Dynamic Network Performance with an Application to Japanese Cooperative Shinkin Banks

1. Dynamic Network Performancewith an Application to Japanese Cooperative Shinkin Banks Hirofumi Fukuyama1* and William L. Weber2 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 y=(y1,…,yM) desirable outputs b=(b1,…,bJ) undesirable outputs P(x)=the output possibility set ={(y,b): x can produce (y,b)} x=(x1,…xN) inputs

5. Directional Distance Function y y+βgy P(x) (b,y) gy b gb b-βgb

6. y1 P(xd, xu) P(xd’,xu’) y2 0

7. y P(xd,xu) P(xd’,xu’) 0 b

8. DEA (CRS) Production Technology

10. y=loans, securities investments xd=desirable inputs=labor, physical capital, net assets (equity capital) b=non-performing (bad) loans xu=undesirable input=bt-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 y t=(yt1,…,ytM) bt=(bt1,…,btJ) Stage 2 P2(z)={(y,b) that can be produced by z} zt=intermediate output=deposits Stage 1 P1(x,b)={z that can be produced by (x,b)} xt=(xt1,…xtN), bt-1=(bt-11,…bt-1J)

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= ct ctaffects stage 2 production in period t+1 ct= carryover assets= Assets – Required Reserves – physical capital – loans - securities Total output consists of final outputs and carryover assets Bad loans produced in period t-1, bt-1, become an undesirable input in stage 1 production in period t

19. Dynamic Network Model (y=fy+c) (yt, bt) (yt+1,bt+1) (yt+2,bt+2) ct ct+1 P2(zt P2(zt+1, ct) ct-1 P2(zt+2, ct+1) ct+2 , ct-1) zt zt+1 zt+2 P1(xt,bt-1) P1(xt+1,bt) P1(xt+2,bt+1) bt+2 xt,bt-1 xt+1 bt xt+2, bt+1

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. Descriptive Statistics (Pooled data 269 banks x 8 years, 2002-2009 Except labor, all variables in billions of Japanese yen deflated by the Japanese GDP deflator

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

31. Estimates for 2003-2005

32. Estimates of Dynamic Inefficiency

33. Frontier Banks

34. Optimal and Actual Values of Carryover Assets

35. Calculating optimal deposits from the intensity variables two

36. Ratios of Optimal Deposits to Actual Deposits

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