1. 1
Lost Profit in Commercial Litigation
Dr. R. McKay White
I. Introduction
Lost profits are commonly claimed as damages in commercial litigation, whether due to breach
of contract, negligence, or infringement of intellectual property. Profit may be lost due to
productive assets forced to be idle1, delayed completion of works or services needed for
production2, or some other diminution of the plaintiff’s ability to earn profit. In the vast majority
of such cases, it is impossible to state with certainty the quantum of the lost profit.
Uncertainty in the quantum of damages is not a bar to recovery. However, the courts increasingly
expect parties to do more to assist the courts in estimating what that quantum may be. The more
evidence and the more certainty a plaintiff can provide, the better the outcome and the less
damages are reduced to account for contingencies.
For commercial litigation, the Canadian bar has typically relied on accounting and financial
experts to estimate lost profits. Their methodology is limited, particularly when it comes to
forecasting future lost profit. I know of one otherwise unremarkable lawsuit in which the well-
known accounting firm approached by the plaintiff to provide an opinion on lost profit replied
that it couldn’t be done. The firm was wrong. It could be done, just not with the usual
methodology such firms employ.
The American bar has, for some time, used economic experts employing econometric
methodology to estimate lost profit in commercial litigation. I propose the Canadian bar ought to
catch up to this development. As I demonstrate in this post, econometric methods are very useful
and, in my opinion, superior to the accounting methods typically employed.
Econometrics is already used in other types of litigation. It is used in antitrust litigation for issues
such as defining markets, modeling prices, and estimating the impact of anti-competitive
behaviour or mergers on prices and markets. More relevant to the present discussion,
econometrics is also used in personal injury litigation to estimate a plaintiff’s loss of future
income. Given the similarity between a loss of future income and a loss of profit, it is surprising
that econometrics has not typically been used for this latter issue.
II. Econometric Methods
A company’s sales, revenue and growth are economic data. So are the “vicissitudes of the
marketplace”3, and the general economic environment in which a business operates. It makes
1 Conmac Western Industries v. Budd Brothers Ltd. (1990), 75 Alta. L.R. (2d) 313 (Alta. Q.B.)
2 Canada Foundry Co. v. Edmonton Portland Cement Co., [1918] 3 W.W.R. 866, (P.C.)
3 Nathu v. Imbrook Properties Ltd., [1992] 4 W.W.R. 373 (Alta. C.A.), para 23

2. 2
sense, then, that analysis of such data, and determination of the relationships between them,
ought to be done using economics.
Econometrics is the empirical branch of economics. It is the use of statistical methods for
estimating economic relationships and testing economic theories4, including the forecasting of
economic time series5. These statistical methods have been used for decades, and continue to be
developed and refined. They are directly applicable to the economic data in matters of lost
profits.
The basic question with which we are concerned is: What would the plaintiff’s sales have been
but for the actions of the defendant? Upon estimating what sales would have been, one can apply
the appropriate gross profit margin to determine the lost profit6.
There are a number of methods a forensic economist, such as myself, can use to make such
estimates. The one I choose depends on the particular circumstances7. Deterministic time trend
modeling is one such method. I can implement this method with only data on the plaintiff’s sales,
and use established econometric methods to model the plaintiff’s sales over time. This model is
an equation expressing sales in a given time period as a function of time, and sometimes
previous realized values of sales. One example of such a model is given by Equation 1.
(1) 𝑠𝑎𝑙𝑒𝑠𝑡 = 𝛼𝑡 + 𝛽𝑡2
+ 𝛿𝑠𝑎𝑙𝑒𝑠𝑡−1 + 𝜀𝑡
where salest = sales in period t
𝜀𝑡 = error term in period t
I use regression methods to estimate the coefficients , , and . Then, I use the model to
estimate sales in any given time period. If the event complained of, such as a breach of contract,
occurred in period 10, I use this model to predict what sales ought to have been in period 11,
period 12, and on. I compare the forecasted sales to the actual sales to determine the damages.
Such deterministic time trend models do not explicitly account for outside factors that may affect
sales, such as economic conditions or changes in the plaintiff’s business plan. I can, however,
provide an opinion on the impact of such “vicissitudes”, and provide an appropriate contingency
factor to adjust the estimated lost profit.
4 Jeffrey M. Wooldridge, Introductory Econometrics: A Modern Approach,2e (Ohio: South-Western,2003), at page
1
5 A “time series” is a series of observations ofthe value of a particular variable in set time periods, such as monthly
sales or annual government expenditures. A forecast of a time series is an estimate of what the values will be in
future time periods.
6 Carroll Foster & Robert R. Trout, “Estimating Economic Loss for the Multi-Product Business” (2006) 87
Developments in Litigation Economics 307, at page 308
7 Ibid at page 308; Daniel L. Jackson & Sandra Cable, “Forecasting Data in Litigation Utilizing Correlation,
ARIMA and Curve Estimation” (2002-2003) 12 J. Legal Econ. 39, at page 40

3. 3
If there is a sufficient amount of data, such time series models provide the additional advantage
of posing hypotheses and statistically testing them. One such hypothesis is whether there was
actually a change in the time path of the plaintiff’s sales when the event complained of occurred.
I can test whether such a change occurred and whether actual sales are statistically different from
estimated sales. If there is a change in the time path of sales, and no other major events occurred
at the time of the break, it is evidence the defendant’s actions caused the change in sales.
This method of estimating lost profit has the advantage of being easier to explain and implement,
and of having the ability of forecasting into the future. I can also perform statistical tests to assist
with issues other than quantum of damages. Its disadvantage is that it doesn’t explicitly account
for economic and market conditions. I must provide an opinion on how such conditions affect the
estimate, which opinion will be, to some extent, subjective.
Another method is to create regression or even cointegration8 models that incorporate other,
external variables. Rather than expressing sales as a function of time only, I estimate the
relationships sales has with events in the market in which the plaintiff operates and in the
economy as a whole. The result is a model similar to Equation 1, but including variables such as
gross domestic product, labour and other input prices, government expenditures, and market
output. As with the deterministic time trend model, I can estimate what sales would have been,
but for the event complained of.
This method explicitly accounts for the impact of market and economic conditions. It also has
the ability to use statistical tests to provide evidence regarding causality. Its primary
disadvantage is that it is limited to estimating past lost profit only. Because the model requires
other data as inputs, I can’t use it to forecast into the future.
III. An Example of Estimating Lost Profits
This example is based on an actual dispute for which I was retained and uses real data. I have
modified the information to protect confidentiality.
Consider a situation in which a breach of contract by XYZ Inc. affected ABC Corp.’s provision
of construction services. As a consequence, ABC Corp.’s reputation was severely damaged,
which resulted in lost sales and lost profit. ABC Corp. was in its growth phase, and therefore
alleges that it lost not only existing customers, but also business that would have developed with
potential customers. The breach occurred in year 16.
The issue we are interested in is how to estimate the lost profit caused by XYZ Inc.’s breach of
contract. This requires first an estimate of the lost sales. Then, by applying an appropriate gross
profit margin, we obtain the lost profit. Table 1 below provides ABC Corp.’s sales data; Figure 1
graphs it.
8 Cointegration models require longer time periods.

4. 4
Table 1: Sales of ABC Corp.
Year Sales
1 $652,840
2 $1,576,502
3 $2,366,788
4 $2,478,726
5 $2,101,698
6 $2,598,369
7 $2,833,028
8 $3,293,576
9 $3,296,117
10 $2,717,649
11 $2,577,248
12 $4,496,958
13 $4,423,792
14 $6,631,903
15 $6,255,182
16 $7,747,494
17 $6,469,342
18 $10,494,526
19 $10,325,242
20 $12,116,042
21 $14,112,424
22 $18,821,890
23 $20,408,445
24 $17,342,094
25 $29,224,082
26 $33,622,553
27 $25,381,382
Figure 1: Sales of ABC Corp.

5. 5
The most basic approach, which is the one likely most often employed by accounting experts, is
to analyze ABC Corp.’s sales data and identify specific customers that stopped using or reduced
use of ABC Corp. Using these customers’ sales history, one can estimate what those customers
would have purchased, but for the breach of contract. This approach yields an estimate of
damages of approximately $3.45 million. However, this approach misses a large portion of lost
profit. As proposed above, ABC Corp. was in its growth phase. It is therefore reasonable to
presume that existing customers would have increased purchases, but did not; and other entities
would have become customers, but did not. These lost sales cannot be captured by examining
past purchases of existing customers for reductions in purchases.
The damage to ABC Corp.’s growth is not obvious from examining sales. There is a reduction in
sales in year 17, after the breach, but such drops are not unusual. Thereafter, sales generally
grow. To establish ABC Corp.’s claims, we must demonstrate that revenue growth would have
been greater but for the breach of contract.
Econometrics provides mathematically sound methods of measuring the lost profit from all
sources. I will demonstrate both methods discussed above, namely, deterministic time trend
models and regression models. My objective is to model ABC Corp.’s sales to estimate the lost
sales, if any.
In order to explore the existence of damages, and thereby estimate their value, I make use of a
“dummy variable”. This is a variable that equals 1 during the hypothesized damages period and 0
otherwise. If its coefficient is statistically significant, it means something affected sales during
the proposed damages period.
My analysis considers three different scenarios:
1. No damages period.
2. An open damages period, in which damages began in year 17 and are ongoing.
$0
$500,000
$1,000,000
$1,500,000
$2,000,000
$2,500,000
$3,000,000
$3,500,000
$4,000,000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

6. 6
3. A closed damages period, in which damages began in year 17 and ended in year 24. This
is based on the observation that customers ABC Corp. had lost returned in year 25.
A. Deterministic Time Trend Model
Scenario 1: No Damages Period
This scenario assumes ABC Corp.’s sales were not affected by the breach of contract. This
means assuming the time trend of sales remained constant over the entire 27 years for which we
have data. Our objective is to find statistically acceptable models of how sales change over time.
The data in this example have two good candidates:
(1) 𝑆𝑎𝑙𝑒𝑠𝑡 = 718,120𝑡 − 69,235𝑡2
+ 3250.9𝑡3
+ 𝜀𝑡
(2) ln( 𝑆𝑎𝑙𝑒𝑠𝑡) = 13.227 + 0.52385𝑡 − 0.060244𝑡2
+ 0.0031955𝑡3
−
0.000055069𝑡4
+ 𝜀𝑡
Figure 2 compares actual sales with the sales estimated by Model 1, and Figure 3 compares
actual sales with the sales estimated by Model 2.
Figure 2: Actual Sales and Sales Estimated by Model 1
Figure 3: Actual Sales and Sales Estimated by Model 2
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Actual Model

7. 7
Observationally, the second model looks to be superior. Model 1 proposes that sales increases
exponentially, indefinitely. Model 2 explicitly has sales level off. This latter effect is more
reasonable, as companies generally enter a mature phase after their growth phase, in which sales
are more flat.
We can also compare the models statistically by calculating each model’s Mean Squared Error
[“MSE”]. This is a measure of by how much the estimated sales depart from the actual sales. The
lower the measure, the better the model performs. This measure does not tell us in absolute terms
how good a model is. It is only useful for comparison. The MSE of Model 1 is 2,207,438;
whereas the MSE of Model 2 is 2,037,139. Since Model 2 has a lower MSE, it performs better
statistically. In my opinion, it is a better model of sales than Model 1.
Both models provide an interesting observation. The residual in a particular year is the difference
between actual sales and estimated sales. In Model 1, the average residual for the years up to and
including year 17 is $114,404; the average residual thereafter is -$328,816. We have a similar
result with Model 2: the average residual for the years up to an including year 17 is $173,903;
the average residual thereafter is -$25,538. In both models the average residual is positive before
the contract breach, then negative after the contract breach. This is consistent with some shock in
year 17 making sales lower than it was before. If sales in the first 17 years were on a high path,
and sales in the remaining years were on a low path, the average of the two paths would be low
during the first 17 years and high during the remaining.
Scenario 2: Open Damages Period
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Actual Model

8. 8
I could not make a deterministic time trend model of sales in which the dummy variable for the
open damages period is statistically significant. This means that the open damages period
hypothesis is statistically insupportable.
Scenario 3: Closed Damages Period
I found three workable models of sales based on time and a dummy variable for the closed
damages period. These are Models 3, 4 and 5. They are exhibited against actual sales in Figures
4, 5 and 6.
(3) 𝑆𝑎𝑙𝑒𝑠𝑡 = 1,603,800𝑡 − 318,620𝑡2
+ 22,957𝑡3
− 439.17𝑡4
− 5,265,600𝐷𝑡 + 𝜀𝑡
(4) ln( 𝑆𝑎𝑙𝑒𝑠𝑡) = 13.131 + 0.60112𝑡 − 0.077164𝑡2
+ 0.0044582𝑡3
−
0.000082599𝑡4
− 0.40985𝐷𝑡 + 𝜀𝑡
(5) 𝑆𝑎𝑙𝑒𝑠𝑡 = 2,609,000 + 2,916,300𝑡 − 507,610𝑡2
+ 32,977𝑡3
− 610.97𝑡4
+
3,077,700,000𝑡𝐷𝑡 − 229,720,000𝑡2
𝐷𝑡 + 7,583,500𝑡3
𝐷𝑡 −
93,439𝑡4
𝐷𝑡 − 15,391,000,000𝐷𝑡 + 𝜀𝑡
Figure 4: Actual Sales and Sales Estimated by Model 3
Figure 5: Actual Sales and Sales Estimated by Model 4
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9. 9
Figure 6: Actual Sales and Sales Estimated by Model 5
In all three models, all coefficients of variables involving the dummy variable are significant.
This means there is something different about sales during the closed damages period.
By combining the dummy variable with measures of time, Model 5 captures more variation in
how the damages period may affect sales. This can, as here, result in superior estimations.
Observationally, Model 5 appears to have the best fit. This is confirmed by statistical analysis.
The MSE of Model 3 is 1,643,385; the MSE of Model 4 is 1,695,441; and the MSE of Model 5 is
1,302,362.
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Actual Model
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10. 10
Comparison
The first and most important result is that the dummy variable for the closed damages period is
statistically significant, whereas the dummy variable for the open damages period is not. I
therefore conclude that sales were different during years 17 through 24. Something change the
time trend of sales for this period of time. This alone is reason for choosing one of the models
from the closed damages period over the no damages models.
Secondly, the models assuming a closed damages period perform better statistically. From lowest
to highest MSE, the models rank as follows:
a. Model 5
b. Model 3
c. Model 4
d. Model 2
e. Model 1
All the models in the closed damages period perform better than the models in the no damages
period. From the analysis thus far, I conclude that the closed damages period is correct.
B. Regression Model
The deterministic time trend models revealed that we are working with a closed damages period.
This means a regression model is even more useful, because we don’t have to forecast into the
future. We can use historical data, and explicitly account for the “vicissitudes of the
marketplace”.
Though we know there is a damages period, I still develop a regression model excluding a
damages period to provide a frame of reference. However, I ignore the open damages period
because that hypothesis has already been rejected.
We need variables that are related to ABC Corp.’s market and that are highly correlated with
sales. Many of ABC Corp.’s customers are municipal governments. Variables relevant to their
spending may therefore be useful. We also want variables that measure different aspects of the
economy, such as gross domestic product.
After analyzing a large list of such variables, I narrowed the focus to the following for use in
modeling sales:
a. Corporate gross fixed capital formation [“CCFORM”]
b. Government expenditures [“GEXP”]
c. Government gross fixed capital formation [“GCFORM”]
d. Total institutional structures building construction price index [“INST”]
e. Input price index [“INP”]
f. Gross domestic product [“GDP”]

11. 11
The actual models likely won’t use all of the above variables. I will exclude any that are
statistically insignificant.
Scenario 1: No Damages Period
I began with all of the above variables and the time variables to develop a model in which all
variables are statistically significant. I found only one workable model – Model 6.
(6) 𝑆𝑎𝑙𝑒𝑠𝑡 = 41,319𝑡2
+ 90.576𝐺𝐸𝑋𝑃𝑡 + 231.26𝐺𝐶𝐹𝑂𝑅𝑀𝑡 − 135.28𝐺𝐷𝑃𝑡 + 𝜀𝑡
Figure 7: Actual Sales and Sales Estimated by Model 6
One will notice that this model has a lot more variation than the deterministic time trend models.
This is because it incorporates market movements and changes.
The MSE of Model 6 is 1,838,442. This is better than the MSE of Model 1 and of Model 2.
Statistically, then, it has the best fit of all the models without a damages period. However, it still
has a higher MSE than any of the models with a closed damages period.
This model retains the observation made with the deterministic time trend models. The average
residual up to year 17 is positive, whereas the average residual thereafter is negative. It is still
consistent with a shock in year 16 making sales lower than they otherwise would have been.
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12. 12
Scenario 3: Closed Damages Period
The proper approach is to begin with all candidate variables and refine by excluding those that
are statistically insignificant. For the purpose of comparison, however, I start with Model 6 and
add the dummy variable. This results in Model 7.
(7) 𝑆𝑎𝑙𝑒𝑠𝑡 = 40,963𝑡2
+ 71.151𝐺𝐸𝑋𝑃𝑡 + 203.32𝐺𝐶𝐹𝑂𝑅𝑀𝑡 − 110.47𝐺𝐷𝑃𝑡 −
2,162,900𝐷𝑡 + 𝜀𝑡
Figure 8: Actual Sales and Sales Estimated by Model 7
All the variables in this model are statistically significant. That the dummy variable is significant
confirms, again, that there is a damages period and it is incorrect to exclude the dummy variable.
This model will therefore be a better fit. This is confirmed by comparing the MSEs. The MSE of
Model 7 is 1,671,219.
Having confirmed that the damages period is appropriate, I built a new model following proper
procedures, in which I start with all variables. This resulted in Model 8.
(8) 𝑆𝑎𝑙𝑒𝑠𝑡 = 96,172,000 + 20,786,000𝑡 − 2,972,500𝑡2
+ 186,260𝑡3
−
3,369.3𝑡4
− 181.43𝐶𝐶𝐹𝑂𝑅𝑀𝑡 − 464.37𝐺𝐸𝑋𝑃𝑡 − 4,200,800𝐼𝑁𝑆𝑇𝑡 +
0
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13. 13
3,635,600𝐼𝑁𝑃𝑡 − 8,575,900𝐷𝑡 + 𝜀𝑡
Figure 9: Actual Sales and Sales Estimated by Model 8
Visually, this model looks better than Model 7. It also performs better statistically, with a MSE
of 1,251,938.
C. Overall Comparison and Selection
Having concluded that the closed damages period is correct, we are interested in comparing the
models that explicitly account for it. I use each model to estimate what sales would have been,
but for the breach of contract. The difference between actual sales and the “but for” sales
provides the lost sales for ABC Corp. By applying the appropriate gross profit margin, in this
case estimated to be 25%, we determine lost profit. Table 2 compares these values.
Table 2: Comparison of Lost Sales and Lost Profit
Model Lost Sales Lost Profit
3 $42,693,275 $10,673,319
4 $60,210,822 $15,052,706
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14. 14
5 $49,225,646 $12,306,411
7 $18,210,240 $4,552,560
8 $68,461,281 $17,115,320
Models 7 and 8 explicitly account for changes in the market, whereas models 3, 4 and 5 require a
subjective consideration of how the market might affect damages. The estimated lost profit from
these three models therefore is not yet final. Because of the subjective component in the
deterministic time trend models, the regression models will generally be preferred, because they
remove more uncertainty from the damages estimate. There may be some concern, however, in
that the two estimates are so very different. Why is Model 7’s estimate of damages so far below
all the others?
The reason is that Model 7 used improper methodology. It is based on Model 6, which assumed
no damages. The foundation for the model is incorrect; therefore, its results are suspect.
Statistically, the best models are Model 8, which estimates damages of $17,115,320; and Model
5, with a preliminary estimate of $12,306,411. The regression model estimates higher damages.
It explicitly accounts for changes in the market and the economy, whereas the deterministic time
trend model does not. That the regression model estimates higher damages means that there were
market conditions during the damages period that ABC Corp. should have been able to take
advantage of to increase profits, but wasn’t able to because of the contract breach.
My opinion is that ABC Corp.’s damages due to the breach of contract are a total of
$17,115,320. This model performs the best statistically out of all the candidate models, and it
explicitly accounts for external economic factors.
This example does not illustrate all of the models and statistical tests in an economist’s arsenal. It
is simply meant to demonstrate that we can provide a robust estimate of lost profit from all
sources, based on sound econometric methods. The methods used will depend on the particular
circumstances of a given case. They reduce the guesswork and conjecture required to estimate
profit losses, and provide insight into all issues related to the damages the plaintiff suffered.
IV. Conclusion
It is trite that commercial litigation often involves allegations of lost profit. Measuring lost profit
is, by nature, uncertain. Courts have recognized the difficulty in measuring such damage, and
therefore grant recovery despite the uncertainty in estimation. Increasingly, however, courts have
expected parties to eliminate as much guesswork as possible. Methods of estimation must be
justified and based on reasonable assumptions. Standard accounting methods used in the past
have provided some help, but in many ways are inadequate in estimating lost profit from all
sources.

15. 15
Econometric methods have long been used in other areas of law, most notably in personal injury
and claims for loss of future income. I demonstrated above that such methods are also valuable
for estimating lost profit in commercial litigation. With these methods I can capture all sources
of lost profit; enable the use of statistical tests to provide evidence of causation and liability; and
provide several methods to give a more robust analysis of loss. I illustrated one example of two
econometric methods: deterministic time trend models and regression models. These methods
were applied to an actual (adjusted) example of a dispute. The example demonstrated how lost
sales and profit can be estimated, and how these methods assist in determining the actual
damages period. I was able to provide an opinion not only of the damages suffered, but that there
were damages and the period of time over which the damages occurred.
In conclusion, lawyers ought to consider how to make better use of these methods in their
litigation. Econometrics has the potential to be an invaluable tool in a commercial litigator’s
arsenal, whether addressing matters of breach of contract, negligence, appropriation of tangible
or intangible assets, or any other situation of commercial loss.