Tenure dependence in consumer-firm relationships: an empirical analysis of consumer departures from automobile insurance firms.

Updated Probability of Type [[tau] [[rho].sup.[epsilon].sub.3] [[rho].sup.[epsilon].sub.4] 1 .141 .146 2 .144 .151 3 .145 .157 4 .146 .162 5 .147 .165 6 .146 .168 7 .145 .171 8 .144 .173 9 .143 .174 10 .141 .176 11 .139 .177 12 .137 .177

Updated Probability

of Type

Departure [[tau] [[rho].sup.[epsilon].sub.5] Probability 1 .208 .071 2 .222 .082 3 .240 .077 4 .257 .067 5 .272 .056 6 .286 .060 7 .301 .053 8 .316 .048 9 .329 .048 10 .342 .039 11 .354 .037 12 .365 .037 All computations are for a base-case consumer. TABLE 8 Cumulative Decline in Departure Probability by Source

Total Tenure Effects Percent of Period Change Alone Change 2 (base) .0824 .0824 N/A 2 [right arrow] 3 -.0056 .0007 -12.5% 2 [right arrow] 4 -.0152 -.0046 30.3% 2 [right arrow] 5 -.0266 -.0141 53.0% 2 [right arrow] 6 -.0225 -.0048 21.3% 2 [right arrow] 7 -.0294 -.0102 34.7% 2 [right arrow] 8 -.0342 -.0137 40.1% 2 [right arrow] 9 -.0344 -.0114 33.1% 2 [right arrow] 10 -.0431 -.0219 50.8% 2 [right arrow] 11 -.0450 -.0230 51.1% 2 [right arrow] 12 -.0450 -.0212 47.1%

Selection Percentage Period Alone Change 2 (base) .0824 N/A 2 [right arrow] 3 -.0062 110.7% 2 [right arrow] 4 -.0114 75.0% 2 [right arrow] 5 -.0158 59.4% 2 [right arrow] 6 -.0195 86.7% 2 [right arrow] 7 -.0226 76.9% 2 [right arrow] 8 -.0253 74.0% 2 [right arrow] 9 -.0277 80.5% 2 [right arrow] 10 -.0297 68.9% 2 [right arrow] 11 -.0316 70.2% 2 [right arrow] 12 -.0332 73.8% All computations are for a base-case consumer. Tenure effects alone are computed by fixing [epsilon] = -.1275 to match the period-2 departure probability from the full model. Selection alone is computed by setting [[alpha].sub.1] ([tau]) = [[alpha].sub.1] (2) for all r [greater than or equal to] 2. TABLE 9 Estimates Without Heterogeneity or Tenure Effects

No No Tenure

Base Model Heterogeneity Effects Tenure Effects Increase: period 2-12 .162 .406 0

[[alpha].sub.2](2) 1.022 .895 1.091

[[alpha].sub.2](3) -.005 .039 0

[[alpha].sub.2](4) .037 .072 0

[[alpha].sub.2](5) .071 .098 0

[[alpha].sub.2](6) -.070 -.037 0

[[alpha].sub.2](7) .040 .062 0

[[alpha].sub.2](8) .027 .047 0

[[alpha].sub.2](9) -.018 .004 0

[[alpha].sub.2](10) .085 .097 0

[[alpha].sub.2](11) .010 .023 0

[[alpha].sub.2](12) -.015 .001 0 Heterogeneity Distribution

[sigma] ([epsilon]) .525 0 .598

[[epsilon].sub.1] -.955 N/A -.949

[[epsilon].sub.2] -.131 N/A -.265

[[epsilon].sub.3] -.039 N/A .123

[[epsilon].sub.4] .150 N/A .211

[[epsilon].sub.5] .806 N/A .841

[[rho].sub.1] .143 N/A .171

[[rho].sub.2] .362 N/A .329

[[rho].sub.3] .141 N/A .111

[[rho].sub.4] .146 N/A .145

[[rho].sub.5] .208 N/A .244 TABLE 10 Firm's Willingness to Pay for Higher Tenure in "Markup" Units

Base Tenure "Full" Tenure Base as Percentage Tenure Effects Effects of Full 3 .16 .48 33.3% 4 .35 .93 37.6% 5 .49 1.28 38.3% 6 .53 1.48 35.8% 7 .69 1.78 38.8% 8 .79 1.99 39.7% 9 .87 2.14 40.7% 10 .99 2.30 43.0% 1I .98 2.33 42.1% 12 .96 2.33 41.2% Computations are for a base-case consumer with [epsilon] set to zero. TABLE 11 Extensions

Extension 1

Standard Category Parameter Estimate Error Alternate company [[delta].sub.0] .039 .112

effect [[delta].sub.1] -.014 .010 Price sensitivity [[rho].sub.v] N/A N/A

error [v.sub.1] N/A N/A

[v.sub.0] N/A N/A

[[sigma].sub.v] ([v.sub.1]) N/A N/A Information [[beta].sub.0] N/A N/A

[[beta].sub.1](1) N/A N/A

[[beta].sub.1](2) N/A N/A

[[beta].sub.1](3) N/A N/A

[[beta].sub.2] N/A N/A

[[beta].sub.3] N/A N/A

[[beta].sub.4] N/A N/A

[[beta].sub.5] N/A N/A

[[beta].sub.6] N/A N/A True tenure effects [[alpha].sub.2](1) 1.168 .009

[[alpha].sub.2](l) -.142 .012

[[alpha].sub.2](l) -.006 .021

[[alpha].sub.2](1) .035 .019

[[alpha].sub.2](1) .067 .022

[[alpha].sub.2](1) -.073 .025

[[alpha].sub.2](1) .039 .030

[[alpha].sub.2](1) .026 .032

[[alpha].sub.2](1) -.020 .037

[[alpha].sub.2](1) .082 .044

[[alpha].sub.2](1) .010 .044

[[alpha].sub.2](1) -.019 .043 Heterogeneity [[epsilon].sub.1] -.950 .171

distribution [[epsilon].sub.2] -.130 .189

[[epsilon].sub.3] .049 N/A

[[epsilon].sub.4] .141 .212

[[epsilon].sub.5] .802 .230

[[rho].sub.1] .150 .091

[[rho].sub.2] .361 .130

[[rho].sub.3] .141 N/A

[[rho].sub.4] .146 .084

[[rho].sub.5] .202 .091

Extension 2

Standard Category Parameter Estimate Error Alternate company [[delta].sub.0] N/A N/A

effect [[delta].sub.1] N/A N/A Price sensitivity [[rho].sub.v] .391 .244

error [v.sub.1] .461 .388

[v.sub.0] -.296 N/A

[[sigma].sub.v] ([v.sub.1]) 1.213 .434 Information [[beta].sub.0] N/A N/A

[[beta].sub.1](1) N/A N/A

[[beta].sub.1](2) N/A N/A