A Note on Productivity Change in European Co-operative Banks: The Luenberger Indicator Approach



This aggregate efficiency indicator is referred to as a structural efficiency indicator, and the
aggregate Luenberger productivity indicator (AL) is constructed as follows:9

KK

AL ∣∑ zt, ∑ zkk+ι

V k =1 k=1


K

Dt+ι∣ Σzt

V =1


K

Dt+11 Σ

V t =1


zt
zt+1


+ Dt


K
∑
t=1


ztt


Dt


K
∑
t=1


zt
zt+1


, (8)


Equation [8] allows similar decompositions to equation [6].

4. Data and Results

We use the dataset on European co-operative banks of Molyneux and Williams
(2005). Table 1 shows the number of cooperative banks in the sample by country and across
1996 to 2003. Clearly, the sample is dominated by observations of German and Italian co-
operative banks. Nevertheless, it must be noted that co-operative banking sectors have been
consolidated into a large entity in countries like the Netherlands.

Table 1: Number of Co-operative Banks & Observations: by Country, 1996-2003

1996

1997

1998

1999

2000

2001

2002

2003

Total

Austria

19

18

26

31

45

50

40

20

249

Belgium

10

9

8

7

7

7

7

6

61

Finland

1

1

1

1

1

1

1

1

8

France

64

67

70

101

106

104

91

83

686

Germany

1,012

993

1,184

1,171

1,069

974

816

370

7,589

Italy

181

428

417

475

482

500

477

132

3,092

Luxembourg

2

2

2

2

2

2

2

2

16

Netherlands

2

2

1

1

1

1

1

1

10

Portugal

1

1

1

1

2

2

2

1

11

Spain

10

15

13

8

11

15

13

7

92

All banks

1,303

1,537

1,723

1,798

1,726

1,656

1,450

623

11,816

Source: BankScope.

We construct aggregate efficiency and productivity measures for co-operative banks in
ten EU countries. Banks are assumed to produce four outputs: (i) total customer loans, (ii)
interbank loans, (iii) securities, and (iv) off-balance-sheet items, from two inputs: (v) fixed
assets and (vi) variable cost. The descriptive statistics are shown in Table 2.

9 See Fare and Primont (2003) and Fare and Grosskopf (2004) for discussion of the aggregation of the
Luenberger productivity indicator.



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