Eldon
Ball,
Sun Ling Wang,
and Richard Nehring,
Economic Research Service, USDA
This data set provides estimates of productivity growth for the
aggregate farm sector for the period 1948-2008, and estimates of
the growth and relative levels of productivity for the individual
States for the period 1960-2004.
Changes Introduced With This Release
The productivity estimates have been revised with this release.
The revisions were necessitated by the adoption of new sources for
data on employment, hours worked, and compensation per hour. The
data on self-employed and unpaid family workers are taken from the
decennial Census of Population and the annual Current Population
Survey. We introduced the new data series when our original data
source—the Farm Labor Survey administered by USDA's National Agricultural
Statistics Service—was discontinued after 2002. The National Income
and Product Accounts (NIPA) are the source for data on employment,
hours worked, and compensation of hired farm workers. The adoption
of the new data sources has allowed us to extend our estimates of
labor input (and hence productivity) beyond 2002, but has also required
that we revise these series for the years prior to 2002.
We also introduced changes in the way we measure capital input.
There has been a long-standing debate over whether an ex post or ex
ante measure of the user cost of capital should be used in
growth accounting. In the ex post approach (see, for example,
Jorgenson and Griliches, 1967; Christensen
and Jorgenson, 1969;
Jorgenson, Gollop, and Fraumeni, 1987), it is assumed that the
rate of return is equalized across assets. Then this unknown rate
can be found by using the condition that the sum of returns across
assets (where the return on an asset is the product of its user
cost and the flow of services it yields) equals observed gross
profits. The alternative ex ante approach (see Coen,
1975;
Penson, Hughes, and Nelson, 1977; Diewert,
1980; Romain, Penson,
and Lambert, 1987; Ball et al., 2008) employs a rate of return
derived from financial market data, together with estimates of
expected rather than actual asset price inflation. We adopt the
latter approach. The ex ante rate is calculated as the
nominal yield on investment grade corporate bonds adjusted for
expected, rather than actual, price inflation. Inflation is modeled
as an autoregressive process.
Our estimates of the stock of land are based on county-level data
on land area and value obtained from the Census of Agriculture.
Data for the inter-census years are obtained through interpolation
using spline functions. The Census reports the value of farm real
estate ( i.e., land and structures), as opposed to the
value of land. Historically, the value of farm real estate was
partitioned into components using information from the Agricultural
Economics and Land Ownership Survey (AELOS). However, the AELOS
was last published in 1999. More recently, we have relied on data
from the annual Agricultural Resource Management
Survey (ARMS) to partition real estate values into its components.
Pesticides and fertilizer are important intermediate inputs, but
their data require adjustment since these inputs have undergone significant
changes in input quality over the study period. Since input price
and quantity series used in a study of productivity must be denominated
in constant-efficiency units, we construct price indexes for fertilizers
and pesticides from hedonic regression results. The corresponding
quantity indexes are formed implicitly as the ratio of the value
of each aggregate to its price index.
The Role of Productivity Growth in Agriculture
The rise in 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 by Kendrick
and Grossman (1980) and Jorgenson,
Gollop, and Fraumeni (1987) share this common
conclusion. In a recent study,
Jorgenson, Ho, and Stiroh (2005) find that productivity growth in agriculture averaged 1.9 percent
over the 1977-2000 period. Output grew at a 3.4 percent average
annual rate over this period. Thus productivity growth accounted
for almost 80 percent of the growth of output in the farm sector.
Moreover, only three of the forty-four sectors covered by the
Jorgenson et al. (2005) study achieved higher rates of productivity
growth than did agriculture.
USDA has been monitoring agriculture's productivity
performance for decades. In fact, in 1960, USDA was the first
agency to introduce multifactor productivity measurement into the
Federal statistical program. Today, the Department's Economic Research
Service (ERS) routinely publishes total factor productivity (TFP)
measures based on a sophisticated system of farm production accounts.
Its TFP model is based on the transcendental logarithmic (translog)
transformation frontier. It relates the growth rates of multiple
outputs to the cost-share weighted growth rates of labor, capital,
and intermediate inputs.
See Ball et al. (1997, 1999) for a complete description
of the USDA model.
The applied USDA model is quite detailed. The changing demographic
character of the agricultural workforce is used to build a quality-adjusted
index of labor input. The estimates of depreciable capital are
derived by representing capital stock at each point of time as
a weighted sum of past investments where the weights correspond
to the relative efficiencies of assets of different ages. The
same pattern of decline in efficiency is used for both capital
stock and the rental price of capital services, so that the requirement
for internal consistency of a measure of capital input is met.
The index of land input is based on the
physical characteristics (i.e., quality)
of a parcel of
land and its location relative to population centers. The contribution
of feed, seed, energy, and agricultural chemicals are captured
in the index of intermediate inputs. An important innovation
is the use of hedonic price indexes in constructing measures of
fertilizer and pesticide consumption.
The result is a USDA time
series of total factor productivity indexes now spanning the
period 1948-2008 (see tables 1-2).
Measures of economic performance of the individual States are
also compiled for the period 1960-2004. The State series provides
estimates of the growth and relative levels of total factor productivity
(see tables
3-22).
Farm Sector Productivity Growth in the U.S.
Input 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 this to be
the case for the aggregate economy for every subperiod over 1948-79.
Denison (1979) draws a similar conclusion
for all but one subperiod, covering the longer period 1929-76.
In their sectoral analysis, Jorgenson, Gollop, and Fraumeni find
that output growth relies most heavily on input growth in 42 of
47 private business sectors in the 1948-79 period, and in a more
aggregated study (Jorgenson and Gollop, 1992) that extends through
1985, in 8 of 9 sectors.
Agriculture turns out to be one of the few exceptions: productivity
growth dominates input growth. This
is confirmed
in table 2 that
reports the sources of output growth in the farm
sector for the entire 1948-2008 period and 10 peak-to-peak subperiods.
(The subperiods are not
chosen arbitrarily, but are measured from cyclical peak to peak
in aggregate economic activity. Since the data reported for each subperiod are
average annual growth rates, the unequal lengths of the subperiods
do not affect the comparisons across subperiods. This convention
and these subperiods have been adopted by the major productivity
studies). Applying the USDA model, output growth equals the
sum of contributions of labor, capital, and materials 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.
The singularly important role of productivity growth in agriculture
is made all the more remarkable by the dramatic contraction in
labor input in the sector, a pattern that persists through
every subperiod. Over the entire 1948-2008 period, labor
input declined
at an average annual rate of nearly 2.5 percent. When weighted
by its 20-percent share in total costs, the contraction in
labor input contributes an annual average -0.51 percentage point
per year to output growth.
Capital input (excluding land) in the sector exhibits a
different history. Its contribution to output growth alternates
between positive and negative over the 1948-2008 period. On average,
however, capital input increases over the period. Its
positive growth contributes an annual average 0.01 percentage
point to output growth.
Land input declined throughout the study period. Its contribution
to output growth averaged a -0.10 percentage point per
year over the full sixty-year period.
Material input's contribution was negative in
three of the five most recent subperiods, but averaged a substantial positive
rate equal to 0.66 percent per year over the postwar period. Though large, this
positive contribution just offsets the negative contributions through labor
and land. The net contribution of all four inputs was a mere 0.06 percentage
point per year, leaving responsibility for positive growth in farm sector output
substantially to productivity growth.
In examining the results in table
2, some authors (e.g., Alston et al., 2010) find evidence
of a slowdown in the rate of productivity growth. If productivity
growth falters, growing global demand will lead to sharp increases
in food prices and to increased environmental stress as more
marginal lands are brought into production. Meanwhile, funding
for agricultural research, a major driver of productivity growth,
has lagged, both domestically and internationally.
Longrun trends in productivity growth can be obscured by short-term
factors such as extremes in weather or changes in agricultural
policies. For example, output and TFP growth both fell sharply
away from trend in 1983, 1988, and 1993, years of drought and/or
flooding. Productivity also fell in 2007, as the expansion of corn-based
ethanol production prompted a departure from the normal corn-soybean
crop rotation. Corn acreage increased in 2007. But yields per acre
were essentially flat despite increases in chemical (i.e., fertilizer
and pesticides) and energy consumption. Still, statistical analysis
of the data does not provide evidence of a longrun productivity
slowdown.
One way of estimating the productivity growth rate is to fit a
trend line to the logarithm of TFP. First, however, we test whether
the growth rate has changed over time. Stated differently, we test
the null hypothesis of a stable linear model against the alternative
of "breaks" in the parameters in the time series regression.
We reject the hypothesis of a fixed slope coefficient over time,
indicating the presence of a structural break or breaks.
Next, we test whether the TFP time series is stationary. This
is an important step given that it is not admissible to use classical
techniques for inference in models with non-stationary components.
A number of alternative tests have been proposed. These are discussed
in Dickey and Fuller (1979), Phillips
and Perron (1988), and Kwiatkowski,
Phillips, Schmidt, and Shin (1992). The test results indicate that
the TFP series is stationary with trend. Zivot
and Andrews (1992) extend these results to the case where the effects of a structural
break(s) are present. Using the Zivot and Andrews (1992) procedure,
we find the series to be stationary in levels, with a structural
break occurring in 1985.
As a final step, we compare the rates of growth for the subperiods
1948-1985 and 1985-2008. The trend rate of growth for the latter
period is somewhat faster (1.48 percent vs 1.61 percent). However,
this difference is not statistically significant.
Measuring State Productivity
A properly constructed measure of productivity growth for the
aggregate farm sector is certainly important. It provides a useful
summary statistic indicating how economic welfare is being advanced
through productivity gains in agriculture, but it may mask
important State-specific or regional trends. For
this reason, USDA has constructed estimates of the growth and relative
levels of productivity for the 48 contiguous States for the 1960-2004
period (estimates are not made for Alaska and Hawaii). These indexes,
expressed relative to the level of TFP in Alabama in 1996,
are presented in table
19 along
with their percentage rates of growth. In the
table below, we
rank the States by their level of TFP in 2004. We also include
in the table each State's rank in 1960 and the average annual
percentage growth from 1960 to 2004.
States ranked by level and growth
of total factor productivity |
State |
Rank in 2004 |
Level in 2004 |
Rank in 1960 |
Level in 1960 |
Average annual change,
1960-2004 |
Rank |
Change (%) |
California |
1 |
1.7979 |
2 |
0.8643 |
25 |
1.66 |
Florida |
2 |
1.6304 |
1 |
0.8649 |
38 |
1.44 |
Iowa |
3 |
1.5297 |
4 |
0.6733 |
17 |
1.87 |
Illinois |
4 |
1.5297 |
7 |
0.6456 |
11 |
1.96 |
Delaware |
5 |
1.4345 |
6 |
0.6498 |
22 |
1.80 |
Idaho |
6 |
1.4285 |
15 |
0.5891 |
8 |
2.01 |
Indiana |
7 |
1.4220 |
27 |
0.5211 |
5 |
2.28 |
Rhode Island |
8 |
1.4192 |
35 |
0.4766 |
2 |
2.48 |
Georgia |
9 |
1.3891 |
12 |
0.5986 |
14 |
1.91 |
Massachusetts |
10 |
1.3877 |
28 |
0.5069 |
4 |
2.29 |
Arizona |
11 |
1.3847 |
3 |
0.7057 |
33 |
1.53 |
Arkansas |
12 |
1.3705 |
16 |
0.5864 |
12 |
1.93 |
North Carolina |
13 |
1.3554 |
11 |
0.6023 |
19 |
1.84 |
Connecticut |
14 |
1.3209 |
29 |
0.5028 |
6 |
2.20 |
Oregon |
15 |
1.3154 |
46 |
0.4231 |
1 |
2.58 |
New Jersey |
16 |
1.2831 |
10 |
0.6161 |
24 |
1.67 |
Maryland |
17 |
1.2457 |
19 |
0.5578 |
20 |
1.83 |
Minnesota |
18 |
1.2359 |
23 |
0.5462 |
18 |
1.86 |
Ohio |
19 |
1.2075 |
38 |
0.4673 |
7 |
2.16 |
Alabama |
20 |
1.1791 |
5 |
0.6599 |
40 |
1.32 |
Nebraska |
21 |
1.1619 |
17 |
0.5746 |
30 |
1.60 |
Maine |
22 |
1.1458 |
31 |
0.4966 |
15 |
1.90 |
Washington |
23 |
1.1457 |
25 |
0.5362 |
23 |
1.73 |
New York |
24 |
1.1327 |
14 |
0.5898 |
36 |
1.48 |
Mississippi |
25 |
1.1306 |
36 |
0.4738 |
10 |
1.98 |
South Carolina |
26 |
1.1247 |
20 |
0.5531 |
28 |
1.61 |
Wisconsin |
27 |
1.1130 |
22 |
0.5523 |
31 |
1.59 |
Michigan |
28 |
1.1058 |
47 |
0.3832 |
3 |
2.41 |
Vermont |
29 |
1.0762 |
26 |
0.5274 |
26 |
1.62 |
South Dakota |
30 |
1.0760 |
21 |
0.5530 |
35 |
1.51 |
Pennsylvania |
31 |
1.0601 |
34 |
0.4781 |
21 |
1.81 |
Colorado |
32 |
1.0325 |
9 |
0.6359 |
45 |
1.10 |
North Dakota |
33 |
1.0278 |
41 |
0.4461 |
16 |
1.90 |
Missouri |
34 |
1.0212 |
30 |
0.5012 |
27 |
1.62 |
New Hampshire |
35 |
1.0204 |
45 |
0.4231 |
9 |
2.00 |
Kansas |
36 |
1.0124 |
8 |
0.6377 |
46 |
1.05 |
Louisiana |
37 |
0.9904 |
44 |
0.4241 |
13 |
1.93 |
Virginia |
38 |
0.9660 |
32 |
0.4933 |
34 |
1.53 |
Nevada |
39 |
0.9640 |
18 |
0.5594 |
42 |
1.24 |
Utah |
40 |
0.9638 |
33 |
0.4874 |
32 |
1.55 |
Kentucky |
41 |
0.9403 |
40 |
0.4634 |
29 |
1.61 |
New Mexico |
42 |
0.8925 |
37 |
0.4728 |
37 |
1.44 |
Texas |
43 |
0.8873 |
24 |
0.5376 |
43 |
1.14 |
Montana |
44 |
0.8145 |
42 |
0.4447 |
39 |
1.38 |
Oklahoma |
45 |
0.7693 |
13 |
0.5962 |
48 |
0.58 |
Tennessee |
46 |
0.7648 |
39 |
0.4661 |
44 |
1.13 |
West Virginia |
47 |
0.5777 |
48 |
0.3278 |
41 |
1.29 |
Wyoming |
48 |
0.5712 |
43 |
0.4281 |
47 |
0.66 |
These data are available in Excel as Table
22. |
One remarkable similarity exists across all States for the full
1960-2004 period. Every State exhibited a positive and generally
substantial average annual rate of TFP growth. There is considerable
variance, however. The median TFP growth rate over the 1960-2004
period was 1.67 percent per year. However, 9 of the 48 States had
productivity growth rates averaging more than 2 percent per year.
Only Oklahoma and Wyoming had average annual rates of growth less
than 1 percent per year. The reported average annual rates of growth
ranged from 0.58 percent for Oklahoma to 2.58 percent for Oregon
(see
map).
Cumulated over the entire 45-year period, productivity growth in
Oklahoma was responsible for only a 30-percent increase in that
State's output. Over the same period, TFP growth in Oregon resulted
in a 319-percent increase in the State's agricultural output.
The wide disparity in productivity growth rates over the 1960-2004
period resulted in substantial changes in the rank order of States.
Florida and California remain at the top of the pack, although
California rose from second in 1960 to first in 2004.
The largest relative gains in TFP were made by Indiana, Rhose Island,
and Oregon. Indiana jumped from 27th to 7th among the 48 States,
Rhode Island rose from 35th to 8th, and Oregon advanced from 46th
to 15th. This finding is consistent with Gerschenkron's
(1952) notion of the advantages of relative backwardness.
Those States/regions that lagged particularly far behind the technology
leaders had the most to gain from the diffusion of technical knowledge,
and, hence, exhibited the most rapid rates of productivity growth.
Methods
Ball et al. (2004) estimated each State's
growth and relative level of productivity for the period 1960-99
using an index number approach, and this method is used to extend
the series through 2004. A productivity index is generally defined
as an output index divided by an index of inputs. The individual
State productivity indices are formed from Fisher quantity indices
of outputs and inputs. In comparing relative levels of productivity,
we first construct bilateral Fisher indices of output and input
among States. Unfortunately, there is no guarantee of transitivity
in such comparisons, i.e. direct comparisons between two States
may give different results than making indirect comparisons through
other States. Eltetö and
Köves
(1964) and Szulc (1964) proposed independently a
method ("EKS" index) which achieves transitivity
while minimizing the deviations from the bilateral comparisons.
The EKS index is based on the idea that the most appropriate
index to use when comparing two States is the binary Fisher
index. However, when the number I of States in
a comparison is greater than two, the application of the Fisher
index number procedure to the I(I-1)/2 possible pairs
of States gives results that do not satisfy Fisher's circularity
test. The problem, therefore, is to obtain results that satisfy
transitivity, and that deviate the least from the bilateral Fisher
indexes.
Let denote
the bilateral Fisher quantity index for State j relative
to State k. If denotes
the multilateral quantity index, then the EKS method suggests
that should
deviate the least from the bilateral quantity index .
Thus, should
minimize the distance criterion:
Using the first-order conditions for a minimum, it can be shown
that the multilateral quantity index with the minimum distance
is given by:
The EKS quantity index may, therefore, be expressed as the
geometric mean of the I indirect comparisons of j and k through
other States.
We have constructed EKS indices of relative levels of output
and input among all 48 States for a single base year.
We have also constructed these quantity indices for each State
for the period 1960-2004. We obtain indexes of output and input
quantities in each State relative to those in the base State
for each year by linking these time-series quantity indexes with
estimates of relative output and input levels for the base period.
Tables 3-22 present indexes of relative output, input, and productivity
levels among the States for the period 1960-2004, with a base
equal to unity in Alabama in 1996.
Production accounts used in constructing these indices are derived
from State and aggregate accounts for the farm sector constructed
by USDA. 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. The existence of the value-added
function requires that intermediate inputs be separable from primary
inputs (capital and labor). This places severe restrictions on
marginal rates of substitution that are not likely to be realistic.
Moreover, even if the value-added function exists, the exclusion
of intermediate inputs assigns all measured technical progress
to capital and labor inputs, ruling out increased efficiency in
the use of purchased inputs. Accordingly, inputs are not limited
to capital and labor, but include intermediate inputs as well.
Both State and aggregate accounts view all of agriculture within
their respective boundaries as if it were a single farm. Output
includes all off-farm deliveries but excludes intermediate goods
produced and consumed on the farm. The difference is that output
in the aggregate accounts is defined as deliveries to final demand
and intermediate demands in the non-farm sector. State output accounts
include these deliveries plus interstate shipments to intermediate
farm demands.
The next section is organized by component measures:
Output
The output measure begins with disaggregated data for physical
quantities and market prices of crops and livestock compiled for
each State. The output quantity for each crop and livestock category
consists of quantities of commodities sold off the farm, additions
to inventory, and quantities consumed as part of final demand in
farm households during the calendar year. Off-farm sales in the
aggregate accounts are defined only in terms of output leaving
the sector, while off-farm sales in the State accounts include
sales to the farm sector in other States as well.
One unconventional aspect of our measure of total output is the
inclusion of goods and services from certain non-agricultural or
secondary activities. These activities are defined as activities
closely linked to agricultural production for which information
on output and input use cannot be separately observed. Two types
of secondary activities are distinguished. The first represents
a continuation of the agricultural activity, such as the processing
and packaging of agricultural products on the farm, while services
relating to agricultural production, such as machine services for
hire, are typical of the second.
The total output of the industry represents the sum of output
of agricultural goods and the output of goods and services from
secondary activities. We evaluate industry output from the point
of view of the producer; that is, subsidies are added and indirect
taxes are subtracted from market values.
Intermediate Input
Intermediate input consists of goods used in production during
the calendar year, whether withdrawn from beginning inventories
or purchased from outside the farm sector or, in the case of the
State production accounts, from farms in other States. Open-market
purchases of feed, seed, and livestock inputs enter both State
and aggregate farm sector intermediate goods accounts. Withdrawals
from producers' inventories are also measured in output, intermediate
input, and capital input. Beginning inventories of crops and livestock
represent capital inputs and are treated in the discussion of capital
below. Additions to these inventories represent deliveries to final
demand and are treated as part of output. Goods withdrawn from
inventory are symmetrically defined as intermediate goods and recorded
in the farm input accounts.
Data on current dollar consumption of petroleum fuels, natural
gas, and electricity in agriculture are compiled for each State
for period 1960-2004. Prices of individual fuels are taken from
the Energy Information Administration's Monthly
Energy Review.
The index of energy consumption is formed implicitly as the ratio
of total expenditures (less State and Federal excise tax refunds)
to the corresponding price index.
Pesticides and fertilizers have undergone significant changes
in input quality over the study period. Since input price and
quantity series used in a study of productivity must be denominated
in constant-efficiency units, we construct price indexes for fertilizers
and pesticides using hedonic methods.
Under this approach, a good or service is viewed as a bundle of characteristics
which contribute to the productivity (utility) derived from its use. Its price
represents the valuation of the characteristics "that are bundled in it", and
each characteristic is valued by its "implicit" price (Rosen, 1974). However,
these prices are not observed directly and must be estimated from the hedonic
price function.
A hedonic price function expresses the price of a good or service
as a function of the quantities of the characteristics it embodies.
Thus, the hedonic price function for, say pesticides, may be expressed
as ,
where represents
the price of pesticides, X is a vector of characteristics
or quality variables, and D is a vector of other variables.
Kellogg et al. (2002) have compiled data on characteristics that
capture differences in pesticide quality. These characteristics
include toxicity, persistence in the environment, and leaching
potential, among others.
Other variables (denoted by D) are also included in the
hedonic equation, and their selection depends not only on the underlying
theory but also on the objectives of the study. If the main objective
of the study is to obtain price indexes adjusted for quality, as
in our case, the only variables that should be included in D are
time dummy variables, which will capture all price effects other
than quality. After allowing for differences in the levels of the
characteristics, the part of the price difference not accounted
for by the included characteristics will be reflected in the time
dummy coefficients.
Finally, economic theory places few if any restrictions on the
functional form of the hedonic price function. We adopt a generalized
linear form, where the dependent variable and each of the continuous
independent variables is represented by the Box-Cox transformation.
This is a mathematical expression that assumes a different functional
form depending on the transformation parameter, and which can assume
both linear and logarithmic forms, as well as intermediate non-linear
functional forms.
Thus the general functional form of our model is given by:
where is
the Box-Cox transformation of the dependent price variable, ;
that is,
Similarly, is
the Box-Cox transformation of the continuous quality variable where if and if .
Variables represented by D are time dummy variables, not
subject to transformation; ?, a, and ? are unknown parameter vectors,
and e is a stochastic disturbance.
The corresponding pesticide quantity index is formed implicitly
by taking the ratio of aggregate expenditures for pesticides to
the hedonic price index.
Other purchased inputs collectively account for about 15 percent
of the input service flow. We compute price and implicit quantity
indexes of purchased services such as contract labor services,
custom machine services, machine and building maintenance and repairs,
and irrigation from public sellers of water. Indexes of total intermediate
input are constructed by aggregating across each category of intermediate
input described above.
Capital Input
Measures of capital input and capital service prices for each
State are estimated from the capital stock and rental price for
each asset type for each State.
The perpetual inventory method is used to develop stocks of depreciable capital
from data on investment.
Implicit
rental prices for each asset are based on the correspondence between
the purchase price of the asset and the discounted value of future
service flows derived from that asset.
Under the perpetual inventory method, capital stock at the end
of each period is measured as the sum of all past investments,
each weighted by its relative efficiency. We assume that the relative
efficiency of capital goods declines with age, giving rise to the
need for replacement of productive capacity. The proportion of
investment to be replaced is equal to the decline in efficiency
during each period. These proportions represent mortality rates
for capital goods of different ages. Replacement requirements in
each period are the weighted sum of past investments, where the
weights are the mortality rates. The change in capital stock in
any period is equal to the acquisition of new investment goods
less replacement requirements.
Estimating Replacement
To estimate replacement, we must introduce an explicit description
of the decline in efficiency. This function, d, may be
expressed in terms of two parameters, the service life of the
asset, say L, and a curvature or decay parameter, say ß. Initially,
we will hold the value of L constant and evaluate the efficiency
function for various values of ß. One possible form for the efficiency
function is given by:
This function is a form of a rectangular hyperbola that provides
a general model incorporating several types of depreciation as
special cases.
The value of ß is restricted only to values less than or equal
to one. For values of ß greater than zero, the efficiency of the
asset approaches zero at an increasing rate. For values less than
zero, efficiency approaches zero at a decreasing rate.
Little empirical evidence is available to suggest a precise value
for ß. However, two studies (Penson, Hughes and
Nelson, 1977; Romain,
Penson and Lambert, 1987) provide evidence that efficiency
decay occurs more rapidly in the later years of service, corresponding
to a value of ß in the
0 to 1 interval. For purposes of this study, it is assumed
that the efficiency of a structure declines slowly over most of
its service life until a point is reached where the cost of repairs
exceeds the increased service flows derived from the repairs, at
which point the structure is allowed to depreciate rapidly (ß=0.75).
The decay parameter for durable equipment (ß=0.5) assumes that
the decline in efficiency is more uniformly distributed over the
asset's service life.
Consider now the efficiency function that holds ß constant
and allows L to vary. This concept of variable service
lives is related to the concept of investment, where investment
is a bundle of different types of capital goods.
Each of the different types of capital goods is a homogeneous
group of assets in which the actual service life, L,
is a random variable reflecting quality differences, maintenance
schedules, etc. For each asset type, there exists some mean
service life,
,
around which there exists some distribution of actual service
lives. In order to determine the amount of capital available
for production, the actual service lives and their frequency
of occurrence must be determined. It is assumed that the underlying
distribution is the normal distribution truncated at points
two standard deviations above and below the mean service life.
Once the frequency of occurrence of a particular service
life has been determined, the efficiency function for that
service life is calculated using the assumed value of ß.
This process is repeated for all possible service lives. An
aggregate efficiency function is then constructed as a weighted
sum of the individual efficiency functions, using the frequency
of occurrence as weights. This function not only reflects changes
in efficiency, but also the discard distribution around the
mean service life of the asset.
Finally, beginning
inventories of crops and livestock are also included in capital
input. We estimate the stock of inventories using the perpetual
inventory method, assuming zero replacement.
Capital Rental Prices
The behavioral assumption underlying the derivation of the rental
price of capital is that firms buy and sell assets so as to maximize
the present value of the firm. This implies that firms will add
to the capital stock so long as the present value of the net revenue
generated by an additional unit of capital exceeds the purchase
price of the asset. This can be stated algebraically as:
where p is the price of output, wK is
the price of investment goods, and r is the real discount
rate. To maximize net present value, firms will continue to add
to capital stock until this equation holds as an equality:
where c is the implicit rental price of capital.
The rental price consists of two components. The first term, rwK,
represents the opportunity cost associated with the initial investment.
The second term, is
the present value of the cost of all future replacements required
to maintain the productive capacity of the capital stock.
Let F denote the present value of the stream of capacity
depreciation on one unit of capital according to the mortality
distribution m:
where
Since replacement at time t is equal to capacity depreciation
at time t :
so that
The real rate of return, r in the above expression, is
calculated as the nominal yield on
Moody's AAA-rated corporate bonds less the rate of inflation as measured
by the implicit deflator for gross domestic product. An ex ante
rate is then obtained by expressing observed real rates as an ARIMA
process. We then calculate F holding
the required real rate of return constant for that vintage of capital
goods. In this way, implicit rental prices c are calculated
for each asset type.
Indexes of capital input in each State are constructed by aggregating
over the different capital assets using as weights the asset-specific
rental prices. Service prices for capital input are formed implicitly
as the ratio of the total current dollar value of capital service
flows to the quantity index. The resulting measure of capital input
for each State is adjusted for changes in input quality.
Land Input
To obtain a constant-quality land stock, we first construct intertemporal
price indexes of land in farms. The stock of land is then constructed
implicitly as the ratio of the value of land in farms to the intertemporal
price index. We assume that land in each county is homogeneous,
hence aggregation is at the county level.
Differences in the quality of land across States and regions prevent
the direct comparison of observed prices. To account for these
quality differences, we calculate relative prices of land from
hedonic regression results.
As noted above, the hedonic approach views land as a bundle of
characteristics which contribute to output derived from its use.
The World Soil Resources Office of the USDA's Natural Resource
Conservation Service has compiled data on land characteristics
(see Eswaren,
Beinroth, and Reich (2003)). They develop a procedure for evaluating
inherent land quality, and use this procedure to assess land resources
on a global scale.
Given the Eswaren, Beinroth, and Reich database, we use GIS to overlay State
and county boundaries. The result of the overlay gives us the proportion of
land area of each county that is in each of the soil stress categories.
These characteristics
include soil acidity, salinity, and moisture stress, among others.
The "level" of each characteristic is measured
as the percentage of the land area in a given region that is subject
to stress. A detailed description of the characteristics included
in the hedonic model is provided in Ball et
al. (2007). The environmental
attributes most highly correlated with land prices in major agricultural
areas are moisture stress and soil acidity. In areas with moisture
stress, agriculture is not possible without irrigation. Hence irrigation
(i.e., the percentage of the cropland that is irrigated) is included
as a separate variable. Because irrigation mitigates the negative
impact of acidity on plant growth, the interaction between irrigation
and soil acidity is included in the vector of characteristics.
In addition to environmental attributes, we also include a "population
accessibility" score for each county in each State. These indices
are constructed using a gravity model of urban development, which
provides a measure of accessibility to population concentrations.
A gravity index accounts for both population density and distance
from that population. The index increases as population increases
and/or distance from that population center decreases.
Labor Input
The USDA labor accounts for the aggregate farm sector incorporate
a demographic cross-classification of the agricultural labor force.
Matrices of hours worked and compensation per hour have been developed
for laborers cross-classified by sex, age, education, and employment
classemployee versus self-employed and unpaid family workers.
ERS developed a set of similarly formatted but otherwise demographically
distinct matrices of labor input and labor compensation by State
by combining the aggregate farm sector matrices with State-specific
demographic information available from the decennial census of
population. The result is State-by-year matrices of hours worked
and hourly compensation with cells cross-classified by sex, age,
education, and employment class and with each matrix consistent
with the USDA hours-worked and compensation totals.
Labor compensation (opportunity cost) data for self-employed and
unpaid family workers are not
observed. As a result, for each
State and year, self-employed and unpaid family workers in each
State are imputed using the mean wage earned by hired workers with
the same demographic characteristics.
Indexes of labor input are constructed for each State over the
1960-2004 period using the demographically cross-classified hours
and compensation data. Labor hours having higher marginal productivity
(wages) are given higher weights in forming the index of labor
input than are hours having lower marginal productivities. Doing
so explicitly adjusts indexes of labor input for quality change
in hours.
Ongoing and Planned Research
Productivity Growth in U.S. Agriculture and the Role of Public
R&D
We use the production accounts for the States to estimate both
the Luenberger productivity indicator and its dual, the Bennet-Bowley
productivity indicator. This work takes a broader view of the production
process to account for the relationship between productivity change
and changes in prices and profits. This allows us to decompose
changes in profitability in agriculture into a normalized price
change indicator and a Bennet-Bowley productivity indicator. We
then investigate the relationship between productivity growth and
public investment in research and development. The relationship
between price change and R&D is negative, and there is a weak
negative relationship between R&D and profits, which is consistent
with our decomposition of profit change into price and productivity
components. Contact Eldon
Ball.
Impact of Local Public Goods on U.S. Agricultural
Productivity Growth
This study looks at the impact
of public R&D expenditure on U.S. agricultural productivity growth.
We estimate a dual cost function using state-by-year panel data. Capital
stocks include "own" R&D and "spill-in" R&D from other states.
The latter is measured based on both geographic location and product
mix. We also examine the roles of extension, infrastructure, and human
capital in the dissemination of technology. Our results indicate that
higher levels of "public goods" result in lower cost of production, although
the social rates of return differ markedly across states. Contact: Sun
Ling Wang.
Productivity Growth Decomposition in U.S. Agriculture
This study uses State-level panel data to estimate total factor
productivity (TFP) change components. Our focus is on the measurement
and decomposition of TFP change into technical change and scale
components as well as distortions in output and input prices.
A multi-output, multi-input transformation function is used
to derive the components of TFP change. These components are
then computed from the multi-output translog cost function
estimated using a system approach. We also consider an estimation
approach in which the TFP change equation is added to the cost
system to avoid the discrepancy between parametric and non-parametric
measures of TFP change. Our results indicate that at the mean
TFP change is driven by technological change. That is, distortions
and scale components do not contribute much to the mean TFP
change. However, these components vary substantially as evidenced
from their percentile values, as well as their values by state.
Output (input) price distortions are found to have positive
(negative) impact on TFP change for most of the states. We
argue that output price distortions are the result of government
intervention in output markets. More specifically, the distortions
are caused by the divergence between observed and shadow output
prices (i.e., effective prices that include the effects of
government subsidies). Input price distortions more likely
reflect quasi-fixity of inputs. Contact: Eldon
Ball.
Productivity and International Competitiveness of
Agriculture in the European Union and the United States
This study looks at international competitiveness of agriculture
in the United States and the European Union. At the outset
it is necessary to define a measure of competitiveness. We
define international competitiveness as the price of output in
the Member States of the European Union relative to that in the
United States. We then decompose relative price movements into
changes in relative input prices and changes in relative productivity
levels. Our price comparisons indicate that the United States
was more competitive than its European counterparts throughout
the period 1973-2002, except for the years 1973-74 and 1983-85.
Our results also suggest that the relative productivity level
was the most important factor in determining international
competitiveness. Over time, however, changes in
competitiveness were strongly influenced by variations in
exchange rates through their impact on relative input prices.
During the periods 1979-1984 and 1996-2001, the strengthening dollar
helped the European countries improve their competitive position,
even as their relative productivity performance lagged. Contact Eldon
Ball.
Quality-Adjusted Price and Quantity Indices for Pesticides
Revisited
The use of quality-adjusted pesticide price and quantity indices
is critical in calculating agricultural productivity and in estimating
aggregate supply models. Indices need to be adjusted
for quality differences across pesticides and years because there
are important inherent differences in pesticide characteristics
that prevent the direct comparison of observed prices of pesticides
over time and across regions. We develop quality-adjusted
measures by estimating hedonic pesticide price functions; hedonic
functions express the price of a good or service as a function
of the quantities of the characteristics it embodiesin this
case, pesticide potency, hazardous characteristics, and persistence.
When we control for such pesticide characteristics in a hedonic
price function, we can then derive quality-adjusted pesticide price
indices for States and major crops 1960-2005, updating a previous
database that ended in 1999. Contact Richard
Nehring.
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