A Dynamic Network Production Model for Bangladeshi Banks Seyd Akther 1, Hirofumi Fukuyama 1* and William L. Weber 2 1. Faculty of Commerce, Fukuoka University, Japan 2. Department of Economics and Finance, Southeast Missouri State University, U.S.A.

Standard Black Box Model x=(x 1,…x N ) inputs P(x)=the output possibility set y=(y 1,…,y M ) desirable outputs b=(b 1,…,b J ) undesirable outputs

y=loans, securities investments x=labor, physical capital, equity b=non-performing (bad) loans b t-1 is an undesirable input that impacts the period t technology b t is an undesirable output for the period t technology that becomes an undesirable input for the period t+1 technology Bank Production Model-Asset Approach

y1 y2 P( x d, x u ) 0 P( x d ’,x u ’)

y b P(x d,x u ) 0 P(x d ’,x u ’)

z=intermediate output=deposits Are deposits an input or an output? Both? Core deposits=input Transaction deposits=output

A Two Stage Network Model Stage 1 P 1 (x,b)={z that can be produced by (x,b)} Stage 2 P 2 (z)={(y,b) that can be produced by z} x t =(x t 1,…x t N ), b t-1 =(b t-1 1,…b t-1 J ), Final Outputs y t =(y t 1,…,y t M ) b t =(b t 1,…,b t J ) z t =intermediate output

The Network Technology

The two constraints First Stage Second Stage Can be rewritten as

Dynamic Model Production in period t-1 affects the technology in period t Intermediate output produced in the second stage of production= iy t iy t affects stage 2 production in period t+1 iy t = Assets – Required Reserves – physical capital – loans - securities We will assume that intermediate and final outputs are additive fy t + iy t

Dynamic Network Model P 1 (x t,b t-1 ) P 1 (x t+1,b t )P 1 (x t+2,b t+1 ) P 2 (z t P 2 (z t+1, iy t ) P 2 (z t+2, iy t+1 ) x t,b t-1 x t+1 x t+2, ztzt z t+1 z t+2 (fy t,b t )(fy t+1,b t+1 ) (fy t+2,b t+2 ) btbt iy t iy t+1 iy t-1 b t+1, iy t-1 )iy t+2 b t+2

Dynamic Network Technology

In the intermediate periods, t=2,…,T-1

And in the final period, T,

In the intermediate periods, t=2,…,T-1

And in the final period, T,

meanStd. dev.MinimumMaximum Required reserves Unused assets= iy Loans= y Investments=y NPL=b Capital=x Equity=x Deposits=z Employees=x assets Table 1. Descriptive Statistics, 20 Banks, 2004 to 2009

The choice of directional vector: will be the percent of the mean Let T=3.

t=1 in: (0.062) (0.063) (0.035) (0.060) (0.037) (0.039) (0.054) (0.051) (0.063) (0.165) (0.131) (0.125) # of banks with # of banks with Estimates

t=1 in: (1812) 1564 (1039) 5309 (11309) 1588 (1092) 5191 (11349) 4986 (10299) 874 (1903) 605 (1128) 768 (2801) 2868 (2482) 3463 (3948) 6768 (11773) 3463 (3948) 6768 (11773) 6446 (10935) 6768 (11773) 6446 (10935) 8011 (10214) Actual and optimal unused assets