Five Decades of Productivity and E ﬃ ciency Changes in World Agriculture (1969–2013)

: The present study applied the Färe–Primont index approach to estimate the total factor productivity (TFP) growth of world agriculture, covering the period 1969–2013. Overall, the world agricultural TFP grew at a rate of 0.44% p.a. This growth was mainly contributed to by technological progress and mix e ﬃ ciency changes, while the contributions of technical e ﬃ ciency and scale e ﬃ ciency changes were negligible. TFP growth varied across regions, with South Asia at the top of the list (1.05% p.a.), and East Asia and the Paciﬁc (0.18% p.a.) at the bottom. TFP components exerted di ﬀ erential inﬂuences amongst regions. For instance, mix e ﬃ ciency played a dominant role in Sub-Saharan Africa, the Middle East and North Africa, whereas it was technical e ﬃ ciency change in Latin America and the Caribbean region. The paper argues for region speciﬁc policy interventions emphasizing technical progress through investment in R&D and price and non-price interventions to improve economies of scope and scale of operation in the agricultural sector.


Introduction
Agriculture is not only a source of food, but also a source of vast employment and rural development; hence, its development and growth have always been and will remain one of the topmost priority agendas in the development arena, particularly for the policy makers in the least developed and developing countries. This is because food security is one of the prime goals of the governments of these countries. Agriculture has a pivotal role in poverty alleviation and economic development [1]. The nexus between agricultural productivity growth and poverty reduction is well documented in the literature [2,3]. Shane et al. [4] provided empirical evidence that gaining agricultural productivity is the most effective strategy for poverty alleviation. It is true that, at the global level, the sector has lost its previous importance, particularly in terms of contribution to GDP and employment generation. For example, in 2016, the agricultural sector merely contributed 4.00% to the global GDP, but the contribution is relatively much higher in low-income countries, amounting to an average of 30.00% of the national GDP. The contribution of agriculture to national economies has decreased over the years, as countries have moved upward to upper income classes. Still, 26.48% of the world's total employment is offered by this sector [5]. Through an extensive review of 25 reports on the incidence of the global food price hike that occurred during the end of the last decade, Abbott et al. [6] concluded that the hike was largely fueled by declining agricultural productivity, though Fuglie [7] did not find empirical evidence that agricultural TFP declined until 2006. This certainly advocates for more Given this backdrop, the present study aims to analyze agricultural productivity and associated efficiency measures at the global scale, covering large number of countries (i.e., 104 in total) for a 45-year period (1969-2013). The contribution of this study to the existing literature is two-fold. First, we have adopted the FPI approach proposed by O'Donnell [32], which circumvents all the methodological weaknesses identified above. Though this approach is adopted in a couple of earlier studies in estimating the productivity growth of world agriculture [27,28], we suspect that their results may be misleading due to the aggregation of output into a single index. Second, we have estimated and reported six finer TFP components (i.e., technical change, technical efficiency change, scale efficiency change, mix efficiency change, residual mix efficiency change and residual scale efficiency change) which were not reported in earlier studies. Thus, this study offers a greater insight on the sources of growth and enables us to draw a wider range of policy implications.

Measuring TFP and Its Different Components
Inspired by the theoretical superiority of the FPI [29,31,32] over other competitive index methods (e.g., Hicks-Moorsteen index (HMI) proposed by Bjurek, [35]), we adopt the FPI approach, which is developed with distance function as the aggregator function. Based on the economic connotations of related efficiencies, it is possible to decompose FPI into the product of technological progress (i.e., movements in the production frontier), technical efficiency (i.e., change is a measure of movements towards the frontier), scale efficiency (i.e., measures of movements around the frontier surface to capture economies of scale) and residual mix efficiency changes (i.e., measures of movements around the frontier surface to capture economies of scope), which are not sensitive to measurement units. That is, inputs and outputs can be measured either in physical quantities or in monetary values at constant prices, or a combination of both, because the computed results are ratios, which are unit free.
The FPI is based on two indices from Färe and Primont [30], and is defined as the ratio of an aggregate output (q) to an aggregate input (x): Following O'Donnell [31], the aggregated outputs and inputs can be estimated as The above two equations are Shephard output and input distance functions, respectively, which are in nature linearly homogenous, always positive and non-decreasing [36], and represent the production technology available in period t. The FPI score for firm i in period t relative to firm h in period s is [31] TFP hs,jt We have worked out the following finer measures of efficiency changes by decomposing output-oriented TFP changes, which are counterparts of the input-oriented technical efficiency measures (details of input-oriented TFP measures are available at [29]. The output-oriented technical efficiency, OTE, is defined as the maximum possible aggregate output produced while holding the input vector and output mix fixed (Figure 1). Other relevant output-oriented components are presented in Figure 1 [8,29,37,38]. These efficiency measures are defined and described with reference to two production frontiers: a mix-restricted production frontier (when the combination of outputs and inputs are supposed to be fixed) and unrestricted production frontier (when both input and output mixes are allowed to be different), where each point refers to a combination of aggregate input and output ( Figure 1, adapted from [37,38]). where * is the maximum TFP possible with the available technology and given input bundle, ; = / ( , , ) is the maximum aggregate output produced by keeping input vector and output mix fixed, and represents the maximum aggregate output that is produced when only the input vector is fixed and there are no restrictions on output mix. The OTE estimates the productivity shortfall associated with operating below the production frontier; the OME defined by (6) measures productivity shortfalls associated with diseconomies of scope [8,29,37,38]. OME is the change in productivity when the assumptions about input and output mixes are relaxed, and is estimated as the ratio of restricted and unrestricted production function (i.e., ⁄ in Figure 1) [29,37,38]. OSE (= ⁄ in Figure 1) is the typical measure of output-oriented scale efficiency, which is the productivity difference between TFP at a technically efficient point and the maximum attainable TFP whilst holding the output and input mixes fixed [29,37]. The residual output-oriented scale efficiency, ROSE (= ⁄ in Figure 1), is the difference between TFP at an output-mix-efficient point and the maximum possible TFP [29,37]. However, the term 'residual' here means that, although all points on the unrestricted frontier are mix efficient, each has different input and output mixes. Finally, residual mix efficiency, RME (= ⁄ in Figure 1), allows probable changes in scale, estimated as the difference between TFP at a scaleefficient point and the maximum possible TFP [29,37,38].
The common measures of efficiency used in economic literature are derived as ratios of different TFP measures [31]. For instance, an alternative output-oriented measure can be shown as [37]: where output-oriented technical efficiency (OTE) is the conventional efficiency measure that measures the shortfall in productivity associated with operating below the production frontier, as noted by O'Donnell [32], i.e., the difference between aggregated output that a firm produces utilizing the given resource base at the maximum attainable output possible from that resource base. The output-oriented scale efficiency (OSE) and output-oriented mix efficiency (OME) account for The OTE estimates the productivity shortfall associated with operating below the production frontier; the OME defined by (6) measures productivity shortfalls associated with diseconomies of scope [8,29,37,38]. OME is the change in productivity when the assumptions about input and output mixes are relaxed, and is estimated as the ratio of restricted and unrestricted production function (i.e., slope OCslope OV in Figure 1) [29,37,38]. OSE (= slope OCslope OD in Figure 1) is the typical measure of output-oriented scale efficiency, which is the productivity difference between TFP at a technically efficient point and the maximum attainable TFP whilst holding the output and input mixes fixed [29,37]. The residual output-oriented scale efficiency, ROSE (= slope OVslope OE in Figure 1), is the difference between TFP at an output-mix-efficient point and the maximum possible TFP [29,37]. However, the term 'residual' here means that, although all points on the unrestricted frontier are mix efficient, each has different input and output mixes. Finally, residual mix efficiency, RME (= slope ODslope OE in Figure 1), allows probable changes in scale, estimated as the difference between TFP at a scale-efficient point and the maximum possible TFP [29,37,38].
The common measures of efficiency used in economic literature are derived as ratios of different TFP measures [31]. For instance, an alternative output-oriented measure can be shown as [37]: where output-oriented technical efficiency (OTE) is the conventional efficiency measure that measures the shortfall in productivity associated with operating below the production frontier, as noted by O'Donnell [32], i.e., the difference between aggregated output that a firm produces utilizing the given resource base at the maximum attainable output possible from that resource base. The output-oriented scale efficiency (OSE) and output-oriented mix efficiency (OME) account for productivity shortfalls associated with diseconomies of scope, which arises when a multiple output producing firm is less efficient than the specialized firms producing a single product. The measure of residual output-oriented scale efficiency (ROSE) is the ratio of TFP at a technically and mix-efficient point to the maximum TFP that is possible, where higher TFP is certainly a scale effect since the improvement is essentially a shift towards higher mix-efficient point along the unrestricted production frontier [37]. O'Donnell used the term residual since different points on the unrestricted frontier represents different input-output mixes, though all are mix-efficient [37]. The residual mix efficiency (RME) is the remaining component after accounting for pure technical and pure scale efficiency effects [31], which can be obtained as the difference in TFP between the point of MIOS (i.e., the optimal point on the restricted frontier) and the point where productivity is maximum (i.e., the optimal point on the unrestricted frontier), the difference between which is a mix effect [37]. Finally, following O'Donnell [8,29,37,38], the overall TFP can be estimated as O'Donnell [29,37] decomposes the multiplicatively complete TFP index when the output distance function is well-defined and the maximum TFP possible in each period is finite and non-zero. The resulting equation, where the first term on the right-hand side is a measure of technical change and the remaining terms indicate efficiency changes, can be written as where TFP * i is the maximum TFP possible with the available technology and given input bundle, X it ; is the maximum aggregate output produced by keeping input vector and output mix fixed, andQ it represents the maximum aggregate output that is produced when only the input vector is fixed and there are no restrictions on output mix.
We have used the DPIN 3.0, which uses a Data Envelopment Analysis (DEA) linear programming (LP) technique, to describe the production technology (and associated measures of productivity and efficiency) [31]. The details are available in the Appendix A. We have used eight output and six input variables to determine TFP. The input-output variables. along with their estimation techniques and sources. are available in Table 1. Livestock is the aggregate number of animals in 'cattle equivalents', and includes cattle, camels, water buffalos, horses and 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 [43]: 1.38 for camels, 1.25 for water buffalo and horses, 1.00 for cattle and other equine species, 0.25 for pigs, and 0.13 for small ruminants. Labour Total economically active population (000) working in agriculture.

Gross cropped area
Gross cropped area (GCA) is the summation of the total area (000 ha) under all types of crops in a country in a year.

Fertilizer
Total consumption of the major three nutrients (N, P and K) in metric tons from all types of fertilizers (e.g., urea, single superphosphate, triple superphosphate, diammonium phosphate, muriate of potash, etc.) is estimated. Nutrient consumption figures for the years 2002-2013 were available in the FAOSTAT. For the earlier years, the physical quantities of different fertilizers were collected from the FAOSTAT, and were converted to actual nutrient quantity.

Irrigation
Proportion of land under irrigation is taken from the FAOSTAT. The missing information was filled by interpolation or extrapolation through the simple linear trend method.
Some manipulation tasks had to be undertaken because there were missing data points. Missing data were extrapolated using the average growth rate in Fuglie [44], and Rahman and Salim [45] used a standard linear trend interpolation model for the missing data. The following manipulation techniques were followed:

1.
Data manipulation was performed only on the finalized output-input groups, e.g., cereals, pulses, etc. and not on individual crops. This was done to keep the level of adjustments to a minimum.

2.
For countries with complete set of missing data for some of the input-outputs, an arbitrary scalar of 10 was inserted throughout so that we can still include the country in the analysis. As we followed non-parametric procedure, this scalar value has no influence on the calculation of the frontier whose values are invariably larger than 10 in all cases.

3.
For interpolation of the missing data, the average annual change between two available data points was estimated and then that rate of annual change was applied to the missing years, which is a standard practice.

4.
For extrapolation, we estimated the annual growth rate from the available data series. Then, that growth rate was applied from the actual data available next to the missing data point, to fill and create the extrapolated series.
While conducting the extrapolation (both for extrapolating backward or forward), if the extrapolated values went below 10 (as happens when negative growth rates were used to extrapolate the missing series), extrapolation was stopped at the year with the value nearest to the scalar 10. Then, that extrapolated value was replicated for the remaining missing years. This was done to avoid negative values when extrapolating missing data backwards, or even forwards with a negative growth rate estimated from actual data points, as by definition inputs and outputs cannot be negative in an economy.
Since we examine the differences and changes in TFP and its finer components across 104 countries over 45 years, technological heterogeneity across countries and over time is an important issue. Alvarez and del Corral [46] criticized the popular trend in the literature which assumes homogenous technology for all the producers, and applied a latent class model approach to empirically prove that such simplified assumptions result in biased estimates. Similarly, Cillero applied a latent class model to investigate the consequences of differences in production technology on Irish beef farms [47], whereas few studies have applied random parameter models [48,49]. A very similar one to ours is the work of Baráth and Fertő [50], who applied O'Donnell's FPI index framework and estimated TFP parameters and convergence to European agriculture. In the process, to acknowledge the productivity consequences of technological heterogeneity across European farms, the authors applied a cluster analysis. However, a cluster analysis requires additional information about farm production environments and weather conditions for grouping [50]. Since we are dealing with large number of countries covering a long period, gathering such information was difficult, and even after admitting the importance of technological heterogeneity, we had to proceed with the assumption of homogenous technology. However, further research acknowledging technological heterogeneity will provide more in-depth understanding of TFP dynamics.

The Study Countries and Time Period
We have selected those countries where agriculture contributed more than 4% of the total GDP, and/or countries where at least 4% of the total employment was in the agricultural sector in 2013. This resulted in a total of 137 countries. However, due to the unavailability of the required input-output data in the FAOSTAT database, only 104 countries could be included in the analysis (please refer to Appendix A Table A1 for the list of selected countries). The FAOSTAT reports input-output data from 1961. Many countries have several missing data for the earlier years (prior to 1969). Hence, for the sake of consistency, it was decided to cover 45 years (1969-2013).

TFP Change and Its Components: Global Level Estimates
At the global level, the level of TFP, i.e., the ratio of aggregate output to aggregate input, was estimated at 0.20, implying that more aggregate inputs are needed to produce one unit of aggregate output, whereas the estimated technical efficiency of 0.91 implies that aggregate output could be increased by about 10% by removing inefficiency in production alone ( Table 2). The estimated almost unitary values of pure technical and scale efficiency (0.97) scores, and the relatively lower values of the pure mix efficiency index (0.78), imply that world agriculture has done well in terms of pure technical and scale efficiencies, but lacks the ability to derive economies of scope by changing optimal input and output mixes ( Table 2). The relatively lower residual mix efficiency, which is estimated to be 0.29 (Table 2), implies that countries are not doing well in terms of reaping the benefits of economies of scope. This suggests that there has been an upward shift in the production possibility frontier, most likely driven by innovation and the adoption of technologies, such as the Green Revolution technologies (i.e., a combination of high yielding varieties of rice/wheat/maize and inorganic fertilizers with supplementary irrigation and drainage controls) that created world-wide impact during 1980s, arguing that farmers are rationally adjusting the scale but lag behind in terms of deriving economies of scale. During the period under consideration, TFP grew at a rate of 0.44% p.a., which is relatively low (Figure 2). However, an important and encouraging feature is that world agriculture has maintained this growth rate of TFP for a period of four and half decades.
A summary of some influential related studies is presented in Table 3. To estimate TFP changes, Coelli and Rao [24], Ludena et al. [25], Ludena [26] and Headey et al. [17] applied MI. Ludena et al. [25], who incorporated three outputs (crops, ruminants and non-ruminants) and nine inputs (feed, animal stock, pasture, land under crops, fertilizer, tractors, milking machines, harvesters, threshers and labor) in their analysis of 116 countries and reported that, during the period 1961-2001, the annual TFP growth rate was 0.72%. Ludena [26] estimated that at the global level agricultural productivity growth rate was 1.7% p.a. between 1961 and 2007. The author included 26 Latin American and Caribbean countries and considered two outputs (crops and livestock), and five inputs (animal stock, land, fertilizer, tractors and labor). Headey et al. [17] used two outputs (crops and livestock) and five inputs (land, tractors, labour, fertilizer, and livestock) for 88 countries, and estimated the annual TFP growth to be 1.7% and 1.4%, according to the SFA and DEA model. Coelli and Rao [24] estimated a 2.1% annual growth rate in agricultural productivity for 93 countries over the period of 1980 to 2000.They considered two outputs (crops and livestock) and six inputs (area, tractor, labour, fertilizer, livestock and irrigation). Due to differences in methodology and the disaggregation of outputs into specific crop groups, our estimated figures are not comparable with the literature. The main source of difference may also be due to the aggregation of all types of outputs into one single index and/or use of livestock output in those studies.
There are two sources of differences in TFP growth rates between ours and the three mentioned studies above, though all utilized the FAOSTAT database. Firstly, the same time period and input-output items are not covered across the studies. Secondly, Fuglie [27] applied the 'growth accounting' approach, and converted all the crops and livestock items into a single output measured in constant prices. Le Clech and Castejón's [28] work is based on the data from Fuglie [27], with an update on later years supplied by the USDA-ERS. But such aggregation of output data may affect estimated values [25]. Finally, Nin-Pratt and Yu [51] employed MI to estimate TFP growth and used agricultural production as a single output.
The Green Revolution brought modern science to tackle the widening Asian food crisis in the 1960s. For this purpose, Bangladesh adopted several agricultural policies for robust technological progress, leading to the widespread farm-level dissemination of paddy-based GR technology packages. As a result, the growth in TFP was not uniform. Prior to 1985, TFP grew at a relatively slower pace, which then accelerated and went through several cycles of fluctuations (Table 3). Rahman [52] termed the era after 1985 as the mature stage of GR technology adoption. A similar pattern of TFP growth rate was observed not only in country specific studies for Bangladesh [45] and India [53], but also in regional level studies [54] for Asia, for Latin America and the Caribbean region [26] and at the global level [17,25,27].
Technological progress and mix efficiency changes were the two major drivers behind the growth in TFP (Figure 2). The dominant role of technology in agricultural development and growth is well documented in the literature [20,25,52]. The changes in both technical efficiency and scale efficiency were almost negligible, estimated to be 0.05% and 0.04% p.a., respectively (Figure 2). The implication is that, though world agriculture has managed to maintain positive change in technical efficiency and scale efficiency, the contribution of these two components to TFP growth are almost negligible.

TFP Change and Its Components: Regional Level Estimates
The estimated changes in TFP and its components for different regions are presented in Figure 3a-f, whereas the associated geomean and growth rates are presented in Figures 4 and 5 respectively. South Asia (SA) was the best performer in terms of TFP growth rate (1.05% p.a.), followed by the Middle East and North Africa (MENA; 0.70% p.a.), Sub-Saharan Africa (SSA; 0.66% p.a.), Europe and Central Asia (ECA; 0.57% p.a.) and Latin America and the Caribbean (LAC; 0.40% p.a.). East Asia and the Pacific (EAP) was the worst performer, with an annual TFP growth rate of only 0.18% p.a. [24] reported that Asia recorded the highest TFP growth, followed by North America (consisting of USA and Canada), Australasia, Europe, Africa and South America. Avila and Evenson [55] also noted that Asia (2.21%) had the highest TFP growth, followed by LAC (1.85%) and Africa (1.44%) during the period of 1961-2001. However, this contrasts with Headey et al. [17] who observed that TFP growth was fastest in MENA and East Asian regions, unstable in LAC and SSA, and generally quite low in SA during the period 1970-2000. On the other hand, the TFP growth rate for SSA is consistent with Fuglie and Rada [56]. Their estimation of TFP growth for the region was 0.59%, while ours is 0.66%; a negligible difference of 0.07%. The present study estimated negligible decline in technical, scale and mix efficiency in SA, whereas technological progress was the main driver of TFP growth during 1969-2013. This result is partially consistent with Anik et al. [57], who reported that the four SA countries experienced little or no variation in technical, scale and mix efficiency changes during the period 1980-2013. The findings are also consistent with the findings of Rahman and Salim [45] on the TFP growth of Bangladeshi agriculture. This growth pattern of technological progress (0.23% p.a.) is similar for all other regions. Therefore, we did not find any evidence of global or regional technological regress. The principal source of TFP growth was efficiency change (or 'catch-up'). However, according to Fuglie [27], Africa was the continent with the highest TFP growth rate, followed by South America, North America, Australasia and Asia. Europe was at the bottom of the list. Baráth and Fertő [50] reported that, although there are considerable differences across countries, the agricultural TFP in the EU countries during 2004-13 showed a decreasing trend.

Coelli and Rao
Mix efficiency is the major driver behind TFP growth in the SSA and MENA, implying that both regions successfully changed their input-output mixes through policy adjustment to derive economies of scope (Figure 3a-f). TFP in LAC was driven by technical efficiency change. Among all the regions, LAC was observed to have the highest annual growth rate (0.21% p.a.) of technical progress (Figure 3d). Lachaud et al. [58] also found that technological progress has been the key driver of agricultural productivity growth in LAC. They also stated that investment in R&D to facilitate access to the best available technologies is critical in the region, and investments in training and education to enhance the absorptive capacity of existing and/or new technologies are also important. Similarly, in the neighboring US states, technical progress was the major driver behind TFP change, with high and stable technical efficiency levels, but the scale-mix efficiency levels were relatively lower and fluctuating [29]. SA and EAP experienced declines in technical efficiency change, though the rate was negligible in SA (−0.01% p.a.) and high for EAP, estimated at −0.11% p.a. (Figure 3b,e). Both these regions also observed declining scale efficiency. Mix efficiency declined annually by 0.02% p.a. in SA, indicating the inability of the region to derive economies of scope (Figure 3b). These findings show that EAP and SA deviated from the available technological level; however, LAC moved closer to the available technological frontier.  Table 3. Selected studies of total factor productivity analysis.

Conclusions and Policy Implications
The present study assessed the productivity growth of world agriculture (104 countries) for a 45 year period (1969-2013) by applying the Färe-Primont TFP index to the FAOSTAT database. The study decomposed the TFP index into six finer components (i.e., technical change; technical, scale and mix efficiency changes; and residual scale and residual mix efficiency changes). The global level TFP was estimated at 0.20, technical efficiency level at 0.91, scale efficiency level at 0.97, mix efficiency level at 0.78, residual scale efficiency level at 0.37 and residual mix efficiency level at 0.29, respectively. The estimated levels imply that, although world agriculture has done well in terms of pure technical and scale efficiencies, there are deficiencies in the ability to derive economies of scope by changing input and output mixes to optimal levels. The annual TFP growth rate was estimated at 0.44% p.a. The growth rate varied over time, but accelerated after 1985. The major two contributors to TFP growth were technological progress and mix

Conclusions and Policy Implications
The present study assessed the productivity growth of world agriculture (104 countries) for a 45 year period (1969-2013) by applying the Färe-Primont TFP index to the FAOSTAT database. The study decomposed the TFP index into six finer components (i.e., technical change; technical, scale and mix efficiency changes; and residual scale and residual mix efficiency changes). The global level TFP was estimated at 0.20, technical efficiency level at 0.91, scale efficiency level at 0.97, mix efficiency level at 0.78, residual scale efficiency level at 0.37 and residual mix efficiency level at 0.29, respectively. The estimated levels imply that, although world agriculture has done well in terms of pure technical and scale efficiencies, there are deficiencies in the ability to derive economies of scope by changing input and output mixes to optimal levels. The annual TFP growth rate was estimated at 0.44% p.a. The growth rate varied over time, but accelerated after 1985. The major two contributors to TFP growth were technological progress and mix efficiency change, whereas the contributions of technical efficiency and scale efficiency changes were minimal.
Notable differences exist in regional TFP growth rates and their drivers. The highest TFP growth rate was observed in SA (1.05% p.a.), followed by MENA (0.70% p.a.), SSA (0.66% p.a.), ECA (0.57% p.a.) and LAC (0.40% p.a.). EAP was at the bottom of the list, with a growth rate of only 0.18% p.a. The TFP growth in SSA and MENA were largely driven by mix efficiency change, whereas it was technical efficiency change for LAC region. The LAC region is the world leader in terms of technical efficiency change. SA and EAP showed a declining trend in both technical efficiency and scale efficiency changes.
The estimated low level of TFP growth highlights that the sector needs special attention in order to fulfil the basic requirement of food and fibre for the growing global population. Appropriate economic-policy instruments have to be designed so that world agriculture can derive economies of scope by changing optimal input and output mixes. Several policy implications can be derived from the results of this study, though the specific prescription should be region specific, based on their respective TFP and efficiency performances. Firstly, policies for enhancing technical efficiency and scale efficiency changes in the form of increasing investment in R&D and human capital should be prioritized, particularly in EAP, MENA and SSA countries. Second, regions lagging behind in mix efficiency (e.g., SA) need to adopt both price (e.g., procurement programme, tax and/or subsidy, etc.) and non-price policies (e.g., agricultural extension and advisory services, etc.) so that farmers can utilise optimal input and output mixes. Third, policies for enhancing scale efficiency should be in the priority list of ECA and LAC countries. Countries should emphasize the rational allocation of agricultural inputs, particularly capital investment, so that they can avoid over-investment associated with adverse impacts from diseconomies of scale. Fourth, access to markets (both domestic and international) will help the producers in many instances, particularly against the odds associated with the reciprocal relationship between productivity and price.
Along with the bio-physical dimension, TFP has economic and social dimensions and is thus critical for the sustainability of any production system [59]. We could not incorporate this into our study since this is beyond the scope of the present study, but research on this dimension is highly required from both a policy and academic perspective. Additionally, we recommend an in-depth analysis of the potential determinants of differences across regions.

Conflicts of Interest:
The authors declare no conflict of interest.

DEA Estimation Technique
In DEA the (local) output distance functions in period t demonstrating the available technology can be expressed as [60] D The output-oriented solution requires the unidentified parameters of the input oriented technical efficiency to diminish technical efficiency: where Q is a J × M t matrix of observed outputs, X is a K × M t matrix of observed inputs, t is an M t × 1 unit vector, and M t denotes the number of observations used to estimate the frontier in period t [31].
To calculate Färe-Primont aggregates, DPIN 3.0 uses a variant of this LP that begins by solving the following [31]: Following this, the aggregated outputs and inputs of the FPI can be derived as [25] Q it = q it α 0 /(γ 0 + x 0 β 0 ) (A4) where α 0 , β 0 , Φ 0 and η 0 are solved at sample mean vectors as representative output and input vectors. According to O'Donnell [46], the Färe-Primont TFP index is: The representative technology in this LP is the technology achieved under the assumption of no technical change, which permits the technology to demonstrate variable returns to scale (VRS). In a case where technology is assumed to exhibit constant returns to scale (CRS), DPIN 3.0 sets δ = 0 [61].
In DEA, there is an issue of the curse of dimensionality. Although our sample size is much larger than the rule of thumb dictates (i.e., max k > 3 [m + n]; k > m * n ) [57], there may be issues related to using too many inputs and outputs. Therefore, in order to check the robustness and stability of our results, we conducted a sensitivity analysis by reducing the number of outputs to five by aggregating fruits, vegetables, oilseeds and cash crops into one cash value output, and inputs to five by adding livestock inputs (after converting into horsepower) with the machinery input. The results show very little difference in TFP levels over time (see Figure A1). Therefore, we are confident that using a large number of inputs and outputs did not pose any problems, because we had very large sample size to begin with. The curse of dimensionality is more of an issue if the number of samples is relatively small. The representative technology in this LP is the technology achieved under the assumption of no technical change, which permits the technology to demonstrate variable returns to scale (VRS). In a case where technology is assumed to exhibit constant returns to scale (CRS), DPIN 3.0 sets = 0 [61].
In DEA, there is an issue of the curse of dimensionality. Although our sample size is much larger than the rule of thumb dictates (i.e., max { > 3 [ + ]; > * }) [57], there may be issues related to using too many inputs and outputs. Therefore, in order to check the robustness and stability of our results, we conducted a sensitivity analysis by reducing the number of outputs to five by aggregating fruits, vegetables, oilseeds and cash crops into one cash value output, and inputs to five by adding livestock inputs (after converting into horsepower) with the machinery input. The results show very little difference in TFP levels over time (see Figure A1). Therefore, we are confident that using a large number of inputs and outputs did not pose any problems, because we had very large sample size to begin with. The curse of dimensionality is more of an issue if the number of samples is relatively small. Figure A1. Comparison of TFP with a reduced number of inputs and outputs with the original specification. Table A1. Countries and regional groupings included in the TFP Analysis.  30 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 Table A2. Descriptive statistics of the input-output variables.

Variables
Mean Std. Dev. Min Max