Agricultural Productivity in the United States: Data Documentation and Methods

This data set provides estimates of productivity growth in the U.S. farm sector over the period 1948-2004, and estimates of the growth and relative levels of productivity across the individual States for the 1960-2004 period.

The data series has been revised with this release. Historically, the Farm Labor Survey, administered by USDA's National Agricultural Statistics Service, provided estimates of the number of self-employed and unpaid family members working on farms, but this series was discontinued in 2002. We have adopted a new source for this information, drawing these data from the decennial Census of Population and the annual Current Population Survey (CPS). The new data source allowed us to extend estimates beyond 2002, but also required that we revise estimates for the years prior to 2002.

Studies About Agricultural Productivity

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 more recent study, Jorgenson and Gollop (1992) find that productivity growth over the 1947-85 period accounted for 82 percent of output growth in agriculture, compared with 13 percent in the private nonfarm economy. Moreover, the rate of productivity growth over this period in agriculture (1.58 percent) was nearly four times the corresponding rate in the nonfarm economy (0.44 percent).

Further evidence of the importance of productivity growth in agriculture is provided by Jorgenson, Ho, and Stiroh (2005). They find that productivity growth in agriculture averaged 1.9 percent over the 1977-2000 period and output grew at a 2.4 percent average annual rate over this period. Thus, productivity growth accounted for almost 80 percent of the growth of output in the farm sector. Only three of the forty-four sectors covered by the Jorgenson et al. study exhibited higher rates of productivity growth than did agriculture.

How USDA Estimates Productivity

USDA has been monitoring the 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) publishes total factor productivity (TFP) measures based on a sophisticated system of farm production accounts. The ERS 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 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 contributions 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 spanning the period 1948-2004 (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 the graph and in the table below that reports the sources of output growth in the farm sector for the full 1948-2004 period and 10 peak-to-peak subperiods. (The subperiods are not chosen arbitrarily, but are measured from cyclical peak to peak. 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 labor, capital, and material inputs and TFP growth. (The contribution of each input equals the product of the input's growth rate and its respective share of total cost.)

Sources of growth in the U.S. farm sector (average annual growth rates in percent)
	1948- 2004		1948- 1953	1953- 1957	1957- 1960	1960- 1966	1966- 1969	1969- 1973	1973- 1979	1979- 1989	1989- 1999	1999- 2004
Labor	-0.56		-0.86	-1.14	-0.89	-0.86	-0.65	-0.42	-0.22	-0.35	-0.24	-0.78
Capital	-0.08		0.61	0.01	-0.06	0.06	0.14	-0.12	0.39	-0.67	-0.28	-0.11
Materials	0.61		1.56	1.16	1.45	0.74	1.23	0.76	1.01	-0.66	1.24	-1.15
Total factor productivity	1.77		0.45	1.00	3.80	1.11	1.56	2.24	1.28	2.53	1.44	2.79
Total output growth	1.74		1.76	1.03	4.31	1.04	2.28	2.46	2.46	0.86	2.17	0.75
Output growth equals the sum contributions of labor, capital, and materials inputs and total factor productivity growth. These data are available in Excel as Table 2.

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 full 1948-2004 period, labor input declined at an average annual rate of nearly 2.6 percent. When weighted by its 22-percent share in total costs, the contraction in labor input contributes an annual average -0.56 percentage point per year to output growth.

Capital input in the sector exhibits a different history. Its contribution to output growth alternates between positive and negative over the 1948-2004 period. On average, however, capital, like labor, contracts over the full period. Its negative growth contributes an annual average -0.08 percentage point to output growth.

Material inputs contribution was negative in two of the three most recent subperiods, but averaged a substantial positive rate equal to 0.61 percent per year over the full period. Though large, this positive contribution was not sufficient to outweigh the negative contributions of labor and capital. The net contribution of all three inputs was -0.03 percentage point per year on average, leaving the positive growth in farm sector output wholly attributable to productivity growth.

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 not reflect important regional or State-specific 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.

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, 10 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 0.50 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 25-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, Washington, and Oregon. Indiana jumped from 27th to 7th among the 48 States, Washington rose from 25th to 8th, and Oregon advanced from 45th 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
• Intermediate Input
• Capital Input
• Land Input
• Labor Input

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 1960-2004 period. Since input price and quantity data 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. A price index of fertilizers is formed by regressing the prices of single-nutrient and multigrade fertilizer materials on the proportion of nutrients contained in the materials. Price differences across pesticides are assumed due to differences in physical characteristics such as toxicity, persistence in the environment, and leaching potential. The corresponding quantity indexes are formed implicitly as the ratio of the value of each aggregate to its 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, w_K 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, rw_K, 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

It can be shown that:

so that

The real rate of return, r in the above expression, is calculated as the nominal yield on investment grade 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, indexes of relative prices of land are constructed using hedonic methods where land is viewed as a bundle of characteristics which contribute to the output derived from its use. According to the hedonic approach, the price of land represents the valuation of the characteristics "that are bundled in it," and each characteristic is valued by its implicit price. However, these prices are not observed directly and must be estimated from the hedonic price function. If we observe different "quality combinations" selling at different prices, it is possible to estimate, at the margin, the prices of these characteristics.

The World Soil Resources Office of the USDA's Natural Resource Conservation Service has compiled data on characteristics that capture differences in land quality (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. We overlay U.S. State and county boundaries onto this data. 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 class—employee 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 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 about this research.

Decomposition of Measured Agricultural Productivity Change Using the Shadow Price Approach

The current U.S. Department of Agriculture practice for measuring total factor productivity growth in agriculture is based upon the economic approach to index numbers (Diewert, 1976; Caves, Christensen, and Diewert, 1982) and the assumption that agricultural producers are both allocatively and technically efficient. This approach relies exclusively on observed price and quantity data. Therefore, if observed prices differ from prices used in production decisions, the index number results will likely be ‘inappropriate.' The divergence of observed and producer prices will lead to an inefficient allocation of resources (or allocative inefficiency). This research will address the price divergence issue and decompose measured productivity change into a component arising from distortions due to government intervention in agricultural markets and components measuring technical change and scale economies. Contact Eldon Ball about this research.

Productivity and International Competitiveness of European Union and United States Agriculture

This study examines the role of variations in exchange rates, changes in relative prices of factors of production, and the relative growth of total factor productivity in explaining the competitiveness of European Union and United States agriculture. At the outset it is necessary to define a measure of competitiveness. Our measure of competitiveness is the price of industry output in the member countries relative to the price in the United States. Relative output prices are summarized by means of purchasing power parities. To account for changes in competitiveness, we calculate purchasing power parities for inputs employed in agriculture—capital, land, labor, and materials. The final step in accounting for competitiveness is to measure relative levels of productivity. For this purpose we employ a multilateral model of production. This model allows us to express the price of output in each country as a function of prices of inputs and the level of productivity in that country. We account for differences in relative prices of output among countries by allowing input prices and levels of productivity to differ across countries. We find that the main factor behind changes in international competitiveness is the gap in relative productivity levels. However, changes in international competitiveness over time are strongly influenced by variations in exchange rates through their impact on relative input prices. Contact Eldon Ball about this research.

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 embodies—in 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 about this research.

References

Ball, V. Eldon, William Lindamood, Richard Nehring and Carlos San Juan Mesonada. "Capital as a Factor of Production: Measurement and Data," Applied Economics 39 (December 2007): 1-25.

Ball, V. Eldon, Jean-Pierre Butault, Carlos San Juan Mesonada, and Ricardo Mora. "Productivity and International Competitiveness of European Union and United States Agriculture, 1973-2002," Unpublished manuscript, 2007.

Ball, V. Eldon, Charles Hallahan, and Richard Nehring. "Convergence of Productivity: An Analysis of the Catch-up Hypothesis within a Panel of States," American Journal of Agricultural Economics 86 (December 2004): 1315-1321.

Ball, V. Eldon, Jean-Christophe Bureau, Jean-Pierre Butault, and Richard Nehring. "Levels of Farm Sector Productivity: An International Comparison," Journal of Productivity Analysis 15(2001): 5-29.

Ball, V. Eldon, Frank Gollop, Alison Kelly-Hawke, and Gregory Swinand. "Patterns of Productivity Growth in the U.S. Farm Sector: Linking State and Aggregate Models," American Journal of Agricultural Economics 81(February 1999): 164-179.

Ball, V. Eldon, Jean-Christophe Bureau, Richard Nehring, and Agapi Somwaru. "Agricultural Productivity Revisited," American Journal of Agricultural Economics 79 (August 1997): 1045-1063.

Caves, D.W., L.R. Christensen, and W.E. Diewert. “Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers,” The Economic Journal 92 (1982): 73-86.

Denison, Edward. "Explanations of declining productivity growth," Survey of Current Business 59 (August 1979): 1-24.

Diewert, W. E. 1976. "Exact and superlative index numbers,"Journal of Econometrics 4: 115-146.

Eltetö, O. and P. Köves, "On an Index Computation Problem in International Comparisons," Statisztikai Szelme 42 (1964): 507-18.

Eswaren, H., F. Beinroth, and P. Reich. "A Global Assessment of Land Quality," in Keith Wiebe, ed. Land Quality, Agricultural Productivity, and Food Security. Cheltenham, UK: Edward Elgar, 2003.

Gerschenkron, A. “Economic Backwardness in Historical Perspective,” in B.F. Hoselitz (ed.) The Progress of Underdeveloped Areas. Chicago: University of Chicago Press, 1952.

Jorgenson, D., M. Ho, and K. Stiroh. Productivity: Information Technology and the American Growth Resurgence. Cambridge: The MIT Press, 2005.

Jorgenson, D., and F. Gollop. "Productivity Growth in U.S. Agriculture: A Postwar Perspective." American Journal of Agricultural Economics 74 (August 1992): 745-50.

Jorgenson, D., F. Gollop, and B. Fraumeni. Productivity and U.S. Economic Growth. Cambridge MA: Harvard University Press, 1987.

Kendrick, J.W., and E.S. Grossman. Productivity in the United States, Trends and Cycles. Baltimore MD: The Johns Hopkins University Press, 1980.

Penson, J.B., D.W. Hughes and G.L. Nelson. "Measurement of Capacity Depreciation Based on Engineering Data," American Journal of Agricultural Economics 35 (1977): 321-329.

Romain, R., J.B. Penson, and R. Lambert. "Capacity Depreciation, Implicit Rental Prices,and Investment Demand for Farm Tractors in Canada." Canadian Journal of Agricultural Economics 35 (1987): 373-78.

Szulc, B. "Indices for Multiregional Comparisons," Przeglad Statystyczny 3 (1964): 239-54.