Profitability, Growth and Efficiency in the US Life Insurance Industry By William H. Greene New York University [email protected]Dan Segal University of Toronto [email protected]We appreciate the helpful comments from Joshua Livnat, Ajay Maindiratta, Stephen Ryan, James Ohlson, and workshop participants at the Hebrew University of Jerusalem, New York University, Yale University, London Business School, and the University of Toronto. LOMA kindly provided some of the data.
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Profitability, Growth and Efficiency in the US Life ... · profitability measures such as the return on equity (ROE) and growth. Similarly, we find that relatively efficient firms
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We then compute the average efficiency for each efficiency measure and test whether the
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average efficiency of HROA, HROE, HGR, and HCA is greater respectively than that of
LROA, LROE, LGR, and LCA.
This leads to the next set of hypotheses (stated in null form):
H1e: Eff(HROA) ≤ Eff(LROA)
H1f: Eff(HROE) ≤ Eff(LROE)
H1h: Eff(HGR) ≤ Eff(LGR)
H1i: Eff(HCA) ≤ Eff(LCA),
where Eff is the average efficiency of UNOR and UEXP. Testing Hypotheses H1e
through H1i together with H1a through H1d as already stated would indicate whether a
significant relationship exists between inefficiency and ROA, ROE, GR, and CA. That is,
rejection of all of the null hypotheses would indicate that inefficiency has negative
impact on ROA, ROE, GR, and CA and conversely that firms with low ROA, ROE, GR,
and CA are also less efficient.
Efficiency and Organizational Form
The data contain 20 mutual companies that had converted to stock companies
during the 1995-98 period. To control for demutualization, we omit from the analysis the
68 firm-year observations following the conversions. The sample then consists of 404
observations, of which 107 are mutual-years and 297 stock-year observations.
To use a statistically efficient test of the relationship between firm-specific
variables and inefficiency, as suggested by Huang and Liu (1994), we re-estimate the
frontier using a Cobb-Douglas cost function with the mean of the inefficiency term, di,
formulized as
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di = α + β1STOCKi + β2MIXi, (3)
where STOCK is a dummy variable valued at 1 for stock companies and 0 for mutual
companies, MIX is the policy-mix ratio, and i indexes the firms. (We add MIX to the
equation since we estimate the frontier over the entire data.15)
We then test the following hypotheses (stated in null form):
H2a: β1≥0
H2b: β2≤0
VI. Results
Table 1 provides descriptive statistics about the sample. Panel A of Table 1 shows
that the average size (total assets) of the sample firms ranges from $4,435 million in 1995
to $5,430 million in 1998. In 1998, the aggregate total assets of these firms were about
$657 billion, approximately a third of all assets in the industry. Thus, our sample covers a
material portion of all firms in the industry. Panel B of Table 1 presents the percentage of
direct premium revenues by line of business.
[Insert Table 1]
Table 2 demonstrates the effect of inefficiency on earnings. The table presents the
median and mean cost of inefficiency as a percentage of earnings before tax and as a
percentage of revenues, denoted EFFIN and EFFREV, respectively. We compute the cost
of inefficiency as one minus the exponent of -U times the inputs. We calculate the cost of
inefficiency in operating expenses, which comprise labor-related expenses (not including
commissions), physical capital, and all other expenses (Thus, our cost of inefficiency
does not include any inefficiency in the amount of financial capital held nor in the
commissions paid to agents16).
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[Insert Table 2]
The median of EFFIN in 1995 through 1997 is around 60%; in 1998, EFFIN is
much higher- 75%. The median of EFFREV is stable across the period, indicating that the
cost of inefficiency as percentage of revenues is 4.5%. Hence, inefficiency is substantial
relative to earnings and revenues.
Table 3 sets out the average inefficiency of the sample firms. The mean
inefficiency over the entire period is approximately 38%. This finding is consistent with
those of Cummins and Zi (1998) and Yungert (1993), which also document inefficiency
in the range of 30% to about 40%.
[Insert Table 3]
Panel A of Table 4 shows the distribution of firms across the three efficiency
groups (consistently efficient, partially efficient, and consistently inefficient), as well as
the mean inefficiency of each group. About 25% of the firms are considered to be
consistently efficient, 27% consistently inefficient and the reminder partially efficient.
The average inefficiency of the consistently inefficient (efficient) firms is 54% (25%).
Panel B of Table 4 provides descriptive statistics about the profitability and
growth measures. The means of ROA, ROE, GR, and CA over the entire period are 1.8%,
10%, 7%, and 6%, respectively. Panel C of Table 4 shows the Spearman correlations of
the efficiency measure of the entire sample with the value drivers. All correlations are
positive, i.e., efficiency is positively associated with ROA, ROE, CA, and GR and, in
general, significant at 5%.
Panel D of Table 4 presents the mean and average Wilcoxon rank scores of the
value drivers of the consistently efficient and inefficient firms. For example, the mean
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ROA of the consistently efficient (inefficient) firms is 2.3% (1.3%), and the Wilcoxon
rank is 105 (88). The profitability and growth measures are significantly, generally at the
5% level, higher for consistently efficient firms. Efficient firms have higher return on
assets, higher return on book value of equity, higher growth rate and higher ratio of
operating cash flows to total assets.
[Insert Table 4]
To test whether the differences in ROA and ROE can be explained by operational
inefficiency, we compute the yearly net income of the sample firms as if they were fully
efficient. For each firm, we add to net income and to operating cash flows the cost of
inefficiency in operating expenses after tax.17 We then test whether the adjusted ROA,
ROE, and CA differ between consistently efficient and inefficient firms. Panel E of Table
4 presents the mean and average Wilcoxon rank scores of the adjusted profitability
measures for the portfolios of consistently efficient and inefficient firms. The results
indicate that the differences in the adjusted ROA and ROE between the portfolios
become insignificant. The adjusted mean CA is still significantly (10%) higher for
efficient firms. Hence, these results appear to suggest that operational inefficiency
explains the differences in profitability between the consistently efficient and inefficient
firms.
To test hypotheses H1g through H1j we created portfolios of firms with the
highest (lowest) ROA, ROE, GR, and CA, denoted HROA (LROA), HROE (LROE),
HGR (LGR), and HCA (LCA), respectively. Panel F of Table 4 provides the average of
each efficiency measure of each portfolio. The mean and Wilcoxon rank score tests
indicate that the mean efficiency of HROE is significantly (5%) greater than the mean
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efficiency of LROE; the mean efficiency of HCA is significantly greater than the mean
efficiency of LCA, the difference is significant at 10%. The differences in efficiency
between HGR and LGR and between HROA and LROA are not significant.
In sum, the results suggest a one-to-one relationship between ROE and CA, and
the efficiency score of the firm – the higher the efficiency score, the higher are ROE and
CA, and vice versa.
Our second research question relates organizational form to efficiency. We repeat
the estimation of inefficiency, assuming a positive half-normal distribution (of the
inefficiency component) where the mean is a function of organizational form and policy
mix, using the Cobb-Douglas functional form. Panel A of Table 5 shows the regression
results. We find that the coefficient of STOCK, a dummy variable set at zero for mutual
companies and one for stock companies, is negative and significant, indicating that the
latter are significantly more efficient than the former. The coefficient of MIX is, as
expected, positive and highly significant, indicating that failure to account for the type of
policy (whole vs. term) results in higher inefficiency scores for firms that primarily issue
whole life policies; the most likely reason is that SAP ignore the matching concept.
Finally, Panel B of Table 5 provides the means and average Wilcoxon rank scores
of the profitability and growth measures of the two organizational forms. Over the entire
period, the stock companies have significantly (5%) higher ROA, ROE, CA, and GR. On
a yearly basis, the ROA and CA of stock companies are significantly, higher in every
year, at 10% or better. The ROE of stock companies is significantly higher in 1995 and in
1996, while GR is significantly higher in 1996 and in 1998.
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Overall, we find that stock companies are significantly more efficient than mutual
companies, and that their growth rates and profitability are significantly higher. Given
our prior results, the two findings may be related: that is, since stock companies are more
efficient they are more profitable and grow faster.
VII. Summary and Conclusion
The main purpose of this study is to explain cross-sectional differences in
profitability and growth rates of life insurance companies. Since the life insurance
industry is mature and highly competitive, we hypothesize that operational inefficiency
may have a strong negative effect on earnings and consequently on growth. We measure
inefficiency and the profitability and growth measures using the regulatory reports, which
are prepared according to the SAP. Since the SAP ignores the matching concept, we
distinguish between the different types of life policies results in order not to bias the
inefficiency scores.
We find that the industry is, on average, 38% inefficient. We also find that
efficiency is paramount to profitability and growth. Efficient firms have significantly
ROA and ROE, higher GR, and higher CA ratios. Furthermore, after adjusting net
income to the cost of inefficiency, we find that the differences in profitability between
efficient and inefficient firms become insignificantly different from zero. Thus,
operational inefficiency seems to explain the variation in profitability and growth. In
addition, high-value firms--i.e., those firms with the highest ROE, and CA--are more
efficient than low-value firms. These findings suggest the existence of a one-to-one
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relationship between value and efficiency; efficient firms have higher value, and higher
value firms are more efficient.
The two main organizational forms of life insurance companies are mutual
(owned by policyholders) and stock (owned by shareholders). Since the mutual form of
ownership allows less effective mechanisms for controlling and disciplining managers
than the stock ownership, we hypothesize that stock companies are more efficient than
mutual companies, and therefore, are also more profitable and grow faster. Our results
support the hypothesis: stock companies are indeed more efficient. Also, they exhibit
significantly higher ROA, ROE, CA, and GR than mutual companies.
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Table 1 – Descriptive Statistics Table 1, Panel A – Total Assets ($million) Sample Year N Mean Min. Max. Entire Sample 95 121 4,435 1.8 125,831 96 126 5,263 1.9 120,823 97 121 5,505 2.2 128,035 98 121 5,430 2.7 125,620 Stock Companies 95 99 4,641 1.8 125,831 96 96 2,948 1.9 85,694 97 98 3,458 2.2 92,455 98 96 3,585 2.7 100,251 Mutual Companies 95 22 3,506 11 38,311 96 30 12,670 103 120,823 97 23 14,225 103 128,035 98 25 12,518 102 100,251 Table 1, Panel B – Analysis of Percentage of Premiums by Line of Business Year N Mean
Notes: 1. Mean Premium is the average direct premium revenues of the sample firms. 2. Life, Annuity, and A&H stand for the life insurance, annuity, and accident and health lines of businesses, respectively.
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Table 2 – The Median (Mean) Cost of Inefficiency as a Percentage of Income before Tax and as a Percentage of Revenues
N Year CoI EFFIN 116 95 0.63
(1.15) 121 96 0.63
(1.05) 114 97 0.58
(1) 114 98 0.75
(1.34) EFFREV 116 95 0.04
(0.05) 121 96 0.044
(0.053) 114 97 0.042
(0.05) 114 98 0.045
(0.055) Notes: 1. CoI is the cost of inefficiency, which is computed as one minus the exponent of minus the efficiency measure, ui, times total
general expenses. 2. EFFIN is the ratio of cost of inefficiency over absolute value of income before taxes. 3. EFFREV is the ratio of cost of inefficiency over revenues. 4. We omitted from the analysis observation for which the ratio total general expense to revenues was greater than one, or
observations for which the ratio of total general expense to absolute value of income before tax is greater than 25.
Table 3 – The Stochastic Frontier Measure of Inefficiency YEAR N UNOR
95 121 0.35 96 126 0.39 97 121 0.38 98 121 0.38
Average 0.38 Notes (Table 3): 1. UNOR is the means of ui, the inefficiency component in the estimated stochastic frontier, where ui is assumed to have half-
Normal distribution. The inefficiency score is computed as 1-exp(-ui).
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Table 4 – Analysis of Profitability, Growth and Inefficiency Measures Table 4, Panel A – Distribution of Efficient, Partially Efficient and inefficient Firms and Their Mean Inefficiency Portfolio N % Mean
Inefficiency Inefficient 92 25 0.54 Partially 176 48 0.36 Efficient 100 27 0.25 Notes: 1. The inefficient, partially, and efficient portfolios consist of firms that are, respectively, consistently inefficient, partially
inefficient, and consistently efficient. Table 4, Panel B – Means and Medians of Value Drivers
YEAR N ROA ROE GR CA 95 92 0.018
(0.011) 0.10
(0.09) 0.06
(0.05) 0.06
(0.06) 96 92 0.019
(0.011) 0.10
(0.08) 0.07
(0.05) 0.07
(0.05) 97 92 0.019
(0.012) 0.11
(0.10) 0.08
(0.05) 0.05
(0.05) 98 92 0.016
(0.012) 0.09
(0.09) 0.06
(0.04) 0.05
(0.05) Mean 368 1.8% 10% 7 % 6%
Notes: 1. ROA is net income (t) over average total assets at the end of year t-1 and year t. 2. ROE is net income (t) over average book value of equity (including the AVR) at the end of year t-1 and year t. 3. GR is two years average growth in direct premiums. 4. CA is operating cash flows (t) over average total assets at the end of year t-1 and year t. Table 4, Panel C – Spearman Correlations between Efficiency Measures and Value Drivers (N=368) Value Driver UNOR ROA 0.075* ROE 0.105** CA 0.14** GR 0.087** Notes: 1. * (**) indicates significance level of 10% (5%) for the test of equality between the efficient and inefficient portfolio or for
correlations between variables. 2. For definitions of ROA, ROE, CA and GR refer to the notes to Table 4, Panel B. 3. For definition of UNOR refer to the notes to Table 3.
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Table 4, Panel D - Means and Average Wilcoxon Rank Scores (in parentheses) of Value Drivers, by Portfolio
Value Driver
Portfolio UNOR
ROA Efficient Inefficient
0.023**(105)** 0.013 (88)
ROE Efficient Inefficient
0.13** (109)** 0.08 (83)
GR Efficient Inefficient
0.087* (103)** 0.055 (90)
CA Efficient Inefficient
0.08** (105)** 0.05 (87)
Notes: 1. * (**) indicates significance level of 10% (5%) for the test of equality between the efficient and inefficient portfolio or for
correlations between variables. 2. For definitions of ROA, ROE, CA and GR refer to the notes to Table 4, Panel B. 3. The Efficient (Inefficient) portfolio consists of consistently efficient (inefficient) firms. Table 4, Panel E –Means and Average Wilcoxon Rank Scores (in parentheses) of Profitability Measures Adjusted for Inefficiency, by Portfolio Profitability Measure
Portfolio UNOR
ROA* Efficient Inefficient
0.035 (96) 0.029 (98)
ROE* Efficient Inefficient
0.21 (96) 0.17 (97)
CA* Efficient Inefficient
0.10* (101) 0.07 (91)
Notes: 1. * (**) indicates significance level of 10% (5%) for the test of equality between the efficient and inefficient portfolio or for
correlations between variables. 2. ROE*, ROA* and CA* are computed as described in the notes to Panel B but with the cost of efficiency (after tax) with respect
to total general expenses added to net income and operating cash flows. 3. The Efficient (Inefficient) portfolio consists of firms with the highest (lowest) profitability measure. 4. For definition of UNOR refer to the notes to Table 3. Table 4, Panel F – Mean Efficiency Measures for the Portfolios of Firms with the Highest and Lowest ROA, ROE, and CA Portfolio N UNOR
HROA LROA
92 76
0.53 (80) 0.55 (90)
HROE LROE
84 88
0.46** (67)** 0.55 (81)
HGR LGR
88 88
0.57 (77) 0.55 (79)
HCA LCA
92 104
0.47* (80)* 0.52 (91)
Notes: 1. * (**) indicates significance level of 10% (5%) for the test of equality between the efficient and inefficient portfolio or for
correlations between variables. 2. HROA (LROA) is the portfolio of firms with the largest (smallest) ratio of return on assets, computed as net income in year t
over average total assets at the end of year t-1 and year t. 3. HROE (LROE) is the portfolio of firms with the largest (smallest) ratio of net income in year t over average book value of equity
at the end of year t-1 and t. 4. HGR (LGR) is the portfolio of firms with the highest (smallest) two-year average growth in direct premiums revenue. 5. HCA (LCA) is the portfolio of firm with the largest (smallest) ratio of operating cash flow in year t over average total assets at
the end of year t-1 and year t.
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Table 5 – Analysis of Efficiency Measures and Organizational Form Table 5, Panel A – Regressions Results of Stochastic Frontier in Cobb-Douglas Functional Form: ln C = αααα0 + ∑∑∑∑JααααJln(PJ) + ∑∑∑∑mBmtQm + vi+ui, ui~N(di, σσσσu
2), di = αααα + ββββ1STOCKi + ββββ2MIXi
Intercept 3.4 (5.9) Amt 0.58 (19) Ann 0.047 (4.2) Ah 0.06 (6.3) Pl 0.011 (0.3) Pk 0.19 (3) Pm 0.19 (5) Alpha -13 (-3.9) STOCK -0.04 (-2) MIX 13.4 (3.9) Table 5, Panel B – Means and Wilcoxon Rank Scores (in parenthesis) of Profitability and Growth Measures by Organizational Form Year Type of firm N ROA ROE CA GR
95 Stock Mutual
37 72
0.02* (48)** 0.014 (59)
0.11* (50) 0.09 (58)
0.067 (50)* 0.055 (58)
0.077 (53) 0.051 (56)
96 Stock Mutual
25 77
0.017 (56)** 0.007 (36)
0.10* (54)** 0.06 (41)
0.08** (57)** 0.03 (33)
0.077* (53)* 0.031 (44)
97 Stock Mutual
23 74
0.02** (52)** 0.01 (39)
0.11 (49) 0.09 (46)
0.058**(53)** 0.028 (49)
0.086 (50) 0.045 (45)
98 Stock Mutual
22 74
0.017* (51)* 0.01 (40)
0.1 (49) 0.8 (46)
0.053* (53)** 0.023 (32)
0.086**(50)* 0.029 (42)
Overall Stock Mutual
100 389
0.02**(216)** 0.01 (164)
0.1** (210)** 0.08 (181)
0.065**(220)** 0.037 (153)
0.08** (209)** 0.04 (183)
Notes (Table 5): 1. Amt – total amount of insurance. 2. Ann – total annuity considerations. 3. AH – total A&H considerations. 4. Pl – price of labor. 5. Pk – price of capital. 6. Pm – price of indirect expenses. 7. Alpha – intercept of di. 8. MUTUAL– dummy variable that takes the value of 1 if stock company and 0 otherwise. 9. MIX is the mix of life policies ratio – amount of insurance of whole life policies sold during the year over the total amount of
insurance (whole + term) 10. In Panel A, T values appear in parentheses. 11. For definition of ROA, ROE, CA, and GR see notes to Table 4.
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1 Prior to Gramm-Leach-Bliley act of 1999 banks could not underwrite insurance.
However, they could sell insurance and have made major inroads into the annuity market.
2 Additional encouragements for demutualization are greater access to capital markets,
potential tax savings, and greater financial incentives for executives.
3 The truncated normal, which Stevenson (1980) suggested, avoids the restriction of a
zero mean for the normal distribution. However, it is not clear whether this restriction has
any effect on the efficiency estimates. Moreover, based on our experience, when µ (the
mean of u) is unrestricted, the log-likelihood seems to be ill behaved, the standard errors
of the parameters are inflated, and the function cannot converge. The normal/gamma
distribution, which Greene (1990) suggested, is superior to the other distributions since it
does not restrict either the location or the shape of the distribution. However, the log-
likelihood is currently highly complicated to estimate. In general, the ranking of the firms
according to the efficiency score is preserved across the different distributions of u.
4 Although OLS provides consistent estimates of the parameters with the exception of the
constant term, maximum likelihood estimation provides more efficient estimates of the
parameters.
5 The choice between this cost function and the regular translog function relies on the
statistical power of the estimated regression. The full translog function would increase
the number of variables significantly. Given our sample size (see the Data Section) that
would hamper seriously the statistical properties of the estimated regression and therefore
of the inefficiency estimates.
6 By using this measure we implicitly ignore the intermediary output associated with
whole life policies. In this type of policies, insurance companies make a profit both on
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the insurance and on the investments of the savings portion of the policy. However, we
believe that the main output of the life insurance line of business is the insurance risk
assumed by the insurer. Second, given the data limitations, it is impossible to separate the
premiums on whole life policies into their insurance and savings components.
7 Another potential proxy is the change in the amount of insurance in force during the
year. It would measure the net additional amount of risk that the company assumes
during the year. However, this measure could take on negative values in cases of
reinsurance or when the amount of insurance paid is greater than the amount of insurance
sold in any given year.
8 Cummins and Zi (1998) and Grace and Timme (1992) control also for group and
individual policies in the cost function. Given our sample size, we do not control for
group and individual policies because of lack of degrees of freedom. Another important
aspect that might affect the results is the marketing distribution system of the firm.
Insurers use various marketing distribution systems such as branch offices, agencies and
direct marketing. The results reported here are possibly associated with the distribution
system. Most insurers, however, employ more than one distribution system and hence
one cannot determine the unique distribution system of each firm.
9 The AVR does not reflect future obligations (as do other reserves) but is set aside to
protect against an extreme decline in the value of the assets that back up liabilities.
10 We are aware that the financial capital is a stock variable while physical capital is a
flow variable. We assume that flow is a fixed proportion of the stock.
11 We measure these ratios over five years, rather than averaging the yearly ratios, in
order to mitigate the influence of extreme fluctuations in the returns’ ratios on the price
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of capital. If the price of capital in a particular case is negative--that is, if the five-year
investment return was greater than the return on equity--we compute the price of capital
as the average price of capital of the sample for that year.
12 We do not account for the price of the physical capital in the aggregate price of capital
since the related expenses are rather negligible compared to the magnitude of the
financial capital.
13 The data do not contain information as to the number of insured under A&H group
master policies. Therefore, we used the number of master policies in the computation.
14 EMaP is a detailed expense study of life insurance companies that chose to participate
in the program. LOMA agreed to provide the data as part of a study of the cost structure
of the life insurance industry.
15 We did not use this procedure in estimating the SF measures for two reasons related to
the software (Frontier (Coelli (1984)): (1) the program allows for only the half normal
distribution assumption of the inefficiency component; and (2) the program uses only a
simple Cobb-Douglas cost function, which imposes constant returns to scale.
16 We did not include commissions and amount of financial capital in the computation of
the cost of inefficiency because we believe that these variables are subject to less
discretion by management as compared with other operating expenses.
17 We computed the tax rate as the four-year mean of the ratio of tax expense to earning
before income tax. If the computed tax rate is greater than 35% or negative, we changed