# Documentation and Methods

### Methodology for Measuring International Agricultural Total Factor Productivity (TFP) Growth

The documentation and methods are organized in the following sections:

See Summary Findings and details for the Update and Revision History and References also available.

#### Overview

Improving agricultural productivity has been the world's primary means of assuring that the needs of a growing population don't outstrip the ability 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). The most informative measure 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 over time given available data on agricultural outputs, inputs, and their prices. The approach described here gives internationally consistent and comparable agricultural TFP growth rates, but not TFP levels. Most of the data on production and input quantities used in this analysis come from FAOSTAT database of the United Nations Food and Agriculture Organization (FAO). In some cases FAO input and output data are supplemented with data from national statistical sources. The methodology and data are also fully described in Fuglie (2012, 2015).

#### How These Estimates Differ From Other ERS Productivity Accounts for the United States

To facilitate international comparisons in ERS International Agricultural Productivity (IAP) data product, certain simplifying assumptions must be made. As such, the estimates of TFP growth reported here may differ from TFP growth estimates reported in other studies using different assumptions, data sources, or methods. In particular, the TFP estimates reported here for the United States differ somewhat from those reported in the ERS Agricultural Productivity in the U.S. data product. The principal differences are (i) the Agricultural Productivity in the U.S. data product uses prices received by U.S. farmers to measure output growth, whereas the IAP data product uses global average agricultural prices to aggregate output; (ii) in the Agricultural Productivity in the U.S. data product, agricultural labor is quality-adjusted by labor’s demographic characteristics—including sex, age, educational attainment, and employment class, whereas the IAP data product uses a headcount of agricultural labor unadjusted for quality differences; (iii) the Agricultural Productivity in the U.S. data product uses a perpetual inventory method to measure farm capital stock (i.e., current capital stock is a function of past capital expenditures, appropriately discounted for depreciation), whereas the IPA data product uses the current inventory method (based on the number of major pieces of machinery in-use on farms) to measure farm capital; and (iv) the Agricultural Productivity in the U.S. data product includes direct measures of more purchased services (such as pesticides, seeds, energy, intermediate services), while the IAP data product accounts for those inputs by assuming that their growth rate reflects the growth rate of other measured inputs. 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 Agricultural Productivity data product reported here is better suited for making comparisons of agricultural TFP growth between the United States and other countries.

#### Model

Total factor productivity (TFP) is defined as the ratio of total output to total inputs. Let total output be given by Y and total inputs by X. Then TFP is simply:

$TFP=Y/X$

(1)

It is often difficult to provide meaningful definitions of real output or real input due to the heterogeneity of outputs produced and inputs used. However, it is possible to provide meaningful definitions of output growth and input growth between any two periods of time using index number theory (Caves, Christensen and Diewert, 1982). 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

$\frac{d\ln(TFP)}{dt}=\frac{d\ln(Y)}{dt}-\frac{d\ln(X)}{dt}$

(2)

which simply states that the rate of change in TFP is the difference between 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 production function, producers maximize profits so that the output elasticity with respect to an input equals the cost share of that input, and markets are in long-run competitive equilibrium so that total revenue equals total cost, then equation (2) can be written as

$\ln\left(\frac{TFP_t}{TFP_{t-1}}\right)=\sum_{i}R_i\ln\left(\frac{Y_{i,t}}{Y_{i,t-1}}\right)-\sum_{j}S_j\ln\left(\frac{X_{j,t}}{X_{j,t-1}}\right)$

(3)

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 output 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 in Eq. (3) is thus the value-share-weighted difference between total output growth and total input growth.

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. In agriculture, 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.

To reduce potential index number bias in TFP growth estimates, cost shares are varied by decade whenever such information is available. For outputs, 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 in the Output subsection under Data). The base period for output prices is 2004-06.

Direct estimates of cost shares were assembled for 22 countries from 16 studies. These 22 countries account for about two-thirds of world agricultural output. For another set of countries where input prices are not available or market-determined, (Sub-Saharan Africa and transition economies of the former Soviet Union and Eastern Europe), three studies provide econometric estimates of production elasticities, which were used in place of cost shares. These regions account for another 8 percent of world agricultural output. For remaining countries, representing about 25 percent of world agricultural output, 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.

The framework outlined above provides a simple means of decomposing the relative contribution of TFP and inputs to the growth in output. Using the function g(.) to signify the annual rate of growth in a variable, the growth in output is simply the growth in TFP plus the growth rates of the inputs times their respective cost shares:

$g(Y)=&space;g(TFP)&space;+\sum_{j=1}^{J}S_jg(X_j)$

(4)

Equation (4) is a cost decomposition of output growth since each Sjg(Xj) 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:

$g(Y)=&space;g(X_1)&space;+&space;g\left&space;(&space;\frac{Y}{X_1}&space;\right&space;)$

(5)

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:

$g(Y)=g(X_1)+&space;g(TFP)&space;+&space;\sum_{j=2}^{J}S_jg\left(\frac{X_j}{X_1}\right)$

(6)

Equation (6) is 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.

Figure 1 gives a graphical depiction of the growth decomposition described in equation (6). The height of the bars indicate the growth rate of real output. Growth in real output is first decomposed into growth attributable to agricultural land expansion (extensification) and growth attributable to raising yield per hectare (intensification). Finally, yield growth itself is decomposed into input intensification (i.e., more capital, labor and fertilizer per hectare of land), and TFP growth, where TFP reflects the efficiency with which all inputs are transformed into outputs. Improvements in TFP are driven by technological change, improved technical and allocative efficiency in resource use, and scale economies. The decomposition of output growth into these components is both intuitively appealing and has direct policy relevance: land expansion and input intensification are strongly influenced by changes in resource endowments and relative prices, whereas TFP growth is strongly influenced by long-term investments in agricultural research and extension services, education, and infrastructure, and changes in resource quality and institutions.

#### Data

FAO’s 1961-2016 annual time series of crop and livestock commodity outputs and land, labor livestock, farm machinery, and animal feed inputs, ILO modeled estimates of agricultural labor since 1990, and International Fertilizer Assocation’s IFADATA data on fertilizer use, are the primary data used to construct the national, regional and global quantity measures. In some cases these are modified or supplemented with data from other sources when they are considered to be more accurate or up-to-date, as described below. Other data sources include national statistical agencies, EUROSTAT, the National Statistical Bureau of China, and the Groningen Growth and Development Center (GGDC). The TFP estimates use the latest available data from these sources. These sources sometimes revise data from previous years to reflect more complete information on these series. Updates to the ERS International Agricultural Productivity database include these revisions to previous years’ data from these sources.

##### Outputs

For agricultural outputs, FAO publishes estimates of annual production of 198 crop and livestock commodities by country since 1961. FAO also aggregates production into a measure of gross agricultural output using a common set of global average commodity prices from 2004-2006 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. The FAO also provides a measure of output net of domestic production used for feed and seed. However, the net production measure does not exclude imported grain that may be used as feed or seed, or grain that is exported and used in another country for these purposes.

Because current (or near current) prices are fixed to aggregate quantities and measure changes in real output over time, the FAO gross agricultural output 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.

Previous updates to these data have smoothed the FAO gross agricultural output data using the Hodrick Prescott filter to disentangle short-run volatility due to weather and other factors from long-run trends. The present data are no longer smoothed to allow users the opportunity to examine the causes of these short-run fluctuations.

##### Inputs

Inputs are divided into six categories: farm labor, agricultural land, two forms of capital inputs (farm machinery and livestock), and two types of intermediate inputs (inorganic fertilizers and animal feed). The primary source of information is FAO, which published annual estimates beginning in 1961 for each country (except for countries created since that time, such as countries that made up the former Soviet Union, Yugoslavia, Czechoslovakia, Ethiopia and Sudan). For countries created after 1961, the TFP series begins at the time of independence, except for countries of the former Soviet Union, for which time time series have been extended back to 1961 using data from Shend (1993) and Lerman et al. (2003).

Farm labor is the total number of adults (males and females) who are economically active in agriculture. The International Labor Organization’s ILOSTAT modeled estimates of agricultural labor are used for years after 1990, and are extrapolated back to 1961 using previously published (and since discontinued) farm labor estimates from FAO. The one exception is Argentina, where ILO modeled estimates are unreasonably low, and appear to be based on labor force surveys conducted only in urban areas. For Argentina, agricultural labor force estimates are from the 10-Sector Database maintained by the GGDC (Timmer et al., 2015). The GGDC estimates for agricutural labor in Argentina are reported annually through 2011, and are extrapolated for more recent years using the 2008-11 average annual growth rate from this series.

Agricultural land is the area in permanent crops (perennials), annual crops, and permanent pasture. Cropland (permanent and annual crops) is further divided into rainfed area and area equipped for irrigation. The areas of rainfed cropland, irrigated area, and permanent pasture are then aggregated into a quality-adjusted measure that gives greater weight to irrigated cropland and less weight to permanent pasture to account for relative land productivity (see the next section on Land Quality). However, for agricultural cropland in Sub-Saharan Africa total area harvested for all crops is used rather than the FAO cropland series (Fuglie and Rada, 2013). For China we use sown crop area (National Bureau of Statistics of China) for cropland, given unreasonable discontinuities in the cropland series of both the FAO and Chinese government sources (Fan and Zhang, 2002). For New Zealand, FAO cropland series prior to 2002 fails to reflect changes in a consistent definition over time. We therefore use the area in grain, seed, fodder, and horticultural crops from Statistics New Zealand (2003) for 1961-2001, and FAO data from 2002 onward. For similar reasons, cropland in Indonesia prior to 1990 is based on national agricultural statistics as reported in Fuglie (2010b).

Farm machinery is the total metric horse-power (CV) of major farm equipment in use. It is the aggregation of the number of 4-wheel riding tractors, 2-wheel pedestrian tractors, power harvester-threshers, and milking machines, expressed in "40-CV tractor-equivalents." The average CV per machine is assumed to be 40 CV per 4-wheel tractor, 12 CV per 2-wheel tractor, 20 CV per power harvester-thresher, and 1 CV per milking machine. However, due to insufficient information no adjustment is made for differences across countries or over time in farm machinery sizes within these categories, except for China, which reports farm machinery inventories in power units (National Statistical Bureau of China). Also, for Indonesia, the FAO figure for the number of power thresher-harvesters in use includes both pedal and power threshing machines. We include only power thresher-harvesters from Indonesian national statistics, as reported in Fuglie (2010b).

The FAO reports continuous time series data for 4-wheel tractors, harvest-threshers and milking machines, but not 2-wheel walking tractors. For many developing countries, particularly in Asia, 2-wheel tractors have been a major component of farm mechanization. For 2-wheel tractors, FAO reports numbers in use for 1970s but then discontinued this series until recommencing it in 2002. For interim years, national farm machinery statistics were collected on 2-wheel tractors in use from the agricultural censuses of China, Japan, South Korea, Taiwan, Thailand, Philippines, Indonesia, Indian, Bangladesh, Pakistan, and Sri Lanka, and interpolated between census years. These countries constitute most of the global use of 2-wheel tractors in use on farms.

Presently, FAO farm machinery statistics only extend to 2009 (and for many countries they may not extend past 2005). To extend estimates of farm machinery to 2012, national statistics on the number of tractors and combine-harvested from more recent years were collected for a number of countries: Bangladesh (Hassan, 2013), China (National Statistical Bureau of China, 2014), Europe (Eurostat), India (Singh et al., 2015), Japan (Ministry of Agriculture, Forestry and Fisheries, 2012), Russia (Russian Federation Federal State Statistics Service, 2015), and the United States (National Agricultural Statistical Service, 2014).

To extend estimates of farm machinery stocks held on farms beyond the last available census or survey estimate, two approaches were used. The first approach uses annual data on new machinery sales, taking into account obsolescence of older machinery, assuming a 15-year useful lifespan for new farm machinery. Data on annual sales of new farm tractors and combine-harvesters during 1991-2013 were collected from farm machinery manufacturers (sources: VDMA, Verband Deutscher Maschinen- und Anlagenbau, or the Mechanical Engineering Industry Association, and John Deere corporate reports) for the United States, Canada, Brazil, Argentina, Mexico, South Africa, and European countries. Estimates of farm-held machinery stocks were extended from the latest available census year by adding the number of new machinery sales since the census year and subtracting the number of tractors purchased 15 years earlier. In other words, if Mc is the stock of machines held on farms in census year c, then the number estimated to be held on farms in year c+1 is:

$M_{c+1}=&space;M_{c}+S_{c+1}-S_{c+1-15}$

(7)

where Sc+1 is the number of new machinery sales in year c+1 and Sc+1-15 is the number of sales 15 years prior to year c+1. Farm machinery stock in year c+2 is estimated as Mc+2 = Mc+1 + Sc+2 – Sc+2-15, and so on for subsequent years. Individual types of farm machinery were then aggregated into the total stock of metric horsepower held on farms using the weights described in the Data section.

The second approach, used for countries for which we do not have information on annual machinery sales, uses an econometric model to estimate the change in farm-held machinery stocks over time since the latest available data on farm machinery stocks. The econometric model is based on the Kislev-Peterson model of farm machinery adoption and farm size. Kislev and Peterson (1982) hypothesized that as non-farm wages rose, farm labor would be induced to migrate to the non-farm sector. This would stimulate farm consolidation and mechanization to replace the labor leaving farms. Thus, farm mechanization would be correlated with non-farm wages and farm size. While the Kislev-Peterson model was developed in specific reference to the United States, in a comparative historical assessment of agricultural mechanization, Binswanger (1986) found a "remarkable similarity in the early mechanization experiences of developed and developing countries." He showed that farm machinery was typically first used for power-intensive operations such as tillage and transport, while mechanization of control-intensive operations like weeding and fruit picking came later, especially in response to rising wages.

Using panel data on countries from 1990 to 2003, we estimated the following fixed effects model:

$ln\left&space;(&space;\frac{CV}{Worker}&space;\right&space;)=&space;\alpha&space;_{c}&space;+&space;\beta_{r}ln\left&space;(&space;\frac{Cropland}{Worker}\right&space;)+\gamma&space;_{r}ln\left&space;(&space;\frac{GDP}{Population}&space;\right&space;)$

(8)

where CV/Worker = metric horsepower of farm machinery per agricultural worker, Cropland/worker = hectares of cropland per agricultural worker (representing average farm size), GDP/Population = GDP per capita in constant 2005 PPP\$ (a proxy for non-farm wages), and α, β, and γ, are parameters to be estimated. The parameter values for β and γ vary by region r (the five regions include developing countries in Asia, Latin America, Sub-Saharan Africa, West Asia-North Africa, Transition countries of the former Soviet Union and eastern Europe, and all other developed countries). Since this is a fixed effect model, the intercept term varies for each country c to account for unobserved country-specific factors.

With parameter estimates of β and γ, (shown as β hat and γ hat in the formula below) then the percent change in CV/Worker can be estimated for countries and years for which data on CV are missing (the symbol ∆ln(quantity) below refers to the percent rate of change in the quantity in parentheses):

$\Delta&space;ln\left&space;(&space;\frac{CV}{Worker}&space;\right&space;)=&space;\hat{\beta&space;_{r}}\Delta&space;ln\left&space;(&space;\frac{Cropland}{Worker}&space;\right&space;)+\hat{\gamma&space;_{r}}\Delta&space;ln\left&space;(&space;\frac{GDP}{Population}&space;\right&space;)$

(9)

The annual growth rate in the total stock of farm machinery is simply the growth rate in CV per agricultural worker given by the formula above plus the growth rate in total agricultural workers. Using this growth rate estimated for each year, the stock of farm machinery is then extended from the last census observation or FAO estimate available.

The Table 1 gives the econometric estimates of β and γ from equation (9). All coefficients are statistically significant at the 1 percent level except the estimate of γ for Sub-Saharan Africa (which is therefore fixed at zero in the regression). The results suggest that rising non-farm wages has been relatively more important in Asia in stimulating farm mechanization compared with other regions.

Table 1. Regression coefficients for predicting growth in farm machinery per worker (see equation 9)
Region Cropland/worker (β) GDP/worker (γ)
Asia & Pacific 0.2753 1.5334
Sub-Saharan Africa 0.1046 0.0000
Latin America & Caribbean 0.1064 0.1168
West Asia-North Africa 1.4186 0.6628
Transition economies 1.0201 0.1808
Developed countries 0.5275 0.3410
Source: USDA, Economic Research Service, International Agricultural Productivity data product. Data and methods as of October 2018.

Livestock Capital is the aggregate value of animals used for breeding, milking, egg laying, wool production, and to provide animal traction. To approximate livestock capital, total inventories of animals on farms, measured in "cattle equivalents" are used. Inventories include dairy cows, other cattle, water buffalo, camels, horses, other equine species (asses, mules, and hinnies), 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, dairy cows and horses, 1.00 for other 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. The source of the data is the International Fertilizer Association’s IFADATA. For small countries, IFADATA only reports regional aggregates for all "other" countries in a region. We apportion this total among these small countries according to their share of total crop area harvested among the group of countries.

Animal Feed is the total energy content of crop (except fodder), animal, and fish products used for feed, measured in thousands of mega-calories (mcal). Data on quantities of each type of animal feed are from the FAO Commodity Balance Sheets. Parameters for the mcal per kg of each feed type are from the National Research Council (1982). The FAO Commodity Balance Sheets are available for each country annual from 1961 to 2013. For beyond 2013, total feed use is assumed to grow at the same rate as the size of the national animal heard, measured in "cattle equivalents" (see Livestock Capital above).

Other Inputs. While these six inputs account for the major part of total agricultural input usage, there are a few types of inputs for which complete country-level data are lacking, namely, use of chemical pesticides, seed, veterinary pharmaceuticals, energy, and services from farm structures. However, more detailed input data are available from several of the national studies from which input cost shares are derived (see section below on Input Cost Shares). To account for these inputs, we assume that their growth rate is correlated with one of the six input variables just described and include their cost with the related input. For instance, 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 veterinary medicines are included in the animal feed cost share, and energy costs are included in the farm machinery cost share. So long as the growth rates of the observed input and its unobserved counterparts are similar, then the model captures the growth of the unobserved inputs in the aggregate input index.

##### Land Quality

The FAO agricultural database provides time-series estimates of agricultural land by country and categorizes this as either permanent pasture or cropland (which is further divided in arable and permanent crop land). 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, however. 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, irrigated cropland, rain-fed cropland, and permanent pastures are converted into "rainfed cropland equivalents" based on their relative productivity (Fuglie, 2010a). Productivity weights vary regionally. In order not to confound the land quality weights with productivity change itself, the weights are estimated using country-level data from the beginning of the period of study (i.e., using average annual data from 1961-65). Let Regioni be a set of indicator variables representing five global regions (i=1,2,…5). For each country, Regioni takes a value of either 1 if the country is in the region and zero otherwise. Regions as (1) developed and former Soviet bloc countries, (2) Asia-Pacific, (3) Latin America and the Caribbean, (4) West Asia and North Africa, and (5) Sub-Saharan Africa. Define agricultural yield as total output Y divided by the sum of cropland and pasture area. We then regress agricultural yield against the proportions of agricultural land in rain-fed cropland (Rainfed), irrigated cropland (Irrig), and permanent pasture (Pasture). Multiplying the land-use proportions by the regional indicator variables allows the coefficients to vary among regions:

$ln\left(\frac{Y}{CroplandPasture}\right)=\sum_{i=1}^{5}\alpha_i(Rainfed*Region_i)+\\\Sigma_i\beta_i(Pasture*Region_i)+\Sigma_i\gamma_i(Irrig*Region_i)$

(10)

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 will countries with more cropland relative to pasture. The estimates of the parameters in equation (10) reflect these differences and provide a ready means of weighting the relative qualities of these land classes.

Table 2 gives the estimated land quality weights from the regression of equation (10) and are from Fuglie (2010a). These indicate that, on average, one hectare of irrigated land was between 1.1 to 3.0 times as productive as rainfed cropland, which in turn was 10-20 times as productive as permanent pasture. The results give plausible weights for aggregating agricultural land across broad quality classes. The approach to account for land quality differences is similar to one developed by Peterson (1987), who derived land quality weights by regressing average cropland values in U.S. states against the share of irrigated and unirrigated cropland and long-run average rainfall. He then applied these regression coefficients to data from other countries to derive an international land quality index. The advantage of the present model is that it is based on international rather than U.S. land yield data and provides results for a larger set of countries.

Table 2. Land quality weights used to measure land area in "rainfed-equivalent" hectares
Region Rainfed cropland Permanent pasture Irrigated cropland
Asia & Pacific 1.0000 0.0566 2.9933
Sub-Saharan Africa 1.0000 0.0155 1.7431
West Asia-North Africa 1.0000 0.0239 1.4508
Latin America & Caribbean 1.0000 0.0298 1.0094
Transition economies & Developed countries 1.0000 0.0942 2.1451
Source: Fuglie (2010a).

This adjustment for changes in different classes of land allows us to further refine the resource decomposition of output growth in equation (6) to isolate the contribution of irrigation apart from expansion in agricultural area to output growth. Letting X1 be the quality-adjusted quantity of land (and for simplicity, dropping the Region subscripts on the land quality parameters), then a change in X1 is given by

$\Delta&space;X_1=\alpha\Delta(Cropland)+\beta&space;\Delta&space;(Pasture)+(\gamma&space;-&space;\alpha)\Delta(Irrig)$

(11)

The first two right-hand-side terms indicate the expansion in land area (with growth in pasture area adjusted for quality to put it in comparable terms with cropland expansion). The third term isolates the contribution of irrigation expansion: (γ-α)*100% gives the percent augmentation to yield, holding other factors fixed, from equipping a hectare of cropland with supplemental irrigation. Dividing equation (11) 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 expansion of agricultural land, extension of irrigation, intensification of other inputs per hectare, and improvements in TFP:

$g(Y)=\left[\theta_c\alpha&space;g(X_{1c})+\theta_p\beta&space;g(X_{1p})+\theta_w(\gamma-\alpha)g(X_{1w})\right]+\sum_{j=2}^{J}S_jg\left(\frac{X_j}{X_1}\right)+g(TFP)$

(12)

where θc,θp,and θw are the shares of quality-adjusted agricultural land in crops (X1c), pasture (X1p), and irrigated area (X1w), respectively (note:X1=X1c+X1p+ X1w). The first two terms [θcαg(X1c)+θpβg(X1p)] give the share of output growth attributable to land expansion (holding yield fixed), while the third term [θw(γ-α)g(X1w)] indicates the share of output growth due to the extension of irrigation (holding other inputs fixed). The fourth term of equation (12) gives the contribution to growth of input intensification and the last term the contribution of growth in total factor productivity.

##### Input Cost Shares

The FAO (and supplementary) quantity data allow us to calculate the growth rates for six categories of production inputs (land, labor, machinery capital, livestock capital, and material inputs represented by fertilizer and feed), but to combine these into an aggregate input measure requires information on their cost shares or production elasticities. For this we draw upon 19 studies that have estimated nationally or regionally representative cost shares or production elasticities for agricultural inputs. These costs shares are assumed to be representative of not only those nations but also for other countries in the same region. For instance, the cost shares from India were applied to other countries in South Asia, the cost shares for Indonesia were applied to other countries in Southeast Asia and the Pacific, the cost shares for Mexico were assigned to other countries in Central America and the Caribbean, and the cost shares for Brazil were applied to other countries in South America as well as the North Africa-West Asia region. 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. For agricultural capital, some of these studies only reported an aggregate cost share for all capital services. To partition capital services into machinery and livestock capital services, the average proportions of capital stock in machinery, livestock and tree capital for low, middle and high income countries reported in Butzer, Mundlak and Larson (2012) are used. The cost share of capital services from trees is assigned to land.

While the lack of direct observations on input cost shares for most countries introduces uncertainty in the TFP estimation, the countries for which cost shares are observed represent about 70 percent of the global agricultural economy. This proportion rises to almost 80 percent when Sub-Saharan Africa and non-Russian republics of the former Soviet Union are included–regions where econometrically-estimated production elasticities are used in place of cost shares. Thus, countries to which input cost shares were imputed represent only about 20 percent of world agricultural output. Another argument in support of this approach is that there is a significant degree of congruence among the cost shares reported for these country studies. For the developing countries for which cost shares data are available (India, Indonesia, China, Brazil and Mexico), farm-supplied inputs (land, labor, and livestock capital) account for between 60 and 90 percent of total costs, while inputs supplied by industry (machinery, or fixed capital, and purchased materials such as fertilizers and processed animal feed), accounted for a far smaller share of resources. The cost share of inputs supplied by industry rises with the income of a country, and accounts for a third or more of total costs in the more highly industrialized countries. The use of modern inputs in transition countries, on the other hand, fell sharply after reforms were initiated in the early 1990s. These patterns of input use is reflected in cost shares estimated or imputed for these countries.

Where data permit, average cost shares are estimated for each decade (1961-70, 1971-80, etc.). This helps avoid index number bias when cost shares evolve over time, for example, if the cost share for intermediate inputs rises relative to those of other inputs. In the dataset tables, the most recent cost shares refer to the decade of 2011-20. The cost shares for this decade are currently based on data only through 2016, and will be updated in future database releases as new data become available.

##### Country and Regional Productivity

Using the methodology and data described above agricultural TFP indexes are estimated for nearly every country of the world on an annual basis beginning in 1961. However, some countries have dissolved or are too small to have complete data. For the purpose of estimating long-run productivity trends, some national data are aggregated to create consistent political units over time. For example, data from the nations that formerly constituted Yugoslavia are added together to make comparisons with productivity before Yugoslavia’s dissolution. Similarly, data were aggregated for Czechoslovakia, Ethiopia and the former Soviet Union to construct continuous data series over 1961-2016. For countries and territories established after 1961, TFP series generally begin in the year in which the country was recognized by the United Nations, depending on data availability. Because some small island nations have incomplete or zero values for some agricultural data, three composite territories were constructed by adding up available data for island states in the Lesser Antilles, Micronesia, and Polynesia. The agricultural TFP index for the West Bank and Gaza begins in 1994.

Altogether, the countries included in the analysis account for more than 99.9 percent of FAO’s global gross agricultural output.

In addition to individual countries, data are aggregated and TFP indexes estimated at the regional level and for countries grouped by their current per capita income level. Input and output quantity aggregation is straightforward since they are all measured in the same units (although not adjusted for quality differences in the inputs). Cost shares are the weighted averages of the national cost shares for the countries in a region or income group.

See References for a list of citations mentioned above.

The provided spreadsheets contain the 1961-2016 annual agricultural TFP indexes, as well the input and output data used in their construction. See the "Explanation" tab in each workbook for a detailed description of the content. The structure of all three files is identical. See the main data page to access the files.

• AgTFPindividualcountries.xlsx provides data for each country/territory listed in Table 3.
• AgTFPcountrygeographicgroups.xlsx provides data for countries/territories grouped by geographic regions as defined in Table 3.
• AgTFPcountryincomegroups.xlsx provides data for countries/territories grouped by income levels according to the 2017 World Bank income classification system.
Table 3—Countries/territories and regional groupings included in the productivity analysis
Sub-Saharan Africa (SSA)
Central Eastern Horn Sahel Southern Western Nigeria
Cameroon
Central African Republic
Republic of the Congo
Democratic Republic of the Congo
Equatorial Guinea
Gabon
Sao Tome & Principe
Burundi
Kenya
Rwanda
Seychelles
Tanzania
Uganda
Djibouti
Ethiopiab
Ethiopia (from 1993)
Eritrea (from 1993)
Somalia
Sudanb
Burkina Faso
Cape Verde
Gambia
Mali
Mauritania
Niger
Senegal
Angola
Botswana
Comoros
Lesotho
Malawi
Mauritius
Mozambique
Namibia
Réunion
Swaziland
Zambia
Zimbabwe
Benin
Côte d’Ivoire
Ghana
Guinea
Guinea-Bissau
Liberia
Sierra Leone
Togo

Latin America & Caribbean (LAC) North America Africa, developed
Northeast Andes Southern Cone Central America Caribbean
Brazil
French Guiana
Guyana
Suriname
Bolivia
Colombia
Peru
Venezuela
Argentina
Chile
Paraguay
Uruguay
Belize
Costa Rica
Guatemala
Honduras
Mexico
Nicaragua
Panama
Bahamas
Cuba
Dominican Republic
Haiti
Jamaica
Lesser Antillesa
Puerto Rico
United States
South Africa
Asia West Asia & North Africa
Developed NE Asia, Developing South Asia SE Asia Pacific West Asia North Africa
Japan
Korea Republic
Taiwan
Singapore
China
Korea, DPR
Mongolia
Afghanistan
Bhutan
India
Nepal
Pakistan
Sri Lanka
Brunei Darussalam
Cambodia
Indonesia
Laos
Malaysia
Myanmar
Philippines
Thailand
Timor-Leste
Viet Nam
Fiji
Micronesiaa
New Caledonia
Papua New Guinea
Polynesiaa
Solomon Islands
Vanuatu
Bahrain
Iran
Iraq
Israel
Jordan
Kuwait
Lebanon
Oman
Qatar
Saudi Arabia
Syria
Turkey
UAE
Yemen
Algeria
Egypt
Libya
Morocco
Tunisia
Europe Former Soviet Union Oceania
Northwest Southern Eastern Europe Transition Baltic East Europe Central Asia & Caucasia
Austria
Belgium-Luxembourgb
Denmark
Finland
France
Germany
Iceland
Ireland
Netherlands
Norway
Sweden
Switzerland
United Kingdom
Cyprus
Greece
Italy
Malta
Portugal
Spain

Albania
Bulgaria
Czechoslovakiab
Czechia (from 1994)
Slovakia (from 1994)
Hungary
Poland
Romania
Yugoslaviab

Estonia
Latvia
Lithuania
Belarus
Kazakhstan
Moldova
Russia Fed.
Ukraine
Armenia
Azerbaijan
Georgia
Kyrgyzstan
Tajikistan
Turkmenistan
Uzbekistan
Australia
New Zealand
a Composite countries composed of several small island nations.
b Statistics from the successor states of Ethiopia (Ethiopia and Eritrea), Sudan (Sudan and South Sudan), Czechoslovakia (Czechia and Slovakia), Yugoslavia (Slovenia, Croatia, Bosnia, Macedonia, Serbia, and Montenegro) were merged to form continuous time series from 1961 onward. Separate TFP indexes for the former Yugoslav Republics are available from 1994 and for Belgium and Luxembourg from 2002.

Last updated: Tuesday, September 29, 2020