1. Measuring Technical Efficiency in the Canadian P&C Insurance Industry Using DEA Gilles Bernier, Ph.D., Industrial-Alliance Insurance Chair, Laval University, Quebec City Komlan Sedzro, Ph.D., University of Quebec at Montréal WRIA Meeting, Las Vegas, January 4, 2004.

2. Outline of Presentation Introduction Purpose Literature Review: Efficiency Measurement Concepts Efficiency in Canadian P&C Insurance: Prior Studies Estimating Efficiency with DEA: A basic example Data Measures of Outputs/Inputs and their Prices Results Implications of Results Limitations of Study

3. Introduction The Canadian P/C Market 2.53% of the world market (7 th ) Currently, 198 companies are monitored for financial soundness by OSFI (93 Canadian, 105 Foreign). P/C is a less concentrated market than L/H: –Specific regional markets or specific product lines. Top 5 MS in 2001: 34% (CGU Group Canada, ING Canada, Co-operators Group, Royal & Sun Alliance, Economical Ins.Group) Broker Co’s still have a dominant MS of 67% in 2001 (24% for Direct Writers and 9% for Reinsurers only)

4. Purpose Our goal is to rely on frontier methodologies to measure firm performance relative to “best practice” frontiers derived from firms operating in the Canadian P&C industry (benchmarking). Using the technique called DEA to estimate cost efficiency frontiers, we hope to be able to answer to the following research questions: –Are P&C Insurers Operating in Canada Technically Efficient? –What can be said about the degree of « Scale Economies » in the Canadian P&C Industry?

5. Literature Review Efficiency Measurement Concepts For a specific firm, cost efficiency (the firm’s success in minimizing costs) can be decomposed as follows: Cost = Technical x Allocative Efficiency Efficiency Efficiency where, Technical = Pure Technical x Scale Efficiency Efficiency Efficiency Pure technical efficiency measures the firm’s success in using the best available technology. Scale efficiency indicates whether the firm is operating with IRS, DRS or CRS (ideal). Allocative efficiency measures the firm’s success in minimizing operating costs by choosing the optimal mix of inputs.

6. Efficiency in Canadian P&C Prior Studies In a study of the Canadian P&C insurance industry using a translog cost function, Suret (1991) concludes as follows: –“Our evidence of slight economies of scale and no economies of scope is compatible with observation that many insurance companies in Canada are small and undiversified”. U of T’s CMTE has an ongoing research program on firms’ performance in the Canadian financial services industry (Banks, Mutual Funds, P&C Insurers): –Hewlitt (1998) uses DEA to measure the relative efficiency of 120 Canadian P&C insurers. She concludes that variable returns to scale (VRS) exist in the industry.

9. SOLVING THE « LP »MODEL FOR DMU # 3 Min ,  Subject to: -y 3 + (y 1 1 + y 2 2 + y 3 3 + y 4 4 + y 5 5 ) ≥ 0,  x 13 – (x 11 1 + x 12 2 + x 13 3 + x 14 4 + x 15 5 ) ≥ 0,  x 23 - (x 21 1 + x 22 2 + x 23 3 + x 24 4 + x 25 5 ) ≥ 0, ≥ 0, where = ( 1, 2, 3, 4, 5 )′.

13. Data Sources: –A. M. Best’s WinTRAC 2000 (P&C) for yearly financials (drawn from the regulatory annual statements filed by insurers with OSFI) and ratings. –Statistics Canada (Catalogue No.72-002-XPB) for the wage variables of labor inputs (agents and business services). –Bank of Canada’s Web site for average yearly risk- free rates (10-year Gov. Bonds) for cost of equity capital estimation. Period covered: 1996-2000 Sample: We eliminated firms with unusual characteristics and/or incomplete information. Final sample consisted of 92 firms per year (70 Canadian, 22 Foreign).

14. Measures of Outputs/Inputs and their Prices Inputs Input Prices Agent labor Real wages rates for insurance agents Business services Real wages rates for business services Property investment Price = 1 Equity capital Three-tier estimates of cost of equity capital (CAPM-type) based on ratings Outputs Reserves Invested Assets

15. Table 1 Technical Efficiency (TE) CRSVRS AverageStd-devAverageStd-dev 199668.45 %23.56 %80.13 %20.23 % 199771.56 %22.35 %82.18 %19.50 % 199868.21 %22.60 %79.22 %18.71 % 199975.12 %20.92 %82.60 %17.75 % 200073.08 %20.78 %82.32 %18.44 %

16. Table 2 TE - Canadian vs Foreign (CRS) 19961997199819992000 Canadian- Canadian 65.51 %68.87 %65.70 %72.72 %69.85 % Foreign- Foreign 77.81 %80.10 %76.21 %82.74 %83.37 %

17. Table 3 TE - Canadian vs Foreign (VRS) 19961997199819992000 Canadian- Canadian 79.33%80.93 %78.80 %81.34 %80.17 % Foreign- Foreign 82.67%86.15%80.55 %86.61 %89.17 %

18. MAIN RESULTS FOR “TE” - Table 1 shows that, average TE (CRS) reached a peak of 75% in 1999. Overall, results show a rather weak performance over the period 1996-2000. -Tables 2 and 3, indicate that foreign companies have shown higher TE, than domestic insurers over the entire period.

19. Table 4 Cost Efficiency (CE) AverageStd-dev 199626.08 %17.38 % 199728.64 %20.21 % 199812.07 %17.10 % 19999.99 %13.01 % 200023.61 %18.53 %

20. Table 5 CE - Canadian vs Foreign 19961997199819992000 Canadian- Canadian 21.46 %23.91 %9.38 %6.73 %17.93 % Foreign- Foreign 40.81 %43.65 %20.62 %20.36 %41.66 %

21. MAIN RESULTS FOR “CE” -On average, P&C insurers operating in Canada have shown rather low CE, especially in 1999 (with only 10%) as shown in Table 4. -When it comes to CE, foreign P&C insurers have a much better average performance (42%) than domestic ones (18%), as shown in Table 5.

22. Table 6 Allocative Efficiency (AE) AverageStd-dev 199637.71 %17.60 % 199739.13 %20.23 % 199816.15 %17.33 % 199912.60 %12.71 % 200031.35 %19.27 %

23. Table 7 AE - Canadian vs Foreign 19961997199819992000 Canadian- Canadian 33.66 %35.07 %13.47 %9.45 %26.1% Foreign- Foreign 50.61 %52.06 %24.67 %22.61 %48.2 %

24. MAIN RESULTS FOR “AE” -As expected, Table 6 shows that AE is also very weak (about 31% in Y2000). -It appears to be due mostly to domestic insurers as indicated in Table 7. For example, AE for domestic insurers was only 26% in Y2000 compared to 48% for foreigners.

25. Table 8 Scale Efficiency (SE) AverageStd-dev 199686 %19 % 199789 %15 % 199886 %17 % 199991 %14 % 200089 %14 %

26. Table 9 % of Companies Operating with DRS, CRS and IRS DecreasingConstantIncreasing 199640.22 %16.30 %43.48 % 199735.87 %19.57 %44.57 % 199830.43 %17.39 %52.17 % 199931.52 %21.74 %46.74 % 200039.13 %20.65 %40.22 %

27. Table 10 SE - Canadian vs Foreign 19961997199819992000 Canadian- Canadian 82.87 %87.94 %83.55 %89.40 %87.43 % Foreign- Foreign 94.11 %93.96 %93.26 %95.36 %93.50 %

28. MAIN RESULTS FOR “SE” -As indicated in Table 8, SE averages were very high during the period 1996-2000 (near or just below 90%), while standard deviations were low. -From Table 9, we see that more insurers were operating with CRS in 2000 compared to 1996. However, in Y2000, the vast majority of insurers (about 80%) were still operating with either DRS or IRS. -Domestic insurers have shown weaker SE scores than foreign insurers over the entire period according to Table 10 (e.g. 87% vs 94% in Y2000).

29. Table 11 - Industry Leaders Companies # of times in dominating sets TE (CRS) TE (VRS) PTECEAE Commerce & Industry Insurance Company Of Canada 48100% 34.65% ACE INA Insurance 45100% 46.33% Lloyd's Underwriters 28100% 9.99% Coachman Insurance Company 26100% 15.10% Primmum Insurance Company 25100% 17.74% GE Reinsurance Corporation 19100% GE Frankona Rückversicherungs- Aktiengesellschaft 14100% 67.31% Nordic Insurance Company of Canada (The) 13100% 26.42% NAC Reinsurance Corporation 8100% 26.70% American Home Assurance Company (Canadian Branch) 6100% 62.39%

30. CHARACTERISTICS OF INDUSTRY LEADERS -The 10 industry leaders shown in Table 11 are defined as the companies which have appeared most often in the dominating sets of other sampled companies. -Among the 10 leaders, only the GE Reinsurance Corporation has shown an average AE score of 100% over the entire period. - Over the period 1996-2000, the leaders have shown average AE and CE scores of 40.66%.

31. Table 12 Malmquist Index : Statistics AverageStd-dev 96-971.070.22 97-9810.37 98-991.232.17 99-001.050.28

32. Table 13 TE changes: Statistics AverageStd-dev 96-971.20.58 97-981.090.31 98-990.910.21 99-001.040.17

33. Table 14 Technological changes: Statistics AverageStd-dev 96-970.960.16 97-980.930.23 98-991.231.16 99-0010.18

34. MAIN RESULTS MALMQUIST INDEX -On average, P&C insurers operating in Canada, have improved their productivity over the entire sampled period, as shown in Table 12. But, this result is driven by only 41 insurers (out of 92) which have really improved their productivity. -The productivity improvement is due, almost symmetrically, to the TE changes and the technological changes especially in 1999 and 2000, as indicated in Tables 13-14.

35. Table 15 Malmquist Index - Canadian vs Foreign 96-9797-9898-9999-00 Average Canadian 1.061.021.271.04 Std-dev Canadian 0.220.42.440.26 Average Foreign 1.110.951.111.08 Std-dev Foreign 0.250.260.980.35

36. Table 16 Technological changes (Canadian vs Foreign) 96-9797-9898-9999-00 Average Canadian 0.970.941.240.98 Std-dev Canadian 0.160.221.270.14 Average Foreign 0.930.871.211.07 Std-dev Foreign 0.160.240.770.26

37. Table 17 TE changes - Canadian vs Foreign 96-9797-9898-9999-00 Average Canadian 1.171.070.921.05 Std-dev Canadian 0.560.270.210.17 Average Foreign 1.301.140.911 Std-dev Foreign 0.660.430.190.17

38. MAIN RESULTS MALMQUIST INDEX According to Table 15, it appears that the productivity improvements were about similar for domestic and foreign insurers. However, results for domestic insurers show a greater standard deviation in 1999. According to Tables 16-17, these productivity improvements seem to be due mostly to TE changes rather than technological changes. That seems to be even more so in the case of domestic insurers.

39. Limitations of Study General limitations of DEA apply. –DEA being an extreme point technique, measurement error (noise) can cause problems. –Need to analyze 1999 results further. Need to improve upon our measurement of inputs/outputs. – Value-added approach [Cummins & Weiss (2000)] Time period is rather short. –Need to extend tracking window. Additional work on the determinants of P&C insurers’ efficiency in Canada is also needed.