A Generalized Stochastic Frontier Analysis (Tables)

Table 1: Summary Statistics Variable Mean Standard Minimum Maximum Deviation Number of Observations Stage 1 Ln(Output norm) 7.48 2.30 -0.09 13.32 1431 Ln(Deposits) 7.62 2.59 -4.61 13.52 1431 Ln(Labor) 3.60 2.37 -3.91 9.19 1431 Ln(Capital) 2.88 1.95 -3.22 8.00 1431 Ln(θinv ) -0.20 0.62 -6.47 0.42 1431 Ln(Technical Efficiency) -0.40 0.23 -1.82 -0.02 603 Ln(No. of Branch) 6.08 1.49 0.00 9.35 603 Ln(Capital Adequacy Ratio) 2.46 0.37 -2.81 4.10 603 Stage 2 Notes: Stage 1 variables are measured in millions of Indian rupees Table 2: Measuring Technical Efficiency with Unbalanced Panel Dependent Variable: Ln(Output) Variables Ln(Deposit) Ln(Output) 0.191*** (0.012) Ln(Labor) 0.299*** (0.021) Ln(Capital) 0.409*** (0.026) Ln(θinv (rad)) 0.034* (0.020) Yearid 0.044*** (0.004) Constant 3.686*** (0.089) η -0.030*** (0.006) Observations Number of Companyid Waldχ2 (5) 1431.00 125.00 7565.12 Notes: ***p<0.01, *p<0.1. Standard errors in parentheses. Coefficient estimates of ln(Deposit), ln(Labor), and ln(Capital) represent elasticity of output with respect to deposit, labor and capital respectively. Estimated coefficient of Yearid represents change in the actual output due to technological changes over time. Sign of estimated η implies the direction of change in technical efficiency over time. Table 3: Average Technical Efficiency Scores Based on Ownership All Banks Public Private Indian Private Foreign Private Year TE No. of Banks TE No. of Banks TE No. of Banks TE No. of Banks TE No. of Banks 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 78.92 80.81 79.82 75.22 72.31 71.95 70.88 68.72 64.58 63.84 63.36 61.80 61.54 60.47 60.12 59.59 59.69 58.48 59.48 61.00 71.11 4 10 21 31 55 63 82 89 101 103 102 101 100 95 97 97 92 92 85 78 31 84.00 86.43 84.72 84.41 78.93 77.66 75.98 75.55 75.01 74.39 74.90 74.09 73.45 74.04 73.40 72.73 71.82 71.14 71.45 70.77 73.04 2 5 12 15 20 24 29 30 32 32 31 31 31 30 30 30 31 31 30 30 23 73.84 75.19 73.09 66.64 68.75 68.40 67.90 65.19 59.68 58.96 58.11 56.48 56.39 54.22 54.20 53.45 53.20 51.59 52.58 54.89 65.56 2 5 9 16 35 39 53 59 69 71 71 70 69 65 67 67 61 61 55 48 8 82.92 73.59 69.34 68.43 67.59 67.82 66.73 65.07 64.27 63.96 61.73 62.94 58.22 55.48 53.38 52.49 51.05 53.30 57.03 65.58 0 1 5 9 13 16 26 27 29 29 27 27 25 27 31 33 32 31 26 21 6 73.84 73.26 72.59 63.55 72.58 68.89 67.98 63.95 55.94 55.37 54.54 53.14 52.73 51.22 53.04 53.51 53.92 52.08 52.00 53.23 65.52 2 4 4 7 22 23 27 32 40 42 44 43 44 38 36 34 29 30 29 27 2 Total 63.73 74.43 57.96 Note: All technical efficiency values are expressed in percentage terms. 60.34 56.09 Table 4: Effects of Financial Reforms on Technical Efficiency - Unbalanced Panel Dependent Variable: Ln(Technical Efficiency) Variables Ln( No. of Branch) Ln(Capital Adequacy Ratio) 1993-1996 1998-2001 2002-2005 2006-2009 Constant Observations Adj. R-squared Number of companyid (1) (2) (3) All Banks Public Private 0.002 -0.013 0.009 (0.005) (0.024) (0.006) -0.009* -0.008 -0.011* (0.005) (0.006) (0.007) 0.028*** 0.009 0.038*** (0.008) (0.006) (0.011) -0.019*** -0.017*** -0.027*** (0.004) (0.003) (0.007) -0.062*** -0.054*** -0.077*** (0.006) (0.006) (0.010) -0.103*** -0.087*** -0.131*** (0.008) (0.009) (0.015) -0.333*** -0.154 -0.442*** (0.034) (0.171) (0.030) 603 319 284 0.718 0.749 0.74 72 30 42 *** p<0.01, * p<0.10. Robust standard errors clustered at bank level in parentheses. A one percent increase in CAR results in a 0.009% decrease in technical efficiency for All banks in the sample. Estimates of the year-dummies show effects of different phases of reforms. Reform coefficient estimates are negative and significant at the 1% level for All banks in the sample 50 Technical Efficiency 60 70 80 90 Figure 1: Average Technical Efficiency Scores of Sample Banks 1990 1995 2000 Year All Private Foreign Private 2005 Public Indian Private 2010 Appendices A Description of Variables Investment- Investment in assisted companies, shares, mutual funds, government securities, etc. Loans - Loans and advances made by banks. Deposits - Deposits accepted by commercial banks. There are three types of deposits: demand deposits, savings deposits and term deposits. This data field captures the total deposits collected and outstanding with the bank. Labor - Measured by compensation to employees. It includes payments made in cash or kind by companies to their employees. Such expenses include salaries, bonus, contribution to provident funds, training costs, and other labor related expenses. Capital - Sum of expenses on power, fuel and water, payment of indirect taxes e.g. service tax, rents and lease rents, repair expenses, printing and stationary expenses and depreciation. Output - Eucledian norm of two types of output vectors - investment, and loans and advances. Capital Adequacy ratio - Banks are required to maintain a certain amount of capital in relation to other assets, such as, loans and investments as a cover against possible losses in these assets. Capital adequacy ratio is the percentage of the total capital funds to the total risk-weighted assets. B Generalized Stochastic Production Frontier A multiple-output generalized stochastic production model (Löthgren(1997)) defines a ray production function based on polar coordinates, allowing for the primal-based estimation of multiple output production frontiers and bank specific technical efficiencies that vary over time. The output mix is represented by the output polar-coordinate angles. For a given output mix and input level, the generalized production function, also known as the ray production function, gives the maximum Euclidean norm of the output vector that is attainable given the technology. Formally, for a production technology with multiple inputs, x ∈ Rd+ , that are used to produce multiple outputs y ∈ R+p , the generalized production function represents the output vector in polar-coordinate form as y = l · m(θ) where l = l(y) = kyk = p P i=1 (B.0.1) !1/2 y2i denotes the Euclidean norm of the outputs, m(θ) = y/ kyk represents the transformation function of the polar-coordinate angles θ to the output mix vector. The function m : [0, π/2] p−1 → [0, 1] p is defined in terms of the output polar-coordinate angles as mi (θ) = cosθi i−1 Y sinθ j , i = 1, ..., p (B.0.2) j=0 where θ ∈ [0, π/2] p−1 , and sinθ0 = cosθ p = 1. The polar coordinate angles θ are obtained recursively from the inverse transformation m−1 (y/ kyk) as   i−1 Y   θi (y) = cos yi / kyk sinθ j  , i = 1, ..., p −1 (B.0.3) j=0 The first angle is given by θ1 = cos−1 (y1 / kyk), which is used in the calculation of the second angle θ2 = cos−1 (y2 / kyk sinθ1 ). The remaining angles θi , i = 3, ..., p − 1 are calculated following continuous recursion. The ray production function, as illustrated by Löthgren(1997), is closely related to the output distance function in (Shephard (1970)). This output distance function is defined as D0 (x, y) = min {δ > 0 : y/δ ∈ P(x)} (B.0.4)  where, P(x) = y ∈ R+p : x can produce y is the output set. Given weak disposability of outputs11 , the output distance function provides a complete representation of the technology (Färe (1988)) in the sense that D0 (x, y) ≤ 1 ⇔ y ∈ P(x) (B.0.5) The isoquant of the output set, or the output frontier is defined as I soqP(x) = {y : y ∈ P(x), λy < P(x), λy > 1} (B.0.6) If D0 (x, y) = 1, then the output is technically efficient and belongs to the output frontier. On the other hand, D0 (x, y) < 1 signifies technical inefficiency or output being lower than the frontier level. The ray production function provides a generalization of the single-output production function to multiple-output technologies as output distance function. Formally, the ray production function is given by f (x, θ) = max {l ≥ 0 : l · m(θ) ∈ P(x)} (B.0.7) The output distance function is given by the ratio of the output norm to the frontier output norm (Färe (1988)). Since, by definition y = l · m(θ) and f (x, θ) · m(θ) belongs to the isoquant (frontier) of the output set, the distance function can be expressed in terms of the ray production function as D0 (x, y) = kyk / y f = kyk / f (x, θ) (B.0.8) The curvature of the production frontier can be derived from the partial derivatives of the ray function with respect to the polar-coordinate angles, ∂ f (x, θ)/∂θi , i = 1, ..., p − 1. For a given level of inputs, ∂ f (x, θ)/∂θi captures the change in the output norm when the output mix changes along the frontier (Gerdtham et al. (1999)). For example, for a technology with three outputs, the first angle θ1 represents the angle from y1 axis towards the plane spanned by the y2 and y3 axis. θ2 represents the angle between y2 and y3 in the y2 − y3 plane. Therefore, the derivative ∂ f (x, θ)/∂(θ1 ) represents the change of the frontier output norm for changes in 11 Weak disposability of outputs implies that proportional reduction in inputs is feasible. the output mix along the output frontier with fixed proportions between y2 and y3 . Similarly, ∂ f (x, θ)/∂(θ2 ) represents the change of the frontier output norm for changes in the output mix with the level of y1 held constant. A ray production function for a two-output technology is illustrated in Figure 2. y2 yf y θ P (x) y1 Figure 2: P(x) is the output set. The output mix of the output y is represented by the angle θ. y f = f (x, θ) · m(θ)is the ray production function or the frontier output. Output y is technically inefficient. C Balanced Panel Regression Results Table 5: Measuring Technical Efficiency with Balanced Panel (1995-2007) Dependent Variable: Ln(Output) Variables Ln(Deposit) Ln(Output) 0.659*** (0.022) Ln(Labor) 0.065*** (0.018) Ln(Capital) 0.156*** (0.025) Ln(θinv (rad)) -0.050*** (0.015) Yearid 0.081*** (0.007) Constant 2.106*** (0.161) η -0.051*** (0.007) Observations Number of companyid Waldχ2 (5) 579.00 46.00 4303.76 Notes: ***p<0.01, *p<0.10. Standard errors in parentheses. Coefficient estimates of ln(Deposit), ln(Labor), and ln(Capital) represent elasticity of output with respect to deposit, labor and capital respectively. Signs of estimated η implies the direction of change in technical efficiency over time. Table 6: Effect of Reforms on Technical Efficiency - Balanced Panel (1995-2007) Dependent Variable: Ln(Technical Efficiency) Variables Ln(No. of Branch) Ln(Capital Adequacy Ratio) 1998-2000 2001-2003 2004-2007 Constant Observations Adj. R-squared Number of companyid (1) (2) (3) All Banks Public Private -0.093* -0.054 -0.114** (0.049) (0.046) (0.048) -0.014** -0.019 -0.014*** (0.006) (0.011) (0.004) -0.075*** -0.067*** -0.107*** (0.009) (0.005) (0.021) -0.197*** -0.184*** -0.240*** (0.011) (0.008) (0.024) -0.356*** -0.333*** -0.420*** (0.016) (0.014) (0.030) -0.016 -0.179 -0.104 (0.325) (0.337) (0.252) 313 212 101 0.889 0.897 0.898 35 22 13 *** p<0.01, ** p<0.05, *p<0.10. Robust standard errors clustered at bank level in parentheses. D Table: Average Bank Technical Efficiency Scores Average Technical Efficiency Scores of Banks – Highest to Lowest Bank TE Rank I D B I Bank Ltd 97.82 1 Bank of Nova Scotia 94.04 2 British Bank of the Middle East 93.91 3 Antwerp Diamond Bank N V 93.91 4 State Bank of India 93.11 5 Jammu & Kashmir Bank Ltd. 92.07 6 I C I C I Bank Ltd. 92.06 7 Indusind Bank Ltd. 91.38 8 Bank of India 89.19 9 Global Trust Bank 84.94 10 Oriental Bank of Commerce 84.34 11 Sakura Bank Ltd. 84.13 12 Credit Lyonnais 82.98 13 UCO Bank 82.66 14 Union Bank of India 81.87 15 State Bank of Patiala 81.8 16 Bank of Baroda 81.69 17 Indian Overseas Bank 80.71 18 Canara Bank 80.62 19 Axis Bank Ltd. 80.44 20 Central Bank of India 80.28 21 State Bank of Hyderabad 79.88 22 Punjab National Bank 79.68 23 Bank of America 79.64 24 Corporation Bank 79.53 25 continued on next page Table continued from previous page Bank TE Rank United Bank of India 78.36 26 Federal Bank Ltd. 78.08 27 Karnataka Bank Ltd. 77.48 28 State Bank of Travancore 76.53 29 Abu Dhabi Commercial Bank 76.01 30 Allahabad Bank 74.91 31 Syndicate Bank 74.78 32 Indian Bank 74.51 33 American Express Intl. Banking Corpn. 73.61 34 State Bank of Indore 72.07 35 J P Morgan Chase Bank 70.81 36 H D F C Bank Ltd. 69.84 37 Vijaya Bank 69.36 38 Pinakini Grameena Bank 68.98 39 Bank of Maharash 68.77 40 I D B I Bank Ltd. 68.75 41 Toronto-Dominion Bank 68.34 42 I N G Vysya Bank 68.29 43 Andhra Bank 68.13 44 State Bank of Mysore 67.63 45 State Bank of Bikaner & Jaipur 67.55 46 Karur Vysya Bank 67.03 47 Yes Bank Ltd. 66.83 48 A B N-Amro Bank N V 66.8 49 U F J Bank Ltd. 66.22 50 Punjab & Sind Bank 66.09 51 South Indian Bank 65.82 52 continued on next page Table continued from previous page Bank TE Rank Citibank N A. 65.74 53 Standard Chartered Bank 65.39 54 City Union Bank 65.33 55 United Western Bank 64.92 56 Societe Generale 64.64 57 Sumitomo Bank Ltd. 64.42 58 Dena Bank 63.86 59 Calyon Bank 63.79 60 State Bank of Saurashtra 63.28 61 Banque Nationale de Paris 62.84 62 Tamilnad Mercantile Bank Ltd. 62.18 63 State Bank of Mauritius Ltd. 60.86 64 Hongkong & Shanghai Bank 60.72 65 Lakshmi Vilas Bank Ltd. 58.61 66 Times Bank Ltd. 57.82 67 Bank of Punjab Ltd. 57.67 68 Development Credit Bank Ltd. 56.48 69 Bank of Rajasthan Ltd. 55.26 70 Deutsche Bank A G 55.11 71 D B S Bank Ltd. 54.48 72 Standard Chartered Grindlays Bank Ltd. 54.39 73 S B I Commercial & International Bank Ltd. 54.15 74 Bank of Tokyo-Mitsubishi U F J Ltd. 53.1 75 Benares State Bank Ltd. 52.82 76 Siam Commercial Bank 51.88 77 Mizuho Corporate Bank Ltd. 51.4 78 Bank of Madura Ltd. 51.34 79 continued on next page Table continued from previous page Bank TE Rank Nedungadi Bank Ltd. 51.06 80 Dhanalakshmi Bank Ltd. 50.55 81 Sangli Bank Ltd. 50.21 82 50 83 Centurion Bank of Punjab Ltd. 49.67 84 Barclays Bank Plc. 49.52 85 B N P Paribas 49.51 86 Kotak Mahindra Bank Ltd. 49.24 87 Bank of Ceylon 48.38 88 Bharat Overseas Bank Ltd. 47.78 89 Ganesh Bank of Kurundwad Ltd. 46.15 90 Bank of Bahrain 45.75 91 Chase Manhattan Bank N A 45.57 92 Mashreqbank P S C 45.47 93 Nainital Bank Ltd. 44.27 94 Vinayak Local Area Bank Ltd. 43.33 95 Lord Krishna Bank Ltd. 43.22 96 Bareilly Corporation Bank Ltd. 42.16 97 Oman International Bank 41.75 98 Sumitomo Mitsui Banking Corpn. 38.6 99 American Express Bank Ltd. 38.43 100 Ratnakar Bank Ltd. 36.39 101 Santhal Parganas Gramin Bank 36.22 102 I N G Bank N V 35.93 103 Karad Urban Co-op Bank Ltd. 35.73 104 Mapusa Urban Co-op Bank Ltd. 35.69 105 Shinhan Bank 35.22 106 Catholic Syrian Bank Ltd. continued on next page Table continued from previous page Bank TE Rank Cho Hung Bank 33.81 107 Commerzbank A G 32.92 108 Bank Muscat S A 32.83 109 Chinatrust Commercial Bank 32.37 110 Mahakaushal Kshetriya Gramin Bank 32.17 111 Capital Local Area Bank Ltd. 30.94 112 K B C Bank N V. 30.35 113 Shri Arihant Co-op Bank Ltd. 29.21 114 Dresdner Bank A. G. 26.14 115 Sree Narayana Guru Co-op Bank Ltd. 22.39 116 Bank International Indonesia 21.52 117 Krishna Bhima Bank Ltd. 18.11 118 A B Bank Ltd. 17.05 119 Oversea-Chinese Banking Corpn. Ltd. 16.77 120 Shreeji Bhatia Co-op Bank Ltd. 16.47 121 Bank Muscat Al Ahli 14.9 122 Krung Thai Bank 11.81 123 South Gujarat Local Area Bank Ltd. 10.69 124 Sonali Bank 8.04 125