Economic subjects | Finance » Kim-Lee - Fiscal Policy, Overconsumption and Sovereign Debt Crisis, A Collateral Lending Approach

Source: http://www.doksinet Fiscal Policy, Overconsumption and Sovereign Debt Crisis: A Collateral Lending Approach ∗ Yong Jin Kim,† Ajou University Chul-In Lee,‡ Seoul National University September 2011 Abstract. Using an equilibrium framework, we provide predictions that are consistent with the recent experience of sovereign debt crisis in Southern Europe: (i) generous public spending leads to high consumption, real estate bubbles, and large current account deficit and public debt relative to GDP, and (ii) economies with large fiscal deficits ironically grew fast but became susceptible to a sudden financial and/or fiscal crisis. A surprising aspect of our model is that given the availability of cheap borrowing from EU countries with current account surplus, southern Europe countries with high public deficit can lock into a steady-state Ponzi growth equilibrium with asset bubbles. As long as loan-to-collateral value (LTV) ratio exceeds a certain threshold adopted in the

banking sector, households continue to borrow at a lower interest rate of countries with current account surplus than the domestic rate while asset bubbles based on over-consumption can support a constant LTV, establishing a steady-state Ponzi growth equilibrium. When adverse shocks hit the economy and the expected loan-to-collateral value (LTV) ratio rises enough to move the economy into a self-fulfilling crisis region, the steady-state Ponzi growth equilibrium can break down with a bust of asset bubbles, even in the face of a mere psychological pessimism of investors. JEL Classification number: E44, F34, O16 Key Words: South European sovereign debt crisis, over-consumption, self-fulfilling crises, collateral, steady-state Ponzi equilibrium. ∗ Acknowledgments: The authors are grateful to Tack Yun for helpful discussions. †: Address: San 5 Wonchun-dong, Division of Economics, College of Social Science, Ajou University, Youngdong-gu, Suwon, Korea 442-749; email: yongkim@ajou.ackr;

phone: 82-031-219-2744; fax: 82-031-219-1618 ‡: Address: Email: leeci@snuackr Address: 599 Gwanak-ro Gwanak-gu, Department of Economics, Seoul National University, Seoul, 151-746, Republic of Korea; phone: 82-2-880-6345. Source: http://www.doksinet I. Introduction The purpose of this paper is to present a coherent framework that explains some salient features of the South European crises. The growth process of the South European economies is typically characterized by a set of stylized facts: high levels of consumption and household debt, construction industry boom, real estate bubbles, and high levels of government debt and current account deficits, followed by sudden financial and fiscal crises. Until recently, the South European economies displayed high levels of financial activities (borrowing and lending), and rather rapid GDP growth. Along with these expansionary signs, those economies have seen a few negative ones such as declines in productivity, increases in current

account deficits, and accumulation of household and government debts. Then, suddenly, banking and fiscal crises swept through these countries. This paper attempts to show that given the availability of cheap borrowing from countries with current account surplus, southern Europe countries with high public deficit can lock into a “steady-state” Ponzi growth equilibrium with asset bubbles, a constant loan to value, and continuous borrowing, but become extremely vulnerable to banking and fiscal crises. Essential elements of the model include collateral lending (Kiyotaki, 1997) and expectation-driven multiple equilibria. The model presented in the paper describes an economy in which, when provision of government subsidies are combined with collateral lending practices, both households and firms have incentives to consume and invest excessively, respectively. In the model economy, government accumulates its debt by borrowing from foreign investors, i.e, countries with surplus in current

account, at lower interest rates And government as well as households can borrow on collateral from foreign investors up to a certain fraction of the collateral value that is generally accepted in the banking sector, the so- 1 Source: http://www.doksinet called threshold LTV ratio. Through this process, foreign debt can continue to accumulate, as long as domestic banks and foreign investors are willing to provide funds to the government and households. Drawing on the real world financial practice based on LTV, domestic banks and foreign investors will continue lending to households (government) as long as the value of the household’s real estate collateral (the government’s asset) exceeds accumulated loans. Through this collateral lending practice combined with an access to foreign funds at a low interest rate, a Ponzi equilibrium has steady state in contrast to the usual macro equilibrium, and it can persist unless external shocks or sudden changes in expectations about future

asset values disturb the economy. In our model, such an over-consuming economy, caused by a higher level of government subsidies to households, exhibits a high level of real estate price, a higher current account deficit, and high public debt. And it also shows that subsidies to firms increase the investment share in GDP, a high growth rate of real estate price and the GDP growth. Therefore, this model implies that an over-consuming economy is more likely to be subject to a crisis. What separates our model from existing ones is to establish another channel of crisis arising from the public sector: government subsidies can motivate the moral hazard behavior of individuals and that of firms and banks as well, 1 causing both overconsumption and overinvestment, i.e, sources of asset bubbles In particular, our model emphasizes the role of the collateral lending practices of banks in financial crises, which lead to asset bubbles and bust in the economy. However, we admit that our model

shares a similar spirit with the literature on the moral hazard behavior, overinvestment of the firms in their context, of firms and banks (e.g, McKinnon and Pill, 1997; Krugman, 1998; and Corsetti et al., 1999b) Our model also retains 2 Source: http://www.doksinet the feature of self-fulfilling crisis, as stressed by another line of work in the “third generation” crisis models, 2 such as Chang and Velasco (1998), and Aghion, Bacchetta, and Banerjee (2000). It also shows that, despite high growth, the underlying financial fragility engenders the whole economy extremely vulnerable to adverse shocks, triggering a self-fulfilling crisis. When the adverse shocks hit the economy and foreign investors suspect that domestic banks are too risky, financial panic and economic crises can suddenly occur. As soon as foreign investors start to cast doubt on the safety of their assets loaned to domestic agents, expected real estate prices fall to such a level that the market value of real

estate can no longer cover the foreign borrowings. This is because agents in the economy know that discontinuation of government subsidies due to a sudden end of foreign borrowing lowers economic growth and thus the asset prices. Therefore, similar in spirit to the bank run mechanism of Diamond and Divbig (1983), this process triggers a self-fulfilling crisis. Crisis begins at one part of an economy, and it spreads to other parts, amplifying the crisis. The rest of the paper is organized as follows. Section II describes the basic structure of the model and characterizes its equilibrium. Section III presents mechanisms for self-fulfilling crisis and a triggering mechanism behind the South European sovereign debt crisis, and derives several implications. Concluding remarks follow in Section IV 1 In our model, each agent’s borrowing decision does not incur any individual specific cost, but in aggregate it entails a substantial aggregate cost to the economy. Thus, agents do not take

into account the fact that higher debt, private or public, leads to crisis more likely. 2 A number of “third generation” crisis models are still competing with each other to explain the 1997 Asian crisis (See, e.g, Kaminsky and Reinhart, 1996; Demirguc-Kunt and Detragiache, 1997; and Eichengreen and Rose, 1998). Among major economic crises, the East Asian crisis of 1997 exhibits a complex mixture of currency crisis, banking crisis, and foreign debt crisis, and therefore it is hard to tell a single, dominant factor as a major source of recent crises. Empirical studies examine a large sample of countries but cannot offer clear answers (See Krugman (1999) among others for the discussion of the ‘third-generation’ crisis models that can explain the Asian crises.) 3 Source: http://www.doksinet II. The Model The model economy consists of identical households, firms, banks (foreign investors), and the government. The household owns a firm through holding shares in the

competitive financial markets. The household consumes three goods: commodity c, service s, and housing service h The household owns a house as real estate and uses it as collateral to borrow from banks (foreign investors). 3 In our model, the foreign investors lend to the household or to the government, as long as the household’s accumulated debt remains within the market value of collateral assets. The commodity producing firms as well as service providing firms have an AK type production technology (Rebelo, 1991 and Barro and Sala-I-Martin, 1995, chapter 4). There are neither technological changes nor capital depreciation. To simplify the story, we assume that the capital is putty-putty . In this section, we assume that the government restricts the foreign capital inflow up to the size of current account deficit, such that open economy equilibrium occurs as in the international finance literature. Agents’ behaviors are described as follows For the definition of parameters and

variables, refer to Table 1. 1. Firms’ Maximization We assume that commodity-producing firms use the capital input only in their AK type production technology and pay dividends, while service-producing firms use labor only in their AK type one and pay wages. The maximization problem of service-providing firms is simple, since we assume that each household’s labor is inelastically supplied by l . This leads to the 3 Both domestic banks and foreign investors supply loans to individuals and firms, and therefore they are used interchangeably, except for the case where the former goes bankrupt. 4 Source: http://www.doksinet equilibrium service production of s = As l , where As represents the technology level of the service sector. Thus, we solve only the maximization problem of commodity-producing firms Therefore, in what follows, a firm represents a commodity-producing firm, unless specified otherwise. The firm produces output Y t through the linear technology Yt = At k t where k

t is the capital. For simplicity, we assume that each period’s productivity of At is constant without technological changes. In addition, we assume that a certain fraction of government subsidies is provided to firms in proportion to output through the relationship of ω (σ − τ )( A + 1)k , where σ and τ are the fractions of government subsidies and taxes, respectively, to GDP plus capital, ( A + 1)k . 4 Here, ω represents the fraction of the total net subsidies (subsidies minus taxes: (σ − τ )( A + 1)k ) given to firms, while 1 − ω is the comparable share given to households. Then, the firm owned by households maximizes its expected discounted profit with respect to the capital stock k t as (1) ∞  k 1 max Et ∑  ∏  k =0  i =1 rt +i   {[1 + ω (σ − τ )]( A + 1)k t + k − (1 + rt + k )k t + k }   where rt represents the domestic interest rate at time t. We assume that the firm finances its investment by issuing

stocks and pay dividends for stocks. To simplify the problem, we also assume that firms pay out dividends at the market interest rate like a coupon bond whose maturity is infinity. Thus, we have 5 4 Because technology is assumed to be putty-putty without depreciation for simplicity, we can therefore assume a linear technology (A+1)k instead of Ak, and a 100% depreciation. Meanwhile, when we focus only on a simple steady state without dynamic shocks where capital stock increases at a constant rate, we would not need the assumption of putty-putty technology. 5 In contrast to borrowing at a low foreign interest rate up to the level of current account deficit, other domestic 5 Source: http://www.doksinet 1 + rt = [1 + ω (σ − τ )](1 + At ) . (2) From equations (1) and (2), the firm’s profit will be Πt = 0 . (3) 2. Households’ Maximization The representative household lives in a house, paying (implicit) rents to the house owner. 6 The agent living infinitely maximizes his

life time utility with the following preferences: (4) ∞  U = Et ∑ β t + j {log(ct + j ) + θ s log(st + j ) + θ h log(ht + j )} ,  j =0  where Et [⋅] represents an expectation operator conditional on the information set of time t, ct is the consumption of commodity c at time t, st = As l is the consumption of the service at time t, ht is the consumption of housing service, and β is the time discount rate with 0 < β < 1 . Given that all the labor supply is inelastically supplied to the service sector and service is produced only with the labor input in the AK type production technology, we do not consider the consumption and production of service st in the household’s utility maximization problem. economic activities such as the firm’s investment are financed at the domestic (high) interest rate. 6 Given the representative nature of our model, the rent can be seen as “implicit” rents for owner-occupied housing. 6 Source:

http://www.doksinet Thus, not only in the utility function but also in the budget constraint below, we do not consider the service sector to simplify the problem. 7 To describe the budget constraint, we need some discussion of the underlying economic environment. We first assume that a household receives government subsidies of S t = (1 − ω )σ ( At + 1)k t , which are spent in the form of e.g, unemployment insurance, retirement annuities, medical insurance and others, proportional to the income level of the country. Generous subsidies cause the household to over-consume. 8 We simply express the household’s tax burden by a lump-sum tax of Tt = (1 − ω )τ ( At + 1)k t which is imposed to partially finance the government subsidy S. Each household owns the fixed h units of real estate and rents it to other households. We define the stock of bank loans to the household at time t as Lt Then, the borrowing (flow) of households on a real estate collateral in each period is ∆Lt =

Lt − Lt −1 , where borrowing is expressed as a constant share η in national wealth (capital stock plus GDP in our model): ∆Lt = Lt − Lt −1 = η ( At + 1)k t . This is not just for simplicity Using the externally given value of η , we can express the idea that the government allows the inflow of cheap foreign funds to the household to a certain limited degree only; therefore η is not determined by the household. For this reason, the foreign interest rate does not affect the intertemporal choices of agents in our model. The public debt is defined as Dt . The government’s budget deficit (flow) depends on both subsidies and taxes that apply to both firms and households. The deficit, Dt − Dt −1 , is supported by borrowing from foreign investors, and is described by the relationship: 7 We include the service sector in the model to see the dynamics of wages. The government subsidy plays a key role in this model. Due to the government subsidy, households consume above

their productivity of labor and capital they own. We call this phenomenon as “over-consumption” 8 7 Source: http://www.doksinet (5) Dt − Dt −1 = σ ( A + 1)k t − τ ( A + 1)k t . The agent maximizes the discounted utility (4) under the budget constraint: (6) ct + rh ,t ht + I t +1 + k t = (1 + rt )k t + Rt + S t − Tt + ∆Lt = ( At + 1)k t + Rt + (σ − τ + η )( At + 1)k t ⇔ ct + rh ,t ht + k t +1 = ( At + 1)k t + Rt + (σ − τ + η )( At + 1)k t where rh ,t denotes the rental price of a unit of housing service, I t +1 investment (saving), rt = [1 + ω (σ − τ )]( A + 1) − 1 is the domestic interest rate of k t at time t in the competitive financial market, and Rt is the rental income from owning a house with size ht (real estate) at time t. 9 Here, we assume the inequality of σ − τ > 0 in order to reflect the large government budget deficit that has happened in southern Europe. We assume that the household also pays rh ,t h = Rt as a rental

cost to real estate owners. That is, households receive the market equilibrium yield for owning the real estate. (7) Rt = rh ,t h We can solve the equilibrium of the above economy. The equilibrium paths of income, consumption, investment, rental prices of capital and real estate, and dividends of the above competitive economy described by equations (1) through (7) are exactly identical to those of another competitive economy that has the production technology of (1 + σ − τ + η ) Ak , instead of Ak , and that has no government intervention in each period. Given that there are neither 9 More specifically, we can assume that the household owns real estate firms by holding their shares. The household obtains profit through the form of dividends. To simplify the problem, we assume that the dividend equals the rent rh ,t ht for an arbitrage among investment in real estate firms and housing. 8 Source: http://www.doksinet frictions nor distortionary tax wedges in our model, below

we solve the equilibrium of the latter competitive economy without considering the government debt – this is because of a Ponzi growth equilibrium feature of the model, which will be discussed later more in detail. In this problem we have two resource constraints. (i) One is the fixed supply of real estate described by h = h , and (ii) the other one is imposed on the goods supply. The latter constraint is derived as follows. Using equations (2) and (7), equation (6) can be transformed to: ct + I t +1 + k t = ct + k t +1 (8) = (1 + σ − τ + η )( A + 1)k t where I t represents the household’s saving (investment). Given that the logarithmic utility function combined with a AK technology yields a constant share of investment in output Yt = (1 + σ − τ + η )( A + 1)k t , we suppose the existence of a certain value of α , and solve for the next period’s capital k ′ as k ′ = k + I = α (1 + σ − τ + η )( A + 1)k (9) ⇒ I = α (1 + σ − τ + η )( A + 1)k − k

where α is the constant investment share out of the broadly defined income (1 + σ − τ + η )( A + 1)k , which will be determined later using an equilibrium condition. Note that the income measure here includes government subsidies, bank borrowing and last period’s capital. It is determined as follows The household’s Euler equation and other intertemporal conditions Now, we consider the Euler equation of the economy, which is expressed as follows: 9 Source: http://www.doksinet (10) 1 + rt = u ′(ct ) , βEt [u ′(ct +1 )] where rt is the domestic interest rate. The specific form of the Euler equation depends on the crisis probability and behavioral assumptions after the crisis. We assume the following: (i) all agents expect crises with a constant probability of π , (ii) once crises occur, they incur a constant crisis cost to every agent by γ ( A + 1)k , where γ is a certain fraction with 0 < γ < 1 ; and the economy returns to a “normal” economy in

which deficit and borrowing are no longer possible with α = β , σ − τ = 0 and η = 0 : government subsidies should balance with taxes and further borrowing from banks is no longer possible. Substituting the marginal utility at each contingent state depending on the probabilistic arrival of shocks into the Euler equation (10) along with an optimization condition 1 + rt = (1 + ω (σ − τ ))(1 + A) , we now can determine α : (10′) −1 α   1− π π + [1 + ω (σ − τ )](1 + A) =   . β (1 − α )  (1 − α )( A + 1)(1 + s − τ + η ) (1 − β )( A + 1)(1 − γ )  Solving for α yields the following: (10′′) α = β (1 + ω (σ − τ ))[(1 + σ − τ + η )π + (1 − β )(1 − γ )(1 − π )] . (1 + σ − τ + η )[ β (1 + ω (σ − τ ))π + (1 − β )(1 − γ )] While the expression for α looks a bit complex, equation (10) implies that an increase in government subsidies and loans to households lowers α , while an increase

in the crisis cost raises it. Now, for the sake of exposition, we consider a special case where π = 0 , ie, crisis is 10 Source: http://www.doksinet perfectly unexpected; this may reflect the economy before the 2008 financial crisis. With π = 0 , we have α= (11) β [1 + ω (σ − τ )] . 1+ σ −τ +η Equation (11) implies that given 0 < β < 1 and 0 < ω < 1 , a higher fraction of government subsidies to households leads to over-consumption, and to a decrease in the investment share in income: ∂α / ∂ (σ − τ ) < 0 . In contrast, as the government subsidies to firms, ω , increase, α increases, leading to over-investment: ∂α / ∂ω > 0 . And with σ − τ = 0 and η = 0 , α = β . 10 Also, from equations (8) and (9), we can solve for an optimal consumption decision as (12) c = (1 − α )(1 + σ − τ + η )( A + 1)k . Equations (9), (11) and (12) produce the optimal growth rates of consumption and capital stock, g c and g k , as:

(13) k′ = α (1 + σ − τ + η )( A + 1) k c′ = α (1 + σ − τ + η )( A + 1) c The expressions for g c and g k show that the steady-state, if any, has the growth rate equal to α (1 + σ − τ + η )( A + 1) . When the crisis probability π is zero (ie, the crisis is perfectly unexpected), the growth rates are expressed as: 10 Over-consumption and over-investment mean excessive consumption and investment compared to those for the normal economy with σ − τ = 0 , η = 0 , and α = β . 11 Source: http://www.doksinet k′ = β [1 + ω (σ − τ )]( A + 1) k c′ = β [1 + ω (σ − τ )]( A + 1) c (14) We can see that the higher fraction ω of government subsidies goes to firms, the higher growth of consumption and capital stock does the economy show. Also for the service sector, considering the logarithmic utility function and the inelastic labor supply, we derive the price of services Ps along a growth path while normalizing the price of commodity c at unity

Pc = 1 : Ps′s ′ Ps′As l Ps′ c ′ = = = = α (1 + σ − τ + η )( A + 1) Ps s Ps As l Ps c (15) ⇒ Ps′ = β [1 + ω (σ − τ )]( A + 1) Ps if π = 0. Therefore we can see that the wage rate in the service sector increases at the same rate with the growth rates of consumption and the capital stock. Now, we can determine wages, which is equal to the marginal productivity of labor at the service good sector, i.e, w = Ps As Given the log-linear utility function, in which the consumption share of each good is constant in each period, we obtain the optimization relationship: c = (1 − α )(1 + σ − τ + η )( A + 1)k = 1 θs Ps As l , we can express the wage rate as follows: (16) w = Ps As = = θ s (1 − α )(1 + σ − τ + η )( A + 1)k l θ s [1 − β + (1 − βω )(σ − τ ) + η ]( A + 1)k l 12 with π = 0 Source: http://www.doksinet Equation (16) implies that wages rise with government subsidies and the fraction of government subsidies

attributed to households. Meanwhile, utilizing the properties of a logarithmic utility function, we can solve for the price of the housing service rh ,t with a general equilibrium condition ht = h as rh ,t = (17) θ h ct h 3. The Steady-state Ponzi Growth Equilibrium We focus on the balanced growth path in which level variables including debts in our model economy grow at a constant rate. Equation (13) shows that consumption and capital grow at the rate of α (1 + σ − τ + η )( A + 1) . The shares of consumption and investment relative to income stay constant over time, as we can see from (10) and (12). As indicated in equation (8), the household budget exceeds the domestic disposable output A(k t + 1) in each period because (1 + σ − τ + η )( A + 1)k t > A(k t + 1) . In an open economy setting as in ours, the resulting excess demand of (σ − τ + η ) A(k t + 1) will be financed by the current account deficit. As long as government subsidies and borrowings from banks

continue with collateral lending conditions not to be violated, households perceive that their income is permanently increased and the current account deficit also can persist. Meanwhile, an economy with σ − τ + η = 0 satisfies the general equilibrium condition with a current account balance. See the comparison about the over-consumption economy with the normal economy, summarized in Table 2. 4. Banks’ Behavior 13 Source: http://www.doksinet In our model the government allows domestic banks to borrow from foreign investors in order to finance the current account deficit, and to lend the money to households and government at the foreign, low interest rate. 11 Further we assume that the banks will continue lending to households and the government as long as collateral values cover the accumulated bank loans to households and the government. We also assume that domestic banks and foreign investors are risk neutral, concerned about expected returns only. Therefore, if the

expected return of loans falls below a certain threshold level, they stop providing funds for households and the government. When the expected ratio of their loans to collateral value exceeds a certain specified threshold level, foreign investors do not continue to lend to domestic banks. In addition, the collateral value of banks themselves falls below their accumulated borrowings from foreign banks, which is equal to the total accumulated loans both to households and the government, foreign banks do not lend to domestic banks. Domestic banks are also assumed to behave as foreign investors by lending to households and the government under the same collateral constraint as foreign banks. 12 Note however that foreign funds are available to agents as much as trade deficit, and therefore the domestic interest rate is higher than that of foreign funds. 5. Housing and Stock Prices In the presence of generous welfare subsidies and collateral lending, borrowing from foreign investors covers

the over-consumption which leads to the current account deficit. Note 11 We consider domestic banks and foreign investors as different economic agents despite their similar roles in the economy in order to account for the role of weak domestic financial sector in the occurrence of South European fiscal crises. 12 Even though a foreign investor’s loan-to-value (LTV) threshold can be much lower than a domestic bank’s, we simply assume that they are identical. This assumption does not influence the main results because, as long as the foreign investor’s LTV threshold is lower than or equal to the domestic bank’s, the crisis depends only on the 14 Source: http://www.doksinet also that the foreign, world interest rate is lower than the domestic rate, and that we assume for simplicity that the expected crisis probability is zero. The price of a unit of real estate Ph ,t is set such that the discounted flow of future rents is equal to the price of a house with size h . Using

equations (2), (12) and (17), it is given by: (18) ∞  j 1 Ph ,t h = Et ∑  ∏  j =0  k =1 rt + k   rh ,t + j h    ∞  j 1 = Et ∑  ∏  j =0  k =1 rt + k   θ h ct + j    ∞  j g = Et ∑  ∏ t + k  j =0  k =1 rt + k   θ h ct    = θ h ct (1 − β ) −1 1−α θ h (1 + σ − τ + η )( At + 1)kt 1− β 1 = θ h {1 − β + (1 − βω )(σ − τ ) + η }( At + 1)kt with π = 0 1− β = where g = c′ k ′ = = α ( A + 1)(1 + σ − τ + η ) = β [1 + ω (σ − τ )]( A + 1) with π = 0 as long as the c k economy stays in this steady state, and g t represents the gross growth rate of income at time t+1 along the balanced growth path. Equation (18) says that real estate prices are higher in an overconsuming economy with positive government subsidies σ − τ > 0 , and that they grow at the rate of g = β [1 + ω (σ − τ )]( A

+ 1) . Thus we can see that given the growth rate at the balanced growth path: g = β [1 + ω (σ − τ )]( A + 1) , the real estate price grows faster than in an economy with σ − τ = 0 unless ω is zero. In addition, we can see that while a higher fraction of government subsidies given to firms, ω , lowers the real estate price, it boosts the growth rate as well as the domestic interest rate. 13 foreign investor’s, not on the domestic bank’s. 13 If we use the international interest rate as the discount factor when calculating real estate price, the price goes to 15 Source: http://www.doksinet Then, the ratio of real estate value to output is determined as follows: (19) Ph ,t h Ak t =  1  1 θ h [1 − β + (1 − βω )(σ − τ ) + η ]1 +  . 1− β  At  Equation (19) implies that an increase in government subsidies or in borrowing raises this ratio The assumption that the world interest rate is different from the domestic rate implies

that the stocks and the real estate are traded in the domestic, local markets. With the assumption that the stock market is not globalized, the stock price PST ,t is the sum of the value of future dividend flows discounted by the domestic interest rate rt . Therefore it is expressed as: 14 (20) PST ,t = 1 [1 + ω (σ − τ )]( At + 1) 1 + rt =1 Now, recall that the domestic bank provides loans to households and to the government by borrowing from foreign investors, as long as their accumulated borrowings do not exceed the collateral value of their assets. We further assume that the lending rate at which domestic banks provide loans to households and the government is the foreign interest rate r f . 15 infinity. To avoid such an unrealistic case, we therefore assume that the real estate market is not exposed to international investors. 14 However, if the stock market is exposed to the international capital market, then the discount rate should be the international interest rate

as PST′ ,t = ( A + 1) /(1 + r f ) = (1 + r ) /(1 + r f ) . Below, we assume that the stock market is not integrated to the world capital market. 15 The result will not change qualitatively when banks are allowed to charge firms a lending rate higher than the foreign rate, as long as this rate is smaller than βrt . We can assume that the domestic lending rate will fall to the 16 Source: http://www.doksinet 6. Collateral Lending Conditions Collateral Lending Condition for the Government From equation (5), we can calculate the accumulated government debt arising from borrowings to cover each period’s deficit at time t as: { } Dt = (σ − τ ) ( A + 1)k t + (1 + r f )( A + 1)k t −1 + (1 + r f ) 2 ( A + 1)k t − 2 + . + (1 + r f ) j ( A + 1)k t − j + (21)  1 + r f  1 + r f = (σ − τ )( A + 1)k t 1 + +   1 + g  1 + g 1+ g ( A + 1)k t = (σ − τ ) g −rf 2 1+ r f   + . +   1+ g  j    + . 

 where g is the growth rate at the balanced growth path [see the definition of g in equation (13)]; and hence 1 + g = β [1 + ω (σ − τ )]( A + 1) . Collateral lending condition here is defined as follows. The banking sector permits lending and debt rollover as long as a certain fraction φG of the expected value of the next period assets exceeds the value of standing debt, the so-called LTV principle. Using (21), the collateral lending condition for the government is described by: (22) Dt +1 < φG (stock t +1 + real estate t +1 ) ⇔ (σ − τ )   1+ g 1 θ h ( A + 1)k t +1 (1 − β + (1 − βω )(σ − τ ) + η ) ( A + 1)k t +1 < φG ( A + 1)k t +1 + f 1− β g −r   ⇔ (σ − τ )   1+ g 1 θ h (1 − β + (1 − βω )(σ − τ ) + η ) ( A + 1)k t +1 < φG ( A + 1)k t +1 1 + f g −r  1− β  (σ − τ ) ⇔ 1+ g g −rf 1 θ h {1 − β + (1 − βω )(σ − τ ) + η } 1+ 1− β < φG level of the

foreign rate through competition among banks. 17 Source: http://www.doksinet where the numerator (σ − τ ) 1 + gf is the accumulated debt from the past, while the denominator g −r 1+ 1 θ h [1 − β + (1 − βω )(σ − τ ) + η ] is simply the expected value of the next period asset under 1− β the expectation of no crisis. Hence the ratio is the loan-to-value (LTV) φG is a certain specified limit that the banking sector assigns for its safe asset management. Equation (22) implies that the less likely this inequality holds, when the world interest rate increases, and/or when the future productivity decreases – both lowers the expected real estate price. Collateral Lending Condition for the Household Similarly, based on the model described earlier, we can define the household’s accumulated borrowing from banks at time t as follows: { } Lt = η ( A + 1)k t + (1 + r f )( A + 1)k t −1 + (1 + r f ) 2 ( A + 1)k t −2 + . + (1 + r f ) j ( A + 1)k t − j + (23)

 1 + r f  1 + r f +  = η ( A + 1)k t 1 +  1 + g  1 + g 1+ g =η ( A + 1)k t g −r f 2 1+ r f   + . +   1+ g  j    + .   Equation (23) implies that the total amount of bank loans can remain within the collateral value at any point in time, if the inequality of 1 + g = α ( A + 1)(1 + σ − τ + η ) = β [1 + ω (σ − τ )]( A + 1) > 1 + r f holds for each period. Below, we assume that this inequality holds true. This inequality implies the following The higher are the domestic productivity A and the net subsidy σ ′ ≡ σ − τ , and the lower is the foreign interest rate r f , the more likely does this relationship hold. 18 Source: http://www.doksinet Therefore, in a similar manner as before, we can derive the collateral lending condition for households. As long as household debt is less than a certain fraction φH of the household asset, household borrowing can continue: Lt +1 < φ

H (stock t +1 + real estate t +1 ) ⇒ (24) η   1+ g 1 θ h ( A + 1)k t +1 (1 − β + (1 − βω )(σ − τ ) + η ) ⇒ ( A + 1)k t +1 < φ H ( A + 1)k t +1 + f 1− β g −r   η   1+ g 1 θ h (1 − β + (1 − βω )(σ − τ ) + η ) ⇒ ( A + 1)k t +1 < φ H ( A + 1)k t +1 1 + f g −r  1− β  η 1+ g g −rf   1 θ h (1 − β + (1 − βω )(σ − τ ) + η ) < φ H 1 +  1− β  Note that a decrease in the expected TFP, At +1 , raises the LTV ratio by lowering the collateral value of the RHS in the third line of (24), less than the accumulated amount of the loan of the LHS of the third line of (24). Thus, for example, a negative shock to the terms of trade, which lowers At +1 , raises this ratio, more likely violating the inequality (24). We call the condition of the expected ratio, as expressed by (22) and (24), being less than φi as the “collateral lending condition.” 16 We assume that

domestic banks will continue to lend money to households and government as long as these collateral lending conditions hold. At this point, we further assume that foreign investors will also lend to domestic banks, as long as these collateral lending conditions are satisfied, for domestic banks to lend to domestic households and the government. Collateral Lending Condition for Domestic Banks 16 The condition that the LTV ratio is less than unity is commonly adopted to describe the bank’s behavior of collateral lending as in Kiyotaki and Moore (1997) and Schneider and Tornell (1999). 19 Source: http://www.doksinet We assume that households and the government can borrow through the financial intermediation of domestic banks. The domestic bank’s accumulated loan from foreign banks at time t is described by (25) { } Lt + Dt = (σ − τ + η ) ( A + 1)k t + (1 + r f )( A + 1)k t −1 + (1 + r f ) 2 ( A + 1)k t − 2 + . + (1 + r f ) j ( A + 1)k t − j +  1 + r f  1

+ r f = (σ − τ + η )( A + 1)k t 1 + +   1 + g  1 + g 1+ g = (σ − τ + η ) ( A + 1)k t g −rf where 1 + g = 2  1+ r f  + . +    1+ g j    + .   ct +1 k t +1 = = α ( A + 1)(1 + σ − τ + η ) = β (1 + ω (σ − τ ))( A + 1) with π = 0. ct kt Equation (26) implies that the total amount of domestic bank loans should remain within the borrowing country’s collateral value at any point in time, if the inequality of g > r f holds in each period. In the discussion below, we assume that this inequality holds true This inequality implies the following. Without this condition, in the steady state, collateral lending condition cannot hold, because the principal plus interest of the total lending will increase faster than the value of collateral does. Thus, the higher are the domestic productivity A and the net subsidy σ ′ = σ - τ and the lower is the foreign interest rate r f , the more likely

does this relationship hold. In addition, as the subsidies to firms increase (ie, as ω increases), the growth rates of GDP and asset prices increase, thus making the LTV ratios more easily satisfied. Thus, we have the collateral lending condition for domestic banks of (26) Dt +1 + Lt +1 < φ B (stock t +1 + real estate t +1 ) . 20 Source: http://www.doksinet ⇔ (σ − τ + η )   1+ g 1 θ h ( A + 1)k t +1 (1 − β + (1 − βω )(σ − τ ) + η ) ( A + 1)k t +1 < φ B ( A + 1)k t +1 + f 1− β g −r   ⇔ (σ − τ + η )   1+ g 1 θ h (1 − β + (1 − βω )(σ − τ ) + η ) ( A + 1)k t +1 < φ B ( A + 1)k t +1 1 + f g −r  1− β  ⇔ (σ − τ + η ) 1+ g g −rf   1 θ h (1 − β + (1 − βω )(σ − τ ) + η ) < φ B 1 +  1− β  III. Self-fulfilling Crisis and Propagation to Other Sectors 1. Self-fulfilling Crisis Region (SFCR) We assume the existence of the crisis costs. If a

crisis occurs due to the household debt problem, this crisis incurs a crisis cost of ΓH = ( A + 1)k ⋅ γ H to each agent in the economy. And if a banking crisis occurs, then another crisis cost incurs to all agents in the economy by as much as ΓB = ( A + 1)k ⋅ γ B . Finally, an additional occurrence of fiscal crisis (sovereign debt crisis) entails another crisis cost of ΓG = ( A + 1)k ⋅ γ G . The self-fulfilling crisis region, SFCR, is defined as follows. If a crisis occurs by violating one of the three different collateral lending conditions described above, the corresponding borrowing and lending cannot be implemented any more. Combined with the related crisis cost, the inability to carry out financial activities will decrease the next period’s broadly defined disposable income, thus the next period’s real estate prices and stock prices fall. Considering this mechanism, we can see that there exists a certain range of collateral value ratios in which, with normal

borrowing and lending possible, this ratio remains below the threshold ratio, while without normal borrowing and lending, the ratio increases above the threshold, leading to a crisis. The self-fulfilling crisis regions are described below 21 Source: http://www.doksinet First, the self-fulfilling crisis region of the collateral lending condition for the government is described by: (σ − τ ) (27) 1+ g g −rf (σ − τ )   1 1 + 1 − β θ h (1 − β + (1 − βω )(σ − τ ) + η )    < φG < LTV under normal financial activities 1+ g g −rf    1 θ h (1 − β + η )  (1 − γ G )1 + 1− β        LTV under crisis: govt financial activities are not possible where we assume the other collateral lending conditions are not violated. Note that in (27) once crisis occurs, the usual debt rollover is not

possible and the government has to implement a budget balance: σ − τ = 0 . 17 Along with the related crisis cost, these behavioral changes reduce the collateral value, increasing the LTV ratio. Here, we assume that other collateral lending conditions hold, and households and banks are not in their SFCR’s (i.e, other collateral conditions are in the safe regions). Also the self-fulfilling crisis region of the collateral lending condition for the household is described by (28) η 1+ g g −rf 1 1+ θ h [1 − β + (1 − βω )(σ − τ ) + η ] 1 β −  LTV under normal financial activities η < φH < 1+ g g −rf   1 (1 − γ H )1 + θ h [1 − β + (1 − βω )(σ − τ )]  1− β     LTV under crisis: households financial activities are not possible where we assume the other collateral lending conditions are not violated, nor in

their SFCR’s. Note that in (28) once crisis occurs, the usual debt rollover is not possible and the household 17 Here, household borrowing is assumed to be possible. 22 Source: http://www.doksinet cannot borrow to over-consume: η = 0 . This as well as the related crisis cost reduces the collateral value, increasing the LTV ratio. The self-fulfilling crisis region of the collateral lending condition for domestic banks is described by: 1+ g g −rf . < φB < 1 (1 − γ G − γ H − γ B )(1 + θ h ) θ h (1 − β + (1 − βω )(σ − τ ) + η ) 1+  −β 1 LTV under crisis: normal financial activities   are not possible (σ − τ + η ) (29) 1+ g g −rf (σ − τ + η ) LTV under normal financial activities With a banking crisis, neither government nor household can borrow, exacerbating the crisis, because domestic banks’ intermediation between domestic borrowers and foreign

investors no longer functions. This is why the denominator of (29) is given by (1 − γ G − γ H − γ B )(1 + θ h ) 2. A Crisis Can Induce a Cascade of Other Crises The previous section dealt with the SFCR in a partial equilibrium context – each crisis has an independent impact on the economy and do not interact with other types of crisis. In fact, an occurrence of a crisis would raise the probability that other crises occur conditional on a crisis that has already happened, because agents in a macro economy are tightly linked together. In some instances, an unexpected crisis would trigger other crises to happen subsequently, incurring additional crisis costs. To clarify the concept, suppose that (i) all three collateral lending conditions specified earlier were satisfied, and (ii) inequality (28) was satisfied: the economy has been in the SFCR for household, while (27) and (29) were not. In other words, the collateral condition for the household debt crisis is in the SFCR,

while those for banks and the government are in the safe 23 Source: http://www.doksinet region. When a self-fulfilling crisis of the household debt crisis occurs, triggered by, for instance, a decrease in A and pessimism, it first exacerbates the household debt problem, which incurs a crisis cost of ΓH = ( A + 1)k ⋅ γ H to each agent in the economy. Then asset prices fall, and the economy would now move into the SFCR for fiscal crisis (sovereign debt crisis) described by equation (30) below 18. And a mere psychological pessimism of banks and foreign investors can trigger a fiscal crisis, Then the government is unable to provide subsidies to firms and households, lowering collateral values further. : 1+ g g −r f . < φG < (1 − γ H − γ G )(1 + θ h )   1  θ h (1 − β + (1 − βω )(σ − τ )) (1 − γ H )1 + midified upper threshold of (27) 1− β    (σ −

τ + η ) (30) 1+ g g −rf (σ − τ + η ) LTV under household crisis In other words, if inequality (30) holds, mere pessimism pushes the economy into the region for a fiscal crisis, violating its collateral lending condition, then the subsequent banking crisis takes place, incurring crisis costs to all agents in the economy by as much as ΓB = ( A + 1)k ⋅ γ B . A substantial fall in asset values due to the fiscal crisis can push the economy into the SFCR of a banking crisis as described by: 1+ g 1+ g (σ − τ + η ) f g −r g −rf . < φB < (1 − γ H − γ G )(1 + θ h ) (1 − γ H − γ G − γ B )(1 + θ h )   (σ − τ + η ) (31) LTV under household and fiscal crises modified upper threshold under all crises Then, if (31) holds, pessimism of bankers and foreign investors can induce banking crisis, incurring crisis costs and leading to a further drop in asset values and income. 18 Here, we

are assuming that banks and the foreign investors are myopic in the sense that they do not take into 24 Source: http://www.doksinet Note that the SFCR expands with contagion when a household debt shock propagates instantaneously to the public sector and then to the banking sector. As the example above shows, how crises occur sequentially depends on the parameter values such as the sizes of crisis costs, the threshold values of LTV ratios, the relative movements of stock price vs. real estate price, and others. 3. Discussions In this section we discuss key assumptions and limitations of the model. We view exogenous changes, such as a decrease in the productivity caused by the global financial crisis or an increase in the effective real exchange rate due to joining the Euro zone, as possible sources of pessimism triggering the mechanism for self-fulfilling crisis. For instance, an expectation about a decrease in future TFP A can push the economy into SFCR by lowering the collateral

value of an affected country. While we assume for exposition that agents do not expect any possible occurrences of crises in our calculation of SFCR, it is not difficult to discuss more realistic cases of a positive crisis probability using a calibration model. We think that our model sheds some light on understanding the crises in southern European countries such as Spain and Greece. These countries share the common features: weak industry base, high levels of private and government debts, high fiscal deficits, high current account deficits, and real estate bubbles. Under these economic circumstances, external shocks can easily trigger a crisis in one part of an economy and propagates to other sectors of an economy. For instance, a household debt crisis after a bust of real estate bubbles leads to a government debt management/ fiscal crisis, and in turn to a banking sector crisis. account the other crisis possibilities, even though a series of crises can happen sequentially. 25

Source: http://www.doksinet Moreover, an overly pessimistic view of foreign investors can easily initiate a financial crisis, especially when the economy is located in the SFCR. In fact, foreign investors are found to be less tolerant than domestic banks in evaluating the situation of an indebted economy because they do not hold collateral directly, nor do they have the loan guarantee from the government unlike domestic financial institutions. IV. Concluding Remarks This paper provides a model that accounts for the South European sovereign debt crises characterized by high capital inflows, real estate bubble, over-consumption and over-investment, and sudden fiscal crisis. The model describes a steady-state Ponzi growth equilibrium in which households, heavily subsidized by the government, have incentives to over-consume and overinvest, and banks lend money to households and the government by financing funds from international capital market at a lower rate. The model shows that a

high growth economy caused by high government subsidies becomes more vulnerable to adverse shocks and more likely to be subject to banking and fiscal crises, when foreign investors stop lending to domestic banks. The model provides several predictions that may well be consistent with the South European countries that experienced sovereign debt crises. First, higher government welfare subsidies generate higher consumption and investment, higher GDP growth, higher level and growth of real estate price, and a higher income share of current account deficits. Second, the rapid growth induced by government subsidies makes the economy vulnerable to adverse shocks. When adverse shocks hit the economy and the expected loan-to-collateral value ratio 26 Source: http://www.doksinet rapidly increases, foreign investors become suspicious about the financial soundness of domestic households, banks, and the government, and they begin to withdraw their loans. Subsequently, financial panic can

easily trigger household debt crisis, banking crisis, and fiscal crisis. The model also stresses the self-fulfilling prophecy nature of crises. When foreign banks or foreign investors start to view an economy too risky, then it will surely become risky. One foreign investor’s withdrawal of fund from a domestic bank can trigger other investors’ withdrawal from other banks. The bank run feature of the model implies that financial crises can be contagious among similar countries with high debts. Once foreign investors have experienced a crisis in a country, they will become more cautious in making investment in economies with similar financial systems. In fact, the recent South European crises showed this self-fulfilling feature across the countries. Moreover, one type of crisis can trigger another different type of crisis. For example, a household debt crisis can trigger a fiscal crisis, and subsequently a banking crisis. Alternatively, a household debt crisis can lead to a banking

crisis, and subsequently to a fiscal crisis, depending on their threshold value of LTV and the magnitude of the crisis cost. Although the contagion process in EU may differ from that in US, we think that our model provides a useful basis for understanding recent financial crises. References Aghion, Philippe, Philippe Bacchetta, and Abhijit Banerjee, 2000, “A Simple Model of Monetary Policy and Currency Crises,” European Economic Review 44, 728-738. 27 Source: http://www.doksinet Barro Robert, and Xavier Sala-I-Martin, 1995, Economic Growth, McGraw-Hill, Cambridge, MA. Borensztein, Eduardo and Jong-Wha Lee,1998, “Credit Allocation and Financial Crisis in Korea,” International Monetary Fund Working Paper WP/99/20. Chang, Roberto and Andres Velasco, 1998, “Financial Crises in Emerging Markets: A Canonical Model,” NBER working paper No.6606 Classens, Stijn, Simon Djankov, Joseph P.H Fan, and Larry H P Lang, 1999, “Corporate Diversification in East Asia: The Role of

Ultimate Ownership and Group Affiliation,” Policy Research Working Paper, World Bank. Cole, Harold L. and Timothy J Kehoe, 1996, “A Self-fulfilling Model of Mexico’s 1994-1995 Debt Crisis,” European Economic Review 41, 309-330. Corsetti, Giancarlo, Paolo Pesenti, and Nouriel Roubini, 1999a, “What Caused the Asian Currency and Financial Crisis?” Japan and the World Economy 11, 305-373. Corsetti, Giancarlo, Paolo Pesenti, and Nouriel Roubini, 1999b, “Paper Tigers? A Model of the Asian Crisis,” European Economic Review 43, 1211-1236. Demirguc-Kunt, Ash and Enrica Detragiache, 1997, “The Determinants of Banking Crises: Evidence from Developing and Developed Countries,” IMF Working paper 97/106. Diamond, Douglas and Phillip Dybvig, 1983, “Bank Runs, Deposit Insurance, and Liquidity,” Journal of Political Economy 91(3), 401-19. Eichengreen, Barry and Andrew Rose, 1998, “Staying Afloat When the Wind Shifts: External Factors and Emerging-Market Banking Crises,” NBER

Working paper No. 6370 Goldstein, Morris, 1998, The Asian Financial Crisis: Causes, Cures and Systematic Implications, Institute for International Economics. 28 Source: http://www.doksinet Hussain, Mumtaz, and Steve Radelet, 2000, “Export Competitiveness in Asia,” in The Asian Financial Crisis. Lessons for A Resilient Asia edited by Wing T Woo, Jeffrey D Sachs, and Klaus Schwab, The MIT Press. International Monetary Fund, World Economic Outlook, Interim Assessment, December 1997. Johnson, Simon, Peter Boone, Alasdair Breach, and Eric Friedman, 1999, “Corporate Governance in the Asian Financial Crisis,” Manuscript, MIT. Kaminsky, Graciela and Carmen Reinhart, 1996, “The Twin Crises: The Causes of Banking and Balance of Payments Problems,” Working Paper, Federal Reserve Board. Kiyotaki, Nobuhiro, and John Moore, 1997, “Credit Cycles,” Journal of Political Economy 105(2), 211-248. Krugman, Paul, 1998, “What Happened to Asia?” Manuscript, M.IT Krugman, Paul,1999 ,

“Balance Sheets, Financial Crises, and the Transfer Problem,” Manuscript, MIT. Lee, J.-W, 1996, “Government Interventions and Productivity Growth,” Journal of Economic Growth 1(3), 391-414. McKinnon, Ronald, and Huw Phil, 1997, “Credible Economic Liberalization and Overborrowing,” American Economic Review Papers and Proceedings 97, 189-93. Radelet, Steve and Jeffrey Sachs, 1998, “On the Onset of the East Asian Financial Crisis,” Development Discussion Paper, Harvard Institute for International Development. Rebelo, Sergio,1991,”Long-run Policy Analysis and Long-run Growth,” Journal of Political Economy 99(3), 500-21. Rodrik, Dani, 1995, “Getting Interventions Right: How Should Korea and Taiwan Grew Rich,” Economic Policy 20. 29 Source: http://www.doksinet Romer, Paul M., “Endogenous Technological Change,” The Journal of Political Economy, 98 (5, Part 2), 1990, S71-S102. Sachs, Jeffrey D. and Wing T Woo, 2000, “A Reform Agenda for a Resilient Asia,”

in The Asian Financial Crisis. Lessons for A Resilient Asia edited by Wing T Woo, Jeffrey D Sachs, and Klaus Schwab, The MIT Press. Schneider, Martin and Aaron Tornell, 1999, “Lending Booms and Asset Price Bubbles,” Mimeo., Harvard University World Bank, 1993, East Asian Miracle: Economic Growth and Public Policy. World Bank, 1998, East Asia: The Road to Recovery. 30 Source: http://www.doksinet Table 1. Definitions of parameters, variables and notations Parameters or variables meanings σ Ratio of subsidy to output τ Ratio of taxes to output σ ′ = σ −τ Ratio of net subsidy to output ω share of subsidy for individuals relative to firms β Time discount rate A TFP As TFP for service good c Consumption s Service h Housing service pc = 1 Price of consumption, normalized at unity ps Price of a unit of service ph Price of a unit of housing rh Rent of a unit of housing Rt = rh ,t h Rent for housing service h PST ,t Price of stock w Wages

θh Scale parameter for housing in utility function θs Scale parameter for service good in utility function g Growth rate at the steady state r Domestic interest rate rf World interest rate l Inelastic supply of labor k capital I investment L Household borrowing 31 Source: http://www.doksinet α constant investment share out of the broadly defined income (1 + σ − τ + η )( A + 1)k i Agents: G (government), H (household) and B (bank) D Public debt Dt − Dt −1 Fiscal deficit η Borrowing rate out of output π Probability of crisis occurrence φG LTV for government borrowing φH LTV for household borrowing φB LTV for bank borrowing ΓG = ( A + 1)k ⋅ γ G Total crisis cost to the government ΓH = ( A + 1)k ⋅ γ H Total crisis cost to household ΓB = ( A + 1)k ⋅ γ B Total crisis cost to banks γG Fraction of crisis cost to output for the government γH Fraction of crisis cost to output for households γB Fraction of crisis

cost to output for banks 32 Source: http://www.doksinet Table 2. Comparison between two model economies Over-consumption Economy Normal Economy β (1 + ω (σ − τ ))( A + 1) β ( A + 1) [1 − β + (1 − βω )(σ − τ ) + η ](1 + 1 / A) (1 − β )(1 + 1 / A) Investment / Output β (1 + ω (σ − τ ))(1 + 1 / A) β (1 + 1 / A) Land Value / Output θ (1 + σ − τ + η )(1 + 1 / A) θ (1 + 1 / A) (σ − τ + η )(1 + 1 / A) 0 Growth rate of output and real estate prices Consumption / Output Trade Deficits / Output National Debt / Output Gross Interest Rates (σ − τ + η )(1 + 1 / A) g g −r f (1 + ω (σ − τ ))( A + 1) 33 0 A +1