Documentation and Methods
Methodology for Measuring International Agricultural Total Factor Productivity (TFP) Growth
The documentation and methods are organized in the following sections:
Improving agricultural productivity has been the world's primary assuring that the needs of a growing population don't outstrip the ability of humanity to supply food. Over the past 50 years, productivity growth in agriculture has allowed food to become more abundant and cheaper (see New Evidence Points to Robust But Uneven Productivity Growth in Global Agriculture, Amber Waves, September 2012). A broad concept of agricultural productivity is total factor productivity (TFP). TFP takes into account all of the land, labor, capital, and material resources employed in farm production and compares them with the total amount of crop and livestock output. If total output is growing faster than total inputs, we call this an improvement in total factor productivity ("factor" = input). TFP differs from measures like crop yield per acre or agricultural value-added per worker because it takes into account a broader set of inputs used in production. TFP encompasses the average productivity of all of these inputs employed in the production of all crop and livestock commodities.
"Growth accounting" provides a practicable way of measuring changes in agricultural TFP across a broad set of countries and regions, and for the world as a whole, given limited international data on production outputs, inputs, and their economic values. The approach described here gives agricultural TFP growth rates, but not TFP levels, across the countries and regions of the world in a consistent, comparable way. Most of the data for the analysis comes from FAOSTAT. In some cases Food and Agriculture Organization (FAO) input and output data are supplemented with data from national statistical sources. The methodology and data are also fully described in Fuglie (2012).
How These Estimates Differ From Other ERS Productivity Accounts for the United States
To facilitate international comparisons, certain simplifying assumptions must be made, and as such the estimates of TFP growth reported here may not be exactly the same as TFP growth estimates reported in other studies using different assumptions or methods. In particular, our TFP estimates for the United States differ slightly from those reported in ERS' Agricultural Productivity in the U.S. data product. The principal differences are (i) the Agricultural Productivity in the U.S. accounts use prices received by U.S. farmers to measure output growth, while for international comparisons, we use a common set of global agricultural prices; (ii) in Agricultural Productivity in the U.S., agricultural inputs are quality-adjusted, while for international comparison purposes, we do not have sufficient data for such quality adjustments; and (iii) Agricultural Productivity in the U.S. accounts use a perpetual inventory method to measure farm capital stock (i.e., current stock is a function of past capital expenditures, appropriately discounted for depreciation), while we use a current inventory method (based on the number of major pieces of machinery in use on farms). Generally, the TFP index reported in the Agricultural Productivity in the U.S. data product should provide a more accurate measure of the rate of technical change in U.S. agriculture. However, the international series reported here are better suited for making comparisons of agricultural TFP growth between the United States and other countries.
Define total factor productivity (TFP) as the ratio of total output to total inputs in a production process. Let total output be given by Y and total inputs by X. Then TFP is simply:
Changes in TFP over time are found by comparing the rate of change in total output with the rate of change in total input. Expressed as logarithms, changes in equation (1) over time can be written as:
which simply states that the rate of change in TFP is the difference in the rate of change in aggregate output and input.
Agriculture is a multi-output, multi-input production process, so Y and X are vectors. When the underlying technology is represented by a constant-returns-to-scale Cobb-Douglas production function and where producers maximize profits so that the output elasticity with respect to an input equals the cost share of that input and markets are in longrun competitive equilibrium so that total revenue equal total cost, then the equation can be written as:
where Ri is the revenue share of the ith output and Sj is the cost-share of the jth input. Total output growth is estimated by summing over the growth rates for each commodity weighted by its revenue share. Similarly, total input growth is found by summing the growth rate of each input, weighted by its cost share. TFP growth is just the difference between the growth of total output and total input.
One difference among growth accounting methods is whether the revenue and cost share weights are fixed or vary over time. Paasche and Laspeyres indexes use fixed weights, whereas the Tornqvist-Thiel and other chained indexes use variable weights. Allowing the weights to vary reduces potential "index number bias." Index number bias arises when producers substitute among outputs and inputs depending on their relative profitability or cost. In other words, the growth rates in Yi and Xj are not independent of changes Ri and Sj. For example, if labor wages rise relative to the cost of capital, producers are likely to substitute more capital for labor, thereby reducing the growth rate in labor and increasing it for capital. For agriculture, index number bias in productivity measurement appears to be more likely for inputs than outputs. Cost shares of agricultural capital and material inputs tend to rise in the process of economic development, while the cost share of labor tends to fall. Commodity revenue shares, on the other hand, appear to show less change over time.
To reduce potential index number bias in TFP growth estimates, input cost shares are varied by decade whenever such information is available. For outputs, however, base year prices (or equivalently, base year revenue shares) are fixed, since these depend on FAO’s measure of constant, gross agricultural output (described in more detail below). The base period for output prices is 2004-06.
A limitation in using equation (3) for measuring agricultural productivity change is a lack of representative cost share data for most countries. Many types of agricultural inputs (such as land and labor) may not be widely traded and heterogeneous in quality, making price or cost determination difficult. We compile estimates from previous studies of input cost shares or production elasticities for individual countries or regions and apply these to equation (3). For countries for which we lack data on cost shares, cost shares are approximated by applying cost shares from a "like" country. The section below on "input cost shares" provides details on the data sources and assumptions. This is similar to the approach used by Avila and Evenson (2010), who applied agricultural input cost shares from Brazil and India to other developing countries, except that we use a richer set of information on cost shares and include industrialized and transition countries in the analysis.
The framework outlined above provides a simple means of decomposing the relative contribution of TFP and inputs to the growth in output. Using a dot above a variable to signify its annual rate of growth, the growth in output is simply the growth in TFP plus the growth rates of the inputs times their respective cost shares:
Equation (4) is an input cost decomposition of output growth since each term gives the growth in cost from using more of the jth input to increase output. It is also possible to focus on a particular input, say land (which we designate as X1), and decompose growth into the component due to expansion in this resource and the yield of this resource:
This decomposition corresponds to what is commonly referred to as extensification (land expansion) and intensification (land yield growth). We can further decompose yield growth into the share due to TFP and the share due to using other inputs more intensively per unit of land:
Equation (6) gives a resource decomposition of growth since it focuses on the quantity change of a physical resource (land) rather than its contribution to changes in cost of production.
FAO’s annual time series from 1961 of crop and livestock commodity production and land, labor, machinery and animal capital, and fertilizer consumption are the primary source for agricultural outputs and inputs used to construct the national and global productivity measures. In some cases these are modified or supplemented with data from national statistical agencies where alternative data are considered to be more accurate or up to date, as described below.
For agricultural output, FAO publishes data on annual production of 189 crop and livestock commodities by country since 1961, aggregates this into a measure of the gross production value using a common set of commodity prices from 2004-06, and expresses this in constant 2005 international dollars. FAO excludes production of animal forages, but includes crop production that is used for animal feed and seed in estimating gross agricultural output.
Because current (or near current) prices are fixed to aggregate quantities and measure changes in real output over time, the FAO gross agricultural production is equivalent to a Paasche quantity index. The set of common commodity prices is derived using the Geary-Khamis method. This method determines an international price pi for each commodity, which is defined as an international weighted average of prices of the i-th commodity in different countries, after national prices have been converted into a common currency using a purchasing power parity (PPPj) conversion rate for each j-th country. The weights are the quantities produced by the country. The computational scheme involves solving a system of simultaneous linear equations that derives both the pi prices and PPPj conversion factors for each commodity and country. The FAO updates these prices every five years and recalculates its index of gross production value back to 1961 using its most recent set of international prices. See Rao (1993) for a thorough description and assessment of these procedures.
We use FAO gross agricultural output in constant 2005 international dollars as the basis for a consistent measure of output for each country and the world over time. However, because of the influence of weather and other factors, agricultural production is exceptionally volatile from year to year, and it can be difficult to disentangle shortrun fluctuations from longterm trends. To relieve the data of some of these fluctuations, the output series is smoothed for each country using the Hodrick-Prescott filter (setting λ=6.25 as recommended for annual data by Ravn and Uhlig, 2002).
For agricultural inputs, FAO publishes data on cropland (total and irrigated), permanent pasture, labor employed in agriculture, animal stocks, the number of farm machinery in use, and inorganic fertilizer consumption. We supplement these data with better or more up-to-date data from national or industry sources when available. For fertilizer consumption, the International Fertilizer Association (IFA) has more up-to-date and accurate statistics than FAO on fertilizer consumption by country, except for small countries. For agricultural statistics on China, a relatively comprehensive dataset is available from ERS with original data from the National Bureau of Statistics of China. For Brazil, we use results of the recently published 2006 Brazilian agricultural census (IBGE) and for Indonesia, we use improved data from Fuglie (2010a) on agricultural land and machinery use which draws on national statistical sources for that country. For Taiwan, we use statistics from the Executive Yuan, Council of Agriculture. For the countries of the former Soviet Union, FAO reports data only from 1991 and onward. We extend the time series for each of the former Soviet Socialist Republics (SSRs) back to 1965 from Shend (1993). Also, since FAO labor force estimates for former SSRs and Eastern Europe are not reliable for the post 1990 years (Lerman et al, 2003; Swinnen, Dries, and Macours, 2005), our sources for agricultural labor data for these countries are EUROSTAT for the Baltic states and Eastern Europe, CISSTAT for Russia, Belorussia and Moldova, the International Labor Organization’s LABORSTA for Ukraine, and national data reported by the Asian Development Bank for Asiatic former Soviet republics.
Inputs are divided into five categories. Farm labor is the total economically active adult population (males and females) in agriculture. Agricultural land is the area in permanent crops (perennials), annual crops, and permanent pasture. Cropland (permanent and annual crops) is further divided into rainfed cropland and cropland equipped for irrigation. However, for agricultural cropland in Sub-Saharan Africa we use total area harvested for all crops rather than the FAO series on arable land. For China, we use area sown to crops reported by ERS because of unreasonably discontinuities in both the FAO and ERS' arable land series for China.
To adjust for differences in productivity quality across agricultural land types, we aggregate rainfed cropland, irrigated area and permanent pasture into a quality-adjusted measure that gives greater weight to irrigated cropland and less weight to permanent pasture in assessing agricultural land changes over time (see the next section on "land quality"). Livestock is the aggregate number of animals in "cattle equivalents" held in farm inventories and includes cattle, camels, water buffalos, horses and other equine species (asses, mules, etc.), small ruminants (sheep and goats), pigs, and poultry species (chickens, ducks, and turkeys), with each species weighted by its relative size. The weights for aggregation are based on Hayami and Ruttan (1985, p. 450): 1.38 for camels, 1.25 for water buffalo and horses, 1.00 for cattle and other equine species, 0.25 for pigs, 0.13 for small ruminants, and 12.50 per 1,000 head of poultry. Fertilizer is the amount of major inorganic nutrients applied to agricultural land annually, measured as metric tons of N, P2O5, and K2O nutrients. We aggregate fertilizer quantities using annual average nutrient prices for N, P2O5, and K2O fertilizers from the International Monetary Fund. Expressing fertilizer consumption in terms of metric tons of "N-fertilizer equivalents," the aggregation weights (relative price of one metric ton of nutrient) are 1.000 for N, 1.36 for P2O5, and 0.85 for K2O. Farm machinery is an aggregation of 4-wheel riding tractors, 2-wheel pedestrian tractors, and power harvester-threshers in use, using metric horsepower (CV) to express total farm tractor and power harvester-threshes in "40-CV tractor-equivalents." The FAO reports time series data for only 4-wheel tractors and harvest-threshers; it recorded information 2-wheel tractors in the 1970s then discontinued this series until recommencing it again in 2002. For interim years, we collected national farm machinery statistics on 2-wheel tractors for the countries where pedestrian tractors are widely employed in farming: China, Japan, South Korea, Taiwan, Thailand, Philippines, Indonesia, Indian, Bangladesh, Pakistan, and Sri Lanka. For aggregation purposes, we assume the following average CV per machine: 40 CV for 4-wheel tractors, 12 CV for 2-wheel tractors, and 25 CV for power harvester-threshers.
While these inputs account for the major part of total agricultural input use, there are a few types of inputs for which complete country-level data are lacking, namely, use of chemical pesticides, seed, prepared animal feed, veterinary pharmaceuticals, energy, and farm structures. However, more detailed input data are available for several of the countries from which we have data on input cost shares. To account for these inputs, we assume that their growth rate is correlated with one of the five input variables just described and include their cost with the related input. For example, services from capital in farm structures as well as irrigation fees are included with the agricultural land cost share; the cost of chemical pesticide and seed is included with the fertilizer cost share; costs of animal feed and veterinary medicines are included in the livestock cost share; and other farm machinery and energy costs are included in the machinery cost share. So long as the growth rates for the observed inputs and their unobserved counterparts are similar, then the model captures the growth of these inputs in the aggregate input index.
The FAO agricultural database provides time-series estimates of agricultural land by country and categorizes this as either cropland (arable and permanent crops) or permanent pasture. It also provides an estimate of area equipped for irrigation. The productive capacity of land among these categories and across countries can be very different. For example, some countries count vast expanses of semi-arid lands as permanent pastures even though these areas produce very limited agricultural output. Using such data for international comparisons of agricultural productivity can lead to serious distortions, such as significantly biasing downward the econometric estimates of the production elasticity of agricultural land (Peterson, 1987).
To account for the contributions to growth from different land types, each of the three land types (irrigated cropland, rain-fed cropland, and permanent pastures) are weighted based on their relatively productivities. The weights are estimated using country-level data from 1961-65. Using regional indicator variables (REGIONi, i=1,2,…5, representing developed counties and SSRs, Asia-Pacific, Latin America and the Caribbean, West Asia and North Africa, and Sub-Saharan Africa, respectively), the log of agricultural land yield is regressed against the proportions of agricultural land in rain-fed cropland (RAINFED), permanent pasture (PASTURE), and irrigated cropland (IRRIG). Including slope indicator variables allows the coefficients to vary among regions:
The coefficient vectors α, β and γ provide the quality weights for aggregating the three land types into an aggregate land input index. Countries with a higher proportion of irrigated land are likely to have higher average land productivity, as are countries with more cropland relative to pasture.
This adjustment for changes in different classes of land allows further refinement of the resource decomposition of output growth in equation (6) to isolate the contribution of irrigation apart from expansion in cropland area to output growth. Letting X1 be the quality adjusted quantity of (rainfed cropland equivalent) land, a change in X1 is given by
The first two terms indicate the expansion in land area (with growth in pasture area adjusted for quality to put it on comparable terms with cropland expansion). The third term isolated the contribution to growth from irrigation expansion: (γ-1)*100% gives the percent augmentation to yield by equipping an acre of cropland with supplemental irrigation. Dividing equation (7) by X1 converts the expression into percentage changes so that it shows the respective contributions of changes in rainfed cropland, pasture area, and irrigation to output growth. Combined with equation (6), the resource decomposition expression shows the contributions to agricultural growth from changes in agricultural land, water resource use, other inputs per hectare of land, and TFP.
Input Cost Shares
The FAO (and supplementary) quantity data allow us to calculate the growth rates for five categories of production inputs (land, labor, machinery capital, livestock capital, and material inputs represented by fertilizer), but to combine these into an aggregate input measure requires information on their cost shares or production elasticities. For this, we draw on other productivity studies that have compiled relatively complete measurements for selected countries and then assign these as "representative" input cost shares for different regions of the world. For instance, the cost shares for Brazil were applied to South America, West Asia, and North Africa; the cost shares for India were applied to other countries in South Asia; and the cost shares for Indonesia were applied to developing countries in Southeast Asia and Oceania. These assignments were based on judgments about the resemblance among the agricultural sectors of these countries. Countries assigned to the cost shares from Brazil tended to be middle-income countries having relatively large livestock sectors, for example.
Countries and Regions
The methodology and data described above allow us to calculate agricultural TFP indexes for nearly every country of the world annually since 1961. However, some countries have dissolved or are too small to have complete data. To estimate longrun productivity trends, we aggregate some national data to create consistent political units over time. For example, data from the nations that formerly constituted Yugoslavia are aggregated to make comparisons with productivity before Yugoslavia’s dissolution; data were aggregated similarly for Czechoslovakia, Ethiopia, and the former Soviet Union. (We also construct TFP series for individual SSRs beginning in 1965.) Because some small island nations have incomplete or zero values for some agricultural data, we constructed three composite "countries" by aggregating available data for island states in the Lesser Antilles, Micronesia, and Polynesia. The countries included in the analysis account for more than 99.7 percent of FAO’s global gross agricultural output. The only areas not included in the analysis that have significant agricultural production are the West Bank and Gaza.
In addition to individual countries, we aggregate the data and construct TFP indexes for major global regions and for the world as a whole. Input and output quantity aggregation is straight forward since they are all measured in the same units (although not adjusted for quality differences in the inputs). To obtain cost shares at the regional level, we take the weighted averages of the cost shares for the countries composing that region. The weights are the country’s share of total costs (or revenue) within the region. Table 1 provides a complete list of countries included in the analysis and their regional groupings.
|Table 1—Countries and regional groupings included in the productivity analysis
|Sub-Saharan Africa (SSA)
Central African Republic
Democratic Republic of the Congo
Sao Tome & Principe
|Latin America & Caribbean (LAC)
Trinidad and Tobago
||Former Soviet Union
|NE Asia, Developing
|Central Asia & Caucasia
||West Asia & North Africa
United Arab Republic
Papua New Guinea
a Composite countries composed of several small island nations.
b Statistics from the successor states of Ethiopia (Ethiopia and Eritrea), Czechoslovakia (Czech and Slovak Republics), and Yugoslavia (Slovenia, Croatia, Bosnia, Macedonia, Serbia and Montenegro) were merged to form continuous time series from 1961 to 2010.
The provided spreadsheets contain the agricultural TFP indexes, as well as all of the input and output data used in their construction. See the "Explanation" tab in the workbooks for a detailed description of the content.
The chart below shows that global agricultural growth (measured by the height of the bars, in average annual percent growth by decade) was slowing in the 1970s and 1980s but then accelerated in the 1990s and 2000s. In the latest decade (2001-10), global output of total crop and livestock commodities was expanding by about 2.5 percent per year.
The different colors of the bars show how much of this growth came from bringing new resources into production (new land, extension of irrigation, and input intensification per acre) and how much came about by raising the TFP of these resources. In the decades prior to 1990, most output growth came about from intensification of input use (i.e., using more labor, capital, and material inputs per acre of agricultural land). Bringing new land into agriculture production and extending irrigation to existing agricultural land were also important sources of growth. Over the last two decades, however, the rate of growth in agricultural resources (land, labor, capital, etc.) has significantly slowed. What has allowed agricultural output to continue to grow despite this slowdown in agricultural resources is productivity—getting more output from existing resources. In the most recent 2001-10 decade, improvements in TFP accounted for more than three-quarters of the total growth in agricultural output worldwide. This TFP reflects the use of new technology and changes in management by agricultural producers around the world.
TFP has replaced resource intensification as the primary source of growth in world agriculture.
While productivity has been the major source of agricultural growth in developed countries for at least the past half-century, the recent acceleration of global TFP growth has occurred through better productivity performance in developing countries and the transition economies of the former Soviet Union and Eastern Europe. In developed and transition countries, total agricultural resources used in agriculture (the amounts of land, labor, capital, and fertilizers) are declining, although output continues to grow because of greater productivity. In developing countries, agricultural resources (except labor) continue to expand and at the same time the productivity of these resources is improving. But productivity improvement accounts for most of the growth in output in all developing-country regions except Sub-Saharan Africa. A key determinant of long-term agricultural TFP growth worldwide is public and private investment in agricultural research and development.
|Table 2—Productivity is the prime driver of agricultural growth in all global regions except Sub-Saharan Africa
||Total factor productivity
||Average annual growth over 2001-10, percent per year
|East & South Asia
|West Asia & North Africa
|Source: USDA, Economic Research Service, International Agricultural Productivity data product.
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 Fan and Zhang (1997) also used sown area in their study of agricultural productivity in China. Both the FAO and ERS series on arable land in China show huge discontinuities in the 1970s or 1980s due to statistical changes to reporting methods. Nonetheless, the sown area series likely overstates growth in cropland somewhat since it includes increases in cropping intensity due to expansion of irrigation and other factors.
 Some adjustments to these data should be noted. The FAO figure for the number of power thresher-harvesters in use in Indonesia actually includes both pedal and power threshing machines. We include only power thresher-harvesters from Indonesian national data. China reports total "power" employed in agriculture in terms of kilowatts, but this likely includes some post-harvest processing machinery like grain mills and oilseed crushers in addition to on-farm machinery. We only include tractors (4-wheel and 2-wheel) and power thresher-harvesters in estimating total farm machinery horse power for China.