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Measuring cost inefficiency in the UK lifeinsurance industryPhilip HardwickPublished online: 06 Oct 2010.

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Applied Financial Economics, 1997, 7, 37 Ð 44

Measuring cost ine¦ ciency in the UKlife insurance industry

PHILIP HARDWICK

Department of Accounting and Finance, Bournemouth University, Fern Barrow, Poole,BH21 5BB, UK

To identify likely gainers and losers and to examine the e� ects of increasing competi-tion on the structure of the UK life insurance industry, the cost ine� ciency of UK lifeinsurance companies is analysed. A ¯ exible stochastic cost frontier is estimated for theindustry using a sample of 54 companies over ® ve years. The estimated frontier is thenused to compute measures of economic’, scale’ and total’ ine� ciency for di� erentcompany size groups. The results show that, on average, larger life insurance com-panies are less ine� cient than smaller companies, but there are substantial variationsin the degree of ine� ciency within size groups.

I . INTRODUCTION

The UK life insurance industry consists of many companiesof di� erent sizes, each supplying a range of products, underthe general headings of life insurance, pensions, annuitiesand permanent health insurance. Like the rest of the ® nan-cial services sector, the industry has been operating in anincreasingly competitive domestic and international envi-ronment. Several factors have brought this about: variousregulatory changes within the UK; the World Trade Organ-isation’s liberalization of trade in services following theUruguay Round; and the gradual arrival of the single Euro-pean market in ® nancial services. Recent research suggeststhat economies of scale exist in the industry, and with suchan intensi® cation of competitive pressures, one might expectto see an increase in the degree of market concentration.

Table 1 summarizes some measures of the structure of theUK life insurance industry in 1983 and 1993, using worldwide premium income as an indicator of company size. Itshows that there has indeed been a signi® cant increase in thedegree of concentration, with the proportion of worldwidepremium income earned by the top ® ve UK companiesrising from 32.1% in 1983 to 38.7% in 1993, and withsimilar rises in the proportions earned by the top 10 and top20 companies. Over the same period the Hir® ndahl indexrose from 0.036 to 0.046.

Nevertheless, it is probable that the life industry has so farmanaged to insulate itself to some extent from competitivechanges. Competition from the European Union (EU) has

not yet posed a really serious threat to UK life insurers andit can be argued that factors such as imperfect knowledge onthe part of consumers, product di� erentiation and the re-maining obstacles to international trade in life insurancehave allowed less e� cient companies to continue in busi-ness. However, the implementation of commission dis-closure, the introduction of more direct selling methods andthe increasing importance of cross-border trade and estab-lishment throughout the European Union may well changethis situation in the coming years. Indeed, many commenta-tors see larger companies playing a more and more domi-nant role in both the UK and the European Union. In orderto determine the likely e� ects of these changes on the UKlife insurance industry and, in particular, to identify thelikely gainers and losers among UK life insurance com-panies, it is important to be able to measure their costine� ciency and to compare ine� ciencies across companysize groups and other appropriate categories.

In view of the various changes a� ecting the ® nancialservices sector, one might have expected a ¯ ood of researchpapers on the competitiveness and relative e� ciency of® nancial services ® rms. It is true there have been severalstudies of US commercial banking (e.g. Ferrier and KnoxLovell, 1990; Berger and Humphrey, 1991; Grabowski et al.,1994; Kaparakis et al., 1994), but there have been very fewUK studies. Field (1990), Drake and Weyman-Jones (1992)and Piesse and Townsend (1995) have looked at the relativee� ciency of UK building societies, and Drake and How-croft (1994) have investigated the relative e� ciency of UK

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1 Drake and Howcroft (1994) give an application of DEA to the measurement of the e� ciency of bank branches.

Table 1. Concentration in the UK life insurance industry

1983 1993

Concentration ratio, C5 (%) 32.1 38.7Concentration ratio, C10 (%) 47.1 54.2Concentration ratio, C20 (%) 68.7 73.9Her® ndahl indexa 0.036 0.046

a The Her® dahl index (HI) was estimated using the top 50 com-panies and the formula: HI = + s2 , where s is each company’sshare of total worldwide premium income.Source: calculated by the author using data provided by the Asso-ciation of British Insurers.

bank branches. But there has been nothing on the UKinsurance industry.

This paper aims to ® ll this gap by undertaking a study ofthe relative cost ine� ciency of life insurance companies inthe UK, using a ¯ exible cost frontier approach. Section IIbrie¯ y outlines the non-parametric and parametric ap-proaches to the estimation of a cost (or production) frontierand presents a summary of the di� erent concepts of coste� ciency. Section III constructs a life insurance ¯ exible costfrontier and discusses the explanatory variables and thedata. The model is then estimated using data from 54 UKcompanies over the ® ve years 1989 Ð 1993. The estimationresults and calculated ine� ciency estimates are summarizedin Section IV, which also includes an analysis of the possiblelinks between ine� ciency and company size, organizationalform and location. Section V is a brief conclusion.

II . COST INEFFICIENCY

Cost and production frontiers

Studies of ine� ciency have developed two main approachesto the estimation of cost and production frontiers: dataenvelopment analysis (DEA) and an econometric approach.The DEA method uses non-parametric programming tech-niques to estimate a cost or production frontier.1 Datapoints on the resulting frontier are assumed to be e� cient,whereas points o� the frontier are assumed to be ine� cient.The main disadvantage of the approach is that, in general,no allowance is made for random errors, and results can beseriously a� ected by outliers. But the method has the ad-vantages of not having to specify a functional form fora production or cost function and not having to rely onad hoc distributional assumptions to separate measures ofine� ciency from random disturbances.

The econometric (or parametric) approach estimatesa production or cost function with a disturbance term whichis assumed to include a measure of ine� ciency. Earlier

studies tended to estimate deterministic frontiers (perhapsusing corrected ordinary least squares) and interpret allresiduals as indicators of ine� ciency, with no allowancemade for random errors. More recent studies, however, haveused the stochastic (or composed error) model in whichvarious distributional assumptions are made to enable one-sided ine� ciencies to be estimated separately from the sym-metric, random component of the disturbance term. Al-though the choice of distributional assumption for the one-sided disturbance term can a� ect the resulting ine� ciencyestimates, it is important to retain a random component tocapture the e� ects of excluded independent variables,measurement errors, unpredictable company behaviour orjust variations in luck, all of which can lead to a company’sactual production or cost being di� erent from that predictedby the frontier.

Several one-sided distributions have been suggested tomodel the ine� ciency component. The most popular, andthe one used in this paper, is the half-normal distributionsuggested by Aigner et al. (1977). Others include the ex-ponential distribution, also suggested by Aigner et al. (1977);the truncated normal distribution, suggested by Stevenson(1980); and the two-parameter gamma distribution, pro-posed by Greene (1990). Evidence suggests that the choice ofdistributional assumption has only a small e� ect on theine� ciency estimates and hardly any e� ect on the e� ciencyrankings of ® rms. For example, Kaparakis et al. (1994)obtained very similar ine� ciency results using the half-normal and truncated normal distributions. Greene (1990)reported similar rankings using the half-normal, truncatednormal, exponential and gamma distributions, but sug-gested that applications of the single-parameter distri-butions may yield higher overall estimates of ine� ciencythan the two-parameter gamma distribution (Greene, 1990,p. 158).

Results like this, which suggest that the choice of theone-sided distribution has only a minor e� ect on the in-e� ciency results together with the use of ¯ exible functions(such as the translog), which partly alleviate the problem ofselecting the most appropriate functional form for the pro-duction or cost function, suggest that the econometric es-timation of stochastic frontiers represents an appropriateway of estimating ine� ciencies.

Concepts of ine¦ ciency

Most studies of ine� ciency have used concepts based on thediscussion of production e� ciency by Farrell (1957); thisstudy is no exception. Three measures of cost ine� ciencyare calculated for a sample of life insurance companies,together with a measure of ine� ciency for the life insuranceindustry as a whole and measures of overall (or ray) econo-mies of scale. The three company ine� ciency measures are

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2 This measure of the user cost of capital is not net of taxation, so it does not take into account the e� ects of variations in corporation taxrates and allowances. However, corporation tax changes during 1989 Ð 1993 were relatively minor, so they are unlikely to representa serious source of distortion.

economic ine¦ ciency, which combines both technical’ andallocative’ ine� ciency, scale ine¦ ciency and total ine¦ -ciency. The industry measure will be called structuraleconomic ine¦ ciency.

Economic ine� ciency measures the deviation of a ® rm’sactual cost from the minimum cost for that size of ® rm, asindicated by the cost frontier. The economic ine� ciency of,say, ® rm 1 producing an output of y1 is calculated as C1 /C= 1 ,where C1 is the actual cost for ® rm 1 and C= 1 is the (® tted)minimum cost for a ® rm producing output y1 . A valuegreater that one implies either that the ® rm is producing lessthan the maximum possible output from the inputs it isemploying (i.e. that it is not technically e� cient) and/or that,given input prices, the ® rm is not employing the cost-minimizing combination of inputs (i.e. that it is not price, orallocatively, e� cient). The term economic ine¦ ciency may bethought of as being indentical in meaning to the concept ofX-ine� ciency, introduced by Leibenstein (1966).

Scale ine� ciency measures the deviation of the ® tted costfor each size of ® rm from the minimum cost of the opti-mum’ size of ® rm. Thus, the scale ine� ciency of ® rm 1 iscalculated as C= 1 /C= 0 , where C= 0 is the ® tted cost of a ® rmwith the optimum size. A value greater than one implies thatthe ® rm is smaller or larger than the optimum size. If smallerit will not be able to take full advantage of the economies ofscale in the industry; if larger it may be experiencing dis-economies of scale.

Total ine� ciency is a measure of economic and scaleine� ciency combined; for ® rm 1 it is calculated as C1 /C= 0 .The total ine� ciency measure for each ® rm is simply theproduct of the economic and scale ine� ciency measures.

Of the three measures, economic ine� ciency is probablythe most useful indicator of how well an individual ® rm isusing its resources, and is therefore the most appropriate forranking companies. The measure of structural economicine¦ ciency for the industry as a whole can be calculatedsimply as a weighted average of the individual ® rms’measures of economic ine� ciency, using output weights.

III . A LIFE INSURANCE COST FRONTIER

To construct a life insurance cost frontier, we assume thatlife companies are analogous to manufacturing companiesin the sense that they attempt to minimize the cost of usingvarious labour and capital inputs to produce outputs (in thiscase, insurance services) which are then sold to consumers.The cost frontier relates minimum cost to a company’soutputs, input prices and other independent variables.In general terms, a multiproduct cost frontier may bewritten as C = f (y, w, z), where y is a vector of outputs,

w is a vector of input prices, z is a vector of other indepen-dent variables and C is the minimum cost of producing y, forgiven values of w and z.

In this study, a life company’s activities have been aggreg-ated into just three products: life insurance, pensions andpermanent health insurance, and in each case the quantityof output is indicated by the constant price value of pre-mium income. The problems associated with using premiumincome as an output proxy have been discussed extensivelyelsewhere (e.g. O’Brien, 1991). In spite of these problems, wefollow many other insurance researchers (e.g. Colenutt,1977; Grace and Timme, 1992; Gardner and Grace, 1993) inassuming that premium income is the most acceptable indi-cator currently available of a company’s annual provision ofinsurance services. Instead of using three separate outputvariables in the cost function, Geehan (1977, 1986) proposedthe use of a single output measure constructed as a weightedaverage of each company’s insurance activities, using costsas weights. But in the absence of disaggregated cost data,this method is not yet feasible for the UK life industry.

The labour input is undoubtedly the most signi® cantresource used in producing insurance services. For mostcompanies, sta� wages and salaries, taxes and commissionsaccount for over 80% of total cost. Other expenses can beregarded primarily as payments for the use of capital, main-ly o� ce buildings, vehicles and o� ce equipment. Two inputprices are therefore included in the cost frontier function:a wage rate and a price of capital. To capture the e� ects ofvariations over the ® ve years of the study, the wage rate ismeasured by the average gross weekly earnings of full-timenon-manual workers in the insurance sector, as publishedby the Department of Employment. Following Jorgenson(1967) the user cost of capital is estimated as the long-terminterest rate (measured by the yield on ® ve-year Britishgovernment stocks), plus the annual depreciation rate in thelife insurance industry (assumed to be 2% per annumthroughout the period), less the expected annual rate ofcapital gain (measured using the price indices for plant andmachinery bought as ® xed assets in the banking and ® nancesector’ published in Business Monitor MM17 by the Cen-tral Statistical O� ce.2 This measure of the user cost ofcapital was used in a study of New Zealand life insurance byKhaled et al. (1995).

Two other independent variables are included in thefunction. First, it is not unreasonable to suppose that re-gional’ companies (de® ned as those whose head o� ces orprincipal administrative o� ces are located outside London)will face di� erent costs to companies based in London. Tocapture this, a dummy variable is included which is set equalto zero for regional companies and one for London-basedcompanies. De® ned in this way, we expect to ® nd a positive

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3 To maintain some degree of homogeneity in the outputs, all industrial business has been excluded from the analysis.4 The estimation was performed using TSP version 4.2B. Unfortunately, the input share equations could not be estimated jointly with thecost frontier because of the di� culties of obtaining companies’ cost share data. Given the relatively large sample size, this should not haveserious consequences for the e� ciency of the estimates.

relationship between this dummy variable and total cost.Secondly, another dummy variable is used to capture thein¯ uence of organizational form (i.e. to allow for cost di� er-ences between mutual and stock companies). This dummy isset equal to zero for mutuals and one for stock companies.The expected sign of the partial derivative of total cost withrespect to this variable is indeterminate. It could be arguedthat mutual companies are subject to less corporate controlfrom the market and so are likely to be less e� ective inkeeping down costs than stock companies (Hansmann,1985). On the other hand, both forms of organization havebeen operating in less than perfectly competitive conditions,so stock companies may not have been as cost-conscious asis sometimes assumed.

The model

It is assumed that the technology of the life insuranceindustry can be represented by a translog multiproduct costfrontier, according to which the natural logarithm of totalcost is approximated by a quadratic in the natural logar-ithms of the three output variables, the two input prices andthe other explanatory variables. Thus, the cost frontier to beestimated may written in full as follows:

ln C = a 0 + +i

a i ln y i + 0.5 +i

+j

a ij ln y i ln yj

+ +h

b h ln wh + 0.5 +h

+k

b hk ln wh ln wk

+ +h

+i

g hi ln wh ln y i + d 1 d1 + +i

d 1 id1 ln y i

+ +h

d 1 hd1 ln wh + d 2 d2 + +i

d 2 id2 ln y i

+ +h

d 2 hd2 ln wh + u + v

where i, j = 1, 2, 3 and h, k = 1, 2. Symmetry requires thata ij = a j i and b hk = b kh . The following restrictions are alsoimposed in the estimation to ensure linear homogeneity ininput prices:

+h

b h = 1

+h

b hk = +h

g hi = +h

d 1 h = +h

d 2 h = 0

And whereC = a life company’s total cost, which includes all man-

agement expenses and commissionsy1 = total premium income from all outstanding life in-

surance policies, de¯ ated to 1989 pricesy2 = total premium income from all outstanding pen-

sions and annuities, de¯ ated to 1989 prices

y3 = total premium income from all outstanding perma-nent health insurance policies, de¯ ated to 1989 prices

Total premium income for all three output measures isde® ned as net premiums receivable, less rebates and refunds,comprising the sum of new business, in-force regular pre-miums and single premiums, net of reinsurance, for ordinarybranch business only3 for UK contracts and global businesswritten in the UK. All three outputs are de¯ ated to 1989prices using data on price in¯ ation for insurance products,computed from statistics published by Cambridge Econo-metrics (1994).

w1 , w2 = wage rate and user cost of capital, respectively

d1 = 5 0 for regional insurance companies1 for London-based insurance companies

d2 = 5 0 for mutual companies1 for stock companies

The expression (u + v) represents the two-part disturbanceterm designed to capture both ine� ciencies and randomerrors. We follow Aigner et al. (1977) in assuming that u hasa non-zero, positive mean and a half-normal distribution(intended to capture the economic ine� ciency of each com-pany) with a constant variance, s 2

u , and that v is the trulyrandom error, normally distributed with a zero mean andconstant variance, s 2

v .Data on costs and premium incomes from life insurance,

pensions, annuities and permanent health insurance wereobtained for a sample of 54 companies of di� erent sizes andproduct mixes for the ® ve years 1989 Ð 1993 from Form 41 ofthe companies’ DTI returns, as summarized in Carter andDiacon (1991/2) and Insurance Company Performance (Uni-versity of Nottingham Insurance Centre (1993, 1995). Thecompanies included in the sample had positive levels of allthree outputs in all ® ve years. Data on organizational formand company locations were obtained from the Post Maga-zine Green Book (1995).

IV . RESULTS

A maximum likelihood procedure was used to estimate thecost frontier4 using the pooled time series/cross-sectiondata for the 54 companies in 1989 Ð 1993 (making a totalsample size of 270). A number of estimates in the estimationwere found to be insigni® cantly di� erent from zero. Thismeant a stepwise experimental procedure was followed,causing some terms to be omitted from the function, butwith no signi® cant e� ect on the maximized value of thelog-likelihood function. Table 2 shows the remaining

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5 An alternative would be to calculate the expected value of the conditional distribution of u given (u + v), using the formula given in Bauer(1990, p. 43).

Table 2. Parameter estimates and test statistics

Parameter Estimatea Parameter Estimatea

a 0 0.545 (0.177) b 1 1 - 10.064 (5.940)a 1 0.457 (0.121) b 1 2 10.064 (5.940)a 2 0.100 (0.061) g 1 1 - 0.989 (0.373)a 3 0.078 (0.037) g 1 2 0.865 (0.392)a 1 1 0.059 (0.039) g 2 1 - 1.530 (1.029)a 2 2 0.052 (0.011) g 2 2 1.694 (1.064)a 1 2 - 0.028 (0.016) d 1 0.440 (0.180)a 1 3 - 0.025 (0.011) d 1 1 - 0.268 (0.054)a 2 3 - 0.040 (0.010) d 1 2 0.183 (0.035)b 1 2.360 (0.863) d 2 3 0.086 (0.022)b 2 - 1.360 (0.863) l 2.998 (0.749)

1/ s 2.373 (0.172)

a Standard errors in parentheses.Number of observations 270Mean of dependent variable 4.13Standard deviation of dependent variable 1.05Log of likelihood function - 23.94Standard error of regression 0.28*R2 0.93*Breusch Ð Pagan test x 2 = 0.85*

An asterisk indicates that the statistic applies to the least-squaresestimates used as starting values for the ML frontier estimation.According to the Breusch Ð Pagan test, the hypothesis of homo-scedasticity cannot be rejected at the 0.05 level.

Table 3. Analysis of variance stability tests: F-statistics

1989 Ð 1990 0.1231990 Ð 1991 0.0871991 Ð 1992 0.1011992 Ð 1993 0.1241989/91 Ð 1991/93 0.384

Critical value of F at 0.05 level = 1.74

parameter estimates, together with estimates of l = s u / s v

and 1/ s , where s = Ï (s 2u + s 2

v ), and a set of diagnosticstatistics.

The pooled model can only be used to compute inef-® ciency statistics if the parameter estimates have remainedstable over the ® ve years of the study. To investigate this, themodel was re-estimated for each of the ® ve years separatelyand for four two-year periods (1989/1990, 1990/1991,1991/1992 and 1992/1993). Analysis-of-variance (Chow)tests were then performed to test for parameter stabilitybetween each pair of years. The entire sample was thendivided into two equal periods (1989/1991 and 1991/1993)and the test repeated. The resulting F-statistics are shown inTable 3, where it is clear that none of the stability hypothe-ses can be rejected at the 0.05 level. The average ine� ciency

Table 4. Premium income size groups and economic ine¦ ciency

Mean premiumSize income range Number ofgroup (£ million) companies EIa

A 0 Ð 99 13 1.39 (0.08)B 100 Ð 249 13 1.49 (0.10)C 250 Ð 499 14 1.43 (0.09)D 500 Ð 749 7 1.28 (0.07)E > 750 7 1.25 (0.03)

Structural economic ine� ciencyAll ® ve years SEI = 1.30 (0.01)1989 SEI1 = 1.34 (0.05)1990 SEI2 = 1.30 (0.05)1991 SEI3 = 1.24 (0.05)1992 SEI4 = 1.27 (0.04)1993 SEI5 = 1.32 (0.05)

a Standard errors in parentheses.

estimates are therefore based on the parameter estimatesobtained from the pooled model, as shown in Table 2.

Ine¦ ciency results

Estimates of economic ine� ciency (EI ) were obtained foreach of the 54 life insurance companies in each of the ® veyears by computing the following formula suggested byKalirajan and Flinn (1983):

EI = exp [r s 2u /( s 2

u + s 2v )]

where r is the residual (i.e. the di� erence between thelogarithm of each company’s actual and ® tted cost) andr s 2

u / (s 2u + s 2

v ) represents an estimate of the mode5 of theconditional distribution of u, given (u + v). The results werethen averaged over the ® ve years and categorized into ® vesize groups, based on the life insurance companies’ meanpremium incomes over the ® ve years, as shown in Table 4.

The estimates of EI were calculated for each size group asweighted averages of the company measures (using meanannual premium incomes as weights). It seems that thelarger companies in groups D and E are on average moreeconomically e� cient than the smaller companies in groupsA, B and C, though this may be a little misleading becausethere is considerable variation within groups, as indicatedby the standard errors. Notice that, even in the most e� -cient group (E), life companies are operating on averagewith costs 25% above the level that could be achievedthrough a more e� cient use of resources.

The industrial measure of structural economic ine� c-iency (SEI), also shown in Table 4, was computed as

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Table 5. Scale and total ine¦ ciency estimates

Size group OESa SI TI

A 0.81b 1.73 2.40(0.04)

B 0.87b 1.35 2.01(0.02)

C 0.87b 1.20 1.72(0.02)

D 0.88b 1.12 1.43(0.03)

E 0.92 1.00 1.25(0.044)

a Standard errors in parentheses.b Signi® cantly less than one at the 0.05 level.

a weighted average of all the individual companies’ eco-nomic ine� ciency estimates. The average of 1.3 for all ® veyears suggests that, on average, the life insurance industry inthe UK is operating with costs 30% above the level achiev-able with a more e� cient use of resources, but with nochanges in company location or organizational form. Thestructural economic ine� ciency measure was also cal-culated separately for each of the ® ve years and the resultsare summarized (as SEI1 to SEI5 ) in Table 4. These ® guressuggest that the degree of economic ine� ciency fell mark-edly from 1989 to 1991 then increased again from 1991 to1993, changes which may re¯ ect the cost-cutting undertakenby many ® nancial ® rms during the UK recession of1990 Ð 1991.

To investigate scale ine� ciency, estimates of overall (orray) economies of scale (OES) were calculated by evaluating

OES = +i

d ln C/d ln yi (i = 1, 2, ¼ , 5)

for the average size of company in each size group. Usingthis formula, a value less than one indicates economies ofscale, whereas a value greater than one indicates dis-economies of scale. The results are shown in the ® rst columnof Table 5. These estimates provide evidence for the exist-ence of statistically signi® cant economies of scale for com-panies in size groups A to D. There is also evidence ofeconomies of scale for companies in group E, but this is notstatistically signi® cant at the 0.05 level. There is no evidencefor the existence of diseconomies of scale in the industry.

In an attempt to measure the degree of scale ine� ciency(SI ), the average size of company in group E, with a meanpremium income of approximately £1500 million, was takento represent the `minimum e� cient scale’ of life company.The ® tted costs of the average companies in each of thesmaller size groups were then compared to the ® tted cost ofa company with a total premium income of £1500 million,but with the same output mix as the smaller company. To

Table 6. E¦ ciency, organizational form and location

EI

Mutual 1.27Stock 1.33t-value 0.84a

Regional 1.29London 1.34t-value 0.79a

a Cannot reject null hypothesis of equality at the 0.05 level (one-tailed test).

explain this more clearly, consider the average company insize group A which has premium income of approximately£30 million from life insurance, £20 million from pensionsand £5 million from permanent health insurance, makinga total premium income of £55 million. Fitting these outputvalues, together with the average values for the other inde-pendent variables, into the estimated cost frontier givesa predicted cost of £20.3 million, which is £0.37 per pound oftotal premium income. If the scale of the company is nowincreased to a total premium income of £1500 million,keeping the output proportions unchanged, the recalculatedpredicted cost becomes £320.25 million, which is just £0.214per pound of total premium income. Calculating the ratio ofthe predicted costs per pound of premium income gives theSI value of 1.73 shown in Table 5. Similar calculations forthe other size groups give the other SI ® gures shown in thetable.

The total ine� ciency (TI ) measures, shown in the ® nalcolumn of Table 5, suggest that the smaller life insurancecompanies in groups A and B are at a considerable costdisadvantage compared to larger companies when the aver-age levels of economic and scale ine� ciency are combined.Although there is some degree of variation within the sizegroups, there is little doubt that small life insurance com-panies with above average levels of economic ine� ciencyare likely to become increasingly vulnerable as competitivepressures in the EU mount.

Finally, statistical tests are performed to determinewhether the measure of economic ine� ciency is related tothe size, organizational form and location of companies.With regard to size, the correlation coe� cient betweeneconomic ine� ciency and premium income, using averagedata for the ® ve years for the 54 companies in the samplewas found to be - 0.18, indicating generally lower levels ofeconomic ine� ciency for larger companies. But this is a fair-ly weak degree of correlation, and in fact is not statisticallysigni® cant at the 0.05 level.

Table 6 summarizes the average economic ine� ciencymeasures for stock and mutual companies, and for regionaland London-based companies, and gives t-values to testfor equality between the mean ine� ciency measures. With

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regard to organizational form, the mutual companies in thesample are on average less economically ine� cient than thestock companies, though the di� erence in ine� ciency is notstatistically signi® cant at the 0.05 level. Thus, the null hy-pothesis of equality between the two means cannot berejected. A similar result is found when comparing regionaland London-based companies: regional companies are onaverage less economically ine� cient, but the di� erence be-tween the means of EI are not statistically signi® cant at the0.05 level.

V. CONCLUSIONS

The main ® ndings of the study may be summarized asfollows:

1. The UK life insurance industry is characterized byfairly high levels of economic ine� ciency, to the extentthat companies’ costs are on average about 30% abovethe estimated cost frontier.

2. There are signi® cant positive economies of scale in theUK life insurance industry and no evidence of dis-economies of scale, even for the largest companies. Onaverage, the smallest companies have (ray) averagetotal costs over 70% higher than the largest companies.

3. There is evidence for the view that regionally based,mutual life insurance companies are less economicallyine� cient than London-based stock companies,though the di� erences observed are not statisticallysigni® cant.

4. Even though the UK life insurance industry as a wholeis likely to bene® t from the European single market,there will also be losers. Larger companies have loweraverage levels of economic ine� ciency, but there isconsiderable variation within size groups. The exist-ence of di� erently sized companies with varying de-grees of ine� ciency operating side by side means thatfurther intensi® cation of competitive pressures in theEuropean Union will threaten the survival of com-panies in all size groups, though it is likely that the lessscale e� cient, smaller companies will be most at risk.

5. The principal bene® ciaries from the European singlemarket are likely to be those large (i.e. scale-e� cient)companies which have lower levels of economic ine� -ciency. Companies that are not so large and havelower levels of economic ine� ciency may need to gainin scale in order to compete e� ectively in the Europeanmarket.

6. The vulnerability of small companies and the oppor-tunities for growth facing large companies suggestthat, alongside developments in the increasingly openand competitive Europen market, there will be inevi-table increases in the concentration of the UK lifeindustry.

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