Risk-premium φ can be expected to be positively related to price variability faced by producers: as discussed below, Argentine farmers have not only faced unfavorable input/output price ratios, but have also experienced significant between-year variability in these prices. “Noise” in price signals can be expected to dampen the impact that these signals have on necessary farmer adaptation, either because of risk-premiums associated with input use, or simply due to the information-processing limitations of decision-makers.

Identifying the impact of risk on producer demand is a complex endeavor: even a sophisticated (and costly) approach based on deriving utility functions is of questionable value due to the inherently normative – and not necessarily descriptive - nature of this approach. Indeed, as pointed out be cognitive psychologists (see, e.g. Kahneman and Tversky, 1979), normative models do not necessarily represent actual decision-making processes.

But even ignoring the problem of risk and risk attitudes, an additional issue merits attention: how agricultural producers adapt to both new technical opportunities (“technical change”) as well as to shifting relative price ratios.

II.1 Technical change and input productivity

Technical change is defined as an increase in output resulting from a given input bundle, or alternatively, a reduction in input needed for a given output. Factor prices influence the direction of technical change: in agriculture “land-saving” and “labor-saving” technical change has been identified, respectively, with land-scarce and labor-scarce agricultural economies (Hayami and Ruttan, 1985). If technical change can be assumed “neutral”, in the sense of leaving substitution rates among inputs unchanged, a Cobb-Douglas production technology can be used to represent production possibilities. Here technical change is modelled in a shift through time in the parameter A(.).

[1]

Under this model, not only output will increase for every input vector, but input marginal productivity as well. Marginal productivity, in effect, is directly proportional – for a given input level of X₂ - to A(t).

MP_i = αA(t)Y/X_i [2]

Which results in input demand:

Xi*(w,p) = [(pA(t) X₂^β) /w]^1/(1-α) [3]

Input demand schedule is thus a function of technical change incorporated into the production process.

II.2 Producer learning and technology adoption

T.W. Schultz (1975) distinguishes between “static” and ‘dynamic” conditions of the economic environment. In the former, adaptation is unnecessary: “trial and error” methods have been used over the years and have resulted in “optimum” levels of input use and output patterns. The “poor but efficient” hypothesis results: in less developed economies, slow or no introduction of new technologies results in absence of opportunities for re- source re allocation (Schultz, 1964). In contrast with the above, returns to the “ability to deal with disequilibrium” are high in economies where a steady inflow of new technologies opens up opportunities for change. Huffman (1977) estimates the relationship between farmer education and agricultural extension services on adjustment in fertilizer use to changing relative prices and crop fertilizer response. Huffman reports a significant relationship between these two variables on the observed adjustment process (for a survey on the impacts of human capital on adoption of technologies see Huffman, 2000).

Classical papers focused on fertilizer demand include Griliches (1958 and 1959) and Heady and Yeh (1959). Estimated demand elasticities range from -0.5 in the short-run, to -2.0 in the long run. These studies highlight the importance of data availability for the study of input demand. The approach used in this paper (Section IV below) is presented as a first approximation to the determinants of fertilizer demand based on limited data available at this time.

The relative role of prices and non-price factors in explaining producer decisions has been subject to debate. A frequently-cited case is the exchange between Zvi Griliches (an economist) and Everett Rogers (sociologist). Focus here was on the determinants of the adoption of corn hybrid seeds in the U.S.A. Griliches emphasized profit opportunities as the main factor explaining adoption, while Rogers highlighted aspects such as knowledge diffusion, community networks and related aspects (Griliches, 1962, Rogers y Havens, 1962). Although apparent conflict exists between these two visions, points in common emerge: as pointed out by Griliches, many of the factors considered important by sociologists (e.g. learning processes, information channels, community leadership) are themselves a response to changing economic opportunities.

Production processes generate information, and this information is used to update beliefs. For example, a farmer adopts a new technology on a trial basis or changes the level used of a given input. Prior to observing results, the farmer forms expectations on output resulting from this technology. A-posteriori, new results emerge. An adaptive behavior to changing opportunities is to be expected. The efficiency with which this adaptation occurs is a function of formal and informal human capital of the relevant decision-maker.

Summarizing the above: the quantity demanded of an input results from an optimization process where producers attempt to equate perceived input marginal productivity with the relevant price ratio. But perceived productivity may be quite different from the objective productivity that can be expected on a given plot of land. Change over time in production possibilities, producer knowledge about these, price changes and variability in production conditions result in the “profit maximizing” input level being an elusive target. Further, risk attitudes introduce additional complications: as (unobserved) utility, and not profits, may be the relevant objective function to be taken into account (Andeerson, Dillon and Hardaker, 1977). Issues such as these most probably play an important role in cases such as analyzed here where in a three-decade period where use of an input (fertilizer) evolved from practically less than half a million to five million tons a year.

III. The fertilizer input in Argentine agriculture

III.a Overview

Crop production in Argentina dates from the second half of the XIX century. In the early 1900’s some 4 million hectares were planted, increasing to 20 million by the 1930’s. As a result of both of policies which resulted in distortion of incentives, as well as neglect of agricultural research and the development of new technologies, planted area remained unchanged for half a century. Only in early 1980s area started to steadily grow, reaching in 2020 38 million hectares in extensive grain production (Reca, 2016).

The rate of introduction of new technologies picked up in the early 1960’s, after the creation of INTA, the national institute for agricultural research. Modern (“mexican”) wheat varieties, hybrid sunflower, new corn hybrids and improved crop management practices were adopted. In this period, however, the very low level of fertilizer used is an anomaly of Argentine agriculture with respect to other important grain producers. Indeed, in the mid 1970s, most of the national demand for fertilizers (some 70.000 tons annually) was accounted for by fruit and horticultural crops (which represented less than 10 percent of the value of output), and practically none by the important grain producing sector. Fertilizer use increased steadily during the 1990’s, averaging some 500.000 tons in the 1990/94 period, and 4.7 million tons three decades later (Figure 1).

Despite the substantial increase that has occurred in the last three decades, per-hectare fertilizer levels in Argentina are still ¼ to ½ of that in other important temperate-climate producers such as the U.S, Canada, France and Germany (Table 1).

Up to the 1960’s low fertilizer use can be explained by depressed crop prices (result of export taxes and exchange rate controls), high fertilizer prices (result of import restrictions) as well as limited availability of technologies complementary with the fertilizer input (in particular – but not only - high fertilizer response seeds). The steady flow of new technologies occurring in the 1970’s set the stage for increased adoption of fertilizers. However unfavorable relative price ratios hampered this process. Cirio, Danelotti and White (1981) report that in the 1970’s, in Argentina 6-10 kg of wheat was necessary to purchase 1 kg of fertilizer (elementary nitrogen), while in Australia, the U.S and France the relative price was one-third to less than one-half of the above. Price differentials are thus a strong candidate explaining low fertilizer use.

The long long-term trend of real fertilizer prices faced by Argentine producers (Figure 2) shows a decline through time. However, this trend obscures variability in different periods. During the 1970’s prices, though lower than those of the previous decade, were still high by international standards: as shown in Figure 2, during the 1980s and 1990s, approximately 2 kg of wheat were necessary to purchase a kg on nitrogen in the U.S.; in Argentina, relevant price ratios varied from 4 to more than 6: a two or three- fold increase. Elimination of barriers to trade, and exchange rate controls resulted during the 1990’s in relative prices converging – albeit slowly - to international levels. After 2001 re-imposition of export taxes for agricultural commodities drove the relative price upward, although not to the level of the 1980’s and (particularly) the 1970’s. A brief period of market liberalization resulted (2016/19) in a new period of relative price decline. However, prices were still substantially (+ 60 %) above those faced by U.S. producers.

Argentine producers not only faced substantially higher input/output price ratios than those of U.S. producers, but also higher variability (as measured by CV’s) as well: as shown in Figure 3, fertilizer/wheat price CVs were, during the 1980’s and 1990s, more than double of those in the U.S. As mentioned previously, price variability not only increases risk premium (or “required rate of return”), but also introduces noise into the decision-making process.

III.b Production response – late 1970’s early 1980’s

Only selected highlights relative to production response to fertilizers will be presented. Focus is in obtaining rough parameters that allow inferences to be made on the role of prices and overall technical change on observed increases in the adoption of the fertilizer technology.

Economic analysis of fertilizer demand in the wheat crop as of the early 1980s is found in Gallacher (1982). This study focused on the main corn/soybean area of the country. Increased yields for “average” fertilizer levels (40 kg/ha elementary nitrogen) were 11 percent of base yields on high fertility soils, and 16 percent of base yields for soils of low fertility. Higher (80 kg/ha) levels resulted in increases ranging from 17 to 28 percent of base yields. Percentage-wise yield increases are a positive function of fertilizer dose, as absolute yield increases with fertilizer dose, while base yield remains constant[2]. The higher fertilizer response observed in “new” as compared to “older” wheat varieties is reported in Gallacher (1986). For the case of phosphorous fertilizer, the Marginal Product (MP) schedule for “older” varieties MP = 8.6 − 0.06 P (P = phosphorous dose per hectare) shifts upward to MP = 12.9 − 0.06 P for the newer ones. This results in a significant increase in the “optimum” fertilizer rate for “new” as compared to “old” varieties.

For a relative price of 6 (phosphorous/wheat price) the profit maximizing fertilizer level is 12 kg/ha with the older, as compared to 83 kg/ ha for the newer ones. This result highlights the importance of technical change (in this case, wheat germplasm) in determining usage of the fertilizer input. Additional results of fertilizer response in wheat production in the late 1970’s to early 1980’s are reported in Gallacher (1986)[3]. Yield increases resulting from the application of 40 kg/ha on nitrogen are .68 and .82 tons/ hectare for, respectively, Marcos Juarez and Pergamino, two important agricultural areas of the country. Yield increases from the fertilizer dose used here for calculations (40 kg/ha) represented, respectively 31 end 38 percent of baseline (i.e no fertilizer) yield. Given the prevailing the fertilizer/wheat prices, profit maximizing nitrogen fertilizer levels were respectively 40 and 60 kg/ha for these two areas. Extrapolating these experimental results to commercial farms, a substantial disequilibrium in nitrogen use is evident: farm-level fertilizer use in the early to mid-1980s was extremely low, despite results such as those above suggesting opportunities for increased use of these inputs. Risk aversion and lack of knowledge are two possible factors explaining these results.

Evidence presented above broadly suggests response to the fertilizer input in the early to mid-1980’s. These response results are a function of crop production knowledge incorporated into decision-making processes at that time. As mentioned previously, increases in crop area, and in the production of major grain crops occurred starting in the late 1980s – early 1990s. The 1980s thus represent a period where Argentine agriculture transitions from a use of land characterized by crop-pasture rotations to one where in many areas increased emphasis is put on annual crops, pastures being thus relegated to land with variable types of agronomic constraints. It is expected that higher cropping intensity will result in declining soil fertility, and thus increased demands for the fertilizer input.

III.c Production response: late 1990’s to the present

Systematic research on fertilizer response started in the late 1960’s as a result of a joint project between INTA, CYMMIT and the Ford Foundation. A decade later, response models were available for selected areas of the country (García and Darwich, 2009). Despite these early research efforts, take off in fertilizer use had to wait at least until the early 1990s, that is, two decades later than when fertilizer research was initiated. High fertilizer prices during the 1970s and 1980s are the most likely explanation for this fact.

Interest in the fertilizer input increased in the early 1980’s, leading to additional applied agronomic research by both INTA as well as private groups. A swap program of fertilizers for grain was implemented by the Mi nistry of Agriculture in 1983, and the first large-coverage soil fertility maps were completed by INTA. The first manual of soil fertility and fertilizer use was published in 1989 (García and Darwich, p.428). Crop area increased modestly, if at all, during the 1980’s, but significantly during the 1990’s and, particularly in the 2000-2010 period. Area of major crops thus jumped from some 17 million hectares in the 1980s, to 36 million in 2019. As mentioned previously, the doubling of crop area resulted in abandonment of the traditional crop-pasture rotation, as well shift in land use from natural grasses and forest/scrubland to crops. Agronomists are insistent on their concern related to increased “pressure” put by continuous cropping on soils (see, e.g. Sainz Rosas and others, 2019) and on the “deficit” resulting from fertilizer levels not covering nutrient extraction by crops (see Grassini and Monzón, 2021).

Although an important volume of research related to fertilizer use has been completed since the 1990s (see, e.g. Álvarez and others [2015], Correndo, Boxler and García [2015], García and Salvagiotti [2009]) summarizing results for economic analysis is not easy. Figure 11 in García and Darwich (p. 434) provide a starting point. Table 2, adapted from this figure, reports yield estimates for the fertilized and non-fertilized wheat crop (experimental results).

Two issues stand out. First, in the period analyzed yields for the non-fertilized treatment increased 75 percent, most possibly as a result of improved seeds[4]. Second, response to the fertilizer input increased both in absolute as well as relative terms: the average product of the fertilizer input was 500 kg/ha in 1970 (25 percent of baseline yield), but 2000 kg/ha in 2000 (57 percent of baseline). Although these – admittedly “rough and ready”- result pertain only to the wheat crop, they are illustrative of changes occurring in the Argentine agricultural sector.

García and Darwich (Table 10, p. 438) summarize the “agronomic efficiency” of fertilizer use in the wheat, corn and soybeans crops of Argentina. This term is used to denote additional output resulting from added input (fertilizer). In the language of microeconomics, the Average Product (AP) resulting from the input. Fertilizer AP varies considerably among crops, nutrient and experimental trials. However, a first approximation of 15 -20 kg/kg for wheat, 15-30 kg/kg for corn, and 12-20 kg/kg for soybeans can be taken as a starting point.[5]

Opportunities opened up by lower fertilizer prices, as well as by technical developments related to fertilizer use result in an increase in the demand for information leading to improved decision-making. Figure 4 shows an index of the number of soil samples tested in a private laboratory in the 1991- 2020 period. Soil tests increased nearly 400 percent between the beginning and the end of the period. The soil-testing lab from which this data originates started operations in 1962, thus growth in the 1991-2020 period most probably reflects growth in demand for services, and not mere “growth in customer base” due to recent starting of operations.

IV. Accounting for the increase in fertilizer use

Total growth in fertilizer use in Argentina in the 1990-2019 period results from (a) a doubling of crop area and (b) increase in fertilizer use per unit of crop area. To be explained here is the increase in fertilizer use per unit of area.

Two sub-periods are distinguished in these 3-decade period: 1990 –1999 and 2000-2019.

The first (“Period 1”) is labelled “learning/adoption” stage, where (relatively recent) experimental and farm-level results are gradually made available to producers. Note that while fertilizer research was underway since the early to mid-1970’s, it is only in the mid to late 1980’s that fertilizer prices show a steady decline, thus making it “worthwhile” for producers to invest in information-gathering related to use of this input. Indeed, and as pointed out in the Griliches-Rogers debate discussed earlier, it is only “rational” to invest in information search if this information can be put to profitable use. This appears to have happened when the fertilizer-wheat price started to fall in the mid-1980s. Period 1 therefore marks the start of widespread adoption of fertilization in extensive crop production.

“Period 2” (2000-2019) corresponds to the “knowledge” stage, characterized by a significant stock of agronomic research as well as on-farm experience related to fertilizer use. Increased knowledge on the use of this input suggests a decrease in the risk premium associated with allocating funds for fertilization. Further, gradual crop intensification suggests tightening of constraints related to soil fertility.

Focus is placed on fertilizer use per unit of area. For a fixed input of land and (non-fertilizer) input services complementary to land, output is assumed to result from:

Y(F) = A(t) F ^α [4]

Where Y is output per unit of land and F fertilizer input per unit of land. A(t) results from overall improvements in technology or technical change, a function of time. For simplicity, A(t) also includes the contribution of the non-fertilizer inputs such as land (assumed unchanging through time). The profit (“B”) maximizing level of input F results from equating input marginal productivity to the relative input/output price:

B(F) = pA(t) F^α− wF [5]

dB/dF = αp A(t)F^(α-1)−w = 0 [6]

F^*(p,w) = [α (p/w) A(t)]^1/(1-α) [7]

Denoting by t = 0 or t = 1 for initial and final stages of the two periods analyzed here (1990/99, 2000/19), the predicted increase in the use of F is:

The above can be decomposed in “’price effect” and a “technology effect”:

Price effect = [(p/w)₁/(p/w)₀ ]^1/(1-α) [9]

Technology effect = [A(1)/A(0)]^1/(1-α) [10]

Expression [9], represents movement along the derived demand function for the fertilizer input. In turn, expression [10] captures the shifts in fertilizer demand resulting from shifts in “technology” (A(t)).

Changes in fertilizer demand are also a function of α, the elasticity of output with respect to the fertilizer input. It is possible that α changes over time. This can occur via two channels. First, improved soil diagnosis and fertilizer application methods. Second, and probably more important, gradual decline in soil fertility due to continuous cropping. As mentioned previously, evidence of both these factors is available.

Impacts of the above may be modelled by assuming α(t) = α₀(1 + δ) where δ = 0 for the Period 1 (“learning/adoption” stage), and δ > 0 for Period 2 (“knowledge” stage). A value of 0.3 will be assumed here for δ.

Table 3 reports assumed valued for price ratios, accumulated technical change for the “learning adoption” and “knowledge” periods and output elasticity of the fertilizer input. As shown, α is assumed equal to 0.25 in the learning/adoption and 0.32 in the knowledge periods, respectively. The Appendix provides background for the chosen values. Estimates of the impact of prices and technical change are also shown in Table 3.

In Period 1 (1990-1990), real fertilizer prices fell from an index of 100 in the late 1980’s, to 65 a decade later. Fertilizer use in this period nearly trebled (x 2.81). As shown in Table 3, while this increase is accounted primarily by the reduction in the fertilizer/crop price ratio, technical change also played an important role.

In turn, in the Period 2 (the “knowledge” period, 2000-2019), the effect of technical change results in fertilizer usage increasing by a factor of 1.78. Technical change accounts for all of this increase, as the relative fertilizer/crop price ratio remained unchanged during the period.

How do these predictions compare with observed changes in the 1990-2019? In Period 1 (1990-1999), the prediction increase (per-hectare) fertilizer demand is somewhat lower than the observed increase (181 vs 210 percent). In Period 2 (2000-2019), predicted change is very close to the observed change (78 vs 82 percent). Overall observed increase in the 1990-2019 period (470 percent) is higher than the one estimated here (400 percent). However, given the “rough and ready” model used for estimation, results can be considered quite good.

Comparison of “observed” with “estimated” figures should be made cautiously, as they are highly sensitive not only to assumptions on technical change and fertilizer output elasticity, but also on assumptions on prices used by farmers in the decision-making process: in particular under the highly volatile economy of Argentina, ex-ante price expectations can be quite different from what ex-post statistical data shows.

V. Final Comments

Argentine agriculture experienced significant growth in the last half-century. This has occurred despite policies that resulted in a distortion of the incentives faced by producers. This paper attempts to understand determinants of the fifteen-fold increase in fertilizer use that has occurred since 1990. Evidence presented her suggests that previous to the late 1980’s, unfavorable price ratios were a significant constraint to fertilizer adoption. But prices were not the only factor: incipient developments of fertilizer use technology (in particular, soil testing), as well as variable and frequently low fertilizer response were contributing factors.

During the 1990’s, more favorable relative price ratios, significant improvements in overall crop productivity, and increased cropping intensity (with resulting increase in fertilizer response) triggered growth in fertilizer application per unit of land. As shown in Figure 2, relatively low fertilizer/ crop prices during the 1990s were followed by two decades of substantially rising (+ 50 percent or more) fertilizer prices. Fertilizer use, however, continued to grow. An intriguing question is the role that favorable prices on a given period have in input use of subsequent periods: favorable prices encourage increased input use, and indirectly, accumulation of knowledge related to this technology. A possible hypothesis is that the economic liberalization that occurred in Argentina in the 1990s, contributed to growth not only in this period but in subsequent periods as well – a “catalyst” effect of the improvement in relative prices on subsequent input demand.

The evidence presented in this paper suggests that both reductions in relative prices (in particular, in the 1990/99 period, as compared to the previous decade) as well as overall technical improvements were responsible for increased fertilizer use. Crop productivity (and thus response to fertilizer) as a determinant of demand for the fertilizer input is particularly important after 2000, when despite variable or even increasing real fertilizer prices, demand for this input continued to increase.

The fact that fertilizer demand is driven not only by relative prices, but by overall technology as reflected in response to this input should not obscure the fact that improvements in relative prices can have a significant impact on the overall output of the Argentine agricultural sector. Indeed, the contrafactual that deserves attention is what would output and output growth would have been in the last two decades with Argentine relative prices similar to those found in other major exporters.

Disentangling the effects of prices and input productivity in producer decision-making is a complex but important research topic. Progress in this area will most possibly require close collaboration between professionals with backgrounds in agronomy with those in economics. The important fertilizer price increases occurring in late 2021-early 2022 highlight the relevance of research aimed at understanding fertilizer demand in Argentina. Further work on this topic can make useful progress taking as a starting point the “classical” papers on fertilizer demand commented on the previous sections (Griliches, 1958 and 1959, Heady and Yeh, 1959).

VI. References

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VII. Appendix

Assumed values for technical change (A(t)), relative prices (w/p) and fertilizer output elasticity (α)

Technical change (A(t))

Lema (2016) reports estimates of TFP change in Argentine agricultu re during the last decades. Table 3 summarized results as follows:

For Period 1 (1990-99) the value of 3.89 per year reported by Lema is used. For Period 2 (2000-2019) the average estimated by Lema for the 2002-2007 and 2008-2013 (2.3 % per year) are taken as representative. To tal TFP change is thus 41 percent for Period 1 (1.0389⁹ – 1) and 54 percent

(1.023¹⁹ – 1) for Period 2.

Relative prices (w/p)

An index of fertilizer/crop prices is used. For year t fertilizer (Pf) and crop price (Pc) indexes are, respectively:

[A.1]

Where Pn and Pp correspond, respectively to pert-on price (US$) of nitrogen (urea) and phosphorous (diammonium phosphate) fertilizers, and weights correspond to approximate shares of these two inputs in the Argentine fertilizer market.

[A.2]

Where p and q correspond respectively to prices and quantities, and i= 1….3 correspond to the three crops considered (corn, wheat and soybeans) The resulting input/output price ratio is then:

( = [A.3]

Prices were obtained from Márgenes Agropecuarios (several years).

Using calculated relative prices:

Period 1: Price ratio of 100 was assumed at the beginning of the period (prevailing price late 1980s, early 1990s). Price ratio of 65 follows from calculations for the end of the period.

Period 2: Price ratio of 65 follows from calculations for both the beginning (2000-2004) as well as the end (2016-2019) of the period.

Fertilizer Output Elasticity (α)

Only rough estimates of elasticity of output with respect to fertilizer application are available. Some figures are reported in Section III of this report. The objective here is not to attempt to obtain “the” relevant value for α for the Argentine agricultural sector, but only to discuss possible implications of input marginal productivity and prices in explaining shifts in fertilizer use. The following are some examples that have been commented in Section III (yield increases resulting from fertilizer use):

Overall assessment by García and Darwich (2009) indicate “agronomic efficiency” (i.e Average Product) of fertilizer use of 15-20 for wheat, 15-30 for corn and 12-20 for soybeans. Assuming an input use of 60 kg/ha for wheat and corn, and 40 kg/ha for soybeans, this would result in yield increases of 900-1200, 900-1800 and 480-800 kg/ha for the three crops considered here. These increments represent, respectively 27-36; 15-30 and 18 – 30 percent of country-wide yields. Note that all “elasticity” values reported here result from experimental plots and not farmer fields. Farmer response can be expected to be somewhat lower due to managerial and constraints operating on the system.

As a result of the evidence presented above, and admittedly in an ad- hoc manner, a value of α=0.25 will be assumed for Period 1, and α=0.25(1 +δ) = 0.25(1 +0.3 ) = 0.32

for Period 2.

Fertilizer usage per hectare

Fertilizer use data is reported by Fertilizar Asociación Civil. Area of major crops by the Ministry of Agriculture (SAGPyA).

For Period 1, increase in fertilizer is expresses as the ratio between the 1998-2000 and 1990-1992 average annual use per hectare of land sown to the main grain crops (rice, soybeans, peanuts, wheat, soybeans, sunflower, grain sorghum and barley). For Period 2, the ratio between 2018-2020 and 2000-2002 averages is used.

Marcos Gallacher

I. Introduction

II. Input demand and adaptation to change