Cost Of Equity Definition.pdf

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Estimating the Cost of Equity for
Canadian and U.S. Firms
Lorie Zorn, Financial Markets Department*

• There has been a concern among policy-
makers that the cost of equity financing may
be higher in Canada than in the United
States, but the empirical evidence supporting
this view is mixed.
• We improve on previous studies by imple-
menting a forward-looking, firm-specific
approach to estimating the nominal cost of
equity for Canada and the United States that
controls for firm characteristics, industry
effects, and business cycle effects.
• We find that greater firm size and greater
liquidity of a firm’s stock are associated with
a lower cost of equity, while greater firm
leverage and greater dispersion in analysts’
earnings forecasts are associated with a
higher cost of equity. Moreover, we find that
higher yields on longer-term sovereign bonds
increase a firm’s cost of equity.
• After taking firm-level and aggregate-level
factors into account, the cost of equity was
approximately 30 to 50 basis points higher
in Canada than in the United States over
the 1988–2006 period as a whole, but this
differential appears to be lower in the post-
1997 period.
* The research reported in this article is summarized from a working paper
written by Jonathan Witmer and the author (Witmer and Zorn 2007).

inancing costs are important for both firms
and the economy, affecting investment deci-
sions and, ultimately, economic growth. Since
equity is an important component of a firm’s
financing structure, Canadian firms may not under-
take as many projects that could potentially enhance
growth if the cost of equity financing in Canada is
relatively high. Considering the overall size of the
equity stock in Canada, even small differences in the
cost of equity financing can have a substantial impact.1
The cost of equity, which can be defined as the return
expected on a firm’s common stock, represents the
compensation demanded by shareholders for providing
capital and assuming the risk of waiting for this return.2
Thus, in addition to the risk-free return, the cost of
equity incorporates an equity-risk premium—the
incremental payoff from holding a risky equity security
rather than a risk-free security.
There has been a concern among policy-makers that
financing costs may be persistently higher in Canada
than in the United States. The Capital Markets Leader-
ship Task Force begins its 2006 report, for example,
with the premise that the cost of capital in this country
needs to be reduced for Canadian firms to compete
effectively with those in the United States (Boritz 2006).
Similarly, the report of the Task Force to Modernize
Securities Legislation in Canada (2006) reinforces
the notion of a “made-in-Canada” risk premium that
1.  As of 31 December 2006, the market capitalization of the Toronto Stock
Exchange (TSX) was just over $2 trillion. During 2006, TSX firms raised over
$41 billion through share issues. Available on the TSX website at <http://
www.tsx.com>.
2. The cost of equity can be expressed in real or nominal terms, depending on
whether real or nominal returns per share are used in its estimation.
F
27
BANK OF CANADA REVIEW • AUTUMN 2007
increases the cost of equity capital in Canada and
discounts the trading price of Canadian shares.3
The empirical evidence supporting this view is mixed.
Multi-country studies indicate that the costs of equity
for Canada and for the United States are compara-
tively close on a worldwide scale. The magnitude and
relative ranking of these estimates vary across studies,
however. Claus and Thomas (2001), for example,
calculate a cost of equity for Canada that is 20 basis
points (bps) lower than that of the United States.4 The
frequently cited results of Hail and Leuz (2006) indi-
cate a cost of equity for Canada that is 30 bps greater
than that of the United States.5
Policy efforts aimed at fostering a
healthy environment for investment
financing in Canada can be enhanced
by a better understanding of the
drivers of the cost of equity.
Canadian policy-makers have an interest in fostering
a healthy environment for investment financing and,
in the end, economic growth in Canada. Policy efforts
can be enhanced by a better understanding of the
drivers of the cost of equity in Canada, particularly
compared with those of other countries.
This article presents estimates of the influences on the
cost of equity in Canada and the United States using
an updated methodology that controls for firm char-
acteristics and aggregate-level factors. We begin
with a brief review of the empirical literature. Next,
we summarize the key factors that affect the cost of
equity. We then present a comparison of Canadian and
U.S. firms. Finally, the contributions of key factors
to the cost of equity for Canadian and U.S. firms are
quantified and discussed, along with implications for
policy-makers.
3.  The report cites the findings of Hail and Leuz (2006) and King and Segal
(2003, 2006).
4.  They estimate that Canada’s cost of equity is 10.8 per cent over the period
1985–98, compared with 11 per cent for the United States.
5. Hail and Leuz estimate a cost of equity for Canada of 10.5 per cent over the
period 1992–2000, versus 10.2 per cent for the United States.
28
BANK OF CANADA REVIEW • AUTUMN 2007
Estimating the Cost of Equity
Only a handful of studies over the past 15 years have
estimated a cost of equity for Canada, and the results
vary. The studies not only disagree on the size of
Canada’s cost of equity, with estimates ranging from
5.4 per cent to 10.8 per cent, but they also disagree on
how Canada compares with the United States. Some
estimate a slightly higher cost of equity in Canada;
some estimate that Canada’s cost of equity may be
3 per cent lower.6
Why has the empirical literature failed to provide
solid conclusions? One likely reason is that only
recently has a true forward-looking, firm-specific
approach to estimating the cost of equity been applied
to Canada. Because sufficient firm-level data were not
available before the mid-1990s, most estimates are
based on realized, market-level returns on stocks and
sovereign bonds. Typically, the methodology used in
these studies estimates a constant equity-risk premium
based on the differences in nominal returns earned on
equities and bonds during a lengthy period of time
(often 50 years or more). Because of historically lower
stock market returns and higher bond yields in Canada
relative to the United States, these studies have
tended to find a lower equity-risk premium for Canada.
Although risk-free rates have tended to be slightly
higher in Canada, the result is often a lower cost of
equity for Canada relative to the United States.7 How-
ever, the period over which this market-level risk
premium is calculated can lead to very different cost-
of-equity results.
In addition, research to date has not been focused on
making a thorough comparison between Canada and
the United States. Rather, the cost of equity has often
been estimated as a preliminary step to answering
other questions (such as whether differences in a
country’s legal environment have an impact on the
cost of equity). These country cost-of-equity estimates
typically do not account for firm-specific characteristics
and aggregate-level factors that could affect the cost of
equity. Differences across these studies could therefore
be attributed to the different characteristics of individual
firms in each sample. In addition, variations in the
estimates might be exacerbated by using a relatively
small sample of firms in Canada compared with the
United States.
6.  See Witmer and Zorn (2007) for a discussion of the empirical literature.
7. See, for example, Booth (2001); Jorion and Goetzmann (2000); and Hannah
(2000).

Lastly, although the cost of equity is, by definition,
linked to the risk-free rate, it may also be insightful to
consider the interest rate environment and how this
affects the financing costs of individual firms in Canada.
Using information from stock prices
and stock analysts’ forecasts of firm
earnings, we estimate a nominal cost
of equity for Canadian and U.S.
firms, then compare these estimates.
We address all of these issues by employing a meth-
odology that uses information from stock prices and
stock analysts’ forecasts of firm earnings to estimate a
nominal cost of equity for each firm.8 Our cost-of-
equity estimates are intuitively appealing because
they reflect expected future returns to shareholders: in
this approach, the cost of equity is the rate of return
that sets the current stock price equal to the present
value of expected future cash flows to shareholders.
We compare these estimates for Canadian and U.S.
firms over the 1988–2006 period, first at a broad level,
and then controlling for firm characteristics, industry
effects, and business cycle effects in a panel regression
analysis. As an additional step, we examine the impact
of longer-term sovereign bond yields (a proxy for the
risk-free rate) on these cost-of-equity estimates.
What Drives the Cost of Equity?
A firm’s cost of equity can be affected by several factors,
which can be classified both at a firm level and at a
broader level. Generally, the more these variables
increase the perceived riskiness or uncertainty of
future returns to shareholders, the more shareholders
will demand to be compensated for this risk, and the
higher will be the firm’s cost of equity. Because our
analysis incorporates these variables, it is important to
establish their expected effect on a firm’s cost of equity
in order to help interpret our results:
• Firm size: Since there is usually more infor-
mation regarding the management and
potential earnings of larger firms, the
uncertainty regarding the future returns of
8.  See Witmer and Zorn (2007) for details on our methodology, including
potential shortcomings.

such firms is reduced. Thus, we would
expect a firm’s cost of equity to be nega-
tively related to its size.
• Financial leverage: Given that payments to
debt holders have priority, an increase in
debt (or greater financial leverage) and
fixed interest costs will make returns to
equity holders more sensitive to changes in
earnings (i.e., more risky). Thus, we would
expect greater financial leverage to increase
a firm’s cost of equity.
• Corporate taxes: Corporate taxes have an
indirect effect on the cost of equity by
reducing the impact of financial leverage.
Since interest payments on debt are tax
deductible, corporate taxes reduce the
effective cost of debt. So where corporate
taxes are levied, leverage provides a risk-
less tax shield, such that the overall risk of
the firm is lower for the same amount of
financial leverage. Through this link with
financial leverage, we would expect the
cost of equity to be negatively related to
corporate taxes.
• Stock liquidity: Investors require extra com-
pensation to cover the costs of buying and
selling a security. These transactions costs
tend to be lower for more frequently traded
or more liquid stocks.9 Thus, we expect
firms with greater stock liquidity to have a
lower required return and, hence, a lower
cost of equity.
• Forecast dispersion: Investor uncertainty
regarding future returns could grow with
the variability and reduced accuracy of
analysts’ earnings forecasts for a firm.
Thus, we would expect greater disagree-
ment or dispersion in analysts’ forecasts to
increase the cost of equity.
In addition to these firm-specific characteristics,10
other factors affect the cost of equity at a broader level:
9.  Securities regulation and competition between trading platforms or
exchanges have an impact on average stock liquidity as well.
10.  Although not included in our analysis, ownership structure may also
affect a firm’s cost of equity. King and Santor (2007) find that Canadian firms
with dual-class shares have a lower equity valuation than those firms with
non-dual-class shares. Given the inverse relationship between a firm’s cost of
equity and its share price, this implies a higher cost of equity for firms that
use dual-class shares.
29
BANK OF CANADA REVIEW • AUTUMN 2007
• Industry factors: Certain cost-of-equity driv-
ers will be common across firms in the same
industrial group. For example, industries
such as mining will have a high proportion
of fixed costs. This higher operating leverage
will cause profits to be more sensitive to
changes in revenue, thus increasing the risk-
iness of returns to the firms’ shareholders
and the cost of equity in these industries. We
attempt to capture industry-wide effects
on the cost of equity by including industry
dummy variables in our analysis.
• Economic conditions: Studies have shown
that expected returns for equity markets
tend to be countercyclical; i.e., they are
lower under strong economic conditions
and higher under weak economic condi-
tions. Thus, we expect business cycle effects
on the cost of equity as well and include
dummy variables for each year in our sam-
ple period to account for this.
Differences in the cost of equity across firms can also
be affected by such variables as the degree of financial
market segmentation, unexpected movements in
exchange rates, inflation uncertainty, differences in
personal taxes, and different legal and regulatory
environments, including enforcement. Because our
focus is on firm-level drivers of the cost of equity that
can easily be represented, we do not address these
other factors. (Although other studies have examined
the relationship of some of these factors with the cost
of equity, none has comprehensively included all of
these variables.) An analysis of some of these other
effects is planned in future work, however, and this
might shed further light on the cost of equity for
Canadian firms.
Empirical Results
Canada-U.S. comparison
Given the factors affecting the cost of equity, it is inter-
esting to first compare Canadian and U.S. firm charac-
teristics. Taking a sample of firms over the period 1988
to 2006,11 tests are performed to determine whether
there are differences between the Canadian and U.S.
11.  Our sample contains Canadian and U.S. non-financial firms covered by
the Institutional Brokers Estimate System (I/B/E/S) and Compustat. After
merging the two datasets, we have 3,419 Canadian and 31,005 U.S. observa-
tions.
30
BANK OF CANADA REVIEW • AUTUMN 2007
median for the five identified firm characteristics
(Table 1). The tests indicate that, compared with U.S.
firms, Canadian firms in our sample are smaller, have
a lower effective tax rate, a higher amount of debt in
their capital structure, a lower stock turnover (a proxy
for stock liquidity), and a higher dispersion of forecasts
among analysts. When the cost of equity is estimated
for each firm and year, we find that the median cost of
equity is 11.5 per cent for Canadian firms, compared
with 10.9 per cent for U.S. firms over the 1988–2006
period.12 Given the differences in firm characteristics,
it is not surprising that the median cost-of-equity
estimate for firms in the Canadian sample is higher
than that for firms in the U.S. sample.13 As such, it is
important to control for these firm-level differences in
order to make a relevant comparison across countries.
12.  We use an average of four forward-looking models to estimate the nomi-
nal cost of equity. For more details, including robustness to different assump-
tions, see Witmer and Zorn (2007).
13.  Our cost-of-equity estimates are likely higher than those from previous
studies because our sample includes more small firms.
Table 1
Sample Statistics for Canadian and U.S. Firms,
1988–2006
Canada
United States
Median
difference
Size (total assets)
US$364.2
US$446.8
-US$82.7*
million
million
million
Financial leverage
0.36
0.33
0.03*
Taxes
0.35
0.36
0.01*
Stock liquidity
0.30
0.94
-0.64*
Forecast dispersion
0.06
0.03
0.03*
Cost of equity
11.49
10.86
0.64*
* Significant at 1 per cent
Notes: Size is calculated using book values from Compustat and is converted
into U. S. dollars. Financial leverage is calculated as the ratio of long-
term debt to equity using book values. Tax is the ratio of income taxes
to pre-tax income and is restricted to a range between 0 and 1. Stock
liquidity is proxied by turnover and is the number of shares traded in
the previous year divided by the total number of shares outstanding in
Compustat. Forecast dispersion is the cross-sectional standard devia-
tion of analysts’ earnings forecasts denominated in U.S. dollars. The
nominal cost of equity is based on forecasted earnings from I/B/E/S
and is calculated using the average of four different forward-looking
models.

It is not surprising that the median
cost-of-equity estimate for firms in
the Canadian sample is higher than
that for firms in the U.S. sample.
Next, we break out industry and business cycle effects,
presenting the cost-of-equity estimates by industry
grouping (Chart 1) and by year (Chart 2). Grouping
firms by their two-digit Standard Industry Classifica-
tion code, it appears that Canada has a higher cost
of equity in four of the six broad industry groups
(although, again, we are not at this point controlling
for all of the aforementioned firm characteristics).
Looking at Chart 2, some general observations can be
made: there is a downward trend in the cost of equity
for both countries; there are similar cycles in the cost
of equity for Canada and the United States; and
Canada appears to have a higher cost of equity for
most of the period. This reinforces the notion that the
cost of equity is not static, but time varying. However,
there are also differences in our sample of firms across
time and countries. For example, at the beginning of
the period, the Canadian sample is dominated by
larger firms, but the median firm size falls over time as
Chart 1
Median Cost of Equity by Industry, 1988–2006
Cost of equity (%)
0
5
10
15
MI
M
TCU
WT
RT
SI
0
5
10
15
United States
Canada
Note: MI = Mineral industries, M = Manufacturing,
TCU = Transportation, communication and utilities,
WT = Wholesale trade, RT = Retail trade, and
SI = Service industries.

the proportion of smaller firms rises. In contrast, the
median firm size in the U.S. sample increases signifi-
cantly over time. Because of sample differences such
as this, there is a need to incorporate all of the identi-
fied factors into our analysis before making conclu-
sions about the relative cost of equity.
Regression analysis
A regression analysis (see Box) can be used to identify
the effects of the selected firm-level, industry-level,
and business cycle effects on the cost of equity (COE).14
In this model, we explicitly control for firm size, as
measured by the logarithm of book value of total
assets (BV), financial leverage (LEV), effective corpo-
rate tax rates (TAX), the liquidity of a firm’s stock
(LIQ), and analysts’ forecast dispersion (DISP). We
control for changing economic conditions and indus-
try effects by including year (YEAR) and industry
(IND) dummy variables. The model also includes
dummy variables denoting whether a firm is a U.S.
firm (US) or a cross-listed Canadian firm (XLIST).
14.  Again, we do not control for all possible influences on the cost of equity.
Note: The cost of equity is weighted by firm size for Canada and
the United States on a yearly basis. Early in the period,
when the Canadian sample is dominated by large firms,
Canada’s cost of equity is smaller. Over time, the median
firm size for Canada falls as the proportion of smaller firms
rises. Other factors that affect differences in firms’ cost of
equity are not controlled for here.
Chart 2
Cost of Equity by Year, 1988–2006
Weighted average cost of equity (%)
0
5
10
15
0
5
10
15
1988
1993
1998
2003
Canada
United States
31
BANK OF CANADA REVIEW • AUTUMN 2007
Box: Cost-of-Equity Regression
The cost-of-equity differential
between Canada and the United
States over the 1988–2006 period is
in the range of 30–50 bps.
Using a regression analysis that includes these firm
characteristics, the results indicate that almost all
of these control variables are statistically significant
and have the expected relationship with the cost of
equity (Table 2). For example, greater firm size is
associated with a lower cost of equity; firms with more
debt have a higher cost of equity; firms with higher
stock liquidity have a lower cost of equity; and firms
with more imprecise earnings estimates by analysts
have a higher cost of equity. Once we account for all of
these differences, plus the effects of industry member-
32
BANK OF CANADA REVIEW • AUTUMN 2007
ship and business cycles, U.S. firms in our sample
appear to have a lower cost of equity, by approximately
47 bps, than do the Canadian firms. After subjecting
our regression results to a number of sensitivity
tests,15 we conclude that for our sample of firms the
cost-of-equity differential between Canada and the
United States over the 1988–2006 period is in the range
of 30 to 50 bps.
This analysis has improved upon previous studies by
accounting for some of the differences across firms. It
does not yet address, however, the possibility that
differences in the risk-free rates faced by these firms
could also be affecting their cost of equity. Failing to
allow for different interest rate environments across
countries may not lead to a fair comparison. The risk-
free rate, typically represented by the longer-term
sovereign bond yield, captures an important part of
15. All of our regression results are subjected to various robustness checks. In
addition, results using other economic models are not significantly different
from our own. See Witmer and Zorn (2007) for a discussion of these issues.

Using a panel data set, i.e., observations from many
firms over many years, can present challenges for
regression analysis, since the independent variables
will vary both by time and by firm. This is compli-
cated by the presence of time-invariant (dummy)
variables. We overcome these difficulties by taking
a two-step approach. In the first stage, a fixed-effects
model is run using the time-varying independent
variables:
.
In the second stage, a weighted least-squares model
is run, which regresses the firm fixed-effect coef-
ficient (
) from the first-stage regression on the
time-invariant independent variables (the U.S. and
industry dummy variables), as well as the firm
averages of the time-varying independent variables
COEi t
,
α βXLIST XLIST i t
,
βYEAR_tYEARi t
,
t=1989
2006
∑
+
+
=
+βBV BV i t
,
βLEV LEV i t
,
βTAXTAXi t
,
βLIQLIQi̇ t
,
+
+
+
+βDISPDISPi t
,
ui
εi t
,
+ +
ui

(to control for correlation between these variables
and the firm fixed effects):
.
This set-up assumes common coefficients for all of
the firms, both Canadian and U.S., in our sample
and does not account for possible non-linear effects
of our variables on the cost of equity.
With this approach, the resulting coefficient on the
U.S. dummy variable (
) can be considered as
the difference between Canadian firms’ and U.S.
firms’ cost-of-equity financing (and, if multiplied
by 100, it can then be expressed in basis points
after accounting for the other regression variables).
ût ω βUSUSi
βIND_k INDi k
,
γ XLIST XLIST i
+
k
1
=
K
∑
+
+
=
+
γ YEAR_tYEARi
γ BV BV i
γ LEV LEV i
+
+
t
1989
=
2006
∑
+γ TAXTAXi
γ LIQLIQi t
,
γ DISPDISPi t
,
νi
+
+
+
βUS

the macroeconomic environment faced by firms. It
reflects differences in monetary and fiscal policy
regimes, including their effects on inflation uncertainty.
As Chart 3 shows, 10-year government bond yields
declined between 1988 and 2006, roughly parallel with
the decline in the cost of equity. However, there also
appear to be two distinct interest rate periods. Canadian
yields were much higher than U.S. yields during the
first half of the sample period (1988–97), because
investors demanded a higher risk premium to com-
pensate for various factors, including high government
debt levels and Quebec-related political uncertainty.
Since 1997, there have been relatively small differences
in yields between the two countries.
To examine the relation between bond yields and the
cost of equity in our sample, we re-do our regression
analysis in two different ways. First, we reformulate
our regression equation to include nominal 10-year
government bond yields as a right-hand-side variable16
and find that a 100 bp increase in 10-year yields con-
tributes to an increase of almost 20 bps in a firm’s cost
of equity.17 With this specification, including the same
regression variables plus 10-year yields, our tests are
unable to conclude definitively that there is a differ-
ence between the Canadian and U.S. cost of equity.
As a second test, we split our sample into two equal
periods along the lines of the two interest rate periods
16.  In this model, the dependent variable is the firm’s nominal cost of equity
in its local currency.
17. Without year dummies, the estimated effect is closer to a 40 bp increase in
a firm’s cost of equity.
Table 2
Cost-of-Equity Regression Results, 1988–2006
βi
t-statistic
Constant
12.015
26.21*
Size (total assets)
-0.247
3.87*
Financial leverage
0.64
12.43*
Taxes
-0.009
3.45*
Stock liquidity
-0.101
2.69*
Forecast dispersion
8.56
13.94*
U.S. firm
-0.465
3.40*
* Significant at 1 per cent
Notes: This table presents results for a 2-stage regression involving the U.S.
dollar nominal cost of equity for Canadian and U.S. firms. For conven-
ience, we do not report values for industry, year (business cycle), and
cross-listed dummy variables. Absolute values of t-statistics are ad-
justed for heteroscedasticity of errors at a firm level.

that were identified: 1988–97 and 1998–2006. When
our regression analysis is repeated, we find that, for
1988–97, the estimated differential between Canadian
and U.S. cost of equity is very close to the full sample
result in terms of sign, size, and statistical significance.
However, in the latter period when sovereign bond
yields were broadly similar in the two countries, the
difference between the costs of equity in the two
countries is lower, by about 20 bps, and is no longer
statistically significant. This suggests that differences
in longer-term sovereign bond yields may be a factor
in explaining differences in the cost of equity.
Conclusions
The cost of equity for a firm is affected by several
factors, some of which are related to characteristics of
the firm itself, while others stem from the macroeco-
nomic environment in which it operates. We find that
greater firm size and greater liquidity of a firm’s stock
are associated with a lower cost of equity, while greater
firm financial leverage and greater dispersion in ana-
lysts’ earnings forecasts are associated with a higher
cost of equity. Moreover, longer-term sovereign bond
yields also seem to play a role in a firm’s cost of equity.
After taking firm-level and aggregate-level factors
into account, the cost of equity in our sample was
approximately 30–50 bps higher in Canada than in the
United States over the 1988–2006 period. The cost-of-
equity differential appears to be lower in the post-1997
Canada
Chart 3
10-Year Government Bond Yields, 1988–2006
10-year yields
0
5
10
15
0
5
10
15
1988
1993
1998
2003
United States
33
BANK OF CANADA REVIEW • AUTUMN 2007
period, when sovereign bond yields were relatively sim-
ilar in the two countries.
These results have policy implications. For example,
since a smaller firm size adds to the financing cost of
Canadian firms, promoting firm growth could have
the positive effect of reducing the cost of equity. Higher
forecast dispersion, or disagreement among equity
analysts regarding firm earnings, is associated with
a higher cost of equity. If better disclosure contributes
to better forecasting of firm earnings, then improved
disclosure regulation and practices in Canada might
contribute to a lower cost of equity for firms. Perceived
improvements to securities regulation and enforce-
ment might also lead to greater trading and liquidity
of Canadian stocks, in turn reducing the Canadian
cost of equity. Finally, longer-term sovereign bond
yields matter. This suggests that recent fiscal and
monetary policy regimes, which have focused on
pursuing a low debt-to-GDP ratio and anchoring
inflation expectations to a low-inflation target, have
had beneficial effects on the cost of capital for Canadian
firms.
34
BANK OF CANADA REVIEW • AUTUMN 2007
Longer-term sovereign bond yields
seem to matter for a firm’s cost of
equity, suggesting that recent fiscal
and monetary policy regimes have
had beneficial effects for Canadian
firms.
A sizable band of error accompanies the cost-of-equity
estimates presented in this article, so a precise numerical
value for Canadian cost of equity cannot be produced.
In the same vein, Canada-U.S. differences are repre-
sented as an approximate value. To refine our estimates
further, other methodologies could be applied and
other factors could be considered, such as currency
risk, inflation uncertainty, degree of market integration,
personal taxes, and differences in regulatory environ-
ments. By incorporating proxies for these factors and
perhaps extending our comparison to more countries,
we might obtain better precision in the estimates and
a broader international context for interpreting the
results.

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