1. 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.

2. 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

3. 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

4. y1 y2 P( x d, x u ) 0 P( x d ’,x u ’)

5. y b P(x d,x u ) 0 P(x d ’,x u ’)

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

7. 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

8. The Network Technology

9. The two constraints First Stage Second Stage Can be rewritten as

10. 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

11. 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

12. Dynamic Network Technology

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

14. And in the final period, T,

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

17. And in the final period, T,

18. meanStd. dev.MinimumMaximum Required reserves153418342828591 Unused assets= iy 1 523281849851652 Loans= y 1 29510315161413165043 Investments=y 2 71391130369562793 NPL=b300977191740510 Capital=x 2 7571195506446 Equity=x 3 478318196527144249 Deposits=z38360458607049214787 Employees=x 1 3045527026024450 assets47182582679126301001 Table 1. Descriptive Statistics, 20 Banks, 2004 to 2009

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

20. t=1 in: 200520062007 0.024 (0.062) 0.039 (0.063) 0.022 (0.035) 0.044 (0.060) 0.023 (0.037) 0.029 (0.039) 0.044 (0.054) 0.039 (0.051) 0.042 (0.063) 0.112 (0.165) 0.101 (0.131) 0.093 (0.125) # of banks with 876 131110 # of banks with 999 889 Estimates

21. t=1 in: 200520062007 2160 (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