Productivity and Growth Productivity and Growth in U.S. Agriculture: 1948-2008in U.S. Agriculture: 1948-2008

Eldon Ball and Sun Ling WangEldon Ball and Sun Ling WangEconomic Research ServiceEconomic Research Service

USDAUSDA

Prepared for Presentation at World KLEMS Conference Prepared for Presentation at World KLEMS Conference at Harvard Universityat Harvard University August 19-20, 2010August 19-20, 2010

The views expressed herein are those of the authors, The views expressed herein are those of the authors, and not necessarily those of the U.S. Department of Agriculture.and not necessarily those of the U.S. Department of Agriculture.

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Productivity and GrowthProductivity and Growth

The growth of agricultural productivity has long The growth of agricultural productivity has long been chronicled as the single most important been chronicled as the single most important source of economic growth in the U.S. farm sector source of economic growth in the U.S. farm sector

Though their methods differ in important ways, Though their methods differ in important ways, the major sectoral productivity studies (Kendrick the major sectoral productivity studies (Kendrick and Grossman, 1980; Jorgenson, Gollop, and and Grossman, 1980; Jorgenson, Gollop, and Fraumeni, 1987; Jorgenson and Gollop, 1992; Fraumeni, 1987; Jorgenson and Gollop, 1992; Jorgenson, Ho, and Stiroh, 2005) share this Jorgenson, Ho, and Stiroh, 2005) share this common conclusioncommon conclusion

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The U.S. Department of Agriculture (USDA) has The U.S. Department of Agriculture (USDA) has been monitoring the industry’s productivity been monitoring the industry’s productivity performance for decadesperformance for decades

In fact, in 1960, the USDA was the first agency In fact, in 1960, the USDA was the first agency to introduce multifactor productivity to introduce multifactor productivity measurement into the Federal statistical measurement into the Federal statistical programprogram

Today the USDA’s Economic Research Service Today the USDA’s Economic Research Service (ERS) routinely publishes total factor productivity (ERS) routinely publishes total factor productivity (TFP) measures from production accounts (TFP) measures from production accounts distinguishing multiple outputs and inputs and distinguishing multiple outputs and inputs and adjusting for quality change in each input adjusting for quality change in each input categorycategory

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Indexes of productivity are constructed for each Indexes of productivity are constructed for each state and the aggregate farm sectorstate and the aggregate farm sector

The state series provide estimates of the growth The state series provide estimates of the growth and relative levels of productivityand relative levels of productivity

There is also an ongoing effort to provide There is also an ongoing effort to provide international comparisons of agricultural international comparisons of agricultural productivity (Ball et al., 2001; 2008; 2010)productivity (Ball et al., 2001; 2008; 2010)

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MethodologyMethodology

The USDA constructs the following “translog” The USDA constructs the following “translog” index of total factor productivity:index of total factor productivity:

(1)(1)

where where kk and and ll are adjacent time periods, the Y are adjacent time periods, the Yii are the output indexes, the Xare the output indexes, the Xjj are input indexes, are input indexes, the Rthe Rii are output revenue shares, and the W are output revenue shares, and the Wjj are are input cost sharesinput cost shares

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The subscripts The subscripts kk and and ll in (1) can be interpreted in (1) can be interpreted as time periods or as states/countriesas time periods or as states/countries

When the number (K) of states/countries When the number (K) of states/countries exceeds two, the application of (1) to the [K(K-exceeds two, the application of (1) to the [K(K-1)]/2 possible pairs of states yields a matrix of 1)]/2 possible pairs of states yields a matrix of bilateral comparisons that may not satisfy bilateral comparisons that may not satisfy transitivitytransitivity

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Caves, Christensen and Diewert (1982) proposed Caves, Christensen and Diewert (1982) proposed the following index for bilateral comparisons:the following index for bilateral comparisons:

(2)(2)

where a bar indicates the arithmetic mean and a where a bar indicates the arithmetic mean and a tilde indicates the geometric meantilde indicates the geometric mean

The use of (2) for bilateral comparisons results in The use of (2) for bilateral comparisons results in transitive multilateral comparisons that retain a transitive multilateral comparisons that retain a high degree of characteristicityhigh degree of characteristicity

jl

jl

j

jjl

j j

jkjjk

i i

iliil

i

ik

i

iik

l

k

x

xww

x

xww

Y

YRR

Y

YRR

TFP

TFP~ln

2~ln2

~ln2

~ln2

ln

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The Production Accounts: The Production Accounts: OutputOutput

The USDA constructs both state and aggregate The USDA constructs both state and aggregate farm sector accountsfarm sector accounts

The accounts are consistent with a gross output The accounts are consistent with a gross output model of productionmodel of production

Output is defined as gross production leaving Output is defined as gross production leaving the farm, as opposed to real value addedthe farm, as opposed to real value added

Inputs are not limited to capital and labor, but Inputs are not limited to capital and labor, but include intermediate inputs as wellinclude intermediate inputs as well

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Both state and aggregate models view Both state and aggregate models view agriculture within their respective geographic agriculture within their respective geographic boundaries as a single farmboundaries as a single farm

Output includes deliveries to final demand and to Output includes deliveries to final demand and to intermediate demand in the non-farm sectorintermediate demand in the non-farm sector

State output accounts include these deliveries State output accounts include these deliveries plus interstate shipments to intermediate farm plus interstate shipments to intermediate farm demanddemand

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An unconventional aspect of our measure of total An unconventional aspect of our measure of total output is the inclusion of output of “inseparable” output is the inclusion of output of “inseparable” secondary activitiessecondary activities

These activities are defined as activities whose These activities are defined as activities whose costs cannot be observed separately from those of costs cannot be observed separately from those of the primary agricultural activitythe primary agricultural activity

Services relating to agricultural production (e.g., Services relating to agricultural production (e.g., machine services for hire; contract feeding of machine services for hire; contract feeding of livestock) are typical of these activitieslivestock) are typical of these activities

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Translog output indexes are formed by Translog output indexes are formed by aggregating over agricultural goods and goods aggregating over agricultural goods and goods and services from secondary activities using and services from secondary activities using revenue-share weights based on shadow pricesrevenue-share weights based on shadow prices

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Intermediate InputIntermediate Input

Intermediate input consists of all goods and Intermediate input consists of all goods and services used in production during the calendar services used in production during the calendar year, whether withdrawn from beginning year, whether withdrawn from beginning inventories or purchased from outside the farm inventories or purchased from outside the farm sectorsector

In the case of the state accounts, intermediate In the case of the state accounts, intermediate input also includes purchases from farms in other input also includes purchases from farms in other statesstates

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Price and quantity data corresponding to Price and quantity data corresponding to purchases of feed, seed, and livestock are purchases of feed, seed, and livestock are available and enter the calculation of available and enter the calculation of intermediate inputintermediate input

Translog indexes of energy input are constructed Translog indexes of energy input are constructed by weighting the growth rates of petroleum fuels, by weighting the growth rates of petroleum fuels, natural gas, and electricity by their shares in the natural gas, and electricity by their shares in the overall value of energy inputsoverall value of energy inputs

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Pesticides and fertilizer are important Pesticides and fertilizer are important intermediate inputs, but price/consumption data intermediate inputs, but price/consumption data require adjustment since these inputs have require adjustment since these inputs have undergone significant changes in input qualityundergone significant changes in input quality

Price indexes for pesticides and fertilizer are Price indexes for pesticides and fertilizer are constructed using hedonic methods constructed using hedonic methods

The corresponding quantity indexes are formed The corresponding quantity indexes are formed implicitly by taking the ratio of the value of each implicitly by taking the ratio of the value of each aggregate to corresponding hedonic price indexaggregate to corresponding hedonic price index

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Finally, price and implicit quantity indexes of Finally, price and implicit quantity indexes of purchased services (e.g., custom machine purchased services (e.g., custom machine services; contract feeding of livestock; contract services; contract feeding of livestock; contract labor services) are constructedlabor services) are constructed

A translog index of total intermediate input is A translog index of total intermediate input is constructed for each state and the aggregate constructed for each state and the aggregate farm sector by weighting the growth rates of farm sector by weighting the growth rates of each category of intermediate input by their each category of intermediate input by their value shares in the overall value of intermediate value shares in the overall value of intermediate inputinput

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LaborLabor

The labor accounts incorporate demographic The labor accounts incorporate demographic cross-classifications of the agricultural labor force cross-classifications of the agricultural labor force developed by Jorgenson, Gollop, and Fraumeni developed by Jorgenson, Gollop, and Fraumeni (1987)(1987)

Hours worked and compensation per hour are Hours worked and compensation per hour are cross-classified by sex, age, education, and cross-classified by sex, age, education, and employment class (employee versus self-employment class (employee versus self-employed and unpaid family workers)employed and unpaid family workers)

Self-employed and unpaid family workers are Self-employed and unpaid family workers are imputed the mean wage of hired workers with imputed the mean wage of hired workers with the same demographic characteristicsthe same demographic characteristics

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Indexes of labor input are constructed for each Indexes of labor input are constructed for each state and the aggregate farm sector using state and the aggregate farm sector using demographically cross-classified hours and demographically cross-classified hours and compensation datacompensation data

Labor hours having higher marginal productivity Labor hours having higher marginal productivity (wages) are given higher weights in the index (wages) are given higher weights in the index than hours having lower marginal productivitiesthan hours having lower marginal productivities

This procedure explicitly adjusts state and This procedure explicitly adjusts state and aggregate farm sector time series of labor input aggregate farm sector time series of labor input for “quality” changes in labor hoursfor “quality” changes in labor hours

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CapitalCapital

Measurement of capital input begins with Measurement of capital input begins with estimating the capital stock and rental price estimating the capital stock and rental price for each asset type for each asset type

Stocks of depreciable capital are the Stocks of depreciable capital are the cumulation of all past investments adjusted for cumulation of all past investments adjusted for discards of worn-out assets and loss of discards of worn-out assets and loss of efficiency of assets over their service lifeefficiency of assets over their service life

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Asset discards are calculated based on an Asset discards are calculated based on an assumed mean service life for a homogeneous assumed mean service life for a homogeneous group of assets and a distribution of actual group of assets and a distribution of actual discards around this mean service lifediscards around this mean service life

Efficiency loss is assumed to be a function of Efficiency loss is assumed to be a function of age of the assetage of the asset

The function relating efficiency to age of the The function relating efficiency to age of the asset is approximated by a rectangular asset is approximated by a rectangular hyperbola concave to the originhyperbola concave to the origin

The USDA constructs an The USDA constructs an ex anteex ante measure of the measure of the user cost of capital user cost of capital

The The ex anteex ante rate of return is calculated as the rate of return is calculated as the nominal yield on investment grade corporate nominal yield on investment grade corporate bonds adjusted for expected rather than actual bonds adjusted for expected rather than actual price inflationprice inflation

The same pattern of decline in efficiency is used The same pattern of decline in efficiency is used both for the capital stock and the price of capital both for the capital stock and the price of capital services so that the requirement for internal services so that the requirement for internal consistency of a measure of capital input is metconsistency of a measure of capital input is met

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To estimate the stock of land we construct price To estimate the stock of land we construct price and implicit quantities of land in farmsand implicit quantities of land in farms

We assume that land in each county is We assume that land in each county is homogeneous, hence aggregation is at the homogeneous, hence aggregation is at the county levelcounty level

Beginning inventories of crops and livestock are Beginning inventories of crops and livestock are treated as capital inputs, while net additions to treated as capital inputs, while net additions to inventory during the calendar year are inventory during the calendar year are considered a component of outputconsidered a component of output

Translog indexes of capital input in each state Translog indexes of capital input in each state and the aggregate farm sector are formed by and the aggregate farm sector are formed by aggregating over the various capital assets using aggregating over the various capital assets using cost-share weights based on asset-specific rental cost-share weights based on asset-specific rental pricesprices

As is the case for labor, the resulting measure of As is the case for labor, the resulting measure of capital input is adjusted for changes in asset capital input is adjusted for changes in asset qualityquality

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Sources of GrowthSources of GrowthInput growth typically has been the dominant Input growth typically has been the dominant source of economic growth for the aggregate source of economic growth for the aggregate economy and for each of its producing sectorseconomy and for each of its producing sectors

Jorgenson, Gollop, and Fraumeni (1987) find Jorgenson, Gollop, and Fraumeni (1987) find that output growth relies most heavily on input that output growth relies most heavily on input growth in forty-two of forty-seven private non-growth in forty-two of forty-seven private non-farm business sectors, and in a more aggregate farm business sectors, and in a more aggregate study (Jorgenson and Gollop, 1992) in eight of study (Jorgenson and Gollop, 1992) in eight of nine sectorsnine sectors

Agriculture turns out to be one of the few Agriculture turns out to be one of the few exceptions; productivity growth dominates input exceptions; productivity growth dominates input growth growth

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Using equation (1), output growth equals the sum of Using equation (1), output growth equals the sum of the contributions of labor, capital and intermediate the contributions of labor, capital and intermediate inputs and TFP growthinputs and TFP growth

The contribution of each input equals the product of The contribution of each input equals the product of the input’s growth rate and its respective share in the input’s growth rate and its respective share in total cost total cost

Over the full 1948-2008 period labor input declined Over the full 1948-2008 period labor input declined at a 2.6% annual rateat a 2.6% annual rate

When weighted by its 20% cost share, the When weighted by its 20% cost share, the contraction in labor contributes an average -0.51 contraction in labor contributes an average -0.51 percentage points to output growthpercentage points to output growth

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Growth of capital input (excluding land) contributed Growth of capital input (excluding land) contributed just 0.01 percentage points to output growthjust 0.01 percentage points to output growth

Land input declined at a -0.55% average annual Land input declined at a -0.55% average annual rate; its contribution to output growth averagedrate; its contribution to output growth averaged-0.10 percentage points-0.10 percentage points

Intermediate input’s contribution averaged a Intermediate input’s contribution averaged a substantial positive rate equal to 0.66% per yearsubstantial positive rate equal to 0.66% per year

The net contribution of all inputs was less than one-The net contribution of all inputs was less than one-tenth of one percent, leaving responsibility for tenth of one percent, leaving responsibility for positive growth in farm sector output to positive growth in farm sector output to productivity growthproductivity growth

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Table 1. Sources of Growth: U.S. Farm Sector (Average Annual Growth Rates) 1948-2008 1948-1953 1953-1957 1957-1960 1960-1966 1966-19691969-19731973-19791979-19811981-19901990-20002000-20072007-2008

Output growth 0.0158 0.0115 0.0100 0.0410 0.0125 0.0227 0.0270 0.0224 0.0138 0.0096 0.0178 0.0085 -0.0087

Sources of growth

Input growth 0.0006 0.0131 0.0030 0.0049 0.0010 0.0054 0.0076 0.0146 -0.0225 -0.0123 0.0013 0.0014 -0.0660

Labor -0.0051 -0.0081 -0.0108 -0.0083 -0.0081 -0.0061 -0.0038 -0.0019 -0.0022 -0.0043 -0.0034 -0.0034 -0.0047Capital (excluding land) 0.0001 0.0054 0.0015 0.0003 0.0008 0.0031 0.0014 0.0032 0.0022 -0.0062 -0.0021 0.0005 0.0005Land -0.0010 -0.0011 -0.0017 -0.0016 -0.0007 -0.0022 -0.0029 0.0000 -0.0012 -0.0010 0.0000 -0.0008 -0.0012Inputs of farm origin 0.0036 0.0069 0.0117 0.0083 0.0055 0.0066 0.0054 0.0057 -0.0088 -0.0008 0.0032 0.0016 -0.0203Energy 0.0001 0.0014 0.0000 0.0000 0.0006 0.0001 -0.0001 0.0015 -0.0019 -0.0009 0.0004 0.0000 -0.0073Agricultural chemicals 0.0012 0.0014 0.0008 0.0021 0.0031 0.0046 0.0071 0.0006 -0.0019 -0.0003 0.0007 0.0012 -0.0200Purchased services 0.0017 0.0070 0.0020 0.0042 0.0000 -0.0006 0.0005 0.0047 -0.0078 0.0008 0.0025 0.0022 -0.0130Miscellaneous 0.0001 0.0001 -0.0006 -0.0002 -0.0001 -0.0001 0.0000 0.0006 -0.0009 0.0004 0.0001 0.0002 0.0000

Total factor productivity 0.0152 -0.0016 0.0070 0.0361 0.0115 0.0172 0.0194 0.0078 0.0363 0.0219 0.0164 0.0071 0.0573

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A more detailed discussion of methods and data A more detailed discussion of methods and data and complete references can be found at our and complete references can be found at our

websitewebsite

http://www.ers.usda.gov/Data/AgProductivity/

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