                 UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
                NATIONAL VEHICLE AND FUEL EMISSIONS LABORATORY
                             2000 TRAVERWOOD DRIVE
                           ANN ARBOR, MI  48105-2498


										     OFFICE OF
										AIR AND RADIATION

June 8, 2016
MEMORANDUM
From:	Todd Sherwood
	Assessment and Standards Division, U.S. EPA

To:	Air Docket EPA-HQ-OAR-2015-0827

Subject: Learning Curves used in Developing Technology Costs in the Draft TAR
Introduction
Since the late 1990s, EPA's Office of Transportation and Air Quality (OTAQ) has included a learning effect when estimating the costs of emissions standards.  Specifically, technology costs -- for technologies added to mobile sources to allow for compliance with new emissions standards -- are estimated to decrease in the years following first implementation.  This decrease in technology costs, either due to the volume of production or to time, is considered to be due to learning.  Learning may reflect efficiencies gained in production processes, improvements in tooling and in the design of the manufactured components, increased proficiency of individual employees, and improvements in the organization's structure or some combination of these factors.
This learning effect has been studied by academia and industry for more than 60 years.  Many studies are available that examine the learning effect, or aspects of it; the vast majority of these studies conclude that cost reductions through learning do, in fact, occur.  Other studies assume that cost reductions will occur based on this body of evidence and incorporate learning effects into their analysis, as EPA does in its cost analyses.
While there is little doubt that this learning effect occurs, the learning estimates used by OTAQ in its cost analyses are based on somewhat dated studies that are not specific to the mobile source sector.  Therefore, EPA contracted ICF International to develop a single compendium study on industrial learning in the mobile source sector and, using that information, to recommend an updated mobile source progress ratio that could be used in EPA's future mobile source cost analyses.  ICF performed this literature review and analysis of learning in the mobile source sector with the assistance of a Subject Matter Expert (Dr. Linda Argote of Carnegie Mellon University).  The draft report, Cost Reduction through Learning in Manufacturing Industries and in the Manufacture of Mobile Sources, was subsequently peer-reviewed by three well-known experts in the field of learning (Marvin Lieberman, Ph.D., University of California, Los Angeles (UCLA) Anderson School of Management; Natarajan Balasubramanian, Ph.D., Whitman School of Management, Syracuse University; and Chad Syverson, Ph.D., University of Chicago Booth School of Business).  The peer review was carried out for EPA by RTI International based on EPA Science Policy Council Peer Review Handbook, 4[th] Edition, and was completed in May 2016. 
As of May 2016 EPA is in the process of working with ICF International and Dr. Argote to respond to the peer review comments and finalize the mobile source learning study. EPA will plan to make the final report, and the peer review report, available publicly once this work is completed. In the meantime, EPA is using the newly estimated mobile source sector progress ratio presented in the peer-reviewed draft study to estimate the individual technology costs presented in our 2016 Draft Technical Assessment Report (TAR). 
This memorandum provides the mobile source progress ratio from the peer-reviewed draft mobile source learning study and describes how EPA used those results in developing the technology costs used in the Draft TAR.
Results from the Draft Final Report on Learning
The mobile source learning study consists of two parts:  a literature review and an estimate of a mobile source progress ration.  A total of 53 studies on learning were examined, with 20 of these selected for detailed review (the other 33 received a more cursory review and are not discussed in detail in the report).  Five of these studies, set out in the table below, were used as the basis to estimate the progress ratio for the mobile source sector.  
      
         Confidence Intervals of Progress Ratios from Selected Studies
Author 
(Publication Date)
Industry
Progress Ratio 
(Cumulative Output Approach)
Confidence Interval
Learning Coefficient
Standard Error of Coefficient
                                      (1)
                                      (2)
                                      (3)
                                      (4)
                                      (5)
                                      (6)
Argote, Epple, Rao, & Murphy (1997)
                                    Trucks
                                      86%
                                  (85%, 87%)
                                    -0.221
                                     0.007
Benkard (2000)
                             Aircraft (commercial)
                                      82%
                                  (80%, 84%)
                                    -0.290
                                     0.020
Epple, Argote, & Devadas (1991)
                                    Trucks
                                      87%
                                  (85%, 90%)
                                    -0.197
                                     0.021
Epple, Argote, & Murphy (1996)
                                    Trucks
                                      86%
                                  (85%, 86%)
                                    -0.226
                                     0.007
Levitt, List, & Syverson (2013)
                                  Automobiles
                                      82%
                                  (81%, 83%)
                                    -0.289
                                     0.007

On the basis of these studies, the Subject Matter Expert noted: 
      The mean learning rate is estimated to be -0.245, with a standard error of 0.0039.  Thus, the lower bound for a 95% confidence interval for the learning rate is -0.253; the upper bound is -0.238.  These estimates translate into a mean progress ratio of 84.3%.  The confidence interval around this number ranges from 83.9% to 84.8%, suggesting that one can be reasonably confident that the progress ratio falls in this interval.  Thus, the best estimate of the progress ratio in mobile source industries is 84%.
To use these conclusions to estimate impacts on future costs, we used the following equation, which is the classic learning curve expression:
      
yt+1=xt+1xtbyt
      (Eq. 6)
      
      yt+1	=	Costs required to produce a unit at time t+1
      yt	=	Costs required to produce a unit at time t
      xt	=	cumulative units produced as of time (t)
      xt+1	=	cumulative units produced as of time (t+1)
      b	=	A parameter measuring rate unit costs change as cumulative output increases  -  the learning rate
      
Use in the Draft TAR
In the Draft TAR, we have used equation 6 shown above along with the conclusion stated just following the table excerpted above, "The mean learning rate is estimated to be -0.245." The tables and charts below show the input metrics used in generating the new (since the 2012 FRM, see 77 FR 62623) learning curves 23 through 32 as used in the Draft TAR. Also presented are the similar learning curves applied in the 2012 final rule (77 FR 62623). Throughout these examples, we generally assume full production of 450,000 units for consistency with teardown cost estimates upon which many of our technology costs have been based (see Final Joint Technical Support Document, EPA-420-R-12-901 at page 3-8). Admittedly, we have also used production levels to drive learning impacts loosely consistent with those supporting past light-duty final rulemaking analyses (see Final Joint Technical Support Document, EPA-420-R-12-901 at page 3-23, and Final Joint Technical Support Document, EPA-420-R-10-901 at page 3-17). For some curves, we have assumed that production has been ongoing for years and, therefore, cumulative production is high. For illustration in the tables, we have used an estimated technology cost of $100 per unit unless otherwise noted.























Draft TAR Curve 23 (2012 FRM Curve 11)
Curve used for high production technologies for which steeper learning impacts have occurred and for which our estimated cost is considered valid in 2012.
            Table 1 Draft TAR Curve 23 along with 2012 FRM Curve 11
                                     Year
                                  Cumulative
                                  Production
                                   Cost/unit
                                   Draft TAR
                                Cost Reduction
                                   Draft TAR
                               Learning Factors
                                   2012 FRM
                                Cost Reduction
                                   2012 FRM
                               Learning Factors
                                     2012
                                   4,500,000
                                    $100.00
                                     100%
                                     1.00
                                     100%
                                     1.00
                                     2013
                                   4,950,000
                                    $97.69
                                      98%
                                     0.98
                                      97%
                                     0.97
                                     2014
                                   5,400,000
                                    $95.63
                                      96%
                                     0.96
                                      94%
                                     0.94
                                     2015
                                   5,850,000
                                    $93.77
                                      94%
                                     0.94
                                      91%
                                     0.91
                                     2016
                                   6,300,000
                                    $92.09
                                      92%
                                     0.92
                                      89%
                                     0.89
                                     2017
                                   6,750,000
                                    $90.54
                                      91%
                                     0.91
                                      87%
                                     0.87
                                     2018
                                   7,200,000
                                    $89.12
                                      89%
                                     0.89
                                      85%
                                     0.85
                                     2019
                                   7,650,000
                                    $87.81
                                      88%
                                     0.88
                                      83%
                                     0.83
                                     2020
                                   8,100,000
                                    $86.59
                                      87%
                                     0.87
                                      82%
                                     0.82
                                     2021
                                   8,550,000
                                    $85.45
                                      85%
                                     0.85
                                      80%
                                     0.80
                                     2022
                                   9,000,000
                                    $84.38
                                      84%
                                     0.84
                                      78%
                                     0.78
                                     2023
                                   9,450,000
                                    $83.38
                                      83%
                                     0.83
                                      77%
                                     0.77
                                     2024
                                   9,900,000
                                    $82.43
                                      82%
                                     0.82
                                      75%
                                     0.75
                                     2025
                                  10,350,000
                                    $81.54
                                      82%
                                     0.82
                                      74%
                                     0.74


                                       
           Figure 1 Draft TAR Curve 23 along with 2012 FRM Curve 11


Draft TAR Curve 24 (2012 FRM Curve 12)
Curve used for high production technologies for which steeper learning impacts have occurred and for which our estimated cost is considered valid in 2015.

            Table 2 Draft TAR Curve 24 along with 2012 FRM Curve 12
                                     Year
                                  Cumulative
                                  Production
                                   Cost/unit
                                   Draft TAR
                                Cost Reduction
                                   Draft TAR
                               Learning Factors
                                   2012 FRM
                                Cost Reduction
                                   2012 FRM
                               Learning Factors
                                     2012
                                   3,150,000
                                    $109.13
                                     109%
                                     1.09
                                     110%
                                     1.10
                                     2013
                                   3,600,000
                                    $105.62
                                     106%
                                     1.06
                                     106%
                                     1.06
                                     2014
                                   4,050,000
                                    $102.61
                                     103%
                                     1.03
                                     103%
                                     1.03
                                     2015
                                   4,500,000
                                    $100.00
                                     100%
                                     1.00
                                     100%
                                     1.00
                                     2016
                                   4,950,000
                                    $97.69
                                      98%
                                     0.98
                                      97%
                                     0.97
                                     2017
                                   5,400,000
                                    $95.63
                                      96%
                                     0.96
                                      95%
                                     0.95
                                     2018
                                   5,850,000
                                    $93.77
                                      94%
                                     0.94
                                      93%
                                     0.93
                                     2019
                                   6,300,000
                                    $92.09
                                      92%
                                     0.92
                                      91%
                                     0.91
                                     2020
                                   6,750,000
                                    $90.54
                                      91%
                                     0.91
                                      89%
                                     0.89
                                     2021
                                   7,200,000
                                    $89.12
                                      89%
                                     0.89
                                      88%
                                     0.88
                                     2022
                                   7,650,000
                                    $87.81
                                      88%
                                     0.88
                                      86%
                                     0.86
                                     2023
                                   8,100,000
                                    $86.59
                                      87%
                                     0.87
                                      84%
                                     0.84
                                     2024
                                   8,550,000
                                    $85.45
                                      85%
                                     0.85
                                      83%
                                     0.83
                                     2025
                                   9,000,000
                                    $84.38
                                      84%
                                     0.84
                                      81%
                                     0.81


                                       
           Figure 2 Draft TAR Curve 24 along with 2012 FRM Curve 12


Draft TAR Curve 25 (2012 FRM Curve 16)
Curve used for developing or recent technologies for which steeper learning impacts have recently occurred or are currently occurring and for which our estimated cost is considered valid in 2015.
            Table 3 Draft TAR Curve 25 along with 2012 FRM Curve 16
                                     Year
                                  Cumulative
                                  Production
                                   Cost/unit
                                   Draft TAR
                                Cost Reduction
                                   Draft TAR
                               Learning Factors
                                   2012 FRM
                                Cost Reduction
                                   2012 FRM
                               Learning Factors
                                     2012
                                    50,000
                                    $203.02
                                     203%
                                     2.03
                                     110%
                                     1.56
                                     2013
                                    125,000
                                    $162.20
                                     162%
                                     1.62
                                     106%
                                     1.56
                                     2014
                                    325,000
                                    $128.34
                                     128%
                                     1.28
                                     103%
                                     1.25
                                     2015
                                    900,000
                                    $100.00
                                     100%
                                     1.00
                                     100%
                                     1.00
                                     2016
                                   1,350,000
                                    $90.54
                                      91%
                                     0.91
                                      97%
                                     1.00
                                     2017
                                   1,800,000
                                    $84.38
                                      84%
                                     0.84
                                      94%
                                     0.97
                                     2018
                                   2,250,000
                                    $79.89
                                      80%
                                     0.80
                                      91%
                                     0.94
                                     2019
                                   2,700,000
                                    $76.40
                                      76%
                                     0.76
                                      89%
                                     0.91
                                     2020
                                   3,150,000
                                    $73.57
                                      74%
                                     0.74
                                      86%
                                     0.89
                                     2021
                                   3,600,000
                                    $71.20
                                      71%
                                     0.71
                                      83%
                                     0.86
                                     2022
                                   4,050,000
                                    $69.18
                                      69%
                                     0.69
                                      81%
                                     0.83
                                     2023
                                   4,500,000
                                    $67.41
                                      67%
                                     0.67
                                      78%
                                     0.81
                                     2024
                                   4,950,000
                                    $65.86
                                      66%
                                     0.66
                                      76%
                                     0.78
                                     2025
                                   5,400,000
                                    $64.47
                                      64%
                                     0.64
                                      74%
                                     0.76


                                       
           Figure 3 Draft TAR Curve 25 along with 2012 FRM Curve 16

Draft TAR Curve 26 (2012 FRM Curve 19)
Curve used for developing technologies for which steeper learning impacts are currently occurring and for which our estimated cost is considered valid in 2025. Here we have assumed annual production growth on the order of 30,000 units/year. For illustration, we have also used a cost per unit value starting with $531/kWh, roughly in line with the battery cost per kWh in 2012.
            Table 4 Draft TAR Curve 26 along with 2012 FRM Curve 19
                                     Year
                                  Production
                                  Cumulative
                                  Production
                                   Cost/unit
                                   Draft TAR
                                Cost Reduction
                                   Draft TAR
                               Learning Factors
                                   2012 FRM
                                Cost Reduction
                                   2012 FRM
                               Learning Factors
                                     2012
                                    60,000
                                    60,000
                                     $531
                                     305%
                                     3.05
                                     305%
                                     3.05
                                     2013
                                    90,000
                                    150,000
                                     $424
                                     244%
                                     2.44
                                     305%
                                     3.05
                                     2014
                                    120,000
                                    270,000
                                     $367
                                     211%
                                     2.11
                                     244%
                                     2.44
                                     2015
                                    150,000
                                    420,000
                                     $330
                                     189%
                                     1.89
                                     244%
                                     2.44
                                     2016
                                    180,000
                                    600,000
                                     $302
                                     174%
                                     1.74
                                     195%
                                     1.95
                                     2017
                                    210,000
                                    810,000
                                     $281
                                     161%
                                     1.61
                                     195%
                                     1.95
                                     2018
                                    240,000
                                   1,050,000
                                     $263
                                     151%
                                     1.51
                                     156%
                                     1.56
                                     2019
                                    270,000
                                   1,320,000
                                     $249
                                     143%
                                     1.43
                                     156%
                                     1.56
                                     2020
                                    300,000
                                   1,620,000
                                     $237
                                     136%
                                     1.36
                                     125%
                                     1.25
                                     2021
                                    330,000
                                   1,950,000
                                     $226
                                     130%
                                     1.30
                                     125%
                                     1.25
                                     2022
                                    360,000
                                   2,310,000
                                     $217
                                     125%
                                     1.25
                                     125%
                                     1.25
                                     2023
                                    390,000
                                   2,700,000
                                     $209
                                     120%
                                     1.20
                                     125%
                                     1.25
                                     2024
                                    420,000
                                   3,120,000
                                     $202
                                     116%
                                     1.16
                                     125%
                                     1.25
                                     2025
                                    450,000
                                   3,570,000
                                     $195
                                     112%
                                     1.12
                                     100%
                                     1.00

                                       
           Figure 4 Draft TAR Curve 26 along with 2012 FRM Curve 19
Draft TAR Curve 28 (2012 FRM Curve 21)
Curve used for high production technologies for which steeper learning impacts have occurred and for which our estimated cost is considered valid in 2016. For this curve, we have used the factors for curve 24 but have shifted them by one year from a 2015 basis to a 2016 basis.

            Table 5 Draft TAR Curve 28 along with 2012 FRM Curve 21
                                     Year
                                   Cost/unit
                                   Draft TAR
                                Cost Reduction
                                   Draft TAR
                               Learning Factors
                                   2012 FRM
                                Cost Reduction
                                   2012 FRM
                               Learning Factors
                                     2012
                                    $113.33
                                     113%
                                     1.13
                                     116%
                                     1.16
                                     2013
                                    $109.13
                                     109%
                                     1.09
                                     113%
                                     1.13
                                     2014
                                    $105.62
                                     106%
                                     1.06
                                     110%
                                     1.10
                                     2015
                                    $102.61
                                     103%
                                     1.03
                                     106%
                                     1.06
                                     2016
                                    $100.00
                                     100%
                                     1.00
                                     103%
                                     1.03
                                     2017
                                    $97.69
                                      98%
                                     0.98
                                     100%
                                     1.00
                                     2018
                                    $95.63
                                      96%
                                     0.96
                                      97%
                                     0.97
                                     2019
                                    $93.77
                                      94%
                                     0.94
                                      94%
                                     0.94
                                     2020
                                    $92.09
                                      92%
                                     0.92
                                      91%
                                     0.91
                                     2021
                                    $90.54
                                      91%
                                     0.91
                                      89%
                                     0.89
                                     2022
                                    $89.12
                                      89%
                                     0.89
                                      86%
                                     0.86
                                     2023
                                    $87.81
                                      88%
                                     0.88
                                      84%
                                     0.84
                                     2024
                                    $86.59
                                      87%
                                     0.87
                                      82%
                                     0.82
                                     2025
                                    $85.45
                                      85%
                                     0.85
                                      81%
                                     0.81


                                       
           Figure 5 Draft TAR Curve 28 along with 2012 FRM Curve 21

Draft TAR Curve 30 (2012 FRM Curve 21)
Curve used for mass reduction technologies for which our estimated cost is considered valid in 2020 (Draft TAR) and in 2017 (2012 FRM). For the Draft TAR, learning curve factors are set equal to those used for Draft TAR curve 24, but are shifted by 5 years for a 2015 basis to a 2020 basis.
            Table 6 Draft TAR Curve 30 along with 2012 FRM Curve 21
                                     Year
                                  Cumulative
                                  Production
                                   Cost/unit
                                   Draft TAR
                                Cost Reduction
                                   Draft TAR
                               Learning Factors
                                   2012 FRM
                                Cost Reduction
                                   2012 FRM
                               Learning Factors
                                     2012
                                   2,700,000
                                    $128.53
                                     129%
                                     1.29
                                     116%
                                     1.16
                                     2013
                                   3,150,000
                                    $124.39
                                     124%
                                     1.24
                                     113%
                                     1.13
                                     2014
                                   3,600,000
                                    $120.39
                                     120%
                                     1.20
                                     110%
                                     1.10
                                     2015
                                   4,050,000
                                    $116.51
                                     117%
                                     1.17
                                     106%
                                     1.06
                                     2016
                                   4,500,000
                                    $112.76
                                     113%
                                     1.13
                                     103%
                                     1.03
                                     2017
                                   4,950,000
                                    $109.13
                                     109%
                                     1.09
                                     100%
                                     1.00
                                     2018
                                   5,400,000
                                    $105.62
                                     106%
                                     1.06
                                      97%
                                     0.97
                                     2019
                                   5,850,000
                                    $102.61
                                     103%
                                     1.03
                                      94%
                                     0.94
                                     2020
                                   6,300,000
                                    $100.00
                                     100%
                                     1.00
                                      91%
                                     0.91
                                     2021
                                   6,750,000
                                    $97.69
                                      98%
                                     0.98
                                      89%
                                     0.89
                                     2022
                                   7,200,000
                                    $95.63
                                      96%
                                     0.96
                                      86%
                                     0.86
                                     2023
                                   7,650,000
                                    $93.77
                                      94%
                                     0.94
                                      84%
                                     0.84
                                     2024
                                   8,100,000
                                    $92.09
                                      92%
                                     0.92
                                      82%
                                     0.82
                                     2025
                                   8,550,000
                                    $90.54
                                      91%
                                     0.91
                                      81%
                                     0.81


                                       
           Figure 6 Draft TAR Curve 30 along with 2012 FRM Curve 21


Draft TAR Curve 31 (2012 FRM Curve 24)
Curve used for developing or recent technologies for which steeper learning impacts have recently occurred or are currently occurring and for which our estimated cost is considered valid in 2015. For this curve, we have used the factors used for curve 25 but have shifted them by two years.
            Table 7 Draft TAR Curve 31 along with 2012 FRM Curve 24
                                     Year
                                   Cost/unit
                                   Draft TAR
                                Cost Reduction
                                   Draft TAR
                               Learning Factors
                              (relative to 2025)
                                   2012 FRM
                                Cost Reduction
                                   2012 FRM
                               Learning Factors
                              (relative to 2025)
                                     2012
                                    $318.08
                                     318%
                                     3.18
                                     156%
                                     1.56
                                     2013
                                    $254.12
                                     254%
                                     2.54
                                     156%
                                     1.56
                                     2014
                                    $203.02
                                     203%
                                     2.03
                                     125%
                                     1.25
                                     2015
                                    $162.20
                                     162%
                                     1.62
                                     125%
                                     1.25
                                     2016
                                    $128.34
                                     128%
                                     1.28
                                     100%
                                     1.00
                                     2017
                                    $100.00
                                     100%
                                     1.00
                                     100%
                                     1.00
                                     2018
                                    $90.54
                                      91%
                                     0.91
                                      97%
                                     0.97
                                     2019
                                    $84.38
                                      84%
                                     0.84
                                      94%
                                     0.94
                                     2020
                                    $79.89
                                      80%
                                     0.80
                                      91%
                                     0.91
                                     2021
                                    $76.40
                                      76%
                                     0.76
                                      89%
                                     0.89
                                     2022
                                    $73.57
                                      74%
                                     0.74
                                      86%
                                     0.86
                                     2023
                                    $71.20
                                      71%
                                     0.71
                                      83%
                                     0.83
                                     2024
                                    $69.18
                                      69%
                                     0.69
                                      81%
                                     0.81
                                     2025
                                    $67.41
                                      67%
                                     0.67
                                      78%
                                     0.78

                                       
           Figure 7 Draft TAR Curve 31 along with 2012 FRM Curve 24


Draft TAR Curve 32 (2012 FRM Curve 25)
Curve used for developing technologies for which steeper learning impacts are currently occurring and for which our estimated cost is considered valid in 2021. For this curve, we have used the factors used for curve 26 but have shifted them by four years.
            Table 8 Draft TAR Curve 32 along with 2012 FRM Curve 25
                                     Year
                                   Cost/unit
                                   Draft TAR
                                Cost Reduction
                                   Draft TAR
                               Learning Factors
                                   2012 FRM
                                Cost Reduction
                                   2012 FRM
                               Learning Factors
                                     2012
                                     $174
                                     174%
                                     1.74
                                     156%
                                     1.56
                                     2013
                                     $161
                                     161%
                                     1.61
                                     156%
                                     1.56
                                     2014
                                     $151
                                     151%
                                     1.51
                                     156%
                                     1.56
                                     2015
                                     $143
                                     143%
                                     1.43
                                     156%
                                     1.56
                                     2016
                                     $136
                                     136%
                                     1.36
                                     156%
                                     1.56
                                     2017
                                     $130
                                     130%
                                     1.30
                                     156%
                                     1.56
                                     2018
                                     $125
                                     125%
                                     1.25
                                     156%
                                     1.56
                                     2019
                                     $120
                                     120%
                                     1.20
                                     125%
                                     1.25
                                     2020
                                     $116
                                     116%
                                     1.16
                                     125%
                                     1.25
                                     2021
                                     $112
                                     112%
                                     1.12
                                     100%
                                     1.00
                                     2022
                                     $109
                                     109%
                                     1.09
                                      97%
                                     0.97
                                     2023
                                     $106
                                     106%
                                     1.06
                                      94%
                                     0.94
                                     2024
                                     $104
                                     104%
                                     1.04
                                      91%
                                     0.91
                                     2025
                                     $101
                                     101%
                                     1.01
                                      89%
                                     0.89

                                       
           Figure 8 Draft TAR Curve 32 along with 2012 FRM Curve 25

