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Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

ii

Table of Contents

Executive Summary ....................................................................................................................................... 1

Introduction .................................................................................................................................................. 2

Program Description and Background ...................................................................................................... 2

Data Description ....................................................................................................................................... 3

Data Preprocessing ................................................................................................................................... 4

Research Question: Public Incentive Programs for Ecosystem Services .................................................. 4

Section 1 – Descriptive Statistics .................................................................................................................. 6

Initial Descriptive Statistics ....................................................................................................................... 6

Time Series Analysis .................................................................................................................................. 7

Section 2 – Model Hypothesis Testing ........................................................................................................ 13

Assumptions and Limitations .................................................................................................................. 13

Individual Model Testing Results ............................................................................................................ 14

All Installation Types by Cost per Square Foot over Time .................................................................. 15

Cost per Square Foot by Land Use Type ............................................................................................. 15

Costs per Square Foot by Install Type and Land Use Type ................................................................. 16

Costs per Square Foot for Large Installations (>10,000 sq ft) ............................................................. 18

Labor Costs per Square Foot by Land Use Type .................................................................................. 18

Section 3 – Conclusions and Future Recommendations ............................................................................. 20

Works Cited ................................................................................................................................................. 22

Appendix: Technical Analyses ..................................................................................................................... 24

Table of Figures

Figure 1: Housing Price Index and the Duration of the Ecoroof Incentive Program..................................... 3 

Figure 2: Histogram of Installation Costs per Square Foot ........................................................................... 6 

Figure 3: Size of Installations by Land Use Type ........................................................................................... 7 

Figure 4: Installation by Land Use Type (Grouped Types) ............................................................................ 8 

Figure 5: Cost per Square Foot by Project Over Time ................................................................................... 9 

Figure 6: Scatterplot of Installation Costs by Program Year ....................................................................... 10 

Figure 7: Box plot of install cost by type and year ...................................................................................... 11 

Figure 8: Cost per Square Foot by Land Use Type ...................................................................................... 12 

Figure 9: Scatterplot of Cost data and Robust Regression Model Plot ....................................................... 15 
Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

iii

Figure 10: SFR Installation Scatterplot and Robust Regression Plot ........................................................... 16 

Figure 11: Cost Scatterplot for New Installs for All Land Uses and Robust Regression Plot ...................... 16 

Figure 12: Cost Scatterplot for Retro Installations for All Land Use Types and Robust Regression Plot .... 17 

Figure 13: Cost Scatterplot for Single Family Residence Installations not Using Tray Type Technology and 

Regression Plot ........................................................................................................................................... 17 

Figure 14: Cost Scatterplot for Large Installations (>10,000 sq ft) and Robust Regression Plot ................ 18 

Figure 15: SFR Labor Costs per Square Foot Scatterplot and Robust Regression Plot (Non‐Tray Type) .... 19 

Table of Tables

Table 1: Basic Descriptive Statistics on Installation Costs per Square Foot .................................................. 6 

Table 2: Count and Total Area by Land Use Type ......................................................................................... 7 

Table 3: Count of Installations by Land Use Type and Sum of Area ............................................................. 8 

Table 4: Count of Installations by Land Use and Year ................................................................................. 11 

Table 5: Median Cost per Square Foot by Land Use Type .......................................................................... 11 
Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

1

Executive Summary

The City of Portland Bureau of Environmental Services’ Ecoroof Program instituted an incentive that 

supported installations of ecoroofs for five years from 2009‐2014. The program collected extensive data 

from the participants in the ecoroof incentive. One goal for the program was to support the use of 

ecoroofs by increasing the extent and rate of installation. The program also had the goal of reducing the 

cost of ecoroof installation through economies of scale and maturation of the industry through 

increased adoption of the technology. This report shares the results of an analysis of these data to 

understand if there was a change in the per‐unit cost to install ecoroofs. 

We conclude that the data do not support a statically significant relationship between the ongoing 

incentives distributed during the program and the installation per unit costs. This relationship was 

evaluated through a variety of techniques. We conclude that there is not a statistically significant 

relationship because either the relationship between the incentive and ecoroof costs is not direct or 

strong enough to affect a change, or that the data collected from participants in the program were not 

consistent enough to support statistical relationships. 

Despite these conclusions, we find that the program dataset provides important information on the 

distribution of costs by installation type and land use. Descriptive statistics indicate that median 

installation costs range from approximately $6.00 per square foot for single‐family residences up to 

$15.55 per square foot for institutional installations. The program included over 330,000 square feet of 

ecoroof installations with a total private investment of over $6 million. 

The data collected through the incentive support several conclusions regarding the incorporation of 

ecoroof technology into the broader Portland community. First, these data help to facilitate a public 

understanding of the types and variations of ecoroof installation costs in the Portland area which helps 

guide future technological development. Second, the variation in cost data suggests other possible 

program tools may be more effective in increasing ecoroof adoption, such as credit and market based 

systems or reverse auctions. Finally, these data provide a strong foundation and lessons learned for 

future cost evaluation projects. 
Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

2

Introduction

The City of Portland’s ecoroof incentive was developed as a means to expand the City’s green 

stormwater management infrastructure by increasing the frequency and affordability of installing green 

roofs on private and public buildings within the City. Additionally, the City hoped that the incentive 

would promote the development of a small, local, industry of contractors and installers by decreasing 

installation costs while the industry developed. In an effort to assess the success of the incentive, the 

City collected data on the installation costs of each participating project. This report presents an 

evaluation of these data and attempts to identify relationships which suggest an installation cost benefit 

from the incentive. The primary benefit being assessed is a decreasing per‐unit cost to install these 

facilities over time. The main hypothesis being tested in this analysis is whether or not these data 

suggest that the incentives program has caused a change in the per‐unit cost over the duration of its 

implementation. Testing of this hypothesis includes time series analyses and requires some 

assumptions about the role of the City’s incentives in the larger market. 

Program Description and Background

The Ecoroof Program grew out of the Sustainable Stormwater Management Division that was formed in 

2001. Program activities were focused on demonstration projects, technical assistance, and monitoring 

for stormwater performance. 

The Ecoroof Program was expanded in 2008 by the Grey to Green Initiative, which provided a direct 

financial incentive of $5 per square foot to boost implementation. During this time, the Ecoroof Program 

hosted annual seminars and symposia to build awareness and connect willing property owners with 

ecoroof professionals. Leading researchers and policy makers from Portland, and around the globe, 

were invited to participate and share the most current information on successful green roof technology. 

The incentive helped to fund 134 projects with $1.9 million over 5 years. 

In all, the ecoroof incentive allowed the program to leverage multiple partnerships, resources, and 

funding opportunities. The primary goal of the incentive was to reduce upfront costs so that more 

ecoroofs would be used in Portland and to jump start a forming industry. 

The Ecoroof Program provided the incentive during a unique period in the US housing market and for 

the economy as a whole. The Portland housing market increased steadily through, and out of, the short 

2001 recession but beginning in 2004 the rate of home price increased quickly. Home prices, as 

measured in the Case‐Shiller Home Price Index, increased over 80% from 2000 to its peak in the 

beginning of 2008 when the Great Recession began. From this period forward home prices quickly fell. 

The Portland Ecoroof Incentive program data begins in 2009 and runs through 2014. Figure 1 shows the 

housing price data along with the duration of the Ecoroof data. As the index shows, housing prices go 

through a U‐shaped curve over this time window. This curve may have influenced ecoroof costs and, if 

so, influenced them in two directions. This creates a challenge for analysis of the relationship between 

the real estate market and ecoroof costs. 
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Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

4

institutional installations that approached 30,000 square feet. The differences in costs, associated with 

these extreme variations, appear in the data and contribute to its variability. Larger installations may 

have required cranes or other mechanical tools not typically used for smaller installations, and may have 

also used higher cost prevailing wage labor. The smaller installations may have used volunteer labor and 

simple tools. These factors impacted the cost data, and our ability to assess change over time. 

Data Preprocessing

Throughout the initial cost analysis, several decisions were made which had impacts on how the final 

analysis would be conducted. While other options were explored, the following decisions resulted in 

the most appropriate application of these data to the cost analysis process. First, the installation costs 

that were considered did not include the membrane cost. When included, the membrane cost 

contributed significantly to the noise and outliers of the dataset, the removal of these costs provided 

the first step in normalizing the comparison between data. Second, the six land use categories were re‐

evaluated and generalized into three new categories which were similar in design and installation 

criteria, but contained more sample points, which increased the potential to identify significant trends. 

The three new groups are Single Family Residence (SFR) containing 59 installations; Mixed‐use, 

Commercial, and multi‐family residence (MXDMFR) containing 36 installations; Institutional and Hospital 

(INST) containing 10 installations. While an initial analysis was conducted which assessed the potential 

for trends in each of the land use categories throughout the duration of the project, only the Residential 

category had sufficient samples during the initial analysis, across the entire timespan of the project, to 

support a potentially significant trend. Third, several outliers were identified and investigated, which 

resulted in the implementation of corrections to the initial data collection or transcription process, 

further helping to support the analysis. These pre‐processing steps were necessary to provide the 

highest potential for identification of trends within the dataset. 

Research Question: Public Incentive Programs for Ecosystem Services

The management of stormwater, air and water pollutants, and urban heat island effect are three classes 

of environmental goods and services that ecoroofs provide (Rowe 2011). These environmental goods 

and services are supplied by the natural biophysical system as ecosystem services, until development 

occurs (Bolund and Hunhammar 1999; Hassan et al. 2005). With development, replacement of these 

services is required, normally this is accomplished through engineered solutions. In the context of 

impervious surfaces, new conveyance and treatment facilities are required for stormwater. Ecoroofs 

represent a hybridization of engineered and natural systems to replace services lost to development 

while retaining the benefits of urban development. This is a form of urban “domestication” of natural 

systems to better serve human communities (Kareiva et al. 2007). 

The benefit of ecoroofs has been a growing object of empirical and modeled research. A recent meta‐

analysis of existing research identified a wide suite of benefits from these green roof technologies (Rowe 

2011). These benefits include the above mentioned stormwater, air and water pollution filtration, and 

urban heat island effect reductions. For example, one square meter of green roof removes the same 

amount of particulate matter as that produced by the average automobile (Rowe 2011:2102). 
Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

5

Stormwater reductions can range from 50‐100% depending on local climactic and design considerations 

(Rowe 2011:2104). Other benefits include reducing building heating and cooling energy requirements, 

urban noise, and reduced life‐cycle costs of roofing materials. Longer range modeling of green roof 

installation shows large reductions in life cycle costs. Using Washington, DC’s 20‐20‐20 initiative to 

develop 20 million square feet of green roofs, Niu et al. found that green roofs would be 30‐40% less 

costly in net present value (2010). Based on this modeling, the break even for using green roofs over 

conventional roofing would occur after 7 years. 

Based on these findings, local jurisdictions are seeking policy tools to expand the rate and extent of 

ecoroof adoption. For ecosystem services and environmental programs there are several existing policy 

tools. These range from command type tools that require particular design standards, to voluntary 

subsidy or incentive programs and on to market based solutions (Tietenberg 2006). Green roof programs 

have focused on the first two options, with more applying incentive programs (Carter and Fowler 2008; 

Mees et al. 2014). The City of Portland fits these models through its Ecoroof incentive. This leads to the 

basis of the research question, how effective can the incentive be at increasing the adoption of ecoroof 

technology? 

More specifically for this report, the hypothesis is: The public incentive reduced the per‐unit installation 

costs for ecoroofs in the City of Portland while it was active. This hypothesis is based on an assumption 

that the incentive provides a price effect through changing demand, increasing quantities of installation, 

and developing benefits from economies of scale and industry maturity. This process assumes the 

following steps: First, the subsidy shifts the demand curve to the right where more quantities of goods 

are produced for the same price. Next, this shift in the demand curve is realized by consumers (or 

building owners) as a decrease in price per square foot. Finally, the increase in the quantity of 

installations then introduces economies of scale and maturation in the industry. Economies of scale and 

maturity are seen through increases in contractor firms, improvement of installation skills, and 

decreases in material and labor costs as the technology moves from an emerging technology to a 

common application. These assumptions are supported by empirical data showing US costs of 

installation are higher in comparison to conventional roofs, while in Europe the two types are marginally 

similar (Blackhurst, Hendrickson, and Matthews 2010:142). As the European market for ecoroofs 

predates that of the United States, this observation suggests policy measures may close the gap 

between the two technology types. 

The following sections review descriptive statistics from the City’s program to understand the general 

trends and distributions of values in the dataset. The first section provides a basis for characterizing the 

cost of installations across multiple land use and installation types. While these data show some mixed 

results, they are informative for future program development. The next section seeks to test the above 

hypothesis using several different approaches. The statistical models do not reject the null hypothesis 

that there is no effect. Therefore we cannot settle the question of whether the incentive had an effect 

on installation costs. However these data provide insight on possible progress in other policy tools. The 

final section concludes by reviewing what was learned from the analyses and proposes several options 

for future research and policy development. 
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Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

9

Table 3 provides a summary of the count, area and total cost for each land use grouping.1 Of these 

installations, nine are 10,000 square feet or larger. Institutional large installations provide 44,621 square 

feet of green roof and multi‐family/MXD/commercial installations provide 151,595 square feet. These 

large installations comprise approximately 60% of the area installed through the incentive. Of all of the 

installations, 61 were new and 44 were retrofit. 

  

Figure 5: Cost per Square Foot by Project Over Time

A scatterplot of these data suggests that the SFR installations may show a slight decline. Figure 6 shows 

the distribution of installation costs for each year in a scatterplot and by land use type. Also included are 

simple regression lines to indicate any directionality – though not with a measure of significance. 

 

1 Note that some totals vary slightly between figures as the analysis moves to the hypothesis testing. In the 

statistical analysis some cases were removed after review with City staff, others were removed based on outlier 

analysis. The data presented here has the larger dataset before excluding any data for analytical purposes.

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t of costs per 

he box plot’s 

e costs are to 

tal Services 

2013

2 

7 

14 

eliable measure

ars 2009 and 2

ercial S

 $

, by land use 

ile value. This

value due to 

square foot f

median value

the median. 

201

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e of distributio

2014.

Single Family

Residential

$6.07 

3.62 to $10.8

group. The ra

s represents t

skewed 

for all installa

es are the dar

Single family

11

14

ons

y

85 

ange 

the 

ations 

rk 

y
residence

cost value

Figure 8: Co

Pr

e shows a nar

es. 

ost per Square F

repared for C

rower groupi

oot by Land Use

Ecoroo

ity of Portlan

ng, but with s

e Type

of Cost Analys

d, Bureau of 

some notable

sis 

Environment

 outliers and

al Services 

 a skew towards the highe

12

r 
Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

13

Section 2 – Model Hypothesis Testing

Assumptions and Limitations

The starting hypothesis for this project is that the City incentives for ecoroof installation allowed for an 

increase in installations and a decrease in the per‐unit cost. Section 1 reviewed the descriptive statistics 

to begin exploring this hypothesis. The descriptive data revealed that for all installations there did not 

appear to be a decrease over time. There may be some decreases over time, however, within subsets of 

installation based on the land use, size, and technology used. The descriptive statistics also revealed 

some of the technical challenges for regression models with the installation data. 

Before discussing the models and techniques used in this report, the general challenges for statistical 

modeling need to be addressed. Once this background is established, the particular model choices can 

be explored in more detail. One of the most common regression techniques for this type of analysis is 

the ordinary least squares (OLS) (Burt and Barber 1996). Regression techniques such as OLS are based on 

four primary assumptions: normal distribution of variables; a linear relationship between dependent 

and independent variables; low or no measurement error; and errors are homoscedastic (Osborne and 

Waters 2002). 

The first assumption means that the frequency of the variable observations centers on a mean value 

with equal increments of observations to the right and the left of the mean. The histogram in Figure 2 

shows an example of examining a variable for normality. The figure shows a skewedness that must be 

addressed to perform an OLS regression. This can be accomplished with transformations. 

Transformations are the use of an equation to change the value of each observation such that the 

frequency becomes normal. For example, by raising the cost per square foot by 0.20, the distribution 

approximates normality, although this also makes interpretation of results more challenging as the 

coefficients from the regression model become relative, rather than absolute. As observed in Figure 2, 

normality in distributions is a challenge for these data. We try to address this in the models below with 

several techniques. Another related challenge to normality is the existence of outliers. Outliers have 

been a challenge in these data and we have removed some and corrected others as identified by the 

project team. 

The second assumption (of a linear relationship) is a requirement based on the structure of OLS or 

multiple regression techniques. If the relationship is curvilinear it can be managed, but we did not detect 

this as a problem in these data. 

The third assumption (low or no measurement error) is a challenge in this project. As discovered with 

the City of Portland team, the self‐reporting of data appears to be a large and uneven source of error in 

the data. There is no technique to address this except to try and subset these data into categories where 

at least the error might be standardized. However, this is a large limitation of this study and needs to be 

kept in mind as the results are reviewed. 
Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

14

The final assumption on error homoscedasticity appears not to be a challenge in the models presented 

below. This assumption is based on the idea that the distribution of error is consistent across the 

analysis and would be violated if there were time windows in which the distribution was significantly 

tighter than others. We do explore the distributions of error as we evaluate various model and 

regression techniques. 

While we have identified some tools to correct these data to meet the four assumptions, some of the 

distributional issues are being managed through transformation techniques. Alternatively there is a 

family of regression techniques known as robust regression. Robust regression methods have been 

developed to address the problems of outliers and to some degree issues of distributions (Andersen 

2008). Several techniques are available for robust regression, based on the challenges faced in this study 

we have used M‐estimator as the primary technique and this is supported by empirical research as a 

good fit for the data challenges present in this study. 

 Several models were crafted based on the subset of data used as well as the management of these data 

through transformations to address distributions and outliers. 

The following models were tested: 

 All installation types, cost per square foot over program 

 Cost per square foot over program by land use type 

 Cost per square foot over program by land use type and installation type 

 Cost per square foot over program for large installations (>10,000 square feet) 

 Labor costs per square foot for all installation types 

 Labor costs per square foot by land use type 

The goals for each of these models are to explore a refined subset of the data in an attempt to address 

the limitations discussed above. The subsets allow for testing that controls for some error types, or 

provide subsets which show better distributions. However this can also introduce new problems. By 

creating subsets of these data, the number of observations are reduced which can introduce new 

sources of error which represent a limitation for the analysis. As found in the descriptive statistics, the 

single family residence installations provide the most observations and thus allow for subsets on 

multiple variables. Other land use types do not have a large enough set of observations to address 

multiple variables. This strategy has allowed us to detect some new possible trends in these data. 

Individual Model Testing Results

For all of the following models, we were not able to reject the null hypothesis. We present these 

findings to show how we tested these data. But the conclusion overall in these statistical tests is that we 

cannot claim the program’s hypothesis of reducing per‐unit costs can be supported or rejected. The 

Appendix provides detailed regression tables for the models tested. 
All Instal

Initial OLS

significant

positive c

means tha

tested hy

Figure 9: Sc

Cost per

SFR result

better fit.

and the re

means tha

tested hy

the distrib

Pr

llation Type

S results: posi

t. Initial robu

orrelation ov

at there is no

pothesis.

atterplot of Cos

Square Foo

ts show a very

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eported R2 is 

at there is no

pothesis. Sim

butional issue

repared for C

es by Cost pe

itive correlati

st regression 

ver time. This 

o explanation 

st data and Robu

ot by Land U

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ke other mode

very small. Th

o explanation 

milar to all land

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Ecoroo

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with power t

model report

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ust Regression M

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15

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retrofitted

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Figure 11: C

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the reliability

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Cost Scatterplot

repared for C

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examined the

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we did not fi

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Ecoroo

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16

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Figure 12: C

Figure 13: C

Pr

Cost Scatterplot

Cost Scatterplot

repared for C

for Retro Instal

for Single Famil

Ecoroo

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of Cost Analys

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and Use Types a

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17

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Figure 15: S

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test the h

none of th

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ypothesis as 

he models me

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repared for C

per Square Foot

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et statistical s

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19

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Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

20

Section 3 – Conclusions and Future Recommendations

This section briefly reviews the analytical results from Section 2, the interpretation of these results, and 

then shifts to understand what information these data do provide. This section also presents several 

data, program, and policy recommendations. 

The results of the various models were not found to be statistically significant. Therefore the null 

hypothesis cannot be rejected. This means these data do not support the conclusion that the incentive 

decreased costs over time. There are several reasons why the hypotheses may not be supported. First is 

the possible lack of a causal relationship in the economic dynamics behind the cost of ecoroof 

installations. These costs may not be affected by the City’s incentive. As discussed in the first section, 

the proposed causal relationship was based on seeing increased economies of scale and maturity in the 

ecoroof industry. While over 300,000 new square feet were supported with this program, 60% of that 

area was accomplished with 9 large projects. This may have limited the ability of economies of scale to 

be realized across the diverse set of installations. 

It is also possible that the underlying costs benefited from economies of scale but these benefits did not 

influence much of the total costs. We tested for the maturation of the industry by using labor costs as a 

measure of possible efficiencies. Unfortunately, these metrics also failed to support a statistically 

significant relationship. One limitation for this analysis was that the labor data was not complete across 

the entire dataset. 

Another reason for the possible lack of a relationship is that the set of projects included in the data 

collection are a unique sample of all projects installed in Portland. It is possible that property owners 

who chose to participate in the program were skewed by the available incentive, leading to a sample of 

projects with unique or non‐representative costs. While the descriptive data does not suggest a per unit 

skewedness, there is a possibility of selection bias based on the incentive. To adjust for this, future data 

collection would need to randomly sample installations not participating in the incentive program to 

survey for similar cost data. 

The last challenge for the analysis is data quality. As the descriptive statistics review was developed with 

City staff it was acknowledged that the reporting of the data from participating installers was not 

consistent. There was variation in how costs were included or excluded in the reporting, as well as how 

costs were categorized. We suspect this variation had a powerful impact on the data. It increased 

outliers and skewed data distributions. We attempted to control for this by subsetting data into 

categories where the error may have been more uniform, however these methods were also 

unsuccessful in the identification of statistically significant relationships. These efforts also created 

subsets of data with fewer cases and thus, further complicated developing statistical tests. 

These two issues do not mean the data is not of some value for the City in evaluating the program. The 

data collected around these installations provides a valuable snapshot of the economics of ecoroof 

installation. This is a useful tool for future program development and policy adoption. Based on our 

review of the data we offer the following conclusions and their implications. 
Ecoroof Cost Analysis 

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21

Conclusion 1: Data from Program Supports Better Policy and Public Information

Environmental programs to incent landowners or developers are often hampered by “information 

asymmetry” (Ferraro 2008). Information asymmetry is the situation where landowners or developers 

better understand the financial impacts of proposed regulations on their practices than regulating 

entities. This higher quality information allows for more successful negotiation to reduce costs for 

regulation as the agency often does not know the true “cost of doing business.” By collecting these data, 

the City has a better understanding of how costs are distributed through the city, and can more 

appropriately compare these to other conventional costs. These conclusions have the same caveats as 

noted above in the data quality discussion. But we believe these data to be insightful at this level. 

Further, this first phase of data collection can be seen as a pilot for further data collection. A key role for 

government in speeding innovation and adoption of new environmental technology is to reduce 

information costs and make the findings from data a public good for all parties to use (Jaffe, Newell, and 

Stavins 2005). Findings from this program should be shared with the public and participating contractors 

to grow the body of knowledge among practitioners. 

Conclusion 2: Cost Data is Highly Variable Within and Across Installation Types

The descriptive statistics show that installation costs vary considerably. This is true within, and across, 

land use types. We also did not see that variability declined over time. This difference means that some 

building owners have very low cost installations (typically single family) and others have higher costs 

(larger installations and institutional land uses). When large differences in cost are known to exist, one 

policy tool that can be effective is market based systems (Carter and Fowler 2008:154). 

Conclusion 3: Data Collection Improvements Can Expand Usefulness of Program

As the previous two conclusions have shown, using the incentive to collect cost information from 

contractors is itself a public benefit. Further developing the cost data collection protocols can improve 

the quality and extent of the data for future evaluations. While this research did not directly review data 

collection practices, the team did discuss challenges experienced through the program. Self‐reported 

data requires more protocols to guide the respondents. This is especially true for data that varies greatly 

on how the technology is used. For example the tray‐type installations appeared to embed costs 

differently than other technologies. Another challenge was making sure that data was completed and 

checked for accuracy. Labor data, membrane costs, and other components were inconsistently reported 

or were missing from the data. Developing more involved protocols or instructional materials may 

improve data quality. Random selections of reports should be reviewed by staff over the phone or in 

person to assess data quality as well. This random calling would also provide an opportunity for 

qualitative data collection. A survey could be developed to allow for open‐ended questions to explore 

drivers in costs or installation challenges. The results of these surveys and interviews could change how 

data is collected to better capture the information needed. 

 
Ecoroof Cost Analysis 

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22

Works Cited

Alma, Özlem Gürünlü. 2011. “Comparison of Robust Regression Methods in Linear Regression.” 

International Journal of Contemporary Mathematical Sciences 6(9):409–21. 

Andersen, Robert. 2008. Modern Methods for Robust Regression. Los Angeles: Sage Publications. 

Blackhurst, Michael, Chris Hendrickson, and H. Scott Matthews. 2010. “Cost‐Effectiveness of Green 

Roofs.” Journal of Architectural Engineering 16(4):136–43. 

Bolund, Per and Sven Hunhammar. 1999. “Ecosystem Services in Urban Areas.” Ecological Economics

29(2):293–301. 

Burt, James E. and Gerald M. Barber. 1996. Elementary Statistics for Geographers. New York: Guilford 

Press. 

Carter, Timothy and Laurie Fowler. 2008. “Establishing Green Roof Infrastructure Through 

Environmental Policy Instruments.” Environmental Management 42(1):151–64. 

Ferraro, Paul J. 2008. “Asymmetric Information and Contract Design for Payments for Environmental 

Services.” Ecological Economics 65(4):810–21. 

Hassan, Rashid M., R. J. Scholes, Neville Ash, and Millennium Ecosystem Assessment (Program). 

Condition and Trends Working Group. 2005. Ecosystems and Human Well‐Being : Current State

and Trends : Findings of the Condition and Trends Working Group of the Millennium Ecosystem

Assessment. Washington, DC: Island Press. 

Jaffe, Adam B., Richard G. Newell, and Robert N. Stavins. 2005. “A Tale of Two Market Failures: 

Technology and Environmental Policy.” Ecological Economics 54(2–3):164–74. 

Kareiva, Peter, Sean Watts, Robert McDonald, and Tim Boucher. 2007. “Domesticated Nature: Shaping 

Landscapes and Ecosystems for Human Welfare.” Science 316(5833):1866–69. 

Krzywinski, Martin and Naomi Altman. 2014. “Points of Significance: Visualizing Samples with Box Plots.” 

Nature Methods 11(2):119–20. 

Mees, Heleen LP et al. 2014. “A Method for the Deliberate and Deliberative Selection of Policy 

Instrument Mixes for Climate Change Adaptation.” Ecology and Society 19(2):58. 

Niu, Hao, Corrie Clark, Jiti Zhou, and Peter Adriaens. 2010. “Scaling of Economic Benefits from Green 

Roof Implementation in Washington, DC.” Environmental Science & Technology 44(11):4302–8. 

Osborne, Jason and Elaine Waters. 2002. “Four Assumptions of Multiple Regression That Researchers 

Should Always Test.” Practical Assessment, Research & Evaluation 8(2):1–9. 

R Core Team. 2012. R: A Language and Environment of Statistical Computing. Vienna, Austria: R 

Foundation for Statistical Computing. Retrieved (http://www.R‐project.org/). 
Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

23

Rowe, D. Bradley. 2011. “Green Roofs as a Means of Pollution Abatement.” Environmental Pollution

159(8):2100–2110. 

Tietenberg, Thomas H. 2006. Environmental Economics and Policy. 5th ed. Boston: Pearson/Addison 

Wesley. 
Ecoroof Cost Analysis 

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Appendix: Technical Analyses

Following the evaluation of the descriptive statistics, the analysis team was concerned that the 

distribution of the variables and the change of the mean over time would not support a significant 

finding. We chose to explore these concerns through several OLS models and robust regression models 

(M‐estimator). Due to the number of observations and the distributions we focused our models on 

single family residences where the assumptions of cost error estimation might be more similar, reducing 

measurement error effects. 

The following tables work though the several models we have developed to explore these data. The first 

set of regression tables are the OLS results for three models with cost per square foot without 

membrane as the dependent variable: a univariate model with the program month; a multivariate 

model with program month and size of the installation in square feet, and a multivariate model adding a 

dummy variable for installation type to the previous model. The data was examined and identified 

skewedness in the dependent variable. Using the Box‐Cox technique a power transformation was 

applied. Initial plots identified outliers that were reasonable to remove. 

Based on these analyses we are not confident that the program duration and the incentives provided 

during it resulted in a change in cost per square foot for installations. As discussed in the conclusion 

there are a number of ways to understand this. 

Following are the resultant tables for the three models using this single family residence data from the 

ecoroof master dataset: 

MODEL 1: Univariate CPSF and Program Month

=============================================== 

 Dependent variable: 

 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

 cpsf_wo_memb0.2 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

progmo ‐0.0004 

 (0.002) 

 

Constant 1.475*** 

 (0.061) 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Observations 55 

R2 0.001 

Adjusted R2 ‐0.017 

Residual Std. Error 0.186 (df = 53) 

F Statistic 0.073 (df = 1; 53) 

=============================================== 

Note: *p<0.1; **p<0.05; ***p<0.01 
Ecoroof Cost Analysis 

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MODEL 2: CPSF by Size and Program Month

=============================================== 

 Dependent variable: 

 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

 cpsf_wo_memb0.2 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

progmo 0.002 

 (0.002) 

 

sizesf ‐0.0001** 

 (0.0001) 

 

Constant 1.479*** 

 (0.058) 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Observations 55 

R2 0.109 

Adjusted R2 0.075 

Residual Std. Error 0.178 (df = 52) 

F Statistic 3.188** (df = 2; 52) 

=============================================== 

Note: *p<0.1; **p<0.05; ***p<0.01 

   
Ecoroof Cost Analysis 

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MODEL 3: CPSF by Size, Program Month and Install Type

=============================================== 

 Dependent variable: 

 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

 cpsf_wo_memb0.2 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

progmo 0.002 

 (0.002) 

 

sizesf ‐0.0001** 

 (0.0001) 

 

newdummy ‐0.002 

 (0.050) 

 

Constant 1.480*** 

 (0.062) 

 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Observations 55 

R2 0.109 

Adjusted R2 0.057 

Residual Std. Error 0.179 (df = 51) 

F Statistic 2.085 (df = 3; 51) 

=============================================== 

Note: *p<0.1; **p<0.05; ***p<0.01 

   
Ecoroof Cost Analysis 

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27

In addition to the OLS models we attempted robust techniques to both examine outliers and leverage 

points as well as to assess the coefficients and standard errors under these methods. Due to the small 

dataset we chose M‐Estimator as the most appropriate method (Alma 2011). The results are similar to 

OLS in that coefficients are very close to 0, thus suggesting the null hypothesis cannot be rejected. The 

power transformation should reduce this number as the transformation would approach a zero slope 

further to the right, on higher dependent values. Regardless, the low coefficient is still too low. 

MODEL 4: Robust (M‐Estimator) CPSF by Program Month

=============================================== 

 Dependent variable: 

 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

 cpsf_wo_memb0.2) 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

progmo ‐0.001 

 (0.002) 

 

Constant 1.469*** 

 (0.070) 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Observations 58 

Residual Std. Error 0.243 (df = 56) 

=============================================== 

Note: *p<0.1; **p<0.05; ***p<0.01 

MODEL 5: Robust (M‐Estimator) CPSF by Program Month and Size

=============================================== 

 Dependent variable: 

 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

 cpsf_wo_memb0.2 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

progmo 0.002 

 (0.002) 

 

sizesf ‐0.0001*** 

 (0.0001) 

 

Constant 1.466*** 

 (0.058) 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Observations 55 

Residual Std. Error 0.186 (df = 52) 

=============================================== 

Note: *p<0.1; **p<0.05; ***p<0.01 

   
Ecoroof Cost Analysis 

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MODEL 6: Robust (M‐Estimator) CPSF by Program Month, Size and Install Type

=============================================== 

 Dependent variable: 

 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

 cpsf_wo_memb0.2 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

progmo 0.002 

 (0.002) 

 

sizesf ‐0.0001** 

 (0.0001) 

 

newdummy 0.006 

 (0.050) 

 

Constant 1.463*** 

 (0.062) 

 

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Observations 55 

Residual Std. Error 0.183 (df = 51) 

=============================================== 

Note: *p<0.1; **p<0.05; ***p<0.01 

The analysis for this project was conducted in the R statistical scripting and analysis language using R 

Studio for a user interface (R Core Team 2012). The MASS and ggplot2 packages were used to support 

this analysis as well. The following code was used to generate these analyses from Section 2. Data was 

subsetted to new dataframes as needed for these analyses. The primary subsetting is listed below with 

dataframe name in parentheses: 

 Observations with SFR Land Use Type (cleandataSFR) 

 Large Installations => 10,000 sq ft (largeinstalldata) 

 New installations (cleandata.allnewinstall) 

 Retro installations (cleandata.allretroinstall) 

 Tray type installations (traydata) 

Regression Analyses: 

Figure 9: Scatterplot of Cost data and Robust Regression Model Plot 

rlm((cleandata$cpsf_wo_memb^.2)~cleandata$progmo) 

Figure 10: SFR Installation Scatterplot and Robust Regression Plot 

rlm((cleandataSFR$cpsf_wo_memb^.2)~cleandataSFR$progmo) 

Figure 11: Cost Scatterplot for New Installs for All Land Uses and Robust Regression Plot 

rlm(sfr.notray$laborsf^.18 ~ sfr.notray$progmo) 
Ecoroof Cost Analysis 

Prepared for City of Portland, Bureau of Environmental Services 

29

Figure 12: Cost Scatterplot for Retro Installations for All Land Use Types and Robust Regression Plot 

rlm((cleandata.allretroinstall$cpsf_wo_memb^.2)~cleandata.allretroinstall$progmo) 

Figure 13: Cost Scatterplot for Single Family Residence Installations not Using Tray Type Technology and 

Regression Plot 

rlm(sfr.notray$cpsf_wo_memb^.18 ~ sfr.notray$progmo) 

Figure 14: Cost Scatterplot for Large Installations (>10,000 sq ft) and Robust Regression Plot 

rlm((largeinstalldata$cpsf_wo_memb^.5)~largeinstalldata$progmo) 

Figure 15: SFR Labor Costs per Square Foot Scatterplot and Robust Regression Plot (Non‐Tray Type) 

rlm((cleandataSFR$laborsf^.2)~cleandataSFR$progmo)