1. INTRODUCTION
For the past decades, the insurance industry has observed various
changes in economic conditions and changes in regulatory factors. The
technological advancement and advances in financial engineering could
change the way of insurers' doing business in various ways.
Moreover, the trends of mergers and acquisitions generally affect the
market structure, especially firm size and growth rate. Along with firm
growth, failure of financial intermediaries may generate adverse
consequences in the industry and then public concerns arise regarding
this matter. In the insurance area, to protect the policyholders and
other beneficiaries of policies due to the resulting insolvency of
insurers, a guaranty fund system has been created and implemented for
the current system since late 1960s. As a result, the presence of
guaranty funds has affected the business of various sizes of insurers,
especially smaller firms.
Small firms are surviving in the U.S. property and liability (P-L)
insurance industry and the guaranty fund system may provide a positive
impact on the persistence of small firms in the market. The guaranty
fund law, which may help small firms more, protects up to $300,000 in
most states and the protection cap has remained the same since 1981.
However, the real value of state protection has declined over time.
Then, the relatively reduced protection from the guaranty fund may
adversely affect smaller firms' operation since large accounts are
seeking large and stable insurers because the coverage guaranteed by the
law is well below their desired protection. This research question can
be tested empirically and this paper examines the impact of decreased
levels of real guaranty fund protection on insurers' prices for
large and small P-L insurance firms.
A company level analysis is used for the period of 1992 to 2000.
Based on total assets, U.S. P-L insurers are divided into two groups,
small insurers and large insurers, and then the impact of guaranty fund
system on insurance prices is tested for the two groups. Also, it is
tested for the two different sub-periods, 1992-1996 period and 1997-2000
period, based on the underwriting profit cycle.
This research is the first study to examine the potential impact of
the guaranty fund system on firms of different sizes. Empirical results
of this paper will provide useful information on the public policy issue
on firms' activities of different sizes in the U.S. P-L insurance
industry.
2. LITERATURE REVIEW
One of common causes of P-L insurers' failures is rapid
overexpansion and diversification along with managerial inefficiencies.
For an obvious reason, insurance industry concerns are about the
insolvency of insurance firms. Since 1969, as a result, a guaranty fund
has been developed to protect the parties in the insurance contract if
an insurer goes bankrupt. By year 1981, every state has enacted its own
guaranty-fund law. The coverage provided by the guaranty fund is limited
and most states follow the model law suggested by the National
Association of Insurance Commissioners (NAIC). On average, the
guaranty-fund law covers up to $300,000 in most states and the amount of
coverage hasn't been changed in over three decades.
There were no prior studies to examine the relationship between the
guaranty fund system and insurance prices. Many studies, however,
focused on the impact of guaranty fund on the firm risk-taking behavior
(e.g., Cummins, 1988, Lee, Mayers and Smith, 1997, and Downs and Sommer,
1999). Cummins (1988) argued that the guaranty fund system should be
changed to risk-based assessment to reduce high-risk strategies which
were caused by the current flat premium rate assessment in which the
level of firm's risk was not linked to the assessment. Lee, Mayer
and Smith (1997) asserted the risk-subsidy hypothesis and provided
evidence from stock companies. Under the risk-subsidy hypothesis, the
enactment of state guaranty fund law has increased the risk of
insurers' asset portfolios. Downs and Sommer (1999) examined the
risk-subsidy hypothesis for the stock companies with the perspective of
inside ownership structure. They also support the risk-subsidy
hypothesis and find a positive relationship between the inside ownership
and risk-taking behavior.
Unlike other prior research, this paper directly addresses the
impact of the state protection system on P-L insurers' operation.
Since the nominal value of state protection was unchanged at $300,000,
the real value of guaranty funds has declined over time. By year 2002,
the real value has dropped more than 50 percent of the original value
started in 1981. The limited and declined real value of guaranty fund
protection impacts on the large accounts that need more than the
statutory coverage. So, their tendency is to seek large and
well-established insurers who may have a conventional conception of
'Too Big To Fail.' Consumers also tend to find financially
sound firms because of limited protection (Klein and Barth, 1995).
Furthermore, there exists a prevailing perception that small insurers
are riskier than larger insurers. Hence, the decreased level of guaranty
fund protection might adversely affect small firms. That is, there might
be a tendency to decrease prices to mitigate the increased risk due to
decreased protection from the safety net (see Epermanis and Harrington,
2006). The impact might be greater for smaller firms since their
business is more tied to guaranty fund protection.
In summary, we can state the following testable hypothesis for P-L
insurers:
Hypothesis 1. Since insurers have to mitigate the risks, the
decreased level of guaranty fund protection negatively impacts on
insurers' prices. The price reduction is relatively higher for
small insurers compared to large insurers.
The P-L insurance industry generally experiences an underwriting
cycle measured by the industry's combined ratio (see Figure 1). A
value of 100 indicates a break-even point and high value of the combined
ratio indicates losses from underwriting performance. More competition
and price reductions are characterized during the period when the
underwriting cycle is downward, i.e., 1992-1996 period. On the other
hand, less competition and rising prices are commonly found during the
period when the underwriting cycle is upward trend, i.e., 1997-2000
period. Browne and Hoyt (1995) and Kleffner and Lee (2009) show a high
correlation between the underwriting cycle and insurers'
insolvency. Thus, we expect that the impact of the guaranty fund system
on prices is different for the different underwriting cycles in the
following way:
Hypothesis 2. The impact of guaranty fund protection is greater
during the period when the industry experiences poor underwriting
performance compared to the period when the industry experiences
improved underwriting profits.
3. DATA AND MODEL SPECIFICATION
3.1 Data
Various firm-specific variables are obtained from the Annual
Statement from NAIC Database. Gross Domestic Product (GDP) is available
from the U.S. Department of Commerce. To get the real value of a
guaranty fund, the cap amount has been deflated using the personal
consumption expenditures implicit price deflator obtained from Bureau of
Economic Analysis, U.S. Department of Commerce. Data for the insurer
agency system is obtained from Best's Key Rating Guide (A.M. Best
Co.). The sample period is 1992-2000.
[FIGURE 1 OMITTED]
3.2 Model Specification
General demand and supply equation deliver the equilibrium point of
insurance price and then a reduced form is obtained to analyze the
impact of the guaranty fund on firm prices. Insurers' prices are
set based on the level of market interest rates, capital adequacy ratio,
product specialization, level of reinsurance utilization, and general
economic conditions. These can be captured in a model of demand for and
supply of prices of each insurer. The regression model is represented by
the following:
[Price.sub.i,t] = [[beta].sub.0] + [[beta].sub.1]Guaranty
[Fund.sub.t] + [[beta].sub.2]Real [GDP.sub.t] +
[[beta].sub.3][Interest.sub.t] + [[beta].sub.4]Market [Share.sub.i,t] +
[[beta].sub.5] [Advertisement.sub.i,t] +
[[beta].sub.6][Leverage.sub.i,t] +
[[beta].sub.7][Diversification.sub.i,t] + [[beta].sub.8][Agent.sub.i,t]
+ [[beta].sub.9][Ownership.sub.i,t] + [[beta].sub.10][Group.sub.i,t] +
[[epsilon].sub.i,t] (1)
where i indicates the insurer and t refers to the year. Price is
estimated as premiums earned divided by losses and loss expenses
incurred (i.e., the inverse of loss ratio and seeWinter, 1994, Cummins
and Danzon, 1997, and Choi and Weiss, 2005). In this paper, premiums,
losses and loss adjustment expenses related to workers'
compensation were deleted to calculate price, advertisement, and
leverage variables, since the workers' compensation line is not
affected by the limit of guaranty fund law.
There is a problem of using 'real value of guaranty fund'
since the value has been continuously decreased over time; even though
the magnitude of decreased level has not been the same (depends on the
price index to get the real value). Thus, the inclusion of real value of
guaranty fund would be spurious in the regression model (Greene, 1993).
Since the real value of the fixed guaranty fund has declined over the
period, a decreased level of protection (high risk to the insurer) is
implicitly offered. Generally reinsurance is utilized as a mechanism
which enables insurers to achieve more efficient risk sharing, thus
supplementing underwriting capacity (Garven and Grace, 200i). That is,
insurers tend to use more reinsurance when they face more risks. Thus,
reinsurance utilization is, instead, used for 'Guaranty Fund'
variable as a proxy. Bassett and Brady (2002) also used a proxy
variable, studying the impact of the decline in the real value of
deposit insurance on the bank performance.
This variable is constructed as follow:
reinsurance ceded/direct premiums written + reinsurance assumed
Many prior studies used this definition of reinsurance utilization
(e.g., Regan and Tzeng, 1999, Garven and Lamm-Tennant, 2003, Viswanathan
and Cummins, 2003, and Cole and McCullough, 2006). Insurers may try to
mitigate increased risk through decreasing prices, if statutory
protection is important for the pricing. That is, because of
risk-sensitive demand, increased risk lowers prices that risk-sensitive
customers are willing to pay (Epermanis and Harrington, 2006).
Insurers' risk taking behaviors from the perspective of
'incentives for safety' have been studied in the insurance
literature, e.g., Lee, Mayers, and Smith, 199i, Downs and Sommer, 1999,
Bohn and Hall, 1999, and Epermanis and Harrington, 2006. The expected
sign of this variable is negative and the magnitude of this impact is
more significant for small insurers and much less (or nil) for large
insurers as stated in Hypothesis 1.
To reflect the business cyclical economic fluctuation, two cyclical
variables are included in the price equation. Firstly, real GDP growth
is measured by dividing the current year's real GDP by the previous
year's real GDP. It is expected to be positive if the GDP growth
boosts demand for insurance. It is also expected that this variable
captures the riskiness of insurers at different points in the business
cycle (see Bassett and Brady, 2002). Secondly, the market interest rate
measured by a one-year T-bill rate is included (in Interest variable).
Two major insurers' earnings are generally from underwriting
business and investment activities. And, market interest rate is
sensitive to the insurance business through investment activities
Leverage is used to identify the capital adequacy of an insurer. It
is defined as the ratio of premiums written to surplus and is the most
widely used leverage ratio in insurance (Cummins and Weiss, 1992). As
the leverage ratio increases, the insurer's ability to cover
unexpected losses is reduced. So, an increase in leverage is associated
with higher risk. High risk may be compensated by a decreased price.
Therefore, the expected sign on this variable is negative.
Advertisement represents advertising intensity which is measured as
the ratio of advertising expenses to net premiums written. It is used to
control the fact that advertising may promote more sales and affect
prices. This variable is also included in the model to control for the
possibility that the two groups (small vs. large insurers) vary as to
the advertising ratio used in a P-L market. The effect from this
variable is uncertain. Increased costs due to high advertisement
expenses may lead to high prices. On the other hand, if advertisements
generate more sales then insurers may reduce prices.
Market Share measures the changes in market share on the individual
firm and it is calculated based on the premiums written each year. Rapid
market growth is considered one of the causes of market failure and
affects prices. Specifically, A.M. Best (2001) reports that a rapid
growth is one of the primary causes of P-L insurers' failure since
it represents 15.1% of total P-L insurers impairment studied for the
period of 1969 to 2006. Also, studies provide evidence of high premium
growth prior to the insolvencies (Grace, Harrington, and Klein, 1995,
and Bohn and Hall, 1999). Growing firms are more likely to charge higher
prices if they try to increase market power. A positive relationship is
expected if firms are able to increase prices as their market share
increases. It is due to the fact that those firms can charge higher
prices with market power. We may have more relative market power if
consumers spend significant search costs to find products and if
consumers have a loyalty to market leaders due to high market share,
i.e., a large and well-established company must be good (Choi and Weiss,
2005).
The lines of business an insurer writes can affect the overall risk
and performance of the firm. Diversification is measured using the
Herfindahl index which is the sum of square of each of four major areas;
short-tail personal lines, long-tail personal lines, short-tail
commercial lines, and long-tail commercial lines. A higher value of the
Herfindahl index indicates a more specialized (less diversified)
company. Insurers that specialize in a few lines may gain greater
expertise in administering these lines, leading to a positive
relationship between diversification and price. On the other hand, it
may be more difficult to achieve economies of scope or cross-sell
business so that price might be reduced for such an insurer.
Three dummy variables are included to control the firm
characteristics of P-L insurance companies; Agent dummy, Stock dummy,
and Group dummy. Insurance is distributed to customers in a number of
different ways, and a different distribution system is variously related
to costs and prices. Thus, the distribution system may play a
significant role in determining prices. For example, direct writers rely
relatively more on factors such as advertising and computer automation
in distributing insurance. However, an independent agency system depends
more on the capacity and expertise of agents. So, their commission rates
are higher than other distribution systems. Insurers using independent
agents are assigned one and zero otherwise.
Organizational forms for insurance companies include mutuals and
stock organizations, each of which has its own objective function and is
effective in solving specific incentive conflicts among the contractual
parties such as owners, managers, and policyholders (Mayers and Smith,
1994 and He and Sommer, 2010). For instance, in mutual organizations the
conflict between policyholders and owners are eliminated because the
policyholder-owner functions are merged. Controlling for organizational
form allows for the possibility of differing levels of risk behavior
among stock and mutual firms (Lamm-Tennant and Starks, 1993, Doherty and
Dionne, 1993, Smith and Stutzer, 1995, and Weiss and Choi, 2008). The
binary variable takes the value of one for stock companies and zero
otherwise.
Controlling for group membership allows for the different behavior
between group members and non- group members in insurance prices. Large
insurers are more likely to be affiliated with a group than small
insurers. Insurers affiliated with a group are assigned one and zero
otherwise.
4. EMPIRICAL RESULTS
The potential sample of insurers consists of all P-L insurers that
write P-L insurance and that report data to the NAIC for the period 1992
to 2000. From this potential sample, insurers with negative surplus,
assets or premiums were deleted. Insurers are allowed to enter and exit
the U.S. market over the sample period, in order to avoid problems
associated with survivor bias for the equation (1). Based on total
assets, large insurers are defined as the top 100 insurers and a rank
below 1,000 are grouped as small insurers. No evidence of
multicollinearity among variables is found.
We look at the differences in performance and market share changes
between the two groups. First, the rate of return on total assets (ROA)
is calculated each year for the small firms and large firms. Figure 2
highlights the different movements of ROA for two groups. It shows that
large insurers generate higher ROA than small firms every year except in
1992. Changes in market share measured by premiums written for the two
groups are also pictured in Figure 2 for the sample period. On average,
large firms account for 53.9 percent of total property-liability
premiums written in the U.S., while small firms represent 3.3 percent of
the total market.
Not surprisingly, significantly different firm characteristics are
reported in Table 1 between small insurers and large insurers. Small
insurers tend to spend more on advertisements compared to their total
premiums' income and show significantly higher levels of leverage.
On the other hand, large insurers are more diversified in their business
structure, use more reinsurance transactions, and are less likely to use
an independent agency system. About 74.7 percent of large insurers are
stock companies and 95.6 percent of them are members of insurance
groups, whereas, for small firms, 61.3 percent are stock ownership
companies and only 43.4 percent are members of insurance groups.
[FIGURE 2 OMITTED]
Table 2 shows that the reinsurance utilization variable is negative
for small insurers and significantly related to insurance price at the 1
percent level. However, this variable is not significantly related to
price for large insurers. Thus, there is strong evidence that small
insurers are more likely to decrease price due to increased risk in
order to attract customers in the competitive market. Otherwise,
consumers do not purchase the product provided by relatively high-risk
insurers (smaller companies), implied by reduced level of real guaranty
fund protection, if prices are same. These results are consistent with
the risk-sensitive demand and franchise value hypothesis by Epermanis
and Harrington (2006) and provide support for Hypothesis 1. This may
result in small insurers having a relatively less competitive position
in the market and may impact adversely on future firm growth.
Table 3 shows that there exist some differences between the two
periods. The coefficient on the reinsurance utilization variable for
small insurers is -0.3639 for the first period, while it is -0.4012 for
the second period. Both are significant and negative like that of Table
2. However, the impact of statutory protection for small insurers is
greater during the period when the industry has experienced decreasing
underwriting profits. This result provides support for the second
hypothesis.
The results in Table 2 indicate that two economic cyclical
variables are all insignificant in the price equation. Thus, real GDP
changes and market interest rates do not affect insurance price. With
respect to the leverage variable, the results for both large and small
insurers are negative and significant for the 1992-1996 period only.
Maybe, publicly available information (e.g., NAIC's Insurance
Regulatory Information System) may prevent those higher risky firms from
charging high prices. However, interestingly, it is positive and
significant for small insurers during the 1997-2002 period.
Advertisements are strongly related to low prices for small
insurers as reported in Tables 2 and 3. This suggests that small
insurers do not charge higher prices even though they have increased
costs from advertisement spending. This variable is not significantly
related to large insurers' pricing. The results for market share
change provide that these coefficients are negative and significant for
the 1992-2000 period and the 1997-2000 period for large insurers only.
Thus, these findings suggest that large firms sacrifice their prices to
gain more market share during this time period and that no market power
theory is implied in this market. Tables 2 and 3 show no significance
for this variable for small firms. Diversification is positively related
to both small and large insurers' price, except for large insurers
for the 1992-1996 period. Thus, non-diversified and specialized insurers
are more likely to charge higher prices and no economies of scope are
presented in the P-L insurance industry during the sample period. The
coefficients on agent variables are positive and significant for the
small insurers for the three different periods, but they are negative
and significant at the 5 percent level for the large insurers for the
1992-1996 period. This suggests that large insurers can utilize
agents' expertise more efficiently than small insurers and that
this efficient utilization may lead to lower prices. The results in
Table 3 indicate that large stock companies are more likely to deliver
their products at higher prices than non-stock companies. Small insurers
are more likely to charge lower prices if they are affiliated with a
group. But, for the large insurers, the coefficients on group dummy
variables are not significant.
5. CONCLUSIONS
This paper analyzes the effects of guaranty fund protection on
insurance prices. The analysis is made on the different firm sizes;
small insurers and large insurers. The empirical analysis also uses two
data sets based on the underwriting performance cyclical movement.
The regression results show the existence of guaranty fund impact
on insurance prices. However, these findings are not applied to large
firms. For small firms only, the results from the guaranty fund related
model suggest some evidence that the guaranty fund effect exists in the
U.S. P-L insurance market. The decreased level of guaranty fund
protection impacts negatively on prices for small insurers. In addition,
we find some evidence that small insurers tend to decrease prices more
during the period when the industry's underwriting profits are
decreasing. Those findings together suggest that small insurers
mighthave disadvantages in pricing in the P-L insurance market to
compete with firms of other sizes or biggerfirms. This position may
adversely impact corporate growth for small insurers. The implications
of this research suggest that regulators should consider changing the
level of current guaranty fund protection.
However, economic cyclical variables, i.e., real GDP growth and
market interest rates, do not provide a significant impact on insurance
prices. Mixed results are found in firm-specific variables for small and
large firms. Moreover, along with those findings, different firm
characteristics are observed between small and large insurers.
The result findings from this paper provide new information on the
impact of the guaranty fund system in the U.S. P-L insurance industry.
Since no prior research examines these causal relations in this
industry, the empirical findings from this study could provide valuable
input for the public and regulators. The results of this paper provide
and meet demanding information market needs.
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Byeongyong Paul Choi, Howard University, Washington, DC, USA
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TABLE 1: DESCRIPTIVE STATISTICS: SMALL VS. LARGE FIRMS
Small Firm
Variables Mean Std. Dev.
Price 1.7164 1.1490
Asset Size $12.78 $8.93
Asset Growth 1.1102 0.3158
Reinsurance Utilization 0.1085 0.2527
Leverage 1.6314 35.1142
Advertisement 0.0164 0.3240
Market Share Change 5.1278 89.0438
Diversification 0.6774 0.2537
Agent Dummy 0.7326 0.4426
Stock Ownership Dummy 0.6130 0.4871
Group Dummy 0.4336 0.4956
Observations 6,268
Large Firm
Variables Mean Std. Dev. t-test
Price 1.3757 0.8684 ***
Asset Size $5,181.29 $7,848.90 ***
Asset Growth 1.1072 1.1587
Reinsurance Utilization 0.2308 0.2510 ***
Leverage 0.9904 0.6068
Advertisement 0.0052 0.0242 ***
Market Share Change 2.7214 36.7285
Diversification 0.5064 0.2041 ***
Agent Dummy 0.6000 0.4902 ***
Stock Ownership Dummy 0.7467 0.4352 ***
Group Dummy 0.9556 0.2062 ***
Observations 900
Note: Units of observation are insurance companies.
Dollars are in millions.
Small firms are companies below 1,000 rank and Large firms
are top 100 companies. *** significant at 1% level;
** significant at 5% level; * significant at 10% level.
TABLE 2. PRICE REGRESSIONS: 1992 TO 2000
Large Firm
Independent Variable Coeff. Std. Err.
Intercept -3.3231 4.9252
Reinsurance Utilization 0.0179 0.0909
Real GDP Growth 3.7900 4.6479
Market Interest (T-Bill) 8.0488 3.5966 **
Leverage -0.0030 0.1019
Advertisement -1.0049 0.6603
Market Share Change -0.0003 0.0001 ***
Diversification 1.0775 0.3209 ***
Agent Dummy -0.1326 0.0912
Stock Ownership Dummy 0.1250 0.0946
Group Dummy -0.0692 0.3249
Observations 900
Adjusted [R.sup.2] 0.0707
Small Firm
Independent Variable Coeff. Std. Err.
Intercept -0.9745 2.6855
Reinsurance Utilization -0.3783 0.0653 ***
Real GDP Growth 2.0153 2.6114
Market Interest (T-Bill) 0.8692 1.9248
Leverage 0.0000 0.0003
Advertisement -0.1061 0.0343 ***
Market Share Change -0.0001 0.0001
Diversification 1.1612 0.0846 ***
Agent Dummy 0.1153 0.0444 ***
Stock Ownership Dummy 0.0018 0.0349
Group Dummy -0.0937 0.0405 **
Observations 6,268
Adjusted [R.sup.2] 0.0612
*** significant at 1% level, ** significant at 5% level,
and * significant at 10% level.
Note: Standard errors are heteroscedastic-consistent
estimators following the method of White (1980).
TABLE 3
PRICE REGRESSIONS: BY UNDERWRITING PROFIT CYCLE
1992 to 1996
Large Firm
Independent Variable Coeff. Std. Err.
Intercept -0.0852 6.5358
Reinsurance Utilization 0.0052 0.1200
Real GDP Growth 1.9800 6.5099
Market Interest (T-Bill) 4.5554 3.5169
Leverage -0.2594 0 0872 ***
Advertisement -0.6904 0.6137
Market Share Change -0.0422 0.0395
Diversification 0.4316 0.2919
Agent Dummy -0.3245 0.1518 **
Stock Ownership Dummy 0.2979 0.1261 **
Group Dummy -0.6679 0.4669
Observations 500
Adjusted [R.sup.2] 0.1068
1992 to 1996
Small Firm
Independent Variable Coeff. Std. Err.
Intercept 1.0563 3.5070
Reinsurance Utilization -0.3639 0.0758 ***
Real GDP Growth 0.0071 3.4149
Market Interest (T-Bill) 2.5238 2.1053
Leverage -0.0002 0.0000 ***
Advertisement -0.0878 0.0280 ***
Market Share Change -0.0001 0.0001
Diversification 1.1261 0.0950 ***
Agent Dummy 0.0965 0.0536 *
Stock Ownership Dummy 0.0291 0.0451
Group Dummy -0.1416 0.0451 ***
Observations 3,645
Adjusted [R.sup.2] 0.0741
1997 to 2000
Larqe Firm
Independent Variable Coeff. Std. Err.
Intercept 18.5577 23.2571
Reinsurance Utilization 0.1417 0.1434
Real GDP Growth 17.1597 21.5185
Market Interest (T-Bill) 13.5064 15.1322
Leverage 0.2761 0.1802
Advertisement -2.0319 1.3203
Market Share Change 0.0002 0.0001 *
Diversification 1.6635 0.5182 ***
Agent Dummy 0.0454 0.1129
Stock Ownership Dummy -0.0030 0.1294
Group Dummy 0.4075 0.4510
Observations 400
Adjusted [R.sup.2] 0.1055
1997 to 2000
Small Firm
Independent Variable Coeff. Std. Err.
Intercept 4.6856 10.0911
Reinsurance Utilization -0.4012 0.1164 ***
Real GDP Growth -2.8774 9.4422
Market Interest (T-Bill) -10.9264 8.1682
Leverage 0.0023 0.0005 ***
Advertisement -0.1727 0.0462 ***
Market Share Change 0.0000 0 0001
Diversification 1.2139 0.1553 ***
Agent Dummy 0.1364 0.0738 *
Stock Ownership Dummy -0.0317 0.0552
Group Dummy -0.0287 0.0757
Observations 2,623
Adjusted [R.sup.2] 0.0490
*** significant at 1% level, ** significant at 5% level,
and * significant at 10% level.
Note: Standard errors are heteroscedastic-consistent estimators
following the method of White (1980).