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					          Non-Performing Loans, Prospective Bailouts, and Japan’s
                                                     Slowdown

                                                  Levon Barseghyan∗
                                                  Cornell University

                        First Version: October, 2002, This Version: October 2008



                                                        Abstract

             In this paper we argue that the delay in the government bailout of the financial sector played a
         key role in Japan’s slowdown during the 1990s and early 2000s. We construct a dynamic general
         equilibrium model in which the government provides deposit insurance to the financial sector.
         The model has the following property: the existence of non-performing loans, combined with a
         delay in the government bailout, leads to a persistent decline in economic activity. The decline
         in output is caused not only by a fall in investment, but also by an endogenous decline in labor
         and total factor productivity, which is consistent with Japan’s experience.
             Keywords: Japan, slowdown, non-performing loans, bad loans, total factor productivity.
             JEL Classification: E00, E32, E65.




   ∗
       I would like to thank the associate editor and the referee for excellent comments and suggestions. I am especially
grateful to Fumio Hayashi for numerous discussions and suggestions which helped to significantly improve this paper.
The paper draws significantly from my dissertation, written at the Department of Economics, Northwestern University.
I am indebted to Larry Christiano, Martin Eichenbaum, and Sergio Rebelo for their guidance, encouragement, and
support. I have benefited from the comments of Gadi Barlevy, Fabio Braggion, Riccardo DiCecio, Janice Eberly, Nir
Jaimovich, Tim Kehoe, Francesca Molinari, and Alex Monge. All errors are my own. Financial support from the
Center of International Economics and Development, Northwestern University, and from the Robert Eisner Fellowship
is gratefully acknowledged.
1    Introduction

From 1990 to 2003 Japan experienced a prolonged slowdown in economic activity. During this
period the growth rate of Japan’s per capita GDP was 1.2% per year, versus 3.5% per year in
the 1980s. This drop was accompanied by declines in the growth rate of total factor productivity
(TFP), investment-output ratio, and aggregate labor, as well as a collapse of bank loans to Japan’s
non-financial corporate sector (see Figure 1).
    It has been widely argued that the large amount of non-performing loans (so called bad loans)
held by Japanese financial institutions lied at the heart of the slowdown. However, the exact mecha-
nism underlying the link between these two phenomena has remained largely unknown. This paper
begins with the premise that bad loans represent a public liability. We then argue that the delay
in expected government bailouts is the main link between the failing banking system and Japan’s
slowdown. We articulate this argument by constructing a dynamic general equilibrium model with
the following key property: when the government provides deposit guarantees to the banks, the
existence of bad loans, combined with a delay in a government bailout, leads to a persistent decline
in aggregate economic activity. Using a version of the model calibrated to Japanese data we argue
that this mechanism played a quantitatively important role in Japan’s slowdown.
    The basic intuition behind the central argument of the paper is as follows: when the government
provides full deposit guarantees to the banks, large losses incurred by the banks (i.e., bad loans)
translate into prospective government debt. Suppose the government postpones the actual payment
of this debt, but insists that banks fully honor their obligations to depositors. Now the banks
face a problem: how to honor their obligations to old depositors, given some of their assets have
disappeared. The only thing the banks can do is to run a Ponzi-like scheme: pay the flow obligations
to old depositors using newly raised funds. With a positive interest rate, the amount of new savings
used by the banks to pay old depositors rises over time. That is, a smaller fraction of savings is
used to finance investment. As long as total private savings do not rise enough to offset the increase
in the present value of future tax liabilities stemming from the prospective bailout, less total loans
will be allocated for capital purchases. This, in turn, implies that the capital stock will fall over
time, leading to a persistent decline in output. The banks cannot run the Ponzi scheme forever
— eventually the new deposits will not be enough to pay off old depositors. At this stage, the
government will have no option but to bail the banks out.

                                                  1
       The delay in the government bailout acts similarly to the crowding out effect that, in many
models, the government debt has on investment. One way to see this in our model is to suppose that
the government immediately bails the banks out, financing the bailout by issuing new debt. Absent
Ricardian Equivalence, private savings will not rise enough to offset the new government debt.
Consequently, the capital stock will fall, and so will output. The same effect arises in a number
of cases that do not rely on the failure of Ricardian Equivalence, for example, when taxes are
distortionary, or when the government finances the bailout by decreasing government purchases.1
       The existing literature has provided alternative hypotheses linking Japan’s weak financial sector
and its slowdown. For example, it is often claimed that the weak financial sector caused a credit
crunch, i.e., an inability of Japanese firms to finance profitable projects (e.g., Bayoumi, 2000, and
Shimizu, 2000). A related argument is that Japanese firms found it difficult to borrow because
the value of their collateral (mostly real estate) declined precipitously over the past decade (e.g.,
Ramaswamy, 2000). While a priori appealing, these explanations have received limited support
from existing empirical studies.2
       Another explanation is that Japan’s poor economic performance was productivity driven. Hayashi
and Prescott (2002) show that the decline in the growth rate of TFP played a significant role in
the slowdown of Japan’s economy.3 Hubbard (2002) states that “...the real problem is that cap-
ital is not being allocated to its most productive uses.” Kashyap (2002a, 2002b) argues that the
slowdown partly reflects the presence of a large number of inefficient and unprofitable firms, so
called “zombies”, which “...distort competition. Other firms that could enter an industry or gain
market share are held back...”(Kashyap, 2002b, p.54). The basic idea is that banks were unwilling
   1
       In an earlier version of this paper, Barseghyan (2002), we provide an extensive discussion of such cases. Dekle
and Kletzer (2003) show that in an economy in which the government taxes the interest earned by the depositors to
pay for the bailout, aggregate savings decline and so does investment.
   2
     After analyzing several data sources, Hayashi and Prescott (2002) conclude that “there is no evidence of profitable
investment opportunities not being exploited due to lack of access to capital markets”. For more details, see Hayashi
and Prescott (2002) and references therein.
   3
     Jorgenson and Motohashi (2003) suggest that the decline in the growth rate of TFP in the 1990s was smaller
than it was originally thought. Chakraborty (2005) conducts the business cycle accounting exercise of Chari et al.
(2006) for Japan and finds that though technology shocks are important, “they are by no means enough to account
for the observed economic fluctuations during this period. Shocks that propagate themselves as investment wedges
play a major role.”




                                                           2
to disclose bad loans. Consequently they supported non-performing zombie firms by offering low
cost loans.4 Because of this, zombie firms continued to operate and dragged overall productivity
down. Caballero et al. (2008) provide empirical evidence which supports this idea.
       In this paper we argue that a part of the decline in TFP observed in Japan can be caused by the
delay in the government bailout. This decline reflects a rise in the fraction of low productivity firms
that are operating, as, it is argued, was the case in Japan. In our model, built upon Hopenhayn’s
(1992) model of industry structure, output is a function of a firm’s productivity, capital, and labor.
In addition, there is an operating cost, which consists of a fixed amount of capital and a wage to
be paid to a manager. A delay in the bailout results in a fall of the capital stock, which reduces
the average firms’ profits and puts downward pressure on the managers’ wage. The decline in the
managers’ wage implies that the operating costs are low. For firms with less gross profits, i.e.,
lower productivity firms, the lower operating costs mean that the net profits (gross profits minus
the operating costs) become positive. Consequently, low productivity firms choose to operate.
To summarize, in our model the delay in the bailout causes the average quality of the operating
firms to fall, resulting in a decline of TFP. While the decline in TFP is caused by an increase in
the fraction of low productivity firms, this increase is not caused by quantity rationing of either
bank loans or capital, as it is typically suggested. Instead, it reflects the response of a perfectly
competitive economy to a fall in capital stock that is generated by the delay in the government
bailout. Such negative relation between TFP and capital stock arises naturally in many models
with pro-cyclical productivity. As a robustness exercise, we study one such model proposed by
Jaimovich and Floetotto (2008).5 In that model, when capital stock falls, the number of operating
firms falls. Competitive pressures ease, mark-ups rise, and productivity falls.
       To assess the quantitative effect of the delay in the government bailout we calibrate a version
of our model using Japanese data. The effect of the bad loans on the economy is the least when
the bailout is expected to start as soon as possible and is expected to be financed by a lump sum
tax increase. To this end, we construct a conservative estimate of the impact of the delay in the
government bailout by assuming that the bailout was expected to start at the end of year 2003,
   4
       Bergoeing at al. (2002) have a related discussion in the context of Mexico and Chile. Chu (2002) shows that a
similar argument applies when there are barriers to exit rising from government’s policies.
   5
     The work on importance of oligopolistic competition and mark-up fluctuations over the business cycle goes back
to Rotemberg and Woodford (1991 and 1992).



                                                          3
and was expected to be financed through non-distortionary taxation. Under these assumptions, the
estimated decline in output due to the delay in the bailout ranges between 0.19 and 0.51 percent
per year. However, when the magnitude of the bad loans problem and the expectations about
the bailout are such that the resulting decline in the investment-output ratio coincides with the
decline in the investment-output ratio observed in the data, the impact of delaying the bailout is a
0.92% yearly decline in output. Absent such a decline, the growth rate of Japan’s per capita GDP
would have exceeded 2%. Since a 2% growth rate is a rough benchmark for a satisfactory economic
performance, we conclude that the delay in the resolution of the bad loans problem can be viewed
as the main reason for Japan’s poor performance in the 1990s.
        The rest of the paper is organized as follows. In Section 2 we briefly review the conditions
of Japan’s financial sector during the period of 1990-2003. Then we present the basic version of
the model in Section 3. Section 4 presents a more elaborate model which we use to conduct a
quantitative analysis. Section 5 discusses some caveats and Section 6 concludes.


2        The Conditions of Japan’s Financial Sector in 1990-2003: An
         Overview6

During the 1990s and the early 2000s Japan’s economy was highly bank-dependent. While large
corporations (especially in manufacturing) had a relatively easy access to alternative ways of fund-
raising, small and medium enterprises7 relied heavily on banks and other domestic lending institu-
tions for their borrowing needs. Bond financing for small and medium enterprises was essentially
nonexistent and equity financing was rare.8 The main sources of funds for these enterprises were
domestic banks, followed by government affiliated financial institutions (see Table 2).
        The profitability of Japanese banks had been declining over the 1980s and the 1990s, and was
negative most of the 1990s. As Hoshi and Kashyap (2000) extensively argue, the primary reason
    6
        A detailed analysis of the Japanese banking system and of the origins of the crisis is provided, for example, by
Hoshi and Kashyap (2000) and (2001). See also Hoshi and Kashyap (2004) for a thorough discussion of the bad loans
problem.
   7
     As Table 1 indicates, these enterprises played a very significant role in Japan’s economy.
   8
     For small and medium enterprises, the equity was only about 1/8 of their total liabilities. This number was more
than twice larger for large enterprises.




                                                             4
for this decline was the financial deregulation which took place in Japan during the 1980s. Hoshi
and Kashyap (2000) predict that to regain profitability, the banking sector would have to shrink
at least by 30%. Unless a massive reduction in the number of operating banks would occur, the
profits would remain low or even negative. Perhaps not surprisingly, during the same period of
time there was no entry into Japan’s banking sector.9
       A major source of problems for Japan’s banks were bad loans. A bad loan is one where payment
has been suspended or renegotiated.10 On average, repayment on these loans was about 12% of
the original amount.11 Hence, banks would bear significant losses if they wrote the debt off.
According to official sources, by the end of 2003, the bad loans held by Japan’s private deposit
taking institutions amount to U53 trillion (10.5% of GDP).12 However, most observers agree that
this number was highly understated. As Kashyap (2002b) reports, analysts of Goldman Sachs
estimated the bad loans to be U236 trillion (47% of GDP), and similarly, Credit Suisse First Boston
estimated that the actual amount of bad loans was about four times higher than the disclosed figure.
       The origins of the bad loans are seen in a prolonged decline in real estate and stock prices,
which followed the real estate and stock market collapse of 1991 (see, e.g., Ueda, 2001). As some
borrowers could not repay their obligations towards the banks, the banks were reluctant to liquidate
the loans through the sale of collateral (mostly real estate), since the recovered amount would fall
short of the original loan, and result in significant losses. The policy of regulatory forbearance and
non-transparency pursued by Japan’s financial authorities, combined with wishful thinking that the
economy (and the non-performing loans with it), would recover,13 led to an increase in the amount
   9
       The role of foreign banks in Japan’s domestic market had remained negligible: their shares of loan and deposits
markets were below .75% and 1.4% respectively. Also, fund raising of Japan’s non-financial sector via overseas
markets was about 30 times less than via domestic markets. Source: Flow of Funds Accounts, available on-line at
http://www.boj.or.jp/en/siryo/siryo_f.htm.
  10
     Japan’s Financial Services Agency defines risk management loans as 1) loans to borrowers in legal bancruptcy,
2) past due loans in arrears by 6 months or more, 3) past due loans arrears by more than 3 months and less than 6
months, and 4) restructured loans.
 11
    Author’s calculation, based on Figure 2-1-2 of “Annual Report on Japan’s Economy and Public Finance, 2000-
2001”.
  12
     The total cumulative loss on Disposal of Non-Performing Loans by the end of fiscal year 2003 was slightly less
than U100 trillion. A large part of these losses occured after 2000. In fiscal year 2001 alone the loss was U10.6 trillion.
  13
     Italics are from Cargill (2001), who also provides a thourough discussion highlighting the main aspects of the
Bank of Japan and Ministry of Finance policies regarding the bad loan problem.



                                                            5
of bad loans throughout the 1990s and the early 2000s. Public opposition to the attempts of using
government funds for helping troubled banks14 further delayed the resolution of the problem.
       Bad loans were held not only by the private sector, but also by public financial institutions and
insurance companies, which have played a significant role in Japan’s economy. For example, at the
end of the 1990s the share of government sponsored financial institutions in the loan market is 26%,
in the deposit market is 34%, and in the life insurance market is 40% (see Fukao, 2002). As Doi
and Hoshi (2002) indicate, by March 2001 Fiscal and Investment Loan Program, Japan’s primary
public lender, held as much as U266.6 trillion of bad loans, most of which were loans to insolvent
public corporations. They estimate the taxpayers cost for cleaning up the bad debt held by public
financial institutions to be around U78.3 trillion. Kashyap (2002b) puts the cost for cleaning up
the banks’ balance sheets at about U40 trillion, which implies the total taxpayers cost of at least
U118.3 trillion (24% of GDP). Hoshi and Kashyap’s (2004) conservative estimate of the taxpayers
cost of the bailout, as of the end 2003, is 20% of GDP.
       In the end of the 1990s, in a series of measures to fundamentally restructure the financial
sector (so called “Big Bang”), Japan’s government had committed about U60 trillion for deposit
protection, bank recapitalization, and nationalization of failed banks. A part of these funds had
been disbursed (see Hoshi and Kashyap, 2001, Ch. 8). During the same period, Japan’s budget
deficit was financed by government debt.
       Finally, an important feature of Japan’s financial sector has been the presence of government
guarantees. Until March 2002 all domestic deposits to the banks were protected by deposit insurance
provided by the government. As a result of Japan’s deposit insurance reform, starting March 2003
only deposits up to U10 million have been fully insured. Despite such guarantees and numerous
public statements by Japanese government officials in support of the banking system, the confidence
in Japan’s banking sector was low. For example, households heavily favored government’s Postal
Savings deposits to bank deposits (between 1991 and 1999, Postal Savings Deposits have increased
  14
       Government funds were used to fight the bad loans problem for the first time in 1996, in the case of the loans to
the so called jusen. The jusen are housing loan cooperatives, which heavily borrowed from the banks before 1991’s
real estate market crush. As the real estate prices dropped, the jusen became incapable to fulfill their obligations to
the lenders. Amid public opposition, the government intervention to solve the problem was delayed by more than 3
years. See Ito (2001) for more details on the jusen problem.




                                                           6
by 62%, while deposits to banks increased only by 18%15 ). Further, in the second half of the last
decade, Japanese banks found it difficult to borrow abroad, and at times they faced significantly
higher interest rates on interbank loans than non-Japanese banks. The so called Japan’s premium,
at its peak, was about 10 basis points on recorded transactions.


3         Bad Loans in an Overlapping Generations Model with Banking
          Sector and Deposit Insurance

In this section, to highlight the main idea of the paper, we present a two-period overlapping
generations (OLG) model with a banking sector. In the next section, for quantitative analysis,
we substitute Diamond’s OLG framework with Blanchard’s (1985) model of perpetual youth, and
modify the production side of the economy to allow for endogenous productivity.
         The economy is populated by two period lived households and firms, infinitely lived banks,
and government. Banks in this economy are financial intermediaries which transform savings into
loans. They face both aggregate and idiosyncratic uncertainty. With probability ea a crisis occurs
and all banks loose a fraction x of their loans. If there is no crisis, only a fraction ei suffers the
loss. The probability of receiving the idiosyncratic shock is i.i.d. across banks and time. A crisis
is followed by a government intervention which (i) promises a future transfer that offsets, at least
in part, the losses stemming from the crisis; (ii) lowers the capital adequacy requirement; and (iii)
allows the banks to carry some of the losses on their books. The government intervention lasts one
period, after which the government reverts to the pre-crisis policies, until a new crisis happens. The
government also provides deposit guarantees: in case a bank fails, the government ensures that the
depositors are paid back in full.


3.1         Banks

There is a continuum of banks, which are potentially infinitely lived. The banks are competitive
both in the deposit and loan markets, and there is free entry into the banking sector. In each period,
after the realization of aggregate and idiosyncratic uncertainty, a bank performs the following
actions. It first chooses to declare bankruptcy or not. If it does, then it collects payments on loans
    15
         Source: Flow of Funds Accounts, available on-line at http://www.boj.or.jp/en/siryo/siryo_f.htm.



                                                            7
made previously, pays off depositors and distributes the remaining amount to the shareholders. If
the bank does not declare bankruptcy, it

      • Collects payments on loans made in the previous period;

      • Pays off depositors from the previous period;

      • Collects new deposits;

      • Pays dividends to (or receives a capital injection from) the shareholders;

      • Receives government transfers (if any);

      • Makes new loans.

      Let the following variables denote corresponding quantities:



 Lt                              loans made in period t;
 Dt                              deposits collected in period t;
  L
 Rt−1                            the realized return on loans made in period t − 1;
  D
 Rt−1                            interest on deposits collected in period t − 1;
       L           D
 Qt ≡ Rt−1 Lt−1 − Rt−1 Dt−1 the bank’s net worth at the beginning of period t;
 Bt                              bad loans: losses stemming from the aggregate shock which the bank
                                 is allowed to carry on its books;
 divt                            dividends paid in period t;
 ∆t                              capital adequacy requirement in period t;
 Gt                              the government transfer in period t (if any).

The bank’s problem can be written as

                            V (Qt , Bt , st ) = max(W C (Qt , Bt , st ), W B (Qt )),




                                                       8
where st is the state variable relevant for the bank’s decision problem; W B is the bank’s value of
bankruptcy: W B (Qt ) = max(Qt , 0); and W C is the bank’s continuation value:
                                               ³                                       ´
                                                          Uc,t+1
          W C (Qt , Bt , st ) = maxLt ,divt ,Dt divt + βEt Uc,t V (Qt+1 , Bt+1 , st+1 )
               s.t.
                                                                                                               (3.1)
               Lt + divt ≤ Dt + Qt + Gt ,                                                            RC
               Lt +Bt
                 Dt     ≥ ∆t .                                                                       CAC

The term Uc,t denotes the marginal utility of the bank’s shareholders in period t. The first constraint
is the bank’s resource constraint (RC), and the second one is the capital adequacy constraint (CAC).
       The Bank’s Problem. We would like to re-write the bank’s continuation problem (3.1) in
a more tractable way. Note that, as long as the deposit rate is larger than one, we can assume
without loss of generality that the bank’s resource constraint holds with equality. We restrict the
discussion below to the case in which every bank faces a positive probability of bankruptcy.16 This
implies that the capital adequacy constraint holds with equality.
       First, we use the resource constraint to substitute for dividends in the bank’s objective function.
Then, we use the capital adequacy constraint to substitute for deposits. The resulting continuation
problem of the bank is
                                     ³                                                                    ´
                                                     Lt +Bt                Uc,t+1
          W C (Qt , Bt , st ) = maxLt Qt + Gt +        ∆t     − Lt + βEt    Uc,t V   (Qt+1 , Bt+1 , st+1 )
                                                                                                               (3.2)
                                             = Qt + Gt + ω(Bt , st ),

where ω(Bt , st ) is the bank’s net (of Qt ) continuation value:
                                 µ                                                    ¶
                                   Lt + Bt              Uc,t+1
              ω(Bt , st ) ≡ max             − Lt + βEt         V (Qt+1 , Bt+1 , st+1 ) ≥ 0.
                             Lt      ∆t                  Uc,t
Thus, the bank’s continuation value is a linear function of its net worth, and the bank’s value is a
piecewise linear function of its net worth:

             V (Qt , Bt , st ) = max(max(Qt , 0), W C (Qt , Bt , st )) = max(Qt + Gt + ω(Bt , st ), 0).

                             ∂Vt+1
The partial derivative       ∂Qt+1     exists almost everywhere and is either zero or one. Furthermore, if a
bank chooses to operate, its optimal choice of new loans does not depend on the bank’s beginning
of the period net worth.
  16
       Our assumptions and parameterization guarantee that in general equilibrium of the model the probability of the
bankruptcy is equal to ei (1 − ea ).


                                                           9
      Next, we characterize the solution of the bank’s continuation problem. Its first order necessary
condition (FOC) is
                                                        µ           ¶
                          1        Uc,t+1 ∂Vt+1           L    D 1
                       1−    ≥ βEt                       Rt − Rt      ( = ⇔ Lt > 0).                         (3.3)
                          ∆t        Uc,t ∂Qt+1                   ∆t
The left hand side (LHS) of this condition represents the cost to the bank’s shareholders of making
an additional dollar of loans: one dollar minus the amount financed through deposits, 1/∆t . The
right hand side (RHS) represents the marginal benefit of making such a loan. This benefit accrues
only in the states in which the bank does not declare bankruptcy ( i.e., in the states in which
                                                        L
∂Vt+1 /∂Qt+1 = 1) and consists of the return on loans, Rt , less the payments on deposits used to
                    D 1
finance the loan, Rt ∆t . It is useful to re-write this condition as
                                                 µ                           ¶
                         Uc,t+1 ∂Vt+1 L       1          D      Uc,t+1 ∂Vt+1
          1
        |{z}       ≥ βEt               R +         1 − Rt βEt                  ( = ⇔ Lt > 0).
                          Uc,t ∂Qt+1 t       ∆t                  Uc,t ∂Qt+1
     marginal cost   |        {z         } |                 {z              }
                        "standard" expected return       net benefit of deposit financing

The second term on the RHS represents the net marginal benefit of deposit financing. Note that
as ∆t tends to infinity, i.e., all loans need to be financed through the shareholders’ capital, the
second term disappears and the expression reduces to the standard first order condition on risky
investment: it compares the cost of making one additional unit of loans to its expected return.
Note also that since Rt is the risk free rate,17 the standard households’ Euler Equation implies
                      D

      D        Uc,t+1                              D        Uc,t+1 ∂Vt+1
that Rt βEt     Uc,t = 1     and, therefore, that Rt βEt     Uc,t ∂Qt+1    ≤ 1. If the probability of bankruptcy
                    ∂V                                      D              Uc,t+1 ∂Vt+1
were zero,    then ∂Qt+1
                       t+1
                             = 1 with probability one, and Rt βEt           Uc,t ∂Qt+1    = 1. That is, the second
term on the RHS would disappear: if the probability of bankruptcy is zero, then the banks repay
deposits with probability one. In such a case, since the shareholders’ opportunity cost of one unit
of financial capital is the risk-free rate, deposit financing does not provide any benefits to the
shareholders.
      Finally, the bank’s decision to declare bankruptcy or not entails comparison between its net
worth and the sum of the government transfer and the net continuation value. For any finite value
of Qt and ω(Bt , st ) there exists a transfer from the government that guarantees that the bank will
refrain from shutting down.
      We now describe the rest of the model. To help the exposition we take into account that, since
the government intervention lasts only one period, at any given point in time there can be only
 17
      We show this is the case when discussing the general equilibrium properties of the model.


                                                          10
two distinct types of banks: incumbents and entrants. Since the banks have linear technology
of transforming savings into loans, the actual size and the number of banks of either type is
indeterminate in equilibrium.18 We assume that the banks of the same type behave identically.
In what follows, we label the quantities referring to incumbents with superscript “I ” and those
referring to entrants - with superscript “E.”


3.2       Households

Households live for two periods. In the first period they inelastically supply one unit of labor. They
use their wage earnings, net of taxes, to finance consumption and savings. Households own all firms
in the economy. The households’ problem is given by:

 max U (cY ) + βEt U (cO )
         t             t+1

 s.t.
                  Y             E       E
 cY + St = wt − gt , St = Dt + qt pE + qt pI ,
  t                                t       t
                          h¡         ¢ E,C             i   h¡     ¢ I,C            i
  O + g O = RD D + q E                             E,B                         I,B
 ct+1    t+1    t   t   t   1 − et+1 Wt+1 + eE Wt+1 + qt 1 − eI
                                 E                       I
                                               t+1            t+1  Wt+1 + eE Wt+1 + π t+1 ;
                                                                           t+1

                                          Y
where cY is consumption, wt is the wage, gt is the lump sum tax — all at time t. Households’
       t
                                                                                    E
savings, St , are used to make deposits, to purchase the shares of entering banks, qt , at a price
                                         I
pE , and the shares of incumbent banks, qt , at a price pI . In period t + 1 households use the
 t                                                       t

proceeds from their savings and profits from the firms, π t+1 , less the lump sum tax, τ O , to finance
                                                                                       t+1
                                                                                  D
their consumption, cO . The government guarantees insure that households receive Rt Dt on their
                    t+1
           E,C      I,C
deposits. Wt+1 and Wt+1 denote, respectively, the entering and incumbent banks’ continuation
                                E,C       I,C
values in the next period; and Wt+1 and Wt+1 , respectively, - their bankruptcy values. The
probabilities that entering and incumbent banks will continue to operate in the next period are
(1 − eE ) and (1 − eI ), respectively. The households’ FOCs are
      t+1           t+1

                                      D     Uc,t+1
                                1 = βRt Et         ,                                                           (3.4)
                                             Uc,t
                                               ¡         ¢ E,C         E,B
                                        Uc,t+1 1 − eE Wt+1 + eE Wt+1
                                                     t+1          t+1
                                1 = βEt                                     ,                                  (3.5)
                                         Uc,t              pEt
                                               ¡         ¢ I,C        I,B
                                        Uc,t+1 1 − eI            E
                                                     t+1 Wt+1 + et+1 Wt+1
                                1 = βEt                                   .                                    (3.6)
                                         Uc,t              pIt
  18
       A simple way to avoid this problem is to introduce a quadratic cost of producing loans, m · L2 , and then take
the limiting case in which the parameter m goes to zero.


                                                           11
We implicitly assumed above that dividends are paid in the beginning of the period, before the old
generation sells the banks shares. Thus, the price of the incumbent banks’ shares is equal to their
continuation value minus the dividends:

                                             pI = WtI,C − divt .
                                              t
                                                             I
                                                                                                   (3.7)

Recall that the banks’ continuation value increases one-to-one with the expected value of the future
government transfer. Thus, the price of the incumbent banks’ shares also increases one-to-one with
the future transfer. Note, that the incumbent banks’ share prices are “end-of-the-period” prices:
they reflect only future expected profits and transfers, and, thus, do not directly depend on the
current period net worth or dividends.


3.3   Firms

Firms live for two periods. They are perfectly competitive and are owned by the households. In
the first period they borrow from the banks to purchase capital. In the next period they hire labor
and production takes place. Firms sell their output and capital stock, and pay wages and their
debt to the banks. The firm’s problem is given by:

                                Uc,t+1
             maxkt+1 ,nt+1 Et    Uc,t {F (kt+1 , nt+1 ) − Rt kt+1   − wt+1 nt+1 + (1 − δ)kt+1 },

where kt+1 is purchased capital, nt+1 is the amount of labor hired in period t + 1, and δ is the
depreciation rate of capital. The production function is Cobb-Douglas: F (k, n) = kα n1−α . The
FOCs for the firm’s problem with respect to capital and labor are given, respectively, by
                                          Uc,t+1
                                Rt = Et    Uc,t    (Fk (kt+1 , nt+1 ) + (1 − δ)) ,
                                wt+1 = Fn (kt+1 , nt+1 ).

3.4   The Government

The government’s budget constraint is

      E        D    E
  eE qt−1 max(Rt−1 Dt−1 − (1 − xi )Rt−1 LE , 0) + eI qt−1 max(Rt−1 Dt−1 − (1 − xi )Rt−1 LI , 0) +
                                    L                 I        D    I               L
  |t                                     t−1
                                               {z t                                      t−1
                                                                                              }
                            amount needed to cover deposits of bankrupt banks

                                                   I         Y    O
                                       + (1 − eI )qt−1 Gt = gt + gt .
                                               t
                                         |     {z       }
                                          transfers to banks


                                                        12
The first term on the LHS of the government’s budget constraint stems directly from deposit guar-
antees: the government has to fully cover deposit obligations of the banks which declare bankruptcy.
The second term represents the transfer to the banks, in case there has been a crisis one period
earlier. The terms on the RHS are the government revenues: the lump sum taxes levied on the
young and old generations.


3.5       Resource Constraint

The resource constraint states that aggregate consumption plus investment should not exceed ag-
gregate output:

                                                                       ¡ E                 ¢
                                                                    L              I
                 cY + cO + kt+1 − (1 − δ)kt ≤ F (kt , nt ) − ei xi Rt−1 qt−1 LE + qt−1 LI
                  t    t                                                      t−1       t−1 .


Note that in every period we net out from aggregate output an amount equal to the one generated
by the idiosyncratic shocks to banks’ returns. Losses in excess of this amount, which would arise
when the economy is hit by an aggregate shock, do not disappear — they are distributed back to
the old generation of households.19


3.6       State Variables and The Nature of Uncertainty

For each bank, the following vector is sufficient to fully describe the state of the economy: (Kt , Qt , Rt ,
 D AG AG ID                   AG     ID
Rt , It−1 , It , It ), where It and It are indicator variables capturing the occurrence of the ag-
gregate and the idiosyncratic shocks at time t, respectively. Recall, that with probability ea a crisis
occurs and all banks loose a fraction x of their total loans and that if there is no crisis, only a
                                                                      L
fraction ei of the banks suffers the loss. Thus, the return on loans, Rt , and the return on capital,
Rt , are related as follows:
                  ⎧
                  ⎪ (1 − x)Rt if I AG = 1 (with prob. ea ),
                  ⎪
                  ⎪
                  ⎨                 t
              L
            Rt =                    AG
                      (1 − x)Rt if It = 0, and ItID = 1 (with prob. ei (1 − ea ) ),
                  ⎪
                  ⎪
                  ⎪
                  ⎩                 AG
                             Rt if It = 0, and ItID = 0 (with prob. (1 − ei ) (1 − ea ) ).
  19
       A more standard way of modelling losses would be to assume that all firms in the economy suffer a productivity
shock. This would generate an income effect that would push down the savings of the young generation, exacerbating
the negative effect of the crisis. Our way of modelling losses is in accord with the view that stock and real estate
market collapses in Japan did not arise from a technology shock.


                                                         13
3.7       Equilibrium
                                      E
Equilibrium is defined as quantities {qt , LE , qt , LI , kt+1 , nt , cY , cO , Dt }, prices {Rt , Rt , wt , pI , pE },
                                           t
                                                I
                                                     t                t    t
                                                                                                   D
                                                                                                             t t
                                                                           Y    O
the banks’ decision to operate or not, and a government policy {Bt , Gt , gt , gt } such that the
government policy is feasible, and given prices and the government policy:

       • consumption and savings solve the households’ problem in each period;

       • capital and labor solve the firms’ problem in each period;

       • the banks’ decision to operate or not maximizes their respective values;

       • loans solve the banks continuation problem; and

       • markets clear in each period:
                                                  ¡ E E
                                                    1
                                                                  ¡         ¢¢
                     E       I
                    qt LE + qt LI ≡ Lt = kt+1 ,
                        t       t                  qt Lt + qt LI + Bt = Dt , nt = 1, and
                                                    ∆t
                                                                I
                                                                      t
                                                                          ¡ E                 ¢
                                                                        L             I
                    cY + cO + kt+1 − (1 − δ)kt = F (kt , nt ) − ei xi Rt−1 qt−1 LE + qt−1 LI
                     t    t                                                      t−1       t−1 .


3.8       A Crisis And Its Aftermath

In this paper we do not estimate the probability of crises or what causes them. Rather, our focus
is on the impact which the bad loans and the delay in the bailout have on economic activity. To
this end, following the literature on financial crisis that studies an aftermath of events which have
a negligibly small probability of occurrence (e.g., Allen and Gale, 2000), we set the parameter ea
to zero.20


3.8.1       The Set Up

        Auxiliary Assumptions. We assume a tax scheme which guarantees that the savings of the
young generation are not affected by a crisis. This assumption implies that occurrence of a crisis
per se has no impact on future economic outcomes and, hence, it allows us to isolate the role of
  20
       Setting ea to zero does not change any of our qualitative conclusions. Numerical simulations show that in our
OLG setting the effect of a crisis on the economic activity is quantitatively robust to small changes in the parameter
ea . The results of these simulations are available upon request from the author.




                                                          14
the government intervention on aggregate economic activity. One such scheme is as follows:

 Y
gt          E        D    E               L
      = ei qt−1 max(Rt−1 Dt−1 − (1 − xi )Rt−1 LE , 0) + ei qt−1 max(Rt−1 Dt−1 − (1 − xi )Rt−1 LI , 0)
                                               t−1
                                                            I        D    I               L
                                                                                               t−1

                    I
         +(1 − ei )qt−1 Gt .

Under the assumptions above, in equilibrium of our model the banks declare bankruptcy if and
only if they receive the idiosyncratic shock. The tax scheme above implies that the cost of these
bankruptcies, in terms of the deposit obligations, is levied on the young generation. To preserve
symmetry, the same amount of taxes is levied on the young also in times of a crisis. If there was
an aggregate shock one period earlier, the young generation carries the burden of the transfers to
the banks.
     Non-Stochastic Steady State. In the non-stochastic steady state the savings of the young
generation are equal to capital:
                                              Sss = kss .

The banks’ share prices are equal to the value of the shareholders’ capital:
                                                     µ       ¶
                               I         I      I          1
                              pss = Lss − Dss = 1 −            LI ,
                                                                ss
                                                           ∆
                                                     µ       ¶
                                                           1
                                                E
                              pE = LE − Dss = 1 −
                               ss        ss                    LE .
                                                                ss
                                                           ∆

We normalize the number of banks in the non-stochastic steady state to one.
     The Government Intervention. If there is a crisis, the government promises to each bank a
transfer in the next period, allows the banks to carry some of the losses on their books and lowers
the capital adequacy requirement by a half, from 8% to 4%. The present value of the transfer is
equal to the amount of bad loans that the banks are allowed to carry on their books:

                                                     1
                                             B0 =      G .
                                                      D 1
                                                    R0

Note, that this amount can be smaller than the value of the original loss, x · Rss Lss . In such a case,
the shareholders’ absorb a part of the loss triggered by the crisis. We assume that the amount
of the transfer is the smallest possible. That is, it is such that the banks are indifferent between
shutting down or continuing to operate.




                                                    15
3.8.2       Crowding out: bad loans as government debt

We assume that the economy at its non-stochastic steady state and that a crisis occurs in period 0.
There are no other crises in subsequent periods. Figure 2.1 illustrates the response of the economy.
On impact, the total amount of new loans falls; lending and deposit rates rise. The next period
output falls. After period 2, once the bailout is complete, the economy quickly recovers and returns
to its non-stochastic steady state.
       To highlight the intuition behind these results it is useful to recall the equation describing the
allocation of aggregate savings:

                                                                              1
                              S0 = pI + q E pE + D0 = pI + q E pE +
                                    0        0         0        0                (L0 + B0 );
                                                                              ∆0

where the second equality stems from the banks’ capital adequacy constraint. Using the households’
FOC with respect to the banks’ share holdings in (3.5) and (3.6), the definition of the banks’
continuation value in (3.2), and the banks FOC with respect to loans in (3.3) we can substitute for
the banks’ share prices:
                                                          B0           ¡       ¢ G1
                                     S0 = L0 +         ei             + 1 − ei    D
                                                                                     .
                                                          ∆                      R0
                                                       | {z 0
                                                            }          |    {z     }
                                                  indirect transfer     direct transfer
Note, that since the present value of the government transfer is equal to bad loans, B0 , in the
special case in which there is no idiosyncratic uncertainty, ei → 0, the expression above reduces to

                                                    S0 = L0 + B0 ;

which implies that the effect of bad loans on economic activity is identical to that of government
debt emphasized by Diamond (1965). Indeed, B0 is equivalent to government debt. Since the
savings of the young generation are not affect by the crisis (or, equivalently, by government debt),
bad loans reduce one-to-one the amount of new loans, i.e., the amount of aggregate investment.
       In the general case, the effect of the government intervention is more nuanced. This effect occurs
through two distinct channels. First, there is the direct transfer effect: the amount of savings that
could be allocated for productive use is reduced by the present value of the government transfer,
¡      ¢ G1
 1 − ei RD .21
              0

  21
       Recall, that in period 1 a fraction ei of the banks will receive the idiosyncratic shock. These banks will shut
down, and, thus, the fraction of banks receiving the government transfer is 1 − ei .


                                                            16
   Second, there is an indirect transfer, which occurs via the capital adequacy constraint. For the
                                                                   B0
fraction of banks which will fail in the next period, the amount   ∆0   represents a pure transfer from
the government: even though these funds are raised via deposits, they are not used to make new
loans. Instead, they are distributed to the shareholders, and when a bank fails, the government
covers this amount as a part of its obligations stemming from the deposit guarantees. In contrast,
the banks which do not fail in the next period, must pay back all deposits, including those used
to make payments to the shareholders. The amount of the indirect transfer depends on the capital
adequacy requirement. Lowering the capital adequacy requirement raises the amount of the indirect
transfer, which generates an additional decline in the amount of new loans. In sum, the present
                                                                  B
                                                                      ¡      ¢ G1
value of the government liabilities arising from the crisis is ei ∆0 + 1 − ei RD .
                                                                    0                0

   The discussion above shows that what determines the size of the crowding out effect and the
subsequent decline in economic activity is the total amount of government liabilities. In particular,
whether these liabilities are direct or indirect is irrelevant. This, in turn, suggests that the effect
of bad loans on economic activity is invariant to a number of modeling choices. These include:

  1. The value of the parameter ei . For a given amount of government liabilities generated by
     the crisis, the magnitude of the decline in new loans does not depend on the probability of
     the idiosyncratic shock faced by the banks.

  2. The timing of the bailout. We assumed that the bailout occurs one period after the
     shock. Suppose, for example, that the bailout occurs two periods after the shock. Then, the
     following equation holds:
                                           ¡      ¢
                                      i B0  1 − ei ei B1 ¡        ¢2 G2
                          S0 = L0 + e    +      D
                                                         + 1 − ei     D D
                                                                            .
                                      ∆0       R0     ∆1             R0 R1
                                    |        {z        } |        {z      }
                                           indirect transfer       direct transfer

     As before, the direct transfer represents the present value of the future transfers to the banks,
     and the indirect transfer captures the increase in the government liabilities associated with
     the deposit guarantees. The overall decline in loans is equal to the total amount of the
     outstanding government liabilities.

   Finally, we remark that both direct and indirect transfer appear as a premium contained in the
incumbent banks’ share prices over the banks’ “fundamental value,” i.e., the net present value of

                                                    17
their future profits.22 That is, the government intervention ends up generating a transfer to the old
generation — the owners of the banks in period 0 — which they collect when selling the banks to the
young generation. The young generation agrees to buy the banks’ shares only because of the future
government bailout of the banks. In other words, the government intervention forces the savings
of the young generation away from productive use into a pure transfer to the old generation. The
longer is the delay in the bailout, the longer this misallocation will last. However, this Ponzi-like
scheme cannot go on forever — eventually the economy will not have enough savings to cover the
transfer to the old generation. That period is the natural upper bound on the date at which the
government transfer must occur.


4         Quantitative Analysis

In this section we access how much of Japan’s slowdown can be explained by the bad loans problem.
We also illustrate that the recession generated by the delay in the bailout, is consistent with the
Japan’s experience. The main difficulty in quantifying the effect of the bad loans problem on Japan’s
economy is the uncertainty regarding the actual amount of the bad loans and the expectations
regarding the government’s bailout policy. To this end, we proceed in two different directions.
         First, we study the case in which the expectations regarding the bailout policy are such that
the effect of the bad loans problem on the model economy is the smallest. We find that the delay
in the bailout slowed the economy at least by 0.19-0.51% per year.
         Second, note that the bad loans cause a decline in economic activity through the crowding
out effect on capital. Therefore, under the assumption that the bad loans problem was the only
force slowing down Japan’s economy, then the observed decline in the investment-output ratio was
solely due to the crowding out effect of the bad loans on capital. Thus, it is possible to actually
infer a set of expectations regarding the bailout policy and the amount of the bad loans which
    22
         In the period of the shock, both the banks’ fundamental value and the banks’ share prices decline. The decline
in the fundamental value reflects the depletion of the banks’ capital caused by the bad loans on their books by the
change in the capital adequacy requirement. Our example here was constructed to deliver a negative fundamental
value in the period of the shock. This feature of the model meant to illustrate the notion that the banks “would be
out of business if regulators forced them to recognize all their loan losses immediately,” just as it happened in Japan,
according to, e.g., Caballero et al. (2008).




                                                            18
are consistent with the data. That is, one can simulate a model calibrated to Japan’s economy,
with different bailout policies and different amounts of bad loans, and single out cases in which the
resulting crowding out effect on capital comes closest to the one observed in Japan. The average
yearly decline in output, which occurs in these cases, is the estimate of the impact of the bad loans
problem on Japan’s economy. We find that when the fall in the investment-output ratio generated
by the model coincides with the one in the data, the implied average yearly decline in output is
0.92%.
      In our quantitative exercises we consider two different structures of the production side of the
economy. Both of them generate a procyclical Solow residual. In the benchmark model, which is a
variant of the Hopenhayn’s (1982) model of industry structure, a decline in capital stock reduces
competition among firms, allowing those with lower productivity to survive. The overall number
of producing firms falls,23 dragging firms’ average productivity down. As a result, TFP declines.
The alternative is a model of counter-cyclical mark-ups, borrowed from Jaimovich and Floetotto
(2008), in which a decline in the capital stock causes a reduction in the number of operating firms.
Competition falls and the firms’ mark-ups rise, which manifests in lower efficiency of the economy.
More precisely, in this model TFP is inversely proportional to the average mark-up in the economy
- a one percent increase in the average mark-up leads to a one percent decline in TFP.
      In the rest of this section we first construct the benchmark model, describe the nature of the
experiments, and present the results. We then briefly describe the alternative model and discuss
the results of the experiments conducted with it.


4.1      The Benchmark Model

The model below is a modified version of the model in Section 3. First, we substitute the overlapping
generations framework with Blanchard’s (1985) “perpetual youth” framework. A property of this
framework is that it preserves the overlapping generations structure, while permitting the study of
the economy’s dynamics at yearly frequencies. Second, following Hayashi and Prescott (2002), we
introduce a tax on capital. Capital taxes are very high in Japan, and the corresponding revenues
constitute a significant share of total government revenues. Therefore, the capital tax cannot be
 23
      In Japan, between 1991 and 2001 the number of establishments declined by roughly 7%.




                                                       19
ignored. In the model below the rate of return on capital and the interest rate are related as follows:

                                            R − 1 = (1 − τ K )(Rf − 1),

where R is the interest rate, τ K ∈ [0, 1] is the capital tax, and Rf is the rate of return on capital.
Third, we endogenize labor supply. Households supply elastically labor and managerial services.
Finally, we modify the production side of the economy to incorporate a model of TFP.


4.1.1       Households24

Households in this economy consume, save and work as labor and managers. Households differ by
their age. In each period a new generation of households of measure p is born. Each household
faces a constant probability p of dying in the next period; p is also the reciprocal of the household’s
expected lifetime.
       The economy is also populated by perfectly competitive insurance companies, which pay a pre-
           p
mium      1−p   per unit of non-human wealth the households possess. In exchange, insurance companies
collect a household’s wealth in the event of its death.
     The utility function of a household born in time t in period s is given by
                                   ⎧    ³                                                   ´
                                   ⎨ log c(s, t) − ψn (s,t)·n(s,t)1+ψ0 − ψm (s,t)·m(s,t)1+ψ0 if alive in period t,
                                                          1+ψ 0                 1+ψ 0
us,t (c(s, t), n(s, t), m(s, t)) =
                                   ⎩ 0 otherwise,

where c(s, t) is consumption, n(s, t) is the labor hours supplied, m(s, t) is the manager hours
supplied, ψ n (s, t) and ψ m (s, t) are the disutility coefficients from labor and managerial effort re-
spectively.25
       With this utility function the problem of a household which is born at time t and alive at time
¯
s is given by
                        P∞                    ³                                                                ´
                                                             ψ n (s,t)·n(s,t)1+ψ0       ψm (s,t)·m(s,t)1+ψ 0
                max p      s
                         s=¯
                                         s
                             [β(1 − p)]s−¯ log c(s, t) −             1+ψ0           −          1+ψ 0
                                                        p              n            m
                s.t. v(s + 1, t) + c(s, t) = Rs [1 +   1−p ]v(s, t) + ws n(s, t) + ws m(s, t) − τ (s, t),

  24
       In modeling households I follow closely Blanchard and Fischer (1989), Ch. 3. The noticable difference is that in
my model the labor supply is endogenous. I use the functional form of Greenwood, Hercowitz, and Huffman (1988),
which preserves the aggregation properities of the perpetual youth model.
 25
    The effort disutility coefficients ψ n and ψm vary over the life-cycle of the households to capture the life-cycle
pattern of labor income, as described below.


                                                            20
                                                      n      m
where v(s, t) is the (non-human) wealth in period s, ws and ws are the wages paid to workers and
managers, τ (s, t) is the (generation specific) lump sum tax, and Rs is the interest rate. The term
    p
Rs 1−p v(s, t) is the premium received from the insurance companies.
   We assume that τ (s, t) is proportional to the labor income of each generation:

                                                               n           m
                                       τ (s, t) = τ s [n(s, t)ws + m(s, t)ws ],

where τ s is the tax rate at time s.
   To capture the life-cycle pattern of the households’ labor income, it is assumed that for a
                                         ¯ s
household born in generation t in period s ψ(¯, t) is given by:

                                        −ψ1          ¡                               ¢
                          [ψ n (¯, t)]
                                s          0   =   an [1 − θ1 ]s−t + an [1 − θ2 ]s−t ,
                                                    1
                                                               ¯
                                                                      2
                                                                                 ¯

                                        −ψ1      ¡                                    ¢
                               s
                         [ψ m (¯, t)]      0   = am [1 − θ1 ]s−t + am [1 − θ2 ]s−t ,
                                                    1
                                                                ¯
                                                                       2
                                                                                   ¯



where an , am < 0, an , am > 0, 0 < θ1 < θ2 < 1.
       1    1       2    2

   It is convenient to denote the following sums as Ψn and Ψm
                                                   s
                                                   ¯
                                                   X                    1
                                                                      −ψ
                                       Ψn ≡ p              ψ n (¯, t)
                                                                s           0   [1 − p]s−t ,
                                                                                       ¯

                                                   t=−∞
                                                    Xs
                                                     ¯
                                                                          1
                                                                        −ψ
                                   Ψm ≡ p                  ψ m (¯, t)
                                                                s           0   [1 − p]s−t .
                                                                                       ¯

                                                   t=−∞

   Then, one can show that the solution of the problem above yields the following equations for
the aggregate consumption Ct and (non-human) wealth Vt+1 :
                                                                                      1+ψ 0                       1+ψ 0
                                                                      1       n        ψ0            1      m      ψ0
         Ct = [1 − β(1 − p)][Rt Vt + [W1,t + W2,t ]] +              1+ψ 0 Ψn wt                +   1+ψ0 Ψm wt             ,
                                 "      1+ψ                         1+ψ 0
                                                                          #
                                                     0
                                       n        ψ0                 m ψ0
         Vt+1 = Rt Vt + (1 − τ t ) Ψn wt                 + Ψm wt                  − Ct ,
                             "                              "                       1+ψ 0                      1+ψ 0
                                                                                                                       ##
                       Rt+1                  ψ0                      an p          n ψ0             am p      m ψ0
         W1,t+1 =   [1−θ1 ][1−p]   W1,t − ( 1+ψ − τ t )           θ1 +p−θ1 p wt
                                                                      1
                                                                                              +   θ1 +p−θ1 p wt
                                                                                                     1
                                                                                                                              ,
                                                   0




                                   "                          "                     1+ψ 0                      1+ψ 0
                                                                                                                       ##
                       Rt+1                  ψ0                      an p          n ψ0             am p      m ψ0
         W2,t+1 =   [1−θ2 ][1−p]   W2,t − ( 1+ψ − τ t )           θ2 +p−θ2 p wt
                                                                      2
                                                                                              +   θ2 +p−θ2 p wt
                                                                                                     2
                                                                                                                              ,
                                                   0




                                                             21
where W1,t and W2,t denote the following quantities:26
                                "             1+ψ 0                 1+ψ 0
                                                                          #
               P∞ ψ0                  np
                                     a1     n  ψ0         mp
                                                         a1       m  ψ0
       W1,t = s=t ( 1+ψ − τ s ) θ1 +p−θ1 p ws       + θ1 +p−θ1 p ws         [1 − θ1 ]s−t R(t, s),
                        0
                                "             1+ψ 0                 1+ψ 0
                                                                          #
               P∞ ψ0                 an p   n ψ0 +       am p     m ψ0
       W2,t = s=t ( 1+ψ − τ s ) θ2 +p−θ2 p ws
                                      2
                                                      θ2 +p−θ2 p ws
                                                          2
                                                                            [1 − θ2 ]s−t R(t, s),
                                 0



       and                                        ⎧
                                                  ⎨    [1−p]s−t
                                                       s               if s > t + 1;
                                      R(t, s) ≡        m=t+1 Rm
                                                  ⎩ 1                     if s = t.
       Finally, the aggregate labor, Nt , and the aggregate managers, Mt , are given by the following
equations:

                                                               1
                                                         n
                                                  Nt = [wt ] ψ0 Ψn ,
                                                                   1                                           (4.1)
                                                         m
                                                  Mt = [wt ] ψ0 Ψm .

4.1.2        Firms

The production side of the economy is modeled along the lines of Lucas (1978), Jovanovic (1982),
Hopenhayn (1992), and Atkeson and Kehoe (2005).                          Firms are heterogenous: each firm has
monopoly power over the good it produces, and the firms have different productivity levels. Two
assumptions regarding the structure of the production side in the economy are crucial for the results
of the paper regarding the dynamics of TFP: there is a sunk entry cost and there is an operating
cost.
       The entry cost. A part of the entry costs stems from satisfying different official regulatory
requirements. As Djankov et al. (2002) report, in Japan “the official cost of following (entry)
procedures for a simple firm” is 11% of per capita GDP (22% if the time cost is included). Entry
costs may also include expenses related to the acquisition of firm specific capital (Shapiro and
Ramey, 2001) and other start-up costs.
       The operating cost. The operating cost typically refers to overhead labor (i.e., managers), and
expenses that are lumpy in nature, for example, renting a physical location. According to findings
  26
       In the Blanchard’s (1985) originial model the sum W1,t + W2,t denotes the aggregate human wealth, that is, the
present value of all labor income of currently alive households. In this model it repesents the same quantity minus
the present value of the aggregate disutility from working of the currently alive households.



                                                          22
of Domowitz et al. (1998), in U.S. manufacturing plants, the overhead labor accounts for 31% of
total labor. Ramey (1991) suggests that overhead labor is about 20%. Basu’s (1996) preferred
estimate of overhead inputs is 28%.
       We assume that firms learn their productivity only after the sunk entry cost is paid. This
assumption reflects very high uncertainty faced by entering firms. After entry, the firms either
grow quickly or exit. This is routinely found in the data and documented, for example, by Klette
and Kortum (2004) as a stylized fact. More recently, Bartelsman et al. (2005) report that the
survival rate for the U.S. manufacturing firms is about 80% at two years of age, and about 66%
at age four. The U.S. manufacturing firms which do not exit at two years of age are on average
ten times larger than when they entered.27 The industry structure literature commonly interprets
these patterns as evidence that firms discover their productivity only after the entry takes place.
       Final good producers. The final consumption good in this economy is produced by perfectly
competitive firms, owned by the households, according to the following production function:
                                        ∙Z μ                ¸λ
                                             t          1
                                   Yt =        [yt (i)] λ di ,
                                                            0

where μt is the number of intermediate goods produced in the economy, λ is a constant which is
greater than one, and yt (i) is the quantity of the intermediate good i. Let pt (i) be the price of ith
intermediate good in terms of the final good. Then, the maximization problem of the final good
producer can be written as
                                          ∙Z     μt              ¸λ Z          μt
                                                            1
                                    max               [yt (i)] di −
                                                            λ                       pt (i)yt (i)di,
                                             0                             0

and the first order optimality condition implies that
                                                                ∙        ¸− λ−1
                                                               yt (i)          λ
                                                      pt (i) =                      .
                                                                Yt

       Intermediate good producers. A firm in the intermediate goods sector lives two periods, is
profit maximizing and owned by the households. All firms are ex ante identical. There is an entry
cost κ. A firm must borrow from the bank in order to pay this cost. Once the entry cost is paid, a
firm gains the ability to produce an intermediate good in the next period. Next, the firm draws a
  27
       These facts are robust across countries. E.g., for the U.K. manufacturing firms, the survival rates at the age two
and four are 79% and 54%, respectively, and at the age of two the firms are about eight times larger than at birth.



                                                                    23
productivity parameter A(j), where j is drawn from an i.i.d. uniform distribution over [0,1]. The
firm has a monopoly power for the good it can produce. The production function for the good j is
given by
                                                      £             ¤γ
                                             [A(j)]1−γ k(j)α n(j)1−α ,

where k(j) and n(j) denote capital and labor respectively. The productivity parameter differs
among the firms. A firm with a higher index has a higher productivity parameter:

                                    A(j) > A(i), for j > i, and i, j ∈ [0, 1].

The parameter γ determines the degree of diminishing returns to scale in capital and labor.28
       In order to produce the firm must borrow to buy capital, as well as to cover the operating cost.
The operating cost consists of wages paid to φm managers,29 and φδ units of capital. The managers
are paid in the beginning of the next period, before the production takes place.
       Consider the decision of a firm born in time t with a draw j. If it decides to produce, its profits
are
                                        h           i λ−1
                                            yt+1 (j) − λ                f
 πP (j) = maxkt+1 (j),nt+1 (j),Lt (j)
  t+1                                        Yt+1           yt+1 (j) − Rt+1 Lt (j) − wt+1 nt+1 (j) + (1 − δ)kt+1 (j),
 s.t.
                      £ α              ¤γ
  yt+1 (j) = [A(j)]1−γ kt+1 (j)n1−α (j) , Lt (j) ≥ kt+1 (j) + φδ + wt+1 φm .
                                t+1
                                                                    m

                                                                                                               (4.2)
       f
where Rt+1 is the interest rate on loans that a firm faces, Lt (j) is the amount of a firm’s loan, wt+1
                        m
is the labor wage, and wt+1 is the managers’ wage. The parameter δ denotes the depreciation rate
of capital used in production. Capital which is used to operate, i.e. φδ , depreciates completely.
The decision whether or not to produce depends on if π P (j) is positive or not. Therefore, the j th
                                                       t+1

firm’s profits π F (j) are given by:
               t+1


                                             π F (j) = max{π P (j), 0}.
                                               t+1           t+1


Lastly, free entry implies that in equilibrium the firm’s profits must be equal to the expected entry
  28
       This is what Lucas (1978) calls managers’ span of control.
  29
       The managers in the model are identical to those in Lucas (1978): each firm requires a fixed number of them,
and they do not affect the marginal product of labor.




                                                             24
cost κ:30                                                 Z     1
                                                     1
                                                    f
                                                                    π F (j)dj = κ.
                                                                      t+1                                          (4.3)
                                                   Rt+1     0

       Firms’ average productivity. First, we determine the lowest productivity level necessary
for a firm to decide to produce. Note that the first order conditions for a firm j which decides to
operate is given by
                                             α λ pt+1 (j)y(j) (j) = Rt+1 − (1 − δ),
                                               γ
                                                    kt+1
                                                          t+1        f
                                                                                                                   (4.4)
                                             (1 − α) λ pt+1 (j)y(j) (j) = wt+1 .
                                                     γ
                                                          nt+1
                                                                t+1


These two conditions imply that for any two operating firms i and j,the following relations hold:
                                   pt+1 (j)yt+1 (j)   kt+1 (j)   nt+1 (j)   a(j)
                                                    =          =          =      ,                                 (4.5)
                                   pt+1 (i)yt+1 (i)   kt+1 (i)   nt+1 (i)   a(i)
                         1−γ
where a(j) ≡ A(j) λ−γ . That is, in equilibrium, the gross profits, capital, and labor ratios of any
two goods are equal to their (scaled) productivity ratio. Denote the operating cost as φO ≡
                                                                                        t+1

(φδ + wt+1 φm ). Then, the first order conditions in (4.4) also imply that the profits from producing
       m


are equal to the firm’s share of the gross profits (1 − γ ) minus the present value of the operating
                                                      λ
      f
cost Rt+1 φO :
           t+1
                                                          γ                      f
                                   π P (j) = (1 −
                                     t+1                    )pt+1 (j)yt+1 (j) − Rt+1 φO .
                                                                                      t+1
                                                          λ
Let Jt+1 be the firm which is indifferent between producing or not,31 i.e.
                                         γ                              f
                                  (1 −     )pt+1 (Jt+1 )yt+1 (Jt+1 ) − Rt+1 φO = 0.
                                                                             t+1                                   (4.6)
                                         λ
Gross profits are increasing in productivity, and so are the net profits. Therefore, firms with indices
higher than Jt+1 will produce, and those with lower indices will not. This implies that the firm’s
expected profits are:
                                         Z   1h                                   i
                                                   γ                     f
                               π t+1 =         (1 − )pt+1 (j)yt+1 (j) − Rt+1 φO dj.
                                                                              t+1                                  (4.7)
                                         Jt+1      λ
Using equations (4.5) and (4.6), the zero profits condition (4.3) can be written as:
                                           Z 1 ∙             ¸
                                       O           a(j)
                                  κ = φt+1                − 1 dj.                                                  (4.8)
                                            Jt+1 a(Jt+1 )
  30
       I assume that the firms’ shareholders have full liability. That is, if after incurring the cost κ and drawing j the
firm decides not to produce, the bank is still paid in full. However, if all (or sufficiently many) firms are owned by
one agent, i.i.d. nature of the productivity draws implies that there is no risk in owning these firms.
  31
     Note that Jt+1 may not exist, because it can be the case that it is optimal to produce at any level of productivity:
πP (j) > 0 for all j. I assume that this is not the case.
 t+1



                                                                     25
The expression above defines the cutoff Jt+1 as an implicit function of the operating cost φO . It
                                                                                          t+1

is straightforward to show that Jt+1 (·) is an increasing function of the operating cost. Therefore,
                                              1
                                              Jt+1 a(j)dj
the firms’ average productivity     aAV
                                    t+1   =     1           is an increasing function of the operating cost. In
                                                Jt+1 dj
particular, when the operating cost declines, the firms’ average productivity falls.
   Entry, the number of producing firms, and average productivity. Let ν t+1 denote the
entry, and μt+1 the number of producing firms. Then
                                                          μ
                                                ν t+1 = R 1 t+1 .
                                                         Jt+1 dj

Next, let me show that the cutoff Jt+1 is an increasing function of μt+1 . First, note that
                                      ∙       ¸     ∙         ¸
                                m       Mt+1 ψ0       μt+1 φm ψ0
                               wt+1 =             =              ,
                                         Ψm             Ψm
where the first equation uses the relation between wages and aggregate number of managers in
(4.1), and the second one uses the market clearing condition for the managers. Therefore, the
                   m
managers’ wage wt+1 is an increasing function of the number of producing firms μt+1 . Note, that
                                   m
                                                                                  R1
Jt+1 is an increasing function of wt+1 , and therefore, of μt+1 . Finally, because Jt+1 dj, is decreasing
in Jt+1 , ν t+1 is an increasing function of μt+1 .
   Therefore, in equilibrium, the entry ν t+1 , the number of producing firms μt+1 , and the firms’
average productivity aAV move in the same direction.
                      t+1

   Aggregation. Let Kt+1 denote the economy’s aggregate capital stock used in production.
Then, the aggregate output in this economy is given by
                  "     Z 1                  #λ "      Z                          #(λ−γ)
                                        1
                                                                   1                       h         i
                                                                                                  1−α γ
                                                                                             α
           Yt+1 = ν t+1      [yt+1 (j)] λ dj   = ν t+1                   a(j)dj             Kt+1 Nt+1 ,
                            Jt+1                                  Jt+1

where the last equation comes from expression in (4.5). Note, that using the firm’s FOC in (4.7)
and expression in (4.5), the rental rate on capital and labor wage can be written as:
                                            γ Y       f
                                          α λ Kt+1 = Rt+1 − (1 − δ),
                                                t+1
                                                                                                          (4.9)
                                                  γ Y       n
                                          (1 − α) λ Nt+1 = wt+1 .
                                                      t+1

                         f                                f
   The relation between Rt and Rt . The (pre-tax) return Rt on capital and the (net of tax)
interest the households receive are related as follows:
                                                           f
                                          Rt = (1 − τ k )(Rt − 1) + 1,
                                                      t

where τ k is the capital income tax rate.
        t


                                                        26
4.1.3       Banks

The banks are identical to the ones described in Section 3. As before, we assume that the probability
of the aggregate shock is negligibly small. In addition, to avoid cumbersome notation, we consider
the limiting case in which ei tends to zero.32 The amount of loans made at time t is given by

                                                 Lt = Vt − Bt + Gt .

Note that Vt in this model and St in the OLG model carry the same interpretation: they both
capture the aggregate amount of resources which households put aside for future consumption.
Thus, the relation between savings, bad loans and new loans is identical to that in Section 3.


4.1.4       Government

The government finances a stream of government purchases gt , collects taxes, and provides deposit
guarantees to the banks. The government’s budget constraint is given by
                             "     1+ψ           1+ψ
                                                     #
                                                    0                  0
                                         n     ψ0             m   ψ0               f
                       Gt + gt = τ t Ψn wt              + Ψm wt            + τ k (Rt − 1)(Vt − Bt ),
                                                                               t


where Gt is the transfer to the banks.


4.1.5       Resource Constraint, Market Clearing Conditions, and Equilibrium

The resource constraint is given by:
                                                    Ct + It + gt = Yt ;

where It is the aggregate investment. The latter includes the aggregate investment into the capital
used in production, and the fixed costs ν t+1 κ and μt+1 φδ . Also, since the managers’ wages are
                                                                    £      m        m
                                                                                      ¤
borrowed in the current period, but paid in the next, the term Mt+1 wt+1 − Mt wt must be
included in the aggregate investment.
       The market clearing conditions are:
                                                  R1                         R1
                   Vt+1 = Lt + Bt+1 , Lt = ν t+1 Jt+1 Lt (j)dj + ν t+1 κ, ν t Jt nt (j)dj = Nt ,
                       R1                        R1
                    ν t Jt φm dj = Mt , and ν t+1 Jt+1 kt+1 (j)dj = Kt+1 .

       Finally, equilibrium is defined as in Section 3.
  32
       As we showed in Section 3 the probability of the idiosyncratic shock does not change the crowding effect of bad
loans in any way.


                                                            27
4.2       The Experiments

        Initial conditions and the bad loans shock. In all simulations it is assumed that initially
the economy is in steady state. At date zero, the crisis occurs. Recall that we assume that in case
of the aggregate shock the funds which have not been repaid to the banks, are distributed to the
households in a lump sum fashion. To insure that the aggregation properties of the model are not
altered, it is assumed that the share of B0 distributed to each household is equal to its share of
labor income in that period.
       Parameter values.33         The parameters in the model can be categorized as “neoclassical”,
“perpetual youth”, “endogenous productivity”, and others.
       The “neoclassical” parameters are chosen based on findings of Hayashi and Prescott (2002). In
particular, the share of capital is set to 0.362, the capital tax rate is set to 0.48. In steady state the
depreciation rate of capital is 8.9%, and the interest rate is 5.0%. Government spending is equal
to 15% of output.
       The “perpetual youth” parameters θ1 , θ2 , an , an , am , and am are chosen as follows. The para-
                                                   1 2 1              2

meter p is chosen such that the resulting age distribution of the households comes closest to that
in the data.34 With this value of p the expected life time of the household is equal to 41.66 years.
The parameters θ1 , θ2 , an , an , am , and am are chosen such that the resulting life-cycle pattern of
                          1 2 1              2

labor income comes closest to that in the data.
       The “endogenous productivity” parameters γ, φδ , φm and function a(j) are chosen as follows.
The parameter γ is set to 0.85, which is the benchmark value of Atkeson and Kehoe (1995, 2005).35
In steady state, depreciation due to the fixed cost φδ is equal to 1.55% of the aggregate capital stock,
and accounts approximately for 18% of total capital depreciation. The parameter φm is chosen so
that in the steady state the managers constitute 25% of the labor force.36 The productivity function
a(j) in the experiments below is given by a(j) = 0.25 + j 36 . This choice implies that the variance of
  33
       The complete list of parameter values is provided in the Appendix.
  34
       That is, p is chosen to minimize the distance between the population age distribution in the data, and the
population age distribution in the model.
  35
     Atkeson and Kehoe (2005) value of γ is the estimate for the U.S. manufacturing sector. To the best of our
knowledge, no estimate of γ is available for Japan’s economy.
  36
     This is roughly the average value of the estimates of overhead inputs reported by Domowitz et al. (1998), Ramey
(1991) and Basu (1996).




                                                        28
the firms’ productivity draws is quite high, consistent with findings of Eaton and Kortum (2002).
The choice of this functional form is motivated by computational reasons because it does not directly
affect the dynamics of the economy per se. The latter depends on the behavior of the function a(j)
around the cutoff Jt+1 . In a neighborhood of the steady state cutoff J, there is a large mass of firms
which have slightly lower than J, but essentially the same productivity.
       We set λ to 1.2, which results in a roughly 40% mark-up. According to Martins et al. (1996),
this is the value of the average mark-up in Japan.


4.3       Results: The Effect of The Bad Loans Problem

In order to simulate the model we need to specify the starting date of the bad loans problem and
the expected date at which the bailout starts, the amount of government liabilities stemming from
the crisis, and the fiscal instruments which the government will use to raise necessary funds.
       We assume that the crisis occurs in 1993. Note that in our model the effect of bad loans on the
economy is smaller, the sooner households expect taxes to be raised. This is because the later is
the tax increase, the lower is the probability that a currently alive household will be affected by it.
In other words, the delay in the tax increase lowers the increase in aggregate savings in response to
the bad loans shock. Thus, we conservatively assume that the bailout starts in 2003, i.e., ten years
after the start the crisis occurs.        37


       As previously discussed, the estimates of the amount of bad loans and the associated bailout
cost vary significantly. We entertain two possibilities. First, we assume that at the end of 2003 the
bailout cost to the taxpayers is 20% of GDP, which is the Hoshi and Kashyap’s (2004) conservative
estimate of the additional government liabilities stemming from the crisis. Second, we assume that
  37
       We recognize that our assumption about the starting date of the bad loans problem is not uncontroversial.
However, the predictions of the model are fairly robust to the starting date of the crisis. This is because the change
in the starting date of the crisis has two effects. On the one hand, if the crisis happens at a later date, but the date
of the bailout remains the same, there is less crowding out of capital - the closer is the date at which the government
will raise taxes, the less the effect of the bad loans problem is. On the other hand, if the crisis happens at a later
date, but the amount of bad loans at the date of the bailout is unchanged (e.g., it is 20 % of GDP), because of the
interest compounding, the size of the shock (i.e., the amount of bad loans at the date of the crisis) must be larger.
                             T
                                    D
In other words, since BT =         Rt−1 Bs , for the same amount BT and roughly the same deposit rate, an increase in s
                             t=s
implies that Bs must increase.



                                                            29
the bailout cost is 30% of GDP. This figure appears reasonable, given that the private estimates of
the bad loans problem exceeded significantly those disclosed by the banks and that the U60 trillion
(12% of GDP) already disposed by the government to deal with the problem were financed via debt
instruments.
       For the case in which the bailout cost is 20% of GDP, we assume that the households expect
the lump sum tax to be raised by 20% ; for the case the bailout cost is 30% - by 30%. The tax
increase is expected to last as long as it is necessary to pay off the full amount of the bad loans
outstanding.38
       Table 3.A presents the effects of the bad loans on the economy for both cases. The average
yearly decline in output is 0.19%-0.28%. Table 3.A also reports the declines in capital, aggregate
labor, and the firms’ average productivity.
       Table 3.B presents the effects of the bad loans problem when the parameter p is set to 0.1.39
Higher p implies that the households care less about the future tax increase. They save less than
in the benchmark case, which causes a larger fall in loanable funds. Consequently, the investment
decline is sharper and the recession is deeper. Overall, with this value of p, the bad loans problem
causes 0.34-0.51% average yearly decline in output.
       Under the assumption that the bad loans problem was the only reason for the slowdown of
Japan’s economy, the model developed here can be used to estimate the impact of the bad loans
problem on Japan’s economy. The estimation strategy is as follows. First, derive the crowding
effect on capital in the data by computing the average decline in investment-output ratio. Next,
simulate the model with different bailout policies and different amounts of bad loans, and single
out cases in which the resulting crowding out effect on capital comes closest to the one observed
in Japan. The average yearly decline in output, which occurs in these cases, is the estimate of the
impact of the bad loans problem on Japan’s economy.
  38
       Of course, if the lump sum tax would be increased more, the effect of the bad loans would be even smaller.
However, in our model the lump sum tax is effectively a labor income tax and. A 20% increase in the labor income
tax seems already unrealistically high. We use a 30% increase in the second case to assure that in both cases the
government completely pays the debt in approximately the same amount of time as in the first case.
  39
     The parameter p in the model is the difference between the discount rate for the human wealth and the interest
rate. Hayashi’s (1982) estimates suggest that the discount rate for human wealth is higher than the interest rate,
and in particular that the implied value of p is 0.1. See Hayashi (1982) and Blanchard (1985) for more details.




                                                        30
       When the fall in the investment-output ratio generated by the model replicates the one in
the data, the implied average yearly decline in output is 0.92%.40 The model’s performance is
satisfactory also in two other dimensions: the fall in aggregate labor is 0.45% per year, which is
about two thirds of that in the data, and the fall in the Solow residual is 0.31%, which is about
one third of the Hayashi and Prescott (2002) benchmark.41


4.4       The Alternative Model

The alternative model differs from the benchmark model only by the structure of the production
side of the economy and labor supply. In this model, all labor input is homogenous. We modify
labor supply accordingly. Below we describe the production side of the economy, following closely
Jaimovich and Floetotto (2008).
       Final good producers. The final consumption good in this economy is produced by perfectly
competitive firms, owned by the households, according to the following production function:
                                                     ∙Z    1                   ¸1
                                                                                ξ
                                                                       ξ
                                              Yt =             [Qt (j)] dj          ,
                                                       0

where ξ is a constant less than one, and Qt (j) denotes the output of sector j. In each of the j
sectors, there are Ft (j) > 1 firms producing differentiated goods:
                                                                 ⎡                       ⎤1
                                                                    Ft (j)                   τ
                                                             1       X
                                      Qt (j) = [Ft (j)]   1− τ   ⎣           yt (j, i)  τ⎦
                                                                                                 ,
                                                                     i=1

where yt (i, j) is the output of firm i and τ is a constant less than one. The market structure of
each sector exhibits monopolistic competition: each yt (j, i) is produced by one firm that sets the
price of its good in order to maximize profits. It is assumed that ξ < τ .
  40
       One such scenario is as follows: the bad loans problem occurs in 1990, the bailout starts 13 periods after the
shock, the government finances the bailout by reducing the government spending by 30%, and the amount of bad
loans is 50% of the GDP. It is important to emphasize that the steady state investment-output ratio is set to the
average investment-output ratio over the period of 1981-1990. If it was set to the 1990 level, the fall in output would
have been more dramatic.
  41
     In this experiment, 1% fall in output is accompanied by 0.3% fall in the Solow residual. In Japan during the
1990s, as measured by Hayashi and Prescott (2002), a 1% fall in (the growth rate of) output was accompanied by
roughly a 1% fall in (the growth rate of) the Solow residual.




                                                               31
      Let Pt (j) be the price of j th intermediate sector good in terms of the final good. Then, the
maximization problem of the final good producer can be written as
                                          ∙Z     1                  ¸1
                                                                     ξ
                                                                             Z    1
                                                              ξ
                                   max               [Qt (j)] dj         −            Pt (j)Qt (j)dj,
                                             0                                0

and the first order optimality condition implies that

                                                                             1
                                                      Qt (j) = Pt (j) ξ−1 Yt .

Similarly, denoting pt (j, i) the price of the ith good in the j th sector, we can derive the demand
function for the ith good:

                                    ∙            ¸     1             ∙          ¸ 1
                                    pt (j, i)        τ −1   Qt (j)     pt (j, i) τ −1         1   Yt
                        yt (j, i) =                                =                  Pt (j) ξ−1        ,
                                     Pt (j)                 Ft (j)      Pt (j)                   Ft (j)
where the price of the sector j good is defined as
                                                                    "F                         # τ −1
                                                       1
                                                         −1          Xt
                                                                                          τ
                                                                                                   τ
                                                       τ
                                        Pt (j) = Ft           (j)          pt (j, i)    τ −1            .
                                                                     i=1

      Intermediate Good Producers. A firm in the intermediate goods sector lives for two periods
and owned by the households. The production function for each good i in sector j is Cobb-Douglas:
kα (i, j) · n1−α (i, j). There is an operating cost φO denominated in units of the intermediate good.
In order to produce the firm must borrow to buy capital. The decision of a firm born in period t
is:
                        n           ¡                ¢ ³ f            ´                                o
      π t+1 (j, i) = max pt (j, i) · yt+1 (j, i) − φO − Rt+1 − (1 − δ) kt+1 (j, i) − wt+1 nt+1 (j, i),
      s.t. yt+1 (j, i) = kt+1 (j, i)n1−α (j, i).
                          α
                                     t+1
                                                                                                            (4.10)
Free entry into each sector implies that in equilibrium the firm’s profits must be zero:

                                                            π t+1 (j, i) = 0.                               (4.11)

The key feature of this model is that, though there is a continuum of sectors, the number of firms
in each sector is finite. This implies that when a firm in sector j sets its price, it takes into account
the effect this will have on the price of the good j. The resulting price elasticity of demand faced
by each firm in sector j depends on the number of firms in that sector. In a symmetric equilibrium


                                                                    32
(i.e., in an equilibrium in which all firms in all sectors make identical decisions), the price elasticity
of demand is                                ∙            ¸
                                       1        1     1    1
                                          +        −         .
                                     τ −1     ξ − 1 τ − 1 Ft
                                                               1
As Ft goes to infinity the expression above collapses to      τ −1   and the model simplifies to the standard
Dixit-Stigitz model with a constant elasticity of substitution between goods. The firms optimally
equate the price to the marginal revenue:
                                                                           1
                          pt+1 (j, i)                (ξ − 1) Ft (j) − (τ − λ )
                                      = μ(Ft (j)) ≡                         1 .                      (4.12)
                          mct (j, i)                τ (ξ − 1) Ft (j) − (τ − λ )

The firms’ FOCs with respect to capital and labor can be written, respectively, as

                              α μ(F1 ) pt+1kt+1 (j,i) (j,i) = Rt+1 − (1 − δ),
                                   t+1
                                           (j,i)yt+1           f
                                                                                                     (4.13)
                              (1 − α) μ(Ft+1 (j)) pt+1nt+1 (j,i)(j,i) = wt+1 .
                                          1           (j,i)yt+1



Free entry implies that the firms’ share of the revenues is equal to the operating cost φO :

                                    (μ(Ft+1 (j)) − 1) · yt (j, i) = φO .

   Aggregation. We assume that the economy is in a symmetric equilibrium. Then, the aggregate
output in this economy is given by

                                                   1      α    1−α
                                      Yt+1 =             Kt+1 Nt+1 ,
                                                μ(Ft+1 )

The rental rate on capital and wage can be written as:

                                          Y       f
                                        α Kt+1 = Rt+1 − (1 − δ),
                                            t+1
                                                Y       n
                                        (1 − α) Nt+1 = wt+1 .
                                                  t+1


Finally, the number of firms in each sector and aggregate output of the economy are related as
follows:
                                                 μ(Ft+1 ) − 1
                                       Ft+1 =                 Yt+1 ,
                                                     φO
with μ(Ft ) defined as in (4.12). The inverse of the mark-up is interpreted as TFP.
   The four equations above, combined with the equations from the benchmark model which
describe the behavior of the households, the banks, and the government, as well as the resource
constraint, fully describe the dynamics of the economy in the alternative model.


                                                     33
         The Effect of The Bad Loans Problem
              Parameter values.42 The “neoclassical” and “perpetual youth” parameters in this model
coincide with those in the benchmark model with the following exceptions. The parameter α is set
to 0.362. The depreciation rate δ is set to 0.089.
         The parameters τ and ω are set, respectively, to 0.949 and 0.001, as in Jaimovich and Floetotto
(2008). The value of the fixed cost φO , is conservatively set to yield the steady state value of the
mark-up of 35%. This is the average between the steady state value of the mark-up in Jaimovich
and Floetotto (2008) and the average mark-up value in Japan reported by Martins et al. (1996)
(30% and 40%, respectively).
         The experiments. Tables 3.C and 3.D present the results of the same experiments as those
performed with the benchmark model and reported in Tables 3.A and 3.B. The effects of bad loans
on economic activity are very close. In the alternative model, the average decline in output ranges
from 0.17% to 0.47%, while in the benchmark model - from 0.19% to 0.51%. Both models generate
a decline in measured productivity, though through very different mechanisms. The magnitude of
the decline is in the alternative model is slightly lower than in the benchmark model.


5         Caveats

          Return on capital. A shortcoming of our model is that the after-tax return on capital does
not fall, as it does in the data.         43   However, even if the output-capital ratio does not decline in the
model, there is essentially no rise in the rate of return on capital — it rises less than two hundredth
of a basis point per year. It is important to note that there are at least two forces which are not
considered in this paper that could make the return on capital fall. First, as Hayashi and Prescott
(2002) show, the changes in the Labor Standards Law in 1988 generated a substantial decline in
aggregate labor supply. Incorporating this decline into the analysis would generate a temporary
decline in the rate of return on capital. Second, Barseghyan (2006) shows that bad loans not only
can crowd out capital but can also induce a decline in the price of existing capital goods.44 Such a
    42
         The complete list of parameter values is provided in the Appendix.
    43
         Note that near the steady state, the output-capital ratio cannot decline when capital falls.That would imply that
the steady state is not stable.
  44
     Note that in Japan during the 1990s the price of capital, as measured by Nikkei 225 Index, had declined.




                                                              34
decline leads to capital losses which can be large enough to offset increases in the marginal product
of capital stemming from the fall in the stock of capital.
   Structure of the banking sector. In our model, there are no entry costs into the banking
sector and banks have a one-to-one technology for transforming savings into loans. Entry costs into
the banking industry and convex costs for producing loans do not preclude in any way the crowding
out effect of bad loans. Thus, our results are robust to these changes of modelling assumptions
about the structure of the banking industry. As noted before, with convex costs, the size and the
number of operating banks in equilibrium is well defined, and predictions about the entry into
banking sector can be derived. In particular, in the model identical to the one in Section 3, but
with quadratic costs of making loans, after a crisis there is no entry into the banking sector, just it
was the case in Japan during the relevant time period.
   Entry into banking sector. The discussion above highlighted how in extensions of our model
no entry into banking sector could arise as an equilibrium outcome. Other reasons for no entry,
which are exogenous to our model, include the deteriorating conditions of Japan’s banking sector
even before the bad loans problem, and, in particular, the strong exit pressures described by Hoshi
and Kashyap (2002).
   Bailout policies and the banks’ incentive to lend. We assumed that there is no uncertainty
about the government intervention — the size of the transfer, the change in the capital adequacy
requirement, and the amount of bad loans which banks can carry on their books are known in the
period of the crisis. Moreover, the size of the transfer does not depend on the banks’ net worth —
each bank receives a transfer equal to a fraction of the loss stemming from the crisis. Provided a
bank does not go bankrupt, its loan and deposit decisions do not affect the amount of the transfer
it will receive from the government in the future. This setting disregards two important channels
that could significantly reduce aggregate investment.
   First, uncertainty about the government bailout policies is likely to translate into uncertainty
about the banks’ survival in the following period. Recall, that the banks’ FOC with respect to
loans is                                               µ             ¶
                                    1                      Rt   1
                                 1−    = (1 − eI )
                                               t+1          D
                                                              −          .
                                    ∆t                     Rt   ∆t
It follows immediately that if the probability of bankruptcy, eI , rises, then, ceteris paribus, the
                                                               t+1

return on capital, Rt , must rise. That is, the capital stock must fall.


                                                  35
       Second, suppose that the government transfer in the next period depends on the banks’ net
worth. Then, the banks’ FOC with respect to loans becomes
                                           µ          ¶µ         ¶
                           1          I      Rt    1        ∂T
                       1−    = (1 − et+1 )    D
                                                −       1+         ,
                          ∆t                 Rt    ∆t      ∂Qt+1
            ∂T
where      ∂Qt+1   denotes the partial derivative of the transfer with respect to the bank’s net worth.
Arguably, this derivative should be negative for undercapitalized banks. The stronger the bank is,
the less incentives it needs to refrain from bankruptcy, i.e., the less is the amount of the transfer
that would keep the bank operating. Thus, if the government is concerned with not letting a large
number of banks to fail, while spending a minimal amount of taxpayers money, a negative relation
between the transfer and net worth would emerge. Ceteris paribus, this would raise the return on
capital, implying a decline in the capital stock. While the negative relation between the expected
amount of government help and the banks’ net worth is only a conjecture, it appears consistent
with the behavior of most Japanese large banks. These banks were reluctant to boost shareholders’
capital and dispose of bad loans on their own.45 Instead, the banks preferred to “wait-and-see,”
meanwhile engaging in creative ways to hide the actual state of their balance sheets.
       The arguments above go through even if the deposit rate remains at its steady state level. In
particular, an increase in the probability of bankruptcy and the negative dependence of the transfer
on the net worth can push the return on capital above its steady state value, even if the government
lowers the capital adequacy requirement. That is, the bad loans problem can cause a recession even
in an economy in which banks can borrow freely from abroad.
       The bad loans problem and lending to ‘zombie’ firms. This paper does not reject the
possibility that other forces may have contributed to Japan’s slowdown. Most importantly, we
abstracted from the bank-firm relationships. A closer study of this relation by Caballero et al.
(2008) reveals an additional channel through which bad loans can cause a fall in economic activity.
In particular, Caballero et al. (2008) argue that because “most large Japanese banks would be out
of business if regulators forced them to recognize all their loan losses immediately” they “keep many
zombie (i.e. low productivity) firms alive by ever-greening their loans — rolling over loans that
they know will not be collected.” This contributes to the congestion of industries which have many
zombie firms and, therefore, discourages entry of new firms. In order for ‘loan ever-greening’ to
  45
       It must be noted that a significant number of banks issued new shares and subordinated debt to prevent their
capital from following too low. I thank the referee for pointing this out.


                                                          36
occur it must be the case that insolvent banks continue to receive deposits and enjoy government
guarantees and that entry into the banking sector is unprofitable. Otherwise, new banks would
enter and attract deposits, insolvent banks would fail and zombie firms would disappear.


6    Conclusions

This paper argued that the delay in the government bailout of the financial sector forces banks
to subtract resources from investment financing. Consequently, the economy falls into a prolonged
recession, which is characterized by declines in output, investment, labor, and TFP. These features
are consistent with Japan’s experience during the “lost decade.”
    To assess the quantitative effect of the delay in the government bailout we calibrated our model
using Japanese data. Our conservative estimate of the decline in output due to the delay in the
bailout ranges between 0.19 and 0.51 percent per year. When the magnitude of the bad loans
problem and the expectations about the bailout were set to match the decline in the investment-
output ratio observed in the data, the impact of the delayed bailout is a 0.92% yearly decline in
output.




                                                37
7       Appendix

                                         Parameter Values.


                     Parameter         Value in the             Value in the
                     or Quantity       Benchmark Model          Alternative Model
                           λ                  1.20                       —
                           γ                  0.85                       —
                           α                  0.38                     0.36
                           δ                 0.0735                    0.089
                            δ    ∗
                         μφ
                        K+μφδ
                                             0.0155                      —
                         R∗∗                  1.05                     1.05
                           ξ                   —                       0.949
                           ω                   —                       0.001
                         φO ∗∗
                         Y                     —                       0.296
                        Rf νκ ∗∗
                         Y                    0.09                       —
                           p                 0.024                     0.024
                           θ1                0.0803                   0.0803
                           θ2                0.0800                   0.0800
                          ψ0                  0.62                     0.62
                          Ψn                 2092.8                   2.3855
                          an
                           1              −2.63 · 105                 -927.4
                          an
                           2               2.63 · 105                 -927.4
                          am
                           1              −8.67 · 104                    —
                          am
                           2               8.67 · 104                    —
                          Ψm                 689.4                       —
                         M      ∗∗
                        M+N                   0.25                       —
                         g ∗∗
                         Y                    0.15                     0.15


    ∗   In the benchmark model, the total depreciation of capital is equal to δK + φδ μ. This quantity
in the steady state is equal to .089. Note that in this model ν t κ is not counted as capital. This is

                                                     38
in line with Atkeson and Kehoe (2005) findings for the U.S. manufacturing sector that about 8% of
the output is not accounted for by payments to either of capital or labor. Also, for a given choice
of    M
     M+N ,   the parameter φδ is set to absorb the remaining part of the firms’ gross profits.
     ∗∗   refers to the steady state values.




                                                   39
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                                                  44
                          Figure 1. Bank loans to nonfinancial corporate sector (Hayashi and Prescott, 2002).

           0.12


           0.10


           0.08


           0.06


           0.04
% of GNP




           0.02


           0.00


           -0.02


           -0.04


           -0.06
                   1984     1986           1988           1990             1992          1994          1996     1998
                                                                     years
                                                              Change in bank loans/GNP
                                  Figure 2. The response of the Economy to the Bad Loans Shock.
                         Aggregate Loans                                                                    Output
110                                                                          105

100                                                                          100

90
                                                                               95
80
                                                                               90
70
                                                                               85
60

50                                                                             80


40                                                                             75
 -2              0            2            4            6                       -2            0            2             4            6




                     Deposit and Loan Rates                                                        The Banks Share Prices
2.6                                                                            20


2.4
                                                                               15
2.2


 2                                                                             10

1.8
                                                                                5
1.6

1.4                                                                             0
  -2             0            2            4            6                       -2            0            2             4            6
       Notes. (i) The horisontal axes show the number of periods after the shock. (ii) Aggregate loans and output are plotted as % of their
       respective values in the non-stochastic steady state. (iii) Deposit and loan rates move very closely, the loan rate is always slightly
       higher than the deposit rate. (iv) The banks' share prices are normalized by the size of the banks' assets.
Table 1. Relative Weights of Industries, By Sector and Size of Capital.

                                all industry                                      manufacturing                                    non-manufacturing
      share of                      A        B         C         D       C+D        A       B            C         D       C+D       A       B       C        D     C+D

      capital stock               1.00      0.69      0.09      0.22      0.22      0.41      0.34     0.03      0.05      0.07         0.59   0.35   0.06   0.18   0.24

      operating profits           1.00      0.49      0.12      0.38      0.38      0.36      0.22     0.04      0.10      0.15         0.64   0.27   0.08   0.28   0.36

      current profits             1.00      0.49      0.12      0.39      0.39      0.42      0.26     0.05      0.10      0.15         0.58   0.22   0.07   0.29   0.36

      sales                       1.00      0.40      0.16      0.44      0.44      0.30      0.17     0.04      0.09      0.13         0.70   0.24   0.12   0.35   0.46
      Industry's
      contribution to GDP         1.00                                              0.26      0.11   see note1              0.15        0.74
      Size of capital: A is all sizes, B is 1 billion yen or over, C is 100 million yen to 1 billion yen, D is 10 to 100 million yen
      Main figures are 1990-2002( II quarter) averages.
      Note 1: break down of manufacturing sector on this line is on two groups:
      with employees above 300, and the rest. The former is in column B.



Table 2. Bank Dependence By Sector and Size of Capital.

                                          all industry                            manufacturing                          non-manufacturing
                                              A        B         C         D        A       B            C         D       A       B       C           D

      long term bank borrowing/             0.26      0.21      0.25      0.31      0.20      0.12     0.21      0.34      0.28         0.25   0.27   0.30
      total liabilities                     0.25      0.18      0.21      0.34      0.19      0.12      0.19      0.32      0.28        0.22   0.22   0.34

      total bank borrowing/                 0.45      0.38      0.48      0.51      0.37      0.28     0.41      0.52      0.48         0.44   0.50   0.50
      total liabilities                     0.42      0.34      0.43      0.50      0.34      0.26      0.39      0.49      0.44        0.37   0.44   0.50

      long term bank borrowing/             0.60      0.45      0.68      0.74      0.51      0.31     0.63      0.82      0.63         0.51   0.69   0.72
      long term liabilities                 0.55      0.39      0.58      0.72      0.47      0.30      0.56      0.75      0.58        0.43   0.59   0.71

      Size of capital: A is all sizes, B is 1 billion yen or over, C is 100 million yen to 1 billion yen, D is 10 to 100 million yen.
      Main figures are 1990-2002( II quarter) averages, small italics are levels as of August 2002.

      Source: White Paper on Small and Medium Enterprises (2001).
Table 3.A. Quantitative effect of bad loans in the benchmark calibrated model.
                                                              Bailout1         Average Decline2 in
                                            B3    Tax         Starts Ends      Output Firms’ Average         Capital      Labor
                                                  Increase4                             Productivity 5
                                             20      20         10      40      0.19          0.06              0.20        0.10
                                             30      30         10      42      0.28          0.08              0.29        0.14


Table 3.B. Quantitative effect of bad loans in the benchmark calibrated model with high discounting.
                                                              Bailout          Average Decline in
                                            B     Tax         Starts Ends      Output Firms’ Average         Capital      Labor
                                                  Increase                              Productivity
                                             20      20         10      45      0.34          0.11              0.35        0.17
                                             30      30         10      47      0.51          0.17              0.52        0.25

Table 3.C. Quantitative effect of bad loans in the alternative calibrated model.
                                                              Bailout          Average Decline in
                                            B     Tax         Starts Ends      Output Inverse of the         Capital      Labor
                                                  Increase                              Mark-up
                                             20      20         10      49      0.17          0.04              0.18        0.10
                                             30      30         10      50      0.25          0.06              0.26        0.15

Table 3.D. Quantitative effect of bad loans in the alternative calibrated model with high discounting.
                                                               Bailout         Average Decline in
                                            B     Tax          Starts Ends     Output Inverse of the         Capital      Labor
                                                  Increase                              Mark-up
                                             20      20         10      53      0.31          0.07              0.33        0.19
                                             30      30         10      59      0.47          0.11              0.49        0.29

Notes: 1) Periods after shock. 2) Average yearly decline, in percent. 3) Percent of GDP. 4) Percent increase in the labor income tax. 5) Scaled by (λ-γ).

				
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