The views expressed are those of the authors and should not be attributed to the 

Economic Research Service or USDA.

Review of

Productivity Accounts

Contractor and Cooperator Report 

No. CCR-69 

August 2017

Abstract

The USDA Economic Research Service has developed national and state-level agricultural productivity 

measures. These productivity measures are widely referred to and used, and international sectoral 

comparisons rely on the ERS production accounts for foundation methodology in constructing agricultural 

productivity accounts in other countries. ERS engaged an external review committee to examine the data 

sources, methodology, ongoing research, documentation, and reporting of the ERS agricultural 

productivity accounts. This report represents the outcome of that review.
September 2, 2014

Dr. Mary Bohman, Administrator

Economic Research Service

1400 Independence Avenue, SW

Mailstop 1800 (mbohman@ers.usda.gov) 

Washington, DC 20250-0002

Dear Mary:

On behalf of the external committee (consisting of Barbara Fraumeni, Lilyan Fulginiti, Jon 

Samuels, Spiro Stefanou, and myself) charged to review the USDA Agricultural Productivity 

Accounts, I am pleased to submit our final report. The report is the culmination of a year-long 

comprehensive review of the productivity accounts by the committee, solicitation of stakeholder 

input, and engagement with other productivity professionals. The review has encompassed the 

full scope of your August 20, 2013 charge establishing the external review committee. It has 

focused on the tasks listed in that charge, but, as instructed, it has not been restricted by them. 

The final report has been approved by all members of the committee following a review for 

factual errors by ERS professional staff. 

This has been a most engaging and fruitful committee experience. All members of the 

committee have been fully vested in its work, and each has contributed significantly throughout 

the entire review process. ERS professional staff have been fully supportive, cooperative, 

informative, and responsive to our work and our need for many details and clarification of 

procedures. A number of stakeholders and productivity professionals have gone well beyond 

expectations in providing insight and help to the committee. For all of which, I am personally 

indebted and appreciative.

Thank you for the trust you have placed in the committee and for the opportunity to recognize 

and help strengthen the high quality Agricultural Productivity Accounts of the Economic 

Research Service and their usefulness. 

Sincerely,

C. Richard Shumway

Regents Professor

Distinguished Professor of Agricultural and Resource Economics

xc: Barbara Fraumeni

Lilyan Fulginiti

Jon Samuels

Spiro Stefanou

School of Economic Sciences
Measurement of U.S. Agricultural Productivity:

A 2014 Review of Current Statistics and

Proposals for Change

C. Richard Shumway, Barbara M. Fraumeni, Lilyan E. Fulginiti, Jon D. 

Samuels, and Spiro E. Stefanou

September 4, 2014

C. Richard Shumway is Regents Professor, School of Economic Sciences, Washington State University. 

Barbara M. Fraumeni is Special-term Professor, Central University for Finance and Economics. Lilyan E. 

Fulginiti is Professor, Department of Agricultural Economics, University of Nebraska. Jon D. Samuels is

Research Economist, Bureau of Economic Analysis, U.S. Department of Commerce and Fellow, Institute 

for Quantitative Social Science, Harvard University. Spiro E. Stefanou is Professor, Department of 

Agricultural Economics, Sociology & Education, Pennsylvania State University and Visiting Professor of 

Business Economics, Wageningen University. 

The authors were appointed by the U.S. Department of Agriculture (USDA), Economic Research Service 

(ERS), as an external committee to review the USDA Agricultural Productivity Accounts produced by the 

ERS. The appointment followed the Office of Management and Budget’s guidelines for the management 

of Federal information resources. Richard Shumway served as chair. Other authors are listed 

alphabetically. We wish to express appreciation for the helpful support of the ERS staff, Rachel 

Soloveichik, Brian Sliker, Erwin Diewert, Dale Jorgenson, Sean Cahill, Julian Alson, Philip Pardey, and to 

all others who responded to our invitation for stakeholder input. 

The views expressed in this paper are solely those of the authors and not necessarily those of the U.S. 

Bureau of Economic Analysis or the U.S. Department of Commerce.

1 
INDEX

INTRODUCTION............................................................................................................................................. 6

Why Undertake Another Review? ............................................................................................................ 8

Scope of This Review and Organization of the Report ............................................................................. 9

Recommendations.................................................................................................................................... 9

Overarching........................................................................................................................................... 9

Website................................................................................................................................................. 9

State-level ...........................................................................................................................................10

PART 1.........................................................................................................................................................11

I. Labor ....................................................................................................................................................11

Procedure Before 1980 AAEA Task Force Recommendations............................................................11

1980 AAEA Task Force Recommendations.........................................................................................11

ERS Implementation of 1980 AAEA Task Force Recommendations...................................................12

ERS Current Practice ...........................................................................................................................12

Contract Labor (in Intermediate Inputs).............................................................................................13

Recommendations..............................................................................................................................14

II. Non-Land Capital................................................................................................................................. 14

Capital Measurement: General Issues................................................................................................15

Equipment and Structures Capital Stock ............................................................................................15

Capital Input........................................................................................................................................17

Inventories..........................................................................................................................................20

Research at BEA ..................................................................................................................................21

Recommendations..............................................................................................................................21

III. Land....................................................................................................................................................21

1980 AAEA Task Force Recommendations.........................................................................................22

ERS Past Implementations of 1980 AAEA Task Force Recommendations..........................................22

ERS Current Practice ...........................................................................................................................22

Recommendations..............................................................................................................................24

IV. Intermediate Inputs...........................................................................................................................24

1980 AAEA Task Force Recommendations.........................................................................................24

Subsequent Guidance .........................................................................................................................24

ERS Current Practice ...........................................................................................................................25

Recommendations.............................................................................................................................. 27

V. Outputs...............................................................................................................................................27

1980 AAEA Task Force Recommendations.........................................................................................27

2 
ERS Current Practice ...........................................................................................................................28

Our Assessment ..................................................................................................................................28

Recommendations ..............................................................................................................................31

PART 2.........................................................................................................................................................32

VI. Quality Adjustments..........................................................................................................................32

A Simple Model of Production with Quality Change ..........................................................................32

Quality and Composition in Productivity Measurement....................................................................33

Recommendations..............................................................................................................................36

VII. Residual Claimants............................................................................................................................36

Recommendation................................................................................................................................37

VIII. Research and Development.............................................................................................................38

R&D in the ERS Agricultural Productivity Account..............................................................................38

Recommendation................................................................................................................................40

IX. Alternative Assumptions....................................................................................................................40

Recommendation................................................................................................................................41

X. Website...............................................................................................................................................41

Accessibility and Findability ................................................................................................................43

Accuracy..............................................................................................................................................43

Completeness......................................................................................................................................43

Searchability........................................................................................................................................44

Legibility ..............................................................................................................................................44

Website and Productivity Program in Context ...................................................................................44

Recommendations..............................................................................................................................45

PART 3.........................................................................................................................................................46

XI. State-level productivity......................................................................................................................46

1980 AAEA Task Force Recommendations.........................................................................................46

ERS Response ......................................................................................................................................46

Our Assessment ..................................................................................................................................48

Recommendations..............................................................................................................................50

XII. Cross-country comparisons...............................................................................................................50

Recommendations..............................................................................................................................52

XIII. ERS Measures of Productivity Compared to Alternative Sources....................................................52

Comparison with Jorgenson, Ho, and Samuels...................................................................................52

Comparison with InSTePP...................................................................................................................53

Recommendation................................................................................................................................63

3 
XIV. Stakeholder Assessment..................................................................................................................63

CONCLUSIONS.............................................................................................................................................65

Recommendations..................................................................................................................................65

Priority A .............................................................................................................................................65

Priority B..............................................................................................................................................66

Priority C..............................................................................................................................................68

ACRONYMS USED IN REPORT .....................................................................................................................69

BIBLIOGRAPHY ............................................................................................................................................70

APPENDICES .............................................................................................................................................................78 

Appendix 1. Personal Communication Documents to Review Committee ..............................................78

Appendix 1.1. Note on user cost of capital by Brian Sliker, BEA .............................................................78 

Appendix 1.2. Document “Review Panel_Capital.docx” from V. Eldon Ball ..........................................85 

Appendix 1.3. Email exchange between Brian Sliker and Eldon Ball on capital input .........................89 

Appendix 1.4. Note on residual claimant in productivity accounts by Erwin Diewert .........................98 

Appendix 1.5. Note on residual claimant inputs by Sean Cahill ............................................................100

Appendix 2. Verbatim Stakeholder Input ....................................................................................................110

Carlos Arnade ...............................................................................................................................................110

J. Christophe Bureau ...................................................................................................................................112

Sean B. Cash .................................................................................................................................................114

Jean Paul Chavas ..........................................................................................................................................115

Ramiro Costa ................................................................................................................................................117 

Kenneth A. Foster ........................................................................................................................................120

Jose Garcia Gasques ....................................................................................................................................122

Nilabja Ghosh, Anita Kumari, M. Rajeshwor ............................................................................................123

Wallace E. Huffman .....................................................................................................................................127

Dale Jorgenson .............................................................................................................................................128

David K. Lambert .........................................................................................................................................129

Will Martin ....................................................................................................................................................131

Carlos San Juan Mesonada .........................................................................................................................132

Catherine Moreddu .....................................................................................................................................133

Yair Mundlak ................................................................................................................................................134

Alejandro Nit Pratt ......................................................................................................................................137

Christopher J. O’Donnell .............................................................................................................................138

Beau Olen .....................................................................................................................................................141

4 
Richard Perrin ...............................................................................................................................................142

Rulon Pope ....................................................................................................................................................144

John Ruser ....................................................................................................................................................145

Randy Schnepf .............................................................................................................................................146

Saleem Shaik ................................................................................................................................................147

Rachel Soloveichik .......................................................................................................................................148

Greg Strain ....................................................................................................................................................160

Sally Thompson ............................................................................................................................................166

Keith Wiebe ..................................................................................................................................................167

Margaret Zeigler ..........................................................................................................................................168

5 
INTRODUCTION

Recent research argues that the preponderance of aggregate postwar economic growth in the U.S. was 

driven by investments in physical and human capital and the expansion of the labor force, while 

productivity growth accounted for a relatively small share of GDP growth. At the industry level, two 

notable exceptions to this aggregate trend were the Computer and electronic products and the Farm 

sectors. Innovation in the Computer and electronic products sector, exemplified by Moore’s law, has led 

to the proliferation of Information Technology products and the so-called Information Age. Innovation 

within the Farm sector has increased abundance, availability, and quality of food products, and limited 

price increases passed on to consumers. Understanding the sources of economic growth is crucial to 

economic policy (Jorgenson 2011). 

The purpose of this report is to review the methods and estimates of the Agricultural Productivity 

Accounts developed by the Economic Research Service (ERS) of the United States Department of 

Agriculture (USDA). These accounts generate the official estimates of productivity in the U.S. farm 

sector. They include estimates of industry outputs and inputs in current and constant prices, and total 

factor productivity (TFP), the preferred measure of innovation according to the Advisory Committee on 

Measuring Innovation in the 21st Century (Schramm et al. 2008). These farm-level industry production 

accounts are an important contribution to the U.S. statistical system, and agricultural policy is both 

related to and informed by them.1

Empirical economic analysis and its conclusions are grounded in issues and concerns about data 

collection, variable definitions and construction, and concordance between economic concepts and 

statistics. Economic policy makers and scholars working on the frontiers of economic research have

relied heavily on the construction of these agricultural production accounts because of their close 

integration of statistical concepts and economic theory. These accounts are constructed with the 

primary purpose of measuring the productivity of the U.S. agricultural sector. ERS has emerged as an 

international leader in construction and integration of these accounts in agriculture, and the national 

(covering all 50 states) and state-level estimates for the 48 contiguous states are widely cited as the 

basis for both policy and research work. The task of assembling the accounts is daunting. To match 

statistics with theory, assembling the accounts often involves creating data series in cases where the 

primary statistical base is insufficient. In some series, economic theory provides the mechanism to 

extrapolate from the survey data to what Gardner (1992b) refers to a “representation of facts” that 

generates “theory-laden data”. 

A principal application of these accounts involves the measurement of agricultural productivity to build 

a clear picture of how the agricultural economy is performing, how it contributes to the expansion of the 

U.S. economy, and to identify the primary drivers of the agricultural sector’s growth. In doing so, we can 

determine to what extent attention should be placed on the mobilization and composition of production 

factors versus the advances in productivity (Jorgenson 1991). From a user’s point of view, Charles 

Schultze notes that productivity accounts help to keep policy makers and their economic advisors 

informed about the current state of the economy. He also asserts that an important avenue through 

which economic statistics have impact is via researchers who consume the data, conduct economic 

1 The Bureau of Labor Statistics (BLS) produces Private Business Sector multi-factor productivity (MFP) that 

includes Farms, Private Non-Farm Business MFP, and MFP for Crop and Animal production NAICS 111, and 112 

covering 1987-2011 as of July 9, 2014. ERS measures differ in the treatment of intrasectoral purchases and labor 

composition, they include quality adjustments for tractors, and include data back to 1947. Bureau of Economic 

Analysis (BEA) and BLS have produced a prototype industry-level production account that covers 1998-2012 and 

includes a labor composition adjustment.

6 

 
analyses, and engage with policy advisers on appropriate policy actions and design (Schultze at al., 1991, 

p 423).

The agricultural accounts at the national and state levels are the subject of a wide range of 

investigations related to a) how intermediate inputs, labor, land and capital use patterns evolve over 

time and serve as factor substitutes, b) how these factors are impacted by policy, c) how technical 

change relates to factor use, and d) how quality adjustments are undertaken to reflect input changes 

and the evolving productive potential of agricultural production. 

The sectoral productivity accounts are often used as a benchmark across sectors within an economy and 

comparison of the sectors across nations to help explain observed differences in aggregate performance

and competitiveness. There is considerable interest in cross-country comparisons that investigate 

international competitiveness and convergence in agricultural productivity across countries. TFP growth 

is a standard measure employed for such comparisons. When markets are perfectly competitive and 

operating in long-run equilibrium, price changes can proxy for cost changes. Under these assumptions

and assuming that the quality of output is the same across countries, relative output prices can proxy as 

a competitiveness measure for purposes of international comparisons. If countries share a common 

stock of knowledge and access to technologies, and if they face no structural barriers to sharing, then 

theory suggests that prices should change at the same rate. When we do not see this equivalence in 

price change, economists tend to look at policy incentives and structural differences to explain why, but 

the appropriate data is necessary to draw such inferences. 

The notion of an aggregate production technology is the starting point for studying productivity and the 

sources of productivity growth. Its origins date back to Tinbergen (1942) and Solow (1957). With the 

need for aggregate measures of production factor and outputs, the construction of indices emerges as a 

necessary starting point. Balk (2008, Chapters 1 and 2) presents a historical overview of the emergence 

of different indices and their evolution. Jorgenson (1991) presents an extensive overview of the 

emergence of the approaches to measuring productivity growth with an eye toward decomposing the 

sources of growth. Considerable efforts are required to bridge the theory with the measurement of 

production factors from observed data. The challenges of adjusting for quality changes and measuring 

capital inputs as services are particularly difficult.

There are three key manuals governing construction of internationally comparable productivity 

accounts. The United Nations System of National Accounts (SNA) is an internationally standard set of 

recommendations on how to compile measures of economic activity. Its recommendations are 

expressed in terms of concepts, definitions, classifications, and accounting rules (UN, 2009). The SNA is 

intended for economic analysis in any country. The Organisation for Co-operation and Economic 

Development (OECD) Productivity Manual (2001b) serves as a standard reference of the theoretical 

foundations to productivity measurement, its implementation, and measurement issues. It seeks to 

harmonize efforts for effective international comparisons at both the aggregate and sectoral levels. The 

European Union Statistical Office’s (Eurostat) (2000) revised manual for constructing the Economic 

Accounts for Agriculture and Forestry is consistent with the SNA and addresses several specific needs of 

the European Union member states for sectoral accounts. Its approach is to break down the agricultural 

economy into production units and household units whose main source of income is agricultural. 

The late 1970s found the commissioning of a joint American Agricultural Economics Association (AAEA)-

USDA Task force to undertake a comprehensive review of the methodologies employed in constructing 

the ERS productivity accounts for U.S. agriculture and the scope these accounts covered. The outcome 

of this task force was a report by Gardner et al. (1980). The recommendations spanned changes in the 

areas of conceptual and practical productivity measurement with major recommendations to a) move 

from partial to total factor productivity measurement, b) address hired, operator and family labor 

7 
separately in the labor accounts, c) use the product approach (or specify production activities) 

regardless of the type of establishment in the agricultural production sector, d) account for input quality 

changes, and use the Divisia index to aggregate inputs and outputs (Gardner 1980, p. iii). The report 

also included specific suggestions related to the construction of particular input and output accounts, 

such as a) using the direct sampling approach to construct labor inputs, b) suggesting procedures to 

convert the land stock to a service flow, and c) several recommendations regarding machinery and 

equipment to improve the statistical data, revise the depreciation procedures, and apply the Bureau of 

Labor Statistics (BLS) machinery price indexes to farm machinery. 

The ERS addressed the Task Force’s findings and recommendations head on and made focused efforts to 

bring the ERS construction of productivity accounts into harmony with state-of-the-art protocols, thus 

becoming an international leader in the statistical community with respect to productivity 

measurement. The National Agricultural Statistical Service (NASS) supports the ERS product accounts 

through the surveys they implement as well as by implementing the Agricultural and Resource 

Management Survey (ARMS) which is jointly administered with ERS.

Why Undertake Another Review?

With the USDA being a principal Federal Statistical Agency, the Office of Management and Budget 

(OMB) mandates standards for data quality and procedural and analytic guidelines for implementing 

policies for the management of Federal Statistical information resources (OMB Memorandum, May 31, 

2011). This also entails a regular program of data quality reviews. There is a history of external review 

of agricultural statistics construction and the surveys that serve as a foundation for these statistical 

products. In addition to the Agricultural and Applied Economics Association (AAEA)-USDA Task Force 

report in Gardner et al. (1980), several related reviews have been undertaken in the last three decades: 

a) AAEA Statistics Committee review of USDA Farm Sector Financial Indicators, 1989-1991 (Boxley 

1989); 

b) General Accounting Office review of Farm Costs and Returns Survey2

, 1992 (USGAO 1992);

c) AAEA Task Force on Commodity Costs and Returns, 1998-2000 (Eidman et al. 2000); 

d) National Academy of Sciences Panel to review USDA's Agricultural Resource Management 

Survey, National Research Council, 2006-2007 (National Research Council 2007); and 

e) ERS independent panel review of financial accounting methods used to summarize the 

Agricultural Resource Management Survey (Moss 2012). 

In 2013, ERS charged our committee to address issues of methodology in the development of estimates, 

provide feedback on ongoing research programs to improve methodology and operations, review 

documentation and reporting of methods and uses of the data, and consider the frequency, timeliness, 

and extent of reporting. The overarching goals of the current USDA ERS Productivity Accounts review are 

to assess current practices used in assembling the agricultural productivity account and review how the 

USDA: a) documents its efforts and facilitates the ability to replicate and ensure comparability, b) 

describes how the community of analysts and scholars use the accounts, c) cooperates with other 

agencies to reduce duplication, achieve consistency across statistical series, get information at lowest 

cost, and capitalize on research and expertise, and d) establishes priorities subject to resource 

constraints.

2 The Farm Costs and Returns Survey is the predecessor to the Agricultural Resource Management Survey.

8 

 
Scope of This Review and Organization of the Report

We undertook a focused review of the ERS agricultural productivity accounts and the data products 

used in their construction. With the full cooperation of the USDA ERS staff that construct, maintain, and 

communicate analysis of these productivity accounts and related data products, this report organizes 

the commentary and review of the production accounts into four main parts. Each part, except for the 

last, includes a number of subsections. 

The first part addresses the core parts of the production accounts, specifically labor, non-land capital, 

land, intermediate inputs, and outputs. The second addresses issues related to the construction and 

interpretation of the accounts. These include quality adjustments made for production factors and 

outputs, how residual claimants are addressed, how R&D is reflected and incorporated, the sensitivity of 

productivity trends to alternative assumptions, and accessibility of these data products on the website. 

The third addresses the state-level production accounts, cross-country comparisons, ERS measures of 

productivity compared to other sources, and stakeholder assessment. The final part concludes and 

categorizes the recommendations by priority level. 

A summary of acronyms used in the report, bibliography cited, and appendices follow these four 

sections. This review engaged stakeholders on issues of methodology in the development of estimates, 

ongoing research programs to improve methodology and operations, documentation and reporting of 

methods and uses of the data, and the frequency and timeliness of reporting. In addition, reputed 

experts from academia and U.S. government and international statistical agencies external to USDA 

were engaged on several issues related to the ERS agricultural production accounts.3 Verbatim input 

from stakeholders and cited personal communications from experts in the field are included in the 

appendices. 

Recommendations 

We include 21 recommendations in the top priority category. Of these, eight are designated by the 

committee as most important. They include two overarching recommendations, two addressing the 

website, and three focusing on the state-level production accounts: 

Overarching

1. Fully document and keep current all procedures followed, from data sources through 

measurement of productivity change, to enable a non-expert to reproduce the accounts.

2. Cooperate with other agencies to reduce duplication, achieve consistency across statistical 

series, get information at lowest cost, and capitalize on research and expertise.

Website

1. Provide detailed documentation online and note ad hoc adjustments to data or deviations from 

the general procedure (e.g., if fixes were required due to negative implied capital rental rates).

2. Expand the website to provide timely access to more detailed data and procedural detail 

underlying the quantity and price aggregate and sub-aggregate national and state-level 

statistics. 

3 Because the U.S. statistical system is decentralized, the ERS relies on data from other statistical agencies in 

assembling the agricultural productivity accounts.

9 

 
State-level

1. Continue to develop and publish the state-level total productivity measures as well as price and 

quantity series (strongly recommended). 

2. Cooperate with other government agencies to achieve the lowest cost method of collecting data 

of sufficient quality to enable the state-level accounts to be extended and maintained. 

3. Investigate the possibility of using information in the American Community Survey to update 

matrix elements in the state labor accounts. 

4. Ensure consistency between the national and state accounts where possible, and explain 

circumstances that prevent total consistency where that is not possible. 

10
PART 1 

The first section of this report reviews the components of the agricultural productivity accounts. The 

fundamental economic entity in the account is the industry. The farm industry as a whole produces 

outputs by employing labor and capital services, purchasing intermediate inputs, and transforming input 

to output with available technology. The ratio of output to input yields a measure of productivity, and 

the theory of productivity measurement provides the conditions such that the growth in output per unit 

of input corresponds to the change in the level of technology, or innovation. Because the productivity 

growth measure is a residual, all measurement problems will affect estimated TFP. In economic terms, 

the objective is to distinguish and measure shifts in the production function from movements along the 

production function. 

I. Labor 

The OECD Productivity Manual (2001b, p. 20) states that “labor is the single most important factor of 

production,” thus highlighting the importance of measurement issues related to the labor input in the 

productivity accounts. As a partial productivity measure, changes in labor productivity (output per hour 

worked) help to understand the development of standards of living and income per person in an 

economy, but these changes embed shifts in the use of capital, the quality of the workforce, and 

technology. According to the ERS productivity accounts, the nominal value share of hired and family 

labor in U.S. agriculture output has averaged about 20 percent over the last 60 years. For accurate 

measurement of productivity, the labor quantity index should capture not only the hours worked but 

also reflect the marginal product of different types of labor working in the sector. While total hours 

worked is the preferred measure of the service flow for a given worker, it does not capture the 

heterogeneity of the labor force. Differences in skills, education, health, and professional experience 

lead to large differences in the contribution of different types of labor. It is necessary then to distinguish 

the labor input by type of skill to adequately capture the effects of changing labor quality on 

productivity. 

Procedure Before 1980 AAEA Task Force Recommendations 

Labor input data was not derived from surveys of actual hours of labor or workers in agricultural 

production but was calculated on a "requirements" basis using estimated quantities of labor required 

for various production activities. The requirement coefficients were obtained on an individual 

commodity basis by means of consultation with state agricultural experiment station and extension 

service experts. Requirement coefficients were developed for 1964 and re-done in 1974 based on cost 

of production surveys. The published estimates of total hours used for farm work for each of 12 

enterprise groups and 10 regions (Durost and Black 1978) were obtained by multiplying labor 

coefficients by estimates of planted acreage (for pre-harvest labor), production (for harvest labor), or 

animal numbers for livestock, and adding 15% for overhead labor. The national labor input index was 

obtained by aggregating over the regions and enterprise groups. The U.S. average hired farm wage rate 

per hour as estimated by USDA's Statistical Reporting Service for 1967-69 was used in the aggregation.

1980 AAEA Task Force Recommendations

The labor input index should be based on direct sampling instead of the requirements approach. 

The labor input data should be handled separately for hired, operator, and family labor, each weighted 

to construct an aggregate by their relative wage rates. 

The Divisia index should be used for aggregation with expenditure shares as weights.

11
ERS Implementation of 1980 AAEA Task Force Recommendations

ERS has implemented the recommendations of the AAEA task force and has used theoretically 

consistent methods to develop Tornqvist (discrete approximation to the Divisia index) and Fisher labor 

input indexes for use in multifactor productivity analysis. Implementation has followed closely 

Jorgenson, Gollop, and Fraumeni (1987) as well as the OECD Productivity Manual (2001b). 

The first set of labor indexes implementing the AAEA Task Force recommendations were reported in Ball 

(1985). Tornqvist indexes for the period 1948-1979 were developed that included hired labor and selfemployed workers (contract labor was included in intermediate inputs). Data on wage rates as well as 

hours worked by characteristics of individual workers were developed by Jorgenson and Gollop and 

provided to ERS by Jorgenson (Ball 1985, p. 476 footnote 3). Matrices of hours worked and 

compensation per hour cross-classified by gender (2), age (8), education (5), employment class (2), and 

occupational group (10) were used. 

Ball et al. (1997) developed Fisher quantity and implicit price indexes for labor for the period 1948-1994. 

This index included hired labor, self-employed, and unpaid family workers. Revised to include unpaid 

family labor in addition to operator labor, data on hours worked and average compensation were from 

the same sources (Ball et al. 1997, p. 1048 footnote 2). Annual data on hours worked and average 

compensation per hour were required for 160 matrix entries based on two genders, eight age groups, 

five educational groups, and two employment classes. Jorgenson and Gollop (1992) used information on 

employment, hours worked and average compensation from the Census of Population and the Current 

Population Survey along with bi-proportional matrix balancing (RAS) techniques to allocate across the 

matrix entries for non-census years. Additional data from the Farm Labor Survey conducted by NASS

were used for unpaid family workers.

ERS has undertaken a continuous process of methodological examination and improvement as 

documented by the use of Tornqvist indexes for 1948-1979 in Ball (1985), Fisher indexes for 1948-1980 

in Ball et al. (1997), and a new series of Tornqvist indexes4 for 1948-2011 available on the ERS 

Agricultural Productivity website.

ERS Current Practice

The description of current practice in this section follows Wang (2013a), the methodological description 

section on the Productivity Accounts on the ERS website, and information provided by direct 

communication with ERS. 

Table 1 on the ERS website presents Tornqvist price and implicit quantity indexes for labor and its subcomponents, hired and self-employed (which includes unpaid operator and family labor), for the period 

1948-2011. Following Jorgenson, Gollop, and Fraumeni (1987), matrices of employment, hours worked, 

and compensation per hour (for hired labor) cross-classified by gender (2), age (8), education (6), and 

employment class (2) are used as indicated in Wang (2013a). These represent 192 entries and are 

slightly different than the cross-classifications used in Ball (1985) and Ball et al. (1997). 

The two gender categories are: male and female. 

The eight age categories are: 14-15 years, 16-17 years, 18-24 years, 25-34 years, 35-44 years, 45-54 

years, 55-64 years, and 65 years and over.

The six education categories are matched to information in the Current Population Survey: 1-8 

years grade school (elementary and middle school), 1-3 years high school (less than high school 

4

 Among other changes, the new series uses new data for labor and for land.

12

 
diploma), 4 years high school (high school diploma), 1-3 years college (three years of college, 

vocational/associates), 4 years college (bachelor’s degree), and more than four years college 

(graduate school, master’s degree, doctorate degree). 

The two employment classes are: wage/salary worker, and self-employed/unpaid family worker.

ERS uses a cross-entropy approach in the Generalized Algebraic Modeling System (GAMS), rather than 

the RAS procedure in Jorgenson, Gollop and Fraumeni (1987), to update matrix elements when new 

information is available. 

Data for hired farm workers (employment, hours worked and compensation) are from the National 

Income and Product Accounts (NIPA), BEA. Total hours worked for self-employed and unpaid farm 

workers are from the Census of Population and the Current Population Survey. Wages for selfemployed and unpaid family workers are imputed using the mean wage of hired workers in the same 

cross-classification.

Control totals for hours worked and compensation for hired workers are from NIPA and from a special 

tabulation by BLS for self-employed and unpaid family workers. 

The ERS implementation of the labor index, while broadly consistent with previous vintages, deviates in 

some ways from previously published approaches. For example, the cross tabulations used by ERS no 

longer contain the occupation dimension. Further, to be consistent with a change in survey questions in 

the Current Population Survey, updates after 1992 treat degree attained as the defining characteristic of 

educational attainment, compared to years of schooling in the previous estimates. Jorgenson, Ho, 

Stiroh (2005) discuss methods for bridging the two treatments.

Jorgenson, Ho and Samuels (2014) develop U.S. industry-level production accounts for 65 industries, 

including agriculture, for the period 1947-2010. As shown in Table XIII.1: Agricultural Output Growth and 

its Sources in this report, the evolution of the agricultural sector labor index differs from that of ERS.5

Given the overlap in source data and methods between ERS and Jorgenson, Ho and Samuels (2014), it 

will be important to investigate reasons for the differences across these labor indexes. 

Contract Labor (in Intermediate Inputs)

Many farms, especially in fruit and vegetable production, hire labor services from contract providers. 

The workers are not employees of the farm, and hence are not counted as hired labor. They are 

reported as purchased contract labor services in intermediate inputs, and farm survey respondents are

able to report expenses but not employment or hours for such workers. Because there is no available 

data on hours worked, ERS estimates implicit quantities of purchased contract labor services by dividing 

expenditures by a wage index. The data consist of nominal expenditures on contract labor. Up to 2000, 

ERS used ‘piece rate information’ from NASS to deflate these expenditures, but this information is no 

longer available. ERS has replaced this information with a wage deflator based on hedonic methods. 

The hedonic framework is used to estimate wage as a function of characteristics, using data from the 

BLS National Agricultural Workers Survey. Included are gender, years of experience, education, 

language skills, legal status, employer type, task type, geographic and time controls. Heckman’s 

procedure is used to correct for sample selection bias.

5 ERS maintains that the differences in the labor series stem in part from differences in coverage of unpaid family 

workers and in part from differences in the imputation of wages for farm operators.

13

 
Recommendations

1. Investigate the reasons for differences in the labor input computed by Jorgenson, Ho, and 

Samuels (2014) (Priority A).

2. Investigate the American Community Survey as an alternative, possibly complementary, data 

source, potentially in collaboration with BEA/BLS (Priority A). 

3. Use the latest revision of information on totals from NIPA and the special BLS tabulation 

(Priority B).

4. Consider further refinements of the cross classification of workers to improve identification of 

quality differences (Priority B). 

5. Adjust for temporal changes in the quality of workers in each demographic group not captured 

in relative wages (Priority B).

6. Clarify if the imputation of wages for self-employed workers exhausts available income and 

report procedures used if this occurs (Priority C).

7. Clarify how sample selection estimation is executed when the Heckman procedure is used for 

the contract labor hedonic wage index (Priority C).

II. Non-Land Capital 

Within the growth accounting framework for decomposing the sources of growth, measuring the 

contribution of capital input requires price and quantity estimates of the capital services that flow into 

production. Like labor, a key feature of the capital input measure is that it must treat a shift in the 

composition of capital towards an asset type with a higher marginal product as an increase in capital 

input used in production. Ignoring this type of composition shift amounts to a systematic bias in 

estimated TFP. Fortunately, research on productivity measurement has established methods to adjust 

for composition changes in capital services, and ERS has, for the most part, adopted these procedures.

ERS has carefully incorporated the recommendations of the AAEA Task Force (Gardner et al. 1980) that 

relate to non-land capital inputs. They include measuring multifactor productivity, improving the quality 

of data on the stocks of machinery and equipment, and modifying structures and capital equipment 

depreciation procedures to better reflect “economic value of services at each point of an item’s 

lifetime” (p. 46). 

Since the 1980 review of measurement of U.S. agricultural productivity, there have been substantial 

developments in the measurement of productivity, particularly in the measurement of capital inputs. 

Two developments which occurred in the early eighties are of particular note: the publication of the 

book on U.S. productivity and economic growth by Jorgenson, Gollop, and Fraumeni (1987) and the first 

release by BLS (U.S. Department of Labor (USDOL) 1983) of multifactor productivity estimates for a 

number of aggregate sectors.6 Both included capital inputs in the production function.7 Similar to ERS, 

the BLS’s Office of Productivity and Technology (OPT) developed multifactor productivity measures as 

recommended by a panel review (see Rees 1979). 

Later, OECD issued two capital manuals on measuring capital and one on measuring productivity (OECD 

2001a, 2001b, 2009). Beginning in 2003 the European Union Capital, Labor, Energy, Materials, Services

(KLEMS) project (Van Ark, O'Mahony and Ypma 2007) began to develop industry-level production 

accounts for European countries; subsequently this effort was extended to other countries through the 

6 Earlier books on productivity and economic growth included Denison (1974) and Kendrick (1961 and 1973).

7 For detailed discussions of capital stocks and capital inputs, see Fraumeni and Jorgenson (1980), Jorgenson 

(1980), and Kendrick (1976).

14 

 
World KLEMS project.8 Since most of the activity related to measurement of multifactor productivity and 

in particular capital inputs occurred subsequent to the 1980 review of measurement of U.S. agricultural 

productivity, we will not refer further to the 1980 review recommendations.

ERS’s methodology is broadly consistent with the approaches used in the literature. The majority of the 

implementation choices made are reasonable and defensible. The review committee, supported by 

productivity expert feedback (Sliker, 2014b), has identified an internal inconsistency and a deviation 

from a typically used approach that are addressed in more detail below. 

Capital Measurement: General Issues

Measurement of capital differs from measurement of hired labor in that wages paid to hired labor are 

recorded, whereas rent paid to capital frequently is unrecorded because capital is more often owned 

than leased. Furthermore, the flow of services from the productive capital stock is unobserved, and the 

productive capital stock is based on the accumulation of past investments. These fundamental 

differences give rise to a number of difficulties and assumptions in capital measurement.

The construction of capital input begins with construction of the capital stock. The perpetual inventory

method is typically used to develop real capital stock estimates:

(II.1) Kt = It + (1-δt-1)Kt-1, 

where Kt is real productive capital stock in period t, It is real gross investment in period t, and δt is the 

rate of efficiency decline in period t. The importance of implementing capital stock construction by 

industry and by asset type has been demonstrated in many empirical applications. 

The next step is to construct the user cost of capital for each asset, which is also called the rental price 

of capital services. It represents the transformation of the acquisition price of capital to the per-period 

usage price:

9

(II.2) pK,t = pI,t (rt + pD) - (pI,t - pI,t-1)

where pK,t, the user cost of capital, is the cost of using the capital asset in period t, pI,t is the period t 

market price of a new asset, rt is the period t interest cost or opportunity cost of employing capital 

elsewhere and is often called the rate of return, pD is the period t rate of depreciation or the rate of loss 

in the value of the asset as it ages, and (pI,t - pI,t-1) measures capital gains, losses, or revaluation of the 

asset between period t and t-1. Some statistical agencies, such as the Australian Bureau of Statistics, 

BLS, and researchers associated with Jorgenson, include tax in the user cost formula.

User costs are then multiplied by the real productive stocks to create nominal capital inputs (or capital 

flows) by asset, which are used as productive capital stock weights in an index number formula to create 

an aggregate real capital input. The theory of production equates these weights to be consistent with 

the marginal product of each capital asset. 

In our review of non-land capital inputs, we focus on these two themes of capital stocks and capital 

inputs, the latter beginning with the construction of the user cost of capital. 

Equipment and Structures Capital Stock

ERS uses three major sources for the nominal investment data: BEA fixed assets data for years prior to 

1975, NASS Farm Production Expenditures Survey data for 1975-1992, and ARMS data for 1993 to the 

8 See http://www.worldklems.net/index.htm for information on World KLEMS. 9 This brief user cost description closely follows OECD (2009, pp. 64-65). 

15

 
present. There are four categories of ERS farm nominal investment data: Autos from 1926, farm 

tractors from 1929, buildings from 1871, and other machinery (an aggregate) from 1914. 

Beginning in the year for which BEA fixed asset data are available on the internet (1901 at the earliest), 

the committee compared the ERS data for all years forward to the BEA fixed asset data.10 This 

comparison is preliminary and suggestive; it should not be construed as a precise or totally accurate 

analysis. However it revealed substantial differences between the current BEA data through 1974 and 

the ERS data, and there is no perceptible pattern of differences, except that ERS data prior to 1975 tend 

to be lower for equipment and higher for buildings than the BEA fixed assets data.11 Beginning in 1975, 

the ERS data are almost always lower for both equipment and structures. 

A comparison was also made between the BEA fixed assets category for all equipment except for autos 

and farm tractors (other equipment) and the ERS category other equipment from 1947 to the present. 

With one exception, the percentage that ERS other equipment is of ERS total equipment is consistently 

lower than the percentage that BEA other equipment is of BEA total equipment, with differences as high 

as 13 percentage points before 1993. After 1987 BEA farm investment categories include computers and 

software and after 1992 wind and solar power. 

Benchmarks and lifetimes

Since the ERS investment data go far back in time relative to the asset lifetimes, it is appropriate to 

assume a zero benchmark as ERS has done. 

The ERS average service lives are 10 for autos, 9 for farm tractors, 17 for other machinery, and 38 for 

buildings. The ERS average lifetimes for farm tractors and buildings match BEA average lifetimes. BEA 

does not use an explicit average service life for autos; rather it develops deterioration rates from 

information on new and used auto prices (see U.S. Department of Commerce (USDOC) 2013).12 In 

addition, the BEA category “autos” refers to all autos listed under private nonresidential equipment. 

This category excludes autos which are classified as durables owned by consumers.13 BLS average 

service lives are also the same as ERS except for tractors, which is 8 years (USDOL 1983).14 

10 Most of the BEA fixed asset data are available at http://www.bea.gov/national/FA2004/Details/Index.html. 

However, some of the early BEA data are not. 11 There are several possible reasons for these differences: The BEA fixed asset data base used by ERS has not been 

re-collected since it was first obtained in 1985 although BEA has revised the earlier data since then. The BEA title in 

the farm category under “total structures” is simply “farms”, so it is not clear if this category only refers to 

nonresidential farm structures. There is a separate category under the farm industry labeled “lodging” with zeroes 

in all entries. Patterns also differ for the equipment subcategories of tractors and autos. 12 In this review, the word deterioration is consistently used to refer to the decline in efficiency of an asset as it 

ages and the word depreciation to the decline in the price of an asset as it ages. This distinction is discussed in a 

later section.

13 Service life references in addition to USDOC (2003) include USDOC (2013), Hulten and Wykoff (1981a, 1981b), 

Wykoff and Hulten (1979), and Fraumeni (1997). A footnote in BEA (1983) specifies that the average service life 

was 8 years for producer durable equipment autos and 14 years for agricultural machinery except tractors; it is 

possible that the latter category includes autos used in agriculture.

14 Since the BLS category tractors does not specify farm tractors, this average life may reflect average service lives 

for farm and construction tractors. The source for ERS average service lives of buildings and agricultural machinery 

except tractors has not been updated since BEA revised its service lives in the latter nineties. See USDOC (2013) for 

the current BEA lifetimes which are mainly taken from Fraumeni (1997) and in most cases do not depend on 

Bulletin F lifetimes.

16

 
Investment deflators

Investment deflators for all capital assets except buildings were obtained from BLS. The investment 

deflator for buildings is from BEA. More information is needed about the specific sources, e.g., whether 

the BLS deflators are those used in the BLS multifactor productivity estimates, whether the BEA 

structures deflators are those for farm buildings, and whether revisions made in BLS and BEA deflators 

since 1985 have been incorporated. 

Deterioration and retirements

ERS estimates deterioration and retirements using methodology almost identical to that used by BLS. 

The deterioration function is a hyperbolic function with β equal to .75 for buildings and .5 for 

equipment. The ERS retirement function is a truncated normal distribution with the spread equal to 

double the average service life, i.e., from 1 to 20 for autos, 1 to 18 for farm tractors, 1 to 34 for other 

machinery, and 1 to 76 for buildings. The spread adopted by BLS is only slightly different: .02 to 1.98 

times the average service life (USDOL 1983, pp. 44-45). This is the only difference between ERS and BLS 

methodology with respect to deterioration and retirements.15 

Capital stock construction

ERS uses a perpetual inventory method to construct stocks. This methodology is also widely used by 

others. However, Sliker (2014b), as discussed below in the depreciation section, questions whether the 

aggregation procedure over individual assets is internally consistent.

Capital Input

Rate of return

The real rate of return r is calculated as the nominal yield on investment grade corporate bonds less the 

expected (forecasted) rate of inflation as measured by the implicit deflator for gross domestic product. 

An ex-ante real rate of return is obtained by expressing inflation as an ARIMA process.16 In the review 

panel’s opinion, it is defensible to use an expected rate of return estimated with an ARIMA process 

instead of an actual rate of return. It is only the choice by ERS of the GDP deflator as the expected rate 

of inflation measure that is unusual. In widely used approaches, the rate of asset capital gain or loss is 

measured by an asset-specific deflator in the real rate of return. The choice of the GDP deflator may 

have been dictated by common problems that researchers have when asset capital gain produces an 

asset-specific real rate of return which varies widely or may even be negative. However, that can be 

resolved by following BLS in the use of a smoothing function that takes the average rate of asset 

inflation over several years. Incorporating asset-specific capital gains is particularly important for assets 

with rapidly changing prices such as computers.

The formula for r is ((1+bond)/(1+expected inflation))-1 where the bond rate is that over all maturities 

for AAA rated bonds.17 The choice of the AAA bond rate as the nominal opportunity cost of invested 

funds stems from the fact that Farm Credit bonds are almost always rated AAA. This choice is defensible 

as the Farm Credit system is a major player in the agricultural credit market. In the construction of user 

cost of capital, r is held constant for a particular vintage of capital goods. No attempt is made to 

separate corporate and noncorporate capital input, which have different implicit rental prices due to 

15 Prior to revising its deterioration methodology sometime after 1997, but before 2003, BEA used skewed Winfrey 

(1967) retirement distributions for some assets. 16 Some researchers argue for ex-post rates of return; others argue for ex-ante rates of return. There is no 

consensus among productivity researchers. See OECD (2001b) for a discussion. 17 See Figure XIII.2 for ERS developed real rate of return.

17

 
differences in tax structures by legal form. As BEA provides BLS with a corporate/noncorporate split, 

such a split could be implemented.18 Additional discussion on the choice of interest rate is included in 

the section on the Residual Claimant. 

Taxation

ERS does not incorporate any tax terms into its user cost formula. This differs from the BLS (Harper 

1999), Australian Bureau of Statistics (2013), and Jorgenson, Gollop, and Fraumeni (1987) practice. As 

noted previously, the decision to exclude tax terms may have been made either because it very 

significantly complicates the user cost of capital equation or because of data availability issues. 

Whatever the reason, an explanation is warranted.

Depreciation

To construct a measure of capital input, first a measure of capital stock is constructed followed by a 

measure of the user cost of capital; the latter requires a measure of depreciation, i.e. equation (II.2).

19

With the perpetual inventory method of constructing capital stocks, real gross investment is 

accumulated and reduced by deterioration of capital stock, which differs conceptually from 

depreciation.

20 

ERS has made assumptions typically employed (for example, by BLS) to measure deterioration and 

create measures of capital stock. However, ERS takes a different approach to implementing the 

measurement of user cost, with components representing the opportunity cost of invested funds and 

the discounted stream of the sum of capacity deterioration, instead of explicitly including a depreciation

term.

21 The ERS approach is at variance with the work of several other capital measurement experts 

who defend the age-price approach (e.g., staff from the Bureau of Labor Statistics’s OPT, Professor Dale 

Jorgenson of Harvard University, Paul Schreyer of OECD – see Harper 1982 and 1999; Jorgenson 1973; 

Ho, Jorgenson, and Stiroh 1999; OECD 2009). However, Sliker (2014a, 2014b) appears to reconcile the 

two approaches.

The difference between deterioration and depreciation comes down to the difference between marginal 

productivity and marginal revenue product and a time factor. Net capital stocks depend only on the 

current and past marginal productivity of the stock. The user cost of capital is a function of the price that 

a buyer is willing to pay for an asset. This price depends upon the current and future revenue stream 

expected from an asset over its lifetime or its current and future marginal revenue product. Marginal 

product is an element of marginal revenue product, but only the latter includes the price for the output 

produced by the input. In addition, the net capital stock construction looks backward, while the user 

cost of capital construction looks forward in time as already noted. Accordingly, there are two 

18 Some researchers such as BLS use an internal rate of return instead of an r dependent upon a bond rate and 

expected inflation rate. See OECD (2001b) for a discussion. However, as in the case of the ex-post versus ex-ante 

choice, ERS’s methodology is defensible.

19 The reference might be to capital service flows or to the rental cost of capital rather than to the user cost of 

capital, but this choice has no bearing on the methodological question. Sometimes the term capital input is used 

as well.

20 In this discussion, the term deterioration is used to refer to the capital stock concept and the term depreciation 

is used to refer to the user cost of capital or capital input concept. 

21 Ball et al. (1997) cite Coen () for their procedure.

18

 
differences between the deterioration and depreciation concepts: the price of the output produced by 

the asset and the time frame.22

An exposition of how these two differences impact on the shape of the deterioration vs. the 

depreciation function is in a 1982 paper by Michael Harper, written when he was an economist with the 

BLS OPT. Harper developed productive capital stocks and the user cost of capital under a variety of 

assumptions about the shape of the deterioration (age/efficiency) function.23 He considered the case of 

a concave deterioration function implemented with a hyperbolic function; this case is the one directly 

relevant to this discussion. He represented the hyperbolic function as:24

(II.3) St = (L – t)/(L – βt)

where St is the relative efficiency of a t-year old asset, L is the lifetime of the asset, and β is the 

hyperbolic shape parameter. The depreciation function Pt for the hyperbolic function, which underlies 

pD,t in the user cost formula, is:25 26

(II.4) Pt = (Στ=t Sτ (1-r)τ-t)/ (Στ=0 Sτ (1-r)τ

) 

where both summations are to infinity, but truncated at 200 years for purposes of illustration with 

negligible effects, and r is an assumed real discount rate. The denominator of the function ratio is the 

sum of the discounted efficiencies of the asset over its entire useful life τ. The numerator is the sum of 

the discounted efficiencies of the asset from the present time t through the end of its useful life τ.

27 This 

function is directly derived from equation (II.3) by using the neoclassical theory of investment without 

assuming that deterioration occurs at a geometric rate.28 Harper considered three possible β shape 

parameters: .5, .75 and .9 and presents the results.29 In all three cases, the deterioration function was 

concave, but the depreciation (age/price) function was convex.30 31 The depreciation function is forward 

looking, but the age-efficiency function is backward looking. As ERS uses the same function for 

deterioration and depreciation, both of their functions are concave.

The 1973 paper by Jorgenson is also particularly relevant to this debate. Although this paper does not 

address the shape of the deterioration versus the depreciation function, it does make the same 

distinction as Harper makes. What Jorgenson calls replacement requirements depends upon a weighted 

22 A special case of deterioration and depreciation is when deterioration is assumed to occur at a constant rate. In 

this special case, depreciation is equal to deterioration. ERS did not make a geometric assumption; accordingly this 

equivalence does not hold.

23 Productive capital stocks are stocks which are used in productivity measures such as that constructed for 

agriculture by ERS.

24 See equation 1 page 9 of Harper (1982) and equation C.2 of USDOL (1983). 25 Depreciation functions are commonly called age/price functions and deterioration functions age/efficiency 

functions.

26 See equation 3 page 10 of Harper (1982) and equation C.3 page 44 of USDOL (1983). 27 With a new asset, this ratio is equal to one. As the asset ages this ratio declines even in the case of a one-hoss 

shay asset as the asset has fewer years of useful service.

28 For the neoclassical theory of investment with a geometric rate of replacement and a discussion of the cost of 

capital, see Jorgenson (1963). 29 The Bureau of Labor Statistics (BLS) continues to use β = .5 for equipment and .75 for structures as described in 

Harper (1999). This was verified in a discussion with Steven Rosenthal of BLS. ERS uses the same values for β. 30 The ‘price’ in an age/price function is the price that someone is willing to pay for new investment which depends 

upon the expected future revenue from that asset as described earlier.

31 This is shown graphically for β = .5 in Figure 1 on p. 12 and in tabular form for all three assumed βs in Table 2, 

page 14.

19

 
summation of past investments. His depreciation depends upon a weighted summation of future rental 

prices. The weights in both cases are efficiency and are given by the mortality distribution or the 

sequence of efficiency declines.32 

As both other experts and ERS agree, the productive stock should be multiplied by user cost to obtain 

capital input. Efficiency decline functions are used by the above experts in deriving capital stocks, and 

through the user cost expression, which is a revenue concept, as part of the expected future revenue or 

marginal revenue product arising from a capital asset when a decision is made to invest in new capital 

by paying a certain price for that asset. Age/price functions critically underlie the revenue (depreciation) 

concept. Equation (4) of the cited 1999 Harper paper does indeed use an age/price formulation for 

depreciation rather than an age/efficiency formulation. ERS clearly contends that there should be no 

difference. 

The user cost methodology was outlined by Ball (2014b) and shared with individuals at BEA and BLS. A 

BEA response (Sliker 2014a) expressed little concern about the appearance of deterioration in the user 

cost of capital expression and provided what appears to be an internally consistent justification for the 

ERS method of measuring productive stock and the capital rental rate.

Of greater concern in Sliker (2014a) was the ERS methodology reported in Ball et al. (2008) concerning 

”construction of a cohort-average replacement function as a weighted average of individual 

replacement functions, where the weights are the frequencies of each lifespan in the cohort’s original 

installation.” See Sliker (2014b, 2014c) for the concern and an outline of a methodology to resolve the 

issue. 

Since neither Sliker’s recommended cohort aggregation procedure nor the ERS user cost of capital 

formulation have been widely vetted, both warrant review by additional experts and practitioners in the 

field before changes are made or final conclusions reached. Vetting is important to determine if changes 

should be made to ERS methodology and to inform other productivity researchers.

Aggregation

Measures of real capital input are constructed with Tornqvist indexes. This is a procedure employed by 

many researchers.

Inventories

Inventories impact the output, intermediate input, and capital input accounts. Additions to inventories 

are output, withdrawals from inventories are intermediate inputs, and the stock of inventories is capital 

input. Inventories include durable assets which produce output, such as milk cows and fruit trees, as 

well as nondurable items. NASS surveys from the early 1980s (since discontinued) were used to 

benchmark farmer-owned inventory stocks. Price deflators for inventory investment come from NASS. 

It is assumed that inventories, including durable assets such as milk cows, breeding livestock, and fruit 

and nut trees, do not deteriorate or depreciate. ERS considered treating milk cows and breeding 

livestock as a durable asset which declines in efficiency over time (Ball and Harper 1990), but decided 

against doing so because of questions about the reliability of the source data (Ball 2014a). Construction 

of inventory capital stock and capital input otherwise parallels the methodology for equipment and 

structures. 

32 See equations 5.35 and 5.36, page 142 of Jorgenson (1973).

20

 
Research at BEA

Researchers at BEA are attempting to develop more comprehensive measures of farm output, 

investment and capital stock for the NIPA (Soloveichik 2014). Some of the findings from the research 

project might impact on BEA methodology and be beneficial to ERS productivity accounts. Agricultural 

productivity over the 1948 to 2011 period as currently measured by ERS has increased 1.42% annually 

(USDA 2014). Treating working farm animals, long-lived farm plants, and land improvements as capital 

assets, introducing quality adjustments for some of these assets, and valuing farmland based on 

agricultural rental rates rather than market value would decrease measured TFP, but the total impact of 

such refinements in methods and the data requirements to support them is research in progress 

(Soloveichik 2014). 

Recommendations

It is the judgment of the committee that the ERS effort to measure agricultural productivity with nonland capital as an input is highly commendable and invokes many of the most important developments 

in productivity theory. While ERS has been a leader in researching the best ways to measure capital

inputs devoted to agricultural production and their prices, we recommend that ERS:

1. Examine non-land capital nominal investment data in consultation with BEA researchers (Priority 

A). 

2. Consider using one or more individual asset deflators in its expected inflation calculation 

(Priority A). 

3. Review investment deflators to determine if sources have been updated or revised since the 

data were last collected (Priority A). 

4. Review average service lives of assets with BEA and BLS to determine if any revisions should be 

made (Priority A). 

5. Investigate whether the indexes of capital service flows during the period 1975-1984 reflect 

changes in capital service use rather than changes in the behavior of the bonds rate used in 

calculating the user cost of capital (Priority A). 

6. Begin a conversation with BEA researchers to determine if any changes should be made to ERS 

measures based on recent BEA research (Priority B). 

7. Review and vet the capital stock aggregation methodology developed by Sliker and consider 

whether to revise ERS methodology in response (Priority B). 

8. Include investment in computers in the ERS investment data (Priority B). 

9. After vetting the current ERS methodology, consider whether to revise its estimate of 

depreciation in the user cost of capital to bring its construction in line with the methodologies 

used by other experts in the field (Priority C). 

10. As a future research project, revisit the treatment of breeding livestock, building on Ball and 

Harper (1990) (Priority C). 

III. Land 

In the agricultural production process, land is a key input. According to the ERS production accounts, 

payments for the services of land average about 15% of total input cost. Land, along with structures, 

equipment, and inventories, is a component of the capital index in the ERS accounts. Many of 

the procedures described in the previous section on non-land capital apply to land. Land, owned or 

rented, provides services that are an input into the production process. Stocks of land from the Census 

of Agriculture are used as a basis for the calculation of flow of services. For owned land, the price of the 

service is the user cost of capital as developed for other capital equipment and structures except that 

21
depreciation is assumed to be zero. ERS treats the total payments to land as a residual (this is discussed 

in more detail in Section VII. Residual Claimants). 

1980 AAEA Task Force Recommendations

The AAEA Task Force (Gardner et al. 1980, pp. 33, 46) recommended several changes in the procedures 

used to convert land stock to a service flow. They recommended that the stock/flow conversion be 

based either on the estimated ratio of base-period cash rental value to stock value or a single interest 

rate of 3 to 4% throughout the whole data series. Whichever is used, it should be used as the conversion 

rate for all land. The ratio of cash rental value to stock value was previously used only for the equity 

portion of land owned. They recommended that property taxes as a fraction of land value be added to 

the conversion factor. They further recommended that service flows from public lands be based on a 

shadow-rent estimate of rental value of comparable private lands rather than on federal grazing fees. 

ERS Past Implementations of 1980 AAEA Task Force Recommendations

Since the AAEA task force recommendations, procedures used by ERS to develop indexes of farmland for 

the purpose of multifactor productivity measurement have been theoretically consistent and follow best 

practices as described in Jorgenson, Gollop and Fraumeni (1987) and in the OECD capital and 

productivity manuals (2009, 2001b). Alternative procedures and sources have been used to develop 

these indexes per descriptions in Ball (1985), Ball et al. (1997), and Ball et al. (1999), with additional 

changes in current calculations. They reflect a continuous process of revision and improvement to 

capture changes in the composition of land, as evidenced by recalculations at lower levels of 

disaggregation.

Ball (1985) reported the first set of indexes implementing the AAEA Task Force recommendations. 

National Tornqvist price and implicit quantity indexes of state-level farmland prices and stocks for the 

period 1947-1978 were constructed (Ball, 1985, page 478). State-level prices were the value of land per 

acre at the state level implying homogeneity of land within the state. The value of service flows was 

obtained as a residual from the accounting identity imposed on the system.

Ball et al. (1997) presented Fisher quantity and implicit price indexes for stocks of farmland for the 

period 1948-1994. These indexes incorporated adjustments for land type by using land area and average 

value per acre at the Agricultural Statistics District level within each state. For 11 Western states they 

further disaggregated land into the following land types: irrigated cropland, dry cropland, grazing land, 

and other land (Ball et al. 1997, p. 1050). Using information from the U.S. Agricultural Census for acres 

and from NASS for annual updates, percentages in each district and use category were interpolated 

between census years. To aggregate the different land categories, land values per acre from the annual 

Agricultural Land Values Survey (USDA) were used.33 Public lands service flows were estimated from 

grazing fees paid (Bureau of Land Management and the Forest Service), which was not consistent with 

the 1980 Task Force recommendation. The value of service flows was obtained as a residual from the 

accounting identity imposed to the system.

ERS Current Practice

The description of current practice in this section is based on the methodological description section of 

Productivity Accounts on the ERS website (USDA 2014), Ball (2013), Wang (2013b), and other direct 

communication with ERS. 

33 Ball et al. (1997) state that land diverted from production due to federal commodity programs and the 

Conservation Reserve Program was not included. ERS notes that it is now included.

22

 
Verified by our examination of detailed spreadsheets, aggregation to construct an index of land stock 

now begins at the county level rather than at the state (Ball 1985) or Agricultural Statistical District (Ball 

et al. 1997) levels. The quantity (acres) of land by county includes all land types from the Census of 

Agriculture except “Land in house lots, ponds, roads, wasteland, etc.” For inter-census years, the 

quantity in each county is adjusted by the percentage change in area in each state from the NASS June 

Area Survey until new Census data become available. When new census data become available, a spline 

technique is used to estimate usable land area by county and revise previous data between census 

years.

Price of land at the county level is the average value of land per acre. The Census of Agriculture provides 

information about the value of land and buildings but not the value of land only nor the value of land by 

use (cropland, pasture, etc.). The value of land per acre at the county level is obtained from the value of 

land and buildings in the Census of Agriculture, multiplied by the ratio of the value of land to the value 

of land and buildings at the state level. The ratio of the value of land to the value of farm real estate 

was taken from the NASS Agricultural Economics and Land Ownership Survey (AELOS) prior to 1999. The 

survey, an irregular census follow-on, will not be conducted again until winter 2015 (for 2014 land 

holdings). To date, the 1999 ratios have been used for subsequent years. 

ERS has implemented an alternative approach for estimating the ratio of the value of land to that of land 

and buildings using data from ARMS. Specifically, ERS uses the ratio of the value of farmland (including 

trees and vines) to the value of farmland and buildings. Because ARMS has small samples for some 

states, ERS uses two-year moving averages for the ratio. The resulting estimates were consistent with 

those based on AELOS for comparisons of nearby ARMS years and the 1999 AELOS.

A Tornqvist state-level price index of county-level land prices is computed before computing a Tornqvist

national price index. Acreage shares in each county (state) are used as the index weights. Land stocks at 

each level are implicit quantity indexes obtained as the value of land divided by the price index of land. 

Only the implicit quantity indexes of land stocks are used from this aggregation in the productivity 

accounts. The value of service flows from land is obtained as a residual when imposing the accounting 

identity at the national level. Thus, land is the residual claimant of revenues after all other inputs have 

been paid.

Soloveichik (2014) questions why the ERS land index seems to follow more closely the evolution of 

Woodland, Pastures and other non-Cropland than that of Cropland. ERS notes that total cropland has 

remained quite stable over time. The ERS land series includes land in farms. The non-cropland part of 

that series has declined substantially over time, in large part because of the shift to confined livestock 

feeding operations. As a result, trends in the ERS series reflect the component that’s changing – noncropland.

ERS uses the Census of Agriculture definition of “Land in Farms” 34 that includes all grazing land 

(includes reservation grazing land, land in grazing associations, and any land leased for grazing), except 

land used on government permits on a per-head basis. Pardey, Andersen, and Acquaye (2006) discuss 

the relevance of using the concept of ‘Land in Agriculture’ rather than ‘Land in Farms’ as well as the 

relevance of valuing irrigated land and pasture land separately from cropland, as the basis for this index. 

They argue that acres in farms should be supplemented by acres out of farms which can be obtained, for 

example, from the Bureau of Land Management and the Forest Service. They point out that ERS’s use of 

an average value of land at the county level does not allow the index to capture quality changes within 

the county. 

34 http://www.agcensus.usda.gov/Publications/2012/Full_Report/Volume_1,_Chapter_1_US/usappxb.pdf (p. 13)

23

 
Recommendations

1. Explore ways to include within-county land type adjustments as well as quality changes given by, 

for example, irrigation or other improvements in farmland (Priority A). 

2. Consistent with the recommendation for non-land capital, replace the GDP deflator used to 

capture general effects of inflation with a price index for land (Priority A).

3. Report separate indexes for Cropland, Woodland, Pasture and Other non-Cropland (Priority B).

4. Investigate the potential departure of the ‘Land in Farms’ definition in the Census of Agriculture 

used by ERS from ‘Land in Agriculture’. This would impact quantity and composition 

adjustments (Priority C).

IV. Intermediate Inputs

Much of what is regarded as variable inputs in agricultural production are aggregated into the 

intermediate inputs category within the production accounts. This aggregate is composed of agricultural 

chemicals, fertilizer, fuel and lubricants, feed, seed, custom services, machinery leasing, purchased 

contract labor services, and miscellaneous expenses associated with agricultural production activities. 

The major issues of concern in this review with regard to accurate measurement of intermediate inputs 

for the purpose of the productivity accounts are:

• Addressing the quality adjustments of many these variable factors of production. 

• Reconciling the ERS and BLS producer price index series for several factors. 

• Considering quality of primary data sources in combination with supplemental data and 

protocols used where gaps occur. 

• Addressing how on-farm consumption of inputs is valued in this production account. 

1980 AAEA Task Force Recommendations

With respect to intermediate inputs, the AAEA Task Force (Gardner et al. 1980) made several 

recommendations: 

• Feed, seed, and livestock service flows that are farm outputs used as inputs on the same farm 

should not be counted as either input or output for productivity measurement purposes. But 

those components of feed, seed and livestock purchases resulting from resources committed in 

the nonfarm sector are properly counted as inputs to agricultural production. 

• Agricultural chemicals need additional attention to the extent that some chemicals should be 

counted as part of veterinary expenses, feed additives, and growth hormones. 

• Index number procedures should move away from the Laspeyres to the Divisia. This was 

mentioned specifically for pesticides, fertilizers and aggregate inputs.

• Input quality adjustments are needed.

• ERS was commended for using the gross output approach to productivity measurement rather 

than the net (value-added) approach used in most non-farm productivity measures. 

All of these recommendations have been adopted.

Subsequent Guidance

An important source of additional guidance on intermediate inputs is the OECD Productivity Manual

(OECD 2001b) regarding Intermediate Input and Valuation (Chapter 6). It identifies input-output tables 

as the principal tool for creating a full set of intermediate input price and quantity indexes. OECD 

considers this to be a preferred mechanism that ensures the consistent treatment of intermediate and 

primary inputs and produces measures that are consistent with the accounts for the economy as a 

24
whole. When the quantity indexes of intermediate products are weighted by their value share in total 

inputs, input substitution towards intermediate inputs with higher marginal products is accounted for as 

a change in the composition of intermediate inputs. 

From the perspective of productivity measurement, the choice of valuation should reflect the price that 

is most relevant for producer decision marking. The basic price is intended to measure the portion of the 

price actually retained by the producer. It therefore excludes taxes paid and includes subsidies received. 

Purchasers’ prices are prices relevant for producer decisions on input choices. For goods intended for 

intermediate consumption, the OECD and the SNA recommend valuing them for the consumer at the 

purchaser’s prices (which includes taxes, transport and other charges paid by the purchaser). The ERS 

practice is consistent with this approach.

ERS Current Practice

The core intermediate input data are input expenditures collected from ARMS surveys conducted by 

NASS in collaboration with ERS. These are expenditure data. For only a few inputs are prices collected. 

The most commonly used source of prices for intermediate inputs is the Prices Paid Survey which

collects price data using telephone enumerated surveys. Prices paid for farm inputs are collected 

annually through a survey of establishments selling production input items to agricultural producers. 

The prices paid index does not adjust for changes in item quality or product enhancements (USDA NASS 

2011, pp. 1-7). NASS estimates monthly price series for major crops and livestock commodities, which 

reflects quality premiums and discounts. These prices are generally related to producer prices at first 

point of sale. 

NASS uses the price estimates to calculate the Index of Production Items, which is one of five 

components in the overall prices paid index for commodities and services, interest, taxes, and farm 

wage rates (PPITW). The other PPITW component indexes are a) interest paid and interest rate on farm 

indebtedness, b) taxes paid on farm real estate, c) wage rates paid to hired farm labor, and d) prices 

paid for family living items. 

Livestock, poultry and related expenses are collected by NASS, and implicit quantities are constructed 

using a NASS prices paid index. Fertilizer, lime and pesticides comprise the broader agricultural chemical 

input. Fertilizer quality changes are addressed by using a hedonic price index that is documented in 

Fernandez-Cornejo and Jans (1995) and in Ball, Hallahan and Nehring (2004). BLS also develops a price 

index for fertilizer. For comparison purposes, the correlation between the BLS index and ERS generated 

hedonic index is 0.93 over the period 1948-2011. However, the growth rates between these series 

correlate at only 0.51, and the average growth rates for the BLS and ERS fertilizer series are 3.6 % and 

2.1%, respectively. 

NASS reports the price per ton of “lime spread on the field” as well as lime expenditures. ERS constructs 

implicit quantities. This is a fairly homogenous input that is not likely to require quality adjustments. 

Nominal expenditures are reported by NASS for pesticides, and hedonic prices accounting for quality 

changes are constructed by ERS (Fernandez-Cornejo and Jans 1995; Fernandez-Cornejo et al. 2014) as 

are implicit quantities. BLS also develops a pesticide price index which has a correlation of 0.90 over the 

entire period, but not as high for major subperiods. In particular, in the post-1973 period, the BLS price 

index changes at a slower rate than the ERS hedonic price. The correlation between the growth rates of 

these two series is only 0.40. It is not clear if these differences are due entirely to ERS accounting for 

changes in quality. 

NASS provides expenditures for fuels and lubricants, including minor fuels (e.g., coal and wood), as well 

as expenditures for the major components: gasoline, diesel, liquefied petroleum gas, natural gas, oil and 

25
lubricants, and electricity. NASS is also the source of price data for gasoline, diesel, and liquefied 

petroleum gas. Natural gas and electricity price data are sourced from the Energy Information 

Administration which is an agency of the U.S. Federal Statistical System. Oil and lubricants price data are 

sourced from BLS. ERS constructs a price index and an implicit quantity for fuels and lubricants by 

deflating total expenditures net of taxes.35 BLS also develops price indexes for several of these fuel 

types. For comparison purposes, four of the five series track closely over the period – the correlation 

between the growth rates in the BLS and ERS series over the entire period is 0.80 for gas, 0.91 for diesel, 

0.68 for LP gas, 0.84 for natural gas, and 0.95 for electricity. 

The NASS expenditures on feed series use the BLS price index for animal feed other than pet food and 

the NASS prices paid index for seed as deflators. The BLS deflator does not include on-farm 

consumption. ERS includes on-farm consumption of feed, as is the practice for the EUROSTAT (2000) and 

the SNA. ERS treats all on-farm feeding as drawn from opening stocks. The price of corn fed on the farm 

is the opportunity cost, i.e., the price received by the farmer for corn sold off the farm, net of price 

supports since the payments are not dependent on end use. The total feed and seed input is an index of 

purchased and on-farm use. This results in a different input price than that proposed by the OECD 

Productivity Manual to the extent that the marketing margins and transportation costs of animal feed 

are not included in the valuation of the BLS price index for animal feeds (OECD 2009, pp. 79-80)

Accumulation of crop and livestock inventories is included in output and the drawdown of inventories is 

included in the intermediate input category. Presumably these intermediate inventories also refer to 

seed, feed, etc. Net inventory changes are also added or subtracted from the inventory component of 

capital. The questionable practice is the treatment of livestock as inventory instead of capital. 

Communication with ERS suggests that embodied technical change is not being addressed by the NASS

price indexes. Since NASS is not adjusting for input quality change, this leads to overstating the price. 

ERS acknowledges that changes in seed consumption are understated because they do not adjust for 

quality changes in this input. ERS indicates they have plans to develop a hedonic price index for seed. 

Hedonic price indexes for machinery are addressed in the quality section of this report. 

Purchased services are another major component of the intermediate input series. Expenditures for 

repairs and maintenance of machinery and buildings use the BLS deflators to construct implicit 

quantities. 

Purchased machine services use the index of machine rental prices (source not clear), implying 

purchased machine services are a perfect substitute for services from own-capital. No data on actual 

prices of purchased machine services are collected. Other purchased services include a) transportation, 

marketing, and warehousing which use the BLS price index series for farm product warehousing and 

storage, and b) veterinary and pharmaceuticals. Custom livestock feeding uses a feed price index 

obtained from an “informal” survey36 as a deflator. Other management expenses use the BLS 

employment cost index for wages and salaries, professional, and related services. 

Miscellaneous expenses include two general categories. The first is irrigation expenditures from public 

sellers of water and the cost maintenance index for water projects compiled by the Bureau of 

Reclamation. The second is general production expenses (tools, shop equipment, and other unallocated 

expenses) which use the BLS price index for hardware as a deflator. 

35 Farmers are eligible to claim a refund of excise taxes on fuel. 36 This survey is a set of several phone calls to livestock feeding operations. It is not conducted annually and the 

survey is not stratified by size of operation, geographic location, or time of year.

26

 
The last component is purchased contract labor services. A hedonic price index is used. This is covered in

the labor section of the report.

The price and quantity series for energy, fertilizer and lime, pesticides, purchased services, and other 

intermediate inputs are available on the ERS website.

Recommendations

1. Examine the robustness of the intermediate input accounts constructed by ERS to the use of 

alternative sources of price deflators (Priority B). 

2. Investigate the logic and practical effect of how ERS intermediate inputs compare to those 

based on input-output tables (Priority B). 

V. Outputs

Accurate measurement of the prices and quantities of agricultural output is critical for accurate 

measurement of productivity growth as well as understanding output supply and other important 

commodity and sectoral relationships. Because a large body of research uses output and input price and 

quantity measures as basic data, it is important that the aggregates as well as the individual 

commodities and inputs be measured accurately and communicated clearly. Timeliness, transparency, 

and public access to the series at each stage of development of the aggregate output series will facilitate 

its broader value for analysis and policy, as well as invite research and exploration on ways to more 

accurately develop the productivity accounts to extend their value.

Major issues of concern with regard to accurate measurement of outputs for purposes of the 

productivity accounts are:

• Measurement of sectoral output and input

• Definition of the sector, i.e., the scope of the establishments to include

• Accounting for quality changes 

• Measurement of prices relevant to the sector, including the effects of different tax and subsidy 

forms 

• Aggregation 

• Type of productivity measures to compute

• Consistency between aggregates and state and international cross-sectional comparisons

• Data quality

1980 AAEA Task Force Recommendations

AAEA Task Force (Gardner et al. 1980) recommendations addressed each of the above issues. They 

recommended that ERS a) account for quality changes to provide a close-to-total productivity measure, 

b) switch from a Laspeyres index procedure in which base weights are held constant for an extended 

period and then spliced with the next period to a Tornqvist discrete approximation to the Divisia index 

procedure that adjusts weights every year, c) focus on TFP for all agricultural output and not develop 

TFP measures for individual outputs, d) use comparable definitions for cross-sectional comparisons 

across states or nations, e) utilize most reliable data sources, and f) report more analysis and fewer 

numbers. 

They also included commendation for focusing on multifactor productivity using gross output measures

and using an index number approach rather than switching to a production function approach (since TFP 

changes account for technical and allocative efficiency changes as well as technical change).

27
However, only two of the recommendations were uniquely output-oriented: a) concentrate on 

productivity measures for a more stable definition of the product, and b) include net indemnity 

payments from publicly-provided disaster insurance in the measure of output. With regard to the first, 

they recommended that the definition be raw agricultural output measured at the first point of 

assembly rather than measured as the output of farms. Their concern was that the output of farms 

depends on what is done and not done on the farm and thus varies with commodity, location, time, and 

business establishment. 

For the most part, their recommendations are consistent with the later OECD Productivity Manual 

(OECD 2009, pp. 23-24). This manual notes that data quality is enhanced when output and input 

measures are based on the same statistical sources. It finds that gross, sectoral, and value-added 

measures all have value as valid complements at the industry level. Sectoral and value-added measures

converge at the aggregate level, but require additional restrictions on the specification of production 

technology related to the separability of primary and intermediate inputs. 

ERS Current Practice

Output is measured as the sum of marketings, net inventory accumulation, and consumption by farm 

households. The gross measure has become the standard now used by many government agencies 

when developing productivity accounts, but the BLS continues to use the sectoral concept. 

It appears that the most appropriate data available are generally used to construct the productivity 

accounts. Production and marketing data are collected by NASS through surveys of farms. Prices 

received data are collected by NASS from surveys of purchasers at the first point of assembly (e.g., 

packers, dealers, auction houses). Use of these data result in a stable product definition of output, i.e. 

raw agricultural product measured at the sector border between agriculture and processing.

Discontinuation of the NASS Farm Labor Survey has resulted in the discontinuation of the state-level 

accounts because other labor data of sufficient quality and breadth do not exist.

Net distorting payments (deficiency, diversion, loan deficiency, market gains, certificate gains, milk 

income loss payments) are added to market prices of individual commodity output prices and distorting 

taxes (dairy assessment) are subtracted. Non-distorting flex payments are treated as transfer payments 

and not included in output price. Although potentially distorting, counter-cyclical payments are also 

ignored because the data are aggregated with flex payments .

They have continued to use an index number approach and have switched from Laspeyres indexes for 

aggregation to Tornqvist indexes that adjust weights every year. They appropriately use revenue or cost 

shares as weights. ERS has discontinued reporting partial productivity measures, and they don’t develop 

productivity measures for individual outputs. They use comparable definitions for cross-sectional 

comparisons. 

More attention has been given to explaining construction of the statistics. In addition to reporting 

statistics, considerable analysis has been conducted and reported. Exploration of alternatives for 

improving the productivity accounts has become a standard part of the ongoing effort. However, while 

considerable attention has been given to measuring quality changes in inputs, quality changes in outputs 

has not been addressed in the productivity accounts. 

Our Assessment 

We concur with the AAEA Task Force in commending ERS for computing gross measures of outputs and 

inputs. While both gross and value-added measures are valid complements at the industry level, the 

gross measures are more appropriate because they do not impose the arbitrary and generally 

unsupported assumption of weak separability of the underlying production function between labor and 

28
capital provided by the sector and inputs provided by other sectors. Many other government agencies 

have now followed ERS in adopting the gross measurement concept for outputs and inputs, or 

something closely related, in their productivity accounts. For example, the Bureau of Labor Statistics 

uses sectoral output defined as gross output less intrasectoral purchases.

We also concur with the AAEA Task Force in commending ERS for focusing on multifactor productivity 

rather than partial productivity measures. We concur with the Task Force that: 

“The most important uses of productivity statistics are: (1) identifying the sources of economic 

growth, (2) justifying the appropriation of agricultural research funds, (3) estimating production 

relationships, (4) serving as an indicator of technical changes, [and] (5) comparing intersectoral 

economic performance ....” (Gardner et al. 2000, p. iii) 

Partial productivity statistics compare intertemporal ratios of output quantity to the quantity of a single 

input. As such, they have important limitations and are often misleading for the decision-making 

purposes for which they are used. ERS appears to have discontinued reports of partial productivity 

statistics. Our internet search failed to identify any partial productivity measures produced by ERS in the 

last decade. 

Several of the issues warrant further comment and/or revisitation, some of which are also addressed in 

other sections. 

Measurement of sectoral outputs which are also inputs

Own-account capital formation, whether building a house for a farm employee, accumulating 

inventories, investing in land improvements such as tiling, or spending on farmer safety, should 

conceptually be treated consistently on both sides of the account. For example, if the labor and 

intermediate materials used in tiling is on the input side of the account, the land improvement should be 

on the output side of the account. Alternatively, the input should be netted out of the input side of the 

account. Similarly, if farm resources are used to build a barn, the barn should be on the output side of 

the account, or the resources used to build the barn should be removed from the input side of the 

account. Feed produced on one farm and used on another is both an output and an input. ERS includes 

the imputed rental value of employer-provided housing and inventory accumulation and the value of 

feed sold and purchased as both input and output. Land improvements, however, are currently included 

only in the input quantity measure but not in output quantity. Recent exploration by ERS has discovered 

that data are available on investment in land improvements to permit their incorporation into the 

output measure, and they plan to incorporate this into future revisions. 

Measurement of prices relevant to the sector 

Although ERS accounts for most distorting government programs in commodity output prices, the 

distorting effects of crop insurance are not included. Because of the subsidy, the effect of crop insurance 

is to increase the effective output price for the insured crop. By increasing effective price while 

simultaneously reducing risk, crop insurance can be expected to induce increases in both outputs and 

inputs. Under decreasing returns to scale this would result in a decrease in productivity, but under 

constant returns to scale, as assumed in the national agricultural productivity accounts, it would have no 

effect. What is clear is that subsidized crop insurance increases the effective price of the insured crop in 

addition to reducing risk and is thus distorting. Thus, the subsidy augments market price and should be 

included in the calculation of the effective price faced by farmers. 

We concur with the way that ERS uses market and distortion policy-adjusted commodity prices. Prices 

inclusive of distorting subsidies and exclusive of distorting taxes are used to aggregate across outputs. 

Market price (alternatively, opportunity cost) is used to value on-farm consumption because the policy 

29
distortions are not dependent on use of the output. The only issue is that the distorting effects of crop 

insurance are not considered in aggregating across outputs.

Aggregation

The Divisia index is an exact aggregator for a linear homogeneous translog production function, so it has 

considerable appeal when production is well represented by the translog production function. The 

Tornqvist discrete approximation is used in implementation of the Divisia index. The Tornqvist index 

uses two-year rolling average revenue shares (expenditure shares for inputs) as the weights in 

computing geometric means of the individual commodity (input) data. This index, recommended by the 

AAEA Task Force and implemented by ERS, is an important improvement over the Laspeyres index 

previously used which uses base weights over extended time periods. However, it is not clear that the

geometric mean is an improvement over the arithmetic mean calculation of the Laspeyres. That 

depends on the nature of the underlying functional form of U.S. agricultural production. 

Unfortunately, there has been little comparative research in the last few decades on the form of the 

agricultural production function.37 There has been more attention to choice of functional form of dual 

models of U.S. and state-level agricultural production. While the evidence is inconclusive, the translog 

has not fared better in empirical tests than alternatives such as the quadratic or generalized Leontief 

(e.g., Perroni and Rutherford 1998; Anderson et al. 1996; Ornelas, Shumway and Ozuna 1994; Shumway 

and Lim 1993; Ornelas and Shumway 1993), both of which are better represented by an arithmetic 

mean than a geometric mean aggregator function. What is clear is that empirical evidence of theoretical 

consistency and policy-relevant implications of the dual production models are both sensitive to choice 

of functional form (e.g., Baffes and Vasavada 1989). The same is true for sectoral productivity measures 

using different aggregator functions when prices change substantially.

Most researchers and government agencies who compute TFP rely on the translog as the underlying 

production function. While it may fail to secure unambiguous empirical support, there is an alternative 

way to arrive at the translog as an appropriate basis for indexing. That is to differentiate the nominal 

accounting identity and the group quantities. Multifactor productivity can then be defined as the 

difference in quantity indexes. The relationship between true technology and measured multifactor 

productivity is broken, but this is still a valid index of productivity in the sense that it takes into account 

all measured inputs weighted appropriately. 

Despite the current dominance of the Divisia index as the aggregator function used for productivity 

measurement and its validity as an index of productivity, alternatives warrant consideration. For 

example, the chained Fisher index is consistent for both extremes of substitutability, i.e., linear and 

Leontief aggregator functions (Diewert 1976).38 

37 Fulginiti (2010) used the square rooted quadratic output distance function to represent the U.S. aggregate 

technology because of its relative ease for imposing regularity conditions. Giannakas, Tran, and Tzouvelekas (2003) 

conducted tests of several functional forms for estimating stochastic production frontiers of Greek olive orchards. 

They concluded that the Box-Cox dominated all nested functional forms including the translog, generalized 

Leontief, and normalized quadratic but that none of three non-nested functional forms (Box-Cox, minflex Laurent 

translog, and minflex Laurent generalized Leontief) dominated another form.

38 Recent work seeking to explain TFP growth in U.S. agriculture has been based on a variety of functional forms, 

including translog cost functions (Plastina and Fulginiti 2012), normalized quadratic value functions (Onofri and 

Fulginiti 2008), and quadratic cost function (Wang et. al. 2012). 

30

 
Data quality

The issue of data quality is an ongoing concern of all involved with data collection, processing, and use. 

Substantial effort has been expended to ensure that the best available data are used in the construction 

of the productivity series. There is considerable coordination between agencies. For example, to 

develop cash output prices, the ERS Farm Income Group develops cash receipts (including net loans) and 

quantities marketed data series from primary data collected by NASS in the ARMS surveys. The ERS 

Productivity Group searches for outliers and works with the Farm Income Group when evidence of 

errors are found before dividing cash receipts by quantities marketed to develop the cash price series 

for each commodity. 

Recommendations

1. To account for the distorting effect of crop insurance when outputs are aggregated, add the 

insurance indemnity to the insured crop’s price and deduct the farmer’s premium (Priority A).

2. Revisit measurement issues related to own account investment, specifically consistency 

between the output and input sides of the account (Priority A).

3. Continue to explore the effect of alternative aggregator functions, including the chained Fisher 

index, on productivity measures and include sufficient detail in the data available on the website 

to enable users to explore them (Priority C).

31
PART 2 

The first section of this report addressed specifics of methodology and measurement issues related to 

the particular outputs and inputs. This section addresses issues that are broader in scope, including 

quality adjustment, residual claimants, research and development spending, alternative assumptions, 

and the ERS website.

VI. Quality Adjustments

The theory of productivity measurement prescribes that the outputs coming from and inputs used in 

production should be measured in constant-quality units (Jorgenson, Ho, and Stiroh 2005; OECD 2001b). 

The intuition for this is that productivity measurement attempts to differentiate between shifts in the 

production function (change in technology) and movements along the production function (input 

substitution or change in input use). Outputs and inputs need to be measured in constant-quality units 

because a change in the quality of one for a fixed level of the other is a shift in production possibilities. 

ERS recognizes the importance of capturing quality in their productivity accounts and uses state-of-theart techniques to adjust a subset of their input series for quality improvements. However, a few open 

questions remain. This section provides a brief overview of quality adjustment and addresses how each 

of the components of the ERS productivity accounts addresses the issue of quality change.

A Simple Model of Production with Quality Change

As an illustrative example of the importance of considering quality change when measuring productivity, 

consider a Cobb-Douglas production function:

(VI.1) (1 ) Q AK Lα α− = 

where Q is the raw number of units of output produced. Allowing for quality change of output and the 

capital input, the production function for quality-adjusted output can be rewritten as:

(VI.2) (1 ) ( ) Y qQ q Aq Y YK K Lα α− = = 

where Y q and K q represent the quality of output and capital input, respectively, and Q andK represent 

the raw quantity of output and capital input. This specification makes it obvious that a shift in A cannot 

be distinguished from a change in Y q and amounts to a shift in the production function forY . An 

increase in K q is movement along the production possibilities curve, i.e., the production of output using 

additional constant-quality capital input. 

Figure VI.1 demonstrates graphically the difference between a shift in production possibilities (TFP 

growth) and a movement along the production possibilities curve by employing higher quality capital.

32
 

Quality and Composition in Productivity Measurement

In discussions of productivity measurement, it is easy to confuse the notions of quality and composition. 

This confusion may occur when discussing both the output and input side of the production account.

Typically, quality refers to a particular characteristic, or set of characteristics, that determines the 

functionality of the output or input. For example, the processing speed and memory of a computer or 

the effectiveness of a particular fertilizer are intuitive examples of characteristics that are important on 

the output and input sides of industry-level economic accounting. For reasons discussed above, it is 

important in productivity analysis and measurement that individual outputs and inputs be measured in 

constant-quality units. 

Composition effects in productivity measurement are related to measures of quality, but composition 

effects are a byproduct of the aggregation of heterogeneous outputs and inputs when constructing 

measures of productivity.39 For example, in the aggregation of multiple individual outputs to a single 

industry-level output, the Tornqvist index weights each output by the average of its revenue share in the 

current and previous period. Thus, outputs with higher revenues receive higher weights when 

aggregating over individual outputs. In comparison, an alternative model of output that is more 

restrictive may impose the condition that all outputs are homogenous and thus have the same price. 

39 In the case of a single output or input, aggregation is a non-issue, but in the farm productivity accounts there are 

multiple outputs and inputs.

33

 
This restrictive assumption provides an alternative measure of industry output growth. The difference 

between the two measures is due to composition, or reallocation.40 

Quality of labor input (non-contract)

The ERS labor measure categorizes workers by gender, age, education, and employment class (and state 

for the state-based estimates).41 The key feature of the ERS methodology on labor input measurement is 

that it identifies industry-wide substitution towards workers of differing marginal products as changes in 

the measure of labor input, consistent with the theory of productivity measurement. In the terminology 

of Jorgenson, Ho, and Stiroh (2005), substitution towards workers with higher marginal products is 

termed a change in “labor quality” (or labor “composition” in the terminology of OECD (2001b)). The 

methodology of constructing labor input as an index number over these different types of workers 

appears to implicitly assume that the quality of worker by each demographic group is constant over 

time. That is, the quality of an hour worked by the self-employed farmer of a given age (experience), 

gender, and educational attainment is the same in 1948 as in 2011. Further, the classification 

presupposes that there are no other dimensions on which workers differ in their marginal productivities. 

For example, to purchase an additional unit of labor services, a farm owner pays workers with and 

without specialized training the same wage rate if the worker is in the same demographic group. It is 

important to note that the assumption of constant quality by worker type is not the same as assuming 

that the marginal product of the workers by type is fixed over time. 

Overall, the ERS labor input measure for non-contract workers follows standard practice with respect to 

controlling for worker quality (Jorgenson, Gollop, and Fraumeni 1987; OECD 2001b).An open question 

remains as to whether there are categories other than gender, age, education, and employment class 

that are important (and feasible) to include in the estimates of labor composition. For example, 

specialized workers within the current demographic groups are not identified, nor are supervisory and 

non-supervisory workers. In a previous version of the data, ERS recognized occupational categories (Ball 

1985). Including occupation has the potential to account for shifts to skilled supervisory workers. A finer 

breakdown of labor attributes might allow for different patterns of quality change. However, it is not 

clear that the data required for a finer breakdown are available.

One potential concern is the implicit argument that age of worker identifies experience. Due to changes 

in preferences, job conditions, or external events (e.g., war), the experience of a given age may be very 

different across cohorts. It is an open question how important this effect is for the measure of labor 

input.

Capital input

The underlying assumption of the capital input measure is that the prices used to deflate investment are 

measured in constant-quality units. Thus, in the estimation of productive capital stock, investment flows 

are added to the stock in constant-quality units. That is, a capital good with double the quality of the 

previous period adds twice as much to the productive capital stock. With measurements of nominal 

investment, controlling for quality occurs by applying the appropriate quality-controlled price index.

The ERS productivity account takes investment deflators from the BEA and BLS. ERS has conducted 

research suggesting the investment price for tractors requires additional quality adjustment, but they 

40 Jorgenson et al. (2007) refers to the difference between value added growth from an aggregate production 

function (homogenous good) and the Tornqvist index on industry value added as reallocation of value added. 41 The ERS website notes that they follow the Jorgenson, Gollop, and Fraumeni (1987) classification but do not 

state explicitly the age and education groupings. The groupings should be included in the website notes.

34

 
currently use the BLS deflator for tractors. They do not make additional adjustments for investment 

good quality. 

For land prices, ERS assumes homogeneity at the county level, and average price per acre is used. There 

have been important changes, mainly with the introduction of irrigation, and these are not captured by 

the procedure used. The data on irrigated acres is available at the county level and there are some 

statistics for rental rates. The assumption of homogenous land at the county level should be 

reevaluated. Furthermore, ERS assumes that additions to and subtractions from acreage within a county 

are for homogenous land, abstracting from the likely alternative that land discards occur in 

unproductive land (see Soloveichik (2014) for a more detailed discussion). 

Intermediate inputs 

The ERS productivity account recognizes the importance of quality change in intermediate products that 

are used by farms. For a subset of the intermediate goods used in the agricultural industry (pesticides, 

fertilizer, and purchased contract labor services), ERS makes adjustments for quality gains using 

hedonics. For other categories, the ERS relies on published price deflators.42 The website mentions that 

“Input measures are adjusted for changes in their quality, such as improvements in the efficacy of 

chemicals and seeds,” but we find no evidence that seed price is adjusted for quality change. Potentially, 

quality adjusted seed prices could be constructed with either hedonics or matched model methods 

depending on data availability.

For the majority of the intermediate inputs ERS relies on input prices from the Survey of Agricultural 

Prices. For purchased services, ERS uses the BLS implicit capital rental price index for machines. The 

rationale for this is the assumption that agricultural services that are outsourced are perfect substitutes 

for own account services. This assumption is debatable because it implies zero productivity gains 

relative to owned machines in the provision of these services, when productivity gains would be a major 

reason to switch to the service. The intuition for why productivity gains in outsourced services could 

induce switching is that productivity can be equivalently identified as a decrease in the output price per 

price of input. Therefore, a productivity gain in Agricultural Services is manifested as a lower price which 

could potentially induce the farmer to switch to outsourcing if not matched by the same productivity 

increase in owned machines. ERS should investigate deflating Agricultural Services with an alternative

price index from BEA or BLS that captures market transaction prices.

Output

Quality improvements in output are not addressed in the ERS accounts. Potential quality improvements 

are the development of organic foods, reduced food-borne illnesses (safer foods), increased availability 

of milk and eggs in the winter due to improved farming methods (not improved transportation), more 

flavorful products, high oleic soybeans, high-total-fermentable-ethanol hybrid corn, specialized corn, 

high protein wheat, chicken with a higher proportion of white meat, lower fat meats, free range meat, 

vegetables that are easier to transport, and increased variety. 

It is unclear whether such commodity-specific quality changes are of sufficient magnitude to alter the 

measurement of sectoral productivity. For example, if prices for groups such as organic fruit and nonorganic fruit are tracked and then aggregated, is the aggregate measure different than if all fruit is 

aggregated first? If it is, then following the pattern of developing hedonic indexes for pesticide and 

42 Hedonics is not the only alternative for quality adjustment, and statistical agencies often use matched-model 

approaches to construct constant quality price indexes. Both hedonics and matched-model approaches are 

potentially effective with the proper source data and econometric techniques, although oftentimes estimates will 

differ across methods (Triplett 2004).

35

 
fertilizer inputs, similar methods could be explored for measuring quality changes in outputs. Matched 

model price indexes are another possibility. The work of Chun and Nadiri (2008) could inform this 

process. 

Recommendations

1. Research methods for incorporating quality adjustments to seed and consider whether seed 

quality change should be treated solely as an input, or both an output and an input (Priority A).

2. Determine whether the degree of quality change in outputs has been sufficient to warrant 

quality adjustment, and, if so, explore alternative methods to adjust productivity measures for 

output quality change (Priority B).

3. Check alternative data sources for price of purchased machine services (Priority B).

4. Research the possibility and ramifications of subdividing labor into supervisory and 

nonsupervisory workers in the cross-classification of labor (Priority C). 

VII. Residual Claimants

In the U.S. and international TFP calculations, it is typical that modelers impose the assumptions that 

producers operate in a perfectly competitive market, face constant returns to scale, and pay each factor 

of production the value of its marginal product. Under this set of assumptions with the additional 

stipulations that outputs and inputs are measured properly and in constant quality units, changes in TFP 

correspond to changes in economic technology, i.e., innovation. For these assumptions to hold, it is 

necessary to “clear the account” to ensure that gross receipts equal gross expenditures. After deducting 

the cost of purchased inputs that are fully utilized in the production period (typically a year), the 

operating surplus is distributed across capital inputs and unpaid operator and family labor.43 This 

distribution requires that one or more of these inputs becomes a “residual claimant” input in deriving its 

rental rate. Whether all or just a portion of the various capital and unpaid labor inputs is designated the 

residual claimant is a decision of judgment influenced but not dictated unambiguously by theory. The 

same can be said about how to allocate the residual if multiple inputs are included as residual claimants. 

One important theoretical consideration in choosing the residual claimant(s) is the length of run 

considered in the TFP calculations. For example, if TFP calculations are based on a relatively long run, 

then the residual claimant(s) should be the input(s) that remain fixed (or quasi-fixed) for the longest 

adjustment period. If TFP calculations are based on the short run (e.g., a single production period), then 

the residual claimants should be all inputs that remain fixed over the selected short-run period. In that 

case the residual should be allocated among claimants in a way that equalizes the rate of return to the 

fixed inputs. Diewert (2012) argues that, when all fixed assets carry the same risk, the real rate of return 

should be the same across the fixed assets, which is consistent with the implementation in Jorgenson, 

Gollop, and Fraumeni (1987). Gu (2012) defends Statistics Canada’s use of the nominal rate of return as 

the equilibrating price, which is consistent with Jorgenson’s recent modeling in which all inputs are

flexible, i.e., long run, no adjustment costs, and perfect foresight (e.g., Jorgenson, Ho, and Stiroh, 2005). 

In the latter case, there are no fixed inputs so all inputs share alike as residual claimants. Approaches to 

rates of return are also considered in the OECD capital manual (OECD 2009, pp. 66-75). 

43 Having unpaid operator and family labor is the most serious issue in mixed-income industries. Such industries 

have a subset of enterprises owned by members of the household who also work without receiving a wage or 

salary. It is not a major issue in industries dominated by publicly-held corporations. The latter may use selfemployed workers, the cost of which is typically included in the productivity accounts as part of labor expense, 

generally as contract labor. It is a severe issue in agriculture. 

36

 
A single fixed input, land, has been chosen for the U.S. agricultural productivity accounts as the residual 

claimant. This is consistent with the view that land is the most nearly fixed of all inputs used in 

agricultural production and consequently is the residual claimant for rents from production. An 

alternative single fixed input, entrepreneurship, could also be considered for the agricultural 

productivity accounts (Diewert 2014). Since data are available on the actual payments for rented land, 

land rents and the imputed wages for unpaid family labor could be subtracted from the net operating 

surplus to obtain the entrepreneurial residual to land and labor supplied by the farm proprietor.

BLS splits the residual between self-employed and non-corporate capital assets. Their logic and 

procedure for implementing the split is documented in a BLS bulletin (USDOL 1983, p. 52).

Agriculture and Agri-Food Canada has chosen self-employed labor as the residual claimant to “clear the 

account”. They argue that this is “consistent with the usual definition of net farm income, where all but 

operator/unpaid family labour is accounted for” (Strain 2013). It is also consistent with Canada’s federal 

tax code for non-corporate farms that allows all expenses except the operator’s labor to be deducted 

from revenue and with Statistics Canada’s definition of net farm income (Cahill 2014). Cahill argues that 

there is little theory to guide the selection of residual claimant(s). They cite Hottel and Gardner (1983) 

and Gardner (1992a) in support of their choice of self-employed labor as the residual claimant.44 There is 

also a practical reason for their choice – they lack a satisfactory data base for imputing the wage for selfemployed labor (Commission of the European Communities, et al. 1993). Diewert (2014) notes that an 

argument against this choice could be made by considering the possible sale of the farm with a 

professional manager subsequently hired to manage it. In this case, both farm labor and manager salary 

would be paid and the residual would accrue to the land owners. The same would occur without a land 

sale by the existing owner-operator choosing to hire a professional manager and no longer working on 

the farm.

In their analysis of Canadian multifactor productivity, Diewert and Yu (2012) use 17 separate capital 

stocks as the residual claimants and assume that all receive the same real rate of return, which was 

computed endogenously. The Statistics Canada’s Canadian Productivity Program spreads the residual 

across all capital inputs by assuming that all capital inputs within a sector receive the same nominal rate 

of return (Gu 2012). This difference in the use of real or nominal rates of return is largely responsible for 

the substantial differences in Diewert-Yu’s and Statistic Canada’s estimated TFP growth over the half 

century, 1961-2011, 1.03% vs. 0.28% average multifactor productivity growth rate (Diewert 2012). 

Diewert defends use of the real rate of return as the balancing price on the basis of better following 

market rents and leasing rates as well as greater stability in the real rate of return over time. Jorgenson, 

Ho, and Stiroh (2005) further argue for incorporating asset-specific capital gains into the calculation of 

the real rate of return since assets, such as computers, with large expected capital losses would only be 

purchased if they have relatively high marginal products. Regardless of how one regards the 

persuasiveness of these arguments, it is clear that how rents to the residual claimants are handled

matters in empirical estimation of TFP. 

Recommendation

The committee does not have an unambiguous recommendation for altering the residual claimant used 

in the national agricultural productivity accounts. Continuing to use land as the residual claimant is 

supported by the logic of selecting the input that is most nearly fixed in long-run supply. It is also an 

44 While Cahill (2014) cites Gardner (1992a) as referring “to the earnings of farm operator households as a 

residual”, Gardner actually refers to these earnings as “part” of the residual which also includes the returns to 

“capital assets” (page 83). 

37

 
intermediate choice between the extremes of a) all capital assets plus self-employed labor and b) 

entrepreneurship. 

The committee does recommend that this be a subject of research and thoughtful consideration in the 

future (Priority B). As a minimum, the sensitivity of the productivity accounts to the alternative residual 

claimant extremes and different choices of expected asset inflation should be explored. 

VIII. Research and Development

It is widely recognized that spending on research and development (R&D) potentially yields future 

improvements in production. This is because current spending on R&D yields a capital service flow over 

time. The 2013 Comprehensive Revision of the U.S. NIPA officially recognized spending on R&D as the 

production of an investment good, and measures of fixed assets, capital stock, capital consumption, and 

GDP were revised to reflect this treatment (McCulla, Holdren, and Smith 2013). This redefinition has 

implications for productivity measurement because recognizing R&D requires potential adjustments to 

the output side (when own-account R&D is produced) and to the input side of the production accounts 

(when R&D capital is used in production). The February 2014 release of the BEA industry accounts 

(including the farm industry) reflects the production of R&D output, and (Rosenthal, et al. 2014) 

incorporates R&D in both the output and input side of the BEA/BLS industry-level production account. 

In practice, on the output side of the account, if R&D is conducted in the same establishment as the 

primary output, this spending on R&D (total expenses) should be added to the value of gross output of 

the industry, and industry value added should increase by the same amount. If there is any own-account 

R&D, the growth rate of the price index for industry output is now an aggregate of the pre-R&D output 

price and the R&D price.45 That is, industries that undertake R&D are modeled as producing two distinct 

outputs. On the input side of the account, flows from R&D capital should be priced by the implicit rental 

rate. It’s noteworthy that while the official GDP by Industry accounts conceptually allows for R&D 

spending by any industry, the current version does not attribute any R&D spending to the Farm sector.

R&D in the ERS Agricultural Productivity Account

Currently, the ERS does not consider R&D on either side of their agricultural production account. This 

section provides some background on R&D measurement and discusses the rationale for and feasibility 

of incorporating measures of R&D into the measure of agricultural productivity. R&D activity has played 

a clear role in the advancement of agricultural production, but the case for adjusting the ERS 

productivity accounts to reflect R&D is not clear cut. 

Between 1948 and 2011, the period covered by the current ERS productivity account, it is not obvious 

what, if any, own-account R&D was taking place on farms. Potential investments in R&D include 

spending on improved breeding methods (for animals and plants), worker safety, and seed 

improvement. Anecdotal evidence from on-farm visits suggests that farmers engage in creating their 

own equipment and other innovations. For example, farmers invest resources in recombining machinery 

parts to create new artifacts, modifying feed ratios and health recommendations, changing application 

of chemicals, and creating GPS maps to inform fertilizer recommendations. These are difficult to 

conceptualize, let alone measure. 

Taking a concrete cast, Monsanto is a company that conducts a significant amount of agriculture-related 

R&D. Compustat reports Monsanto as an agricultural company, implying that R&D spending by 

45 Typically, the R&D output price is based on R&D input price growth, plus a productivity adjustment. See Robbins, 

et al. (2012) for details on the price index and Strassner and Wasshausen (2013) for a discussion of defining 

industry output.

38

 
Monsanto would be treated by Compustat as an output of the agricultural sector within the framework 

of industry-level productivity. But if the primary output of a Monsanto establishment is R&D, not 

agricultural output, then the appropriate place to include this R&D is the R&D sector because outputs 

are grouped by the primary good of the establishment. According to Monsanto’s website, the company 

produces agricultural and vegetable seeds, plant biotechnology traits, and crop protection chemicals. An

open question is whether any R&D takes place as secondary production in establishments where the 

primary output is farm products, for example seed production. If not, then no adjustments to the ERSmeasured farm output are required in this particular case.46 

It’s also noteworthy that the NAICS classification for Farm includes breeding related establishments. To 

the extent that there has been R&D in breeding by these establishments over the time series, an 

adjustment to farm output may be warranted. 

In summary, own-account R&D spending by farms should be added to farm output if it exists, but 

additional research is required to determine what type of farm R&D was conducted, when it was 

conducted, and by whom it was conducted. Further, according to the SNA, “the salaries of employees 

engaged in own account capital formation are directly classified as acquisitions of capital formation,” so 

any paid work done on the farm to build future productive capacity is potentially spending on capital 

formation and should be treated as such (European Commission et al. 2009).

47 

The input side of the productivity account should, ideally, account for all inputs used in production of 

R&D including the flow of services from R&D assets, regardless of the original investor in the R&D. Due 

to limited source data, the investment data by industry and asset that is produced by the BEA (and 

which underlies the ERS capital estimates) includes R&D investment, but the R&D assets are allocated to 

industries by the original funder. Thus, for example, farm-related R&D conducted by the government is 

allocated to the government sector, even though this investment yields a direct service flow to the 

agricultural sector. 

Reconsidering the Monsanto example, presuming that Monsanto were not classified in the Farm

industry, then allocating R&D investment to the capital stock and services of Monsanto is consistent 

with productivity measurement theory, even though the output of Monsanto’s R&D is used by farms. 

The reason why this is a reasonable treatment is that R&D investments and capital used by Monsanto 

presumably leads to quality improvements in farm inputs which are purchased and measured on the 

input side of the agricultural productivity account. 

The recognition of R&D as an investment good reinforces the need for constant-quality prices of outputs 

and inputs in productivity accounting. The provision of government R&D to the agricultural sector is not 

captured in the ERS-productivity estimates, but the unmeasured contribution of government investment 

and services is broader than the single contribution of R&D, and not unique to the agricultural sector.48

In general, national accounting standards and practices do not address the contributions of government 

to industry production, thus government R&D services provided to the agricultural sector need not be 

moved to the input side of the agricultural productivity account, even though a theoretically correct 

measure of TFP should include this input.49

46 The NAICS classification is establishment based so that establishments within a company may be classified to 

different industries.

47 This may be more appropriately thought of as organizational capital, which is an active area of research. 48 E.g., military, weather forecasting, highways, GDP statistics. 49 The government produces both investment and consumption goods. If one allows government production of 

consumption goods to be used as intermediate input by the private sector, official nominal GDP decreases by the 

value of the intermediate purchases, and industry intermediate input would now include these purchases. If one 

39

 
Recommendation 

ERS should follow developments in the literature on accounting for R&D in the productivity measure, 

and, if minimal R&D is conducted on farms, include a note of explanation in the methodology 

description indicating why sectoral R&D is not incorporated in the accounts (Priority B). 

IX. Alternative Assumptions

The current ERS policy toward growth accounting maintains the standard basic assumptions that a) 

factors are paid the value of their marginal products, b) there are no adjustment costs, c) input use is 

correctly measured, d) outputs and inputs are measured in constant-quality units, e) production exhibits 

constant returns to scale, f) firms maximize profit, and g) all input and output markets are perfectly 

competitive. Further, capital utilization is governed by the capital valuation rule (discussed in the nonland capital draft). Capacity utilization is implicitly reflected in the internal, shadow value of capital. This 

value is computed assuming continuous steady-state, long-run equilibrium. Changes in input quality are 

accounted for generally through hedonic pricing models or matched-model methods. While output 

quality is assumed fixed over time, output quality changes potentially could be dealt with by 

constructing constant-quality adjustments for output or as deviations of prices from marginal revenue.

The logic for these assumptions is the perspective that, over the longer term, most of these assumptions 

are easier to justify and it is more appropriate to analyze productivity and its growth in terms of the 

sources of long-term growth. However, there are important examples when long-run equilibrium in the 

agricultural production sector has been a heroic assumption – the 1970s when there was a rapid 

expansion of land and capital (including animals) and the middle-to-late 1980s when there was a period 

of significant financial stress. The significance of the assumption that this sector is always operating at 

the steady state impacts how the marginal productivity of capital relates to the rate of return on capital 

(OECD 2009, p.17-18) and the consequent deviations from productivity growth measurement. 

While it is rare that an input is fully constrained to the point that its level cannot be changed, an input 

can present a limited degree of flexibility in adjustment which leads to its alternative characterization as 

a quasi-fixed factor (i.e., a factor that requires adjustment costs). Oftentimes, a firm cannot readily 

accommodate large changes in factor use within a single production period. This inability to easily 

absorb large changes can be related to forces that are internally driven (e.g., the firm’s processes and 

organization) or externally driven (e.g., transaction costs associated with expansion or contraction, or 

land markets that are not fluid within a decision maker’s sphere of operation). The implication for nonfreely adjustable inputs is that some additional costs must be absorbed by the firm beyond the 

acquisition cost. The consequence of this inflexibility is an economic environment which places a high 

cost on adjusting the factor level. Consequently, the marginal product of the quasi-fixed factors bear an 

extra cost (Eisner and Strotz 1963; Rothschild 1971; Basu, Fernald and Shapiro 2001). Conversely, the 

characterization of freely adjusted factors implies that altering the levels of these factors does not 

impose a penalty on the firm beyond their acquisition cost.

A more appropriate view may be the trichotomy of a) the current period decision (or short-run), b) the 

steady-state equilibrium, and c) the adjustment phase between the current decision and the steadystate equilibrium. The deviations from value of marginal product pricing are the impact of an additional 

unit of the factor that shifts the internal shadow value of quasi-fixed factors. This adjustment phase has 

been characterized as the temporary equilibrium (Berndt and Fuss 1989) which occurs when the shadow 

allows government capital to be used as a productive input by other sectors, aggregate investment is unchanged, 

but the industry capital accounts would have to be reorganized. We are not aware of any proposals to make these 

adjustments.

40

 
value of any input and/or output differs from its market price. In long-run equilibrium or in static 

situations, the shadow values equal market prices for all inputs and outputs. That is, the firm is 

presumed to be making all the right decisions in moving toward the steady-state equilibrium although it 

may not be there yet. 

In an intertemporal production decision environment, there is no longer a short- run period and a longrun period, but rather a continuum of runs. Alchian (1959) and Smith (1961) are two early efforts 

offering a more complete description of dynamic producer behavior by focusing on the minimization of 

the discounted stream of costs. Such a characterization focuses on intertemporal costs as a stock 

concept, while the nested current-period decision problem involves a flow.

The consequence is that the capital factor disequilibrium impact is a component of input growth (Luh 

and Stefanou 1991). That is, we have variable input growth, capital growth (which depends on the firm’s 

shadow value of capital), and growth in the shadow value of capital (which is an internal, endogenous 

‘price’). The calculation of the disequilibrium involves two components: 

1. Valuing the infusions/elimination of the capital stock using the (internal) shadow value of 

capital, and

2. Accounting for changes in the shadow value of capital as the capital stock is adjusting.

When firms are undercapitalized, the first component has a dampening effect on aggregate input 

growth and the second component has an expansionary effect on input growth. When the rate of 

investment is increasing, the overall impact is to dampen input growth. The period of the 1970s was a 

capital expansionary period in U.S. agriculture, so we can expect that productivity growth was undermeasured. During the 1980s firms were overcapitalized and looking to relieve financial stress, so we can 

expect productivity growth to have been biased upwards. The analytical consequence of such 

disequilibria is the need to find the relevant shadow values of the capital input series. This would involve 

an annual calculation either through re-estimation of econometric models [Epstein and Denny 1983] or 

calculation of a nonparametric-based intertemporal cost minimization [Silva, Lansink and Stefanou 

2014]. 

Similar to capital, the assumption that labor input is paid its marginal product in each period is easy to 

challenge. For example, under the hypothesis that some forms of education are merely a signal from 

workers to employers, additional education may have no actual value in the production process. 

Furthermore, worker intensity may vary over the business cycle, breaking the link between hours as a 

measure of labor input. See Basu, Fernald and Shapiro (2001) for an example of a macro model that 

incorporates labor effort.

Recommendation 

Although a disequilibrium approach to capital factors is not widely applied in the productivity literature, 

we recommend that ERS engage the scholarly community in an examination of effective ways to 

account for disequilibrium (Priority C). While there are always legitimate concerns about mixing 

approaches in the construction of data series, ERS has already been a leader in this regard in its 

econometric estimation of hedonic prices and series used in the construction of indexes. 

X. Website

The AAEA Task Force on Measuring Agricultural Productivity (Gardner, et al. 1980) recommended that 

the productivity statistics be made readily available in electronic form. That has been more than fully 

accomplished. All data are maintained electronically. Aggregates and sub-aggregates are publicly 

41
available and accessible from their website. Details of individual commodities and inputs are generally 

available on request. 

The ERS Agricultural Productivity in the U.S. website (http://www.ers.usda.gov/dataproducts/agricultural-productivity-in-the-us.aspx) is the primary means to disseminate ERS productivityrelated products, including the data, results, methodology, and related research. It is also accessible 

through the Agricultural Productivity homepage: http://www.ers.usda.gov/topics/farmeconomy/agricultural-productivity.aspx through the “Agricultural Productivity in the U.S.” link in the 

right sidebar under Related Data. The website includes downloadable Excel files with productivity 

measures and quantity and price indexes for the U.S. and for each of the contiguous 48 states. 

For the U.S. it includes a) productivity measures for several time periods, sources of growth (output and 

input with input decomposed into labor, capital, and materials and further decomposed into quantity 

and “quality” growth) and b) annual price and quantity indexes for the output and input aggregates as 

well as several output and input sub-aggregates. It’s worth noting that the ERS definition of “quality” in 

their tables may be nonintuitive for novice data users.50

The sub-aggregates are tiered. In the first output tier there are three sub-aggregates: livestock (including 

miscellaneous livestock products not separately identified), crops, and farm-related output (which 

includes output of goods and services from certain non-agricultural or secondary activities; these are 

activities closely related to agricultural production for which information on output and input use 

cannot be separately observed). In the second tier, livestock is disaggregated into meat animals, dairy, 

and poultry and eggs; crops are disaggregated into food grains, feed crops, oil crops, vegetables and 

melons, fruits and nuts, and other crops (which include sugar crops, maple, seed crops, miscellaneous 

field crops, hops, mint, greenhouse and nursery, and mushrooms). 

The first input tier consists of three sub-aggregates: capital, labor, and intermediate inputs. In the 

second tier, capital is disaggregated into durable equipment, service buildings, land, and inventories; 

labor is disaggregated into hired and self-employed labor; intermediate inputs are disaggregated into 

farm-origin, energy, fertilizer and lime, pesticides, purchased services, and other intermediate inputs.

In September 2013, the U.S. indexes were provided on the website for the years 1948-2011. Recognizing 

the huge effort required to gather and process the various sources of essential data utilized in 

developing these indexes, we commend ERS for providing them in such a timely fashion and urge that 

the current timeline of the statistics be continued and, if possible without sacrificing quality, even 

shortened. 

State-level productivity, price, and quantity estimates that cover 1960-2004 have been available for 

about a decade, but were first published on the website in September 2013. Although they do not 

satisfy all desirable properties of spatial indexes,51 these indexes are spatially as well as temporally 

comparable and transitive. As with the U.S. aggregate information, they include productivity measures 

for several time periods and annual price and quantity indexes for the output and input aggregates as 

well as several output and input sub-aggregates. The output price and quantity sub-aggregates are the 

same as the first tier of U.S. sub-aggregates – livestock, crops, and farm-related output. The input price 

and quantity sub-aggregates have two full tiers and a third partial tier. The first input tier is the same as 

for the U.S. – capital, labor, and intermediate inputs. In the second tier, capital is disaggregated into 

land and capital services excluding land; labor is disaggregated into hired and self-employed labor; 

50 The ERS definition of quality in Table 2 is the difference between weighting schemes in input aggregation. Some 

others developing productivity estimates refer to this as “composition”.

51 E.g. circularity and identity.

42

 
intermediate inputs are disaggregated into energy, chemical inputs, and other intermediate inputs. In 

the third partial tier, chemical inputs are disaggregated into fertilizer and lime, and pesticides. 

The availability of productivity data on the website is a substantial improvement in making the 

agricultural productivity accounts and major quantity and price indexes used in their development 

publicly available. Since a primary function of ERS productivity accounts is the data product, it is 

imperative that the website that hosts the data not only provides the data but also includes pertinent 

information that helps stakeholders use the data. To be most effective, the website should be a) 

accessible and findable, b) accurate, c) complete (in the sense that the contents cover the ERS 

deliverables) and up-to-date, d) searchable, e) legible, and f) explain the role of the productivity 

program within the context of ERS’s mission and related work. We evaluate each of these criteria in 

turn. Overall, the ERS productivity program’s website is effective, but some changes should be 

considered.

Accessibility and Findability

The Agricultural Productivity homepage is accessible via the ERS homepage (http://www.ers.usda.gov/) 

under “Topics->Agricultural Productivity“. It includes a brief overview of the program with appropriate 

program contacts clearly posted on the bottom of the page. The webpage sidebar splits program 

deliverables into easy-to-access sections: Related Data, Related Reports, and Related Amber Waves 

Articles. 

Information from the productivity program is findable. Searching for “agricultural productivity” in both 

Google and Bing ranks the ERS Agricultural Productivity homepage among the first sites. From the ERS

homepage, searching for productivity yields the Agricultural Productivity homepage as the third result. 

There does not appear to be a direct link from the ERS homepage to the agricultural productivity 

statistics, only to the Agricultural Productivity homepage. Clicking on “Data” on the ERS homepage 

provides a long list of products, the 6th of which links to the Agricultural Productivity in the U.S. website 

with links to the downloadable national and state-level Excel tables. Although there are several ways to 

get to the agricultural productivity pages, links to the productivity statistics might be featured more 

prominently on the ERS homepage. 

Accuracy

The descriptions on the Agricultural Productivity in the U.S. website appear to be accurate, and without 

broken links. One small note is that the “Findings, Documentation, and Methods” section in the left 

sidebar mentions that productivity provides a summary statistic for welfare (paraphrasing). While 

appealing, the economic correspondence between productivity and welfare is often avoided except in 

more academic ponderings. 

Accuracy of the website data relative to their internal calculations was not examined by the committee 

due to limited access to the ERS internal calculations. Verifying that the data posted to the website 

matches internal calculations should be standard part of the ERS web review, if it is not already.

Completeness

As previously noted, the core U.S. and state-level accounts data and methodology are accessible from 

the Agricultural Productivity homepage under the “Related Data” links. In addition to the link for 

“Agricultural Productivity in the U.S., there is a link for “International Agricultural Productivity”. 

The Agricultural Productivity in the U.S. website contains the national data, the state-level data, and a 

findings, documentation, and methods section. The national data include price and quantity of the 

components of farm output and farm input. From these data series, users should be able to replicate the 

43
published ERS-productivity series (this was not verified). The state-level files contain a similar level of 

detail and also state-level sub-aggregates, but only for the period 1960-2004. 

The website International Agricultural Productivity contains international data and productivity 

estimates for 174 countries for the period 1961-2010 and a documentation and methods section. 

Productivity estimates, gross agricultural production, and factor shares and quantities of inputs for each 

country are included in the downloadable data spreadsheets. Downloadable productivity estimates are 

also available for regions.

For both websites, remaining questions are: a) what underlying details of the accounts and their 

components (sub-aggregates) are available, and b) how much of the underlying data detail should be 

posted to the website, since the final estimates are built up from underlying source data. The desired 

goal would be sufficient completeness to enable outside users to replicate the results from the ground 

up and to use the source data for additional purposes. Obviously, that goal must be balanced against 

releasing underlying source data and estimates that may not be as high quality as the top-line estimates 

and also against the burden of building and maintaining an online database of all the source data. 

Nonetheless, it should be pursued to the extent feasible, with priority given to the national accounts and 

followed by the state accounts. Several stakeholders also recommend that more detailed data be made 

available on the website. 

Basic documentation is available on the website and is accessible, although the committee found that 

many important details are missing. In particular, details on the source data and current methodology is 

thin. The committee struggled with the available documentation to understand how the current 

estimates were built up from the available source data.

The “Related Reports” section on the Agricultural Productivity homepage is not linked to the “Related 

Data” pages, so one must go back to the homepage to get to the related reports or vice versa. It is

noteworthy that the publications related to the construction of the statistics are not included in the 

“Related Reports“ section. It’s also noteworthy that the “Related Reports” webpages do not link to the 

“Related Data” webpages nor vice versa. An alternative would be to create a linked “Related Reports” 

page that contains the pertinent reports and is cross-linked with the “Related Data” pages.

Searchability

Data is posted to the website in Excel format, and related reports are posted in a combination of html 

and PDF format. Because the data is posted in Excel, it is not interactive; that is, users cannot make 

queries to request particular components of the data. This is not a major point of concern given the 

nature and primary users of the data.

The research and related reports are posted in the appropriately named sections of the website, are 

easy to locate, and appear to be searchable through the ERS homepage.

Legibility

The website is viewable and legible on various screens and browsers. There does not appear to be a 

mobile version of the webpage, but a mobile version is probably extraneous.

Website and Productivity Program in Context

The productivity program website gives a brief overview of farm productivity but does not put the 

program in context of the USDA mission, nor does it put the agricultural productivity statistics in the 

larger context of industry-level productivity analysis. The program should consider including this 

information in some form on its website.

44
Recommendations

1. Provide detailed documentation online and note ad hoc adjustments to data or deviations from 

the general procedure (e.g., if fixes were required due to negative implied capital rental rates)

(Priority A). 

2. Expand the website to provide timely access to more detailed data and procedural detail 

underlying the quantity and price aggregate and sub-aggregate national and state-level statistics 

(Priority A). The detailed data should include primary data used in the development of each 

statistic, processed only sufficiently to be non-confidential. The procedural detail should be 

sufficient to enable outside users to replicate the results reported on the website from the 

ground up and to use the source data for additional purposes. The data should be maintained in 

a user-friendly environment on the website for convenient downloading and use. 

3. Include a paragraph on typical release dates in addition to the current practice which is to post 

date of “next update”, which as it turns out is blank (Priority B). 

4. At each release, post a note describing revisions and reasons for revisions (Priority B).

5. Change exposition on website about welfare (Priority B). 

6. Include links to other productivity related data and research including the BEA/BLS industrylevel production accounts, BLS Non-Farm Productivity, European Union (EU) KLEMS, and World 

KLEMS (Priority B). 

7. Add a link to a “Related Reports” page that contains links to the pertinent related reports

(Priority C). 

45
PART 3 

Part 3 of this report reviews the State-level productivity accounts, the cross-country comparisons, and 

compares ERS measures to alternatives produced in the research community. Additionally, this section 

includes information on stakeholder feedback on the productivity accounts. 

XI. State-level productivity

During the 1990s and 2000s, ERS prepared state-level productivity measures. They began with the year 

1960 and ultimately included estimates through 2004. They also provided underlying price and quantity 

data series for outputs, inputs, and several disaggregated categories of each component. Since 

September 2013, the historical estimates have been publicly available on the ERS Agricultural 

Productivity in the U.S. website. The productivity measures and the accompanying price and quantity 

series have been widely used by the research community. 

1980 AAEA Task Force Recommendations

The AAEA Task Force (Gardner et al., 2000) recommended that ERS continue to develop regional total 

productivity measures. 

ERS Response

ERS responded to the AAEA Task Force recommendation by developing state-level productivity 

measures for the contiguous 48 states. These accounts have been used extensively in a wide variety of 

research studies and have been influential in policy analysis as well. They constitute a high quality panel 

data set that facilitates econometric model estimation at the national level with greater precision than 

could be achieved with only the national-level accounts. They also permit examination of state and 

regional issues of importance to local legislators and producer groups. 

Unfortunately, the productivity measures have not been updated since 2004 largely because the NASS 

Farm Labor Survey was discontinued which limited ERS ability to develop spatially reliable measures of 

the labor input. State-level price and quantity data for some outputs and inputs have been updated to at 

least 2008, but have not been publicly released.

The most recent state accounts were developed using procedures generally similar to the national 

agricultural accounts. Data on outputs, land input, capital stocks, and capital input are first compiled for 

each state before being aggregated to the national level. 

Outputs

Data from the NASS surveys on output cash receipts, quantities marketed, gross production, and 

inventory change are compiled by commodity in each state before being aggregated to the national 

level. Data on government payments from the USDA Farm Services Agency’s Kansas City office are also 

compiled by commodity in each state before being aggregated to the national level.

Inputs

Although state-level land price and implicit quantity indexes are constructed as an intermediate step in 

aggregation to the national level for the national accounts, a different procedure is followed in the state 

accounts. Spatial price indexes and implicit quantity indexes of land are calculated using a hedonic 

approach to account for differences in land characteristics across states. This permits estimation of a

quality-adjusted price index. This procedure estimates the price of land as a function of soil acidity, 

salinity, moisture stress, irrigation, population accessibility (population density and distance) and other 

46
characteristics as well as state dummy variables. These are used to construct a quality-adjusted price 

index at the county level to use in obtaining the implicit quantities. 

Tornqvist indexes of land prices and implicit quantities at the state level are obtained based on the 

county level information. The value of service flows at the state level are the state-level stocks 

multiplied by the rental rate for land. The rental rate is the expected real rate of return multiplied by the 

state’s land price index. The expected real rate of return for land is an ex-ante rate of return calculated 

in the same way as for non-land capital. It is the nominal average yield on investment grade corporate 

bonds (AAA rated bonds) less the inflation rate captured by the implicit GDP deflator, where inflation is 

modeled as an ARIMA process.

At the national level, the value of service flows from land is obtained as a residual from the imposition of 

the accounting identity. In the state accounts, the value of service flows from land is obtained by 

multiplying the state-level stocks by the expected real rental rate for land. The accounting identity is not 

imposed in the state productivity accounts.

Measures of capital stocks and capital input are developed for each state. Capital stock for each asset 

type is constructed using the perpetual inventory method. User costs for each asset type are obtained 

following the same procedure as for the U.S. aggregate. Investment data is obtained from the ERS 

Resource and Rural Economics Division. BLS asset price deflators from the Producer Price Index for 

automobiles, motor trucks, wheel-type farm tractors, and agricultural machinery excluding tractors are 

used as investment deflators. The implicit price deflator for nonresidential structures is from NIPA. 

Aggregation for each state is accomplished by aggregating over the different capital assets using the 

asset-specific user cost indexes as weights. 

ARMS provides expenditure data for intermediate inputs. For the state accounts, hedonic price 

functions of fertilizer and pesticides are estimated for individual states and the United States. Although 

not publicly released, these input groups and energy have been updated for the states through 2008. 

For the national accounts, the hedonic price functions are conducted at the national level rather than 

being aggregated across states. This could lead to some of the inconsistency between the state and 

national accounts. 

Data on purchased inputs and investment come from ARMS. 

Until 2002, the NASS Farm Labor Survey was used as the primary source of data on hired, self-employed, 

and family labor. It provided sufficient detail to reliably estimate state-level labor quantities and prices.

The same type of matrices for hours worked and hourly compensation were developed for each state as 

for the U.S., controlling for hours worked and compensation totals based on USDA data for the state. 

The farm sector matrices used for the U.S. aggregate were combined with state-specific demographic 

information available from the Census of Population. This was accomplished using the RAS procedure 

(Jorgenson, Gollop, and Fraumeni 1987). Using the cross-classified data, indexes of labor input were 

constructed by state. 

Since the NASS Farm Labor Survey was discontinued in 2002, an adequate source of information for 

updating the cells in the matrices has not been available. At the U.S. level, information is now obtained 

from the Current Population Survey, but sample size is too small to use this source to update matrix 

elements of the worker classification at the state level. The discontinuation of this survey played a major 

role in the decision to discontinue updating the state-level productivity accounts after 2004. 

With ERS and NASS participation, hired labor data used in the national accounts now come from BEA. 

Self-employed labor data in those accounts are from the BLS and are based on the Census of Population 

and the Current Population Surveys. Unfortunately, these sources do not provide sufficient detail to 

47
reliably estimate state-level labor quantities and prices via the cross-classification method. However, 

some alternatives have been identified by ERS personnel that might provide minimally sufficient 

reliability to surmount this obstacle. BLS funds a survey of hired labor. If access to the data can be 

obtained by ERS, it could provide a sufficient information base to compute state-level hired labor 

quantities and prices. The American Community Survey provides additional data that could be useful in 

combination with other sources. ARMS data separate hours worked by hired and self-employed labor. 

While it will not be possible to develop state-level labor quantity and price series with the matrix 

element accuracy possible from the NASS Farm Labor Survey, sufficient data sources appear to be 

available to provide estimates of adequate quality to enable the state-level productivity accounts to be 

reinstated. 

Spatial indexes

ERS currently uses the multilateral chain-linked Caves-Christensen-Diewert index to construct state-level 

input and output price indexes in each state and year.52 This index solves the intransitivity problem of 

binary indexes, but O’Donnell (2013) documents that it does not satisfy the circularity property and is 

thus biased. He demonstrates that three alternative multilateral indexes (Lowe, geometric Young, and 

Färe-Primont) satisfy nine desirable properties, including transitivity and circularity. Each is a properly 

constructed multilateral index and is preferred to the Caves-Christensen-Diewert index. 

Our Assessment 

Continue the state-level accounts 

The lack of data of sufficient quality is most acute for labor because it hinders development of reliable 

state-level labor price and quantity series. The loss of reliable farm labor data has been primarily 

responsible for discontinuing the widely used and important state-level price, quantity, and productivity 

series. This is a great hindrance to high quality research on the economics of U.S. agriculture important 

for public and private decision making. 

Our independent assessment, which is supported by input from several stakeholders, is that the statelevel accounts are too important to be discontinued regardless of data and resource challenges. They 

provide the foundation for the U.S. aggregate accounts and give more detail, consistency, and 

robustness to the U.S. aggregate. These panel data are important in econometric analysis by achieving 

greater statistical efficiency and reliability, and they are widely used. Further, although they may not 

provide the same quality, other options (e.g., BEA/BLS) exist for developing national agricultural 

productivity accounts. No other options exist for reliably developing state-level agricultural productivity 

accounts. 

While U.S. aggregate accounts trace performance across time, they do not provide understanding of 

performance across space. The state-level series are essential to understand differences in regional 

performance driven by differences in endowments and comparative advantage across the U.S. regions. 

They allow examination of the supply of geographically-specific commodities and enhance our 

understanding of the impacts of commodity-specific policies in particular regions and how they alter 

regional terms of trade and geographic distribution of income, in particular returns to labor. Rural 

development, as well as food security policy, is informed by knowledge of the impact of innovations on 

labor and labor mobility across regions and across sectors. The usefulness of the U.S. productivity 

accounts is greatly enhanced when we understand performance of the regional economies and the 

differential impacts of federal policy on regional and state performance. 

52 The ERS Agricultural Productivity in the U.S. website indicates the Elteto-Koves-Szulc index is used to construct 

these indexes.

48

 
The importance of this assessment is evident by the large amount of research and policy work that has 

made use of the state-level data. A considerable number of researchers and analysts have used the 

state-level data for research. This includes a wide array of government and university researchers. For 

example, a Google search of Ball’s productivity research yielded 80 publications, the 4th most highly 

cited of which was Ball et al. (1999) that developed and explained the state-level quantity and price 

series developed by ERS for TFP analysis. The large number of citations helps document the need to 

revive this part of the ERS program. The importance for high quality research of continuing and 

strengthening the state-level series was also registered by stakeholder input. 

Continuing the state-level accounts will not only require additional analytical and data processing effort 

by ERS personnel but will require coordination with the data collection agencies to ensure that farm 

labor data are collected in a way that is regionally reliable and available for interagency use. 

Spatial aggregator index

Alternative spatial aggregation indexes that satisfy all nine desirable properties of spatial aggregation 

indexes, including identity, transitivity and circularity, warrant exploration. They include the Lowe, 

geometric Young, and Färe-Primont indexes. 

Comparability between national and state accounts

The state-level price and quantity indexes have been developed using procedures generally consistent 

with those used to develop U.S. indexes (Ball et al. 1999). We commend ERS for the care used in 

developing the state-level series to ensure considerable consistency with the U.S. series. However, our 

examination of the data available on the ERS Agricultural Productivity in the U.S. website reveals some 

important differences:

• Gross receipts equal gross expenditures in the U.S. series but not in the individual state series 

nor in the sum of the state receipts and expenditures.

• The sum of gross state receipts is not equal to U.S. gross receipts, nor is the sum of gross state 

expenditures equal to U.S. gross expenditures.

Ball et al. (1999, p. 165) provide one explanation for the second difference. They note:

“Interstate deliveries of output (livestock and feed) from farms in one state to farms in other states 

... enter state-specific intermediate input and output accounts. From the perspective of the 

aggregate U.S. farm sector, however, these interstate transactions are wholly internal to the 

nationwide farm sector and therefore do not enter the aggregate accounts.” 

This would imply that the U.S. gross output receipts and gross input expenditures should always be 

smaller than the sum of the corresponding state series. That is not the case in the online data series. In 

some years one or both is smaller and in other years larger. On average, U.S. input expenditures are 

smaller, but output receipts are larger. Consequently, greater consistency between the two series is 

needed as well as clearer explanation of reasons why they cannot be totally consistent, e.g., theoretical 

reasons, lack of consistent data between the two levels of geographic aggregation, data revisions at the 

national level that have not been incorporated into the state-level accounts. 

State-level price and quantity series reported on the website (USDA 2014) are not for the same subaggregates as the national series. Currently, there is an additional tier of output sub-aggregates for the 

U.S. than for the states. It would be helpful to report the additional tier in the state-level series. In the 

second tier of input sub-aggregates, the U.S. series has a larger number of disaggregated capital 

categories. It also has a larger number of disaggregates within the other intermediate input category 

but does not have the chemical aggregate of fertilizer-lime and pesticides. 

49
Recommendations

1. Continue to develop and publish state-level total productivity measures as well as price and 

quantity series – strongly recommended (Priority A). 

2. Cooperate with other government agencies to achieve the lowest cost method of collecting data 

of sufficient quality to enable the state-level accounts to be extended and maintained (Priority 

A).

3. Investigate the possibility of using information in the American Community Survey to update 

matrix elements in the state labor accounts (Priority A). 

4. Ensure consistency between the national and state accounts where possible, and explain 

circumstances that prevent total consistency where it is not possible (Priority A).

5. Report state-level price and quantity series on the website for the same sub-aggregates as the 

national series (Priority B).

6. Update the state-level accounts on the same schedule as the national accounts (Priority B).

7. Place more underlying data detail on the website (Priority B). 

8. If feasible, include Alaska and Hawaii in the accounts (Priority C).

9. Replace the Caves-Christensen-Diewert spatial aggregator index with a Lowe, geometric Young, 

or Färe-Primont index (Priority C).

XII. Cross-country comparisons

There is considerable interest in cross-country comparisons that investigate international 

competitiveness and convergence in agricultural productivity across countries. When markets are 

perfectly competitive and operating in long-run equilibrium, then price changes are proxies for cost 

changes. Under these assumptions, relative output prices can proxy as a competitiveness measure for 

purposes of international comparisons, assuming that the quality of output is the same across countries. 

If countries share a common stock of knowledge and access to technologies, and if they face no 

structural barriers to sharing, then theory suggests that prices should change at the same rate. When we 

do not see this equivalence in price change, we tend to look at the policy incentives and structural 

differences to explain why. 

The ERS program is a leader in the construction and analysis of international comparisons of agricultural 

productivity. The program has focused on US-EU nations and OECD nation comparisons. The ERS 

International Agricultural Productivity website provides Excel spreadsheets with indexes for most 

countries as well as a “Documentation and Methods” link. Fuglie and Wang (2013) provide an 

interpretive overview. In addition, there are several journal articles and chapters that address 

international comparisons (Ball et al. 2001; Ball et al. 2010; Wang, Schimmelpfennig, and Fuglie 2012).

A major challenge of the program is to ensure that data construction is comparable across nations. The 

EU has constructed a system of integrated economic accounts that identifies the concepts, definitions, 

accounting rules and uniform classifications to be used by EU member states that produce economic 

data. There are three key adjustments needed to ensure that the U.S. series are comparable for 

comparisons with EU Member States:

• Inseparable outputs: The EU protocol accounts for outputs, intermediate consumption, 

compensation of employees, labor input, and gross fixed capital formation that cannot be 

separated from information on main agricultural activity. These are referred to as ‘inseparable 

output’ and are reported as agricultural activity under that designation. An example is 

agrotourism activities. ERS products recognize this complication and make adjustments to 

ensure consistency for the purposes of the international comparison. Whether this adjustment 

method is reasonable is another issue. To the extent that on-farm assets and activities are 

50
leveraged to create value for the enterprise, it can be considered a portfolio decision taken at 

the farm level. The ‘inseparable’ output is just that; it demonstrates a technological jointness in 

the original sense of the concept dating back to Carlson (1939). 

• Choice of index formula: The EU protocol measures changes in volume using the Laspeyres-type 

index and changes in price using Paasche-type indexes. The rationale for using these indexes, 

which are generally regarded as inferior to Divisia-type indexes, is that they can be created from 

less intensive data sources. Although U.S. data are aggregated using more appropriate Tornqvist 

and Fisher indexes, ERS makes the necessary adjustments in the cross-country comparisons to 

ensure consistency. Given the European data are available at the farm level in the Farm Data 

Accountancy Network, the re-computation of the EU data are executed at a comparable level as 

the U.S. series. 

• Capital: The EU protocol does not generate a standard procedure for measuring the user cost of 

capital. When precise information on the average probable economic life of a particular stock of 

capital goods is unavailable, the protocol recommends the perpetual inventory method. The 

reference period acquisition price is the replacement value of the assets during the reference 

year. The linear depreciation method is recommended in the protocol, although the geometric 

depreciation approach may be appropriate in certain cases.

a. Livestock is excluded as a component of the consumption of fixed capital because a) 

withdrawal of animals that form the productive herd may be a function of the economic 

environment (e.g., slaughter prices, price of animal feed), and b) animal productivity and 

economic value is linked to age but not by way of a direct continuous function.

b. In EU-U.S. cross country studies, construction of the capital input and rate of return 

measurement follows the ERS protocol. They treat the relative efficiency of new capital 

goods as being the same across countries. 

• Labor and Intermediate Inputs: In addition to direct basic wages and salaries, gross wages and 

salaries in the EU protocol include in-kind compensation (goods and services provided by 

employers to their employees (and family members) free or at a reduced price. There is no 

apparent modification for quality adjustment in labor. No mention is made in publications 

reporting ERS cross-country comparisons how the quality adjustments used in the U.S. series are 

juxtaposed with the EU Member State series. When reviewing the relative labor price for the

U.S. and EU Member States in Table 6 of Ball et al. (2010), the U.S. relative labor price exceeds 

the other nations from the mid-1980s to 2002 (the last year reported). It is not clear to what 

extent quality-adjusted labor is driving this result. The same critique applies to intermediate 

inputs (most notably, pesticides) for which the U.S. uses a hedonic price series to estimate 

quality-constant prices and quantities. 

Across a wider set of countries, challenges include differentiating land quality (e.g., irrigated vs. nonirrigated, semi-arid vs. arable/pasture), cropland definitions (e.g., distinguishing arable/permanent/

pasture), gaps in series, etc. The ERS and country input series are typically grouped into five categories 

(land, labor, machinery capital, livestock capital, and material inputs) and then cost shares are used to 

combine them into an aggregate input (Fuglie 2012). In the absence of complete data series at the 

country level, the construction of the country series often uses a representative country to serve as a 

proxy for the cost shares for other similar nations. For example, Brazilian cost shares in livestock 

production are applied to South America, West Asia and North Africa on the basis that this latter group 

of nations, like Brazil, are middle-income countries with relatively large livestock sectors (USDA 2013). 

These challenges add to the concern about how comparable these series are across nations.

51
Recommendations 

1. ERS should emphasize that cross-country comparisons are really research work and establish 

whether they are an integral part of the ERS agenda (Priority A).

2. The methods used have presumably passed some peer review (because they have been 

published), but there is not a consensus on these methods, in contrast to the well-established 

approaches codified in, for example, the OECD manual on measuring productivity. This work 

raises the question whether ERS series that are quality adjusted (and U.S. specific) should be 

compared to series in other nations that are not quality adjusted (Priority B). 

XIII. ERS Measures of Productivity Compared to Alternative Sources

There are several alternative estimates of agricultural productivity. In this section, the ERS measures of 

productivity are compared to those of Jorgenson, Ho, and Samuels and those of InSTePP.

Comparison with Jorgenson, Ho, and Samuels

In ongoing research into the sources of U.S. economic growth, Dale Jorgenson and collaborators have 

constructed measures of outputs, inputs, and productivity in the farm sector (e.g., Jorgenson, Gollop 

and Fraumeni 1987; Jorgenson, Ho and Stiroh 2005). The conceptual and methodological framework of 

the Jorgenson accounts is similar to that of the ERS accounts, and the empirical results for the period as 

a whole are generally consistent. However, for estimates within output and input components and for 

subperiods within the sample, there are differences that warrant investigation. This section compares 

the sources of growth in the agricultural sector based on the ERS productivity accounts relative to 

growth estimates in the sector for the period 1948-2010 based on Jorgenson, Ho and Samuels (JHS) 

(2014). 

We note five differences between the methodologies used by ERS and JHS. First, JHS bases estimates of 

output and intermediate input on a time series of input-output tables that underlie the official national 

accounts; thus, their measures are consistent with official totals, such as aggregate GDP. These 

underlying input-output tables have approximately 65 intermediate inputs that flow into the farm 

sector. Second, capital service flow estimates are based on the level of detail in the BEA fixed assets 

accounts. This is a finer level of detail than that used by ERS although many of the detailed assets are 

zero in the farm sector. Third, JHS distinguishes between the capital service flow of corporate and 

noncorporate assets by distinguishing the tax structures facing corporate and noncorporate 

establishments. Fourth, the ERS productivity measures include quality adjustments for pesticides, 

fertilizer, labor services, and tractors. Fifth, the ERS accounts provide a state-level dimension that is not 

available in the JHS industry-level production account. 

For the 1948-2010 period as a whole, TFP growth estimates are remarkably similar when comparing the 

ERS estimates to those from JHS. ERS estimates that TFP grew by 1.46% per year on average over the 

period while JHS estimates that TFP grew by 1.44% per year on average. Details are provided in Table 

XIII.1.

Output growth and the contributions of inputs are slightly different when comparing the sources of 

growth. ERS estimates that output grew slower by about 0.2 percentage points per year (1.53% versus 

1.75%) over the 1948-2010 period. The majority of the slower growth estimate occurs after 1973; before 

1973 ERS estimated faster output growth than JHS.

ERS estimates the flow of services from capital input fell slightly over the period as a whole, while JHS 

estimates a small increase. This is largely due to a negative contribution of capital services estimated by 

the ERS between 1973 and 1995. 

52
Table XIII.1: Agricultural Output Growth and its Sources 

Estimates

1948-

2010

1948-

1973

1973-

1995

1995-

2005

2005-

2010

ERS:

Output Growth 1.53 1.82 1.57 1.52 0.30

Contribution of Capital -0.07 0.09 -0.25 -0.08 0.01

Contribution of Labor -0.50 -0.76 -0.17 -0.66 -0.36

Contribution of Intermediate Input 0.64 1.13 0.40 0.29 -0.01

Contribution of TFP 1.46 1.35 1.59 1.98 0.65

Jorgenson, Ho, and Samuels (2014):

Output Growth 1.75 1.69 1.86 1.93 1.20

Contribution of Capital 0.18 0.18 0.23 0.18 -0.07

Contribution of Labor -0.56 -1.03 -0.32 -0.13 -0.15

Contribution of Intermediate Input 0.70 1.31 0.28 -0.08 1.05

Contribution of TFP 1.44 1.24 1.67 1.97 0.37

Notes: Average annual percentages. A contribution is a share-weighted growth rate. ERS data are 

computed from Table 1 posted on the ERS website (USDA 2014), JHS data provided by Jon Samuels.

Estimates of the contribution of labor input to output growth are broadly consistent for the period as a 

whole. Comparing subperiods, ERS estimates a higher contribution of labor through 1995 and a slower 

contribution after. 

The contribution of intermediate inputs to output growth is similar between the two estimates for the 

1948-2010 period. Discrepancies between the two estimates increased after 1995.

Estimates of TFP growth basically match for the period as a whole. By subperiod, the results line up 

closely as well, except for the 2005-2010 period where ERS estimates significantly higher TFP growth 

rates. The discrepancies in later years appear to be tied to the different estimates of output and 

intermediate input growth.

Comparison with InSTePP53 

The International Science and Technology Practice and Policy (InSTePP) Center at the University of 

Minnesota maintains an alternative database of productivity accounts. Documentation and database 

archiving is based at InSTePP (see Pardey, et al. 2006). In this report, we refer to this alternative as the 

InSTePP productivity accounts which date back to the initial efforts of Pardey and Craig (1989) and Craig 

and Pardey (1990a, 1990b, 1996) and have undergone periodic updates with the collaboration of 

additional colleagues. The history of these accounts can be found at 

http://www.instepp.umn.edu/united-states. Overall their approach is to build the productivity accounts 

from the state level up to the national level. Their general approach uses state- or regional-level data 

53 We appreciate the helpful comments of Julian Alston and Philip Pardey on an earlier draft of this section. 

53

 
whenever possible. As of this writing, InSTePP has released their series which runs from 1949 to 2002, 

with an update to 2007 pending. 

They identify four broad input categories: capital, labor, land, and materials. We address each 

separately and compare their series to the ERS series. We conclude with TFP pattern differences.

Capital

An exhaustive set of comparisons between the ERS and InSTePP capital services series is presented by 

state and in aggregate in Andersen, Alston, and Pardey (2011). We summarize primary methodological 

differences between the two approaches in Table XIII.2.

Table XIII.2. Comparison of Capital Services Series Construction for ERS vs. InSTePP

Capital ERS InSTePP

Capital Stock Estimates Perpetual inventory method Physical inventory method

Interest rate Market-based Real Constant (4%)

Level of aggregation National capital stock for the 

national accounts, state-specific 

stock for the state accounts

State-specific

Categories of variables Machinery (4)

Biological (3)

Structures (1)

Machinery (6)

Biological (5)

Buildings (1)

Depreciation Hyperbolic, average service life 

and distribution of asset 

retirement around the average 

following a normal distribution

Geometric pattern for durable 

assets 

Retirement Age Service lives estimated from BEA 

Fixed Assets and Consumer 

Durable Goods, 1925-94

Service life, L, calculated for 

constant depreciation rate, δ, 

such that the threshold is set at 

10%; i.e., (1-δ)L = 0.10

Rental rates Market rate Fixed real interest rate

Data Sources Basic sources: NASS etc. Basic sources plus unpublished 

Association of Equipment 

Manufacturers surveys

When plotting a) tractors and trucks, b) service structures, c) other machinery, and d) aggregate capital, 

the pattern is similar across all categories, although the InSTePP series is smoother than the ERS series. 

In all cases, the ERS series exceeds the InSTePP series as measured in constant 1996 dollars starting in 

the early 1960s. The greatest divergence is between the mid-1970s and 1990. 

54
One point of departure to note between the two series regarding construction of capital services is the 

treatment of machinery. As noted in the table, the InSTePP series use survey data from the Association 

of Equipment Manufacturers (AEM). The type, quality and comparison of these data to the ERS series 

are discussed in Andersen, Alston, and Pardey (2011) and Pardey, et al. (2006). 

ERS treats machinery purchased for on-farm use as part of the capital services series. When machinery 

is hired for on farm use (by either lease or hiring of custom services), it is considered a component of the 

intermediate input services as part of purchased services. Income generated from the farmer hiring out 

services to others is recorded as income.

The InSTePP series use data from the AEM, which is the link in the chain selling equipment to dealers. It 

is the dealers who sell to end users. When machinery is sold to a customer who has a custom hire 

enterprise, this equipment is accounted under the purchased services ledger which is transacted as 

intermediate input. Capital owned by farmers but used on a farm is already counted as an expense in 

the InSTePP series. However, it is not if the AEM survey data are segmented into farm-owned capital 

and otherwise. The documentation available is not clear on this point. Our concern with the capital 

series using the AEM data series is that farm-owned capital may be double counted as being farmowned and also measured in the materials input category.

The capital services series for InSTePP and ERS are presented in Figure XIII.1. Both series in this figure 

exclude land. The ERS series exceeds the InSTePP series by 31.6%, on average over the entire series, 

with the ERS series exceeding the InSTePP series by 85% on average during the 1966-1993 period. The 

trends are countercyclical over significant periods (1965-1972, 1978-1982, 1990-2001). The growth rate 

in capital services between the two series has a correlation of only 0.40. 

Sources include InSTePP Capital series from sheet 4 in InSTePP U.S. Production Accounts (version 4), 

Pardey et al. (2010a), and http://www.instepp.umn.edu/products/instepp-us-production-accountsversion-4-input-q. ERS Capital series less Land is constructed using the data series found in 

http://www.ers.usda.gov/data-products/agricultural-productivity-in-the-us.aspx#28247, National 

Tables, 1948-2011 (posted 27 September 2013). The ERS series for Capital less Land, t K , is 

constructed using Equipment, Buildings and Inventories. The quantities and price indexes for these 

0

50

100

150

200

250

19491951195319551957195919611963196519671969197119731975197719791981198319851987198919911993199519971999200120032005200720092011

Figure XIII.1: Capital Services series, ERS vs InSTePP

USDA 1949=100

InSTePP 1949=100

55
three components of capital are found in Table 1a of this spreadsheet. Specifically, aggregate capital 

is constructed as, ( ) t

K

tt t t t t t PQPQPQPK equipment equipment buildings buildings sinventorie sinventorie ×+×+×= / , with the 

normalizing price of capital less land provided by ERS. This series is then normalized to 1949=100.

For comparison, the following figure shows the expected real rate of return used by ERS to convert nonland capital stocks to flows. Although the expected rate of inflation is subtracted from the nominal AAA 

bonds rate, the real rate still mirrors the evolution of the nominal AAA bonds rate. It shows a sharp 

increase in 1977-1984 during the period of high inflation and peaks just a little later than the largest 

difference between the ERS and InSTePP capital service flow estimates plotted in the previous figure, 

suggesting a potential role of the choice of real interest rate in the difference between the two capital 

measures. 

Figure XIII.2: Ex-Ante Real Rate of Return, R_AAA, used by ERS (real rate on vertical axis). 

Source: Ball (2014c)

Table XIII.3 summarizes the ERS and InSTePP capital services series growth rates by periods. Over the 

1949-2002 period, the ERS series increased an average of 0.6% compared to the InSTePP average of 0%. 

The ERS series presents capital services growth until 1979, followed by a declining period. 

Table XIII.3: Comparison of ERS and InSTePP Capital Services Growth Rates

Years InSTePP ERS

1950-1959 0.001 0.038

1960-1969 -0.001 0.014

1970-1979 0.001 0.023

1980-1989 -0.004 -0.025

1990-2002 0.001 -0.014

1949-2002 0 0.006

NB: Growth rates calculated as log differences.

56
Focusing on the impact of the different assumptions about interest rate, Andersen, Alston, and Pardey 

(2011) recalculated the InSTePP series using the ERS market interest rate assumption to isolate the 

impact of this assumption in explaining the divergent series. This is presented in Figure 4 (first panel) in 

Andersen, Alston, and Pardey (2011) which shows the capital services series are nearly identical up to 

1979, and then the ERS series exceeds the InSTePP series through 2002, with the differences in the early 

1980s being more dramatic than the period from the later 1980s to the end of the series. 

Table 3 in Andersen, Alston, and Pardey (2011) provides the capital productivity (output per unit of 

capital) index values by periods. For the period 1960-2002, the interest rate assumption accounts for 

approximately one-third of the discrepancy between the ERS and InSTePP series. However, the finer 

period breakdown suggests that the interest rate assumption plays no role in explaining differences for 

the 1960-1980 period. For the decade 1980-90, the InSTePP fixed rate assumption accounts for onethird of the difference between the InSTePP and the ERS series. From 1990-2002, the InSTePP series 

calculated with the variable rate runs only 3% lower than the ERS series. 

From 1960 onwards, the differences in the capital series is driven significantly (but not entirely) by the 

constant (InSTePP) versus market (ERS) interest rate assumption in generating the rental rates and 

capital stock calculation. The remaining discrepancies are attributable to the composition of the data in 

terms of level of aggregation for baseline data, the number of capital categories, depreciation rate 

approach, retirement age, and data sources. 

InSTePP justifies its use of the constant interest rate as being more consistent with farmer expectations 

and capital decision making. Their complaint with the use of the variable market rate is that it implies 

that all existing assets are subject to variable use in response to annual variations in interest rates. They 

argue that this is not consistent with the observed structure and nature of capital use in U.S. agriculture, 

where existing assets represent 90% or more of the capital use on farms in a given year. 

InSTePP arguments in support of a constant interest rate include: 

• The expected long term relative interest rates may be relatively insensitive to year-to-year 

fluctuations in observed rates. 

• Once an asset is purchased or rented, transitory changes in real rates are likely to have less 

influence on decisions regarding the use of agricultural capital. 

• Biological capital combined with durable fixed factors show limited flexibility in the short run. 

Therefore, decisions about agricultural production and capital utilization are relatively 

insensitive to short-run changes in input and output prices.

Our assessment of capital methodologies

The 1980s were a period of highly volatile market interest rates. If market interest rate volatility is not 

impacting agricultural capital services, a clear explanation is needed why agriculture is different from 

other sectors of the manufacturing and service economy. If agriculture is not substantially different 

from other firms, then it cannot be argued that agriculture is insensitive to the market interest rate in its 

demand for capital. Crop farmers are borrowing in the market every year. When replacement of capital 

is needed at the time of volatile rates, purchases can be delayed, thus using less productive capital 

longer. Sharp increases in interest rate lead them to hold off investment. Smoothing out the interest 

rate volatility masks the underlying decision environment, which will surely influence investment timing.

Clearly, the choice of interest rate is important. The treatment of capital services relates to the debate 

between the use of ex-ante (Diewert and others) versus ex-post (Jorgensen and others) approach. The 

ex-ante real rate used by ERS is more stable than an ex-post rate such as that used by BLS. The BLS uses 

the ex-post approach (Jorgenson’s) and the perpetual inventory method as well. As apparent from 

57
Table X.1, the JHS capital contribution to growth differed most from the ERS contribution during the 

1973-1995 period, which included the greatest volatility in real interest rate. Although our 

recommendation is to not ignore at least some of the volatility in real interest rate, it is interesting to 

note that the 1980 AAEA Task Force recommended the use of a constant rate of 3 or 4% (Gardner et al. 

1980, p. 33, para. 3) as a proxy for a long-run real interest rate.

An important issue is the choice of deflator to use in obtaining real rates. The perfect deflator would be 

to use the change in prices of the goods of interest or an index that reflects the specific capital goods. 

ERS uses the general GDP deflator and this might result in a real rate with residual inflation for capital 

goods. How much of the ERS capital service flow pattern in the 1980s is induced by the use of a price 

index to deflate the nominal rate that is broader than the prices of these assets? 

Labor

In the InSTePP series, farm operators are set into 30 classes with five age classes and six education 

classes. The Census of Population was used as the source for this series prior to the availability of ARMS 

data. No specific hedonic modeling is used to quality adjust the data. There is a matching of operator 

hourly wages that are calculated by age/education cohort using national-level estimates of annual 

income and state-level estimates of operator hours worked on-farm.

Family labor is one type of labor and its price is generated by a scaled index. The family labor, along 

with the operator and hired labor are obtained from NASS. 

Figure XIII.3 compares the ERS and InSTePP series. The InSTePP series consistently exceeds the ERS 

series from the late 1950s, and the gap grows over time until the InSTePP series exceeds the ERS series 

by 35% on average during the 1990-2002 period. The correlation of the growth rates in these two labor 

series is very low at 0.16.

Source: InSTePP Labor series from sheet 2 in InSTePP U.S. Production Accounts (version 4). February 26, 

2010. http://www.instepp.umn.edu/products/instepp-us-production-accounts-version-4-input-q, ERS 

Labor series found in http://www.ers.usda.gov/data-products/agricultural-productivity-in-theus.aspx#28247, National Tables, 1948-2011. September 27 2013, Table 1, column U (normalized to 

1949=100).

0

20

40

60

80

100

120

1948195119541957196019631966196919721975197819811984198719901993199619992002200520082011

Index

Figure XIII.3: Labor index ERS vs InSTePP

USDA 1949=100

InSTePP 1949=100

58
Land

InSTePP notes ERS practice of using “land in farms” as a measure of the land input is problematic for the 

following reasons:

• Does not allow for consistent and economically meaningful treatment of cross-sectional, 

temporal variation in land quality, and 

• Significantly mis-measures the actual number of acres in agriculture.

InSTePP attempts to measure acreage more accurately by building up from the state level using three 

land categories (cropland, irrigated cropland, and grassland and pasture). The InSTePP distinction is to 

separate grassland and pasture land from cropland. Further, state-level estimates of total irrigated 

acres for cropland and pasture land along with interpolations are used to generate the irrigated land 

series (Pardey, et al. 2006). 

Land rental rates paid differ by agricultural land type. InSTePP uses information on rents from a statelevel series as well as from two other reports (Daugherty 1989; Doll and Widdows 1982). When the data 

are insufficient to differentiate land rental rates between cropland and pastureland, and irrigated and 

non-irrigated land at the state level, one of six alternative methods is used to approximate state rental 

rates. They are then aggregated up to the national level.

Figure XIII.4 compares the ERS and InSTePP land series. The InSTePP series consistently exceeds the ERS 

series, and the gap widens over time. For the 1990-2002 period, the InSTePP series exceeds the ERS 

series by 27% on average. The correlation of the growth rates in these two land series is very low and 

negative, -0.09.

Source: InSTePP Land series from sheet 3 in InSTePP U.S. Production Accounts (version 4) (Pardey et al.

2010a. http://www.instepp.umn.edu/products/instepp-us-production-accounts-version-4-input-q, ERS 

Land series found in http://www.ers.usda.gov/data-products/agricultural-productivity-in-theus.aspx#28247, National Tables, 1948-2011. September 27, 2013. Table 1, column S (normalized to 

1949=100).

0

20

40

60

80

100

120

1948195219561960196419681972197619801984198819921996200020042008

Index

Figure XIII.4: Land Index ERS vs InSTePP

USDA 1949=100

InSTePP 1949=100

59
Materials

The materials input is comprised of fertilizer, pesticides, seed, purchased feed, water use, and other 

operating expenses which include machine hire. The challenge in creating the state series is that the 

collection of data for some inputs was discontinued during the time period. With the goal of developing 

state-level series uppermost in the InSTePP protocol, creative approaches to filling in these series were 

undertaken.

InSTePP made an effort to extend the separate fertilizer commodities by state after 1985, when the 

separation was discontinued. For fertilizer prices, national-level prices post 1988 were extrapolated 

using the trend in average prices of a) urea, b) triple superphosphate and c) muriate of potash/ 

potassium chloride, with the price data coming from Agricultural Prices (NASS publication).

Pesticides prices use ERS series with prices paid indexes from NASS. No quality adjustments are 

addressed. The seed series uses the total nominal expenditure of seed purchases by state in 1949-86 for 

seed used on farms. This series does not include seed grown and used on farm or purchased for resale. 

A national level price index is used. Purchased feed series use the nominal value of expenditures and 

total feed purchases by state for various types. The value of feed used on farm was not included but hay 

purchases were included even though consumed on farm. InSTePP generates the quantity index using 

the price of feed and they do this for 14 feed categories. Water use and other operating expenditures 

use the same data as ERS. 

Figure XIII.5 compares the ERS and InSTePP materials series. The InSTePP begins to differ dramatically 

by the late 1950s with the gap growing dramatically. For the 1990-2002 period, the InSTePP series 

exceeds the ERS series by 21% on average. The correlation of the growth rates in these two 

materials/intermediate input series is 0.76.

Source: InSTePP Materials series from sheet 5 in InSTePP U.S. Production Accounts (version 4). February 

26, 2010. http://www.instepp.umn.edu/products/instepp-us-production-accounts-version-4-input-q. 

0

50

100

150

200

250

300

19491951195319551957195919611963196519671969197119731975197719791981198319851987198919911993199519971999200120032005200720092011

Figure XIII.5 Materials Index USDA vs InSTePP

USDA 1940=100

InSTePP 1949=100

60
ERS Intermediate goods series found in http://www.ers.usda.gov/data-products/agriculturalproductivity-in-the-us.aspx#28247, National Tables, 1948-2011. September 27, 2013. Table 1, column X 

(normalized to 1949=100).

Output

Output quantity and price data are from NASS. They identify three categories – crops, livestock and 

miscellaneous. There are 60 crop outputs grouped into four categories – field crops (17), fruits and nuts 

(21), vegetables (21), and an aggregate nursery/greenhouse products; 9 livestock outputs – broilers, 

cattle, eggs, hogs, honey, milk, sheep, turkeys and wool; and a miscellaneous category with 5 

components that includes machines rented out and Conservation Reserve acreage. Of the 74 outputs, 

71 are based on both quantity and price data collected by national or state-level statistical services. 

Only 3 products (cattle, sheep, and machine hire out) generate a quantity series implicitly using revenue 

data and a price series. 

Figure XIII.6 compares the ERS and InSTePP series. The InSTepp series coincides with the ERS series over 

the entire period, with a correlation of 0.999. 

Source: InSTePP Output series from sheet 1 in InSTePP U.S. Production Accounts (version 4) – Output Q. 

Pardey et al., 2010b. http://www.instepp.umn.edu/products/instepp-us-production-accounts-version4-output-q. ERS Aggregate Output Series found in http://www.ers.usda.gov/data-products/agricultural0

50

100

150

200

250

300

19491951195319551957195919611963196519671969197119731975197719791981198319851987198919911993199519971999200120032005200720092011

USDA 1949 = 100

InSTepp 1949 = 100

61
productivity-in-the-us.aspx#28247, National Tables, 1948-2011. September 27, 2013. Table 1, column B 

(normalized to 1949=100).

Total factor productivity 

While the capital services series receives considerable attention in discussions concerning the 

discrepancies between the InSTePP and ERS series, the discrepancies other input series are not 

insignificant. Figure XIII.7 compares the ERS and InSTePP TFP series. The InSTePP series exceeds the ERS 

series from the outset, with the most dramatic differences emerging in the late 1970s to late 1980s, and 

then generally converging. For the 1990-2002 period, the InSTePP series exceeds the ERS series by 13%. 

The correlation of the growth rates in the TFP series is high at 0.94.

Source: InSTePP Multifactor Productivity Output series in InSTePP U.S. Production Accounts (version 4) – 

Multifactor Productivity. Pardey et al., 2010c. http://www.instepp.umn.edu/products/instepp-usproduction-accounts-version-4-multifactor-productivity. ERS Series from found in 

http://www.ers.usda.gov/data-products/agricultural-productivity-in-the-us.aspx#28247, National 

Tables, 1948-2011. September 27, 2013. Table 1, column AE. (normalized to 1949=100).

Concluding comments

When comparing these series, nuanced differences emerge in the composition of the data in terms of 

levels of disaggregation and the use of state- or regional-level prices when available versus the national 

prices. By focusing on the state-level data series and matching highly disaggregated quantity series with 

their prices, the InSTePP series obviates some of the need for hedonic approaches that are used by ERS 

using national level data. An exception is the ERS land accounts which are not quality adjusted. Starting 

with the most disaggregated level possible can clearly be an advantage in data quality and consistency, 

but this necessitates high quality state-level data.

While there is considerable discussion about the difference between the InSTePP and ERS 

methodological differences in the capital series, controlling for use of the market versus constant 

interest leads to closer harmony between the ERS and InSTePP series. But not to be overlooked, the ERS 

and InSTePP series differ dramatically since the 1960s for labor, land, and materials. 

0

50

100

150

200

250

300

19491951195319551957195919611963196519671969197119731975197719791981198319851987198919911993199519971999200120032005200720092011

Figure XIII.7: TFP Index ERS vs InSTePP

USDA 1949=100

InSTePP 1949=100

62
In the end, the TFP series for ERS and InSTePP tells a more harmonious story than any of the 

components separately. 

Recommendation

Engage with researchers in the field to analyze the sources of differences with alternative estimates and 

to determine whether they warrant changes in data or procedures used (Priority B).

XIV. Stakeholder Assessment

As part of the review process, the committee contacted stakeholders from academia, government, and 

the broader research community for comments on the productivity accounts. Overall, the comments 

were overwhelmingly supportive of the agricultural productivity accounts and repeatedly indicated the 

value of the accounts as analytical, research, and teaching tools. A common theme among stakeholder 

comments was requests for additional documentation, underlying source data, and for re-establishing 

the state-level accounts. The comments from stakeholders who granted permission to have their 

comments included verbatim are included in Appendix 2. 

The call for stakeholder input was announced in the AAEA Newsletter and extended via direct email 

contact to representatives from both the agricultural economics community and the broader 

community of those doing productivity research. The committee received 33 responses. All but two

have agreed to have their comments included verbatim in a supplemental appendix to this report. Three 

are included in Appendix 1 along with other input cited in this report. The remaining 28 are included in 

Appendix 2.

We divided the stakeholder responses into four categories: a) those expressing a complimentary view of 

the accounts, but offering no specific suggestions, b) those with feedback or requests related to the ERS 

productivity program, but no explicit critique or methodological suggestion, c) those with a specific 

critique or methodological concern, and d) those that offered no specific suggestion or critique or were 

not familiar enough with the program to offer feedback. It is important to note that those with a critique 

or methodological concern were often complimentary of the overall program.

Thirteen respondents offered specific suggestions or comments for the ERS productivity program but did 

not convey major methodological critiques. For example, respondents requested more documentation, 

more detailed and timely release of data, reinstatement of the state accounts, additional crop detail, 

coverage of aquaculture, and suggested that the ERS search for ways to make all of the data more 

visible. Within this group, respondents argued that measuring input quality is of utmost importance, 

questioned whether change in TFP should be zero if all inputs are accurately measured, and pointed out 

the potential differences between industry and firm-level TFP estimates. Furthermore, two respondents 

discussed choice of the residual claimant. As noted above, these respondents were often complimentary 

of the program overall. 

Eight respondents offered a complimentary review of the ERS accounts without offering any specific 

suggestions for future directions. These respondents enumerated many reasons for their positive 

assessment of the accounts. In particular, stakeholders noted that ERS has been an international leader 

in productivity measurement and provides useful source data for international comparisons and policy 

work.

Four stakeholders responded with measurement or methodological issues related to the accounts. 

Within this group, respondents mentioned choice of index number formula, the consistency between 

the international and national agricultural accounts, the consistency in aggregation of productive stocks 

63
and the formulation of the rental rate of capital, the inclusion of biological capital, and the 

measurement of agricultural land as important areas that deserve additional attention.

Eight respondents did not offer specific comments or suggestions.

64
CONCLUSIONS 

ERS has emerged as an acknowledged intellectual leader in construction and integration of national and 

state-level productivity accounts in agriculture. The national ERS productivity measures are widely 

referred to and used, and international sectoral comparisons rely on the ERS production accounts for 

foundation methodology in constructing agricultural productivity accounts in other countries.

This leadership role has endured for many decades and accelerated in response to the AAEA Task Force 

review of the agricultural productivity accounts (Gardner et al. 1980). Under the leadership of Eldon Ball, 

the procedures used to construct the productivity accounts underwent a major overhaul, and the bulk of 

the AAEA Task Force recommendations were implemented by the mid-1980s. Despite limited personnel 

and resources, a vigorous research program was initiated and has continued over more than three 

decades to examine additional ways to improve the sectoral productivity accounts and to extend their 

reach and value.

It is with that backdrop of vigorous intellectual leadership that the ERS Agricultural Productivity Account 

Review Committee consisting of Barbara Fraumeni, Lilyan Fulginiti, Jon Samuels, Spiro Stefanou, and 

Richard Shumway (Chair) has examined the data sources, methodology, ongoing research, 

documentation, and reporting of the agricultural productivity accounts. Our recommendations are many 

and some are substantial. In order to guide implementation of the recommendations, we group them 

into three orders of priority based on our collective perception of their importance relative to the cost 

(in intellectual difficulty, time, and resources) of implementation. We judge the most important to be 

the Priority A Overarching, Website, and State-Level recommendations.

Recommendations

Priority A

Overarching

1. Fully document and keep current all procedures followed, from data sources through 

measurement of productivity change, to enable a non-expert to reproduce the accounts.

2. Cooperate with other agencies to reduce duplication, achieve consistency across statistical 

series, get information at lowest cost, and capitalize on research and expertise.

Labor

1. Investigate the reasons for differences in the labor input calculations of Jorgenson, Ho, and 

Samuels (2014). 

2. Investigate the American Community Survey as an alternative, possibly complementary, data 

source, potentially in collaboration with BEA/BLS. 

Non-Land Capital

1. Examine non-land capital nominal investment data in consultation with BEA researchers. 

2. Consider using one or more asset deflators in its expected inflation calculation.

3. Review investment deflators to determine if sources have been updated or revised since the 

data was last collected.

4. Review average service lives of assets with BEA and BLS to determine if revisions should be 

made.

5. Investigate whether the indexes of capital service flows during the period 1975-1984 reflect 

changes in capital service use rather than changes in the behavior of the bonds rate used in 

calculating the user cost of capital.

65
Land

1. Explore ways to include within-county land type adjustments as well as quality changes given by, 

for example, irrigation or other improvements in farmland. 

2. Consistent with the recommendation for non-land capital, replace the GDP deflator used to 

capture general effects of inflation with a price index for land.

Outputs

1. To account for the distorting effect of crop insurance when outputs are aggregated, add the 

insurance indemnity to the insured crop’s price and deduct the farmer’s premium.

2. Revisit measurement issues related to own account investment, specifically consistency 

between the output and input sides of the account. 

Quality Adjustments

1. Research methods for incorporating quality adjustments to seeds and consider whether seed 

quality change should be treated solely as an input or both an output and an input. 

Website

1. Provide detailed documentation online and note ad hoc adjustments to data or deviations from 

the general procedure (e.g., if fixes were required due to negative implied capital rental rates).

2. Expand the website to provide timely access to more detailed data and procedural detail 

underlying the quantity and price aggregate and sub-aggregate national and state-level 

statistics. 

State-level

1. Continue to develop and publish the state-level total productivity measures as well as price and 

quantity series (strongly recommended). 

2. Cooperate with other government agencies to achieve the lowest cost method of collecting data 

of sufficient quality to enable the state-level accounts to be extended and maintained. 

3. Investigate the possibility of using information in the American Community Survey to update 

matrix elements in the state labor accounts. 

4. Ensure consistency between the national and state accounts where possible, and explain 

circumstances that prevent total consistency where it is not possible. 

Cross-country comparisons

1. ERS should emphasize that cross-country comparisons are really research work and establish 

whether they are an integral part of the ERS agenda. 

Priority B

Labor

1. Use the latest revision of information on totals from NIPA and the special BLS tabulation.

2. Consider further refinements of the cross classification of workers to improve identification of 

quality differences. 

3. Adjust for temporal changes in the quality of workers in each demographic group not captured 

in relative wages. 

Non-Land Capital

1. Begin a conversation with BEA researchers to determine if any changes should be made to ERS 

measures based on recent BEA research.

66
2. Review and vet the capital stock aggregation methodology developed by Sliker and consider 

whether to revise ERS methodology in response.

3. Include investment in computers in the ERS investment data.

Land

1. Report separate indexes for Cropland, Woodland, Pasture and Other non-Cropland. 

Intermediate inputs

1. Examine the robustness of the intermediate input accounts constructed by ERS to the use of 

alternative sources of price deflators. 

2. Investigate the logic and practical effect of how ERS intermediate inputs compare to those 

based on input-output tables. 

Quality Adjustments

1. Determine whether the degree of quality change in outputs has been sufficient to warrant 

quality adjustment, and, if so, explore alternative methods to adjust productivity measures for 

output quality change. 

2. Check alternative data sources for price of purchased machine services. 

Residual Claimant

1. Examine the sensitivity of the productivity accounts to the choice of residual claimants and 

different choices of expected asset inflation. 

Research and Development

1. Follow developments in the literature on accounting for R&D in the productivity measure, and, if 

minimal R&D is conducted on farms, include a note of explanation in the methodology 

description indicating why sectoral R&D is not incorporated in the accounts. 

Website

1. Include a paragraph on typical release dates in addition to the current practice which is to post 

date of “next update”, which as it turns out is blank. 

2. At each release, post a note describing revisions and reasons for revisions.

3. Change exposition on the website about welfare. 

4. Include links to other productivity related data and research including the BEA/BLS industrylevel production accounts, BLS Non-Farm Productivity, EU KLEMS, and World KLEMS.

State-level

1. Report state-level price and quantity series on the website for the same sub-aggregates as the 

national series. 

2. Update the state-level accounts on the same schedule as the national accounts. 

3. Place more underlying data detail on the website. 

Cross-country comparisons

1. Because the methods used to develop agricultural productivity accounts for other countries do 

not follow the same procedures ERS uses for the U.S. accounts (e.g., inputs are not quality 

adjusted), determine whether cross-country comparisons should be made. 

ERS Measures of Productivity Compared to Alternative Sources

67
1. Engage with researchers in the field to analyze the sources of differences with alternative 

estimates and to determine whether they warrant changes in data or procedures used.

Priority C

Labor

1. Clarify if the imputation of wages for self-employed workers exhausts available income and 

report procedures used if this occurs. 

2. Clarify how sample selection estimation is executed when the Heckman procedure is used for 

the contract labor hedonic wage index.

Non-Land Capital

1. After vetting the current ERS methodology, consider whether to revise its estimate of 

depreciation in the user cost of capital to bring its construction in line with the methodologies 

used by other experts in the field.

2. As a future research project, revisit the treatment of breeding livestock, building on Ball and 

Harper (1990).

Land

1. Investigate the potential departure of the ‘Land in Farms’ definition in the Census of Agriculture 

used by ERS from ‘Land in Agriculture’.

Outputs

1. Continue to explore the effect of alternative aggregator functions, including the chained Fisher 

index, on productivity measures and include sufficient detail in the data available on the website 

to enable users to explore them.

Quality Adjustments

1. Research the possibility and ramifications of subdividing labor into supervisory and 

nonsupervisory workers in the cross-classification of labor. 

R&D

1. ERS should follow developments in the literature on accounting for R&D in productivity 

measures. If it determines that minimal R&D is conducted on farms, ERS may consider a note in 

its description of the methodology about the reasons it does not and need not include R&D. 

Alternative assumptions

1. Although a disequilibrium approach to capital factors is not widely applied in the productivity 

literature, we recommend that ERS engage the scholarly community in an examination of 

effective ways to account for disequilibrium 

Website

1. Add a link to a “Related Reports” page that contains links to the pertinent related reports.

State-level

1. If feasible, include Alaska and Hawaii in the accounts. 

2. Replace the Caves-Christensen-Diewert spatial aggregator index with a Lowe, geometric Young, 

or Färe-Primont index.

68
ACRONYMS USED IN REPORT

Acronym Definition

AAA Triple A bonds

AAEA American Agricultural Economics Association

AEM Association of Equipment Manufacturers

AELOS Agricultural Economics and Land Ownership Survey

ARIMA Autoregressive integrated moving average 

ARMS Agricultural and Resource Management Survey

BEA Bureau of Economic Analysis

BLS Bureau of Labor Statistics

ERS Economic Research Service

Eurostat European Union Statistical Office

EU European Union

GAMS Generalized Algebraic Modeling System

GDP Gross domestic product

InSTePP International Science and Technology Practice and Policy

JHS Jorgenson, Ho, Samuels

KLEMS Capital, Labor, Energy, Materials, Services

NAICS North American Industry Classification System

NASS National Agricultural Statistics Service 

NIPA National Income and Product Accounts

OECD Organisation for Co-operation and Economic Development

OMB Office of Management and Budget

OPT PPITW

R&D Research and development

RAS Biproportional matrix balancing technique

SNA System of National Accounts

TFP Total factor productivity

USDA U.S. Department of Agriculture

USDOC U.S. Department of Commerce

USDOL U.S. Department of Labor

69
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Appendices 1 and 2 are available at:

http://ses.wsu.edu/wp-content/uploads/2015/06/WP2015-12.pdf