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The Impact of Demographic and Economic Variables on Financial Policy Purchase Timing Decisions

L. Thomas, S. Thomas, L. Tang, O. A. Gwilym* School of Management, University of Southampton * School of Management and Business, University of Wales, Aberystwyth

Abstract . This paper investigates the extent to which consumers’ demographic factors

influence their financial policy purchasing behaviours and also explores how the

external economic environment affects consumers’ propensities to purchase financial

products. The Cox proportional hazard model is used to explore these issues. The

results suggest that consumer decisions on the timing of financial product purchases

are largely explained by changes in economic environment in the terms of stock

market, the housing market, average earnings, consumer confidence, and interest

rates. The influence of customer demographic factors is also important but

secondary.

Keywords: Profit scoring; Cox proportional hazard model; Competing risks; Multiple

purchase event analysis; Separate purchase event analysis; Financial product

purchase propensity.

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1. Introduction Customer relationship management needs at its heart the analytic tools of

data mining and the storage and retrieval efficiencies of a data warehouse. This is true

no matter what the commercial area, but in the insurance and financial industry the

length of time of customer relationships can extend through several economic cycles

and thus one needs to include economic variables as well as customer demographic

and behaviour variables in the models one builds. The most common such models are

propensity ones which ask how likely is the customer to purchase a new financial

product or form a new relationship with the firm. These are exactly the same

approaches as those in credit scoring, where one estimates the propensity to default or

propensity to attrite.

In credit scoring systems there is also a need to introduce economic

variables, especially since the announcement of proposed revisions to the Basle

capital adequacy regulations for international banks. Credit scoring has received

considerable attention both from bankers interested in lending (e.g. Altman1 ) and

from researchers interested in developing credit scorecards systems (e.g. Thomas,

Edelman, and Crook 2 ). Bankers mainly seek to predict the causes that might lead to

default of loans or credit cards, etc. (see Crook, Hamilton, and Thomas 3 ). In contrast,

researchers consider various methods for building credit scorecards, following from

Fisher’ s 4 introduction of discrimination methods. For example, see Grablowsky and

Talley 5 for probit regression, Hand 6 for linear programming, and Stepanova and

Thomas 7 for survival analysis. Recent theoretical development in this field has

moved from credit scoring to profit scoring. Providers are not only interested in

whether their customers will default but also when customers will terminate their

relationships and when customers will purchase various financial products. After all,

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the longer the relationship with the same provider, the more profits that can be made

from the customer. Empirical studies analysing profit scoring are not very numerous.

This paper applies Cox 8 proportional hazard model in survival analysis to

study what socio-demographic and economic conditions lead to increased propensity

to purchase financial products and how long it takes for customers to purchase

different kinds of financial products. The data available for this study contain

information on the demographic and complete financial products purchasing history

information for each customer up to the time of data collection. Our main contribution

consists of incorporating and examining the impacts of various external economic

variables on customers’ financial product purchasing behaviour. To the best of our

knowledge, no previous research studies of this kind have been conducted. The use of

Cox’ s proportional hazard model and duration data make it possible to investigate

these time dependent economic variable issues. In particular, this study analyses the

extent to which multiple purchase events affect purchasing decisions by comparing

multiple events with conventional separate purchase event methods. Finally, this

study explicitly takes into account the impacts of demographic and external economic

variables on the purchase of different financial products. This study reveals that

external economic variables have strong and significant effects on financial policy

purchase decisions.

This paper is organised as follows: Section 2 describes the data and

examines patterns of the purchase of financial products. Section 3 presents Cox’ s

proportional hazard models estimated from this dataset. Section 4 contains the results,

and Section 5 concludes.

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2. Data and Covariates The data are derived from an international insurance company, one of the

largest financial product providers in the UK. The company’ s data warehouse records

all financial purchase information for each customer. Our random sample dataset

consists of individual customer records for all purchasing histories. The data sample

contains 44,680 individual customers, with an age range from 0 to 100 years old, and

there are 49,902 products that have been purchased. From this database we are able to

calculate that on average that each customer purchases 1.2438 products throughout

the whole sample period. A large proportion of the customers (40,120 customers) are

right censored because they have not yet purchased any more products after they set

up their relationships with the insurance company. Thus there are 4,560 customers

that are observed having purchased multiple products in the dataset. Of those multiple

purchase customers, there are 3,808 customers purchased two products, and 578

customers purchased three products. One customer purchases six products.

Each record includes information on each customer ID, timing of customer

purchases, duration of relationship, gender, age, financial ACORN classification,

payment frequency. Other variables describe the product type that is purchased for

each purchase event. The duration relationship variable is defined as the length of the

time between each initial policy start date and the next policy purchase date. This

duration time variable is subject to right-censoring because there are still customers

who may be waiting to purchase at the end of the date sample. The dummy variable,

Gender, equals one for male customers and zero for female customers. The Age

variable uses the values given at the time of each purchases, thus allows age changes

for each customer when duration lengthens.

The financial ACORN classification describes customers’ financial status

and behaviour. This variable in our dataset is categorised into 4 groups, namely

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category A, B, C, and D. Customers in category A are described as financially

sophisticated, and they are also described as wealthy equity holders. Customers in

Category B are usually not as wealthy as category A customers. However, they are

still purchasing various financial services. Category C customers tend to have little

financial activity, such as settled pensioners and people in working families.

Customers in category D have low incomes or are unemployed. However, there is no

Acorn category for some customers, who are then categorised as unknown. Thus, the

financial ACORN variable is classified as 1, 2, 3, 4, and 5 for A, B, C, D, and U,

respectively. The payment frequency is divided into two groups in our data set,

namely, single payment and monthly payment.

The products of the insurance company can be mainly categorised into four

main product groups, which are Collective Investment, Pensions, Protections, and

Life. In the collective investment category, unit trusts, PEP, and ISA are the main

products. Occupational pensions, individual pensions, and pension annuities fall into

the pension product line. The Life category consists of house purchase, regular

savings, and single premium investments. Protection products are fundamentally

different from life products in that they pay out when customers die. Life products

tend to pay out after a fixed term. Thus, the product line variable is denoted as 1, 2, 3,

and 4 for collective investment, pension, protection, and life respectively. In order not

to make an unrealistic assumption that the propensity of purchasing the next product

is unaffected by the purchase of the first product that the customer experienced, we

also include the information of the previous purchased product variable in the model.

We are particularly interested in the impact of the external economic

environment on customers purchasing financial products. There are a number of

variables considered by economists which may be thought to influence the purchase

of goods, services and financial products. Typically, relative prices of goods, income,

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wealth, consumer sentiment, intertemporal preference via the time value of money (

interest rate) variables may all impact on spending and saving decisions. The variables

we looked at as affecting the timing of financial product purchases reflect the data

availability and timeliness and an a priori view of what constitutes the important

economic influences: wealth, which is proxied by house prices and share prices ( the

FT-SE All Share Index) ; income which is reflected in average earnings growth;

confidence as given by a consumer confidence index and intertemporal aspects of

savings and consumption as proxied by the Bank of England base interest rate. No-

one suggests that such a list is exhaustive but it is entirely consistent with economic

theory and we can predict the role of each variable and the sign of its associated

coefficient. These five monthly frequency economic explanatory variables are

collected from Datastream for the period from January 1999 to March 2003. They are

treated as time varying variables in the model because their values keep changing over

the period between two product purchase events. In order to take into account these

time dependent economic variables, we can divide the duration into a series of

monthly intervals such that we can have these economic variable values for each

customer within each interval. Customer-specific covariate information such as

Gender and financial ACORN category can also be presented in each interval. Thus,

the data for customer i, iD , consist of triples � �iikik Zy ,,G where ikG equals one if

customer i purchased one product in interval k and zero otherwise; iky denotes the

five economic variable values in interval k. These values are assumed to be constant

within interval k and varying in different intervals. iZ is customer-specific covariate

information for customer i..

The actual values for each economic variable are shown in Figure 1. It

should be noted that these economic variables can not be simply put into the model in

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levels, because most economic variables are potentially non-stationary, in which past

stochastic errors tend to be accumulated and the underlying distributions change with

time. The Augmented Dickey-Fuller (ADF) unit root test is applied to examine the

order of integration of each economic variable. In ADF tests, the initial lag length is

set at 6, then testing down to the first significant lag. The results of ADF tests for the

five economic variables are presented in Table 1. The results show that t-statistics for

four economic variables, namely FTSE All Share Index, House price index, Average

earnings index, and Bank of England’ s bank base interest rate, are well below (in

absolute value) their 5% critical value so that the null hypothesis of a unit root is not

rejected for the four prices. The null hypothesis of one unit root is rejected at 5% level

for Consumer confidence index. Therefore, the series are transformed to achieve

stationarity by taking first difference of the natural logarithm for FTSE All Share

index and first differences for House price index, Average earnings index, and Bank

of England’ s bank base interest rate. The Consumer confidence index is used in its

levels.

3. Methods The Cox proportional hazard model is applied, which can be represented

mathematically by

where t denotes the waiting time in quarters until the next purchase, � �t

iX is the known

vector of regressor variables associated with customer i at time t, which include both

customer specific covariates and time dependent economic variables, and E is the

vector of respective regression coefficients. . � �� �tii Xth | is the hazard rate of the

purchasing event at time t for the thi customer, while � �th0 is a baseline hazard

� �� � � � � �� �ti

tii XthXth ’

0 exp| E

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function. The Cox proportional hazard function model does not need to estimate � �th0

when estimating the coefficients E .

Since this company has four financial product groups, namely collective investment,

pensions, protection and life, potentially available to each customer, it may be that

each type of financial product may have its own hazard model that governs both the

type of purchase and the timing of that product purchase. So we investigate two

approaches. In the single risk model. We do not distinguish between purchase types

and so estimate the time from one purchase to the next irrespective of what either is.

In the competing risk model, we estimate the time from a purchase of any type to the

next investment purchase and then develop similar models for the three other types of

purchase. We then use the idea of competing risk, i.e. which of the “risks” occurs

first, to estimate the overall purchase pattern. Narendranathan and Stewart 9 ’ s test is

applied to investigate whether customers’ purchasing behaviours are incidental.

Specifically:

LR test statistic ^ `QLL sc ��� maxmax lnln2

Where cLmax and sLmax are the maximised log-likelihood values for the competing risks

model and the single risk model, respectively. The single risk model is the

unrestricted competing risks model without taking into account each specific

purchased product. The term Q is the purchase event frequencies in the sample, which

should be strictly negative as ¦ �

�

4

1ln

j jj pnQ . jn is the observed numbers of

customers who purchase product j and ¦ �

4

1l ljj nnp .

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4. Estimation Results

4.1 Multiple purchase event analysis The estimation results for the single risk and competing risk models outlined

in the previous section are reported in Tables 2 – 4 and the competing risk tests of the

models are reported in Table 5.

We consider the multiple purchase events first, with results reported in Table

2. There are 4,993 further purchase events altogether, including 2,768 for collective

investment products, 505 for pensions, 1,364 for protection, and 356 for life products.

The purchase of investment related products obviously dominates that of the rest

products, accounting for more than half of the purchase events.

Looking at the last four columns of Table 2, the financial status variables

have pronounced different influences on the estimated financial products purchasing

hazards. It can be seen that there is a remarkable rise in propensity to purchase

collective investment and protection products for those customers in financial

ACORN category A. There is about 33.1% and 23.4% higher chances of purchasing

collective investment and protection products respectively for these financial ACORN

A customers than the lower reference financial status customers (financial ACORN

category C and U). The propensities for purchasing life and pension products show

quite different patterns. It is worth noting that the probability of purchasing life

products for the lowest financial status customers (financial ACORN category D) is

significantly higher than that for any other customers by nearly 42%. The financial

ACORN A customers demonstrate the lowest propensity to purchase pensions among

all customers. When comparing the financial status results of single risk model with

competing risk models, it is interesting to see that, in general, high financial status

customers tend to purchase investment related products (such as unit trust) while

lower financial status customers purchase more life related products (such as savings).

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There are virtually no significant differences between female and male

customers to purchase further products both in the single risk and competing risk

models, indicating that both genders have similar propensities to purchase different

types of financial products. However, customers’ age has a significant impact on the

propensity to purchase further each type of financial product. The single risk model in

Table 1 demonstrates that the relative risk for customers aged under 20 purchasing

another product is 0.749, suggesting that these customers are nearly 25% less likely to

purchase than those reference customers aged between 55 and 65. The competing risk

models further suggest that these young customers are the least likely to purchase

investments and pensions while customers aged between 55 and 65 have the highest

probabilities of buying investments and pensions. Customers between 20 and 55 are

more than three times more likely to purchase protection products than the rest of age

group customers. With the exception of purchasing protection products, the single

payment customers are, on average, more likely to purchase their next products by

11.8% (RR = 1.118) than monthly payment customers.

To capture the influence of the external economic environment, all five

external economic variables, namely the consumer confidence index, the log change

in the FTSE ALL Share Index, the change of in the House price index, the change

average earning index, and the change of in the bank base interest rate, enter into the

Cox proportional model as time-varying covariates. The forms of these economic

variables are not critical to our results. However, it has the advantage of avoiding the

statistical estimation problems caused by the non-stationarity of these variables. It

should be noted that the change in all economic variables (except for the consumer

confidence index) are for each month the changes over the last quarters, which

captures the effect of time-varying economic variables on the timing of the financial

product purchase events. Such model design is intended to capture economic

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information more completely than simply using the economic variable information on

the purchasing date.

As shown in Table 2, the sign and significance for most economic variable

coefficient estimates are similar for each financial product. With the rise of the

consumer confidence index and the stock market, people tend to purchase more

collective investment and protection products. A rising stock market increases the

probability of purchasing investment products by 45.8% and the probability of

purchasing protection products by three times. However, rises in the consumer

confidence index and the stock market have no impact on the purchase of pensions. It

seems to suggest that, from the financial product provider’ s point of view, when the

stock market rises and consumer confidence improves, the provider can benefit from

concentrating more efforts on selling investments and protection related financial

products rather than pension related products. It is also interesting to note that the sign

of the life product coefficient is significantly negative (-0.5951), suggesting that the

rise of the stock market has a negative influence on the purchase of life products. The

underlying drivers of this negative effect are unclear at this stage.

Rising house prices have a significantly positive effect on all product

purchase hazards. When comparing the magnitudes of the House price index

coefficients, rising house prices influence existing customers to purchase the

investment and protection products most. Similar to the impact of the house price

changes, customers tend to purchase more financial products when their earnings

increase. However, it has no impact on the sale of life products.

Rising bank interest rates reduce customers’ purchases of further products of

all types. This makes sense in that generally a higher interest rate implies a higher

discount rate, which tends to discourage people to invest more. It may also be that

higher interest rates mean that customers need to spend more of their income on their

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housing repayment and have less cash available to invest in other products. The

purchase of Life products is not sensitive to interest rate changes because the

coefficient is not statistically significant. However, the sign (-0.3260) is negative,

which is consistent with expectations.

4.2 Separate purchase event analysis One other type of segmentation that should be investigated is whether there

is a difference in the time between the first and second purchases and the times

between subsequent purchases. Table 3 and 4 show, respectively, the estimation

results for the second product purchase and the third or more purchase events. When

comparing these results of the separate purchase analysis with the earlier analysis, we

find that the magnitude and significance of most coefficient estimates, especially the

external economic variables, are similar to those of multiple purchase events,

indicating that our results are not very sensitive to the different analysis of the hazard

function.

There are no considerable differences for customers’ gender effects for both

the second purchase and the third (or more) purchase processes. With no exception,

customers aged between 55 and 65 are more likely to purchase any kinds of financial

products than the rest of age group customers. The signs and significance for financial

ACORN variables are not robust to the different treatment of the hazard function,

especially for the third (or more) purchase event. The single payment customers are

more likely to purchase their second products and third products than those monthly

payment customers by roughly 8.7% (RR = 1.087) and 19.3% (RR = 1.193),

respectively.

Concerning the impact of changes in the external economic environment on

the different purchase processes, we notice that the increase in the hazard of the

second and third purchase as housing and stock markets go up. As expected, the

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customers’ confidence and earnings also have strong positive effects on encouraging

people to buy more products. It is also interesting to note that the values of the relative

risk are somewhat larger than the rest of economic variables (10.478 for the second

purchase process and 49.847 for the third or more purchase process), showing the

strong influences of people’ s income on the purchase of financial products. Overall,

the relative risks for the third purchase are higher than those for the second purchase,

suggesting that social-economic characteristic and economic variables are even more

important. Therefore our results do not suffer the so-called selection effects, which we

are not able to control for.

4.3 The comparison of single risk model with competing risks models When comparing the single risk model with the competing risks models, the

general pattern of the estimated effects of most variables in the single risk model is

similar to that in the competing risks models. This similarity is consistent for both

multiple events analysis and separate event analysis. For example, the gender, age,

and payment frequency variables are quite consistent for both single risk and

competing risks models. However, in the single risk model, only those financial

ACORN A customer have significantly different “risks” of purchasing further product

compared with the other Financial Acorn groups, whereas in the competing risks

models, the differences of the financial status effects are very pronounced. This

indicates that the single risk model of estimating purchase events provides less

information on the financial status effects on the probability of purchasing subsequent

products than competing risks models.

Although the signs and significance of external economic variables are also

quite consistent both in the single and competing risks models, the magnitudes (thus

the relative risk values) of these economic coefficients vary in competing risks

models. This shows that change of economic climates tend to have various effects on

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the purchase of different financial products. Thus, more information for different

financial products can be revealed by estimating the competing risks models.

The single risk model is also not as informative as competing risks models

because the latter clearly show that customers tend to purchase the same product as

the previous products they purchased (as all the previous product coefficients are

negative).

The single risk model results show that increases in the stock market and the

consumer confidence index have strong positive effects on the probability of

purchasing the next product while increases in the banks’ base rate have negative

effects on such purchasing probabilities. However, an examination of these effects in

the competing risks models indicates that this is not quite so as the signs and

significance in competing risks models could vary across different products.

One main reason for estimating the single risk and competing risks models to

describe purchase timing decisions is that it facilitates testing for the proportionality

of product-specific hazards. The results of such proportionality tests based on the

Likelihood Ratio statistic are reported in Table 5. For the multiple event analysis and

the separate event analysis including the second purchase and the third or more

purchase, the test statistics, which are distributed as a chi-square distribution with 68

degrees of freedom, are 585.08, 452.90, and 158.53 respectively. These are very

significant at any reasonable significance levels. Thus, the null hypothesis that the

purchase of the three financial products is independent from each other is strongly

rejected.

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5. The comparison of economic variables’ impacts Attention is now turned to the question of how important is the impact of the

external economic variables have been played1. We seek to measure the predicting

power by comparing the model given in Equation (1) with and without incorporating

economic variables. Therefore, the data set was randomly split into two parts, the

training sample and the holdout sample. The training sample, 70% of the whole

population was used to fit the models both with and without economic variables. The

remaining 30% is used as a holdout sample to compare them. We consider two

validation criteria, the log likelihood ratio test and ROC curve to compare the impact

of economic variables for the comparison. For each validation criteria we use the

model coefficient estimations as inputs for models with and without economic

variables based on training data set, and then analyse the purchasing probabilities

produced for the holdout data set sample.

5.1 Multiple purchase event comparison The training sample estimation results for multiple purchase events with and

without incorporating external economic variables are presented in Table 6. Here we

observe that customer’ s age variables are consistent without substantial variation in

models with and without incorporating economic variables. However, the Financial

Acorn A variable becomes insignificant in the model without economic variables.

This seems to suggest that the economic environment could be interacting with the

different financial status of customers in making financial policy purchasing

decisions. The impression of the goodness of fit of the model in incorporating

economic variables that emerges from the log likelihood ratio test (LR) is impressive.

The null hypothesis that the models with and without economic variables are

1 The authors would like to thank the referee’ s comments

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equivalent is rejected at any reasonable level by the LR test using the log likelihood

values in Table 6.

A more common way of estimating the predictive power of a model is to look

at the ROC curves. In these the customers in the holdout sample are ranked according

to the predicted probability of purchase within a given time in the future. These are

compared with the actual outcomes and at for each customer the percentages of the

actual purchasers with predicted probabilities higher than that customer are plotted

against the percentage of non-purchasers with predicted probabilities above that

customer’ s value. This produces a curve going from (0,0) to (1,1) and the nearer it

gets to (0,1) the more accurate is the predicted ranking. Figure 2 shows the results for

the multiple ( third or higher ) purchases over nine time periods form one to nine

quarters for the models with and without the economic variables. The results are

startling in that with the time periods of one ( top left) , two ( top middle ) or three (

top right) quarters the model with economic variables is far superior to that without.

The predictive ability of the economic variable model deteriorates as the time horizon

of interest increases so that estimating purchases over 9 quarters ( bottom right) it is,

if anything, worse than the non-economic variable model. The latter hardy

deteriorates at all, but on the other hand, its predictions are only a little better than

chance to start with.

5.2 Second purchase event comparison The ROC curves for models, predicting the time between first and second

purchase, with and without incorporating economic variables are presented in Figure

3. The results are very similar to those for the higher order purchases except that both

types of models predict second purchases a little better than the subsequent ones .

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(This is probably due to the small number of third and higher order purchases in the

data).

This suggests that it is economic conditions that dominate the purchase of insurance

companies’ products. This is partly due to the limited amount of socio-economic

information in the data warehouse, but the results are so marked it suggests that the

impact of the state of the economy dwarfs any differences in socio-demographic

purchasing patterns.

Conclusions The goal of this paper is to develop a better understanding of the effects of

various demographic and economic variables on profit scoring. We analyse both the

multiple purchase events and the financial product purchase transition to the second

and the third or more products. The competing risks models employed here, based on

Cox’ s proportional hazard model, have enabled us to demonstrate that the purchase

propensity is determined by different measures of each customer’ s demographic

variables and external economic factors. In contrast to previous work on credit

scoring, we examine how customers’ purchasing behaviour changes under different

economic environments.

Our findings show that different age groups of customers tend to have

different propensities to purchase different products. Customers aged under 20 are

less likely to purchase more investment and pension related products than other

customers. Customers aged above 65 are also least likely to purchase any more life

insurance and pensions. Middle-aged customers especially aged between 35 and 55

tend to purchase more protection insurance related products. This is consistent with

expectations that different age group customers have different motivations and needs

to purchase different products. The results obtained also show that multiple purchases

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by the same customer tend to be in the same product group. Financial ACORN

category A customers tend to purchase more investment and protection insurance

products.

We provide interesting new results on the product purchase under different

external economic environments. Rising stock and housing markets encourage

customers to purchase more investment products and customers also purchase more

life insurance products when the house prices rise. We find evidence that when

consumer confidence and earnings rise, there is a significantly higher chance of

purchasing any type of financial products. The findings reported in this paper may

have important implications for profit scoring cards relevance. From the financial

product providers’ point of view, the findings could help those providers to target

specific (or existing) customers by selling them more specific financial products under

particular economic conditions.

Of course we have not put forward a complete, intertemporal optimising

economic model, which encompasses all aspects of financial purchase behaviour, but

we have drawn on relevant micro-economic theories of individual consumer

behaviour together with models of aggregate consumption and savings behaviour to

suggest variables which will influence the timing of the purchase of financial

products. On the basis of both statistical significance and predictive power, we believe

economic variables provide valuable information.

References Altman E (1968). Financial ratios, discrimination analysis and the prediction of corporate bankruptcy, Journal of Finance, 23, 589-609. Thomas L, Edelman D and Crook J (2002). Credit scoring and its applications, SIAM.

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Crook J, Hamilton R and Thomas L (1992). Credit card holders: Users and nonusers, Service Industrial Journal, 12, 251-262. Fisher R (1936). The use of multiple measurements in taxonomic problems, Annual Eugenics, 7, 179-188. Grablowsky B and Talley W (1981). Probit and discriminate functions for classifying credit applicants: A comparison, Journal of Economic Business, 33, 254-261. Hand D (1981). Discrimination and classification, John Wiley, Chichester, UK. Stepanova M and Thomas L (2001). PHAB scores: Proportional hazards analysis behavioural scores, Journal of Operational Research Society, 52, 1007-1016. Cox D (1972). Regression models and life-tables (with discussion), Journal of Royal Statistic Society Service B, 74, 187-220. Narendranathan W and Stewart M (1991). Simple methods for testing for the proportionality of cause-specific hazards in competing risks models, Oxford bulletin of economics and statistics, 53, 331-340.

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Table 1. Unit Root Tests for External Economic Variables (1999:01 - - 2003:03) Confidence FTSE House Earning Interest ADF Tests -3.205** 0.4469 2.217 -1.169 -0.804 Notes: ** denotes significant at the 5% level. ADF denotes Augmented Dickey-Fuller test. ADF tests are conducted using up to two lags of the dependent variables; a maximum of two lagged values is sufficient to render residuals white noise. Critical values for ADF tests are -2.92.

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Table 2. Estimations results for multiple purchase events Competing Risks Variables Single Risk Investment Pension Protection Life

Coef. RR Coef. RR. Coef. RR. Coef. RR. Coef. RR. Male 0.0124

(0.03) 1.012 0.0523 (0.04) 1.05 -0.097

(0.09) 0.908 -0.006 (0.05) 0.993 -0.159

(0.11) 0.853

Ref: 55~ 65

0 < Age ��� -0.2887** (0.08) 0.749 -0.338**

(0.10) 0.713 -1.62** (0.42) 0.197 0.206

(0.48) 1.229 0.62** (0.19) 1.861

20 < Age ���� -0.1658** (0.05) 0.847 -0.121**

(0.06) 0.884 -0.49** (0.15) 0.613 1.10**

(0.29) 3.002 -0.82** (0.22) 0.440

35 < Age ���� -0.1024** (0.04) 0.903 -0.1115**

(0.05) 0.894 -0.34** (0.13) 0.714 1.17**

(0.28) 3.211 -0.126 (0.14) 0.882

Age > 65 -0.0639 (0.05) 0.938 0.0381

(0.05) 1.039 -1.16** (0.22) 0.313 -2.29**

(1.04) 0.101 -0.285 (0.17) 0.752

Ref: C, U

FinAcorn A 0.1252** (0.05) 1.133 0.286**

(0.07) 1.331 -0.80** (0.19) 0.451 0.21**

(0.10) 1.234 0.029 (0.25) 1.029

FinAcron B 0.0499 (0.04) 1.051 0.0861

(0.05) 1.090 -0.46** (0.11) 0.634 0.18**

(0.07) 1.196 0.109 (0.15) 1.116

FinAcorn D -0.0261 (0.04) 0.974 -0.067

(0.05) 0.935 -0.48** (0.11) 0.619 0.14**

(0.07) 1.156 0.35** (0.15) 1.422

Ref: Monthly

Single-pay 0.1115** (0.04) 1.118 0.229**

(0.06) 1.257 -0.104 (0.13) 0.901 -1.11**

(0.15) 0.327 0.73** (0.17) 2.07

Pre-product --- Ref: Investment Ref: Pension Ref: Protection Ref: Life

other than Ref --- -1.56(pen) 0.209 -2.(inv) 0.130 -2.(inv) 0.118 -2(inv) 0.151

other than Ref --- -3.68(pro) 0.025 -2(pro) 0.113 -.4(pen) 0.648 -1(pen) 0.167

other than Ref --- -1.30(lif) 0.273 -1(lif) 0.226 -1(lif) 0.306 -3(pro) 0.026

Confidence 0.0550** (0.01) 1.057 0.037**

(0.01) 1.038 -0.001 (0.02) 0.999 0.19**

(0.01) 1.125 -0.07** (0.02) 0.934

FTSE All 0.5353** (0.07) 1.708 0.377**

(0.09) 1.458 0.020 (0.19) 1.021 1.11**

(0.14) 3.045 -0.59** (0.20) 0.552

House Price 0.9969** (0.04) 2.710 1.027**

(0.04) 2.791 0.40** (0.14) 1.491 1.20**

(0.08) 3.319 0.64** (0.17) 1.904

Earning index 2.6711** (0.15) 14.5 2.10**

(0.20) 8.20 1.86** (0.55) 6.41 4.29**

(0.28) 72.9 0.338 (0.68) 1.403

Interest rate -0.4931** (0.08) 0.611 -0.136

(0.10) 0.873 -1.04** (0.26) 0.353 -0.82**

(0.17) 0.439 -0.326 (0.32) 0.722

No. events 4993 2768 505 1364 356

-2LL 77199.21 40951.90 7463.45 18043.46 5591.28

Notes: Coef. Stands for coefficients. RR stands for relative risk. Relative risk is calculated by exponentiating the values of the corresponding coefficients. ** stands for p<0.05, the statistical significant level. Values in parentheses are the estimated standard errors. LL stands for the log likelihood values. Ref. stands for reference variables.

22

Table 3. Estimations results for the second purchase event

Competing Risks Variables Single Risk Investment Pension Protection Life Coef. RR Coef. RR. Coef. RR. Coef. RR. Coef. RR.

Male 0.012 (0.03) 1.012 0.053

(0.04) 1.05 -0.157 (0.10) 0.854 -0.032

(0.06) 0.968 -0.07 (0.12) 0.934

Ref: 55~ 65

0 < Age ��� -0.261** (0.09) 0.770 -0.375**

(0.12) 0.687 -1.59** (0.46) 0.205 0.235

(0.53) 1.264 0.71** (0.19) 2.027

20 < Age ���� -0.129** (0.06) 0.879 -0.094

(0.08) 0.911 -0.47** (0.17) 0.627 1.19**

(0.31) 3.284 -0.91** (0.26) 0.402

35 < Age ���� -0.050 (0.05) 0.952 -0.054

(0.06) 0.947 -0.32** (0.15) 0.729 1.26**

(0.31) 3.510 -0.133 (0.16) 0.875

Age > 65 -0.0639 (0.05) 0.946 0.076

(0.06) 1.079 -1.47** (0.29) 0.230 -2.09**

(1.04) 0.123 -0.289 (0.19) 0.749

Ref: C, U

FinAcorn A 0.082 (0.06) 1.086 0.202**

(0.09) 1.224 -0.91** (0.22) 0.404 0.24**

(0.11) 1.271 0.160 (0.28) 1.174

FinAcron B 0.052 (0.04) 1.054 0.094

(0.06) 1.099 -0.57** (0.12) 0.567 0.19**

(0.07) 1.212 0.139 (0.17) 1.149

FinAcorn D 0.008 (0.04) 1.009 -0.021

(0.06) 0.980 -0.56** (0.12) 0.673 0.17**

(0.07) 1.183 0.35** (0.17) 1.413

Ref: Monthly

Single-pay 0.084** (0.04) 1.087 0.007

(0.06) 1.007 0.124 (0.15) 1.133 -.891**

(0.16) 0.410 0.88** (0.21) 2.42

Pre-product --- Ref: Investment Ref: Pension Ref: Protection Ref: Life

other than Ref --- -1.60(pen) -2.07(inv) -2.14(inv) -1.89(inv)

other than Ref --- -4.01(pro) -2.16(pro) -0.36(pen) -2.34(pen)

other than Ref --- -1.77(lif) -1.57(lif) -1.18(lif) -3.64(pro)

Confidence 0.044** (0.01) 1.045 0.016

(0.01) 1.016 -0.017 (0.02) 0.983 0.12**

(0.02) 1.125 -0.11** (0.03) 0.893

FTSE All 0.439** (0.08) 1.552 0.190**

(0.10) 1.205 -0.131 (0.22) 0.877 1.11**

(0.14) 3.037 -1.00** (0.23) 0.367

House Price 0.943** (0.04) 2.569 0.981**

(0.05) 2.666 0.282 (0.17) 1.326 1.15**

(0.08) 3.151 0.66** (0.19) 1.941

Earning index 2.349** (0.17) 10.4 1.53**

(0.23) 4.64 1.31** (0.64) 3.72 4.11**

(0.30) 61.2 0.652 (0.72) 1.920

Interest rate -0.346** (0.08) 0.708 0.207

(0.11) 1.229 -1.18** (0.29) 0.306 -0.77**

(0.19) 0.462 -0.237 (0.34) 0.789

No. events 3879 2010 392 1181 296

-2LL 57859.02 28215.63 5596.94 15280.48 4522.92

Notes: See Table 1.

23

Table 4. Estimations results for the third or more purchase events

Competing Risks Variable Single Risk Investment Pension Protection Life Coef. RR Coef. RR. Coef. RR. Coef. RR. Coef. RR.

Male 0.015 (0.07) 1.015 0.073

(0.08) 1.08 0014 (0.22) 1.014 0.054

(0.18) 1.055 -0.473 (0.32) 0.623

Ref: 55~ 65

0 < Age ��� -0.448** (0.22) 0.639 -0.325

(0.23) 0.723 -14.2 (0.27) 0.000 -15.5**

(1.12) 0.000 -0.507 (0.91) 0.603

20 < Age ���� -0.247** (0.11) 0.781 -0.240

(0.14) 0.787 -0.81 (0.35) 0.443 0.719

(1.05) 2.053 -0.414 (0.50) 0.661

35 < Age ���� -0.273** (0.09) 0.761 -0.288**

(0.11) 0.750 -0.556 (0.31) 0.571 0.512

(1.08) 1.669 0.111 (0.42) 1.117

Age > 65 -0.238 (0.10) 0.788 -0.229

(0.11) 0.796 -0.665 (0.42) 0.514 -13.2**

(1.14) 0.000 -0.129 (0.52) 0.879

Ref: C, U

FinAcorn A 0.348** (0.11) 1.416 0.468**

(0.13) 1.596 -0.603 (0.41) 0.547 -0.075

(0.40) 0.928 -0.352 (0.59) 0.703

FinAcron B 0.090 (0.09) 1.094 0.192

(0.11) 1.212 -0.361 (0.30) 0.697 0.032

(0.23) 1.033 -0.205 (0.38) 0.815

FinAcorn D -0.040 (0.09) 0.960 -0.027

(0.11) 0.973 -0.54** (0.26) 0.580 0.074

(0.26) 1.077 -0.116 (0.40) 0.890

Ref: Monthly

Single-pay 0.177** (0.09) 1.193 1.270**

(0.22) 3.561 -1.07** (0.30) 0.34 -17.1

(0.27) 0.000 -0.152 (0.35) 0.859

Pre-product --- Ref: Investment Ref: Pension Ref: Protection Ref: Life

other than Ref --- -1.40(pen) -1.88(inv) -2.06(inv) -1.96(inv)

other than Ref --- -1.80(pro) -2.09(pro) -1.16(pen) -0.99(pen)

other than Ref --- -0.21(lif) -0.91(lif) -0.94(lif) -3.78(pro)

Confidence 0.114** (0.02) 1.120 0.112**

(0.02) 1.118 0.071 (0.06) 1.074 0.12*

(0.05) 1.122 0.127 (0.07) 1.136

FTSE All 1.075** (0.18) 2.929 1.058**

(0.22) 2.879 0.691 (0.53) 1.996 1.07

(0.47) 2.927 1.19 (0.64) 3.312

House Price 1.233** (0.09) 3.432 1.238**

(0.11) 3.448 0.547 (0.35) 1.729 1.50*

(0.29) 4.516 1.06** (0.42) 2.902

Earning index 3.908** (0.39) 49.8 4.07**

(0.47) 58.2 2.51** (1.22) 12.3 4.69*

(1.14) 109 0.143 (1.98) 1.154

Interest rate -1.020** (0.22) 0.361 -0.935

(0.27) 0.393 -0.530 (0.68) 0.589 -1.01

(0.69) 0.365 -1.188 (0.93) 0.305

No. events 818 576 84 114 44

-2LL 9777.41 6693.90 926.82 939.84 498.18

Notes: See Table1.

24

Table 5. Proportionality test results

Multiple purchase analysis 2nd purchase analysis > 3rd purchase analysis

Single risk Competing risk Single risk Competing risk Single risk Competing risk

-2Log-likelihood L 77199.21 72050.9 57859.02 53615.97 9777.41 9058.74

Event frequency Q --- -11000.04 --- -8772.04 --- -877.20

Null Hypothesis results Reject Reject Reject

25

Table 6. The comparison of economic variable impacts for the multiple purchase event

Variables With economic variables Without economic variables Demographic Coefficients Relative Risk Coefficients Relative Risk

Male -0.0076 (0.03) 0.992 -0.0056

(0.03) 0.994

Ref: 55~ 65

0 < Age ���� -0.3248** (0.10) 0.723 -0.3271**

(0.10) 0.721

20 < Age ���� -0.1873** (0.06) 0.829 -0.1813**

(0.06) 0.834

35 < Age ���� -0.1158** (0.05) 0.891 -0.1142**

(0.05) 0.892

Age > 65 -0.0371 (0.06) 0.964 -0.0485

(0.06) 0.953

Ref: C, U

FinAcorn A 0.1320** (0.06) 1.141 0.1215

(0.08) 1.129

FinAcron B 0.0539 (0.04) 1.055 0.0559

(0.04) 1.055

FinAcorn D -0.0226 (0.04) 0.978 -0.0170

(0.04) 0.983

Ref: Monthly

Single-pay 0.0556 (0.04) 1.057 0.1025

(0.04) 1.108

Economic Confidence 0.0653**

(0.01) 1.067

FTSE All 0.4195** (0.09) 1.521

House Price 0.8974** (0.05) 2.453

Earning index 2.1944** (0.20) 8.975

Interest rate 0.0604 (0.10) 1.062

Number of events 3495 3495

-2LL 51569.05 52103.15

26

Table 7. The comparison of economic variable impacts for the second purchase event

Variables With economic variables Without economic variables Demographic Coefficients Relative Risk Coefficients Relative Risk

Male 0.0033 (0.04) 1.003 -0.0001

(0.04) 1.000

Ref: 55~ 65

0 < Age ���� -0.2906** (0.11) 0.748 -0.3539**

(0.11) 0.702

20 < Age ���� -0.11739* (0.06) 0.889 -0.1228**

(0.06) 0.884

35 < Age ���� -0.0478 (0.06) 0.953 -0.0656

(0.06) 0.936

Age > 65 -0.0719 (0.07) 0.931 -0.0890

(0.06) 0.916

Ref: C, U

FinAcorn A 0.1306* (0.07) 1.140 0.1298

(0.08) 1.139

FinAcron B 0.0617 (0.05) 1.064 0.0615

(0.05) 1.063

FinAcorn D 0.0189 (0.05) 1.019 0.0279

(0.05) 1.028

Ref: Monthly

Single-pay 0.0610 (0.05) 1.063 0.0888**

(0.04) 1.093

Economic Confidence 0.2410**

(0.11) 1.272

FTSE All 0.4173** (0.10) 1.518

House Price 0.9356** (0.05) 2.549

Earning index 2.5730** (0.22) 13.10

Interest rate -0.0788** (0.01) 0.924

Number of events 2715 2715

-2LL 38537.39 39104.97

27

Figure 1: Monthly data for external economic variables

0 10 20 30 40 50

2000

2500

3000

3500FTSE_ALL

0 10 20 30 40 50

4

5

6 INTEREST

0 10 20 30 40 50

120

130EARN_INDEX

0 10 20 30 40 50

-10

-5

0CONFIDENCE

0 10 20 30 40 50

200

220

240HOUSE

28

Figure 2: ROC curves comparison for multiple purchases

29

Figure 3: ROC curves comparison for the second purchase