Issues in Panel Data Model Selection: The Case of Empirical Analysis of Demand for Reinsurance

Transcription

1 Issues in Panel Data Model Selection: The Case of Empirical Analysis of Demand for Reinsurance Augusto Carneiro and Prof Mike Sherris UNSW Actuarial Studies Research Symposium 2005, UNSW Sydney, AUSTRALIA Actuarial UNSW p. 1/2

2 Introduction Australian data on demand for reinsurance Actuarial UNSW p. 2/2

3 Introduction Australian data on demand for reinsurance Panel data methodology and models Actuarial UNSW p. 2/2

4 Introduction Australian data on demand for reinsurance Panel data methodology and models Choice of OLS with Panel-Corrected Standard Errors Actuarial UNSW p. 2/2

5 Introduction Australian data on demand for reinsurance Panel data methodology and models Choice of OLS with Panel-Corrected Standard Errors Results from the study Actuarial UNSW p. 2/2

6 Australian Data APRA data general insurers and reinsurers Actuarial UNSW p. 3/2

7 Australian Data APRA data general insurers and reinsurers Panel dataset - 98 insurers and 543 observations Actuarial UNSW p. 3/2

8 Australian Data APRA data general insurers and reinsurers Panel dataset - 98 insurers and 543 observations 70% of all insurers in 2001 by asset value Actuarial UNSW p. 3/2

9 Australian Data Reinsurance demand - ration of reinsurance expense to total premium revenue (REINS); Actuarial UNSW p. 4/2

10 Australian Data Reinsurance demand - ration of reinsurance expense to total premium revenue (REINS); Leverage - ratio of total liabilities to total assets (LEV) Actuarial UNSW p. 4/2

11 Australian Data Reinsurance demand - ration of reinsurance expense to total premium revenue (REINS); Leverage - ratio of total liabilities to total assets (LEV) Size - logarithm of total asset value (LnSIZE) Actuarial UNSW p. 4/2

12 Australian Data Reinsurance demand - ration of reinsurance expense to total premium revenue (REINS); Leverage - ratio of total liabilities to total assets (LEV) Size - logarithm of total asset value (LnSIZE) Tax - ratio of tax expense to total premiums (TAX) Actuarial UNSW p. 4/2

13 Australian Data Expected effects and reasons Reinsurance demand (REINS) and leverage (LEV); more leverage, less capital, more reinsurance (+ive) Reinsurance demand (REINS) and Size (Ln Size); larger insurer, less reinsurance (-ive) Reinsurance demand (REINS)and Tax (TAX); lower tax, more reinsurance (-ive); Reinsurance demand (REINS) and Return (INVEST); more investment income, more risky, less reinsurance (-ive) Actuarial UNSW p. 5/2

14 Australian Data MAX. MIN. MEAN MEDIAN STD. DEV. SKEWNESS REINSURANCE RATIO (REIN S) LEVERAGE (LEV ) SIZE (LnSIZE) TAX RATIO (T AX) RETURN ON INVESTMENT (INV EST ) Actuarial UNSW p. 6/2

15 Reinsurance vs. Size Reinsurance Ratio Graphs by year Size (ln of total asset value) Actuarial UNSW p. 7/2

16 Reinsurance vs. Leverage Reinsurance Ratio Graphs by year Leverage Actuarial UNSW p. 8/2

17 Reinsurance vs.taxes Reinsurance Ratio Graphs by year Taxes (ratio of taxes to premiums) Actuarial UNSW p. 9/2

18 Reinsurance vs. Investment Return Reinsurance Ratio Graphs by year Investment Return Actuarial UNSW p. 10/2

19 Panel Data Methodology and Models Allowed for Year Dummy Variables Groups of Companies Reinsurers Actuarial UNSW p. 11/2

20 Panel Data Methodology and Models Allowed for Year Dummy Variables Groups of Companies Reinsurers Need for careful modelling Standard regression assumptions do not hold Spurious results if not properly modelled Actuarial UNSW p. 11/2

21 Panel Data Methodology, and Models y i,t = β 1 x it,1 + β 2 x it,2 + + β K x it,k + ǫ i,t (1) i = 1,2,... N observation units, t = 1,2,... T time periods, and k = 1,...K explanatory variables Grouping all time periods t = 1,2,... T we get y i = X i β + ǫ i (2) Actuarial UNSW p. 12/2

22 Panel Data Methodology, and Models β = ( N ) 1 ( N ) X i Ω 1 X i X i Ω 1 y i i=1 i=1 (3) Ω = I T Σ = ¼ Σ Σ Σ ½ Σ = ¼ σ 2 1 σ σ 2 1N σ 21 σ σ 2N σ N1 σ N2... σ 2 N ½ Panel heteroscedasticity:e[ǫ 2 it ] E[ǫ2 jt ] but E[ǫ2 it ] = E[ǫ2 is ] Contemporaneously correlated errors: E[ǫ it ǫ jt ] = E[ǫ is ǫ js ] 0, but E[ǫ it ǫ js ] = 0 Actuarial UNSW p. 13/2

23 Panel Data Methodology, and Models Random Effects and Fixed Effects Specification y it = x it + c i + u it t = 1, 2,...,T (4) Ω = E(v i v i) = σc 2 + σu 2 σc 2... σc 2 σc 2 σc 2 + σu 2... σc σ 2 c σ 2 c... σ 2 c + σ 2 u Actuarial UNSW p. 14/2

24 Panel Data Methodology, and Models OLS with Panel Corrected Standard Errors: If errors present panel heteroskedasticity and contemporaneous correlation, then OLS estimates of β are inefficient. However they are still consistent. we can use the OLS residuals to obtain a consistent estimate of Σ. Let e i,t the OLS residual for unit i at time t. An element of Σ can now be estimated by Σ i,j = T t=1 e i,te j,t T (5) Actuarial UNSW p. 15/2

25 Results OLS Variable Coefficient Estimates Standard Errors t-statistic p-value LEV LnSIZE T AX IN V EST D_group D_reinsurer D_ D_ D_ D_ D_ Const Actuarial UNSW p. 16/2

26 Results Random Effects Variable Coefficient Estimates Standard Errors t-statistic p-value LEV LnSIZE T AX IN V EST D_group D_reinsurer D_ D_ D_ D_ D_ Const Actuarial UNSW p. 17/2

27 Results OLS with PCSE Variable Coefficient Estimates Standard Errors t-statistic p-value LEV LnSIZE T AX IN V EST D_group D_reinsurer D_ D_ D_ D_ D_ Const Actuarial UNSW p. 18/2

28 Results from Study - OLS with PCSE Significance of leverage (capital) and link to demand for reinsurance Actuarial UNSW p. 19/2

29 Results from Study - OLS with PCSE Significance of leverage (capital) and link to demand for reinsurance Lack of statistical significance of size, tax, return, group, reinsurer Actuarial UNSW p. 19/2

30 Results from Study - OLS with PCSE Significance of leverage (capital) and link to demand for reinsurance Lack of statistical significance of size, tax, return, group, reinsurer Although not significant, negative effect of size, tax, group and reinsurer and increasing time trend Actuarial UNSW p. 19/2

31 Summary Study confirms role of reinsurance in insurer capital and risk management Actuarial UNSW p. 20/2

32 Summary Study confirms role of reinsurance in insurer capital and risk management As far as we are aware, the first empirical study of demand for reinsurance in Australia Actuarial UNSW p. 20/2

33 Summary Study confirms role of reinsurance in insurer capital and risk management As far as we are aware, the first empirical study of demand for reinsurance in Australia Study addresses important issues in methodology for studies in this area (panel data, model assumptions) Actuarial UNSW p. 20/2

34 Summary Study confirms role of reinsurance in insurer capital and risk management As far as we are aware, the first empirical study of demand for reinsurance in Australia Study addresses important issues in methodology for studies in this area (panel data, model assumptions) Need for better data Actuarial UNSW p. 20/2