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Incentives in allocation of policy loans
European Economic Review 44 (2000) 785}796
Incentives in allocation of policy loans Xinzhu Zhang Research Center for Regulation and Competition, CASS Beijing 100732, People's Republic of China
Abstract Based on the principal}agent framework I develop a simple model of policy loans, which are granted by the government on non-market terms, to formalize this important banking phenomenon in both China and other developing countries. A supply constraint is imposed on the credit allocation process. The incentive compatibility constraints for the implementation of any lending policy with favoritism are related to di!erent observabilities of outputs. The social planner's optimal credit policy is derived as a function of externalities and available funds. Our result shows that favoritism should be implemented to a less extent as the supply of credit decreases, no matter how large the externality is. 2000 Elsevier Science B.V. All rights reserved. JEL classixcation: P31; P34 Keywords: Policy loans; Favoritism; Externalities; Incentives; Observability
1. Introduction The central feature of China's banking system is that it deals with both policy loans and commercial loans. By policy loans we mean those loans that are granted by the government on non-market terms. In contrast, the credit decisions for commercial loans are totally determined by the market conditions. Thus, policy loans are favorable loans either in terms of borrowing rates or in terms of rationing rule under a shortage of credit. In this paper we are mainly concerned by the latter kind of policy loans that imply favoritism. A leading argument for policy loans is that they are employed by the government to correct &market failures' due to externalities. For instance, policy loans include 0014-2921/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 4 - 2 9 2 1 ( 9 9 ) 0 0 0 4 2 - 2
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investments in infrastructures, national strategic projects, and subsidies to loss-making SOEs. Since policy loans are favorable loans, they have given rise to considerable incentive problems in both state banks and SOEs. On the one hand, because the state banks engage in both lines of business (policy loans as well as commercial loans), they often blame policy lending for their poor performance. The government therefore "nds it di$cult to evaluate their performance and provide them with incentives. On the other hand, since subsidized policy loans are easily available, the loss-making SOEs simply have no incentive to improve e$ciency. Besides, since policy loans create rents they have caused serious rent-seeking and corruption activities. For years, a major headache for the Chinese government has been the state banks' abuse of funds aimed at policy loans for commercial lending. The organizational arrangement of the Chinese banking system and the decentralization reform seem to have worsened these problems in some cases. The recent "nancial turmoil in the East Asian countries gives new relevance to the policy loans issue because its fundamental causes have much to do with the policy banking practice. The central questions we address in this paper are: Whether or not policy loans are incentive compatible and what are the conditions that make policy loans incentive compatible? What is the optimal credit policy for the social planner when the supply of credit is restricted? Indeed, the former question reminds us of the famous debate about the incentive incompatibility of planning. To answer these questions we develop a simple principal}agent model in which a benevolent state bank allocates credit to borrowers under asymmetric information about the productivities of the projects these "rms are endowed with. Policy loans or the projects with low productivities are desirable because there are externalities to these projects. And a lending policy with favoritism is justi"ed when credit rationing is prevailing. Therefore, a con#ict of interests arises between the state bank which wants to internalize externalities and the borrowers whose objectives are to make pro"ts. The problem of internalizing externalities while providing incentives is interesting in our context because it is closely related to the so-called irresponsiveness result. Indeed, when the contract space is only one dimensional, we obtain in our model a similar result. However, if one expands the mechanism space by allowing more observability of outputs, it turns out that there is some room to implement a lending policy with favoritism. In other words, favoritism requires some observability of outputs. Moreover, our results show that the observation of the low type "rm's output is in some sense more valuable than that of the high type "rm for implementing any lending policy with favoritism, and that the See Guesnerie and La!ont (1984). The irresponsiveness result essentially states that when the principal's objective is opposite to the preference of the agent, pooling equilibria occur, i.e., all types are o!ered the same contract.
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optimal credit policy the state bank should implement depends on externalities as well as loanable funds. Particularly, as the supply of credit becomes very constrained, favoritism should be implemented to a less extent or less policy loans should be given.
2. The model We consider a problem in a principal}agent relationship where all agents are risk-neutral: a state bank and a representative borrower (SOE). The borrower identi"es a ("xed-size) project and the bank provides it with necessary "nancing. The manager of the "rm exerts e!ort e which, together with a productivity parameter h, determines output: x"h#e with one unit of input. One can either take the loan as direct input or assume a Leontie! technology so that one unit of the loan can be transformed into one unit of input employed in this production function. Thus, each "rm has a 0}1 demand for loans. h is the manager's private information and has support H"+h , h , (p for policy and c for commercial) with *h"h !h '0. Assume that, for the low type project, there is an additional social value or an positive externality, b, to the private gain. b is exogenous and publicly known. The probabilities of h and h are q and 1!q, respectively. Let the total number of "rms be of measure one. Then, by the law of large numbers, q and 1!q are also the proportions of each type of "rm. For speci"city, assume q(1!q and q'*h. The e!ort level e is also unobservable to the state bank. The disutility of e!ort is assumed to be u(e)"e/2 for obtaining speci"c analytical results without loss of generality for most of the paper. Whether or not x is observable will be speci"ed later. Indeed, we will discuss a few cases with di!erent observabilities of outputs. Let us make the convention that the output belongs to the "rm, but it has to pay a pre-speci"ed amount of transfer, t, to the state bank. The "rm's utility function is then e ;"h#e!t! . 2 Since the manager signs the contract after learning the realization of the adverse selection parameter h, he must be compensated for at least his reservation utility in any state of the nature. Assuming the "rm has no cash at all to realize the project or keep the "rm running, the manager has to apply to the state bank for a loan. The state bank provides either policy loans or commercial loans. The former loans refer to those
This assumption reduces the number of cases to consider.
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loans that are used to "nance projects with externalities, i.e., the project with low productivity in our model. And the latter loans are granted to normal projects. But ex ante the state bank does not know what type of project the borrower has. Assuming that there is a shortage of credit, credit rationing is prevailing. So, the manager's application for any loan is approved only with probability n. Let k be the exogenous supply of credit for the state bank, or more precisely, the proportion of "rms that obtain credit. Finally, we assume the state bank is benevolent and maximizes the expected sum of revenues from lending and of social gains. As is now standard in the mechanism design literature, by the Revelation Principle, the state bank can, without loss of generality, o!er the "rm a direct mechanism or contract, +x(hI ), n(hI ), t(hI ), I , FF F where hI is the borrower's announcement of its private information. Denote x "x(h ) and x "x(h ). Transfers t and t and rationing rules n and n can be similarly de"ned. We obtain the following incentive constraints: for the low type "rm,
(1)
(2)
e (e #*h) n h #e !t ! 5n h #e #*h!t ! 2 2 and, for the high type "rm,
e (e !*h) n h #e !t ! 5n h #e !*h!t ! . 2 2 The individual rationality constraints are:
(3)
(4)
e n h #e !t ! 50 2 and e n h #e !t ! 50. 2 In addition, one has the supply constraint: qn #(1!q)n 4k. The state bank's program is to optimize the objective function
(5)
E="qn (t #b)#(1!q)n t (6) subject to constraints (1)}(5) and the feasibility constraints 04n 41 and 04n 41.
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3. Imperfect observation of outputs To focus on the interesting case of credit rationing, let us assume k(1. In addition, assume that there is imperfect observation of outputs. The various cases of imperfect observability will be speci"ed shortly. Indeed, unobservable outputs are common in reality. For instance, one can think of them coming from some institutional constraints or di$culties in auditing. This point is particularly relevant in a developing country such as China where e$cient and sound auditing systems are far from being developed. To analyze the relationship between output observability and the implementation of policy loans, it is useful to consider di!erent cases of the state bank's capabilities to observe outputs. Let us assume "rst that outputs are never observable. Then, outputs are not contractible, and a "xed-price contract is the only feasible contract to o!er. In this case the incentive and participation constraints become n (h #!t )5n (h #!t ), n (h #!t )5n (h #!t )
(7) (8)
and n (h #!t )50, (9) n (h #!t )50. (10) Adding (7) and (8) we have (n !n )(h !h )50 or n 5n . This inequality simply says that, no matter how large the externality is, the state bank does not have any leeway to implement any lending policy with favoritism in the sense of n 'n , because any favoritism is not incentive compatible. In other words, even if the externality to the low type "rm is very large and the state bank would like to have a lending policy with favoritism (externalities are su$ciently large), it is constrained to implement a pooling rationing rule with n "n "k. 3.1. The low type xrm's output is not observed Assume from now on that there are some institutional restrictions that condition the state bank's ability to observe outputs. Consider "rst the case where the low type "rm's output is not observed by the state bank while the high type "rm's output is. In this case the state bank is constrained to o!er the "rm which claims to have low productivity a "xed-price contract. The contracts o!ered are +t , n , and
See Zhang (1997) for the case of observable outputs.
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+x , t , n ,. Under these contracts the output of the "rm which has claimed to have a low type produces at the socially e$cient level. Thus, the incentive constraints are: for the low type "rm,
(e #*h) n (h #!t )5n h #e #*h!t ! 2
(11)
and, for the high type "rm,
e n h #e !t ! 5n (h #!t ). 2
(12)
Constraints (11) and (12) are straightforward. Note that the high type "rm would produce e$ciently (e "1) when mimicking the low type "rm while the low type "rm would exert e!ort e #*h to mimic the high type "rm. The state bank's problem is then to maximize the objective function (6) subject to constraints (4), (5), (9), (11), (12) and the feasibility constraints 04n 41 and 04n 41. For the sake of presenting our "rst result, denote *h b*" , q and 1 b*(k)" 2
1#(*h/2)q k*" 1#*h/2
(1!q)k *h#1!q 2!q ! ! (1!*h) . (k!q)q 2 q
Then, we have: Proposition 1. Suppose the low type xrm's output is not observed. A necessary condition for the state bank to implement any lending policy with favoritism is b5b*. Moreover, the optimal credit policy is characterized by: (1) When k5k*, n "1 and n "(k!q)/(1!q). (2) When k(k* and b5b*(k), the optimal rationing rule is the same as in (1), but the high type xrm's output is distorted beyond the socially ezcient level, i.e., e '1. (3) When k(k* and b(b*(k), k k(e #*h/2) n " and n " . q(e #*h/2)#1!q q(e #*h/2)#1!q The production of the high type xrm is still distorted, but e (1. Proof. See Zhang (1997). Proposition 1 shows "rst that the externality is required to be su$ciently large to justify any lending policy with favoritism. This result is intuitive: the productive e$ciency concern will outweigh that for internalizing externalities
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when the value of the externality is not large enough, so that the optimal rationing rule will favor the high type "rm. The result (1) simply shows that when the available funds are su$ciently large, the optimal rationing rule is to "nance the low type "rm's production with probability one. Moreover, the "rst-best allocation can be achieved, i.e., e "e "1. The allocation is the same as under full information, but for di!erent reasons. That the low type "rm produces e$ciently is due to the fact that it is o!ered a "xed-price contract since its output is not observed. In contrast, the high type "rm also produces e$ciently because it is given incentives by the state bank to maximize its own objective function, which is just the familiar no-distortion-at-the-top result. Note that even though each type of "rm produces e$ciently, the optimal lending policy calls for favoritism. The reason is that the low type "rm would need to exert an e!ort beyond the socially e$cient level (1#*h) if it received the contract designed for the high type "rm. The result in (2) shows that, as the available funds k decrease and the externality is relatively high, the same rationing rule as in (1) prevails, but the allocation is di!erent. More precisely, the high type "rm produces at a suboptimal level, e "(1!q)/(k!q)!*h/2, which is beyond the socially e$cient level. This makes the low type "rm's misreporting very costly and the optimal lending policy with favoritism becomes implementable. Note that e decreases with the supply of credit k: the more constrained the available funds k, the higher the output or e!ort level required for the high type "rm or the more distorted the allocation. In other words, as the supply of credit decreases, the implementation of the optimal lending policy with favoritism requires an additional distortion for the high type "rm's output. As the loanable funds k decrease further, the rationing rule according to which the high type "rm's production is "nanced with probability one is no longer optimal, or more precisely not sustainable, no matter how large the externality is. Therefore, any lending policy with favoritism has to be implemented to a less extent in the sense of n (1. The high type "rm's production is still distorted, but is below the e$cient level. One thus obtains (3). Note that in both (2) and (3), the standard result of no-distortion at top does not apply any more, that is, both e$cient and ine$cient types' outputs are distorted. These various possibilities of adjustment to satisfy incentive compatibility can best be seen from the second-order condition
*h n e # !n 50. 2
(13)
One can easily see that because the high type "rm's output is observed, the contract space is expanded compared with the case of no output being observed, and some lending policies with favoritism become implementable.
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Simple comparative statics shows that the more asymmetric the information (the larger *h is), the less likely it is that the low type "rm's production will be "nanced. This con"rms the perception that, when the information problem is serious, that is the state bank has very limited information about borrowers' production attributes, the implementation of any lending policy with favoritism is rather problematic because of the incentive problems involved. 3.2. The high type xrm's output is unobserved Now we consider the case where the high type "rm's output is not observed due to some institutional constraints. Therefore, the "rm which claims to have a high type is o!ered a "xed-price contract, and the state bank makes contract o!ers (x , t , n ) and (t , n ). Following a similar argument as in the last subsec tion, the high type "rm produces or exerts e!ort at the socially e$cient level, i.e., e "1. In addition, the low type "rm would produce e$ciently if it chose the contract designed for the high type "rm. The incentive constraints are: for the low type "rm
e 1 n h #e !t ! 5n h # !t , 2 2 for the high type "rm and, when e 5*h,
(14)
(e !*h) . n (h #!t )5n h #e !*h!t ! 2
(15)
Adding these two constraints we obtain the second-order condition
*h n !n e ! 50. 2
(16)
One can immediately observe that there is some room to implement policy lending in this case too. As loanable funds decrease, e has to be distorted to a su$ciently low level to ensure incentive compatibility if the state bank wants to implement any lending policy with favoritism (n 'n ). The smaller the supply k the more distorted the low type "rm's production or e!ort e . When the e!ort is distorted to a su$ciently low level such that e (*h, the high type "rm will not need to exert any e!ort to mimic the low type "rm. In this case incentive compatibility should be ensured with a zero e!ort level. In other words, in contrast to the case where the low type "rm's output is not observed, there is the possibility of a change of the high type "rm's incentive constraint as the low type "rm's production is distorted to a su$ciently low level. The new incentive constraint for the high type "rm when e (*h becomes n (h #!t )5n (h #e !t ). (17)
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Hence, the state bank's problem is to maximize the objective function (6) subject to constraints (3), (5), (10), (14), (15) and (17) and the feasibility constraints. For the sake of presenting our next result, denote
*h 1!q b&" 1! *h , q 2q
(1#q)(1!*h) b&Y" , 2(1!q)
1!q *h (1!q)*h k&"q#(1!q) 1! *h! , k&"q# q 2 2 and 2q*h!1#q b&(k)"(2q!k)(*h/2(k!q)(1!q)! 2(1!q)
where k'q.
Then, we have Proposition 2. Suppose the high type xrm's output is not observed. A necessary condition for the state bank to implement any lending policy with favoritism is b5b&. Moreover, the optimal credit policy is characterized by: (1) When k5k&, n "1 and n "(k!q)/(1!q). (2) When k&'k5k& and b5b&Y, the credit rationing rule is the same as in (1), but the low type xrm's output is distorted below that in (1). (3) When k(k& and b&4b(b&Y, k (e !*h/2)k n " and n " , q#(1!q)(e !*h/2) q#(1!q)(e !*h/2) where e is distorted satisfying *h(e (1. (4) When k(k& and b'b&(k), the optimal rationing rule is the same as in (1), but the low type xrm's output is distorted below a suzciently low level, i.e., e (*h. (5) When k(k& and b(b&(k), k*h ke/2 and n " . n " q*h#(1!q)e /2 q*h#(1!q)e/2 The low type xrm's output is distorted to a suzciently low level, i.e., e (*h. Proof. See Zhang (1997). In contrast to Proposition 1, there are "ve regimes of optimal contracts which can be divided into two groups: the contracts in one group, including contracts in (1)}(3), have the property that e 5*h, and the contracts in the other group, including contracts in (4) and (5), satisfy e (*h. In other words, each group of contracts is connected with di!erent incentive constraints of the high type "rm.
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One can easily verify that b*'b&, which means that the lending policy with favoritism when the low type "rm's output is unobserved requires higher externalities than that when the high type "rm's output is unobserved. In this sense favoritism is more demanding in the former case, and one can thus conclude that the observation of the low type "rm's output is a more valuable instrument than that of the high type "rm for policy lending. When the state bank has relatively large loanable funds at its disposal (k'k&), the optimal rationing rule is to "nance the low type "rm with probabil ity one as long as the externality from its production is su$ciently large. The optimal allocation is the same as the second-best result under no supply constraint. Again, as we discussed in the last subsection, even though the low type "rm would produce e$ciently when it mimicked the high type "rm, the lending policy with favoritism is incentive compatible. The reason is the former's production would be distorted to a suboptimal level so that it would have to incur extra disutilities to produce e$ciently. As loanable funds decrease below k&, the original optimal contract becomes incentive incompatible since the costs from misreporting would decline and the low type "rm would want to claim to have a high type. The state bank has two choices to maintain incentive compatibility: Either to distort the low type "rm's production further below the e$cient level if the same rationing rule as in (1) is to be preserved or to adjust both the low type "rm's production and the rationing rule. If the loanable funds are not too small (k'k&), the former option is optimal where the high type "rm's e!ort is e "(k!q)/(1!q)#*h/2. Besides, it requires that the externality be relatively larger, i.e., b'b&Y. Note that e increases with loanable funds so that the supply of credit is required to be su$ciently large to ensure e '*h. Therefore, when the supply k decreases to a su$ciently low level ((k&), the former option remains optimal only if the low type "rm's production is distorted to a very low level, i.e., e (*h. In this case one has to change the incentive constraint of the high type "rm, since it would not need to exert any e!ort to mimic the low type "rm. When the externality is relatively low and/or the supply is very restricted, the original rationing rule is no longer optimal, but one obtains the optimal contracts in (3) with e '*h and the optimal contracts in (5) with e (*h. 4. Conclusion Our model has provided us with some useful results. First, by relating incentive compatibility of favoritism to various observabilities of outputs, we have shown that policy lending can be implemented by expanding the contract space. In other words, the social planner must be able to observe outputs in order to implement any lending policy with favoritism. This is clearly an intuitive result which has important policy rami"cations. In particular, it implies
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that policy lending requires some strong institutional supports such as e$cient accounting and auditing systems. In light of this simple result one may cast some doubt on policy lending in China and other developing countries: If one takes for granted the fact that China's government is constrained to use policy loans for managing the economy, it seems that the necessary institutions to ensure the e!ectiveness of this policy instrument are not in place. Without these institutions, however, it is not guaranteed that the bene"ts of policy loans can be realized. Second, we have shown that the optimal lending policy with favoritism depends not only on the externality, which is easy to understand since the social planner's objective is to maximize social welfare, but also on the supply constraint. More precisely, favoritism should be implemented to a less extent in the optimal credit policy as the supply of credit becomes more restricted, no matter how large the externality is. This result sheds some light on the "nancial problems in China's banking sector and the "nancial crisis in the East Asian countries. In these economies, supply is likely to be highly constrained for at least two reasons: On the one hand, their tax systems are very ine$cient so that tax incomes are rather restricted. For instance, China's tax revenues have been declining steadily since 1988. Since many policy loans imply some subsidies which will eventually become a "scal burden, these economies simply do not have the resources to "nance them. On the other hand, the &soft budget' problem has not been solved yet even though some enterprise reforms have been introduced. Under these conditions our model predicts that much care should be taken in implementing policy loans. However, these countries' experiences seemed to have been contrary to this warning: Too many policy loans were allocated which, together with a large amount of commercial loans, put enterprises in heavy debt. As the economic conditions worsened, too many "rms became insolvent, and a systemic "nancial crisis was formed. And third, to have the incentive compatibility of policy lending, the social planner needs not only to bear the incentive costs of leaving informational rents to e$cient "rms, but also to distort outputs further away from the "rst-best result. Thus, the authority faces a tough trade-o! between favoritism and productive e$ciency. Our result may also shed some light on the banking reform in China, which was meant to transfer policy lending to the newly established policy banks. This organizational change from the U-form to the M-form can be understood as an e!ort to lessen information asymmetry by specialization, since more intense investments in information acquisition are possible after the reform. Our model predicts that it will be less costly to implement lending policies with favoritism after the information constraint is relaxed. Our discussion so far takes it for granted that the social planner chooses to use policy loans to implement their favored industrial polices to promote
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economic development. However, one may raise the question of why policy loans should be implemented in the "rst place. Indeed, in light of the general result by Atkinson and Stiglitz (1976) one may cast some doubt on the whole policy loans enterprise: Why should policy loans be used which distort the prices of capital relative to other goods and services? We believe that given China' institutional characteristics policy loans have been and probably will remain to be a valuable policy instrument for at least the following reasons: First, to put SOEs on debt has good incentive properties compared to direct "scal appropriations. Indeed, this was one of the main motivations for the reform of &transforming appropriations into loans'. Second, China lacks alternative means such as well-functioning capital markets to achieve development tasks. Thus, policy loans are the only choices in the government's control. Last, as we mentioned, China's tax system has low e$ciency, which can be seen by looking at the social cost of public funds. Some studies show that it stands at about 2.0 in China (see Zhang, 1995; La!ont and Senik-Leygonie, 1997) which is much higher than that in the developed economies (about 0.3). This suggests the possibility that the welfare losses from distortions caused by taxation may be higher than those caused by policy loans. However, we are not aware of any study on the welfare losses resulting from the distortion of relative prices by policy loans. Our result points out the importance of building up institutional capacities to establish e$cient accounting and auditing systems. Otherwise China might fall in a vicious development trap: to achieve economic take o!, it needs to rely on strong institutions to provide incentives for improved e$ciency, but the lack of such institutions makes it impossible to realize these bene"ts, and thus handicaps economic development. Acknowledgements I thank Jean-Jacques La!ont, Yingyi Qiang, Patrick Rey, Jean-Charles Rochet, and Jean Tirole for their comments. All remaining errors are my own. References Atkinson, A.B., Stiglitz, J., 1976. The design of tax structure: direct and indirect taxation. Journal of Public Economics 6, 55}75. Guesnerie, R., La!ont, J.-J., 1984. A complete solution to a class of principal}agent problems with an application to the control of a self-managed "rm. Journal of Public Economics 25, 329}369. La!ont, J.-J., Senik-Leygonie, C., 1997. Price Controls and the Economics of Institutions in China, OECD, Paris. Zhang, X.-Z., 1995. The social cost of public funds in China. Discussion Paper, IQTE of Chinese Academy of Social Sciences. Zhang, X.-Z., 1997. An Incentive Theory of Policy Loans. Ph.D. Thesis, UniversiteH des Sciences Sociales de Toulouse, unpublished.
Incentives in allocation of policy loans Xinzhu Zhang Research Center for Regulation and Competition, CASS Beijing 100732, People's Republic of China
Abstract Based on the principal}agent framework I develop a simple model of policy loans, which are granted by the government on non-market terms, to formalize this important banking phenomenon in both China and other developing countries. A supply constraint is imposed on the credit allocation process. The incentive compatibility constraints for the implementation of any lending policy with favoritism are related to di!erent observabilities of outputs. The social planner's optimal credit policy is derived as a function of externalities and available funds. Our result shows that favoritism should be implemented to a less extent as the supply of credit decreases, no matter how large the externality is. 2000 Elsevier Science B.V. All rights reserved. JEL classixcation: P31; P34 Keywords: Policy loans; Favoritism; Externalities; Incentives; Observability
1. Introduction The central feature of China's banking system is that it deals with both policy loans and commercial loans. By policy loans we mean those loans that are granted by the government on non-market terms. In contrast, the credit decisions for commercial loans are totally determined by the market conditions. Thus, policy loans are favorable loans either in terms of borrowing rates or in terms of rationing rule under a shortage of credit. In this paper we are mainly concerned by the latter kind of policy loans that imply favoritism. A leading argument for policy loans is that they are employed by the government to correct &market failures' due to externalities. For instance, policy loans include 0014-2921/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 4 - 2 9 2 1 ( 9 9 ) 0 0 0 4 2 - 2
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investments in infrastructures, national strategic projects, and subsidies to loss-making SOEs. Since policy loans are favorable loans, they have given rise to considerable incentive problems in both state banks and SOEs. On the one hand, because the state banks engage in both lines of business (policy loans as well as commercial loans), they often blame policy lending for their poor performance. The government therefore "nds it di$cult to evaluate their performance and provide them with incentives. On the other hand, since subsidized policy loans are easily available, the loss-making SOEs simply have no incentive to improve e$ciency. Besides, since policy loans create rents they have caused serious rent-seeking and corruption activities. For years, a major headache for the Chinese government has been the state banks' abuse of funds aimed at policy loans for commercial lending. The organizational arrangement of the Chinese banking system and the decentralization reform seem to have worsened these problems in some cases. The recent "nancial turmoil in the East Asian countries gives new relevance to the policy loans issue because its fundamental causes have much to do with the policy banking practice. The central questions we address in this paper are: Whether or not policy loans are incentive compatible and what are the conditions that make policy loans incentive compatible? What is the optimal credit policy for the social planner when the supply of credit is restricted? Indeed, the former question reminds us of the famous debate about the incentive incompatibility of planning. To answer these questions we develop a simple principal}agent model in which a benevolent state bank allocates credit to borrowers under asymmetric information about the productivities of the projects these "rms are endowed with. Policy loans or the projects with low productivities are desirable because there are externalities to these projects. And a lending policy with favoritism is justi"ed when credit rationing is prevailing. Therefore, a con#ict of interests arises between the state bank which wants to internalize externalities and the borrowers whose objectives are to make pro"ts. The problem of internalizing externalities while providing incentives is interesting in our context because it is closely related to the so-called irresponsiveness result. Indeed, when the contract space is only one dimensional, we obtain in our model a similar result. However, if one expands the mechanism space by allowing more observability of outputs, it turns out that there is some room to implement a lending policy with favoritism. In other words, favoritism requires some observability of outputs. Moreover, our results show that the observation of the low type "rm's output is in some sense more valuable than that of the high type "rm for implementing any lending policy with favoritism, and that the See Guesnerie and La!ont (1984). The irresponsiveness result essentially states that when the principal's objective is opposite to the preference of the agent, pooling equilibria occur, i.e., all types are o!ered the same contract.
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optimal credit policy the state bank should implement depends on externalities as well as loanable funds. Particularly, as the supply of credit becomes very constrained, favoritism should be implemented to a less extent or less policy loans should be given.
2. The model We consider a problem in a principal}agent relationship where all agents are risk-neutral: a state bank and a representative borrower (SOE). The borrower identi"es a ("xed-size) project and the bank provides it with necessary "nancing. The manager of the "rm exerts e!ort e which, together with a productivity parameter h, determines output: x"h#e with one unit of input. One can either take the loan as direct input or assume a Leontie! technology so that one unit of the loan can be transformed into one unit of input employed in this production function. Thus, each "rm has a 0}1 demand for loans. h is the manager's private information and has support H"+h , h , (p for policy and c for commercial) with *h"h !h '0. Assume that, for the low type project, there is an additional social value or an positive externality, b, to the private gain. b is exogenous and publicly known. The probabilities of h and h are q and 1!q, respectively. Let the total number of "rms be of measure one. Then, by the law of large numbers, q and 1!q are also the proportions of each type of "rm. For speci"city, assume q(1!q and q'*h. The e!ort level e is also unobservable to the state bank. The disutility of e!ort is assumed to be u(e)"e/2 for obtaining speci"c analytical results without loss of generality for most of the paper. Whether or not x is observable will be speci"ed later. Indeed, we will discuss a few cases with di!erent observabilities of outputs. Let us make the convention that the output belongs to the "rm, but it has to pay a pre-speci"ed amount of transfer, t, to the state bank. The "rm's utility function is then e ;"h#e!t! . 2 Since the manager signs the contract after learning the realization of the adverse selection parameter h, he must be compensated for at least his reservation utility in any state of the nature. Assuming the "rm has no cash at all to realize the project or keep the "rm running, the manager has to apply to the state bank for a loan. The state bank provides either policy loans or commercial loans. The former loans refer to those
This assumption reduces the number of cases to consider.
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loans that are used to "nance projects with externalities, i.e., the project with low productivity in our model. And the latter loans are granted to normal projects. But ex ante the state bank does not know what type of project the borrower has. Assuming that there is a shortage of credit, credit rationing is prevailing. So, the manager's application for any loan is approved only with probability n. Let k be the exogenous supply of credit for the state bank, or more precisely, the proportion of "rms that obtain credit. Finally, we assume the state bank is benevolent and maximizes the expected sum of revenues from lending and of social gains. As is now standard in the mechanism design literature, by the Revelation Principle, the state bank can, without loss of generality, o!er the "rm a direct mechanism or contract, +x(hI ), n(hI ), t(hI ), I , FF F where hI is the borrower's announcement of its private information. Denote x "x(h ) and x "x(h ). Transfers t and t and rationing rules n and n can be similarly de"ned. We obtain the following incentive constraints: for the low type "rm,
(1)
(2)
e (e #*h) n h #e !t ! 5n h #e #*h!t ! 2 2 and, for the high type "rm,
e (e !*h) n h #e !t ! 5n h #e !*h!t ! . 2 2 The individual rationality constraints are:
(3)
(4)
e n h #e !t ! 50 2 and e n h #e !t ! 50. 2 In addition, one has the supply constraint: qn #(1!q)n 4k. The state bank's program is to optimize the objective function
(5)
E="qn (t #b)#(1!q)n t (6) subject to constraints (1)}(5) and the feasibility constraints 04n 41 and 04n 41.
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3. Imperfect observation of outputs To focus on the interesting case of credit rationing, let us assume k(1. In addition, assume that there is imperfect observation of outputs. The various cases of imperfect observability will be speci"ed shortly. Indeed, unobservable outputs are common in reality. For instance, one can think of them coming from some institutional constraints or di$culties in auditing. This point is particularly relevant in a developing country such as China where e$cient and sound auditing systems are far from being developed. To analyze the relationship between output observability and the implementation of policy loans, it is useful to consider di!erent cases of the state bank's capabilities to observe outputs. Let us assume "rst that outputs are never observable. Then, outputs are not contractible, and a "xed-price contract is the only feasible contract to o!er. In this case the incentive and participation constraints become n (h #!t )5n (h #!t ), n (h #!t )5n (h #!t )
(7) (8)
and n (h #!t )50, (9) n (h #!t )50. (10) Adding (7) and (8) we have (n !n )(h !h )50 or n 5n . This inequality simply says that, no matter how large the externality is, the state bank does not have any leeway to implement any lending policy with favoritism in the sense of n 'n , because any favoritism is not incentive compatible. In other words, even if the externality to the low type "rm is very large and the state bank would like to have a lending policy with favoritism (externalities are su$ciently large), it is constrained to implement a pooling rationing rule with n "n "k. 3.1. The low type xrm's output is not observed Assume from now on that there are some institutional restrictions that condition the state bank's ability to observe outputs. Consider "rst the case where the low type "rm's output is not observed by the state bank while the high type "rm's output is. In this case the state bank is constrained to o!er the "rm which claims to have low productivity a "xed-price contract. The contracts o!ered are +t , n , and
See Zhang (1997) for the case of observable outputs.
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+x , t , n ,. Under these contracts the output of the "rm which has claimed to have a low type produces at the socially e$cient level. Thus, the incentive constraints are: for the low type "rm,
(e #*h) n (h #!t )5n h #e #*h!t ! 2
(11)
and, for the high type "rm,
e n h #e !t ! 5n (h #!t ). 2
(12)
Constraints (11) and (12) are straightforward. Note that the high type "rm would produce e$ciently (e "1) when mimicking the low type "rm while the low type "rm would exert e!ort e #*h to mimic the high type "rm. The state bank's problem is then to maximize the objective function (6) subject to constraints (4), (5), (9), (11), (12) and the feasibility constraints 04n 41 and 04n 41. For the sake of presenting our "rst result, denote *h b*" , q and 1 b*(k)" 2
1#(*h/2)q k*" 1#*h/2
(1!q)k *h#1!q 2!q ! ! (1!*h) . (k!q)q 2 q
Then, we have: Proposition 1. Suppose the low type xrm's output is not observed. A necessary condition for the state bank to implement any lending policy with favoritism is b5b*. Moreover, the optimal credit policy is characterized by: (1) When k5k*, n "1 and n "(k!q)/(1!q). (2) When k(k* and b5b*(k), the optimal rationing rule is the same as in (1), but the high type xrm's output is distorted beyond the socially ezcient level, i.e., e '1. (3) When k(k* and b(b*(k), k k(e #*h/2) n " and n " . q(e #*h/2)#1!q q(e #*h/2)#1!q The production of the high type xrm is still distorted, but e (1. Proof. See Zhang (1997). Proposition 1 shows "rst that the externality is required to be su$ciently large to justify any lending policy with favoritism. This result is intuitive: the productive e$ciency concern will outweigh that for internalizing externalities
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when the value of the externality is not large enough, so that the optimal rationing rule will favor the high type "rm. The result (1) simply shows that when the available funds are su$ciently large, the optimal rationing rule is to "nance the low type "rm's production with probability one. Moreover, the "rst-best allocation can be achieved, i.e., e "e "1. The allocation is the same as under full information, but for di!erent reasons. That the low type "rm produces e$ciently is due to the fact that it is o!ered a "xed-price contract since its output is not observed. In contrast, the high type "rm also produces e$ciently because it is given incentives by the state bank to maximize its own objective function, which is just the familiar no-distortion-at-the-top result. Note that even though each type of "rm produces e$ciently, the optimal lending policy calls for favoritism. The reason is that the low type "rm would need to exert an e!ort beyond the socially e$cient level (1#*h) if it received the contract designed for the high type "rm. The result in (2) shows that, as the available funds k decrease and the externality is relatively high, the same rationing rule as in (1) prevails, but the allocation is di!erent. More precisely, the high type "rm produces at a suboptimal level, e "(1!q)/(k!q)!*h/2, which is beyond the socially e$cient level. This makes the low type "rm's misreporting very costly and the optimal lending policy with favoritism becomes implementable. Note that e decreases with the supply of credit k: the more constrained the available funds k, the higher the output or e!ort level required for the high type "rm or the more distorted the allocation. In other words, as the supply of credit decreases, the implementation of the optimal lending policy with favoritism requires an additional distortion for the high type "rm's output. As the loanable funds k decrease further, the rationing rule according to which the high type "rm's production is "nanced with probability one is no longer optimal, or more precisely not sustainable, no matter how large the externality is. Therefore, any lending policy with favoritism has to be implemented to a less extent in the sense of n (1. The high type "rm's production is still distorted, but is below the e$cient level. One thus obtains (3). Note that in both (2) and (3), the standard result of no-distortion at top does not apply any more, that is, both e$cient and ine$cient types' outputs are distorted. These various possibilities of adjustment to satisfy incentive compatibility can best be seen from the second-order condition
*h n e # !n 50. 2
(13)
One can easily see that because the high type "rm's output is observed, the contract space is expanded compared with the case of no output being observed, and some lending policies with favoritism become implementable.
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Simple comparative statics shows that the more asymmetric the information (the larger *h is), the less likely it is that the low type "rm's production will be "nanced. This con"rms the perception that, when the information problem is serious, that is the state bank has very limited information about borrowers' production attributes, the implementation of any lending policy with favoritism is rather problematic because of the incentive problems involved. 3.2. The high type xrm's output is unobserved Now we consider the case where the high type "rm's output is not observed due to some institutional constraints. Therefore, the "rm which claims to have a high type is o!ered a "xed-price contract, and the state bank makes contract o!ers (x , t , n ) and (t , n ). Following a similar argument as in the last subsec tion, the high type "rm produces or exerts e!ort at the socially e$cient level, i.e., e "1. In addition, the low type "rm would produce e$ciently if it chose the contract designed for the high type "rm. The incentive constraints are: for the low type "rm
e 1 n h #e !t ! 5n h # !t , 2 2 for the high type "rm and, when e 5*h,
(14)
(e !*h) . n (h #!t )5n h #e !*h!t ! 2
(15)
Adding these two constraints we obtain the second-order condition
*h n !n e ! 50. 2
(16)
One can immediately observe that there is some room to implement policy lending in this case too. As loanable funds decrease, e has to be distorted to a su$ciently low level to ensure incentive compatibility if the state bank wants to implement any lending policy with favoritism (n 'n ). The smaller the supply k the more distorted the low type "rm's production or e!ort e . When the e!ort is distorted to a su$ciently low level such that e (*h, the high type "rm will not need to exert any e!ort to mimic the low type "rm. In this case incentive compatibility should be ensured with a zero e!ort level. In other words, in contrast to the case where the low type "rm's output is not observed, there is the possibility of a change of the high type "rm's incentive constraint as the low type "rm's production is distorted to a su$ciently low level. The new incentive constraint for the high type "rm when e (*h becomes n (h #!t )5n (h #e !t ). (17)
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Hence, the state bank's problem is to maximize the objective function (6) subject to constraints (3), (5), (10), (14), (15) and (17) and the feasibility constraints. For the sake of presenting our next result, denote
*h 1!q b&" 1! *h , q 2q
(1#q)(1!*h) b&Y" , 2(1!q)
1!q *h (1!q)*h k&"q#(1!q) 1! *h! , k&"q# q 2 2 and 2q*h!1#q b&(k)"(2q!k)(*h/2(k!q)(1!q)! 2(1!q)
where k'q.
Then, we have Proposition 2. Suppose the high type xrm's output is not observed. A necessary condition for the state bank to implement any lending policy with favoritism is b5b&. Moreover, the optimal credit policy is characterized by: (1) When k5k&, n "1 and n "(k!q)/(1!q). (2) When k&'k5k& and b5b&Y, the credit rationing rule is the same as in (1), but the low type xrm's output is distorted below that in (1). (3) When k(k& and b&4b(b&Y, k (e !*h/2)k n " and n " , q#(1!q)(e !*h/2) q#(1!q)(e !*h/2) where e is distorted satisfying *h(e (1. (4) When k(k& and b'b&(k), the optimal rationing rule is the same as in (1), but the low type xrm's output is distorted below a suzciently low level, i.e., e (*h. (5) When k(k& and b(b&(k), k*h ke/2 and n " . n " q*h#(1!q)e /2 q*h#(1!q)e/2 The low type xrm's output is distorted to a suzciently low level, i.e., e (*h. Proof. See Zhang (1997). In contrast to Proposition 1, there are "ve regimes of optimal contracts which can be divided into two groups: the contracts in one group, including contracts in (1)}(3), have the property that e 5*h, and the contracts in the other group, including contracts in (4) and (5), satisfy e (*h. In other words, each group of contracts is connected with di!erent incentive constraints of the high type "rm.
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One can easily verify that b*'b&, which means that the lending policy with favoritism when the low type "rm's output is unobserved requires higher externalities than that when the high type "rm's output is unobserved. In this sense favoritism is more demanding in the former case, and one can thus conclude that the observation of the low type "rm's output is a more valuable instrument than that of the high type "rm for policy lending. When the state bank has relatively large loanable funds at its disposal (k'k&), the optimal rationing rule is to "nance the low type "rm with probabil ity one as long as the externality from its production is su$ciently large. The optimal allocation is the same as the second-best result under no supply constraint. Again, as we discussed in the last subsection, even though the low type "rm would produce e$ciently when it mimicked the high type "rm, the lending policy with favoritism is incentive compatible. The reason is the former's production would be distorted to a suboptimal level so that it would have to incur extra disutilities to produce e$ciently. As loanable funds decrease below k&, the original optimal contract becomes incentive incompatible since the costs from misreporting would decline and the low type "rm would want to claim to have a high type. The state bank has two choices to maintain incentive compatibility: Either to distort the low type "rm's production further below the e$cient level if the same rationing rule as in (1) is to be preserved or to adjust both the low type "rm's production and the rationing rule. If the loanable funds are not too small (k'k&), the former option is optimal where the high type "rm's e!ort is e "(k!q)/(1!q)#*h/2. Besides, it requires that the externality be relatively larger, i.e., b'b&Y. Note that e increases with loanable funds so that the supply of credit is required to be su$ciently large to ensure e '*h. Therefore, when the supply k decreases to a su$ciently low level ((k&), the former option remains optimal only if the low type "rm's production is distorted to a very low level, i.e., e (*h. In this case one has to change the incentive constraint of the high type "rm, since it would not need to exert any e!ort to mimic the low type "rm. When the externality is relatively low and/or the supply is very restricted, the original rationing rule is no longer optimal, but one obtains the optimal contracts in (3) with e '*h and the optimal contracts in (5) with e (*h. 4. Conclusion Our model has provided us with some useful results. First, by relating incentive compatibility of favoritism to various observabilities of outputs, we have shown that policy lending can be implemented by expanding the contract space. In other words, the social planner must be able to observe outputs in order to implement any lending policy with favoritism. This is clearly an intuitive result which has important policy rami"cations. In particular, it implies
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that policy lending requires some strong institutional supports such as e$cient accounting and auditing systems. In light of this simple result one may cast some doubt on policy lending in China and other developing countries: If one takes for granted the fact that China's government is constrained to use policy loans for managing the economy, it seems that the necessary institutions to ensure the e!ectiveness of this policy instrument are not in place. Without these institutions, however, it is not guaranteed that the bene"ts of policy loans can be realized. Second, we have shown that the optimal lending policy with favoritism depends not only on the externality, which is easy to understand since the social planner's objective is to maximize social welfare, but also on the supply constraint. More precisely, favoritism should be implemented to a less extent in the optimal credit policy as the supply of credit becomes more restricted, no matter how large the externality is. This result sheds some light on the "nancial problems in China's banking sector and the "nancial crisis in the East Asian countries. In these economies, supply is likely to be highly constrained for at least two reasons: On the one hand, their tax systems are very ine$cient so that tax incomes are rather restricted. For instance, China's tax revenues have been declining steadily since 1988. Since many policy loans imply some subsidies which will eventually become a "scal burden, these economies simply do not have the resources to "nance them. On the other hand, the &soft budget' problem has not been solved yet even though some enterprise reforms have been introduced. Under these conditions our model predicts that much care should be taken in implementing policy loans. However, these countries' experiences seemed to have been contrary to this warning: Too many policy loans were allocated which, together with a large amount of commercial loans, put enterprises in heavy debt. As the economic conditions worsened, too many "rms became insolvent, and a systemic "nancial crisis was formed. And third, to have the incentive compatibility of policy lending, the social planner needs not only to bear the incentive costs of leaving informational rents to e$cient "rms, but also to distort outputs further away from the "rst-best result. Thus, the authority faces a tough trade-o! between favoritism and productive e$ciency. Our result may also shed some light on the banking reform in China, which was meant to transfer policy lending to the newly established policy banks. This organizational change from the U-form to the M-form can be understood as an e!ort to lessen information asymmetry by specialization, since more intense investments in information acquisition are possible after the reform. Our model predicts that it will be less costly to implement lending policies with favoritism after the information constraint is relaxed. Our discussion so far takes it for granted that the social planner chooses to use policy loans to implement their favored industrial polices to promote
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economic development. However, one may raise the question of why policy loans should be implemented in the "rst place. Indeed, in light of the general result by Atkinson and Stiglitz (1976) one may cast some doubt on the whole policy loans enterprise: Why should policy loans be used which distort the prices of capital relative to other goods and services? We believe that given China' institutional characteristics policy loans have been and probably will remain to be a valuable policy instrument for at least the following reasons: First, to put SOEs on debt has good incentive properties compared to direct "scal appropriations. Indeed, this was one of the main motivations for the reform of &transforming appropriations into loans'. Second, China lacks alternative means such as well-functioning capital markets to achieve development tasks. Thus, policy loans are the only choices in the government's control. Last, as we mentioned, China's tax system has low e$ciency, which can be seen by looking at the social cost of public funds. Some studies show that it stands at about 2.0 in China (see Zhang, 1995; La!ont and Senik-Leygonie, 1997) which is much higher than that in the developed economies (about 0.3). This suggests the possibility that the welfare losses from distortions caused by taxation may be higher than those caused by policy loans. However, we are not aware of any study on the welfare losses resulting from the distortion of relative prices by policy loans. Our result points out the importance of building up institutional capacities to establish e$cient accounting and auditing systems. Otherwise China might fall in a vicious development trap: to achieve economic take o!, it needs to rely on strong institutions to provide incentives for improved e$ciency, but the lack of such institutions makes it impossible to realize these bene"ts, and thus handicaps economic development. Acknowledgements I thank Jean-Jacques La!ont, Yingyi Qiang, Patrick Rey, Jean-Charles Rochet, and Jean Tirole for their comments. All remaining errors are my own. References Atkinson, A.B., Stiglitz, J., 1976. The design of tax structure: direct and indirect taxation. Journal of Public Economics 6, 55}75. Guesnerie, R., La!ont, J.-J., 1984. A complete solution to a class of principal}agent problems with an application to the control of a self-managed "rm. Journal of Public Economics 25, 329}369. La!ont, J.-J., Senik-Leygonie, C., 1997. Price Controls and the Economics of Institutions in China, OECD, Paris. Zhang, X.-Z., 1995. The social cost of public funds in China. Discussion Paper, IQTE of Chinese Academy of Social Sciences. Zhang, X.-Z., 1997. An Incentive Theory of Policy Loans. Ph.D. Thesis, UniversiteH des Sciences Sociales de Toulouse, unpublished.