Has Competition in the Japanese Banking Sector Improved?

competition, whereas θ_i,t = S_i,t for Cournot competition. From (3) and (4), we obtain:⁶

1          ∂C ∂C

P_t (1--θ_{i t}) = rd + —iʌ + —

t               i,t        i,t _{∂d ∂}

^ηt                      i,t      ^qi,t

On the other hand, if the banks are maximizing their joint profits, represented as
P_t (Q_t)Q_t +∑ⁿ (r_i^b_,tb_i,t -r_i,^d_td_i,t -C_i,t(q_i,t,d_i,t)), the first order condition can be expressed as
i=1

equation (5) with θ_i,t = 1 . Furthermore, S_i,t < θ_i,t < 1 represents an array of repeated

game equilibria whose one-shot game is Cournot oligopoly.

Rearranging (5) and defining R_i,t ≡ P_tq_i,t to represent the revenue of bank i generated

by loans, we obtain the following equation:

θ _d        ∂C_it      ∂C_it

R_lt = R- r_i^d_tq_it + q_it——+q_it——.                   (6)

i,t                i,t       i,t i,t        i,t                    i,t

^ηt                   ^∂di,t       ^∂qi,t

θ_t represents the degree of competition. Note that we have dropped out the subscript i

for θ in order to capture the industry average degree of competition.⁷

Because the marginal cost is not observable, we assume the translog cost function:

ln Ctt = ao⁺ aιlⁿ ⅛,_t ⁺¹ a₂(lⁿ ‰^)2+a3l^{n d}i,t⁺¹ a4(^ln d_i,_t⁾²+^a5ln wt +¹ aXln wt⁾²

^,           _______^, 2          ^,__^, 2 _______^,________ ^, 2           ^,           (7)

+a₇(lnq_i,t)(lnw_i,t) +a₈(lnq_i,t)(lnd_i,t) +a₉(lnd_i,t)(lnw_i,t) +ε_i^C_,t,

where w_i,t stands for the wage rate of bank i, ε_i^C_,t is an error term, and variables

with upper bars are the deviations from their means. Given equation (7), our regression

⁶ Equation (3) can be estimated instead of equation (5). Estimation of equation (3), however, did
not generate reasonable results. The reason for the poor results may be that, in the estimation, we
should use as r_i^b_,t the data for securities including stocks, instead of the data for government bonds,
because the revenues from government bonds are not reported. In Japan, however, considerable
parts of stocks are held as the mutual holding, which is not determined based on the short-run
incentives. In addition, although bond yields should include capital gains and losses, they are not
incorporated in the reported data of r^b . Therefore, we present the results based on equation (5).

⁷ See Bresnahan (1989) for this point.

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