I. Introduction

Since the early summer of 2003, Japan started to recover from its long recession.With this recovery, the non-performing loan problems of the major banks appears to be abating. The major banks were helped by large injections of equity from the government and a recovering economy that boosted profits, allowing the major banks to increase their loan-loss reserves and capital-asset ratios. However, difficulties persist with the regional banks, which have been slow to write-off their non-performing loans. Moreover, the growth prospects for the Japanese economy are still uncertain. The persistent difficulties facing the banking sector are a legacy of weak government financial regulation and prudential supervision. This paper considers the possibility that public policy towards the financial system is the root cause of the Japanese banking and growth crisis.

A simple endogenous growth model with a bank-centered financial system is presented and solved for equilibrium in closed-form. Three stylized facts about the Japanese financial are incorporated into the assumptions of our model economy. Domestic investment is financed primarily by bank loans and equity issues. The government provides deposit insurance guarantees to the holders of domestic bank deposits. Prudential regulation and enforcement is weak leading to rises in the non-performing assets held by banks and the deposit insurance liability of the government over time. In our model, banks can accumulate non-performing loans against deposit liabilities when the government guarantees deposits and fails to monitor additions to bank loan-loss reserves.

In the theoretical model, production displays constant returns to a single accumulable factor, capital, and is subject to idiosyncratic productivity shocks. Bank financing of investment by firms dominates direct lending by savers to firms. Bank loans are derived as constrained optimal contracts under standard information assumptions. Productivity shocks are independent across a continuum of firms, and there is no aggregate uncertainty. In equilibrium, the asset portfolios of both banks and households (which hold both deposits and corporate equities) are perfectly diversified. The analysis focuses on how public sector deposit guarantees and regulatory forbearance lead to the accumulation of non-performing bank assets, deposit insurance liabilities and falling growth rates in the endogenous growth model. It shows how a banking crisis can evolve endogenously as investment and output growth decline in the absence of systemic shocks.

Weak prudential regulation is interpreted in our model as a failure of the government to enforce loan-loss reserve accumulations by banks against non-performing corporate loans or, equivalently, the writing off of non-performing assets. In this case, banks are able to make dividend payments to their shareholders against the interest contracted on both performing and non-performing assets. Deposit insurance allows the banks to transfer resources from the government to their shareholders. With regulatory forbearance, the output growth rate falls gradually in equilibrium as non-performing bank loans grow in the economy. The longer the government fails to intervene, the lower the growth rate falls towards zero. If the government fails to intervene before a critical date, the banks will be unable to meet the deposit withdrawal demands of households for consumption leading to a banking crisis. A banking crisis arises endogenously under perfect foresight in our model.

The dynamics for output, consumption and investment under regulatory forbearance and deposit insurance predicted by the model are compared to the recent experience of the Japanese economy. A feature of our model is that we can solve for the equity values of the banking sector and the non-bank corporation sector. A prediction special to our model is that the relative value of bank stocks to the aggregate stock market falls ahead of a banking crisis, while the value of corporate equity can be rising. The model also predicts a collapse in the market for collateral at the moment of the crisis. We also compare these implications to the data for Japan. Our empirical work begins with a test of the maintained hypothesis of perfect foresight. We compare the experience of Japan to the model and test the relationships in our model using structural vector autoregressions.

We argue that the data are consistent with our simple dynamic model that assumes that asset prices correctly reflect fundamentals. We show that for Japan’s recent economic history, fundamentals are important in explaining Japanese stock returns and that the role of bubbles in affecting stock returns may be small or superfluous. Surprisingly, we show that these results hold even for the 1980s, when Japanese equity prices skyrocketed. The data on Japanese macroeconomic aggregates, consumption, investment and growth, are also roughly consistent with the comparative dynamics of our model.

Given that Japanese stock prices roughly correspond to fundamentals, we test the theoretical prediction in our model that the ratio of the value of bank equities to the overall stock market declines before the crisis, and ahead of other macroeconomic aggregates. Our causality tests are consistent with our theory: the ratio of the value of bank equities to the overall stock market precedes the movement in other macroeconomic aggregates, for example, the investment-output ratio.

The model of banking crises presented here complements the traditional view of Japan’s banking crisis in the 1990s. The traditional view places blame for Japan’s banking crisis on the manner of financial sector deregulation initiated in the middle of the 1970s.² In that view, as alternative financial instruments were introduced, large, internationally-oriented firms began to raise funds directly in the domestic and foreign bond markets. As the large banks started to lose their highest quality corporate borrowers in the late 1980s, they began lending to smaller firms. When the asset-market boom for Japan in the late 1980s collapsed, the Japanese economy began its prolonged stagnation, and the non-performing assets of the banking system rose rapidly. Despite the rise in direct borrowing by major corporations, Japanese financial intermediation is dominated by commercial banks. Cargill, Hutchison and Ito [1997] and Cargill [1999] emphasize, as we do, the importance of explicit and implicit deposit guarantees and of regulatory forbearance in the creation of the crisis. This paper contributes a formal model of credit market dynamics that complements our earlier paper, Dekle and Kletzer [2003].³

Our model is one of the few general equilibrium models that analyze the Japanese financial and growth crisis of the 1990s. Banking crises affect capital accumulation and economic growth, while low growth rates exacerbate banking crises. Because of the endogenous mutual relationship between banking crises and growth, partial equilibrium models are severely limited. Three other papers analyze the Japanese economy in the 1990s using a general equilibrium framework. Hayashi and Prescott [2002] present and calibrate a real business cycle model for Japan to show how the decrease in labor supply and total factor productivity growth can account for the growth slump of the 1990s. Hayashi and Prescott argue that credit constraints were not important for reducing investment rates, but they also suggest that weakness of the banking sector might have played a role in lowering the productivity of investment. As in our model, Barseghyan [2002] emphasizes delays in government bailouts of the banking system in an overlapping generations model. In his model, when the government delays bailouts, banks use new deposits to meet the withdrawals by old depositors, as in a Ponzi scheme. Barseghyan calibrates his model to Japanese data and finds a favorable comparison to Japanese growth in the 1990s. The third paper is our earlier model (Dekle and Kletzer [2003]) of endogenous banking crises which presents a somewhat different model and empirical analysis for Japan.

The next section discusses the stylized facts about the Japanese financial system that motivate the simple assumptions of our analysis. Sections 3, 4 and 5 present the endogenous growth model, analyze the effects of weak prudential supervision in the presence of deposit insurance and depict how a banking crisis can occur under perfect foresight, in turn. The next two sections show how our model is consistent with the data and present some econometric analysis supporting the main implications of our model. Section 8 concludes.

II. Three Characteristics of the Financial System of Japan

The theoretical model of this paper incorporates three characteristics of the Japanese financial system into its assumptions. These assumptions are central to the dynamics of economic growth and domestic financial markets before and after a banking crisis that are derived in the model. The first is the predominance of commercial bank intermediation of corporate finance, modeled as arising from the informational advantage of banks over other lenders. The second is the prospect of government-provided deposit insurance, or public sector bailouts of the domestic banking sector. The third is supervisory forbearance and the absence of effective prudential regulation of the banking sector. In this section, we review these three aspects of the financial system of Japan to support the use of our assumptions.

Bank loans comprise an exceptionally large share of Japanese corporate and other firm debt by international comparison. Typically, only large, well-capitalized firms have been able to funds on bond markets. Small- and medium-sized domestic firms continued to rely on bank financing through the 1990s (see Hoshi and Kayshap [2001]). The fraction of small- and medium-sized business loans to total loans increased from 73 percent over the period, 1977-86, to 78 percent over the period, 1987-1990, as reported by Ogawa and Kitasaka [2000]. This reliance on bank financing was especially prevalent for small- and medium-sized firms in the service, construction and real estate sectors. Between 1987-1990, while bank loans to the manufacturing sector increased by 1 percent, loans to the service, construction, and real estate sectors rose by 14 percent, 7 percent, and 18 percent, respectively (Ogawa and Kitasaka [2000]).

Japanese bank deposits have been implicitly guaranteed by the government, traditionally through the “convoy system,’’ or “purchase and assumption,’’ rescue, in which a healthy bank is encouraged by the government to provide assistance to a troubled one. Recently, however, the government has provided implicit guarantees through direct injections of capital to troubled banks.

The government’s system of explicit and implicit guarantees implies that no deposits, large or small, were ever at risk in postwar Japan. Before 1991, the official policy was there would be “no failures of financial institutions.’’ Since 1991, banks have failed; for example, from 1991 to 1995, eleven small banks were formally declared insolvent. However, the guarantees meant that no depositor ever lost any funds.

In our model, the failure of authorities to monitor the accumulation of non-performing assets and holding of loan-loss reserves by banks until the deposit insurance liability of the government has reached either a critical level leads to financial crises and falling GDP growth.

Awareness of the problems with the existing bank supervisory regime led the government to move financial supervision and examination from the Ministry of Finance to the new independent Financial Supervisory Agency in 1996. The government also tried to replace discretion of supervisors by a rule-based scheme, the Prompt Corrective Action system, in 1998. Under Prompt Corrective Action, regulators are required to intervene quickly at poorly capitalized banks. For example, regulators are required to close a bank if the bank’s capital-asset ratio falls below zero.

Initially, these institutional changes led to improvements in prudential supervision and enforcement. The Financial Supervisory Agency moved to examine the books of all banks which led to the immediate closure of five smaller banks. However, as the immediate financial crisis subsided, the regulations were redefined to make them less restrictive. The introduction of the Prompt Corrective Action policy was delayed a year. Accounting standards were changed, so that banks could make their financial statements appear better than they were. Some banks that should have been closed under the statutes were allowed to continue operating because the closure of these banks would add to local unemployment.

III. A Model of Growth and Banking Crises

This section presents a general equilibrium model of endogenous growth with bank-intermediated investment to show how publicly-funded deposit insurance and prudential supervisory or regulatory failures combine to affect investment and output growth. The model differs from our earlier model, Dekle and Kletzer [2003] in a number of respects. There are two important innovations in this paper. The first is that we use an open economy with a banking sector that faces competition for deposits at a given real rate of interest. The second is the production structure. Together these lead to a significant qualitative difference in the dynamics leading up to a bank liquidity crisis.

IV. Growth with Deposit Guarantees and Regulatory Forbearance

To analyze the effects of weak prudential supervision in the presence of publicly funded deposit insurance, we assume that government regulators do not enforce loan loss reserve requirements. They do not audit the balance sheets of the banks and require reserving against accumulated losses on individual loans. This allows banks to keep uncollected interest on their balance sheets as performing assets without using the profits earned on other loans to cover the losses. By doing so, the banks can pay dividends from current loan profits without subtracting current loan losses.

If the liability of shareholders to the holders of bank deposits is limited, banks have an incentive to accumulate non-performing assets and pay out dividends from current loan income. When a bank becomes insolvent, shareholders are spared from liability so that the value of shareholder equity is bounded from below by zero. As a bank accumulates losses as non-performing loans without also saving the surplus, r′ – r, from repaid loans, these losses will be borne eventually by shareholders, depositors or the government through a depositor bailout. If depositors bear the cost and cannot monitor the bank’s accounts⁷, then the rate of interest received by depositors will be driven down and the growth rate of the economy declines.

In our case, the government provides deposit insurance but does not audit the bank loan portfolios or monitor loan-loss reserves. By accumulating non-performing assets and paying dividends equal to the loan income from performing assets, a bank accumulates a deposit insurance claim against the government. The liabilities of the banking system equal the total deposits of savers, and its assets equal the sum of the corporate sector capital stock and the total deposit insurance claim against the government. That is, the accumulated loan losses are assets, but they are claims against the government’s deposit insurance plan rather than against the corporate sector. The deposit insurance liability of the government is a public debt held by the banks. The assets of the banking sector, which are equal to its deposit liabilities, are the sum of k_t and government debt, b_t. Total household interest-bearing assets equal bank deposits, so that α_t = k_t + b_t in equilibrium. The deposit insurance claim of the banks against deposits contrasts with bonds or other forms of public debt issued by the treasury. The deposit insurance liability of the government is created endogenously by the banking sector.

So that banks pay positive dividends in equilibrium, some form of imperfect competition in banking needs to be introduced. This model does not require us to be very articulate about imperfect competition. For simplicity, we let banks compete in individual initial loans but pay out dividends against individual loan profits and accumulate deposit insurance claims against accumulated individual loan losses with a fixed number of banks. The loan rate of interest is r′ as defined be equation (2). If banks did compete away any profits by offering lower interest rates to the corporate sector, the deposit insurance liability of the government will finance dividends to corporate shareholders in exactly the same amount as will go to the bank shareholders here. Since all shares are held by the representative household, nothing but the division between bank dividends and corporate dividends is affected by our assumption.

We consider two simple institutional constraints on the flow of dividends that a bank can pay at each date. One is that if the bank cannot meet its net withdrawal demand at any time, it is illiquid and the government immediately intervenes. The second constraint is that banks cannot accumulate non-performing assets faster than the flow of unpaid interest obligations which equal

in the aggregate. This is the same as loan profits minus the costs of intermediation given by

Total dividends paid to bank equities will equal this amount in equilibrium until regulatory authorities stop allowing the public sector deposit insurance liability to grow. Deposit insurance is a subsidy to shareholders, and banks maximize the value of shareholder equity under limited shareholder liability by making these lump-sum transfers as fast as possible. In this economy, bank dividends are a transfer from the public sector to bank shareholders. The additional institutional assumption is that banks cannot claim larger deposit insurance losses than the deposit cost of accumulated unpaid interest on corporate loans.

We first allow banks to accumulate losses for a fixed period of time, from t = 0 to T. At time T, the government intervenes and stops further accumulation of non-performing loans by the banks. Public sector liabilities, b_T are determined in equilibrium given T, or conversely. The analysis is the same if the government halts the accumulation of deposit insurance liabilities at some time, T, or at some maximum liability, b_T.

Bank dividends,

grow with the capital stock until date T. The capital stock grows as the difference between bank deposits and the deposit insurance claim of the banks. The deposit insurance liability of the public sector grows as

for 0≤ t ≤ T. The value of bank equity evolves according to

At time T, dividends drop permanently to zero, so that V^b must converge to zero at time T. Initially, deposit insurance liabilities (equivalently, non-performing loans) are zero, so that b₀ = 0. The sum of the public sector liability and banking sector equity, b + V^b, grows as

for 0≤ t ≤ T. For this period, the government does not recognize or cover its deposit guarantee liabilities.

The solvency constraint for the public sector implies that after time T, the government must collect revenue to meet its obligation, b_T. In this economy, the government does not have access to lump-sum taxes and imposes a tax on interest income (the interest received on deposits) at a constant proportionate rate, τ. The deposit rate of interest from time T on is $\widehat{r}=\left(1-\tau \right)r$. The flow-budget identity for the public sector from T onward is

and the intertemporal budget constraint for the government is

To simplify the mathematics only, τ is taken to be constant. For the same reason, τ is chosen so that the government is solvent and the ratio of government liabilities to deposits stays constant. This keeps the post-tax rate of interest, $\widehat{r}$, and the ratio b/k constant for t ≥ T.

The equilibrium growth path is derived assuming perfect foresight. That is, households correctly anticipate the future tax on interest earnings imposed at time T. The flow-budget identity for the representative household is given by

and

Maximizing household utility leads to the equilibrium growth rates of consumption,

and

Equilibrium consumption is found by integrating the aggregate resource constraint (3) and is given by

where

and

Consumption as a share of the capital stock rises monotonically, while the national savings rate falls, over time up to date T.

The capital stock grows as

for 0≤ t ≤ T, and

The function, φ(T – t,τ), is decreasing in t for t ≤ T, equals $\frac{\widehat{r}-\rho }{\sigma }$ for t = T and converges to $\frac{r-\rho }{\sigma }$ as T – t goes to infinity. Under perfect foresight, the investment rate and growth rate of output fall as non-performing bank assets rise. The constraint that banks must remain liquid before T date is not binding if $\widehat{r}-\rho >0$.⁸ In the next subsection, we consider the possibility that this inequality does not hold.

To calculate the value of bank equity, recall that shareholder value is maximized if banks pay out the largest possible dividends up to time $T,\left(r^{\prime }-r-\frac{\gamma r^{\prime }}{\alpha }\right)k_t$. The stockmarket value of the banking sector under perfect foresight is given by

Differentiation of equation (23) shows that the ratio of bank equity to the current capital stock, $\frac{V_t^b}{k_t}$, or to gross domestic output, $\frac{V_t^b}{\left(\alpha /2-\left(r^{\prime }/\alpha \right)\gamma \right)k_t}$, falls monotonically to zero up to time T. The total value of bank equity is given by

Aggregate corporate equity is given by the present value of dividends as

After date T, the value of corporate equity grows at the same rate as the capital stock and output, $\frac{\widehat{r}-\rho }{\sigma }$. Up to time T, it also grows proportionately with k_t and output if σ = 1, but grows faster than k_t if σ > 1 and more slowly than k_t if σ < 1. Thus, for an intertemporal elasticity of substitution of one-half (σ = 2), typically assumed in calibrated growth models, the value of corporate equity rises faster than gross domestic output up to time T.⁹ Although the value of corporate equity is continuous at T under perfect foresight, the growth rate of corporate equity suddenly falls at time T to $\frac{\widehat{r}-\rho }{\sigma }$ for σ > 1. This is verified by differentiating equation (25).

The model predicts that the value of bank equity will fall in proportion to gross domestic output before the government realizes its deposit insurance losses in the banking sector. The value of corporate equity rises faster than output before time T, and grows with gross domestic output thereafter. A decline in the value of bank equities foreshadows the banking crisis, but a decline in corporate equity does not under perfect foresight.

V. A Banking Crisis under Perfect Foresight

In the model economy, banks accumulate claims against the government in the form of unrealized deposit insurance liabilities as they accumulate non-performing loans without offsetting loan-loss reserves on their balance sheets. These public sector liabilities held by the banks balance the difference between their total liabilities to depositors and the real assets (capital) of corporate debtors. In paying dividends from what would otherwise be additions to loan-loss reserves, banks create transfer payments from the government to the shareholders. Eventually, the government must raise tax revenue to pay for these transfers and so by taxing depositors. The transfers are possible because the public sector guarantees deposits, either explicitly or implicitly, without adequately monitoring and controlling the growth of its deposit guarantee indemnity or the accumulation of non-performing loans by banks with positive equity values.¹⁰

An interpretation of the government’s policy is that the government forebears regulation and enforcement until its insurance liability reaches some threshold (b_T). To an extent this characterizes the policies followed by many governments that have subsequently faced banking crises. It is clearly not an optimal policy if monitoring is costless. In the model economy, banks can meet household deposit withdrawal demand, given by equation (19), as long as $\widehat{r}\ge \rho$. The longer it takes the government to stop the growth of its deposit insurance liabilities, the larger is its debt when it finally does intervene and begins to finance its insurance losses by taxing interest. The longer regulatory authorities forebear (that is, the larger is T), the lower will the rate of investment and the growth rate of output be after time T.

To show this, we begin with the government’s intertemporal solvency constraint (from equation (14) written as

This can be rewritten using the solution for $e^{-rT}{b}_T$ from integrating the growth equation for the government’s deposit insurance liability, equation (10). This is

The solvency constraint becomes

where $\widehat{r}=\left(1-\tau \right)r$. Total differentiation with respect to T and τ shows that τ, and public debt, b_T, are increasing in T. The long-run growth rate,

falls as the tax rate rises.

For a long enough period of regulatory forbearance, public debt will rise sufficiently so that the tax rate must be raised to the point that the post-tax interest rate on deposits falls below the subjective rate of discount and the long-run equilibrium growth rate is negative. In this case, household savings will be negative, and households will withdraw deposits on net from the banking system. These net withdrawals will force the banks to reduce lending to corporations forcing corporations to scrap capital. Our assumption that investment is irreversible (as an extreme case of downward investment adjustment costs) imposes an upper bound on τ, and therefore on T.

The growth rate of the economy given by equation (21) falls continuously until time T to its long-run level given by $\frac{r\left(1-\tau \right)-\rho }{\sigma }$. If r (1 – τ) < ρ, then the growth rate falls to zero at some time $\overline{T}$ before date T. At date $\overline{T}$, the banking system will able to just meet the withdrawal demands of depositors using the interest paid by corporations less costs of intermediation,

The growth of deposits, the capital stock and gross domestic output all reach zero at time $\overline{T}$. If the deposit insurance liability of the government continues to rise after the growth rate reaches zero at time $\overline{T}$, the anticipated tax rate on interest must also rise. In this economy (in contrast that in Dekle and Kletzer [2003]), the pre-tax deposit rate of interest can rise. Bank returns on loans are maximized when the loan rate of interest reaches α - γ, implying a maximum pre-tax deposit rate of interest given by

Corporate profits fall to

while unpaid interest rises from

where k is constant since the growth rate is zero. The social costs of intermediation also rise to γ(α – γ)/α so that total dividends that are paid out under regulatory forbearance decline. As the pre-tax rate of interest, however, the post-tax rate of interest must remain equal to the discount rate, ρ. At time $\widehat{T}$, the interest rate reaches r* with a tax rate given by r* (1 – τ*) = ρ. The deposit insurance liability of the government reaches b*, determined by the tax rate τ*.

After $\widehat{T}$, banks will only be able to meet the withdrawal demands of depositors by reducing outstanding loans to corporate borrowers. This requires the repayment of loan principal by firms. The entire banking system faces net withdrawal demand at $\widehat{T}$in equilibrium, so that no firm would be able to reduce its debt to one bank by borrowing from another. An existing or new firm could not buy all or part of the firm’s capital either, since it would not be able to get a loan from a bank to finance its purchase. In this economy, banks become illiquid at time $\widehat{T}$ because they have no alternative but to face net withdrawals of deposits that cannot be met. A banking crisis must occur, and the government must stop accumulating deposit insurance liabilities.

The capital stock employed by firms can be interpreted as loan collateral in this economy. Prior to the onset of the crisis, one firm can sell its capital to another and repay its loans fully. This makes a market for collateral with an equilibrium price of collateral equal to one. In a crisis, a bank that attempts to reduce its corporate loans to meet deposit withdrawals would discover that its borrowers are unable to repay their loan principals. If banks foreclose loans in the amount of net withdrawal demand by depositors, the collateral on those loans will have a zero price. This is because no firm will be able to borrow to purchase the collateral. The financing is not available because aggregate bank deposits have decreased by exactly the amount of the foreclosed loans. Loans are not available to potential purchasers of the seized collateral in equilibrium with irreversible investment. There will be no demand for collateral at a positive price in the crisis even though the marginal productivity of capital is positive.

This implies a collapse in the market for collateral in a banking crisis. If banks are heterogenous and become liquidity constrained idiosyncratically, then a decline in the value of collateral (that is, a decrease in Tobin’s q) could result. Bank heterogeneity could be introduced to the model economy by adding assumptions that lead banks to incomplete diversify their loan portfolios in equilibrium (for example, allowing a finite number of firms and increasing returns to scale in banking). This would make the deposit insurance liability and current earnings of each bank depend on the particular history of productivity shocks for its corporate clients. Over time, some banks will earn less from lending than others and might eventually be unable to meet the withdrawal demands of depositors from their net earnings on loans. Banks that do well can acquire borrowers as banks that do poorly shrink.

However, in the presence of deposit insurance with regulatory forbearance, banks that do well pay out dividends to shareholders only over a finite horizon just as in our model of homogeneous banks. New loans generate future dividends for shareholders only until the accumulation of deposit insurance liabilities by the government stops. Therefore, we should expect that the value of collateral will fall as more and more banks become insolvent up to the onset of a banking crisis or the end of regulatory forbearance (the interpretation of what happens if T is less that$\widehat{T}$. Alternatively, with continuously enforced loan-loss reserves, the price of collateral, q, would remain equal to one in this economy.

For many years, the Government of Japan dealt with the problem of troubled banks through the “convoy system,’’ under which weak banks would be merged with strong banks. Under the convoy system the losses of a weak bank are absorbed by the shareholders of the strong bank. An interpretation is that the shareholders of a strong bank absorb the equivalent of the deposit insurance liability in these forced mergers. In this interpretation of the convoy system, the dividends paid to the shareholders of the weak bank are eventually financed by transfers from the shareholders of the strong bank rather than from taxpayers.

This interpretation also suggests that the convoy system should break down. The managers of the strong banks face the same incentives to accumulate deposit insurance claims as do the shareholders of the weak banks. In a heterogeneous economy, their loan portfolios performed well ex post, so that their net asset incomes are higher those that of weaker banks, but the convoy system taxes the higher returns to pay for (past) dividends paid to the shareholders of the weaker banks. It transfers equity from the owners of stronger banks to weaker banks in expectation. When a bank becomes a convoy leader, its shareholder value falls. Therefore, the maximization of shareholder returns implies that a bank should avoid becoming a convoy leader by paying out all the dividends it can over the same horizon as the rest of the banking sector.

In the fiscal policy adopted in our discussion of the analytical model, the tax rate, τ, was constant after date T. This kept the public debt to output ratio constant. Alternative fiscal policies under which the government delays raising revenue or adopts a time-varying tax rate could also be used. For example, regulatory authorities could intervene in the banking system at time T′ with public sector deposit insurance liability equal to b_T′ and fiscal authorities could wait to raise taxes until time $\widehat{T}$. The tax rate imposed at time $\widehat{T}$ will need to be sufficient to service the accumulated public debt $e^{r\left(\widehat{T}-T^{\prime }\right)}{b}_{T^{\prime }}$. With irreversible investment, the growth rate goes to zero at time $\widehat{T}$ if the tax rate implied by this debt level reduces the post-tax rate of return to deposits to the household discount rate. Other possible policy responses include imposing taxes so that b stays constant as the economy grows or b is reduced to zero over some finite horizon. In these cases, the tax rate varies over time. If the deposit insurance liability declines in proportion to output, then the tax rate falls over time and the growth rate of output will rise again. Under these types of fiscal responses, our model would imply a temporary, perhaps sharp, fall in the growth rate of gross domestic output, followed by a recovery.

The model makes two policy assumptions: the deposit insurance liability is not continuously borne by the banks through insurance premium payments and is ultimately financed by a proportional tax on deposits. Both of these are essential to the equilibrium dynamics. The first assumption fits Japan where very little of the cost of risky portfolio choices are borne by bank shareholders. Correct pricing of risk for risk-taker would be the opposite of regulatory inadequacy and forbearance modeled here. Using lump-sum taxes would eliminate the growth effects in the model with a representative agent. In an overlapping generations model, the endogenously growing deposit insurance liability could still depress growth if it is financed through lump-sum taxes which redistribute across generations. Intergenerational redistibution in an overlapping generations model also implies that current generations can benefit through the accumulation of public sector liabilities at a cost to future generations. This gives a simple model for motivating regulatory forbearance in the first place.¹¹

VI. Empirical Tests of Asset Prices and Fundamentals

Before we apply our model to the Japanese experience, we first test whether asset prices correctly reflect economic fundamentals. This is because our model imposes perfect foresight, ruling out bubbles and implying that all asset prices reflect fundamentals. The stock market values of corporations (25), and of the banking sector (24) are assumed to equal the present discounted value of dividends. The deposit insurance liability of the government depends on the growth of stock market values (13), and since the flow-budget identity for the representative household depends on this deposit insurance liability (government debt), the behavior of consumption and other real variables in our model depends on the assumption that stock prices reflect fundamental values. Thus, it is important to ascertain whether bubbles exist, and whether stock values reflect fundamentals. Here we perform some tests, showing that for Japan’s recent history, our assumption that asset prices reflect fundamentals is basically correct.

Campbell, Lo, and MacKinlay ([1997], p. 260) and others argue that bubbles in stock prices are inconsistent with stationary stock returns if the dividend process follows a linear process with a unit root. They also show that prices and dividends, and prices and earnings should be cointegrated. In fact, rational bubbles in stock prices may imply that the series of stock prices, stock returns, dividend-price ratios, and earnings-price ratios follow an explosive process, in which the series keep on increasing to infinity.

A. Unit Root Tests for Bubbles in Stock Prices, Dividends, and Earnings

The validity of these stationarity relationships can be seen in the data as shown in Table 1. Although the relations in equations (1)-(3) are expressed in terms of levels, Campbell, Lo, and MacKinlay ([1997], p. 261) show that they are valid in terms of logs if dividends follow a loglinear process. Stationarity of the series of log differences in stock prices is corroborated by the Phillips-Perron unit root tests reported in Table 1. The hypothesis that log stock price changes are nonstationary is rejected for each period reported.

Table 1.

Phillips-Perron Unit Root Statistics

Rejection of Null Hypothesis of Unit Root:

^***Significant at 1 percent level.

^**Significant at 5 percent level.

^*Significant at 10 percent level.

Table 1.

Phillips-Perron Unit Root Statistics

Dates	1980Q2-2002Q2	1980Q2-1990Q4	1991Q1-2002Q2
Stock Returns	-6.1***	-3.2*	-5.3***
Dividend-Price Ratio	-1.5	-0.98	-1.5
Price-Earnings Ratio	-2.3*	-1.7	-2.3*

Rejection of Null Hypothesis of Unit Root:

^***Significant at 1 percent level.

^**Significant at 5 percent level.

^*Significant at 10 percent level.

View Table

Table 1.

Phillips-Perron Unit Root Statistics

Dates	1980Q2-2002Q2	1980Q2-1990Q4	1991Q1-2002Q2
Stock Returns	-6.1***	-3.2*	-5.3***
Dividend-Price Ratio	-1.5	-0.98	-1.5
Price-Earnings Ratio	-2.3*	-1.7	-2.3*

Rejection of Null Hypothesis of Unit Root:

^***Significant at 1 percent level.

^**Significant at 5 percent level.

^*Significant at 10 percent level.

If log prices and log dividends are cointegrated, then the log dividend-price ratio should be stationary. A simple look at the data suggests that the log dividend to price ratio may be a non-stationary series. Phillips-Perron unit root tests show that for the 1980Q2-2002Q2, and 1991Q1-2002Q2 periods the null hypothesis of nonstationarity is rejected at the 10 percent level, but for the period, 1980Q2-1990Q4, nonstationarity cannot be rejected. However, non-stationarity of the log of the price to earnings ratio is not rejecteed using the Phillips-Perron test for each period. Finally, short-term interest rates (the call rate) are used to discount future dividends and these appear to be stationary until the end of 1991 but not thereafter.

Overall, these results suggest that while the evidence for the existence of bubbles is not compelling, we cannot entirely reject the existence of bubbles, especially in the 1980Q2-1990Q4 period, when there is no cointegration between stock prices and dividends or earnings. However, on balance the evidence suggests that our fundamentals assumption is reasonable.

B. Fundamentals, Bubbles, and the Predictability of Stock Returns

If stock returns are predictable from fundamentals, then bubbles, even if they exist, are small, and are probably not important in affecting stock returns. Table 2 shows some long-horizon regressions, relating stock returns on various fundamentals at horizons of 1 quarter, 4 quarters (1 year), and 12 quarters (3 years). The fundamentals we examine are the log price-earnings ratio, the log dividend-price ratio, and the short-term interest rate. As it is well-known, forecast accuracy increases remarkably as the horizon increases. The coefficients, R-squareds, and T-statistics all increase, as the forecast horizon increases. For example, as the current log price-earnings ratio increases, stocks become overvalued and this overvaluation is corrected after 4 quarters or so. That is, high log price-earnings ratios imply low stock returns, at medium to long horizons. The coefficients on the log-price earnings ratios are negative. A high current log dividend-price ratio implies increasing stock returns. Finally, high current short-term interest rates predict high stock returns at long-horizons.¹²

Table 2.

Long-Horizon Regressions of Stock Returns on Log Price-Earnings and Log Dividend-Price Ratios, and Short Term Interest Rates

Standard-Errors are Newey-West. Sample: 1980:2—2002:2.

Table 2.

Long-Horizon Regressions of Stock Returns on Log Price-Earnings and Log Dividend-Price Ratios, and Short Term Interest Rates

		Forecast Horizon (Quarters)
		1	4	12
Log Price-Earnings
	Coefficient	-0.0076	-0.15	-0.58
	R-squared	0.0017	0.099	0.39
	T-statistic	-0.41	-2.29	-5.18
Log Dividend Price
	Coefficient	-0.017	0.18	0.73
	R-squared	0.067	1.95	0.45
	T-statistic	-0.77	0.09	5.53
Short Term Interest
	Coefficient	0.0027	0.017	0.059
	R-squared	0.011	0.056	0.17
	T-statistic	-0.096	1.36	3.05

Standard-Errors are Newey-West. Sample: 1980:2—2002:2.

View Table

Table 2.

Long-Horizon Regressions of Stock Returns on Log Price-Earnings and Log Dividend-Price Ratios, and Short Term Interest Rates

		Forecast Horizon (Quarters)
		1	4	12
Log Price-Earnings
	Coefficient	-0.0076	-0.15	-0.58
	R-squared	0.0017	0.099	0.39
	T-statistic	-0.41	-2.29	-5.18
Log Dividend Price
	Coefficient	-0.017	0.18	0.73
	R-squared	0.067	1.95	0.45
	T-statistic	-0.77	0.09	5.53
Short Term Interest
	Coefficient	0.0027	0.017	0.059
	R-squared	0.011	0.056	0.17
	T-statistic	-0.096	1.36	3.05

Standard-Errors are Newey-West. Sample: 1980:2—2002:2.

Table 3 depicts the relationship between fundamentals and stock returns in a VAR framework. It appears that some fundamentals have explanatory power, over and beyond lagged stock returns. Both the dividend-price and the price-earnings ratios have high explanatory power. The moderately high R-squared values suggests a modest degree of forecastability for quarterly stock returns. In the last column of Table 3, we added first-differences of the variables that are included in our Vector Autoregression estimates in Section 7. The first difference of lagged credit (actually, the credit-GDP ratio) is highly significant, although none of the other variables are significant. The R-squared value of 0.29 again suggests a moderate degree of forecastability.

Table 3.

Fundamentals and Stock Returns Dependent Variable: Stock Returns

(Sample: 1980Q2-1997Q4)

T-statistics in parentheses.

^1/First Difference of the Lagged Investment-Output Ratio.

^2/First Difference of the Lagged Credit-Output Ratio.

^3/First Difference of the Lagged Landprice.

Table 3.

Fundamentals and Stock Returns Dependent Variable: Stock Returns

(Sample: 1980Q2-1997Q4)

Constant	0.022	0.036	-0.0007
Stock Returns (-1)	(0.95) 0.13 (0.81)	(1.96) 0.22 (1.51)	(-0.69) …
Stock Returns (-2)	-0.11 (-0.92)	-0.84 (-0.69)	…
Dividend-Price (-1)	-0.29 (-2.21)	…	…
Dividend-Price (-2)	0.33 (2.55)	…	…
Price-Earnings (-1)	…	0.17 (2.09)	…
Price-Earnings (-2)	…	-0.25 (-3.04)	…
Short-Term Interest (-1)	0.0053 (0.39)	0.0063 (0.49)	…
Short-Term Interest (-2)	-0.0053 (-0.39)	-0.16 (-1.14)	…
Ch.(INVEST (-1))  1/	…	…	0.0057 (0.21)
Ch.(INVEST (-2))	…	…	0.0062 (0.22)
Ch. (CRED(-1))  2/	…	…	8.89 (1.35)
Ch. (CRED(-2))	…	…	18.84 (2.85)
Ch. (LANDPRIC (-1))  3/	…	…	0.00017 (0.41)
Ch. (LANDPRIC(-2))	…	…	-0.00035 (-0.89)
R-squared:	0.27	0.29	0.29
Adj. R-squared:	0.19	0.22	0.19

T-statistics in parentheses.

^1/First Difference of the Lagged Investment-Output Ratio.

^2/First Difference of the Lagged Credit-Output Ratio.

^3/First Difference of the Lagged Landprice.

View Table

Table 3.

Fundamentals and Stock Returns Dependent Variable: Stock Returns

(Sample: 1980Q2-1997Q4)

Constant	0.022	0.036	-0.0007
Stock Returns (-1)	(0.95) 0.13 (0.81)	(1.96) 0.22 (1.51)	(-0.69) …
Stock Returns (-2)	-0.11 (-0.92)	-0.84 (-0.69)	…
Dividend-Price (-1)	-0.29 (-2.21)	…	…
Dividend-Price (-2)	0.33 (2.55)	…	…
Price-Earnings (-1)	…	0.17 (2.09)	…
Price-Earnings (-2)	…	-0.25 (-3.04)	…
Short-Term Interest (-1)	0.0053 (0.39)	0.0063 (0.49)	…
Short-Term Interest (-2)	-0.0053 (-0.39)	-0.16 (-1.14)	…
Ch.(INVEST (-1))  1/	…	…	0.0057 (0.21)
Ch.(INVEST (-2))	…	…	0.0062 (0.22)
Ch. (CRED(-1))  2/	…	…	8.89 (1.35)
Ch. (CRED(-2))	…	…	18.84 (2.85)
Ch. (LANDPRIC (-1))  3/	…	…	0.00017 (0.41)
Ch. (LANDPRIC(-2))	…	…	-0.00035 (-0.89)
R-squared:	0.27	0.29	0.29
Adj. R-squared:	0.19	0.22	0.19

T-statistics in parentheses.

^1/First Difference of the Lagged Investment-Output Ratio.

^2/First Difference of the Lagged Credit-Output Ratio.

^3/First Difference of the Lagged Landprice.

Overall, these results suggest that fundamentals have good forecasting power, especially at long-horizons. Furthermore, fundamentals appear to have forecasting power, over and beyond lagged stock returns. These results suggest that fundamentals are important in explaining Japanese stock returns, and that the role of bubbles in affecting stock returns, may be small or superfluous.

VII. Application of the Model to the Japanese Economy in the 1990s

In the theoretical model, a banking crisis and growth collapse develops endogenously in the absence of effective prudential regulation in an economy without aggregate production risk and under perfect foresight. Idiosyncratic production risk across firms creates individual loan losses that can be exactly offset by profits on other loans but are not when banks are able to pay out dividends against deposit insurance liabilities subsidized by the government. We argue that the practice of prudential supervision and regulation in Japan over the last two decades matches our assumptions very well. In this section, we consider how well the predictions of the model fit Japanese economic performance.

The model predicts dynamics for investment, consumption, output, bank credit growth, asset prices and the value of collateral assets before and after the crisis that can be compared to the data.Some empirical implications of the model are:

1. As the banking system accumulates a deposit insurance claim in the form of non-performing corporate loans against which dividends were paid, the growth rate of output decreases steadily to its post-crisis level and consumption rises as a share of output under perfect foresight.

2. The stockmarket value of the corporate sector can grow more rapidly than output before the crisis is realized for the empirical plausible case of inelastic intertemporal substitution (σ > 1).

3. The stockmarket value of the banking sector will decline before the crisis, implying that we should observe a decrease in the value of bank stocks relative to the aggregate value of the stock market before the banking crisis.¹³

4. The value of collateral in the model equals q_tk_t which grows proportionately with output until output growth falls to zero in a banking crisis and the market for collateral collapses.¹⁴

Two of the many simplifying assumptions of the model are important to reconsider for comparing its equilibrium dynamics to the empirical record for Japan. The first is the assumption of full information under perfect foresight. In equilibrium, the output share of investment decreases gradually to its long-run value and consumption rises steadily to its long-run share before the banking crisis. Households and firms may be imperfectly informed and receive information over time about the health of the banking sector or future fiscal policies under rational expectations. When there is news about bank balance sheets or the government’s expected response to deposit insurance losses, investment and GDP growth can change suddenly. The second issue is that aggregate productivity for Japan fluctuates. A temporary adverse aggregate productivity shock would lead to a permanent rise in non-performing loans held by the bank sector, moving the beginning of a crisis forward in the model economy. Therefore, such a shock would have a permanent effect on GDP growth under rational expectations.

It is difficult to identify the beginning of the banking crisis in Japan. At least two dates can be suggested readily. In 1992, the Japanese Ministry of Finance first acknowledged rising non-performing bank loans publicly. This followed the beginning of the sharp deterioration of Japanese economic performance in the early 1990s. The second possibility is 1997 to early 1998, when several financial institutions, including banks (Nippon Credit Bank and Hokkaido Takushoku) and major securities companies (Sanyo and Yamaichi securities) collapsed. At the same time, the East Asian financial crisis of 1997-98 provided a major international shock to the Japanese economy. In the interpretation of the model, either or both of these dates may be times that households and firms receive news about problems in the banking sector. The realization that banks have large and growing non-performing assets in the early 1990s could reveal information that starts investment and output growth on the adjustment path predicted by the model as the banking sector deteriorates further. The accumulation of deposit insurance losses may not have ended yet, so that date T in the model may not have been reached. Therefore, we need to remain agnostic about the timing of the onset of the banking crisis.

D. Vector Autoregression Estimates

Our model yields relationships between the ratio of the value of bank stocks to the total stock market value and subsequent investment, output growth, and bank credit growth. For example, a tightening of prudential supervision and regulatory enforcement will reduce and T. This immediately lowers the bank equity ratio, and subsequently raises the path of investment (as a ratio of GDP), lowers the growth rate of bank credit to GDP and the present value of collateral assets (as a ratio of GDP).

We test our theoretical prediction that the future paths of investment, bank credit, and the value of collateral respond to shocks to the ratio, but not the converse. We first estimate Vector Autoregressions (VAR) with the relevant variables, and then perform Granger causality tests to examine whether the bank equity ratio is exogenous in the Granger sense. If so, the bank equity ratio temporally precedes the other variables in our Vector Autoregression. The VAR is formed using four variables, the bank stock to the total stock market value ratio, the investment to GDP ratio, the bank credit to GDP ratio, and an index of land prices. Although land prices are not modeled directly, our model does capture the value of capital as collateral which becomes a fixed asset in a crisis. This mimics land prices in a crisis, so we apply the implications of the model for the value of collateral to land prices.

Table 4 depicts the VAR results with our four variables: BSTS (the bank equity ratio), CRED (the ratio of bank credit to GDP), INVEST (the investment to GDP ratio), and LANDPRIC (land prices). The optimal lag length of two was chosen by the Akaike Information Criterion. In the BSTS equation, besides its own lagged values, none of the other variables are significant. In the CRED equation, besides its own lagged values, only LANDPRIC lagged once is significant. In the INVEST equation, besides its own lagged values, both LANDPRIC lagged once and twice are significant. In the LANDPRIC equation, none of the other variables are significant.

Table 4.

VAR Estimates of the Model

^1/Bank Stock Equity-Total Stock Market Equity Ratio.

^2/Ratio of Credit to GDP.

^3/Investment to GDP Ratio.

^4/Land Prices.

Table 4.

VAR Estimates of the Model

Equation	BSTS	CRED	INVEST	LANDPRIC
Variable
BSTS (-1)  1/	1.09	0.00043	0.023	36.71
BSTS(-2)	(9.75) -0.16 (0.11)	(0.15) 0.0022 (0.75)	(0.0039) 0.79 (1.28)	(1.01) -12.29 (-0.33)
CRED(-1)  2/	1.16 (0.25)	0.76 (6.62)	-8.83 (-0.36)	250.9 (0.17)
CRED(-2)	-3.42 (-0.80)	0.14 (1.36)	2.44 (0.11)	522.7 (0.38)
INVEST(-1)  3/	-0.011 (-0.52)	-0.00048 (-0.91)	0.068 (0.59)	4.63 (0.68)
INVEST(-2)	-0.0021 (-0.099)	0.00026 (0.48)	0.0031 (4.61)	-0.15 (7.02)
LANDPRIC(-1)  4/	0.000021 (0.17)	0.0000064 (2.08)	-0.0029 (-4.51)	1.91 (47.6)
LANDPRIC(-2)	0.000055 (0.45)	-0.0000055 (-1.71)	-0.0029 (-4.49)	-0.95 (23.78)
CONSTANT	0.61	0.014	1.58	-202.96
R-squared:	(0.33) 0.94	(1.71) 0.98	(0.89) 0.98	(-1.91) 0.99
Adj. R-squared:	0.76	0.77	0.78	0.79

^1/Bank Stock Equity-Total Stock Market Equity Ratio.

^2/Ratio of Credit to GDP.

^3/Investment to GDP Ratio.

^4/Land Prices.

View Table

Table 4.

VAR Estimates of the Model

Equation	BSTS	CRED	INVEST	LANDPRIC
Variable
BSTS (-1)  1/	1.09	0.00043	0.023	36.71
BSTS(-2)	(9.75) -0.16 (0.11)	(0.15) 0.0022 (0.75)	(0.0039) 0.79 (1.28)	(1.01) -12.29 (-0.33)
CRED(-1)  2/	1.16 (0.25)	0.76 (6.62)	-8.83 (-0.36)	250.9 (0.17)
CRED(-2)	-3.42 (-0.80)	0.14 (1.36)	2.44 (0.11)	522.7 (0.38)
INVEST(-1)  3/	-0.011 (-0.52)	-0.00048 (-0.91)	0.068 (0.59)	4.63 (0.68)
INVEST(-2)	-0.0021 (-0.099)	0.00026 (0.48)	0.0031 (4.61)	-0.15 (7.02)
LANDPRIC(-1)  4/	0.000021 (0.17)	0.0000064 (2.08)	-0.0029 (-4.51)	1.91 (47.6)
LANDPRIC(-2)	0.000055 (0.45)	-0.0000055 (-1.71)	-0.0029 (-4.49)	-0.95 (23.78)
CONSTANT	0.61	0.014	1.58	-202.96
R-squared:	(0.33) 0.94	(1.71) 0.98	(0.89) 0.98	(-1.91) 0.99
Adj. R-squared:	0.76	0.77	0.78	0.79

^1/Bank Stock Equity-Total Stock Market Equity Ratio.

^2/Ratio of Credit to GDP.

^3/Investment to GDP Ratio.

^4/Land Prices.

We next perform Granger causality tests to ascertain whether one variable temporally precedes another. In a VAR framework, Granger causality tests are Chi-squared tests of exclusion of all the lags of a particular variable. For example, BSTS Granger causes CRED if BSTS(-1) and BSTS(-2) are jointly significant in the CRED equation, but CRED(-1) and CRED(-2) are not jointly significant in the BSTS equation.

Table 5 depicts the results of the Granger causality tests in a VAR framework. In the BSTS equation, none of the variables are significant. In fact, besides lagged BSTS, none of the variables contribute any explanatory power. In the CRED equation, BSTS and LANDPRIC provide good explanatory power. In the INVEST equation, BSTS and LANDPRIC again provide good explanatory power. In the LANDPRIC equation, none of the variables are significant.

Table 5.

Granger Causality/Chi-squared Exogeneity Test

^1/Bank Stock Equity-Total Stock Market Equity.

^2/Ratio of Credit to GDP.

^3/Investment to GDP Ratio.

^4/Land Prices.

^5/Probability Value.

Table 5.

Granger Causality/Chi-squared Exogeneity Test

	BSTS 1/		CRED 2/		INVEST 3/		LANDPRIC 4/
Excluded Variable	Chi-sq	Prob5/	Chi-sq	Prob.	Chi-sq	Prob.	Chi-sq	Prob.
BSTS	3.41	0.18	5.94	0.05	12.81	0.0016	3.65	0.16
CRED	3.11	0.21	6.11	0.03	0.81	0.62	3.21	0.18
INVEST	2.93	0.23	1.91	0.38	0.73	0.69	3.09	0.21
LANDPRIC	4.13	0.13	5.17	0.07	21.3	0	3.35	0.19

^1/Bank Stock Equity-Total Stock Market Equity.

^2/Ratio of Credit to GDP.

^3/Investment to GDP Ratio.

^4/Land Prices.

^5/Probability Value.

View Table

Table 5.

Granger Causality/Chi-squared Exogeneity Test

	BSTS 1/		CRED 2/		INVEST 3/		LANDPRIC 4/
Excluded Variable	Chi-sq	Prob5/	Chi-sq	Prob.	Chi-sq	Prob.	Chi-sq	Prob.
BSTS	3.41	0.18	5.94	0.05	12.81	0.0016	3.65	0.16
CRED	3.11	0.21	6.11	0.03	0.81	0.62	3.21	0.18
INVEST	2.93	0.23	1.91	0.38	0.73	0.69	3.09	0.21
LANDPRIC	4.13	0.13	5.17	0.07	21.3	0	3.35	0.19

^1/Bank Stock Equity-Total Stock Market Equity.

^2/Ratio of Credit to GDP.

^3/Investment to GDP Ratio.

^4/Land Prices.

^5/Probability Value.

Taken together, these results are consistent with our theory. BSTS temporally precedes (Granger causes) CRED and INVEST. That is, shocks to BSTS such as a tightening of prudential regulations raises INVEST and CRED. BSTS does not temporally precede LANDPRIC. That is, BSTS and LANDPRIC appear to be simultaneously determined. This is consistent with models in which as asset prices, both equity and land prices respond to correlated future fundamentals.