1. Dynamic Network Performance with an Application to Japanese Cooperative Shinkin Banks 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. Efficiency Measures-Distance Functions Farrell (JRSS-1957), Shephard (1970) Data Envelopment Analysis-Charnes, Cooper, Rhodes (EJOR-1978) Färe, Grosskopf, and Lovell (Production Frontiers-1994) Directional Distance Functions-Chambers, Chung, and Färe (JET-1996, JOTA-1998), Färe and Grosskopf (2004)

3. Production With Undesirable Outputs Färe, Grosskopf, and Weber (Ecol. Ec.-2006)-Agriculture Färe, Grosskopf, Noh, and Weber (J.Econometrics-2005)- Färe, Grosskopf, Pasurka, and Weber (App. Ec- 2011)-Electric Utilities Fukuyama and Weber (2008, 2009, 2010, 2011)-Financial Institutions Rogers and Weber (2011)-Transportation

4. Standard Black Box Model x=(x 1,…x N ) inputs P(x)=the output possibility set ={(y,b): x can produce (y,b)} y=(y 1,…,y M ) desirable outputs b=(b 1,…,b J ) undesirable outputs

5. Directional Distance Function y b (b,y)(b,y) y+βgyy+βgy b-βgbb-βgb gygy gbgb P(x)

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

7. y b P(x d,x u ) 0 P(x d ’,x u ’)

8. DEA (CRS) Production Technology

10. y=loans, securities investments x d =desirable inputs=labor, physical capital, net assets (equity capital) b=non-performing (bad) loans x u =undesirable input=b t-1

11. Are deposits an input (x) or an output (y)? Both? Sealey and Lindley (J. of Finance -1977)-intermediation approach Hancock (JPE-1985)-User cost approach Core deposits=input Transaction deposits=output Berger and Humphrey (NBER-1992, EJOR-1997) Barnett and Hahm (J. Bus. Ec. Stat.-1994)-Banks produce the money supply Fukuyama and Weber (2010)-Deposits are an input to one stage of production and an output at another stage of production.

12. Network Production Models Färe and Grosskopf (Ec.Letters-1996, SEPS-2000) Färe and Whitaker (1996) (Dynamic and Network) Kao and Hwang (EJOR-2008) Tone and Tsutsui (EJOR-2009) Fukuyama and Weber (Omega-2010) Färe, Fukuyama, and Weber (IJISSC-2011) Akther, Fukuyama, and Weber (Omega-2012))

13. 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 ) y t =(y t 1,…,y t M ) b t =(b t 1,…,b t J ) z t =intermediate output=deposits

15. The Network Technology

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

17. Dynamic Models Färe and Grosskopf (1996, 1997) Bogetoft, Färe, Grosskopf, Hayes, and Taylor (JORSJ-2009) Färe, Grosskopf, Margaritis, and Weber (JPA- 2011)

18. Dynamic Model Production in period t-1 affects the technology in period t Intermediate output produced in the second stage of production= c t c t affects stage 2 production in period t+1 c t = carryover assets= Assets – Required Reserves – physical capital – loans - securities Bad loans produced in period t-1, b t-1, become an undesirable input in stage 1 production in period t Total output consists of final outputs and carryover assets

19. Dynamic Network Model (y=fy+c) P 1 (x t,b t-1 ) P 1 (x t+1,b t )P 1 (x t+2,b t+1 ) P2(ztP2(zt P 2 (z t+1, c t ) P 2 (z t+2, c t+1 ) x t,b t-1 xt+1xt+1 x t+2, ztzt z t+1 z t+2 (y t, b t ) (y t+1,b t+1 ) (y t+2,b t+2 ) btbt ctct c t+1 c t-1 b t+1, c t-1 ) b t+2 c t+2

20. Dynamic Network DEA Technology

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

22. And in the final period, T,

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

25. And in the final period, T,

26. Network Links: in t, In t+1, In t+2, Etc.

27. Dynamic links: Between t and t+1, Undesirable output at stage 2 in t becomes and input to stage 1 in t+1 Carryover assets from period t become an input to stage 2 in period t+1 Similar dynamic links between t+1 and t=2, etc.

28. 269 Japanese Shinkin Banks, 2002-2009 Shinkin Banks are cooperative Accept deposits from members, make loans (real estate and commercial) to member firms within a given prefecture. Decline in Shinkin banks from 401 to 271 during 1998-2011 and shrank in size relative to for profit Regional Banks and City Banks Research by Nishikawa (1973), Miyamura (1992), Miyakoshi (1993), and Hirota and Tsutsui (1992) has generally found some scale economies, not many scope economies. Fukuyama (1996) - large banks more technically efficient than small banks: better managerial oversight dominates any scale economies. Färe, Fukuyama, and Weber (2010)-ex ante merger gains: for infra- prefecture mergers biggest gains in Fukuoka and Saga, for inter-prefecture mergers, biggest gains between banks in Miyazaki and Nagasaki. Fukuyama and Weber (2008)-For profit regional banks were more efficient, had greater technical progress, but a higher shadow cost of reducing bad loans than cooperative Shinkin banks.

29. MeanStd. dev.Min.Max. y 1 =loans246.2321.718.62409.3 y 2 =securities118.8139.72.01119.1 c 1 +c 2 =carryover assets90.9111.25.41023.2 x 1 =labor412408352651 x 2 =physical capital7.29.70.269.3 x 3 =net assets (equity)23.827.70.9204.6 z=deposits431.0523.433.14263.6 b=non-performing loans 19.524.50.8211.9 Except labor, all variables in billions of Japanese yen deflated by the Japanese GDP deflator Descriptive Statistics (Pooled data 269 banks x 8 years, 2002-2009

30. Directional Vector Model uses a three period window: t, t+1, t+2 Need 4 years of data, t-1, t, t+1, t+2 Is the percent of mean inputs and undesirable outputs that can be contracted and percent of mean desirable outputs that can be simultaneously expanded.

31. meanStd. dev. Min.Max.# on frontier 2003-2005 0.0450.03900.23810 0.0450.03800.2259 0.0470.04200.2579 0.1370.11500.6746 Estimates for 2003-2005

32. Estimates of Dynamic Inefficiency

33. 2003-20052004-20062005-20072006-20082007-2009 Karatsu Shinkin Bankx Kanonji Shinkin Bankxx The Kyoto Shinkin Bankxxx Yamanashi Shinkin Bankx Sapporo Shinkin Bankx Johnan Shinkin Bankxx Choshi Shinkin Bankx Sawayaka Shinkin Bankx Osaka Higashi Shinkin Bank xxxx Himawari Shinkin Bankxxx Kochi Shinkin Bankxxxxx Frontier Banks

34. ActualOptimal t-value (prob>t) ActualOptimal t-value (prob>t) 2003-2005 83.4 (104.7) 53.9 (78.6) 10.81 (.01) 87.8 (107.9) 71.5 (100.2) 6.82 (.01) 2004-2006 87.8 (107.9) 70.2 (94.6) 7.28 (.01) 86.7 (108.7) 64.1 (87.1) 8.54 (.01) 2005-2007 86.7 (108.7) 63.4 (88.1) 8.5 (.01) 89.8 (106.0) 57.9 (75.2) 9.93 (.01) 2006-2008 89.8 (106.0) 56.4 (74.6) 10.53 (.01) 97.5 (117.8) 52.2 (80.1) 11.33 (.01) 2007-2009 97.5 (117.8) 48.7 (66.6) 11.67 (.01) 97.2 (119.4) 58.5 (94.9) 10.43 (.01) Optimal and Actual Values of Carryover Assets

35. Calculating optimal deposits from the intensity variables two

36. Mean (s)Min.Max. Mean (s)Min.Max. Mean (s)Min.Max. 2003-2005 0.869 (.097) 0.612 1.313 0.868 (.095) 0.516 1.190 0.893 (.082) 0.545 1.132 2004-2006 0.863 (.100) 0.511 1.362 0.870 (.095) 0.500 1.118 0.895 (.080) 0.544 1.114 2005-2007 0.868 (.099) 0.499 1.178 0.862 (.097) 0.479 1.115 0.903 (.077) 0.574 1.175 2006-2008 0.859 (.106) 0.473 1.268 0.856 (.097) 0.488 1.203 0.921 (.072) 0.646 1.253 2008-2009 0.855 (.099) 0.480 1.122 0.874 (.097) 0.546 1.328 0.922 (.070) 0.658 1.252 Ratios of Optimal Deposits to Actual Deposits

37. Extension Dynamic Luenberger Productivity Growth Policy Implication-”Easy to fix” versus “Hard to Break”