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In addition to the outcomes on settlement amounts and costs considered above, it is possible that the choice of fee scheme affects the duration of a given claim. In principle a regression of settlement durations against case characteristics and fee scheme indicator variables as outlined in the previous section could be undertaken. However, given the

presence of some cases which were withdrawn or repudiated, the sample of cases which went to a settled conclusion is incomplete, leading to so-called “censored” duration data. Consequently it is necessary to model the conditional probability of settlement, using data on settlement timings together with information on each case's disposition at conclusion.

A conventional proportional hazards regression approach is adopted here, where the settlement hazard for case i at a point in continuous time t is given by

t _l

lit =l0( )exp(r ' Xit +sl'Z + ln(ui )) (4)

where l0(t) is the baseline hazard, X and Z are defined as above, and (( and (( are

corresponding vectors of coefficients. Consequently it is assumed that different fee

schemes may have a proportional effect on the baseline hazard, which itself summarises the behaviour of the settlement hazard over time. For estimation it is necessary to choose a specification for the baseline hazard function (0(t), and a conventional choice is the Weibull distribution, which is a two-parameter distribution allowing the hazard to vary monotonically over time. In addition, (i is a component representing the unobserved claim heterogeneity (“frailty”) which is assumed to be distributed as ((1, (). The parameters ((, ((, and ( can be estimated by maximum likelihood methods. An alternative to this parametric approach is to choose an estimator for the hazard function which does not imply any particular functional form for the settlement hazard over time. A partial likelihood approach suggested by Cox (1972) can be used to estimate a proportional hazard model in which the settlement hazard

l0(t) is conditioned out of the likelihood function. This means that there is no need to specify

a functional form for l0(t), and inferences about the parameters can be made without any

constraints of this kind. In Table 2.12, we report estimated values for the parameters using both Weibull and Cox estimators. We are particularly interested in the estimates for (( as these will reflect the impact of fee schemes on the settlement hazard and consequently on the duration of the claim.

Table 2.12: Settlement hazards and fee schemes Weibull Cox Ln (damages) 0.53*** 0.53*** (0.05) (0.06) Admission of Liability 1.02*** 1.02*** (0.01) (0.01) RTA claims 1.25 1.28 (0.22) (0.21) Employment status 0.97 1.01 (0.20) (0.20) CFA funding 0.73 0.74 (0.20) (0.19) CCFA funding 0.87 0.87 (0.19) (0.18) BTE funding 1.91*** 1.77*** (0.35) (0.32) Observations 183 183 Wald (2(7) 103.22 81.77 Pr((2>0) 0.0000 0.0000

Testing hypotheses of fee schemes on settlement hazards (F tests)

CFA vs BTE 13.47 11.23 p-value: 0.00 0.00 CCFA vs BTE 16.04 14.09 p-value: 0.00 0.00 CFA vs CCFA 0.39 0.32 p-value: 0.53 0.57

Robust standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%

The results confirm the evidence we have found elsewhere with other datasets, that

settlement timing is highly sensitive to the parties’ prior estimates about the likely outcome in court, both with respect to quantum and liability. Cases with higher estimated quantum have lower settlement hazards and therefore longer durations, other things being equal. Cases where liability is more fully admitted by the defendant have higher settlement hazards and therefore shorter durations, other things being equal (see Fenn and Rickman, 2000; 2004). We can infer that claimants with weak cases can expect to wait longer for a settlement, as will those with potentially high value claims.

After controlling for these factors which determine the size and complexity of a case, the impact of fee schemes are revealed by the coefficients of the indicator variables for the alternative fee arrangements (the reference category is the “unknown” fee arrangement). It appears from the results in Table 2.12 that the BTE cases have relatively high settlement hazards and therefore shorter durations. The hazard ratio estimates suggest that in any one time period BTE claims are between 77% and 91% more likely to settle than claims in the

“unknown” fee category. The likelihood ratio tests at the foot of the table confirm that there is a significant difference between BTE cases and CFA/CCFA cases – delay is longer for the latter than the former. This finding holds after controlling for differences in case complexity between fee schemes as reported in section 2.3.1 above. It is possible that the delay observed in our sample was influenced by the series of legal disputes over costs over the last few years, which may have particularly affected CFA claims.

2.3.4 Costs

The costs from personal injury cases are characteristically distributed asymmetrically, with a large number of “small” cases and a small number of very large cases. For this reason, multiple regression analyses to test for the impact of fee schemes on the costs of litigation are appropriately estimated in loglinear form. Moreover, this aids the interpretation of the results in terms of proportionate changes attributable to fee scheme differences.

Consequently, in this study we estimate two regressions with the following form:

ln(c

)=

r

' X

+s

' Z +e

where cj indicates one of two measures of cost – base costs and total costs respectively.

Table 2.13: Legal costs and fee schemes (OLS regression)

Ln(base costs) Ln(total costs)

Ln (delay) 0.35 0.19 (0.14) (0.07) Ln (damages) 0.41* 0.42*** (0.11) (0.04) RTA claims -0.02 -0.07 (0.05) (0.06) CFA funding 0.25 0.35*** (0.10) (0.02) CCFA funding -0.01 0.17* (0.07) (0.04) BTE funding 0.31** 0.16** (0.04) (0.02) Issue of proceedings 0.10 0.42 (0.08) (0.17) Constant 2.05*** 3.21** (0.14) (0.53) Observations 179 243 Adj R-squared 0.60 0.49

Testing hypotheses of fee schemes on costs (F tests)

CFA vs BTE 0.34 179.86 p-value: 0.62 0.00 CCFA vs BTE 18.26 0.01 p-value: 0.05 0.93 CFA vs CCFA 2.57 12.39 p-value: 0.25 0.07

As the continuous variables are all in log form, it is possible to interpret the coefficient estimates on these variables, shown in Table 2.13, as elasticities. Hence it seems that a 10% increase in case value increases both base and total costs by just over 4%. Delay also seems to increase costs, although these estimates are not quite statistically significant. After controlling for case value and delay, CCFA cases had significantly lower base costs than (non-conditional) BTE cases. By contrast, CFA cases had significantly higher total costs than BTE cases (as a consequence, we presume, of the success fees and ATE premiums). All other cost comparisons were not statistically significant.