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

Eldon Ball and Sun Ling WangEconomic Research Service

USDA

Prepared for Presentation at National Academy of Economic SciencesBuenos Aires-UBA-FCE-Economic Department, Argentina

30 September 2010

, Argentina 27 September 2010

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

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Productivity and Growth

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

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

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There are, however, dissenting points of view regarding the sector’s performance

Alston et al. (2010) find evidence of a slowdown in the rate of productivity growth

If productivity growth falters, growing global demand will likely lead to sharply higher food prices and to increased environmental stress

The U.S. Department of Agriculture’s estimates do not support the hypothesis of slowing productivity growth

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The USDA’s Productivity Estimates

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

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

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

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

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

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

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Methodology

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

(1)

where k and l are adjacent time periods, the Yi are the output indexes, the Xj are input indexes, the Ri are output revenue shares, and the Wj are input cost shares

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The subscripts k and l in (1) can be interpreted as time periods or as states/countries

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

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

(2)

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

The use of (2) for bilateral comparisons results in transitive multilateral comparisons that retain a high 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: Output

The USDA constructs both state and aggregate farm sector accounts

The accounts are consistent with a gross output model of production

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

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

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

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

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

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

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

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

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

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Intermediate Input

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

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

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

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

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

Price indexes for pesticides and fertilizer are constructed using hedonic methods

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

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

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

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Labor

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

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

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

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

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

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

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Capital

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The net contribution of all inputs was less than one-tenth of one percent, leaving responsibility for positive growth in farm sector output to productivity 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 1966-1969 1969-1973 1973-1979 1979-1981 1981-1990 1990-2000 2000-2007 2007-2008

Output growth 0.0157 0.0114 0.0100 0.0410 0.0125 0.0227 0.0270 0.0223 0.0138 0.0096 0.0178 0.0085 -0.00858

Sources of growth

Input growth 0.0006 0.0130 0.0031 0.0050 0.0009 0.0057 0.0073 0.0147 -0.0223 -0.0121 0.0013 0.0013 -0.0675

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 0.0001 0.0054 0.0015 0.0003 0.0008 0.0031 0.0014 0.0032 0.0022 -0.0062 -0.0021 0.0005 0.0005

Land -0.0010 -0.0011 -0.0017 -0.0016 -0.0007 -0.0022 -0.0029 0.0000 -0.0012 -0.0010 0.0000 -0.0008 -0.0012Materials 0.0066 0.0167 0.0141 0.0145 0.0089 0.0110 0.0126 0.0133 -0.0212 -0.0007 0.0069 0.0051 -0.0621

Total factor productivity 0.0152 -0.0016 0.0069 0.0360 0.0116 0.0169 0.0197 0.0076 0.0362 0.0217 0.0164 0.0072 0.0589

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Do we or do we not have an agricultural productivity

slowdown?

That’s the question!

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Historical Trends

Output expanded at 1.57% average annual rateAggregate input use contracted since early 1980s

Productivity growth was responsible for positive growth in

farm sector output

U.S. agricultural output, input, and total factor productivity

0.00

0.50

1.00

1.50

2.00

2.50

3.00

Source: ERS data product, Agricultural Productivity in the United States

Indices, 1948=1

Output

Input

Productivity

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Unit root and structural break tests

Table 2 Unit root and Structural Break Test for the TFP variableTest Result Test ResultFixed coefficients testElliott-Muller (E-M) qLL test reject

Unit root test without break Unit root test with breakADF unit root test Z-Andrews unit root test with break without trend NS break at 1985 (both trend and intercept) S with trend S

KPSS unit root test CMR unit root test with break without trend S AO1--break at 1981 (one mean shift) NS with trend S AO2--break at 1968, 1986 (double mean shift) NS

IO1--break at 1983 (one mean shift) NSPP unit root test IO2--break at 1956, 1983 (double mean shift) NS without trend NS with trend S"S" indicates stationary; "NS" indicates nonstationary.

TFP growth is not stable for the 1948-2008 periodTFP series is stationary with trendUnit root tests confirm there is a break in both trend and intercept indicating a structural break and TFP growth change

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Productivity Slowdown Table 3: Structural Change Test in the US Agricultural Productivity Growth (national level)Time Period with break in intercept with break in both intercept and trend

During Period After Period Difference P-value During Period After Period Difference P-value1949-1960 1.74 1.7 -0.04 0.82 1.38 1.72 0.34 0.35161949-1970 1.86 1.72 -0.14 0.122 1.67 1.83 0.16 0.224

1949-1980 1.57 1.66 0.09 0.056 1.51 1.84 0.33 0.0023

1949-1990 1.56 1.67 0.11 0.0005 1.57 1.48 -0.09 0.5664

1949-2000 1.68 1.7 0.02 0.4615 1.68 1.29 -0.39 0.4202

Considering break in intercept only, productivity growth is significantly different pre- and post-break with 1980 or 1990 as break point. TFP grows faster in the after break-point period.Considering both breaks in intercept and trend, productivity growth is significantly different with 1980 as break point. Again, TFP grows faster in the after break-point period.

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Productivity Slowdown Tests

Table 4: Structural Change Tests using time trend (national level)

Time Period During Period After Period Difference P-value Chow-test

F statistics P value

1949-1976 1.57 1.87 0.3 0.002 5.51 0.00661949-1977 1.55 1.87 0.32 0.004 5.26 0.0081

1949-1978 1.56 1.89 0.33 0.003 5.59 0.0061

1949-1979 1.53 1.86 0.33 0.002 5.21 0.0084

1949-1980 1.51 1.84 0.33 0.002 5.3 0.0078

1949-1981 1.47 1.78 0.31 0.004 6.96 0.002

1949-1982 1.49 1.77 0.28 0.008 6.57 0.0027

1949-1983 1.51 1.78 0.27 0.015 5.76 0.00531949-1984 1.46 1.64 0.18 0.073 13.73 01949-1985 1.48 1.61 0.13 0.199 12.94 0

Productivity grew faster in the “after-break” period with any year between 1976 and 1984 as break pointChow test confirms significant structural change in any year between 1976 and 1985

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Group Mean Tests

Considering only differences in mean values for each period, productivity growth is not significantly different between “during” and “after” periods

Table 5: Mean Difference Tests in US Agricultural Productivity GrowthTime Period During Period After Period Difference P-value1949-1960 0.765 1.69 0.925 0.41281949-1970 1.18 1.71 0.53 0.56191949-1980 1.25 1.88 0.63 0.6211949-1990 1.51 1.64 0.13 0.92011949-2000 1.5 1.85 0.35 0.8037note: The difference among groups test is Cochran test.

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Conclusions

U.S. Agricultural Productivity:

Slowdown,

Structural Change,

or Short-term Shocks?

That’s the question!

The results say….

Short-term shocks affect output and productivity growth with input growth being more stableThere is evidence of significant structural breaks in both TFP level and TFP growth rateConsidering the structural break effects, there is no evidence of a productivity slowdown

Trends of Relative Productivity Levels

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Belgium

Denmark

Germany

Greece

Spain

France

Trends of Relative Productivity Levels (Cont.)

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Ireland

Italy

Netherlands

Sweden

United Kingdom

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

website

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

THANK YOU!

Q&A