2.1. Methods for TFP measurement
Productivity statistics compare changes in outputs to inputs in order to assess the performance of a sector. Two types of productivity measures are partial and multifactor indices. Partial productivity indices relate output to a single input, such as labor or land. These measures are useful for indicating factor-saving biases in technical change but are likely to overstate the overall improvement in efficiency because they do not account for changes in other input use. For example, rising output per worker may follow from additions to the capital stock and higher crop yield may be due to more application of fertilizer. For this reason, a measure of TFP relating output to all of the inputs used in production gives a better indicator of a sector's efficiency than indices of partial productivity.
TFP is usually defined as the ratio of total output to total inputs in a production process. In other words, TFP measures the average product of all inputs. 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 Eq. (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.
In agriculture, output is a composed of multiple commodities produced by multiple inputs, so Y and X are vectors. Chambers (1988) shows that when the underlying technology can be represented by a Cobb–Douglas production function and where (i) producers maximize profits so that output elasticities equal input shares in total cost and (ii) markets are in long-run competitive equilibrium so that total revenue equal total cost, then Eq. (2) can be written as
where Ri is the revenue share of the ith output and Sj is the cost-share of the jth input. Output growth is estimated by summing over the output growth rates for each commodity after multiplying each by its revenue share. Similarly, input growth is found by summing the growth rate of each input, weighting each by its cost share. TFP growth is just the difference between the growth in aggregate output and aggregate input. The principal difference between this index measure of TFP growth and a more general TFP productivity measure, such as the Tornqvist–Thiel index, is that here revenue and cost shares are held constant while in a Tornqvist–Thiel index these parameters may vary over time. Using fixed revenue and factor shares could potentially give rise to “index number bias” in cases where either the revenue or cost shares are changing significantly. It should be pointed out as well that cost shares are partly dependent on output prices themselves, since a part of agricultural output is used as inputs (seed and feed) in production.
A key limitation in using Eq. (3) for measuring agricultural productivity change is that we lack data on input cost shares for most countries. There is simply no internationally comparable information on input prices, especially for nontraded inputs such as land and labor. Some studies have circumvented this problem by estimating a distance function, such as a Malmquist index, which measures productivity using data on input quantities alone (Coelli and Rao, 2005). But this method is sensitive to aggregation issues as well as data quality (especially, differences in agricultural land quality across countries) and can give unbelievably high or negative growth rates. To address this problem I use the approach developed by Avila and Evenson (2004), who constructed careful estimates of input cost shares for two large developing countries (India and Brazil) from representative farm survey data and from these derived representative cost shares for other developing countries. I extend this approach by assembling cost share estimates for five additional countries (China, Indonesia, Japan, the United Kingdom, and the United States) and then assume that these cost shares are representative of agricultural production for different groups of countries. I describe this more thoroughly in the section on “input cost shares” below.
To summarize, the theory underpinning the TFP productivity index assumes that producers maximize profits so that the elasticity of output with respect to each input is equal to its factor share. It also assumes that markets are in long-run competitive equilibrium (where technology exhibits constant returns to scale) so that total revenue equals total cost. If the underlying production function is Cobb–Douglas, then our index is an exact representation of Hicks-neutral technical change.
2.2. Output and input data
To assess changes in agricultural productivity over time I use FAO annual data on agricultural outputs and inputs over 1961–2006 and in some cases augment these data with updated or improved statistics from other sources. Although we cannot yet estimate TFP changes for 2007 and 2008 (the period when agricultural prices experienced rapid inflation) we should expect to see evidence of a slowdown in productivity growth in the years preceding the recent price rises, if in fact such a slowdown occurred—the reason being that productivity is a long-run phenomenon that reflects the underlying production technology and is unlikely to contract abruptly.
For output, FAO publishes data on production of crops and livestock and aggregates these data into a production index using a common set of commodity prices based on the 1999–2001 period. What is important for estimating output growth are the relative prices of these commodities (since this determines the weights on the commodity growth rates used for deriving the growth rate for total output). In relative terms, the 1999–2001 FAO commodity prices are fairly close to the “wheat equivalent” prices developed by Hayami and Ruttan (1985, p. 453–454) in their seminal study on international agricultural productivity (the FAO prices have a correlation coefficient of 0.86 with the Hayami–Ruttan wheat-equivalent prices). The FAO index of real output excludes production of forages but includes crop production that may be used for animal feed.
To disentangle long-run trends from short-run fluctuations in output (due to weather and other disturbances), I smooth the output series using the Hodrick–Prescott filter setting λ= 6.25 for annual data as recommended by Ravn and Uhlig (2002). This filter is commonly used to remove short-run fluctuations from macro economic time series in business cycle analysis. However, this process does not completely remove the effects of multi-year shocks, so it is still necessary to evaluate observed changes in the rate of TFP growth with auxiliary information about extended periods of unusual weather or other disturbances.
For agricultural inputs, FAO publishes data on cropland (rainfed and irrigated), permanent pasture, labor employed in agriculture, animal stocks, the number of tractors in use, and inorganic fertilizer consumption. For fertilizer input and for selected large producers (China, Brazil, and Indonesia) I supplement FAO statistics with more recent national data on agricultural inputs. The International Fertilizer Association (2008) has more up-to-date and accurate statistics on fertilizer consumption by country than FAO. A relatively comprehensive dataset on China's agriculture is available from the Economic Research Service (with original data coming from the State Statistics Bureau of the People's Republic of China). For Brazil, I use results of the recently published 2006 Brazilian agricultural census (IPGE, 2008) and for Indonesia, Fuglie (2007) compiled improved data on agricultural land and machinery use. These sources together provide a set of global agricultural output and input data for 1961–2005, and for all but land and labor for 2006. To derive preliminary land and labor estimates for 2006 I apply the average annual growth rate from 2002–2005 of these inputs to their 2005 levels. Since aggregate agricultural land and labor usage historically has changed only slowly over time, this extrapolation will likely give a reasonable approximation for 2006.
Inputs are divided into five categories. Farm labor is the total economically active population (males and females) in agriculture. Agricultural land is the area in permanent crops (perennials), annual crops, as well as permanent pasture. Cropland (permanent and annual crops) is further divided into rainfed cropland and irrigated cropland. I also derive a quality-adjusted measure of agricultural land 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” below). Livestock is the aggregate number of animals in “cattle equivalents” held in farm inventories, and include cattle, camels, water buffalos, horses, and other equine species (asses, mules and hinnies), small ruminants (sheep and goats), pigs, rabbits, and poultry species (chickens, ducks, and turkeys), with each species weighted by its size. The weights for aggregation from Hayami and Ruttan (1985, p. 450) are as follows: 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, 25 per 1,000 rabbits, and 12.50 per 1,000 head of poultry. Fertilizer is amount of major inorganic nutrients applied to agricultural land annually, measured as metric tons of N, P2O5, and K2O equivalents. Farm machinery is the number of riding tractors in use.
While these 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, prepared animal feed, veterinary pharmaceuticals, other farm machinery, energy, and farm buildings. However, data on many of these inputs are available for the seven country case studies I use for constructing the representative input cost shares. To account for these inputs I assume that their growth rate is correlated with one of the five input variables described above and include their cost in the related input: services from capital stock in farm buildings as well as irrigation costs are included with the agricultural land cost share; the cost of chemical pesticide and seed are 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 tractor 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.
2.3. Land quality
The FAO agricultural database provides time series estimates of agricultural land by country and divides these estimates into cropland (arable and permanent crops) and permanent pasture. It also provides an estimate of irrigated area. Land quality between classes, and between countries, can be very different, however. For example, some countries count vast expanses of semiarid 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 (Craig et al., 1997; Peterson, 1987). In two recent studies of international agricultural productivity, Craig et al. (1997) and Wiebe et al. (2003) made considerable effort to include in their regression models variables that could account for differences in land quality (such as indices of average rainfall and soil type, the proportion of irrigated or pastureland in total agricultural land, and fixed effect models with regional or country dummies) with some success.
In this study, because I only estimate productivity growth rather than productivity levels, differences in land quality across countries is less problematic. The estimates only depend on changes in agricultural land and other input use over time. However, a bias might arise if changes occur unevenly among land classes. For example, adding an acre of irrigated land would likely have considerably more importance than adding an acre of rainfed cropland or pasture, and should therefore be given greater weight in measuring input changes. To account for differences in land type, I derive weights for irrigated cropland, rainfed cropland, and permanent pasture based on their relative productivity, and allow these weights to 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., I use average annual data for the 1961–1965 period). I first construct regional dummy variables (REGIONi, i = 1 … 5, representing Asia-Pacific, Latin America and the Caribbean, Sub-Saharan Africa, Middle East and North Africa, and developed countries), and then regress the log of agricultural land yield against the proportions of agricultural land in rainfed cropland (CROP), permanent pasture (PASTURE), and irrigated cropland (IRRIG). Including slope dummy variables allows the coefficients to vary across regions
The coefficient vectors α, β, and γ provide the quality weights for aggregating the three land types into an aggregate land input index. Essentially, Eq. (4) asserts that 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 land, and that these differences provide a ready means of weighting the relative qualities of these land classes.2
The results of this land quality adjustment are shown in Table 1. On average, one hectare of irrigated land was more than twice as productive as rainfed cropland, which in turn was 10–20 times as productive as permanent pastures. When summed by their raw values, total global agricultural land expanded by about 10% between 1961 and 2005, with nearly all of this expansion occurring in developing countries. When adjusted for quality, “effective” agricultural land expanded by nearly double this rate. Globally, irrigated cropland expanded by 141 million hectares and this accounted for virtually all of the change in “effective” agricultural land over this period. For the purpose of our TFP calculation, accounting for the changes in the quality of agricultural land over time should increase the growth rate in aggregate agricultural input and commensurately reduce the estimated growth in TFP.
Table 1. Global agricultural land use changes
|Region||Rainfed cropland||Irrigated cropland||Permanent pasture||Total agricultural land|
|1961||2005||% change||1961||2005||% change||1961||2005||% change||1961||2005||% change|
|Raw totals (millions of hectares)|
| Developed countries||363||345|| −5|| 27|| 44|| 63||886||805||−9 ||1,276||1,194||−6 |
| Developing countries||626||685||9|| 99||209||111||1,871||2,215||18||2,596||3,109||20|
| Former USSR countries||279||226||−19|| 11|| 25||127||332||382||15||622||633|| 2|
| World||1,268||1,256|| −1||137||278||103||3,089||3,402||10||4,494||4,936||10|
|Quality adjusted (millions of hectares of “rainfed cropland equivalents”)|
| Developed countries||363||345|| −5|| 58|| 94|| 63|| 84|| 76||−9 ||504||515|| 2|
| Developing countries||626||685||9||247||522||111|| 53|| 63||18||926||1,270||37|
| Former USSR countries||279||226||−19|| 24|| 54||127|| 31|| 36||15||334||316||−5 |
| World||1,268||1,256|| −1||329||670||104||168||175|| 4||1,765||2,101||19|
2.4. Input cost shares
To derive input cost shares I draw upon other studies that reported carefully measured input cost share calculations for selected countries and then I use these cost shares as “representative” of agriculture in different regions of the world. In Table 2 I show the input cost shares from the seven country studies (four developing countries: India, Indonesia, China, and Brazil, and three developed countries: Japan, the United Kingdom, and the United States). The table also shows the regions to which the various cost-share estimates were applied for constructing the aggregate input index. For example, the estimates for Brazil were applied to Latin American and Caribbean countries, North African and Middle Eastern countries, and South Africa, and the estimates for India were applied to other countries in South Asia as well as countries in Sub-Saharan Africa other than South Africa. These assignments were based on judgments about the resemblance among the agricultural sectors of these countries. Countries assigned to cost shares from India, for example, tended to be low-income countries using relatively few modern inputs. Countries assigned to the cost shares from Brazil tended to be middle-income countries and having relatively large livestock sectors.
Table 2. Agricultural input cost shares
|Study||Country/period||Labor||Land & buildings||Livestock & feed||Machinery & energy||Chemicals & seed||Regions to which these factor shares are assigned:||Global production share (%)|
| Evenson et al. (1999)||India 1967,1977, 1987 avg||0.46||0.23||0.25||0.01||0.04||South Asia|| 16.4|
|Sub-Saharan Africa|| |
| Fuglie (2007)||Indonesia 1961–2005 avg||0.46||0.25||0.22||0.01||0.05||SE Asia, Oceania developing|| 5.2|
| Fan & Zhang (2002)||China 1961–1997 avg||0.40||0.22||0.23||0.06||0.09||NE Asia developing|| 16.7|
| Avila & Evenson (1995)||Brazil 1970, 1990 avg||0.43||0.22||0.14||0.14||0.07||LAC, MENA, South Africa|| 15.6|
| Hayami & Ruttan (1985)||Japan 1965–1980 avg||0.39||0.23||0.10||0.05||0.23||NE Asia developed|| 2.0|
| Thirtle & Bottomley (1992)||U.K. 1967–1990 avg||0.30||0.17||0.26||0.17||0.10||Europe except former USSR|| 19.3|
| Ball et al. (1997)||USA 1961–2004 avg||0.20||0.19||0.28||0.14||0.18||N Amer, former USSR, Oceania developed|| 24.9|
| World|| ||0.35||0.21||0.23||0.10||0.10||Average, weighted by production shares||100.0|
While assigning cost shares to countries in this manner may seem fairly arbitrary, an argument in favor is that there is a remarkable degree of congruence among the cost shares reported for the seven country studies shown in Table 2. For the four developing-countries cases (India, Indonesia, China, and Brazil), cost shares ranged from 0.40 to 0.46 for labor, 0.22 to 0.25 for land, and 0.14 to 0.25 for livestock, while cost shares for fertilizer and machinery inputs were not more than 14% of total output. There was a tendency for the labor factor share to fall and the fertilizer and machinery input cost shares to rise with the level of agricultural development, reflecting embodiment of new technology in these inputs. But the fact that for these four developing and three developed countries, the input cost shares show a consistent pattern lends support to using them as representative of global agriculture. The seven countries are also relatively large producers, together accounting for 53% of global agricultural output in 2004–2006, according to the FAO data.
Another argument in favor of using the cost-share estimates reported in Table 2 as representative is that they are reasonably close to econometrically estimated production elasticities from studies that compared agricultural productivity across countries, which is implied from our assumptions about profit-maximization and long-run competitive equilibrium. Hayami and Ruttan (1985), Craig et al. (1997), and Wiebe et al. (2003) all find that labor had the highest production elasticity, followed by land and livestock. The Craig et al. (1997) and Wiebe et al. (2003) studies estimate production elasticities for land that are within the range of the land cost shares reported in Table 2, and about double those estimated by Hayami and Ruttan (1985). The difference between these econometric results can probably be attributed to the land quality variables included in the two more recent studies. However, econometric estimates of production elasticities from panel data on countries are not very robust and sensitive to model specification: all of the authors of these three econometric studies mention significant multicollinearity among the production factors. Further, none of the studies imposed constant returns to scale, and their estimates of scale economies in agriculture are mixed. However, it is not altogether clear how to interpret estimates of “scale economies” using country-level data. Economies of scale is a firm-level concept that does not apply to nations and requires comparisons among firms to test (Coelli and Rao, 2005).
Some limitations of these calculations should be noted, given the nature of the data on which they are based. The first limitation is that I only compute rates of change in TFP. TFP “levels” cannot be compared across countries with this method. A second limitation is that I do not make adjustments for input quality changes other than for land. A third limitation is that revenue and cost shares are held constant over time. However, an examination of the output data show that for major commodity categories (cereal crops, oilcrops, fruits and vegetables, meat, milk, etc.) the global output growth rates were similar over the 1961–2006 period. On the input side there has been more movement in cost shares among the major input categories, but these changes occur gradually over decades. Thus, the likelihood of major biases in productivity measurement over a decade or two are not large, although this does remain a potential source of bias for long-term comparisons. The principal advantage of these TFP growth estimates, however, is that the calculations have a standardized quality. I use a common method, a common period of time for all countries, and a consistent set of definitions for determining factor shares. Moreover, I include 171 countries in the assessment, a nearly complete accounting of global agricultural production of crops and livestock.3 I assess growth in individual countries as well as regions, and while regional averages may mask differences in performance among the countries within a region, the choice of aggregation into regions does not affect individual country results, unlike distance function measures (see Preckel et al., 1997, for a discussion of how aggregation can affect productivity growth estimates using distance functions). See Table 3 for a complete list of countries included in the analysis and their regional groupings.
Table 3. Countries included in productivity analysis and regional groupings
|Sub-Saharan Africa, developed||South Africa|
|Sub-Saharan Africa, developing||Angola||Côte d'Ivoire||Madagascar||Senegal|
|Botswana||Equatorial Guinea||Mali||Sierra Leone|
|Burkina Faso||Ethiopia, former||Mauritania||Somalia|
|Central African Rep.||Guinea||Niger||Togo|
|Congo, Dem. Rep.||Liberia||Sao Tome and Principe|| |
|Latin America and the Caribbean (LAC)||Argentina||Cuba||Honduras||Puerto Rico|
|Belize||Ecuador||Lesser Antilles||Trinidad and Tobago|
|Costa Rica||Haiti||Peru|| |
|North America||Canada||United States of America|| || |
|Northeast Asia, developed||Japan||Korea, Rep.|| || |
|Northeast Asia, developing||China||Korea, DPR||Mongolia|| |
|Southeast Asia||Brunei Darussalam||Laos||Philippines||Viet Nam|
|South Asia||Afghanistan||Bhutan||Nepal||Sri Lanka|
|Eastern Europe||Albania||Czechoslovakia, former||Poland||Yugoslavia, former|
|Middle East and North Africa (MENA)||Algeria||Israel||Morocco||Tunisia|
|Egypt||Kuwait||Qatar||United Arab Emirates|
|Oceania, developed||Australia||New Zealand|| || |
|Oceania, developing||Fiji||New Caledonia||Polynesia||Vanuatu|
|Micronesia||Papua New Guinea||Solomon Islands|| |
|Former USSR countries (analysis of individual countries for 1992 and onward)||Armenia||Georgia||Lithuania||Turkmenistan|