Optimal Banking Sector Recapitalization

Transcription

1 Optimal Banking Sector Recapitalization P. Marcelo Oviedo Shiva Sikdar Iowa State University Iowa State University November 2006 [Preliminary and Incomplete] Abstract More than 100 banking crises have hit developing and developed countries alike since the late 1970 s. The vast majority of these crises have been resolved by resorting to government-financed bank restructuring programs which have at times cost as much as 50% of GDP. We analyze the problem from the point of view of a government that has already decided to recapitalize the banking system, and ask the following: what is the optimal path of a program that weighs recapitalization benefits and the program s costs? We answer this question by building a model where banking credit is essential due to a working capital constraint on firms, and where banks are financial intermediaries that borrow from households and lend to firms. A banking crisis in the model produces a disruption of credit and a fall in output equivalent to those in developing countries affected by banking crises. We characterize the optimal bank restructuring program by formulating a Ramsey problem that considers alternative sources of government financing and the benefits of alternative bank recapitalization paths. Our results indicate that only when the government has access to international credit, is it optimal to recapitalize the banking system in the period following the banking crisis. This highlights the importance of support from multilateral agencies like the IMF in the aftermath of a banking crisis. When the lack of external credit forces the government to finance the recapitalization program domestically, it is never optimal to recapitalize the banks in one period even when non-distortionary (lumpsum) taxes are available. When only distortionary taxes are available recapitalization of the bankrupt banking sector is even slower. Numerical solution of the model highlights the welfare costs of banking crises: even with access to international debt there is a welfare loss of 0.74%, while the use of distortionary taxes to finance the recapitalization without international debt results in a welfare loss of 3.31%. JEL classification codes: E44, E62, H21, G21 Key words: bank recapitalization; banking crises; financial intermediation; banking capital.

2 1 Introduction Banking sector problems leading to bank insolvencies have been frequent in the recent decades in developed and developing countries alike. Between 1980 and 1996, three fourths of the IMF s member countries have experienced significant banking sector problems (Lindgreen et al. (1996)). Using data between the late 1970s and 1999, Caprio and Klingebiel (2003) identify 117 systemic banking crises in 93 countries. The serious macroeconomic consequences of banking crises have been well documented. Demiirgüç-Kunt et al. (2004), for example, study a sample of 36 banking crises in 35 countries between 1980 and Defining a banking crisis as a period in which segments of the banking system become illiquid or insolvent, they find that bank crises cause a sharp decline in the rate of growth of output (of about 4%). Moreover the authors find that financial distress helps in propagating the adverse shocks to the real sectors of the economy when banks reduce lending to creditworthy borrowers as it happens in developing countries hit by banking crises. Dell Ariccia et al. (2005) also find that banking crises have consequences for the real side of the economy. Sectors that depend more on external finance are affected the most. Hence banking crises lead to more severe problems in developing countries as firms have limited alternatives to bank financing. According to the authors their results support the view that banks need to be supported during distress in order to prevent a vicious circle in which banking distress and economic contraction reinforce each other 1. A sound banking system is essential for macroeconomic stability in the economy. Thus in the aftermath of crises the government gets drawn into the restructuring of the banking system. Honohan and Klingebiel (2000) find that in their sample of 40 countries the 1 They conduct an econometric analysis to test whether the effects of banking crisis on the real sector is just a case of reverse causation. Since bank crises tend to occur when the real sectors are hit by a negative shock, it is possible that the real effects are an outcome of this shock and not of the banking problems. They find that this is not the case and that banking crises do have consequences for the real side of the economy. 1

3 governments end up bearing most of the direct costs of the banking crises. The costs have been about 13% of GDP on an average. In developing countries these costs have been higher, at an average of 14.3% of GDP. Figure 1 shows the fiscal costs of bank restructuring programs in some countries. These reported fiscal costs are at best a lower limit for the resources involved as Daniel et al. (1997) point out that the actual costs are substantially higher due to indirect methods of government assistance 2. Caprio and Klingebiel (1996) estimate the amount of resources involved in bank restructuring programs to be 10-20% of GDP in many cases and occasionally as much as 40-55% of GDP. Banking sector distress affects the fiscal balance by affecting both the revenues and the expenditures of the government. Due to the general slowdown of the economy after a banking crisis tax revenues of the government are substantially reduced. On the expenditure side the buildup of direct liabilities from state owned insolvent banks and contingent liabilities from deposit and credit guarantees lead to considerable costs for the government. Furthermore, as discussed in the previous paragraph, in case of systemic bank unsoundness the government invariably ends up bearing a large part (if not all) of the expenditure on bank bailouts and banking sector restructuring. All these factors together have a considerable negative impact on the fiscal balance of the country experiencing a banking sector distress. This paper characterizes efficient bank restructuring programs. It investigates how the optimal path of a government-funded capital injection program has to weigh the benefits of putting afloat its bankrupt banking system and the mechanisms available to the government to finance the restructuring program. We study the resolution of banking crises once they occur; therefore, instead of focusing on a banking system facing a panic or a serious liquidity dry-out, we focus on cases where a banking crisis has already eroded a large fraction of the banking capital. The erosion of capital is considered to have been serious enough that the banking system is providing just a fraction of the efficient level of financial intermediation 2 See Table 1 in Daniel et al. (1997). 2

4 and this considerably depresses economic activity. In this context, we seek to answer the following question: once a government decides to recapitalize a bankrupt banking sector, what is the optimal path of a program that weights recapitalization benefits and the program s costs? By recapitalizing undercapitalized banks we refer to the injection of banking capital that restores the ability of these banks to intermediate financial credit to an efficient level. Although we abstract from the moral hazard problems that could affect financial decisions, it must be said that restructuring undercapitalized banks does not necessarily mean maintaining the management nor the ownership of the bank charter. Here we focus on the public finance aspect of the problem. We conduct our investigation by modeling a perfect foresight economy that is hit by an unforeseen banking crisis that depletes a large fraction of the banking capital. In the model, the banking sector is a financial intermediary that borrows from households and lends to firms. Bank deposits are the only saving mechanism available to households and bank credit is essential due to a working capital constraint that the firms face. The working capital constraint on the wage bill requires the firms to borrow from the banks to finance its wage bill before cashing its sales. Firms combine physical capital with household-supplied labor to produce final output; output is then allocated between private uses, i.e., consumption and saving, and public uses. Public uses are the provision of government consumption during normal times, and the provision of this as well as the recapitalization of the banking system in the aftermath of a banking crisis. Following the empirical literature, we define a banking crisis as an event in which much or all of the bank capital is exhausted (see Caprio and Klingebiel, 2003). And to represent the banks and the banking crisis in the model, we follow Cole and Ohanian (2001) who interpret a banking crisis as loss of intermediation (or banking) capital. Banks combine banking capital and deposits from households to produce loans, which are demanded by 3

5 the goods producing firms who face a working capital constraint. Since our interest is to characterize optimal bank restructuring programs, we abstract from the causes of the banking crisis. We assume that deposits and banking capital are not substitutes in the banking production function. Hence a decline in the stock of banking capital causes the supply of loans to decline. Given the working capital constraint, firms have to reduce their demand for inputs, which in turn causes a decline in production. This mechanism is well cited in the literature. Bernanke (1983), Romer (1993), and Chava and Purnanandam (2006) find that when firms depend on banking credit to fund their working capital, banking sector problems that prevent firms from borrowing can lead to an overall slowdown in the economy. Bernanke (1983) highlights the role of banks in the Great Depression. The failure of banks destroys the information about small borrowers. This information is costly to collect due to frictions such as asymmetric information or agency costs. The increase in the cost of credit intermediation makes it difficult for small firms (that are not easily able to replace bank loans with other forms of financing) to get credit, which in turn results in the firms cutting down on their workforce and/or investment leading to a decrease in output. Bernanke concludes that this increased cost had been instrumental in deepening and prolonging the Great Depression in the U.S. Romer (1993) also suggests that... the banking crises of 1931 and later were a crucial cause of the deepening and sustaining of the Great Depression in the United States.... Chava and Purnanandam (2006) empirically test the effects of an exogenous shock to the US banking sector on firms that are reliant on bank loans. The Russian crisis of 1998 along with the flight of capital from Brazil is considered to be an exogenous shock to the U.S. banking system 3. This led to significant losses for many U.S. banks which had considerable exposure in these two countries. The authors find that the number and dollar value of bank loans dropped in the six month period after the crisis. They also find that in the aftermath of the crisis bank-dependent 3 This adverse shock to the banking sector is independent of the financial health of bank-dependent borrowers and is thus useful in separating supply side effects from demand side effects. 4

6 firms earn statistically significant lower returns than firms which had access to the public debt market. We formulate a Ramsey problem in which the government has to choose a bank restructuring program that can be implemented as a competitive equilibrium. The government s objective in the aftermath of a banking crisis is to endow the economy with the benefits of a well running banking system but internalizing the direct and indirect resource costs of the recapitalization program. Thus, the optimal program hinges upon the means by which the government funds the program. We characterize the optimal bank restructuring program under three alternative sources of public revenue. In the first case rebuilding of the banking sector can only be financed with distortionary labor taxes. In the second case, we allow the government access to lump-sum taxes. And in the third case, while we rule out lump-sum taxes, the government has access to international debt markets to finance the rebuilding of the financial system. We find that only when the government has access to international credit, is it optimal to recapitalize the banking system in the period following the banking crisis. To fix ideas, assume that the government has access to only distortionary taxes to collect fiscal revenue domestically. The banking system is bankrupt in the initial period and the loss of banking capital submerges the economy into a recession in that period. By borrowing abroad the government secures the funds necessary to recapitalize the banks so the economy quickly recovers from the recession in the next period. Moreover, by borrowing from abroad the government can also provide subsidies to the households during this period to alleviate the effects of the recession even while the banking crisis has not been resolved. From then on it is optimal to smooth out the distortionary taxes so that the debt incurred to finance the bank restructuring program is rolled over forever. The results here, in contrast to those arising when external credit is not available, have an interesting policy implication for multilateral organizations since they show that only having access to international credit, 5

7 makes immediate rebuilding of the banking system in the aftermath of a financial crisis (second-best) efficient for the Ramsey planner. When the lack of external credit forces the government to finance the recapitalization program by resorting to domestic taxation, it is never optimal to recapitalize the banks in one period even when lump-sum taxes are available. This is because the lump-sum taxes in spite of being non-distortionary withdraw large amounts of resources from the economy which cause a decline in consumption and hence welfare. The government gradually builds up the stock of banking capital, with the amount of government support declining over time due to the decreasing marginal benefit of adding to the stock of banking capital. By Ricardian Equivalence this case is equivalent to the government issuing domestic bonds and having access to lump-sum taxes 4. When only distortionary labor taxes are available recapitalization of the bankrupt banking sector is even slower. This is because labor income taxation distorts the consumption-leisure choice of the households. Without access to international credit the recapitalization is gradual and welfare effects of a banking crisis are more pronounced. This highlights the importance of assistance of multilateral agencies like the IMF to governments recapitalizing the domestic banking sector. Our results contrast those found in the literature dealing with the microeconomic aspects of bank restructuring policy. The latter often recommends immediate restructuring (including one-shot recapitalization) of the banks. This is to prevent further loss of confidence in the problem-ridden banking system, which could result in bank runs. Repeated incomplete recapitalization increase the fiscal costs and also aggravate the moral hazard problem. Repeated unconditional recapitalization transfers all the risk to the government by encouraging insider activity which affect banks adversely. However, our results weigh the benefits of bank recapitalization with the costs of raising resources to undertake the program, and concludes that without access to international credit a gradualistic approach 4 In our model this is possible because the government can tax the rents accruing to the fixed capital stock. 6

8 to recapitalization is optimal given the amount of resources that need to be spent to recapitalize the banking system. Numerical solution of the model yields welfare effects of banking crises of the order of 0.74% to 5.47% compared to the no-crisis equilibrium. It is also found that the Ramsey planner does not always recapitalize the banking system up to the pre-crisis level. This is because here optimality means that the government equates the marginal cost of financing the injections to the marginal benefit of an extra unit of banking capital. The optimal level of post-crisis banking capital is highest with access to international debt followed by lumpsum taxation financed program, and is lowest when financed by taxes on labor income. However, in case the government borrows from abroad to finance the recapitalization program steady state consumption (labor effort) is lower (higher) because the country needs to pay interest on its debt obligation. The rest of the paper proceeds as follows. In the next section we present the perfect foresight decentralized general equilibrium model and we formulate the corresponding Ramsey problem in Section 3. Section 4 presents the quantitative results and Section 5 concludes. 2 The Model We model a perfect-foresight economy with four types of agents: households, goodsproducing firms, banks and the government. Firms need working capital to pay their wage bill before they get the proceeds from the sale of their output. Banks intermediate savings between the firms and the households. The firms and the banks are owned by the households. The stock of physical capital in the economy is exogenously given and owned by the firms. In the quantitative version of the model, one period will be interpreted as one quarter. To guarantee the consistency of the intertemporal household s deposit decisions with 7

9 the (essentially) atemporal banks and firms optimization problems involving credit, we follow Neumeyer and Perri (2005) to assume that there are two times within each period t. One at the beginning of the period, denoted by t, and one at the end of the period, denoted by t +. We assume that t + and (t + 1) are arbitrarily close. At t banks accept deposits, d t, from the households and use them along with the stock of banking capital, A t, to produce loans. Firms need to borrow from the banks to fulfill their working capital constraint at t. Labor is hired and paid using the loans from the banks at t. Firms use hired labor and capital stock to produce the final good which becomes available at t +. Firms repay their loans along with interest, R bt b t, to the banks at t +. Profits of the firms and banks, π f t and πt b respectively, along with the gross interest income, R t d t, are distributed to the households, who decide between consumption, c t, for this period and savings to be carried into the next period. These savings are the deposits for the next period, d t+1. Within each period the government collects taxes and uses the proceeds to pay for its outlays which include the fixed government expenditure, ḡ, and may also include other transfers related to the recapitalization of the banking system. 2.1 Households The representative household has an infinite life and chooses sequences of consumption, labor supply, and bank deposits, {c t, h t, d t+1 } t=0, to maximize the following lifetime discounted utility β t U(c t, l t ) (1) t=0 where β is a standard discount factor and U is a strictly concave, increasing, and differentiable utility index that depends on consumption, c t, and leisure, l t. The time endowment is normalized to 1, hence labor effort is h t = 1 l t. The utility maximization problem is 8

10 subject to a flow budget constraint, c t + d t+1 (1 τ t )w t h t + R t d t + [π f t + π b t] T t ; t 0 (2) that restricts the household s expenditure to not exceed its income at any time t 0. The sources are composed of net labor income, gross return on deposits, and dividends. The net labor income depends on the wage rate, w t, the amount of labor supplied, h t, and the tax rate, τ t. Bank deposits, d t, are the only saving vehicle available to the household and they are remunerated at the gross rate R t. Furthermore, as the household owns all firms and banks in the economy, it collects the respective profits π f t and π b t. T t is the lump-sum tax collected by the government. The household allocates its resources between savings, d t+1, i.e., deposits payable next period, and consumption, c t. A sequence {c t, h t, d t+1 } t=0 is optimal from the standpoint of the household if it satisfies the resource constraint in Eq. (2) with equality and if the following conditions hold at t 0: U l (t) U c (t) = (1 τ t)w t (3) U c (t) = βu c (t + 1)R t+1 (4) where U c (t) and U l (t) are the marginal utilities of consumption and leisure at time t. Eq. (4) is a standard dynamic efficiency condition for savings that governs the optimal allocation of deposits and Eq. (3) equates the marginal rate of substitution of leisure for consumption to the wage rate net of taxes. The tax on labor income lowers the net wage received by the households, which reduces the consumption-leisure ratio. Thus the substitution effect of a labor tax results in a fall in consumption and labor effort. 9

11 2.2 Firms and the Working Capital Constraint The representative firm owns a fixed capital stock, k, which is combined with labor to produce the final good, y t, using a constant returns to scale production function: y t = f( k, h t ) (5) The firm faces a credit-in-advance constraint on its wage bill: it has to borrow from banks to finance its labor costs before cashing its sales. Hence firms borrow b t (= w t h t ) from banks. Due to rents accruing to the fixed capital stock, the firm makes positive profits which it distributes to the households. The firm chooses h t to maximize its profits, π f t = y t R bt w t h t, taking as given the wage rate, w t, and the gross interest rate on its borrowing, R bt. Optimality requires that: R bt w t = f h ( k, h t ) (6) Hence the linear homogeneity of the production function permits writing the firm s profit as follows: π f t = kf k ( k, h t ) (7) which is the returns to the stock of physical capital. 2.3 Banks Banks are modeled following Cole and Ohanian (2001). The representative bank accepts 1 period deposits, d t, from households and uses them along with the intermediation (banking) capital to produce loans, b t, using a Leontief production function: b t = min(γa t, d t ); γ [0, 1] (8) 10

12 where A t is the banking capital that is owned by the bank and is in fixed supply (Ā) in the pre-crisis equilibrium. The bank chooses d t to maximize its profits, πt b = (R bt 1)b t (R t 1)d t, taking as given the lending rate, R bt, and the deposit rate, R t. The bank s maximization problem leads to the following optimality condition: b t = d t = γa t (9) 2.4 Government Government expenditure, g t, consists of (possibly) two components: a fixed expenditure, ḡ, and some transitory outlays, x t, which in our case will refer to the government transfers towards the recapitalization of the banking sector. In the absence of a crisis the government runs a balanced budget and finances its expenditure, g, using its revenues from lump-sum taxes, T 5 t, i.e., T t = ḡ (10) 2.5 Banking Crises in the Competitive Equilibrium A competitive equilibrium in this economy is a sequence of allocations {c t, h t, d t+1, g t, A t+1 } t=0, a sequence of prices {w t } t=0, a sequence of interest rates {R t, R bt } t=0, and a sequence of government policies {τ t, T t } t=0 such that, given the stock of physical capital, k, the stock of banking capital and deposits, {A t, d t } t=0, prices, and government policies: a) the conditions that guarantee that the household solves its constrained lifetime utility-maximization problem, i.e. Eq. s (2) - (4) hold; b) firms maximize their profits, i.e., Eq. (6) and the working capital constraint on the firm hold with equality; c) banks maximize their profits, i.e., Eq. (9) holds; d) government budget constraint is satisfied; e) the labor market clears, 5 We assume that the government can use lump-sum taxes to finance its fixed expenditure in order to isolate the effects of financing bank recapitalization from that of financing an expenditure that is fixed over time. 11

13 f) the deposit market clears; and g) the loan market clears. We model a banking crisis by assuming an unanticipated exogenous decrease in the stock of banking capital. This is in keeping with the banking crisis documented in Chava and Purnanandam (2006) and the definitions of Caprio and Klingebiel (2003). The stock of banking capital declines from Ā to A. We do not model why nor how this happens; we take it as given and carry out our analysis from then on 6. As has been observed in countries which have faced a banking crisis, the government gets drawn into restructuring the banking sector. This involves undertaking transfers to the banking sector in order to increase the stock of banking capital 7. In the next section we construct the Ramsey planner s problem for optimal recapitalization of the banking sector. 3 Optimal Recapitalization: A Ramsey Approach We formulate a Ramsey problem in which the government optimally decides the amount and time path of government capital injections towards recapitalization of the banking system. The Ramsey planner undertakes injections, x t, towards the stock of banking capital, which thus has the following time path: A t+1 = A t + x t (11) Hence government outlays are: g t = ḡ + x t g t = ḡ + (A t+1 A t ) (12) The planner optimally chooses the time path of A t+1. We discuss three cases below: i) the recapitalization is undertaken using revenue from labor income taxes, ii) lump-sum 6 See Demiirgüç-Kunt and Detragiache (1998) for a discussion of the causes. 7 One might say that banks would issue equity in order to recapitalize themselves but it has been seen that firms and banks are reluctant to issue equity during a downturn. 12

14 taxes finance the recapitalization, and iii) the government can borrow in international debt markets to undertake the recapitalization program. 3.1 Labor Income Taxation In this section we formulate the Ramsey planner s problem when the government has to resort to taxation of labor income to finance recapitalization of the banking system. Hence the government budget constraint is (using Eq. (10)): x t = A t+1 A t = τ t w t h t (13) The implementability constraint for the Ramsey planner is derived by substituting the household s, firm s and bank s optimality conditions along with the expressions for the profits of firms and banks into the household budget constraint. Substituting for the firm s and bank s profits the right hand side of the household budget constraint can be written as (1 τ t )w t h t + R t d t + f( k, h t ) R bt b t + (R bt 1)b t (R t 1)d t T t. Using Eq. s (3), (9), and (10), we get the following implementability constraint: U c (t)[c t + γa t+1 + ḡ f( k, h t )] = U l (t)h t (14) The resource constraint for the economy is derived by combining the household and the government budget constraints: c t + ḡ + (1 + γ)a t+1 = (1 + γ)a t + f( k, h t ) (15) Hence the Ramsey planner s problem is max {c t,h t,a t+1 } t=0 β t U(c t, l t ) s.t. (14), and (15) t=0 13

15 Let β t µ t be the multiplier on the implementability constraint and β t ν t be the multiplier on the resource constraint. Assuming U lc (.) = U cl (.) = 0, the optimality conditions are (along with the implementability constraint and the resource constraint) U c (t) = µ t [U c (t) + U cc (t){c t + γa t+1 + ḡ f( k, h t )}] + ν t (16) U l (t) = µ t [U l (t) U ll (t)h t + U c (t)f h ( k, h t )] + ν t f h ( k, h t ) (17) µ t U c (t)γ + ν t (1 + γ) = βν t+1 (1 + γ) (18) U l (t)h t = U c (t)[c t + γa t+1 + ḡ f( k, h t )] c t + ḡ + (1 + γ)a t+1 = (1 + γ)a t + f( k, h t ) where Eq. s (16), (17), and (18) are the first order conditions with respect to c t, h t, and A t+1 respectively. 3.2 Lump-sum taxes When the planner has access to lump-sum taxes (to finance the recapitalization, apart from financing the fixed expenditure) the government budget constraint is: ḡ + A t+1 A t = T r t (19) where T r t is the lump-sum tax imposed by the government. In the absence of a banking crisis this tax equals ḡ. The household budget constraint, Eq. (2), is now c t + d t+1 w t h t + R t d t + [π f t + π b t] T r t ; t 0 (20) In cases where the planner has access to lump-sum taxes, and there are no other distor- 14

16 tions in the economy, the Ramsey planner s problem involves maximizing the household s objective function subject to the resource constraint. However, in our case due to the presence of the working capital constraint, which is essentially another distortion in the economy, we need to also impose the implementability constraint on the Ramsey planner s problem, which is: U c (t)[c t + (1 + γ)a t+1 + ḡ f( k, h t ) A t ] = U l (t)h t (21) obtained by substituting the profit functions for the firms and banks, the household and bank optimality conditions, and the value of government transfers into the household s budget constraint, Eq. (20). The resource constraint for the economy is the same as before, and is repeated here for convenience: c t + ḡ + (1 + γ)a t+1 = (1 + γ)a t + f( k, h t ) (22) The Ramsey planner s problem is max {c t,h t,a t+1 } t=0 β t U(c t, l t ) s.t. (21), and (22) t=0 Let β t µ t be the multiplier on the implementability constraint and β t ν t be the multiplier on the resource constraint. Assuming U lc (.) = U cl (.) = 0, the optimality conditions are (along with the implementability constraint and the resource constraint) U c (t) = µ t [U c (t) + U cc (t){c t + (1 + γ)a t+1 + ḡ f( k, h t ) A t }] + ν t (23) U l (t) = µ t [U l (t) U ll (t)h t + U c (t)f h ( k, h t )] + ν t f h ( k, h t ) (24) µ t U c (t)(1 + γ) + ν t (1 + γ) = βµ t+1 U c (t + 1) + βν t+1 (1 + γ) (25) 15

17 U c (t){c t + (1 + γ)a t+1 + ḡ f( k, h t ) A t } = U l (t)h t c t + ḡ + (1 + γ)a t+1 = (1 + γ)a t + f( k, h t ) where Eq. s (23), (24), and (25) are the first order conditions with respect to c t, h t, and A t+1 respectively. 3.3 Government access to international debt In order to highlight the importance of assistance from multilateral agencies like the IMF, in this section we allow the government access to international debt at a fixed interest rate, ˆr. The government budget constraint is: (1 + ˆr)ˆb t + g t = τ t w t h t + ˆb t+1 + T t (26) where ˆb t+1 is the government s foreign borrowings at date t. The resource constraint for the economy is derived by combining the household and the government budget constraints: c t + ḡ + (1 + γ)a t+1 + (1 + ˆr)ˆb t = (1 + γ)a t + f( k, h t ) + ˆb t+1 (27) The implementability constraint for the Ramsey planner in this case is: U c (t)[c t + γa t+1 + ḡ f( k, h t )] = U l (t)h t (28) The Ramsey planner s problem is max {c t,h t,a t+1 } t=0 β t U(c t, h t ) s.t. (28), and (28) t=0 Let β t µ t be the multiplier on the implementability constraint and β t ν t be the multiplier on the resource constraint. Assuming U lc (.) = U cl (.) = 0, the optimality conditions are (along 16

18 with the implementability constraint and the resource constraint) U c (t) = µ t [U c (t) + U cc (t){c t + γa t+1 + ḡ f( k, h t )}] + ν t (29) U l (t) = µ t [U l (t) U ll (t)h t + U c (t)f h ( k, h t )] + ν t f h ( k, h t ) (30) µ t U c (t)γ + ν t (1 + γ) = βν t+1 (1 + γ) (31) ν t = βν t+1 (1 + ˆr) (32) U c (t)[c t + γa t+1 + ḡ f( k, h t )] = U l (t)h t c t + ḡ + (1 + γ)a t+1 + (1 + ˆr)ˆb t = (1 + γ)a t + f( k, h t ) + ˆb t+1 where Eq. s (29), (30) (31), and (32) are the first order conditions with respect to c t, h t A t+1, and ˆb t+1 respectively. 4 Quantitative Results In this section we investigate the quantitative implications of a banking crisis, provide the post-crisis transition paths and discuss the welfare effects of government intervention. 4.1 Functional Forms and Parameters To solve the model numerically we assume the following functional forms. The utility function is assumed to be separable in consumption and leisure: U(c t, l t ) = ln c t + θ ln(l t ) 17

19 We assume a Cobb Douglas production function y t = B k α h 1 α t, α (0, 1) The benchmark parameter values are summarized in Table 1. The annual net rate of interest on international debt is set at 4%. The household discount factor, β, is set at to match the world interest rate. The share of leisure, θ, in the household utility is set to 1.5, so that work effort is approximately 1/3 of total time endowment. The share of physical capital in production of the final good, α, is set at 1/3. The capital stock, k, and the productivity parameter, B, are set such that the capital-output ratio at the annual level is about 2. It is assumed that the bank production function is such that optimality requires the use of banking capital and deposits in a one-to-one ratio; hence we set γ = 1. The fixed government expenditure, ḡ, is set equal to 2, to have steady state government consumption of about 15% of total output. The initial steady state level of banking capital, A, is calibrated to match an annual net interest rate on loans of 8.5%, which generates an initial steady state banking capital level, Ā, of Transition Dynamics and Welfare Effects In this section we discuss the transitional dynamics and the welfare effects of a banking crisis which destroys a portion of the stock of banking capital. The timing of the events is as follows: in the beginning of period 0 the economy is in steady state; at the end of the period the economy is hit by the banking crisis and the government starts intervening from period 1 onward to recapitalize the bankrupt banking system. The optimal amount of steady state banking capital depends on the method of financing the recapitalization program. We now discuss the results for a 50% decline in banking capital under the three scenarios. Figure 2 plots the transitional dynamics induced by the banking crisis and the subse- 18

20 quent government intervention for the three cases discussed above. We start our discussion with the closed economy cases where the recovery is gradual. In the first period, which is the period of unraveling of the banking crisis and also of government intervention, consumption declines. On the one hand the low stock of bank capital constrains the loans to the firms, which in turn constrains the amount of labor hired by the firms leading to a decline in output. On the other hand taxes imposed by the government to finance the recapitalization program also takes away resources available for consumption. The first period of restructuring is also the one with the maximum amount of injections because the marginal benefit of increasing the stock of banking capital is at its highest. This requires a high tax on labor which further depresses labor supply. From the next period onward employment gradually rises until it reaches the new steady state. The decline in output is the most pronounced in the case of labor income taxation; this is due to the negative impact on employment both from the supply side and the demand side. Owing to the high resource cost and the distortionary nature of financing them the optimal path for recapitalization is a gradual one, and naturally the amount of injections undertaken by the government decline with time due to the decreasing marginal benefit of adding to the stock of banking capital. The case of lump-sum taxation is equivalent 8 to the government issuing domestic bonds to pay for the restructuring program and then repaying the government debt using taxes on the rents accruing to the stock of capital. Similar to the distortionary taxation case, consumption declines as does output. Since the resources for recapitalization are raised using non-distortionary methods, employment, and hence output, falls less than the case of distortionary taxes. Although the method of taxation is non-distortionary the recapitalization is gradual due to the large amount of resources involved. Again the amount of injections decline over time due to the declining marginal benefit of increasing the stock of banking capital. 8 Ricardian Equivalence holds in this case. 19

21 With access to international debt, the recapitalization is undertaken in one-shot. Banking capital reaches its new steady state level in period 2, while output, consumption and employment adjust to their new steady state level in period 1 itself. This is possible because the government subsidizes labor in period 1 using its borrowing from the international debt market. Thus the tax rate on labor income is negative for period 1 and positive period 2 onward. The economy reaches steady state in period 2. As can be seen from Table 2, the steady state levels of banking capital, deposits, loans, employment and output are the highest when there is access to international debt markets, followed by the case of non-distortionary taxes. However, steady state consumption is the lowest in the case of access to international debt, in spite of employment and output being the highest: this is because part of the output is used to pay the interest on the country s debt obligation, which in turn requires the households to work more. Convergence to steady state is fastest when there is access to international debt, followed by the case of lump-sum taxation, and convergence is slowest when in the closed economy resources for recapitalization need to be financed via distortionary taxes. Welfare comparisons are conducted using the no-crisis equilibrium as the benchmark. The results are summarized in Table 3. Following Lucas (1987), the net welfare effects are measured as the constant percentage decrease in c t that leaves households indifferent between utility obtained in the no-crisis equilibrium and utility under the crisis equilibria (for the different sources of financing). The net welfare loss of a crisis with recapitalization financed by distortionary taxes is 3.31%, while financing recapitalization with nondistortionary taxes results in a welfare loss of 2.96%. Access to international debt eases the welfare loss considerably, resulting in a welfare loss of 0.74%. Thus the welfare effects of banking crises are significant even with government support to the banking system. 20

22 5 Concluding Remarks Banking sector crises which have been prevalent in both developing and developed countries have presented a stiff challenge to policy makers. Given the importance of the banking sector in the economy the government almost invariably ends up bearing the burden of financing the restructuring program for the bankrupt banking system. The high fiscal cost of these programs warrants careful analysis of the financing options used by the government. In this paper we examine the public finance aspect of the government s recapitalization of a bankrupt banking sector. We formulate the Ramsey planner s problem under three scenarios: recapitalization financed using distortionary taxes, using non-distortionary taxes and by borrowing from international debt markets. The model is solved numerically and the welfare cost of a banking crisis is found to be substantial. Even with access to international debt the welfare effect of a banking crisis is of the order of 0.74%. The post restructuring levels of banking capital are different under the three regimes, reflecting the difference in distortions due to the different financing options of the recapitalization program. It has often been suggested that the government should restructure the banking system at one go but our analysis of the Ramsey planner s problem shows that optimality requires a gradual approach unless the economy can borrow from international markets at fixed interest rates. This is due to the high resource cost of the program and optimality dictates that these costs be spread out over time to minimize the distortions in raising these resources. This highlights the importance of access to international debt markets, that allows spreading out the distortions over time. Many developing countries that have suffered from banking crises do not have access to such markets and it is up to agencies like the IMF to lend to these governments in order to alleviate the effects of a banking crisis which can lead to a rather painful and long-drawn adjustment process. We have not considered the moral hazard problems related to government support 21

23 programs. Nor have we incorporated the different methods used for recapitalization 9, which can have different effects on the government budget. These problems are important and present avenues for future research. They have not been incorporated here since the focus of this paper has been the public finance aspect of the problem. We realize that we have taken the government s decision to intervene as given and then carried out our analysis from then on. In a related work in progress we model the non-optimality of the competitive equilibrium which necessitates government intervention. 9 See Daniel et al. (1997) for details. 22

24 References Barro, R. (1974). Are government bonds net wealth. Journal of Political Economy, 82: Baxter, M. and King, R. (1993). Fiscal policy in general equilibrium. American Economic Review, 83(3): Bernanke, B. (1983). Nonmonetary effects of the financial crisis in the propagation of the great depression. American Economic Review, 73(3): Caprio, G. and Klingebiel, D. (1996). Bank insolvencies: Cross country experience. World Bank Policy Research Working Paper, (No. 1620). Caprio, G. and Klingebiel, D. (2003). Episodes of systemic and borderline banking crises. World Bank. Chava, S. and Purnanandam, A. (2006). The effect of banking crisis on bank-dependent borrowers. Working Paper. Cole, H. and Ohanian, L. (2001). Re-examining the contribution of money and banking shocks to the u.s. great depression. In: NBER Macroeconomics Annual,. Eds. Ben Bernanke and Kenneth Rogoff. Daniel, J., Davis, J., and Wolfe, A. (1997). Fiscal accounting of bank restructuring. Dell Ariccia, G., Detragiache, E., and Rajan, R. (2005). The real effect of banking crises. IMF Working Paper. Demiirgüç-Kunt, A. and Detragiache, E. (1998). The determinants of banking crises in developing and developed countries. IMF Staff Papers, 45(1): Demiirgüç-Kunt, A., Detragiache, E., and Gupta, P. (2004). Inside the crisis: An empirical analysis of banking systems in distress. World Bank Policy Research Working Paper. Honohan, P. and Klingebiel, D. (2000). Controlling the fiscal costs of banking crises. World Bank Policy Research Working Paper. Honohan, P. and Laeven, L., editors (2005). Systemic Financial Crises: Containment and Resolution. Cambridge University Press. Juillard, M. (2001). Dynare: A program for the simulation of rational expectation models. CEPREMAP. Lindgreen, C.-J., Gillian, G., and Saal, M. (1996). Bank Soundness and Macroeconomic Policy. IMF. Lucas, R. E. (1987). Models of Business Cycles. Blackwell. 23

25 Miranda, M. and Fackler, P. (2002). Applied Computational Economics and Finance. MIT Press. Neumeyer, P. and Perri, F. (2005). Business cycles in emerging economies: the role of interest rates. Journal of Monetary Economics, 52: Oviedo, P. M. (2005). World interest rate, business cycles, and financial intermediation in small open economies. ISU Working Paper. Romer, C. (1993). The nation in depression. Journal of Economic Perspectives, 7(2): Sargent, T. and Ljungqvist, L. (2004). Recursive Macroeconomic Theory. MIT Press. 24

26 Table 1: Baseline Parameter Values Parameters Values β Discount factor θ Leisure share in utility 1.5 B Productivity parameter 6 k Physical capital stock 115 α Capital s share in output 1/3 γ Ratio of banking capital to deposits in loan production 1 ḡ Fixed government consumption 2 ˆr Quarterly world net interest rate Table 2: Steady State Values Variable No crisis Crisis No intervention Labor tax Lump-sum Tax International Debt A y c h Table 3: Welfare Effects of Banking Crisis 50 % decline in banking capital No Government Intervention 5.47% Labor Tax 3.31% Lump-sum Tax 2.96% International Debt 0.74% Note: The no-crisis case is the benchmark for these welfare comparisons. 25

27 Figure 1: Fiscal costs of banking crises as % of GDP Source: Honohan and Klingebiel (2000) 26

28 Lump-sum tax Labor tax International debt Lump-sum tax Labor tax International debt (a) Banking Capital (b) Output Lump-sum tax Labor tax International debt Lump-sum tax Labor tax International debt (c) Consumption (d) Interest rate on loans Figure 2: Dynamics due to Banking Crisis Note: All values are % deviations from the pre-crisis steady state. 27