NISTIR 7964

Benefits and Costs of Commissioning:

A Case Study Analysis

Stanley W. Gilbert
NISTIR 7964

Benefits and Costs of Commissioning:

A Case Study Analysis

Stanley Gilbert

Applied Economics Office

Engineering Laboratory

October 2013

U.S. Department of Commerce 

Penny Pritzker, Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. 

Such identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose. 
iii

Abstract

Commissioning is a “quality assurance process for the design, construction and operation of buildings.” 

Specifically, Building Commissioning is a process of auditing buildings to help them operate with 

greater efficiency in accomplishing their intended purpose. This typically includes improvements in 

energy usage, reductions in operation and maintenance costs, improvements in occupant comfort, and 

reductions in potential future liability.

This report estimates the Benefit-to-Cost Ratio of commissioning-related energy savings for buildings in 

the International Commissioning Cost-Benefit and Persistence Database. It does so in accordance with 

ASTM Standards while taking into account the decay of cost savings and the time value of money. 

Almost all buildings in the database had a Benefit-to-Cost Ratio greater than one. Most had Internal 

Rates of Return of greater than 100 %. Assuming that the buildings in the database are representative of 

commercial buildings in general, then nearly all commercial buildings can benefit from Commissioning.

Predictors of commissioning-related non-energy savings are evaluated by estimating which task 

implemented as part of the Commissioning process correlates with the desired outcome for five nonenergy benefits in the Annex 47 Database. Due to the small size of the data set, results should be 

considered tentative. The most reliable results are for reduction in O&M Costs. Benchmarking, 

Development of a Commissioning Plan, and the Development of an Energy Model are associated with a 

reduction in O&M Costs.

Keywords: Commissioning; Commercial Buildings; Benefit-to-Cost Ratio; Economic Analysis; 

Standards
iv

Acknowledgements

The author wishes to thank all those who contributed so many excellent ideas and suggestions for this 

report. They include Natascha Milesi-Ferretti and Steven Bushby, of the Energy and Environment 

Division of the Engineering Laboratory (EL) at the National Institute of Standards and Technology 

(NIST) for financial support, and considerable technical assistance for this report. Appreciation is also 

extended to Dr. Robert E. Chapman and Dr. Joshua Kneifel for their comments and suggestions, and to 

Ms. Shannon Takach for her assistance in preparing the manuscript for review and publication. The 

report has also benefitted from the review and technical comments provided by Dr. Nicos Matrys of 

EL’s Materials and Structural Systems Division. As always, all remaining errors are the responsibility 

of the author.
v

Contents

Abstract .......................................................................................................................................................iii

1. Introduction.......................................................................................................................................... 1

2. Cost-Benefit Analysis of Energy Savings ........................................................................................... 2

2.1. Methodology ................................................................................................................................ 2

2.2. Results.......................................................................................................................................... 3

3. Predictors of Non-Energy Savings ...................................................................................................... 6

3.1. Methodology ................................................................................................................................ 6

3.2. Results.......................................................................................................................................... 6

4. Summary and Recommendations for Further Research ...................................................................... 9

4.1. Summary ...................................................................................................................................... 9

4.2. Recommendations for Further Research...................................................................................... 9

Figures

Figure 1: Histogram of Number of Issues for Buildings in the Annex 47 Report...................................... 2

Figure 2: Empirical estimated probability densities for Internal Rate of Return........................................ 3

Figure 3: Cumulative Distribution of Log Benefit-to-Cost Ratios. . ......................................................... 5
vi

Tables

Table 1: Decay Rates .................................................................................................................................. 2

Table 2: Example randomly generated cash flows for Wehner Building at Texas A&M.......................... 3

Table 3: Median IRR and Benefit-to-Cost ratio by project ........................................................................ 4

Table 4: Questions Analyzed for predictors of non-energy savings. .......................................................... 6

Table 5: Tasks potentially performed as part of commissioning studies. ................................................... 7

Table 6: The probability that the Task has no effect on the outcome analyzed.......................................... 7

List of Acronyms

BCR Benefit-to-Cost Ratio

IRR Internal Rate of Return

O&M Operations and Maintenance
1

1. Introduction

Commissioning is a “quality assurance process for the design, construction and operation of buildings. 1

” 

Specifically Building Commissioning is a process of auditing buildings to help them operate with 

greater efficiency in accomplishing their intended purpose. This typically includes improvements in 

energy usage, reductions in operation and maintenance costs, improvements in occupant comfort, and 

reductions in potential future liability.

Recently, the Energy Conservation for Buildings and Community Systems Program, Annex 47: CostEffective Commissioning for Existing and Low Energy Buildings produced a report on “Commissioning 

Cost-Benefit and Persistence of Savings.” The objective of the report was to estimate the payback 

period for commissioning and estimate the persistence of energy savings for commissioning. 

As part of the process of generating the Annex 47 report the task force compiled an International 

Commissioning Cost-Benefit and Persistence Database. That database contains data on 47 buildings 

from seven different countries (Belgium, Canada, Germany, Japan, the Netherlands, Norway, and the 

United States). For each building the database sought to include project information (including cost 

data), information on energy usage and cost savings, non-energy benefits, issues found in each building 

in the study, and corrective measures taken. Data collected was incomplete for all buildings in the 

database.

This report set out to use the Annex 47 database to accomplish two goals. First, this report assesses the 

cost-effectiveness of Commissioning in accordance ASTM Standards maintained by ASTM 

Subcommittee E06.81 on Building Economics, and published as part of the ASTM Standards on 

Building Economics2

. Second, this report attempts to identify predictors of non-energy savings from 

Commissioning.

Based on the results, almost all buildings in the database had a Benefit-to-Cost Ratio (BCR) greater than 

one, indicating that commissioning was cost-effective. Most had Internal Rates of Return (IRR) of 

greater than 100%. For non-energy savings, Benchmarking, Development of a Commissioning Plan, 

and the Development of an Energy Model are associated with a reduction in O&M Costs.

In what follows, Section 2 evaluates the cost-effectiveness of Commissioning for the buildings in the 

Annex 47 Database. Section 3 attempts to identify predictors of non-energy savings from 

Commissioning. Section 4 concludes with a summary and recommendations for future research.

 1 “Commissioning Cost-Benefit and Persistence of Savings”, a Report of Cost-Effective Commissioning of Existing and Low 

Energy Buildings. Directed by the Energy Conservation in Buildings and Community Systems (ECBCS) Program.

2 ASTM International. 2012. “ASTM Standards on Building Economics.” 7th Edition. ASTM International. West 

Conshohocken, PA.
2

2. Cost-Benefit Analysis of Energy Savings

The first goal this report seeks to accomplish is to 

compute the BCR3 and IRR4 of the commissioningrelated energy savings for buildings in the Annex 

47 Database. Costs used for this section were the 

reported costs for Commissioning for each project, 

while total Benefits were the total of all monetary 

energy-related benefits reported for each project.

2.1. Methodology

Of the 47 projects in the database, 22 reported both costs and energy-related benefits. However, one of 

them almost certainly contains a reporting error. For that reason, it was deleted from further 

consideration, leaving 21 projects for the analysis.

Benefits were assumed to accrue as a result of the correction of “Issues.” “Issues” are problems 

identified as part of the commissioning process. Issues commonly include things like sensor problems 

or sub-optimal setpoints for temperature control. 

Each issue was assumed to equally contribute to the 

total benefits. So, for example, the Wehner 

building at Texas A&M reported approximately 

$48,000 in annual savings, and reported five Issues 

corrected. So, for the purpose of this study, it was 

assumed that each Issue contributed $9,600 in 

savings.

Figure 1 shows a histogram of the number of 

Issues reported for buildings analyzed in this 

portion of the report. The average number of Issues 

for buildings that record issues is 6.26. Three 

buildings have no Issues recorded. Projects where 

Issues were not reported were assumed to have 

corrected ten Issues.

Issues were assumed to revert to their 

“uncorrected” state with a probability of δ per year. 

The decay rate (δ) was based on the reports of persistence of benefits from the “Annex 47” report. 

Computed decay rates for the projects for which persistence was analyzed are listed in Table 1.

 3 ASTM Standard E964-06, 2010, “Standard Practice for Measuring Benefit-to-Cost and Savings-to-Investment Ratios for 

Buildings and Building Systems,” ASTM International, West Conshohocken, PA, 2010, DOI: 10.1520/E0964-06R10.

4 ASTM Standard E4157-06, 2010, “Standard Practice for Measuring Internal Rate of Return and Adjusted Internal Rate of 

Return in Buildings and Building Systems,” ASTM International, West Conshohocken, PA, 2010, DOI: 10.1520/E1057-

06R10.

5 This is the Texas A&M results excluding the results for the G. R. White Coliseum and the Kleberg Building, which had 

large degradations in performance due to one or two major failures.

Table 1: Decay Rates

Savings 

Remaining Years Decay Rate

Texas A&M 83 % 2 9.12 %

Texas A&M 5 92 % 2 4.04 %

SMUD 81 % 4 5.13 %

Oregon – Elec. 89 % 5 2.30 %

Oregon – Gas 3 % 5 50.00 %

Colo – Elec. 83 % 7 2.63 %

Colo – Demand 86 % 7 2.13 %

Colo – Gas 100 % 7 0.00 %

CA 75 % 4 6.94 %

Data are drawn from the Annex 47 Data Set and report.

Issues

Frequency

2 4 6 8 10 12 14 16

0 1 2 3 4 5 6

Figure 1: Histogram of Number of Issues for Buildings in the 

Annex 47 Report
3

-200 0 200 400 600

0.0 0.2 0.4 0.6 0.8 1.0

Internal Rate of Return

IRR (%)

y

Based on this data, a 5 % decay rate (which is close to the 

median decay rate) was used for all computations below. 

Monte Carlo methods6 were used to compute BCRs and 

IRRs using a large number of simulations. For each 

simulation, failures were randomly generated and 

distributed by year. Then costs and benefits by year were 

computed. Finally, based on the assumed (stochastically 

generated) cash flow, IRR and BCR were computed. This 

was done for five different study periods (5, 10, 15, 20, 

and 30 years). The BCRs were computed for four 

different discount rates (3 %, 5 %, 7 %, 10 %, and 15 %). 

An example for a single instance is shown in Table 2. In 

the table “Failures” represents the number of corrected 

Issues that fail in that year. “Net Benefit” represents the 

value of energy savings for that year after accounting for 

the cumulative number of corrected Issues that have failed 

up to that point. “Discounted” represents the Present 

value of the net benefits using the 5 % discount rate. For 

each project-study-period combination, 100 000 simulations were generated.

2.2. Results

Median IRR and BCR for the ten-year study period 

and 5 % discount rate are listed in Table 3. The 

highlighted projects are the only ones with a 

negative payoff (i.e., were not cost-effective).

Estimated cumulative probability density 

(estimated using the ‘density’ function in the ‘R’

statistical computing environment7

) for return on 

investment based on the 21 remaining projects are 

shown in Figure 2. As study period increases, the 

percentage of projects that fall below any cutoff 

decreases. However, once the study period reaches 

ten years the difference between IRRs becomes

minimal.

Based on the estimated densities, about 15 % of 

projects can be expected to have an IRR of less 

than 5 %, about 17.5 % of projects can be expected 

to have an IRR of less than 15 %, and about 19.5 % 

 6 ASTM Standard E1369-11, 2011, “Standard Guide for Selecting Techniques for Treating Uncertainty and Risk in the 

Economic Evaluation of Buildings and Building Systems,” ASTM International, West Conshohocken, PA, 2011, DOI:

10.1520/E1369-11.

7 R Core Team, 2013, “R: A Language and Environment for Statistical computing.” R Foundation for Statistical Computing. 

Vienna Austria.

Table 2: Example randomly generated cash flows for 

Wehner Building at Texas A&M—Ten Year study 

period—5 % Discount Rate

Year Failures

Net 

Benefit Discounted

0 0 -$ 66 423 -$ 66 423

1 1 $ 43 255 $ 41 196

2 0 $ 43 255 $ 39 234

3 0 $ 43 255 $ 37 365

4 0 $ 43 255 $ 35 586

5 1 $ 38 449 $ 30 126

6 0 $ 38 449 $ 28 691

7 2 $ 28 837 $ 20 494

8 0 $ 28 837 $ 19 518

9 0 $ 28 837 $ 18 588

10 0 $ 28 837 $ 17 703

Figure 2: Empirical estimated probability densities for Internal Rate 

of Return
4

of projects can be expected to have an IRR of less than 25 %.

Also computed are Cumulative Distribution Functions for the BCR for all the discount rates examined 

(see Figure 3). As with IRR, once the study period exceeds ten years, the probability that a project fails 

to pay off changes very little.

In each of the sub-figures, the horizontal lines show the probability that the BCR falls below one for 

each study period. In each sub-figure, the probability that the BCR falls below one is highest for the 

5 year study period. The probabilities become difficult to distinguish for all longer study periods. 

The probabilities that the BCR falls below one also increase as the discount rate increases, but not by 

much. The probabilities increase because a higher discount rate reduces the value of the future savings, 

thus reducing the value of commissioning the building. However, since the BCR for most buildings are 

so high, the increase in discount rate does not increase the probability that BCR falls below one by 

much.

Table 3: Median Internal Rate of Return and Benefit-to-Cost ratio by project using a 10 year study period and 

a 5 % discount rate. Projects that have a negative payoff are highlighted.

Country Project

Commissioning 

Cost

Annual 

Savings

Median 

IRR

Median 

BCR

Norway Hotel 1 kr 110 000 kr 570 421 516% 31.63

Norway Hotel 2 kr 110 000 kr 275 000 246% 15.28

Norway Hotel 3 kr 110 000 kr 376 750 333% 20.76

Norway Hotel 4 kr 110 000 kr 257 400 225% 14.21

Norway Material Teknisk Bygget kr 33 000 kr 99 667 301% 18.24

United States Blocker $ 77 324 $ 80 678 98% 6.38

United States Eller $ 99 050 $ 112 047 105% 6.86

United States G. Rollie White $ 49 525 $ 124 080 246% 15.48

United States Harrington Tower $ 27 344 $ 63 696 229% 14.39

United States Kleberg $ 59 054 $ 278 331 468% 28.81

United States Koldus $ 41 894 $ 61 802 142% 9.02

United States Richardson Petroleum $ 44 541 $ 126 079 279% 17.49

United States Vet Med Center Addition $ 52 314 $ 101 892 194% 11.79

United States Wehner $ 66 423 $ 48 063 67% 4.47

United States Allied Plaza $ 71 693 $ 26 065 28% 2.24

United States Mark O. Haftield Federal Courthouse $ 180 554 $ 92 962 43% 3.11

Japan Kobe Kanden Building ¥ 10 800 000 ¥ 390 113 -19% 0.22

Japan Nakanoshima 3-chome DHC ¥ 19 800 000 ¥ 260 876 -29% 0.08

Japan CEPCO Atsuta Sales Office ¥ 10 480 000 ¥ 2 828 432 18% 1.63

Canada Palais des congrès de Montréal $ 199 300 $ 309 942 146% 9.41

Canada CETC-Varennes $ 90 000 $ 36 831 33% 2.48
5

Figure 3: Cumulative Distribution of Log Benefit-to-Cost Ratios. The upper left figure is for a discount rate of 3 %. The upper right figure 

is for a discount rate of 7 %. The lower left figure is for a discount rate of 10 %. And the lower left figure is for a discount rate of 15 %.

-4 -2 0 2 4

0.0 0.2 0.4 0.6 0.8 1.0

Discount Rate = 3 %

log(BCR)

y

 5-Year

10-Year

15-Year

20-Year

30-Year

-4 -2 0 2 4

0.0 0.2 0.4 0.6 0.8 1.0

Discount Rate = 7 %

log(BCR)

y

 5-Year

10-Year

15-Year

20-Year

30-Year

-4 -2 0 2 4

0.0 0.2 0.4 0.6 0.8 1.0

Discount Rate = 10 %

log(BCR)

y

 5-Year

10-Year

15-Year

20-Year

30-Year

-4 -2 0 2 4

0.0 0.2 0.4 0.6 0.8 1.0

Discount Rate = 15 %

log(BCR)

y

 5-Year

10-Year

15-Year

20-Year

30-Year
6

3. Predictors of Non-Energy Savings

The Annex 47 Database includes questions asking about a variety of non-energy related benefits that 

could result from Commissioning a building. For the most part the questions are qualitative: that is, they 

ask whether a specific benefit resulted from the Commissioning study, and make no effort to quantify 

the benefit. The Database includes 26 questions about non-energy benefits. 21 of the questions are 

qualitative Yes / No questions about the existence of some benefit. The remaining five questions ask to 

quantify the value of those benefits. The questions were only answered for some of the buildings with a 

different quantity of answers for different questions. Valuation questions were only answered for O&M 

costs, and not for enough buildings to be able to reliably estimate cost savings.

Table 4: Questions Analyzed for predictors of non-energy savings.

Item Label Question Responses

Yes 

Responses

Staff Do O&M staff report increased ability to operate and 

maintain the building as a result of Commissioning? 11 6

Costs Were ongoing operations and maintenance costs 

reduced as a result of Commissioning? 18 8

Air Was indoor air quality improved as a result of 

Commissioning? 11 6

Productivity Was occupant productivity improved as a result of 

Commissioning? 11 7

Liability Was liability reduced as a result of Commissioning? 11 5

This report attempts to identify qualitatively what predicts a positive outcome for a specific type of nonenergy savings. In order to estimate that outcome, two characteristics must hold. First, there must be 

enough answers to the question to produce a reliable result. Second there must be a sufficient variety of 

answers (that is, both yes and no answers) to distinguish between characteristics that predict yes 

outcomes and ones that do not.

3.1. Methodology

Five of the non-energy savings items from the list were selected for further analysis. The five are listed 

in Table 4.

The Tasks that were performed in the Commissioning process were used as predictors of whether a Yes 

response was given to each of the questions above. The Tasks analyzed and their descriptions are listed 

in Table 5. There were simply not enough responses to analyze the Tasks simultaneously, so each was 

regressed individually against each question using a standard Logit analysis.

3.2. Results

The results shown in Table 5 are the probabilities that the Task listed has no effect on the outcome 

analyzed. So, smaller numbers indicate a stronger relationship (i.e., there is a greater likelihood of a 
7

beneficial effect). Cells shown in Red and Blue are significant at the 10 % level and 25 % level, 

respectively. The latter group should be interpreted as Tasks-Outcome pairs that should be analyzed in 

more detail if more data become available.

Table 5: Tasks potentially performed as part of commissioning studies.

Task Description

Benchmarking Benchmarking

Calculate Savings Calculate energy cost savings for findings

Capital Improvements Implement capital improvements

Commissioning Plan Develop a Commissioning Plan

Diagnostic Tools Use of Diagnostic Tools and Cx Automation Techniques

Energy Model Building energy modeling/simulation

Final Report Final Comissioning Report

Document Findings Document master list of findings

Manual Develop systems manual/recommissioning manual

Monitor Persistence Monitor implemented measures for persistence of benefits

O&M Improvements Implement operations and maintenance (O&M) improvements

Project Requirements Document owner's project requirements

Report Present a findings and recommendations report

Trend Analysis Trend Analysis (for example, EMCS, data logging, etc.)

Update Documentation Update system documentation after implementation

Utility Bill Analysis Utility Bill Analysis

Verify Energy Savings Monitor and verify energy savings

The greatest significance occurs for Operation and Maintenance Costs, which, not coincidentally, have 

the most available responses. Benchmarking, Developing a Commissioning Plan, and Development of 

an Energy Model all are predictors of a reduction in O&M Costs.

Table 6: Results show the probability that the Task listed has no effect on the outcome analyzed. Cells shown in Red 

are significant at the 10 % level. Cells shown in blue are “significant” at the 25 % level.

Task Staff Costs Air Productivity Liability

Benchmarking 74.06% 5.97% 38.26% 31.67% 31.67%

Calculate Savings 81.92% 14.84% 15.76% 55.80% 38.26%

Capital Improvements 99.67% 18.85% 99.65% 66.11% 62.40%

Commissioning Plan 31.67% 6.87% 31.67% 99.61% 31.67%

Diagnostic Tools 38.26% 81.41% 99.58% 89.83% 81.92%

Energy Model 62.40% 8.34% 88.66% 99.66% 88.66%

Final Report 38.26% 67.19% 38.26% 31.67% 15.76%

Document Findings 38.26% 21.74% 74.06% 6.75% 31.67%

Manual 99.67% 80.02% 99.65% 66.11% 88.66%

Monitor Persistence 14.15% 67.19% 31.67% 22.35% 74.06%

O&M Improvements 38.26% 11.72% 38.26% 15.76% 81.92%

Project Requirements 99.65% 19.12% 99.60% 89.83% 81.92%

Report 81.92% 99.54% 81.92% 48.22% 99.60%

Trend Analysis 15.76% 99.54% 81.92% 99.71% 39.85%

Update Documentation 99.67% 99.52% 99.65% 99.65% 88.66%

Utility Bill Analysis 74.06% 11.72% 74.06% 81.92% 31.67%

Verify Energy Savings 81.92% 67.19% 74.06% 6.75% 74.06%

Similarly, Documenting Findings, and Verification of Energy Savings were predictors of reporting 
8

Productivity improvements for the building occupants. None of the other questions are significant 

predictors of outcomes. Note that these results should be treated very cautiously. The nature of the data 

makes these results very weak, and additional data would significantly improve the results.
9

4. Summary and Recommendations for Further Research

4.1. Summary

This report estimates the BCR of commissioning-related energy savings for buildings in the Annex 47 

Database. It does so while taking into account the decay of cost savings and the time value of money. 

Almost all buildings in the database had a BCR greater than one. Most had an IRR of greater than 

100 %. Compared to other investments, a 100 % return on investment is exceptionally high. Assuming 

that the buildings in the database are representative of commercial buildings in general, then nearly all

commercial buildings can benefit from Commissioning.

Predictors of commissioning-related non-energy savings are evaluated by estimating which tasks

implemented as part of the Commissioning report correlate with the desired outcome for five non-energy 

benefits in the Commissioning Database. Due to the small size of the data set results should be 

considered tentative. Best results are for reduction in O&M Costs. Benchmarking, Development of a 

Commissioning Plan, and the Development of an Energy Model are associated with a reduction in O&M 

Costs. Results for the other non-energy savings should be understood as suggestive rather than 

definitive.

4.2. Recommendations for Further Research

Commissioning studies frequently cite comfort as one of the objectives of Commissioning work. 

However, the Annex 47 database does not include any information on comfort. If it were possible to 

place a value on the improvements in comfort level, we could get a better sense of the valued added 

from Commissioning.

The following methodology could aid in valuing the improvements in comfort level. The basic 

approach is to estimate the average cost to individuals of being in locations with less-than-optimal 

temperatures. This data would then be used to estimate the hedonic8 cost to people in a building where 

temperature is maintained at a suboptimal level.

Even though commissioning is done in commercial buildings, the best source of information for how 

people value (dis)comfort would be the temperature they maintain in their own homes where they 

control the thermostat versus the cost. Therefore, we would need the following individual-level data for 

households:

• Thermostat settings over time

• Approximate location (sufficiently detailed to determine average temperature throughout the 

year).

• Heated Floor Area

Additional information that would be very helpful in estimating a value of comfort would be:

 8 Rosen, S. 1974. “Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition.” The Journal of 

Political Economy: 34–55.
10

• Number of Stories

• Age of structure

• Number of people in the household

It would be possible to substitute similar data for businesses for household data, but the interpretation of 

the results would be slightly different and the estimation would be potentially more difficult.

The basic approach consists of assuming the people have a utility function of the form:

U = u( v ) – h( T )

where v is other consumption, T is ambient indoor temperature, and h and u are functions.

A number of approaches can be taken, but the simplest is to assume that u is approximately linear over 

the relevant range of consumption. Then utility becomes:

U = m – c( T ) – h( T )

Where m is household income, and c is the cost of setting indoor air temperature to T.

We would expect thermostats to be set in advance, and changed relatively rarely. On that basis, all of 

these terms should be understood as being in expectation.

Cost will depend on a number of factors, and will likely need to be estimated. Taking that into account, 

the utility function would be written as:

U = m – c( T; x, β ) – h( T )

where x represents information known about the structure that affects the cost of heating and cooling and 

β are regression parameters that will be estimated. The function h would be estimated nonparametrically.

We assume that people are utility maximizers, so the problem people solve is:

max

T �m − c(T; x, β) − h(T)�

Solution to that problem will be T such that the following equation holds:

f(T; x, β) = −c ́(T; x, β) − h ́(T) = 0

Or

T� = f−1(0;x, β)

In practice, we would assume that the actual thermostat temperature selected was;

T∗ = f−1(0;x, β) + ε

Where ε is a random variable.
11

This then reduces to two problems. First, estimating the expected cost of setting indoor air temperature 

to T, and second estimate the function h non-parametrically. Most of the data needs above are directed 

toward answering the first question. The estimation is unambiguously non-linear, but the techniques for 

doing so are well established. Provided an adequate data set can be obtained, this should be relatively 

straightforward.