

H 1

s, 0

m

d5

1

F2 2 F1

H 1

d, 0

m

F15

21~F2 2 F1! 1 H 1 2 F1

~F2 2 F1!2 5

H 1 2 F2

~F2 2 F1!2 , 0

m

F25

H 1 2 F1

~F2 2 F1!2 , 0

Therefore,

~p1~A! 2 p1~NA!!

s5 1 2 ~1 1 d!

m

s2

~sd~1 2 m!!

s

5 1 2 d~1 2 m! 2 ~1 1 d 2 ds!m

s. 0

~p1~A! 2 p1~NA!!

F15 2~1 1 d!

m

F12 sd

~1 2 m!

F1

5 2~1 1 d 2 sds!m

F1. 0


~p1~A! 2 p1~NA!!

F25 2~1 1 d!

m

F22 sd

~1 2 m!

F2

5 2~1 1 d 2 sd!m

F2. 0

~p1~A! 2 p1~NA!!

d5 2~1 1 d!

m

d2 s

d~1 2 m!

d

5 ~1 2 s!~1 2 m! 2 ~1 1 d 2 sd!m

d. 0 QED

Proof of Lemma 5.The proof is very similar to the proof of Lemma 4 and alsouses backward induction. First note that

LT21

s5 2

F2~1 2 s! 1 F2s 1 eX

~1 2 s! 2 5 2F2 1 eX

~1 2 s! 2 , 0

LT21

F25

2s

1 2 s, 0

LT21

e5

2X

1 2 s, 0

LT21

X5

2e

1 2 s, 0.

Hence, for an arbitraryi (including i 5 1),

Li

s5

2d~1 2 s! 1 1 1 d 2 ds

~1 2 s! 2 Li11 11 1 d 2 ds

1 2 s

Li11

s

2 F2

~1 2 d!~1 2 s! 1 s 1 d 2 ds

~1 2 s! 2

5Li11

~1 2 s! 2 11 1 d 2 ds

1 2 d

Li11

s2

F2

~1 2 s! 2 , 0

Li

d5 Li11 2 F2 , 0

Li

F25

1 1 d 2 ds

1 2 s

Li11

F22

s 1 d 2 sd

1 2 s, 0

Li

e5

1 1 d 2 ds

1 2 s

Li11

e, 0

Li

X5

1 1 d 2 ds

1 2 s

Li11

X, 0. QED

MAXIM NIKITIN696

Proof of Lemma 6.

a1

e5

2X2 ¥ t50t5T g t

~~1 1 eX! ¥ t50t5T g t! 2 , 0

Note thatai/g , 0 holds for anyi $ 1 becauseg is present only in the term¥ gt,which obviously depends positively ong and affectsai/g negatively. QED

Proof of Lemma 7.First, note that

b

L15

s 1 d 2 ds

1 2 s

F1 2 F2

~L1 2 F1!2 , 0.

Therefore,

b

X5

b

L1

L1

X. 0

b

e5

b

L1

L1

e. 0

b

F15

s 1 d 2 ds

1 2 s

F2 2 L1

~L1 2 F1!2 . 0,

asL 1 does not depend onF 1.

b

F25

s 1 d 2 sd

1 2 s

~1 2 ~L1/F2!!~L1 2 F1! 2 ~L1/F2!~F2 2 L1!

~L1 2 F2!2 . 0

QED

Proof of Lemma 8.Consider a complementary functionf(H) 5 (1 1 d)(H 2F 1)/(F 2 2 F 1) 1 sd(F 2 2 H)/(F 2 2 F 1) 2 (s 1 d). This function is strictlyincreasing in its domain. Moreover,f(F 1) 5 sd 2 (s 1 d) , 0 andf(F 2) 51 1 d 2 (s 1 d) . 0. Hence,f(H) 5 0 has exactly one rootH* on the interval[F 1, F 2]. Also, f(H 1) . 0; i.e., (16) is satisfied, if and only ifH 1 . H*. Inother words, if condition (16) is satisfied, i.e.,H 1 lies to the right ofH*,H 1 . F 1 as well. QED

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an arrears crisis and stabilization failure in a transition economy

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