Implementation of socially optimal outcomes in the liquidation of public enterprises in China

China Economic Review 10 (1999) 41–58

Implementation of socially optimal outcomes in the liquidation of public enterprises in China Shanwen Gao, M.S. a, Yang Yao, Ph.D. b,* a

The People’s Bank of China, 32 Chengfang Street, Beijing 10080, People’s Republic of China b The China Center for Economic Research, Beijing University, Beijing 100871, People’s Republic of China

Abstract The authors study an optimal cost-sharing scheme between the central and local governments in China’s current process of dissolving public firms through mergers and bankruptcies. They first define the social choice rule that minimizes social costs, then design a mechanism that both implements this rule truthfully under imperfect information and minimizes the central government’s payment. Collusion between the local government and local firms as well as competition among local firms are explored. The findings show that writing off the bad loans and hardening the budget constraint are two necessary conditions to provide right incentives for truthful revelation. This result is consistent with the predictions of other theories and some recent proposals of revitalizing the banking system and the state sector in China. © 1999 Elsevier Science Inc. All rights reserved. Keywords: Socialist enterprises; Implementation theory; Information asymmetry

It is well known that China has maintained a gradual approach to its transition from a planned economy to a market economy. One major characteristic of this approach is its aversion to social unrest that could be caused by unemployment or sudden deterioration of the living standard of a significant portion of the population. Because the financial situation of the public sector has been growing worse in recent years, China began the process of dissolving bad public enterprises by means of bankruptcies and mergers. In 1994 the State Council issued a decree that sanctioned the practice of using bankruptcies and mergers to dissolve public enterprises. In 1997, based on the experience accumulated in the last 3 years, it issued another document that put forward detailed guidelines for the dissolution. The 15th Communist Party Congress, held in late 1997, reached a milestone by officially admitting that it is necessary for multiple forms of ownership to exist in China. Since then, the process of dissolving public enterprises in bad financial situations has been accelerated. * Corresponding author. Tel.: 86-10-6275-3103; fax: 86-10-6275-1474; E-mail address: [email protected]. edu.cn (Y. Yao) 1043-951X/99/$ – see front matter © 1999 Elsevier Science Inc. All rights reserved. PII: S1 0 4 3 - 9 5 1 X( 9 9 )0 0 0 0 4 -8

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However, this acceleration does not mean that the Chinese government will give up its gradual approach. It is unlikely that it will abruptly cut off the cash flow in the form of bank loans that is essential for money-losing public enterprises to maintain production because of the fear of massive unemployment. Rather, the central government hopes that these enterprises will be merged by some good enterprises and revitalized. If both merger and maintenance are either impossible or so costly so that bankruptcy is inevitable, the central government puts a great emphasis on settling the laid-off workers. As revealed in the 1997 document, compensation to laid-off workers in the process of bankruptcy takes the first priority in claiming the funds gathered by selling the assets of the bankrupt enterprises. Similarly, if any workers are to be laid off in the process of merger, the merger firm is also required to give them equivalent compensation. Therefore, the costs of both merger and bankruptcy are high. The problem the central government faces is how to divide the costs between itself and the local government in which the public enterprise under consideration is located. Currently, the liquidation of public firms that involve the central government budget is charged to a joint committee comprised of the People’s Bank of China (the central bank), the State Economy and Trade Commission, and the Ministry of Finance. The procedure of liquidation is as follows. The local government first proposes whether an enterprise in its judiciary is to be merged or declared bankrupt. If the public enterprise is to be declared bankrupt, the joint committee in the central government will exempt all the loans it owes the state banks, and the local government is responsible for compensating the laid-off workers by selling the enterprise’s assets. If the funds collected in the sale are less than the compensation needed, the local government is responsible for making up the difference by using its own funds; if the funds are more than needed, the extra amount is used to pay off the state bank loans. If the public enterprise is to be merged by another firm, the central government will only exempt the interest on the state bank loans, and the merger firm is responsible for paying off the principle of the loans. The money the central government has injected into the process has been considerable. In 1996 and 1997, 30 billion yuan RMB was spent in each year. It is estimated that the amount will reach 40 billion yuan RMB in 1998.1 However, the outcome is not all that satisfactory. It is evident that the central government counts on merger to recover the state bank loans. However, the current policy does exactly the opposite: it discourages mergers and encourages bankruptcies because the bad firm’s outstanding loans are totally written off under bankruptcy, whereas only the interest on these loans are exempted under merger. Therefore it is not surprising that more than 80% of the cases covered by the program have been bankruptcies since the policy was implemented in 1994. Many of the cases fall into the so-called “false bankruptcy, true debt evasion” category in which a firm evades all its debts by claiming bankruptcy and reopens on the same site and with the same employees, only under a different name. An example of this strategy is the bankruptcy of Shanxi Cotton Textile Factory located in Taiyuan, Shanxi province. Shanxi Cotton Textile Factory was a large, locally owned firm that employed 14,000 people before 1997 (4,000 were retirees). By the fall of 1996, it had an accumulated debt of 780 million yuan, whereas its net physical assets were only worth 486 million yuan. The employees had not been paid for 16 months and maintaining the factory became obviously impossi1

The People’s Bank of China.

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ble. Under these circumstances, the municipal government decided to let the factory be declared bankrupt. However, the government’s true intention was not to dissolve the factory. Instead, it formed a government-owned holding company that it allowed to participate in the auction of the factory. In the auction, the government adopted the Dutch auction procedures, bidding down from the highest price.2 The head of the newly formed holding company, not surprisingly, raised his price first, 486 million yuan—exactly the net asset value of the factory—and won the bid. The holding company then reopened the factory under a new name, Xinkai Company. It obtained various in-kind and cash subsidies from the municipal government that totaled nearly 400 million as well as eliminating the 780 million yuan state bank loans. With these preferential treatments and a reduced number of employees (it laid off 3,600 employees), the new firm was soon making a profit. In this process, the biggest loser was the state banks, which lost all of their 780 million yuan in loans. Although the local government sustained a substantial loss, it will be paid back both economically and socially if the new company incurred the growth of its profits. The biggest winners, of course, were those employees who were not laid off. The 1997 document was issued partly to address the problem of false bankruptcy, true debt evasion by tightening the control over the process of bankruptcy. However, it did not correct the incentive asymmetry between bankruptcy and merger itself in a substantial way. In fact, the problem has become worse since the party congress that called for the acceleration of the reform of the state sector. Now there are even queues of firms waiting to declare bankruptcy in some cities, indicating how strong the incentive asymmetry is. Even if the asymmetry were corrected, there would be an information problem. It is reasonable to believe that the central government aims at improving the social welfare with a minimum cost incurred to itself. To make this calculation, however, certain information has to be collected. This would include information held by the local government and the merger firm, such as the price of the assets of the bad firm and the profitability of the merger firm. However, it would be very costly or even impossible for the central government itself to collect all this information. Instead, it must rely on the local government and the merger firm to provide part or all of this information. Nevertheless, these two agents are not necessarily concerned with social welfare as much as the central government is, and it may be in their interests to provide false information. For example, the merger firm may underreport its profitability in the hope that it will receive more subsidy from the central government. In addition, the cost shares of the local government under bankruptcy and merger may be different, so it has an incentive to manipulate its report to make its preferred state happen. It is more commonly observed that the local government and the merger firm, as in the case of Shanxi Cotton Textile Factory, are likely to collude with each other to cheat the central government. This paper is concerned with the design of an optimal cost-sharing scheme between the central and local governments that will achieve optimal social outcomes under information 2

According to the revenue equivalence theorem (see, e.g., MacAfee & McMillan, 1987), the existing auctions, Dutch, English, and first-bid sealed auction, will yield the same revenue to the seller under the assumption of independent values among the bidders. Apparently the government feared that some kind of correlation of values was possible in the bidding process so an English auction would drive up the valuation of other bidders, including some private and foreign companies, and the government-owned holding firm would lose the bid, which was considered unacceptable.

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asymmetry. The central government is modeled as the social designer whose aim is to implement the optimal social outcomes. However, it does not make direct decisions. Rather, it relies on the actions of the decentralized decision makers, in this case, the local government and potential merger firms, to reach the social goals. Because of the problems laid out in the preceding paragraph, however, decentralized decision makers do not necessarily act to maximize social gains. Therefore, the central government’s role is to design a mechanism that provides right incentives for the local government and the merger firms to act in a manner by which optimal social outcomes are realized. The methodology we use in designing the mechanism belongs to the Bayesian implementation literature. In addition to solving the problem of information asymmetry, we also study the cases of collusion between the local government and the merger firm and competition among merger firms. It will be shown that the resulting mechanisms are equivalent to a decentralized decision-making process undertaken by the local government and the merger firms under a subsidy scheme delivered by the central government. The major feature of our mechanisms is that under the current practice of bankruptcy, the central government must relinquish all its state bank loans and harden firms’ budget constraints to implement the optimal social outcomes truthfully. In section 1, we set up the problem and put forward the social choice rule. Then we provide a mechanism for the case of perfect information. In section 2, we propose a mechanism that implements the social choice rule in Bayesian Nash equilibrium for the case of imperfect information. In section 3, we consider the case of collusion between the local government and the merger firm. In section 4, we introduce competition among the potential merger firms and discuss the corresponding mechanism. Finally in section 5, we present a short discussion of the policy alternatives. 1. Implementation under perfect information The existence of perfect information is hypothetical. We discuss the mechanism under this hypothetical case to provide a basis for comparison with the mechanisms under imperfect information. 1.1. The social choice rule Suppose there is a public enterprise owned by the local government that is currently operated under loss and is being considered for either bankruptcy or merger by another enterprise.3 Subsequently, we will call this public enterprise “the bad firm.” If this bad firm is allowed to continue its operation, the central and local governments have to bear a total cost of M . 0, an amount that is equal to the sum of the costs the two governments have incurred so far and the discounted value of the total loss they will incur henceforth.4 The share of the

3

In reality, the firm does not need to be owned by the local government. As long as the local government has a stake in the firm, as it always does, our results will not be changed qualitatively. 4 We could also define M as including the political costs the central and local governments would incur under the status quo. These costs are as real in reality as the existence of the bad firm is a manifestation of the incompetence of the two governments.

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central government, MC, consists of the loans the bad firm owes to the state banks and part of the funds for its future operation. The share of the local government, ML, consists of the discounted value of its investment in the bad firm and its share in the costs of maintaining the bad firm’s future operation. That is, both MC and ML consist of two parts of costs: a sunk cost and a discounted future cost. If the bad firm is declared bankrupt, its physical assets (land, buildings, and equipment) are sold on the local market. The order of claim is as follows. The workers who were laid off are compensated first with a once-and-for-all payment, the standard of which is set by the central government. Then, if there is anything left, it is used to pay off the state bank loans. Finally, the residual, if there is any, is claimed by the local government. Compared with maintaining the bad firm, the central and local governments do not need to pay for its future operation under bankruptcy. Their (gross) losses are only the sunk costs that are equal to the bad firm’s outstanding loans and discounted value of investment, respectively.5 Let UC . 0 and UL . 0 denote these two costs, let A denote the selling price of the bad firm’s total assets,6 and let W denote the total amount of compensation paid to the workers. We assume that the state banks cannot fully recover their loans, that is, A 2 W , UC. Then, according to the order of claim, the local government’s cost in bankruptcy is UL 1 max{W 2 A, 0} . 0; the central government’s is UC 1 min{W 2 A, 0} . 0; and the total cost to society is the sum of their costs, U 5 UL 1 UC 1 (W 2 A). If the bad firm is merged with another enterprise, which we will call “the good firm,” the new firm has to incur four kinds of cost. First, it has to pay for the bad firm’s assets. For simplicity, we assume that the payment is equal to the local government’s sunk cost, UL.7 Second, it must inherit the unpaid loans that the bad firm owes the state banks, the value of which is represented by UC. Third, it must employ all the bad firm’s workers or compensate those who were laid off. Finally, it will incur other costs necessary to make the merger profitable (such as new investments to revitalize the bad firm). We group these four costs into one category and denote it by C. It is noteworthy that this cost is a discounted value because it includes the loans and wages that may be paid off in the future. To make the merger profitable, of course, the good firm must gain something. We assume that the discounted current value of its gross gain is R, so its net gain from the merger is R 2 C. Under a merger, both the central and local governments receive compensation for their sunk costs, UC and UL, respectively, so their net gains are both zero. Thus the net gain of society as a whole is the good firm’s net gain, R 2 C. With the above setup, the social optimal actions concerning the status of the bad firm are defined by comparing the social costs of maintaining its operation, bankruptcy, and merger. The rule is as follows:

5 Bankruptcy of a firm leads to the increase of unemployment, which raises the political risk faced by the central and local governments. Therefore, the cost of bankruptcy, as in the case of maintaining, could be defined as including political costs. Our results, however, will not be altered qualitatively. 6 The relationship between the asset price A and UL is not necessarily linear because the value of the bad firm’s assets may vary for different buyers. 7 This assumption is made to normalize the net gain of the local government in merger to zero. Deviation from this assumption, however, will not change our results in a qualitative way.

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( 1a ) Continuing the operation if M ≤ min { U ,C – R }; ( 1b ) Bankruptcy if U ≤ min { M , C – R }; ( 1c ) Merger if C – R ≤ min { M , U }.

(1)

That is, society takes the action that minimizes the social cost (or conversely, that maximizes the social gain). We call Eq. (1) the social choice rule henceforth. The central government’s aim is to implement this rule by designing an optimal cost-sharing scheme in which its budget is minimized. It is noteworthy that when R is greater than C, the good firm will merge the bad firm without intervention from either government. If R , C, but (c) in Eq. (1) still holds, the central government, the local government, or both must give a subsidy of at least C 2 R to induce the good firm to conduct the merger. 1.2. The mechanism With perfect information, M, U, C, and R are public information. The central government knows exactly where society should go. We assume that the central government is able to sign contracts with both the local government and the good firm that are enforceable by legal or administrative means. This assumption is reasonable because the central government is still powerful in controlling the country, especially through administrative channels. With this assumption, ex post collusion between the local government and the good firm in their actions is excluded. Because all the information is public, there is no room for ex ante collusion, either. We also assume that the central government cannot use any kind of noneconomic coercion that forces the local government and the good firm to do what it wants them to do. This means that the mechanism we are about to design must take into account the agents’ incentive and participation constraints. Let SC and SL denote the central and local governments’ shares in the cost of a specific state. We now discuss the values of SC and SL in three cases. 1. When it is optimal to maintain the bad firm. In this case, the sum of SC and SL cannot be smaller than M to insure that there are enough funds for the firm’s operation. In addition, SL cannot be larger than ML, UL 1 max{W 2 A, 0}, or C 2 R, the local government’s cost when it takes unilateral actions to maintain the bad firm, conduct bankruptcy, or subsidize the merger, respectively. However, ML is less than C 2 R because C 2 R # M when maintaining is optimal. Therefore, we conclude that SL 5 min{ML, UL 1 max{W 2 A, 0}}, and SC 5 M 2 SL. 2. When bankruptcy is optimal. The same reasoning also applies to this case. We still have SL 5 min{ML, UL 1 max{W 2 A, 0}}, and SC 5 U 2 SL. 3. When merger is optimal. We discuss three cases. First, it is profitable for the good firm to merge the bad firm by itself, that is, C 2 R # 0. In this case, SL 5 SC 5 0. Second, 0 , C 2 R # min{ML, UL 1 max{W 2 A, 0}}. In this case, the local government itself has incentive to subsidize the merger. Thus SL 5 C 2 R and SC 5 0. Finally, C 2 R . min{ML, UL 1 max{W 2 A, 0}. In this case, the local and central governments share the cost: SL 5 min{ML, UL 1 max{W 2 A, 0}}, and SC 5 C 2 R 2 SL. To summarize, the mechanism is

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Mechanism 1 (perfect information). The local government pays either SL 5 min{ML, UL 1 max{W 2 A, 0}} if the cost for a specific state is greater than min{ML, UL 1 max{W 2 A, 0}} or the cost itself if it is less than SL, and the central government fills the gap between the cost and SL whenever it is necessary. Under this mechanism, both the local government and the good firm have incentive to sign the necessary contracts that implement the social choice rule Eq. (1). It is noteworthy that even with perfect information, the central government cannot make the local government pay its full share under specific social states if coercion is not allowed. For example, when bankruptcy is optimal, the central government cannot ask the local government to pay its share of UL 1 max{W 2 A, 0} if this cost is larger than ML because the local government would prefer to maintain the bad firm. This situation could happen if the central government’s share in maintaining the firm is large and the compensation to the workers is far greater than the firm’s asset value.

2. Implementation under imperfect information The existence of perfect information is hypothetical. In reality, the central government is not likely to know the information held by the local government and the good firm, both of whom have incentives to hold up information so that they will gain from it. On the part of the local government, UL and W are hard to conceal because the former is an historical figure that is likely to be recorded by the bad firm’s bookkeeping, and the latter is often set by the central government itself. In contrast, the bad firm’s asset price, A, is difficult to determine. This is largely because of the lack of a capital market that is accessible to all the firms in China. Currently, the determination of A is often carried out or monitored by the local government itself. On the part of the good firm, both C and R are private information because they are fully or partly determined by the actions taken by the firm only. As we will see in the subsequent analysis, C and R are always linked linearly. For purely simpler exposition, we assume that only R is private information. Therefore, in the subsequent context, we assume that the central government knows neither A nor R, whereas the local government knows A but not R, and the good firm knows R but not A. We first present a mechanism that implements the social choice rule of Eq. (1) in Bayesian Nash equilibrium. Then we revise it to accommodate the possibility of collusion between the local government and the good firm. Finally, we discuss the situation when competition is introduced at the local level. 2.1. A Bayesian mechanism Without knowing A and R, the central government must rely on the announcements made by the local government and the good firm, say A* and R*, respectively, to decide which social action to take. In the subsequent discussion, we use the notation U* 5 UC 1 UL 1 max{W 2 A*, 0} to denote the cost of bankruptcy associated with the local government’s announcement, A*. Our task is to design a mechanism that implements the social choice rule of Eq. (1) with any U* and R* announced by the local government and the good firm. Because of the revelation principle, we can focus on a truthful mechanism that implements the rule

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when A* and R* are equal to their true values, A and R. The assumption that the local government and the good firm do not know each other’s private information is important in the implementation of the social choice rule of Eq. (1). Because of the result of Maskin (1985), it is well known that there is no nondictatorial social choice rule that is implementable in Nash equilibrium if the private agents know each other’s private information. In contrast, when the private agents do not know each other’s private information, a wide variety of social choice rules can then be implemented in Bayesian Nash equilibrium (Mas-Colell et al., 1995). The attainability of the equilibrium, however, rests on the subjective beliefs that the private agents hold about the distribution of each other’s private information and the extent to which the social planner knows their believes. Following the Hasanyi transformation, here we assume that nature assigns a probability distribution f(.) whose cumulative density function is F(.), to the true C 2 R and U on the internal [x0, x1]. Because this distribution is common knowledge, the announcements C 2 R* and U* should have the same distribution. Without loss of generality, we assume that Me [x0, x1]. The following mechanism implements the social choice rule of Eq. (1) truthfully in Bayesian Nash equilibrium. Mechanism 2 (imperfect information). First, the central government announces that from the date of the announcement, it will not pay to maintain the bad firm. Then it decides the social actions and the shares of the costs according to the following rule: (a) U* $ M (a1) C 2 R* $ M maintaining the bad firm, SL 5 ML and SC 5 UC (a2) C 2 R* , M; choosing merger, SL 5 max{C 2 R* 2 UC,0} and S C 5 M 2 SL (b) U* , M (b1) C 2 R* $ U*; declaring bankruptcy, SC 5 UC and the local government bears whatever left that is necessary to make the bankruptcy possible (b2) C 2 R* , U*; choosing merger, SL 5 max{C 2 R* 2 UC, 0} and SC 5 U* 2 SL. The payments specified in this mechanism are enough to make each socially desirable state possible. Although this statement is clearly true in other cases, it needs some explanations for case (a1). Because the central government will not pay to maintain the bad firm in the future, it will only incur its sunk cost, UC, if the bad firm is to be maintained. Because the total cost is still M, this forces the local government’s share, ML, to be increased. Mechanism 2 satisfies the participation constraints. The payment for which the local government is responsible in each state is not larger than the cost it must bear when it takes unilateral actions to make that state happen. Under (a1), the local government’s payment equals its share, ML, when maintaining is chosen. Under (a2) and (b2), merger is chosen. The cost the local government must bear if it takes unilateral actions to make a merger happen is C 2 R*, which is greater than its payment specified in the mechanism. Under (b1), bankruptcy is chosen. The local government’s share of the cost is U 2 UC 5 UL 1 W 2 A, which is not larger than UL 1 max{W 2 A, 0}, its cost when it takes unilateral actions to let the bad firm declared bankrupt. Below we show that Mechanism 2 is incentive compatible, that is, a truthful announcement is optimal for both the local government and the good firm, so the choice rule specified in the mechanism conforms exactly with the social choice rule in Eq. (1).

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2.2. Proof of incentive compatibility Let us study the local government first. We first show that truth-telling is a weak dominant strategy for the local government in two cases: (a) U $ M and U* $ M, and (b) U , M and U* , M. Then we show that when U $ M holds, the local government incurs a lower expected cost by not announcing a U* , M, and when U , M holds, it incurs a lower expected cost by not announcing a U* $ M; that is, truth-telling is a Bayesian Nash equilibrium for the local government. In case (a), the society chooses between maintaining or merger depending on whether C 2 R* is larger or smaller than M. Therefore, the probability that maintaining will happen is 1 2 F(M), and the probability that merger will happen is F(M). Thus the local government’s expected cost is C 1 = [ 1 – Φ ( M ) ]M L + Φ ( M )E ( max { C – R∗ – U C ,0 } C – R∗ < M ) M  Φ( M ) – Φ(UC) 1 - -------------------------------------- ∫ xφ ( x )dx – U C = [ 1 – Φ ( M ) ]M L + Φ ( M )  ------------------------------------Φ( M ) Φ ( M ) – Φ ( U C ) UC  Φ(UC)  + ----------------- × 0  Φ( M )  M

= M L – Φ ( M )M + Φ ( U C )U C + ∫ xφ ( x )dx. UC

(2)

To obtain Eq. (2), the fact that UC 5 MC was used. It is straightforward to see that C1 does not depend on U* at all. Therefore, announcing U* 5 U is a weak dominant strategy for the local government in case (a). In case (b), the society chooses between bankruptcy and merger depending on whether C 2 R* is greater or less than U*. Therefore, the probability that bankruptcy will happen is 1 2 F(U*), and the probability that merger will happen is F(U*). If bankruptcy happens, the lowest cost of the local government is U 2 UC 5 UL 1 W 2 A, because the central government will not pay more than UC. Thus the expected cost of the local government is C 2 = [ 1 – Φ ( U∗ ) ] ( U L + W – A ) + Φ ( U∗ )E ( max { C – R∗ – U C ,0 } C – R∗ < U∗ )  Φ ( U∗ ) – Φ ( U C ) = [ 1 – Φ ( U∗ ) ] ( U L + W – A ) + Φ ( U∗ )  --------------------------------------Φ ( U∗ )  Φ(UC)  U∗ 1 - × 0 ---------------------------------------- ∫ xφ ( x )dx – U C + ---------------Φ ( U∗ ) Φ ( U∗ ) – Φ ( U C ) U C  U∗

= ( U L + W – A ) – Φ ( U∗ )U + Φ ( U C )U C + ∫ xφ ( x )dx . UC

(3)

By taking the first- and second-order derivatives with respect to U*, it is easy to establish in Eq. (3) that C2 is minimized when U* 5 U. That is, truth-telling is a Bayesian Nash equilib-

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rium strategy for the local government in case (b). However, the equilibrium can be strengthened. In fact, this case is completely analogous to the Groves-Clarke mechanism for linear utility (Mas-Colell et al., 1995) and has a weak dominant strategy. Because the proof is virtually the same as that for the Groves-Clarke mechanism, we only provide a sketch here. Consider first the case of C 2 R* $ U. If the local government announces the true U, bankruptcy will be chosen and its share of the cost will be UL 1 W 2 A. If instead it announces another U* # C 2 R* and U, nothing will change. If it announces a U* . C 2 R*, merger will be chosen, but its share of the cost will be C 2 R* 2 UC . U 2 UC 5 UL 1 W 2 A because C 2 R* $ U. Therefore the local government has no incentive to lie. Similarly, one can show that lying is also a weakly dominated strategy for the case C 2 R* , U. Thus true-telling is a weak dominant strategy for the local government for case (b). Our remaining task is to show that the local government does not have any incentive to report a U* , M when U is at least as large as M, or to report a U* $ M when U is less than M. This is performed by comparing C1 and the minimum of C2min, say, under the two circumstances, respectively. As C2 is minimized when U* 5 U, we have that min

C2

U

= ( U L + W – A ) – Φ ( U )U + Φ ( U C )U C + ∫ xφ ( x )dx.

(4)

UC

The difference between C2min in Eq. (4) and C1 is min

C2

U

– C 1 = [ ( U L + W – A ) – M L ] + [ Φ ( M )M – Φ ( U )U ] + ∫ xφ ( x )dx M

U

= ( U – M ) – ∫ Φ ( x )dx. M

(5)

In deriving Eq. (5), we use the technique of integration by parts. When U $ M, we have that min

C2

– C1 ≥ ( U – M ) – Φ ( U ) ( U – M ) = [ 1 – Φ ( U ) ] ( U – M ) ≥ 0

because F(x) is increasing in x. Therefore it does not pay for the local government to report a U* , M when U is at least as large as M. Now, when U is less than M, we have min

C2

– C 1 ≤ ( U – M ) + Φ ( M ) ( M – U ) = – [ 1 – Φ ( M ) ] ( M – U ) ≤ 0,

so that it does not pay for the local government to report a U* $ M in this case. Therefore we conclude that truth-telling is a Bayesian Nash equilibrium strategy for the local government. To study the strategy of the good firm, we restate the decision rule stated in Mechanism 2 as follows: (a) (a1) (a2) (b) (b1) (b2) (b3)

C 2 R* $ M U* $ M: maintaining U* , M: bankruptcy C 2 R* , M U* $ M . C 2 R*: merger M . U* . C 2 R*: merger U* , C 2 R* , M: bankruptcy.

We adopt the same strategy used by us in studying the local government. By the same argu-

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ments used before, it is easy to establish that truth-telling is a weak dominant strategy for the good firm conditional on that both C 2 R and C 2 R* are at least as large as M or conditional on that both C 2 R and C 2 R* are less than M. To show that the good firm has no incentive to report C 2 R* , M when C 2 R is at least as large as M, or to report C 2 R* $ M when C 2 R is less than M, we must know the good firm’s largest expected gain for case (b) (the expected gain for case (a) is zero), which is obtained by announcing its true R. That is, π

max

= [1 – Φ( M )][ M – (C – R)] + [Φ( M ) – Φ(C – R)] { [ E ( U ∗ M > U∗ > C – R ) – ( C – R ) ] + Φ ( C – R ) × 0 }.

(6)

Using the technique used in the case of the local government, Eq. (6) can be reduced to π

max

= [ M – (C – R)] – ∫

M

C–R

Φ ( x )dx.

(7)

Using Eq. (7), we can apply the method used in the case of the local government to show that the good firm has no incentive to report C 2 R* , M when C 2 R is at least as large as M, or to report C 2 R* $ M when C 2 R is less than M. Therefore we conclude that truth-telling is a Bayesian Nash equilibrium strategy for the good firm. One remaining question is whether Mechanism 2 has minimized the central government’s cost. Let us start with the case of (b1) in Mechanism 2. If the central government’s share is reduced from UC by a small amount, e . 0, say, then the local government’s share becomes UL 1 W 2 A 1 e, which is larger than UL 1 max{W 2 A, 0} when W is greater than A, so the participation constraint is violated. Therefore UC is the smallest share that the central government has to bear under (b1). Now turning to (b2), we first observe that paying the good firm less than U may make the society choose bankruptcy when merger is socially optimal because C 2 R may be less than U but greater than the payment. Then we see that the central government cannot reduce its share by a small amount, e, say. If it did, the local government’s share would be C 2 R 2 UC 1 e, which could be larger than U 2 UC 5 UL 1 W 2 A, so the local government would have incentive to report a smaller U* in the hope that bankruptcy would occur. Now let us consider the two cases in (a). For (a1), it is obvious that UC is the smallest share the central government has to bear not to violate the local government’s participation constraint. Then if the central government’s share in case (a2) is reduced by e, the local government’s share will be increased to C 2 R 2 UC 1 e because the good firm must be paid by M to be made sure to report its true R. Then the difference between C2min and C1 as expressed in Eq.(5) becomes Eq. (8): min

C2

U

– C 1 = ( U – M ) – ∫ Φ ( x )dx – [ Φ ( M ) – Φ ( U C ) ]ε. M

(8)

Now, when U $ M holds, the difference could be negative. Therefore when U is close to M, the local government could report a U* that is smaller than M and obtain an expected cost that is close to C2min and smaller than C1. Therefore we conclude that there is not another mechanism that implements the social choice rule of Eq. (1) for certain and in which the central government’s payments are surely smaller than those specified in Mechanism 2. We stress that there are not other mechanisms in which the central government pays surely less because there are

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other mechanisms in which the central government may pay less with some probability. In the above discussion of the participation constraint of case (b1), we emphasized the possibility that W is larger than A. If the reverse were true, the central government would end up with a loss of A 2 W. In this case, it would be better for the central government to ask the local government to pay UL. However, it is not difficult to verify that the local government’s payments in other cases also have to be UL (and the central government pays min{M, U} 2 UL, that is, whatever left to make the specific socially desirable state happen) to make it not lie. This may allow the local government to gain too much if maintaining the bad firm is socially optimal because UL may be much less than ML (remember that ML includes both the sunk costs and the current value of the future payments, whereas UL includes only the sunk costs). This is why we prefer Mechanism 2 instead of the alternative mechanism discussed here. It is noteworthy that the central government must pay more in Mechanism 2 than in Mechanism 1. For example, when merger occurs, the central government must pay UC in Mechanism 2, that is, it has no chance to recover any of its sunk costs. This is contrasted with Mechanism 1, in which the central government can recover parts of its sunk costs when W is less than A. The intuition behind this contrast is quite straightforward: in the case of imperfect information, the local government is entitled to gain a rent from the information it possesses. This is also true for the good firm. Instead of gaining at the margin to merge the bad firm in the case of perfect information, the good firm may gain a lot under imperfect information because its net gain of merger is min{U, M 2 (C 2 R)}, which could be large. Specifically, it can still obtain subsidies even if C is less than R. In the cases of (a1) and (a2) in Mechanism 2, the only uncertainty is the good firm’s revenue, R. Therefore the central government only loses to the good firm: it has to pay UC plus whatever is left from M by the local government’s payment C 2 R 2 MC to induce the good firm to report its true R. In the cases of (b1) and (b2), the central government loses to both the local government and the good firm because the private information of both is needed to decide the socially optimal state. Specifically, the mechanism under (b2) is similar to the Groves-Clarke mechanism, which is proven not to provide the planner a balanced budget (Mas-Colell et al., 1995). 2.3. Further discussions Several remarks are in order regarding Mechanism 2. First, the cost-sharing scheme of Mechanism 2 is consistent with the expected externality mechanism developed in the mechanism design literature. By this mechanism, each private agent’s gain is equal to the total amount of the externality generated by its equilibrium action plus an adjustment to make the budget balanced among all the agents. In our case, we do not require that the budget be balanced for the private agents, that is, the local government and the good firm. Therefore each private agent receives exactly the total amount of the externality brought by its truthful revelation. We illustrate this point with the case of U $ M (case (a) in Mechanism 2). In this case, the society decides between maintaining and merger depending on the good firm’s announcement of R. The case of C 2 R $ M (case (a1) in Mechanism 2) serves as the reference for the status quo, that is, maintaining the bad firm prevails, so the truthful announcement by the good firm will bring it a gain of zero. Then in the case of C 2 R , M, the truthful announcement by the good firm brings a total amount of externality of M (here the externality

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is a certain amount), the sum of the gains of the central and local governments relative to the status quo, so it receives a payment of exactly M. For the local government, its gain is the sum of the gains of the central government UC and the good firm R 2 C; or, expressed in terms of cost, the gain becomes C 2 R 2 UC (to prevent incentive reversal, a lower cap of zero is put on the cost, so we have the SL as expressed in case (a2)). The reader can verify that similar considerations have been built in the case of U , M. Second, when the cost-sharing scheme of Mechanism 2 is used in practice, direct revelation of the private information, that is, the profitability of the good firm and the asset value of the bad firm, may not be feasible. In this case, the central government must rely on an indirect revelation mechanism. Although the truthful implementability of Mechanism 2 guarantees that there exists one such indirect mechanism that has at least one equilibrium in which the social choice rule of Eq. (1) is implemented, it does not exclude the possibility that this mechanism has other equilibria whose outcomes deviate from those of the social choice rule.8 In other words, Mechanism 2 may not strongly implement the social choice rule (Maskin, 1985). In the implementation literature, several approaches have been adopted to solve the problem arising from multiple equilibria. The most recent approach is to resort to a new concept of implementation, virtual implementation, that seeks implementation of a social choice rule by approaching it from a neighborhood that is arbitrarily close to it. This concept was first introduced by Matsushima (1988) and Abreu and Sen (1991) in the case of complete information and later extended by others to the case of incomplete information. In particular, Tian (1997) showed that, for infinite social alternatives and agent types, any social choice rule can be virtually implemented in the environment of incomplete information. In other words, for any social choice rule, there is another social choice rule in its neighborhood that is strongly implementable in Bayesian Nash equilibrium. He also showed that a social choice rule is virtually implementable if and only if it is truthfully implementable. With this result, we are assured that the social choice rule of Eq. (1) can always be implemented virtually in the sense that its outcomes can be approximated with arbitrarily small variations by another social choice function that is strongly implementable. Lastly, Mechanism 2 falls in the line of the Myerson-Satterthwaite theorem, which says that a social choice function cannot be truthfully implemented in Bayesian Nash equilibrium if it satisfies both the balanced budget and the participation constraints of the private agents with risk neutral utility functions (such as the case discussed in this paper). In our case, the participation constraints of the local government and the good firm are satisfied, whereas the budgets between them are not balanced, that is, the gain of the good firm is not equal to the cost borne by the local government whenever both are involved and the local government cannot be made to bear all the social cost when only itself is involved. The role of the central government is precisely to fill the gap of the unbalanced budget. This conclusion has an important practical implication. That is, the central government cannot have a positive gain from bankruptcy or merger. Its cost of maintaining the bad firm is UC; its share in the cost of bankruptcy is also UC; and its share in the cost of merger is min{U, M} 2 [(C 2 R) 2 UC] . UC. In practice, the mechanism requires the central government to announce

8

We thank an anonymous referee for pointing out this possibility.

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that it will give up its right to the loans the bad firm owes the state banks when bankruptcy or merger is socially desirable and pays an additional cost of min{U, M 2 (C 2 R)} when merger is desirable. This requirement coincides with a recent proposal made by Nicholas Lardy (forthcoming), who suggests that the central government write off the nonperforming loans owed by the state enterprises and recapitalize the state banks by issuing government bonds held by the banks to compensate for their losses. He argues that many of the state-owned enterprises are buried by the huge amount of debt that has been accumulated over time and there is no hope that they will be able either to make a profit or to repay the debt. Writing off of these debts is a necessary condition for the enterprises to be revitalized. This is especially pertinent if the central government wants to rely on merger to make use of the bad firm’s assets. As pointed out in the Introduction, the current practice creates an asymmetry between merger and bankruptcy by writing off the loans for the latter, but not for the former. Mechanism 2 shows that this asymmetry ought to be corrected to provide right incentives. In addition, it must be emphasized that cancellation of the debts owed by the bad firm must be accompanied by equivalent disciplines. Lardy stresses that financial disciplines have to be applied to both the enterprises and the banks after the recapitalization to make his proposal work properly. Mechanism 2 has the same precondition by requiring the central government to cut off further bank loans to maintain the bad firm. In either case, hardening the budget constraint of the state enterprises is the key to success.

3. Collusion Collusion between the local government and the good firm has a real possibility because the good firm may also be owned by the local government. When collusion is allowed, Mechanism 2 is no longer incentive compatible. Now the local government and the good firm together maximize the sum of their total revenues. Under Mechanism 2, either the central government will be cheated into paying more, or the social optimum will not be implemented. For example, when merger is socially desirable and it is optimal for the local government and the good firm to let it happen, they would report a larger R* such that C 2 R* # UC and a U* that is slightly smaller than M so the local government does not need to pay anything and the central government ends up paying U*. Take another example when bankruptcy is socially optimal. Under bankruptcy, the local government must bear a cost of UL 1 W 2 A, which is always positive, but it does not need to pay anything under merger if the good firm announces a proper R*, creating an incentive for the two agents together to lie so that merger happens. In addition, if both C 2 R and U are less than M so merger is socially optimal, the good firm also gains from the local government’s announcement of a U* that is close to M. The caveat in the design of Mechanism 2 is that the local government’s payment depends on the good firm’s announcement, whereas the good firm is paid by what the local government announces. Now that the local government and the good firm collude with each other, this strategy does not work to induce truthful revelation. In the new mechanism, the central government’s payments cannot depend on either the local government’s or the good firm’s announcements. However, because of collusion, the local government and the good firm will not cheat each other, so there may be savings on the part of the central government because it does not need to mediate between the two agents. It turns out that the central government

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pays UC for all the cases that constitutes an incentive compatible mechanism (we call it Mechanism 3) when the local government and the good firm collude with each other. This is evident when we compare the joint gains the local government and the good firm obtain under different social outcomes. In the following discussion, we refer to Mechanism 2 with regard to the social outcomes. The joint gains of the local government and the good firm under different conditions in Mechanism 2 are: (a1) (a2) (b1) (b2)

2 ML; R 2 C 1 U C; 2 (UL 1 W 2 A); R 2 C 1 U C.

If U $ M and C 2 R $ M hold, telling the truth will yield a joint gain of 2ML. Reporting false R and U so (i) (a2) happens, the joint gain is R 2 C 1 UC, less than 2 M 1 UC 5 2 ML; (ii) (b1) happens, the joint gain is 2 (UL 1 W 2 A), less than 2 M 1 UC 5 2 ML; (iii) (b2) happens, the joint gain is R 2 C 1 UC # 2 M 1 UC 5 ML. Therefore truth-telling is better. By the same token, one can confirm that truth-telling is also better for the other three cases. In addition, it is easy to verify that this mechanism meets the participation constraints. It is evident from the above discussion that UC is the smallest amount that the central government must pay to obtain a truthful revelation. It is noteworthy that the central government pays less for merger when the local government and the good firm collude with each other than when they do not. This is because the two agents now have no incentive to cheat each other, so the central government does not need to ensure that the good firm will not cheat the local government or vice versa. Would this mechanism also work when the local government and the good firm do not collude? It turns out that it will not. For example, when the two agents do not collude, the local government’s payment must be U* 2 UC under merger if the central government’s share is UC. Then the local government has the incentive to report a smaller U*, and the social outcome may change to bankruptcy. A natural question, therefore, is whether there exists a mechanism that is incentive compatible for both cases. It turns out that there is no such a mechanism. The reasons are as follows. For a mechanism to work when the local government and the good firm do not collude with each other, the local government’s payment has to be either constant or depend on the good firm’s announcement, and the subsidy to the good firm has to be either constant or depend on the local government’s announcement. When the two agents do collude, both the local government’s payment and the good firm’s subsidy have to be constant. Therefore, to work in both cases with and without collusion, the only viable choice of the subsidy to the good firm is M. Let the local government’s payment be a constant S. Now consider the case of U , M and C 2 R $ U. If both the good firm and the local government tell the truth, bankruptcy will be chosen and the joint gain of the two agents is 2 S. If they lie so that C 2 R* , U* holds and merger happens, their joint gain is R 2 C 1 M 2 S, which is greater than 2 S if C 2 R , M, creating an incentive for the two agents to lie. This result creates a problem for the central government in practice if it cannot tell whether the local government and the good firm are colluding. The whole problem, however,

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is created by the lack of competition in the process of dissolving the bad firm. In the next section, we show that introducing competition will solve the problem in an easy manner.

4. Competition Suppose that there are several competing good firms instead just one. Then the following mechanism implements the social choice rule of Eq. (1) truthfully. Mechanism 4 (competition). The central government announces that it will not pay to maintain the bad firm from the date of the announcement. The local government pays ML or UL 1 W 2 A, depending on whether U* is greater or less than M. The firms announce their own R*. The lowest C 2 R* is compared with M and U* to determine the social actions according to the rules listed in Mechanism 2. If merger is socially desirable, the firm with the lowest C 2 R* obtains the right to merge the bad firm and is paid by the smallest of three values: the second lowest C 2 R*, M, and U*. For the local government, this mechanism is the same as Mechanism 2, so it has no incentive to lie. For the firms, the mechanism is exactly the same as the second-price sealed auction, which is well known to be incentive compatible (see, e.g., MacAfee & McMillan, 1987). Collusion between the local government and the winning firm in this case may take two forms. First, the local government could bribe all the firms participating in the auction and ask them to announce a higher C 2 R, expecting that it would split the gain with the winning firm. However, because the bribery becomes a sunk cost borne solely by the local government after the auction takes place, the winning firm can always refuse to collude with the local government at that point and take all the extra gain away. Therefore this form of collusion is not credible. Second, the local government could conduct a simulated auction identical to the auction described in Mechanism 4 before the real auction takes place so it could determine the ranking of the C 2 R of each participating firm and sign a contract with the winning firm to collude in the real auction (suppose there exists a scheme that makes the collusion worthwhile). However, one qualification, among others, makes this form of collusion implausible: the collusion imposes the precondition that the central government could not observe the simulated auction. This precondition is not realistic. In fact, the central government could regard the simulated auction as an indication that some form of collusion would happen in the real auction and take the result of the simulated auction as the final result. Therefore we exclude the possibility of collusion under Mechanism 4. The second-price sealed auction is used purely for exposition. The first-price sealed auction will do the same job as implementing the social choice rule of Eq. (1) truthfully, and it is known by the revenue equivalence theorem that the central government’s payment is the same as in the second-price sealed auction. By either mechanism, the central government’s payment is not greater than its payment in either the case of collusion or the case of no collusion. This is because the competition reveals the information of the good firms, and the central government gains if the second lowest C 2 R is less than min{M, U}. However, the central government still must pay information rents to the winning firm and the local government because the local government does not face any competition at all, and the winning firm, although facing competition, could take advantage of its leading position.

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5. Policy alternatives Based on the study of this paper, the best way of dissolving bad public enterprises is to introduce competition. In reality, the whole problem is created by the lack of a well-functioning capital market in China today. Competition serves as a substitute for the market. At the operational level, the central government could invite bidding from all over the country. However, open selling may not help bring good buyers because the industries or locations of the bad firms are not attractive. Currently, money-losing enterprises are concentrated in the declining or overcrowded industries such as machinery manufacturing and textiles. Many of them are located in northeastern China where heavy industries are concentrated. The current practice is to find a capable local enterprise and arrange its merger with the bad firm. The difficulty for the central government in this case is that it does not know if the good firm and the local government will collude with each other. It has to weigh the risks of following Mechanism 2 or Mechanism 3. Under most circumstances, following Mechanism 3 may reduce the central government’s risk of losing both more money and the socially optimal outcome. Under Mechanism 2, the local government’s payment and the good firm’s gain depend on each other’s announcements. If the two of them did collude, the central government would end up losing enormously, and the social optima would not be implemented. In contrast, under Mechanism 3, the central government’s payment is fixed to be its sunk costs in the bad firm. Thus it will not be cheated into paying more. The only risk is that the local government and the good firm may cheat each other and the social optima are not implemented. Therefore, following Mechanism 3 may be a better strategy for the central government. Mechanism 3 requires the central government to give up its right to its loans in the bad firm. In the current practice, it has already given up this right when bankruptcy happens. It must give up this right under merger to conform with the rule of Mechanism 3. As required by the mechanism, this secession has to be accompanied by the hardening of the firms’ budget constraint, which is also the precondition raised by Nicholas Lardy in his recent proposal of recapitalization of the state banks. It is noteworthy that the current practice of bankruptcy excludes the possibility of converting bank loans into bank equity. This makes bankruptcy always cheaper than merger and forces the central government to bear more costs because the local government’s loss under bankruptcy sets a ceiling for its share of costs under any social state. If the current practice allowed the conversion of bank loans into bank equity, the local government’s ceiling of loss would be raised to that of its ceiling under merger, and the central government then would be exempted from bearing the cost of losing its bank loans (UC in the text) under bankruptcy. However, the state banks, in their current position, do not look like they have the capacity to manage the equity transformed from loans. Therefore it is expected that the current practice will continue. Finally, our mechanisms, as the implementation literature addresses, are designed to make the outcomes of decentralized decisions made by the local government and the merger firms consistent with social optima. As long as the central government adopts the right subsidy scheme, our mechanisms are equivalent to the case in which the central government recedes from the whole process and allows the local players to decide which way to go. In fact, it does not matter at all that who owns the decision rights regarding the fate of the bad firm.

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The central government’s role, through its subsidy scheme, is just to ensure that private decisions are the same as social decisions. Acknowledgments The authors thank two anonymous referees for their helpful comments; and Weiying Zhang, Kenneth Xu, and participants of a seminar in the China Center for Economic Research, Beijing University and the 1998 annual meeting of the Chinese Economists Society held in Baltimore. References Abru, R., & Sen, A. (1991). Virtual implementation in Nash equilibrium. Econometrica 59(4), 997–1021. Lardy, N. (1998) China’s Unfinished Economic Reform. Seminar presented at the China Center for Economic Research, Beijing University. MacAfee, R., & McMillan, J. (1987). Auctions and bidding. J Econ Lit 25(2), 699–738. Mas-Colell, A., Whinston, M., & Green, J. (1995). Microeconomic Theory. New York and Oxford: Oxford University Press. Maskin, E. (1985). The theory of implementation in Nash equilibrium: a survey. In L. Hurwicz, D. Schmeidler, & H. Sonnenschein, (Eds.), Social Goals and Social Organization: Essays in Honor of Elisha Pazner, Cambridge, UK: Cambridge University Press. Matsushima, H. (1988). A new approach to the implementation problem. J Econ Theory 45(1), 128–144. Tian, G. (1997). Virtual implementation in incomplete information environments with infinite alternatives and types. J Math Econ 28, 313–339.