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

[[alpha].sub.2](4) Marginal effect of

tenure 4

[[alpha].sub.2](5) Marginal effect of

tenure 5

[[alpha].sub.2](6) Marginal effect of

tenure 6

[[alpha].sub.2](7) Marginal effect of

tenure 7

[[alpha].sub.2](8) Marginal effect of

tenure 8

[[alpha].sub.2](9) Marginal effect of

tenure 9

[[alpha].sub.2](10) Marginal effect of

tenure 10

[[alpha].sub.2](11) Marginal effect of

tenure 11

[[alpha].sub.2](12) Marginal effect of

tenure 12 Heterogeneity [[epsilon].sub.1] Points of support

distribution [[epsilon].sub.2]

[[epsilon].sub.3]

[[epsilon].sub.4]

[[epsilon].sub.5]

[[rho].sub.1] Probabilities

[[rho].sub.2]

[[rho].sub.3]

[[rho].sub.4]

[[rho].sub.5] Price discount [[delta].sub.1] Price change after

expectations ($100) 6 periods

[[delta].sub.2] Price change after

12 periods

[beta] Discount factor

Standard Category Parameter Estimate Error True tenure effects [[alpha].sub.2](1) 1.161 .007

[[alpha].sub.2](2) -.139 .010

[[alpha].sub.2](3) -.005 .015

[[alpha].sub.2](4) .037 .018

[[alpha].sub.2](5) .071 .019

[[alpha].sub.2](6) -.070 .024

[[alpha].sub.2](7) .040 .027

[[alpha].sub.2](8) .027 .030

[[alpha].sub.2](9) -.018 .034

[[alpha].sub.2](10) .085 .043

[[alpha].sub.2](11) .010 .044

[[alpha].sub.2](12) -.015 .039 Heterogeneity [[epsilon].sub.1] -.955 .104

distribution [[epsilon].sub.2] -.131 .111

[[epsilon].sub.3] -.039 .030

[[epsilon].sub.4] .150 .108

[[epsilon].sub.5] .806 .131

[[rho].sub.1] .143 .044

[[rho].sub.2] .362 .071

[[rho].sub.3] .141 .040

[[rho].sub.4] .146 .039

[[rho].sub.5] .208 .063 Price discount [[delta].sub.1] -.171 .041

expectations ($100) [[delta].sub.2] -.111 .056

[beta] .564 .099 TABLE 5 Cumulative Utility Changes

Change in Tenure Period Effect Dollar Equivalent 2 (base value) 1.022 171.07 3 -.005 -.84 4 .032 5.36 5 .103 17.24 6 .033 5.52 7 .073 12.22 8 .100 16.74 9 .082 13.73 10 .167 27.95 11 .177 29.63 12 .162 27.12

Change in Expected Period Value of [epsilon] Dollar Equivalent 2 (base value) .035 5.93 3 .039 6.41 4 .073 12.10 5 .101 16.89 6 .125 20.76 7 .148 24.65 8 .168 27.99 9 .185 30.94 10 .202 33.77 11 .216 36.08 12 .229 44.17 All computations are for a base-case consumer: with price equal to the market average, no accrued claims free tenure, and all other variables at their sample means. Dollar equivalents are found by dividing by the sample average of [[alpha].sub.1]([y.sub.t]). TABLE 6 Impact of Expected Price Discounts

Expected Price Change ($) Departure [[tau].sup.nc] (Relative to [[tau].sup.nc] = 0) Probability 0 .00 .071 1 -.25 .071 2 -.68 .070 3 -1.45 .070 4 -2.82 .069 5 -5.24 .068 6 -9.53 .065 7 -.04 .071 8 -.32 .071 9 -.81 .070 10 -1.67 .070 11 -3.21 .069 12 -5.94 .067 13 .32 .071 The expected price change is the discounted average of all expected, future, tenure-based price discounts, relative to this average at [[tau].sup.nc] = 0, computed as described in Appendix B. Departure probabilities are computed with tenure equal to one, price equal to the market average, and all other variables set to sample averages. TABLE 7 Departure Probabilities by Type

Departure Probability by Type [[tau] [[epsilon].sub.1] [[epsilon].sub.2] [[epsilon].sub.3] 1 .232 .064 .054 2 .273 .083 .070 3 .275 .084 .071 4 .263 .078 .066 5 .242 .069 .058 6 .263 .078 .066 7 .251 .073 .061 8 .243 .069 .058 9 .248 .071 .060 10 .224 .061 .051 11 .221 .060 .050 12 .225 .061 .051

Departure Probability by Type [[tau] [[epsilon].sub.4] [[epsilon].sub.5] 1 .037 .007 2 .049 .011 3 .049 .011 4 .046 .010 5 .039 .008 6 .046 .010 7 .042 .009 8 .040 .008 9 .041 .009 10 .034 .007 11 .034 .007 12 .035 .007

Updated Probability of Type [[tau] [[rho].sup.[epsilon].sub.1] [[rho].sup.[epsilon].sub.2] 1 .143 .362 2 .118 .365 3 .094 .364 4 .074 .362 5 .058 .357 6 .047 .353 7 .037 .346 8 .029 .339 9 .023 .331 10 .018 .323 11 .015 .316 12 .012 .308